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Excited States of Phosphorescent Platinum(II)Complexes Containing N∧C∧N-Coordinating Tridentate Ligands:Spectroscopic Investigations and Time-Dependent Density Functional Theory CalculationsWataru Sotoyama,*,†Tasuku Satoh,†Hiroyuki Sato,Azuma Matsuura,and Norio SawatariFujitsu Laboratories Ltd.,10-1Morinosato-Wakamiya,Atsugi243-0197,JapanRecei V ed:June22,2005;In Final Form:September4,2005The absorption and emission spectra of the Pt(II)complexes containing N∧C∧N-coordinating tridentate ligands,platinum(II)1,3-di(2-pyridyl)benzene chloride[Pt(dpb)Cl]and platinum(II)3,5-di(2-pyridyl)toluene chloride[Pt(dpt)Cl],together with their corresponding free ligands,1,3-di(2-pyridyl)benzene(dpbH)and3,5-di(2-pyridyl)toluene(dptH),have been analyzed by density functional theory(DFT)for the ground state and time-dependent DFT(TDDFT)for the excited states.T1(A1)and S1(B2)of the complexes(in C2V symmetry)wereassigned on the basis of the calculated excitation energies as well as comparison of the experimentalspectroscopic properties and the calculated states’characteristics.The calculated excitation energies for T1and S1of the complexes as well as those for T1of the free ligands were in good agreement with their observedvalues within600cm-1.The d-π*characters of the excited states were evaluated from the change in electrondensities between the ground and excited states by Mulliken population analysis;values of25%for T1and32%for S1were obtained for both complexes.The calculated values of d-π*character were found to beconsistent with the reported emission lifetimes as well as the observed emission energy shifts from thecorresponding free ligands.Most spectroscopic properties of the complexes and the free ligands,which includesolvatochromic shift,Stokes shifts,methyl substitution shifts,and emission spectra profiles,were well explainedfrom the calculation results.1.IntroductionStudies on phosphorescent transition-metal complexes are ofparticular interest not only from a scientific viewpoint but alsoin development of emissive dopants for phosphorescent organiclight-emitting diodes(OLEDs).1,2The rapid growth of interestin phosphorescent OLEDs has prompted syntheses and photo-physical investigations of a wide variety of phosphorescentcomplexes.3-7Recently,a new class of platinum(II)complexesconsisting of platinum,chloride,and N∧C∧N-coordinatingtridentate ligands[platinum(II)1,3-di(2-pyridyl)benzene chlo-ride,Pt(dpb)Cl,and platinum(II)3,5-di(2-pyridyl)toluene chlo-ride,Pt(dpt)Cl,Figure1]have been synthesized,8,9and highphosphorescence quantum yields ranging from0.58to0.68insolution at room temperature have been reported in these complexes.9Pt(dpt)Cl and its derivative with a phenoxide group that replaces the chloride have been reported to exhibit remark-able performance as emissive dopants of OLEDs.10The lowest excited triplet states(T1)of Pt(dpb)Cl and Pt(dpt)Cl have been assigned to primarily ligand-centered(LC) 3π-π*character from their highly structured emission profile with very small Stokes shifts and relatively long emission lifetimes[Pt(dpb)Cl7.2µs and Pt(dpt)Cl7.8µs in solution at room temperature].9However,these emission lifetimes are not much longer than those of the complexes,which have the triplet-emitting states with metal-to-ligand charge transfer(MLCT) character.For example,in the case of Ir(ppy)3,where ppy represents2-phenylpyridine ligand,the emitting states have been assigned to be mainly3MLCT character by theoretical studies11 and spectroscopic measurements.12The emission lifetimes of this complex were found to be2µs and5µs at room temperature and77K,respectively,in solution.13Taking into account the possible admixture ofπ-π*/d-π*(MLCT)character,which is common for T1of many phosphorescent transition-metal complexes,14-20it is expected that the d-π*character would participate in T1of Pt(dpb)Cl and Pt(dpt)Cl.The d-π* admixture to an excited state,especially to T1,is important even though the state character is primaryπ-π*,since a small amount of d-π*character can dominate the kinetics of the deactivation processes of the excited state by its strong spin-orbit coupling ability to the states with different spin multi-plicities.16,17,21-23In this paper we describe detailed analysis of the excited states of Pt(dpb)Cl and Pt(dpt)Cl by correlating the spectroscopic data with the calculation results based on density functional theory (DFT).The main objectives of this study are assignment of the*To whom correspondence should be addressed:e-mail wataru_sotoyama@fujifilm.co.jp.†Present address:Advanced Core Technology Laboratories,Fuji Photo Film Co.,Ltd.,210Nakanuma,Minamiashigara250-0193,Japan.Figure1.Schematic structure of the two complexes[Pt(dpb)Cl and Pt(dpt)Cl]and the two free ligands[dpbH and dptH]along with the molecular axis.The numbers in the structures designate each carbon atom.9760J.Phys.Chem.A2005,109,9760-976610.1021/jp053366c CCC:$30.25©2005American Chemical SocietyPublished on Web10/11/2005low-lying excited states of the complexes and quantitative evaluation of the d-π*character at the complexes.The free tridentate ligands[1,3-di(2-pyridyl)benzene(dpbH)and3,5-di-(2-pyridyl)toluene(dptH),Figure1]are also investigated to assist in analysis of the excited states of the complexes.Several aspects of the spectroscopic features,such as effect of methyl substitution on the excitation energies and the difference in emission profile between the complexes and the free ligands, will be discussed in light of the calculation results by DFT and time-dependent DFT(TDDFT).2.Experimental Section2.1.Materials and Spectroscopic Measurements.Pt(dpb)-Cl and Pt(dpt)Cl were synthesized from dpbH and dptH, respectively,according to the literature.8,9Absorption and emission measurements in solution were conducted in1cm path length quartz cuvettes at room temperature or in5mm diameter quartz tubes at77K.Absorption spectra were recorded on a Hitachi U-4100spectrophotometer.Emission spectra of Pt(dpb)-Cl and Pt(dpt)Cl were measured on a Minolta CS-1000 spectroradiometer,equipped with an ultra-high-pressure mercury lamp and a visible blocking filter,as the excitation source.The solutions of free ligands(dpbH and dptH)showed phosphores-cence with lifetimes of a few seconds at77K;phosphorescence spectra of these solutions were measured with a phosphoroscope in addition to the above apparatus.putational Details.The ground-state DFT and the excited-state time-dependent DFT(TDDFT)24-26calculations were carried out with the Gaussian98program package.27 TDDFT has been successfully applied to excited-state calcula-tions for many transition-metal complexes.11,28-34All calcula-tions were carried out with the LANL2DZ basis set with the relativistic effective core potential(ECP)for Pt35and the6-31G* basis set for the other elements.The calculation results(orbitals and densities)were plotted with the visualization program(xmo 4.0)in MOPAC2002.36Calculations on the electronic ground state(S0)of the complexes[Pt(dpb)Cl and Pt(dpt)Cl]and the free ligands(dpbH and dptH)were carried out by use of B3LYP density functional theory.37,38The S0geometries were optimized under symmetry constraints of C2V for Pt(dpb)Cl and C s(zx symmetry plane,Figure1)for Pt(dpt)Cl.The optimized planar geometries of these complexes were confirmed by the vibrational frequencies calculations with no imaginary frequencies.The optimized geometry of Pt(dpb)Cl was found to be in good agreement with the X-ray crystallographic data(Table1).8For dpbH and dptH,the geometries optimized within symmetry constraints similar to the complexes(planar forms)were different from those fully optimized without symmetry con-straints(twisted forms).Although the twisted forms have lower S0total energy than the planar forms for both dpbH and dptH, the differences in the S0total energy between the planar and twisted forms were found to be negligible(158cm-1for dpbH and179cm-1for dpbH).On the basis of the minor energy deviations from the twisted forms,we present calculation results at the planar forms of the free ligands in this study for convenience of comparison with the results for the complexes. The geometries for the lowest excited triplet states(T1)of Pt(dpb)Cl and dpbH were optimized at the restricted open-shell B3LYP level.At the respective optimized geometries,TDDFT calculations with the B3LYP functional were carried out.Ten lowest roots for triplet states as well as singlet states were calculated for the complexes and the ligands.In addition to the vertical excitation energies for all calculated roots,the one-particle densities and the dipole moments for the three lowest triplet and singlet roots were obtained for the complexes.3.Results3.1.Absorption and Emission Spectra at Room Temper-ature.Figure2shows absorption and emission spectra of Pt-(dpb)Cl(a)and Pt(dpt)Cl(b)together with the absorption spectra of dpbH(a)and dptH(b)in toluene at room temperature.The spectra of the complexes in Figure2replicate the results reported by Williams et al.9The lowest energy weak peaks in Pt(dpb)Cl and Pt(dpt)Cl absorption spectra are assigned as S0-T1absorp-tion by their mirror-symmetry relation with the emission peak. The strong absorption envelopes at22000-30000cm-1are assigned to the absorptions to the singlet excited states with significant MLCT character involving Pt and Cl orbitals from the comparison with the absorption spectra of the free ligands. The lowest energy peak among these absorptions is considered as the S1peak of the each complex.(Strictly speaking,the absorption spectra do not exclude the possibility of the existence of one or more singlet excited states with very small absorption cross sections at the lower energy side of the S1peak assigned above.However,even if there are such dark states,the discussion about the orbital assignment of the S1peak based on the absorption intensities in section4.1still remains unchanged.)TABLE1:Calculated and Observed X-ray Crystallographic Data for Representative Bond Lengths(Å)and Angles (degree)for Pt(dpb)Cl abond b calcd obsd c Pt-Cl 2.471 2.417Pt-C(1) 1.926 1.907Pt-N 2.065 2.037dC(1)-Pt-N80.4380.5dPt-C(1)-C(2)118.62119.2dPt-N-C(5)113.95114.6da Bond lengths are given in angstroms;bond angles are given in degrees.b See Figure1for numbering of the carbon atoms.c Data from ref8.d Average of two equivalent datapoints.Figure2.Absorption and emission spectra of the complexes alongwith absorption spectra of the free ligands in toluene at roomtemperature:(a)Pt(dpb)Cl and dpbH;(b)Pt(dpt)Cl and dptH.Solidline(green),emission of the complexes;dashed line(purple),absorptionof the complexes;dotted line(red),absorption of the complexes in anexpanded scale(134times);dashed-dotted line(blue),absorption ofthe free ligands.Phosphorescent Platinum(II)Complexes J.Phys.Chem.A,Vol.109,No.43,20059761We observed negative solvatochromic behavior (peak blue shift with increasing solvent polarity)reported in ref 9for S 1and T 1peaks of Pt(dpb)Cl and Pt(dpt)Cl in several solvents.The absorption peak energies in toluene and acetonitrile are presented in Table 2.(See ref 9for further information about spectral data in various solvents including toluene and aceto-nitrile.)According to the theoretical study on solvent effect by Marcus,39,40negative solvatochromic behavior of an absorption peak has been interpreted to be associated with the decrease in dipole moments by excitation.It is observed that the solvato-chromic shifts are fairly larger for S 1peaks than T 1peaks,which would suggest a lager decrease in dipole moment by the S 0-S 1excitation than that of the S 0-T 1excitations of these complexes.3.2.Phosphorescence Spectra at 77K.Figure 3shows the phosphorescence spectra of dpbH and Pt(dpb)Cl (a)and of dptH and Pt(dpt)Cl (b)in toluene at 77K.The highest energy peak of each spectrum (presented in Tables 3and 4)is attributed to the vibrational 0-0origin of the T 1-S 0transition.The phosphorescence origins of the Pt(dpb)Cl and Pt(dpt)Cl have red-shifted 2200and 2580cm -1from those of the corresponding free ligands,respectively.These shifts are much larger than those for complexes with ligand-centered emitting states in the literature,such as [Pt(bpy)2]2+(950cm -1)or [Rh(bpy)3]3+(600cm -1),41where bpy is 2,2′-bipyridine,suggesting significant admixture of the metal character in the emitting state of the complexes.The relative intensity of the origin peak,compared to the peaks of vibrational satellites with frequencies of about 1300cm -1,would become notably larger for the complexes than for the free ligands;these features imply closer equilibrium geometries between S 0and T 1for these complexes compared to those for the free ligands.Similar trends have been observed for complexes having T 1with significant MLCT character,such as [Ru(bpy)3]2+or Pt(thpy)2,where thpy is 2-(2-thienyl)pyridine,in comparison with their corresponding free ligands.17,18,42The characteristics such as the position and profile of the spectraindicate a certain amount of metal d-orbital admixture to T 1of Pt(dpb)Cl and Pt(dpt)Cl.The methyl substitution in place of the hydrogen atom at C(4)of the phenyl ring causes somewhat different effects to the emission spectra between the complexes and the free ligands.Both the methyl-substituted complex [Pt(dpt)Cl]and free ligand (dptH)displayed red-shifted emission from their unsubstituted counterparts [Pt(dpb)Cl and dpbH].However,the spectral shift was found to be substantially greater between the complexes (540cm -1)than between the free ligands (160cm -1).This large difference in methyl-substitution effect would suggest the orbital nature difference of T 1between the complexes and the free ligands.4.Theoretical and Experimental Data Comparison 4.1.Assignments and Excitation Energies of Calculated Roots.Figure 4depicts the four highest occupied and the two lowest unoccupied molecular orbitals (HOMOs and LUMOs)of Pt(dpb)Cl,as well as the HOMO and LUMO of dpbH obtained from the ground-state DFT calculations.The HOMOs and LUMOs for Pt(dpt)Cl and dptH are similar in shape with the corresponding orbitals presented in Figure 4.Every fourTABLE 2:T 1and S 1Absorption Peak Energies for Pt(dpb)Cl and Pt(dpt)Cl in Toluene and Acetonitrile at Room Temperatureabsorption peak energy/cm -1complex state toluene acetonitrile Pt(dpb)Cl T 12040020700Pt(dpb)Cl S 12400025200Pt(dpt)Cl T 12000020300Pt(dpt)ClS 12340024500TABLE 3:Parameters a from Ground-State DFT and TDDFT Calculations for the Three Lowest Excited Triplet and Singlet Roots of Pt(dpb)Cl and Pt(dpt)Cl at the Ground-State GeometriesPt(dpb)ClPt(dpt)Cl root (assignment b )symmetry cdominant excitation c ,d E /cm -1µz (∆µz )/D f E /cm -1µz (∆µz )/D fground state S 01A 1 6.647.07triplet root 1(T 1)3A 1b 1f b 1*20421 5.51(-1.13)20059 6.69(-0.38)2(T 2)3B 2b 1f a 2*20892 1.03(-5.61)20270 2.66(-4.41)3(T 3)3A 1a 2f a 2*22993 4.41(-2.23)22886 5.09(-1.98)T 1(expt e )2058020040singlet root 1(S 1)1B2b 1f a 2*23489-2.43(-9.07)0.07423120-1.04(-8.10)0.0772(S 2)1A 1b 1f b 1*23707 3.06(-3.58)0.00723342 4.64(-2.43)0.0063(S 3)1A 2b 2f b 1*25928-4.95(-11.58)0.00025899-4.47(-11.54)0.000S 1(expt f )2400023400aE ,vertical excitation energy;µz ,z component of dipole moment;∆µz ,dipole moment differences between ground and excited states;f ,oscillatorstrength.Experimental excitation energies are also listed.b See text.c Symmetry of states and orbitals are designated for Pt(dpb)Cl (C 2V ,see Figure 1).d For designation of the orbitals,see Figure 4.e Phosphorescence 0-0peak energy in toluene at 77K.f Absorption peak energy in toluene at roomtemperature.Figure 3.Emission spectra of the complexes and the free ligands in toluene at 77K:(a)Pt(dpb)Cl and dpbH;(b)Pt(dpt)Cl and dptH.Solid line (green),emission of the complexes;dotted line (blue),emission of the free ligands measured with a phosphoroscope.9762J.Phys.Chem.A,Vol.109,No.43,2005Sotoyama et al.HOMOs of the complexes are characterized by significant admixtures by the Pt d-orbitals.Two of them [b 1(HOMO)and a 2(HOMO-3)]are represented by combinations of d orbitals of the Pt and πorbitals of the tridentate ligand and Cl,while the remainder [b 2(HOMO-1)and a 1(HOMO-2)]have σcharacters that are symmetrical about the molecular plane.On the other hand,the LUMOs correspond to the π*orbitals almost localized in the ligand.Table 3summarizes the TDDFT calculation results of the properties that include dominant orbital excitations,vertical excitation energies (E ),dipole moments (z component,µz ),dipole moment differences from S 0(∆µz ),and oscillatorstrengths (f )of the lowest three triplet and the lowest three singlet roots for Pt(dpb)Cl and Pt(dpt)Cl.Table 3also includes the observed excitation energies for T 1(the origins in the low-temperature phosphorescence spectra)and S 1(the absorption peaks in the room-temperature spectra).The lowest three triplet roots as well as the lowest two singlet roots are represented by dominant excitations from mixed d πorbitals to π*orbitals.The third lowest singlet root is represented by a d σ-π*excitation.Excitations with d σ-π*character appear at the fifth lowest and higher roots for triplet states that are not specified in Table 3.The lowest three triplet as well as singlet roots for Pt(dpt)Cl are identical in characteristics of dominant excitations to the counterparts of Pt(dpb)Cl.In succeeding sections,we discuss only about Pt(dpb)Cl and dpbH,unless the methyl substitution effect is explored.We begin the discussion on the comparison of the calculated and experimental data by assignment of T 1and S 1from the calculated triplet and singlet roots for Pt(dpb)Cl.Experimental evidence is needed for the T 1and S 1assignments because both the calculated energy differences between the two lowest roots of triplet as well as singlet are very small.On the other hand,the third lowest roots for triplet and singlet are excluded from the T 1or S 1assignment because they are calculated to be energetically well above the lowest two roots.Considering that the excitation to S 1has a substantial extinction coefficient in the absorption spectrum (section 3.1),the lowest calculated singlet root (1B 2;f )0.074)is assigned to be S 1since the second lowest root (1A 1;f )0.007)is predicted to have 1order smaller absorption intensity.The calculated S 1has a large ∆µz (-9.07D)that is consistent with the experimentally obtained large negative solvatochromic shift of the S 1peak.39,40On the other hand,T 1of Pt(dpb)Cl has different spectral characteristics from S 1as discussed in section 3.1.Therefore,we assign the lowest calculated triplet root (3A 1)to T 1on the basis of the different dominant orbital excitation from S 1(1B 2)and the small ∆µz (-1.13D)that explain the small negative solvatochromic shift along with the small Stokes shift of the T 1peak.39The second and third lowest calculated triplet (or singlet)roots are assigned to be T 2and T 3(or S 2and S 3),respectively.The calculated T 1excitation energies of Pt(dpb)Cl and Pt(dpt)Cl show excellent agreements with the respective ex-perimental phosphorescence origins at 77K;the differences between the calculated and experimental values are found to be less than 200cm -1.In these comparisons,the calculated energies represent the vertical excitation energies at S 0geom-etries,while the experimental energies correspond to the 0-0transitions.However,these comparisons may be justified by the phosphorescence spectra,which indicate close equilibrium geometries between S 0and T 1of these complexes,as shown in section 3.2.(Geometries of T 1together with the adiabatic excitation energies will be discussed in section 4.3.)The calculated S 1excitation energies of the complexes also show good conformity with the experimental absorption peak energies within 600cm -1.Although TDDFT is known to have irregulari-ties in description of long-range charge-transfer excited states,43-45the above calculation results for excitation energies ensure the applicability of the TDDFT calculations for T 1and S 1of the concerned molecules.Hence we further investigate the charac-teristics of T 1and S 1of the complexes by use of the TDDFT calculation results in the following sections.TDDFT calculations were also carried out for the free ligands.Calculated vertical excitation energies and excitation types for the two lowest excited triplet roots of dpbH and dptH are summarized in Table 4together with the experimental energiesTABLE 4:Vertical Excitation Energies (E )from TDDFT Calculations for Triplet Excited States of DpbH and DptH with Experimental Excitation EnergiesE /cm -1root (assignment a )symmetry bdominant excitation b ,c dpbH dptH 1(T 1)3A 1a 2f a 2*23344232172(T 2)3B 2b 1f a 2*2730427077T 1(expt d )2278022620aSee text.b Symmetry of states and orbitals are designated for dpbH (C 2V ,see Figure 1).c For designation of the orbitals,see Figure 4.dPhosphorescence 0-0peak energy in toluene at 77K.Figure 4.Contour plots of the two lowest unoccupied and the four highest occupied molecular orbitals of Pt(dpb)Cl,along with the LUMO and HOMO of dpbH.Phosphorescent Platinum(II)ComplexesJ.Phys.Chem.A,Vol.109,No.43,20059763of the phosphorescence origin.For dpbH,the lowest calculated triplet root (3A 1)was assigned to be T 1on the basis of the large energy separation between the first and second lowest roots.The small differences between the calculated and experimental T 1excitation energies of dpbH and dptH (560-600cm -1)evidenced the accuracy of the TDDFT calculations.4.2.Evaluation of d -π*Character in the Excited States.Evaluation of the degree of d -π*participation for low-lying excited states of mixed π-π*/d -π*character would be very helpful to understand the photophysical properties of the phosphorescent complexes.The zero-field splittings (ZFS)of sublevels of T 1are shown to be a valuable experimental parameter to measure the metal participation in T 1of com-plexes.17-19Theoretical calculation is considered to be an alternative for the evaluation of the metal participation that can be applied to a variety of complexes.The theoretical studies reported so far treat the evaluation of d -π*participation by several methods:the population analysis of orbitals involved in dominant excitations,11the analysis of distribution of spin densities and atomic charges by SCF calculations in T 1,30and the population analysis of metal atoms 46or the metal d-orbitals for the ground and excited states.47We employed the population analysis of metal orbitals in combination with TDDFT calcula-tions as discussed in the following section.We have noted that T 1and S 1of the concerned complexes are each represented by a dominant excitation from a mixed d πorbital to a π*orbital.More detailed pictures of the excited states depicting the changes in electron density 48are provided in Figure 5,for T 1,S 1,and T 3from S 0of Pt(dpb)Cl along with that for T 1from S 0of dpbH.(The changes for T 2and S 2of thecomplex bear resemblances to those for S 1and T 1,respectively.)T 1and S 1of Pt(dpb)Cl are characterized by d-electron density decrease on Pt and π-electron densities on Cl and some of the carbons in the tridentate ligand and by increases of π-electron densities of the tridentate ligand with respect to S 0,which indicate an admixture of d -π*and π-π*characters in each excited states.Considering that TDDFT is a single excitation theory,49the decrease in d-electron densities calculated by TDDFT ap-proximately gives the percentage of d -π*character in the excited state;that is,one electron decrease in d-electron densities represents 100%d -π*character.The decreases in d-electron densities for T 1and S 1of Pt(dpb)Cl are evaluated by Mulliken population analysis.46,47Table 5summarizes the orbital popula-tions of the Pt consisting of atomic orbitals s,p π,p σ,d π,and d σ(πand σdenote antisymmetric and symmetric orbitals about the molecular plane,respectively)for S 0,T 1,and S 1of Pt(dpb)-Cl and Pt(dpt)Cl.The differences between the two complexes are insignificant,and the s,p σ,and d σdensities remain unchanged by the T 1and S 1excitations.The d πdensities decrease in T 1by 0.25e and in S 1by 0.32e from S 0for both of the complexes,suggesting the percentages of d -π*character in T 1and S 1as 25%and 32%,respectively.On the other hand,the p πdensities on Pt increase in T 1by 0.06e [Pt(dpb)Cl]and 0.05e [Pt(dpt)Cl]from S 0,which indicates some delocalization of the spreading of the π*orbitals over the Pt atom.The emitting states (T 1)of Pt(dpb)Cl and Pt(dpt)Cl with 25%d -π*character seem to fall into the intermediate category of significant LC/MLCT admixture in the sequence of complexes ordered by metal -d character (from pure LC to pure MLCT)of the emitting states.18,19The d -π*character in the emitting state of such a complex dominates the kinetics of the deactiva-tion processes by effective spin -orbit coupling with singlet excited states.The evaluated d -π*characters in T 1of Pt(dpb)-Cl and Pt(dpt)Cl are considered to be consistent with the reported emission lifetimes (7-8µs 9)as well as the emission energy shifts from the corresponding free ligands (2200-2600cm -1).It should be mentioned that the d -π*character in T 1does not lead to large ∆µz ,the difference in dipole moment between the ground and excited state,for the objective complexes despite its charge-transfer nature.The d -π*character combined with the small ∆µz in T 1is clearly shown in Figure 5,which depicts the dominant charge flow from Pt,Cl,and phenyl ring to both pyridine rings in the tridentate ligand that cancel each other in the y -axis,thus exhibiting little change along the dipole moment in the z -axis.On the other hand,S 1of Pt(dpb)Cl was calculated to have a considerably larger ∆µz (-9.07D)than T 1,in contrast to the small differences in the d -π*character between T 1(25%)and S 1(32%).The charge flow in S 1is almost“straightforward”Figure 5.Contour plots of changes in electron densities for T 1,S 1,and T 3from S 0of Pt(dpb)Cl,along with that for T 1from S 0of dpbH.TABLE 5:Orbital Populations on Pt for the Ground and Excited States from Mulliken Population Analysis aorbital population (difference from S 0)state s p πb p σb d πbd σb Pt(dpb)Cl S 0 2.712.094.123.784.74T 1 2.71(0.00) 2.15(0.06) 4.12(0.00) 3.53(-0.25) 4.74(0.00)S 12.71(0.00) 2.09(0.00) 4.12(0.00)3.46(-0.32)4.74(0.00)Pt(dpt)Cl S 0 2.712.094.123.834.69T 1 2.71(0.00) 2.14(0.05) 4.12(0.00) 3.58(-0.25) 4.69(0.00)S 12.71(0.00)2.09(0.00)4.12(0.00)3.51(-0.32)4.70(0.00)aOrbital populations are given in unit electron charge.Inner core electrons (1s through 4f)are not included because they are replaced by the effective core potential (ECP).b σand πrepresent symmetrical and antisymmetrical orbitals about the molecular plane,respectively.9764J.Phys.Chem.A,Vol.109,No.43,2005Sotoyama et al.from the Pt and Cl to the phenyl ring that causes a large dipole moment change parallel to the z-axis.parison of Phosphorescence Spectra of the Complexes and Free Ligands:Methyl Substitution Effects and Spectral Features.The methyl substitution causes a substantial decrease in phosphorescence0-0energy from Pt(dpb)Cl to Pt(dpt)Cl(540cm-1),while the difference between the free ligands(dpbH and dptH)is small(160cm-1),as explained in section3.2.These calculations reproduced the differences in the T1excitation energies(362cm-1between the complexes and127cm-1between the free ligands).The difference in the methyl substitution effect between the com-plexes and the free ligands can be assigned to the different orbital nature of T1in respective species.Although T1of Pt(dpb)Cl and dpbH have identical symmetry(A1),they differ in dominant orbital excitations[b1f b1*for Pt(dpb)Cl;a2f a2*for dpbH].Theπorbitals of a2symmetry in dpbH[as well as Pt(dpb)Cl]have no component at the atoms on the symmetry axis,including C(4),as shown in the MO plots(Figure4).Themethyl substitution at C(4)is expected to have a minimal effect on the orbitals of a2symmetry as well as the a2f a2* excitations.On the other hand,the b1orbital(HOMO)of Pt(dpb)Cl spreads over C(4);hence,it resulted in a substantial difference in T1excitation energies between Pt(dpb)Cl and Pt(dpt)Cl.The difference in the dominant orbital excitations between the complexes and the free ligands stated above gives valuable information about the phosphorescence spectra of these species. The phosphorescence spectra of the free ligands(Figure3)show increased vibrational progressions compared to those of the complexes.These spectral features can be explained from the plots of the changes of electron density(Figure5)that show the difference in T1character between Pt(dpb)Cl and dpbH.The changes of the electron density are found on the atoms for Pt-(dpb)Cl,whereas those for dpbH,which show some resemblance to those for T3of Pt(dpb)Cl,are found mainly on the bonds in the phenyl ring and between the phenyl and pyridine rings. These electron-density changes on the bonds,especially in the phenyl ring,are expected to induce significant geometry changes for the free ligands between T1and S0.These geometry changes appear as strong vibrational progressions in the phosphorescence spectra with frequencies of aromatic ring stretching about1300 cm-1.The geometry changes expected by the electron density calculations were confirmed by T1geometry optimizations for Pt(dpb)Cl and dpbH at the restricted open-shell B3LYP level. Geometries were optimized in C2V symmetry and then compared to their S0structures.Particular attention was paid to selection of the initial-guess orbitals for the SCF calculations in T1 geometry optimizations to obtain coherent results with the TDDFT calculations about nature of the singly occupied orbitals. Table6summarizes the changes in bond length between S0and T1.For dpbH,the length of the C(2)-C(3)bond shows a notable increase(0.085Å)by excitation to T1that is consistent with the electron density plot(Figure5),while changes in bond length for Pt(dpb)Cl are rather small compared to those for dpbH,and mainly observed for the bonds between Pt and its neighboring atoms[Cl and C(1)].Additional TDDFT calculations were carried out for both Pt(dpb)Cl and dpbH at the T1optimized geometry to obtain the relaxation energy in T1(the difference between the T1 energies at the S0and T1optimized geometries)and the adiabatic T1excitation energy(the vertical T1excitation energy at the S0 optimized geometry minus the relaxation energy in T1).The obtained T1relaxation energy for Pt(dpb)Cl(631cm-1)is notably smaller than that of dpbH(2070cm-1);this result isconsistent with the above discussion on the phosphorescenceprofiles of Pt(dpb)Cl and dpbH.The adiabatic T1excitationenergies are figured out to be19790cm-1for Pt(dpb)Cl and21274cm-1for dpbH;these values are in good agreement withthe experimental0-0excitation energies in S0-T1transitions.5.ConclusionThe lowest triplet and singlet excited states(T1and S1)ofthe objective complexes Pt(dpb)Cl and Pt(dpt)Cl have beenassigned to3A1(b1f b1*)and1B2(b1f a2*),respectively,from the TDDFT calculations with the assistance of the observedspectroscopic properties.The calculated excitation energies forT1and S1of the complexes show good agreement with theirrespective observed values within600cm-1.These states arepredicted to have mixed characters of d-π*andπ-π*excitations.On the basis of the single excitation nature of theTDDFT approach,the d-π*character in excited states isevaluated from the decrease in the d-electron densities on Ptby excitation;values of25%for T1and32%for S1have beenobtained for both complexes.The emitting states of the freeligands(dpbH and dptH)are predicted to be different in orbitalnature from those of the complexes;this difference in orbitalnature explains the observed difference in methyl-substitutioneffect as well as different emission profiles between thecomplexes and the free ligands.Other spectroscopic featuresof the complexes,such as the negative solvatochromic shift andsmall Stokes shift,are also successfully explained from thecalculation results based on the above assignment.The above results have proved that the TDDFT approach isrational for analysis of the excited-state properties of theobjective complexes.The presented procedure to evaluate thed-π*character may be a useful tool to design highly phos-phorescent complexes.We consider that it is very important toconduct further studies to evaluate d-π*character in the excitedstates of a variety of phosphorescent complexes and then toinvestigate the relationship between the d-π*character andphosphorescence properties of these complexes in order to getan in-depth understanding of the photophysics of the complexes. Acknowledgment.We thank Dr.N.F.Cooray for helpful suggestions and discussions.References and Notes(1)Baldo,M.A.;O’Brien,D.F.;You,Y.;Shoustikov,A.;Sibley,S.; Thompson,M.E.;Forrest,S.R.Nature(London)1998,395,151. TABLE6:Calculated Bond Lengths and Differences between S0and T1of Pt(dpb)Cl and DpbH aPt(dpb)Cl b dpbH b bond c S0T1difference S0T1difference Pt-Cl 2.471 2.444-0.027Pt-C(1) 1.926 1.899-0.027Pt-N 2.065 2.063-0.002C(1)-C(2) 1.403 1.4340.031 1.402 1.397-0.005 C(2)-C(3) 1.402 1.390-0.012 1.405 1.4900.085 C(3)-C(4) 1.401 1.4120.011 1.393 1.386-0.007 C(2)-C(5) 1.469 1.451-0.018 1.492 1.442-0.050 C(5)-C(6) 1.397 1.3970.000 1.406 1.4240.018 C(6)-C(7) 1.392 1.390-0.002 1.392 1.388-0.004 C(7)-C(8) 1.395 1.4080.013 1.393 1.3950.002 C(8)-C(9) 1.391 1.385-0.006 1.396 1.4080.012 C(9)-N 1.343 1.3510.008 1.333 1.321-0.012 C(5)-N 1.379 1.3980.019 1.347 1.3690.022a Bond lengths are given in angstroms.b Geometries are optimized within the symmetry constraint of C2V.c See Figure1for numbering of the carbon atoms.Phosphorescent Platinum(II)Complexes J.Phys.Chem.A,Vol.109,No.43,20059765。
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Conjugation vs hyperconjugation in molecular structure of acroleinSvitlana V.Shishkina a ,⇑,Anzhelika I.Slabko b ,Oleg V.Shishkin a ,caDivision of Functional Materials Chemistry,SSI ‘Institute for Single Crystals’,National Academy of Science of Ukraine,60Lenina Ave.,Kharkiv 61001,Ukraine bDepartment of Technology of Plastic Masses,National Technical University ‘Kharkiv Polythechnic Institute’,21Frunze Str.,Kharkiv 61002,Ukraine cDepartment of Inorganic Chemistry,V.N.Karazin Kharkiv National University,4Svobody Sq.,Kharkiv 61077,Ukrainea r t i c l e i n f o Article history:Received 4August 2012In final form 16November 2012Available online 29November 2012a b s t r a c tAnalysis of geometric parameters of butadiene and acrolein reveals the contradiction between the Csp 2–Csp 2bond length in acrolein and classical concept of conjugation degree in the polarized molecules.In this Letter the reasons of this contradiction have been investigated.It is concluded that the Csp 2–Csp 2bond length in acrolein is determined by influence of the bonding for it p –p conjugation and antibonding n ?r ⁄hyperconjugation between the oxygen lone pair and the antibonding orbital of the single bond.It was shown also this bond length depends on the difference in energy of conjugative and hyperconjuga-tive interactions.Ó2012Elsevier B.V.All rights reserved.1.IntroductionButadiene and acrolein belong to the most fundamental mole-cules in the organic chemistry.They are canonical objects for the investigation of phenomena of p –p conjugation between double bonds and polarization of p -system by heteroatom [1].According to many experimental [2–16]as well as theoretical studies [13,17–23]the molecular structure of butadiene is determined by conjugation between p -orbitals of two double bonds and may be described as superposition of two resonance structures (Scheme 1).The presence of zwitterionic structure causes the shortening of the central single Csp 2–Csp 2bond as compare with similar unconjugated bond [24].Acrolein differs from butadiene by presence of the oxygen atom instead terminal methylene group.According to classical concepts of organic chemistry such replacement should causes polarization of p -system due to presence of highly polar C @O bond [25].This leads to significant increase of the contribution of the zwitterionic resonance structure (Scheme 1)reflecting strengthening of conju-gation between p -systems of double bonds.Therefore the central Csp 2–Csp 2bond must be shorter in acrolein as compared with one in butadiene.However numerous investigations of acrolein by experimental [26–28]and theoretical methods [26,27,29–36]demonstrate an opposite situation:the Csp 2–Csp 2bond length varies within the range 1.469Ä1.481Åin acrolein as compared with 1.454Ä1.467in butadiene.Based on these data one can conclude that conjugation between double bonds in acrolein is weaker than in butadiene.At that time the rotation barrier obtained from quan-tum-chemical calculations is higher in acrolein [26,27],confirming stronger conjugation between double bonds.Thus,results of experimental and theoretical investigations demonstrate the con-tradiction between the strengthening of the conjugation in acrolein as compare with butadiene and the values of the Csp 2–Csp 2bond length in these molecules.Recently such illogical situation was observed also in derivatives of cyclohexene containing conjugated endocyclic and exocyclic double bonds [37].It was assumed that elongation of the Csp 2–Csp 2bond in cycloxen-2-enone as compare with one in 3-methylene-cyclohexene is caused by the influence of n ?r ⁄hyperconjugation.In this Letter we demonstrate the results of the investigation of intramolecular interactions in butadiene and acrolein which ex-plain the experimentally observed contradiction between the length of the Csp 2–Csp 2bond and degree of conjugation in acrolein.2.Method of calculationsThe structures of all investigated molecules were optimized using second-order Møller-Plesset perturbation theory [38].The standard aug-cc-pvtz basis set [39]was applied.The character of stationary points on the potential energy surface was verified by calculations of vibrational frequencies within the harmonic approximation using analytical second derivatives at the same level of theory.All stationary points possess zero (minima)or one (saddle points)imaginary frequencies.The verification of the calculation method was performed using optimization of butadi-ene and acrolein by MP2/aug-cc-pvqz,CCSD(T)/cc-pvtz and CCSD(T)/6-311G(d,p)methods [40].The geometry of saddle points for the rotation process was lo-cated using standard optimization technique [41].The barrier of the rotation in all molecules was calculated as the difference be-tween the Gibbs free energies at 298K of the most stable s-trans0009-2614/$-see front matter Ó2012Elsevier B.V.All rights reserved./10.1016/j.cplett.2012.11.032Corresponding author.Fax:+3805723409339.E-mail address:sveta@ (S.V.Shishkina).conformer and saddle-point conformation.All calculations were performed using the G AUSSIAN 03program [42].The intramolecular interactions were investigated within the Natural Bonding Orbitals theory [43]with N BO 5.0program [44].Calculations were performed using B3LYP/aug-cc-pvtz wave func-tion obtained from single point calculations by G AUSSIAN 03program.The conjugation and hyperconjugation interactions are referred to as ‘delocalization’corrections to the zeroth-order natural Lewis structure.For each donor N BO (i )and acceptor N BO (j ),the stabiliza-tion energy E (2)associated with delocalization (‘2e-stabilization’)i ?j is estimated asE ð2Þ¼D E ij ¼q iF ði ;j Þ22j À2i;where q i is the donor orbital occupancy,e j and e i are the diagonal elements (orbital energies),and F (i,j )is the off-diagonal N BO Fock matrix element.3.Results and discussionThe equilibrium geometry of s-trans and s-cis conformers of butadiene and acrolein calculated by MP/aug-cc-pvtz method (Ta-ble 2)agrees very well with obtained earlier results [2–23,25–34]and data of higher and more computationally expensive methods (Table 1).It can be noted that the C–C bond length in acrolein(Tables 1and 2)is longer as compared with butadiene in all sta-tionary points on the potential energy surface.Such relation does not agree with the conception of the resonance theory [45–47].Analysis of intramolecular interactions in both molecules using N BO theory indicates that acrolein differs from butadiene by pres-ence of intramolecular interaction between lone pair of the oxygen atom and antibonding orbital of the C–C bond (Figure 1)as well as the polarization of one double bond containing more electronega-tive ually the interactions between lone pair and antibonding orbital of single bond are stronger than the interac-tions between the C–H bond and antibonding orbital [48]and they can influence geometrical characteristics.Such type of interactions is named by anomeric effect and it is studied very well for the case when the central bond between interacted orbitals is single [48,49].It is investigated in details [49]an influence of classical anomeric effect on conformation of the substituents about central single bond as well as on values of bond lengths.In the case of hyperconjugation interactions along double bond in acrolein orien-tation of substituents around it is determined by its double charac-ter.Therefore,n ?r ⁄hyperconjugative interaction can influence on the bond lengths of interacted ones only.It can assume the dou-ble character of the central bond must also promote some strengthening of this influence due to shorter distance between the lone pair of the oxygen atom and antibonding orbital of the C–C bond.Results of N BO analysis of intramolecular interactions in butadi-ene and acrolein demonstrate that the energy of n ?r ⁄interaction between lone pair of the oxygen atom and antibonding orbital of the C–C bond in acrolein is twice as high of the energy of r ?r ⁄interaction between the C–H bond and antibonding orbital of the C–C bond in butadiene (Table 2).At that time the energy of n ?r ⁄interaction is close enough to the energy of p –pTable 2The equilibrium geometries (bond lengths,Åand C @C–C @X (X =CH 2,O)torsion angle,deg.),transition state of the rotation process,bond length alternation (BLA)parameter,related energy (D E rel ,kcal/mol),related stability (D G 298,kcal/mol)and energy of strongest intramolecular interactions (E (2),kcal/mol)for butadiene and acrolein optimized by MP2/aug-cc-pvtz method.The wave function calculated by b3lyp/aug-cc-pvtz method was used for N BO analysis.ConformerBond lengths (Å)C @C–C @X torsion angle deg.BLA (Å)D E rel(kcal/mol)D G 298(kcal/mol)E (2)(kcal/mol)C @CC–C C @X p –pn ?r ⁄(C–C)r ?r ⁄(C–C)Butadiene s-trans 1.341 1.453 1.340180.0+0.1120030.74–8.67gauche 1.340 1.465 1.34036.8+0.125 2.83 2.8921.04–8.94TS 1.3361.4801.336101.8+0.1446.446.102.32–10.66Acrolein s-trans 1.339 1.469 1.219180.0+0.1300027.7518.06–s-cis 1.338 1.481 1.2190.0+0.143 2.26 2.2224.6319.05–TS1.334 1.492 1.21692.5+0.1588.017.46–18.78–Acrolein +BH 3s-trans 1.341 1.449 1.235180.0+0.1080033.12 2.4511.43s-cis 1.340 1.460 1.2340.0+0.120 2.45 2.3829.61 2.6011.43TS1.334 1.476 1.23193.7+0.1429.258.61–2.3911.55Table 1The Csp 2–Csp 2bond length in butadiene and acrolein optimized by different quantum-chemical methods.Method of calculationCsp 2–Csp 2bond length (Å)D (Csp 2–Csp 2)(Å)ButadieneAcrolein MP2/aug-cc-pvtz 1.453 1.4690.016MP2/aug-cc-pvqz 1.451 1.4670.016CCSD(T)/cc-pvtz1.461 1.4780.017CCSD(T)/6–311G(d,p)1.4681.4870.019S.V.Shishkina et al./Chemical Physics Letters 556(2013)18–2219conjugation between two double bonds.Therefore it can assume that the influence of p–p conjugation and n?r⁄hyperconjuga-tion on the C–C bond length should be comparable.However two strongest intramolecular interactions in the acrolein differ from each other:p–p conjugation between double bonds causes the shortening of the C–C bond in contrary to n?r⁄hyperconjugation which leads to the elongation of the C–C bond owing to the popu-lation of its antibonding orbital.Taking into account this situation it is possible to conclude that length of the Csp2–Csp2single bond in acrolein is determined by balance of two opposite factors namely p–p conjugation and n?r⁄hyperconjugation which may be considered as bonding and antibonding interactions for this bond(Figure1).In this case the length of the Csp2–Csp2bond in acrolein depends on the con-tribution of each of these factors.The changing of the delocaliza-tion of the structures due to influence of intramolecular interactions can be analyzed easier by mean of the bond length alternation(BLA)parameter(Table2).The analysis of BLA shows the presence of n?r⁄hyperconjugative interaction in acrolein what results in the increasing of alternation of double bonds as compare with butadiene.Clear estimation of influence of both interactions on geometri-cal parameters of molecule may be performed by comparison of properties of single C–C bond and BLA parameter in equilibrium s-trans conformation and in situations where one or both intramo-lecular interactions are absent.It is well known that p–p conjugation between double bonds decreases appreciably up to disappearing(in acrolein)in the tran-sition state for the rotation around single bond process(Figure2). The data of N BO analysis for butadiene and acrolein in the transition state confirm this evidence(Table2).As expected the absence of p–p conjugation results in the elongation of the Csp2–Csp2bond and increasing of BLA as compare with equilibrium geometry.At that time single C–C bond remains longer in the transition state for acrolein as compare with one for butadiene’s transition state.1.4921.4691.4491.476π−π is present n σ* is presentπ−π is absentn σ* is absent without π−πwithout n σ∗Figure2.Influence of p–p⁄conjugation and n?r⁄hyperconjugation on the C–Cbond length in acrolein.Table3The energy(E(2),kcal/mol)of the conjugative(bonding)and hyperconjugative(antibonding)intramolecular interactions influencing the Csp2–Csp2bond length in butadiene, acrolein and its complex with BH3.Molecule Bonding interactions E(2)(kcal/mol)Antibonding interactions E(2)(kcal/mol)Butadienes-trans BD(2)C1-C2–BD(2)C3-C430.74BD(1)C1-H5–BD(1)C2-C38.67 BD(1)C2-H7–BD(1)C3-H87.68BD(1)C4-H9–BD(1)C2-C38.67 gauche BD(2)C1-C2–BD(2)C3-C421.04BD(1)C1-H5–BD(1)C2-C38.94 BD(1)C2-H7–BD(1)C3-C4 5.36BD(1)C4-H9–BD(1)C2-C39.01BD(1)C3-H8–BD(1)C1-C2 5.36TS BD(1)C1-C2–BD(1)C3-C4 3.5BD(1)C1-H5–BD(1)C2-C310.66 BD(1)C1-C2–BD(2)C3-C4 3.46BD(1)C4-H9–BD(1)C2-C310.66BD(1)C3-C4–BD(2)C1-C2 3.46BD(2)C1-C2–BD(2)C3-C4 2.32BD(1)C3-H8–BD(2)C1-C29.57BD(1)C2-H7–BD(2)C3-C49.57Acroleins-trans BD(1)C1-C2–BD(1)C3-O4 2.73BD(1)C1-H5–BD(1)C2-C38.25 BD(2)C1-C2–BD(2)C3-O427.75LP(2)O4–BD(1)C2-C318.06BD(1)C2-H7–BD(1)C3-H8 5.95s-cis BD(2)C1-C2–BD(2)C3-O424.63BD(1)C1-H5–BD(1)C2-C38.76 BD(1)C2-H7–BD(1)C3-O4 4.05LP(2)O4–BD(1)C2-C319.05BD(1)C3-H8–BD(1)C1-C2 5.01TS BD(1)C1-C2–BD(2)C3-O4 2.98BD(1)C1-H5–BD(1)C2-C39.07 BD(1)C3-O4–BD(2)C1-C2 4.48LP(2)O4–BD(1)C2-C318.78BD(1)C3-H8–BD(2)C1-C2 5.85BD(1)C2-H7–BD(2)C3-O4 6.16Acrolein+BH3s-trans BD(1)C1-C2–BD(1)C3-O4 3.07BD(1)C1-H6–BD(1)C2-C38.09 BD(2)C1-C2–BD(2)C3-O433.12BD(1)C2-C3–BD(1)O4-B511.43BD(1)C2-H8–BD(1)C3-H9 5.97LP(1)O4–BD(1)C2-C3 2.45 s-cis BD(1)C1-C2–BD(1)C3-H9 4.98BD(1)C1-H6–BD(1)C2-C38.51 BD(2)C1-C2–BD(2)C3-O429.61BD(1)C2-C3–BD(1)O4-B511.43BD(1)C2-H8–BD(1)C3-O4 4.41LP(1)O4–BD(1)C2-C3 2.60 TS BD(1)C1-C2–BD(1)C3-O40.55BD(1)C1-H6–BD(1)C2-C39.05 BD(1)C1-C2–BD(2)C3-O4 3.01BD(1)C2-C3–BD(1)O4-B511.55BD(2)C1-C2–BD(1)C3-O4 4.90LP(1)O4–BD(1)C2-C3 2.39BD(1)C3-H9–BD(2)C1-C2 6.13BD(1)C2-H8–BD(2)C3-O4 6.8820S.V.Shishkina et al./Chemical Physics Letters556(2013)18–22It is additional argument about the influence of n?r⁄hypercon-jugation on the C–C bond length through the C@O double bond.In contrary to p–p conjugation n?r⁄hyperconjugation is present in all stationary points on the potential energy surface for acrolein(Table2).But this interaction can be shielded by for-mation of dative bond involving lone pair of the oxygen atom and unoccupied orbital of Lewis acid,for example,BH3.The formed O–B bond has r-character and the energy of its interaction with antibonding orbital of the central C–C bond is very close to the en-ergy of similar C–H?r⁄(C–C)interaction in butadiene(Table2). The absence of n?r⁄hyperconjugation results significant short-ening of the Csp2–Csp2bond and decreasing of BLA in all stationary points for acrolein.It is more interesting that the C–C bond in acro-lein becomes shorter and p–p conjugation becomes stronger as compare with ones in butadiene in the case of absence of n?r⁄hyperconjugative interaction(Table2)what agrees well with the resonance theory.This evidence is confirmed also by values of BLA parameter.It is very interesting the situation when both strong intramolec-ular interactions are absent namely acrolein with shielded by BH3 lone pair in the transition state for the rotation process.In absence of p–p conjugative and n?r⁄hyperconjugative interactions the C–C bond length is almost equal to mean value for length of this bond for s-trans and s-cis conformers of acrolein with both interac-tions(Table2).This fact confirms that the C–C bond length in acro-lein in the equilibrium state is determined by balance of p–p conjugation and n?r⁄hyperconjugation.Taking into account the opposite influence of two types of intra-molecular interactions on the C–C bond one may assume that its length depends on the difference in energy of bonding and antibonding interactions for this bond.In such case all bonding for C–C bond and antibonding for it interactions(Table3)must be taken into account.Specially,this is important for transition states where p–p conjugative interaction is minimal and r(c-H)–p interaction appears instead it.This interaction has bond-ing for Csp2–Csp2bond character and it is weaker as compare with p–p interaction.Analysis of relation between C–C bond length and total energy of intramolecular interaction influencing on it demon-strates good correlation between them(Figure3)with correlation coefficient aboutÀ0.93.The barrier of the rotation around ordinary C–C bond is also sensitive to intramolecular interactions.The absence of n?r⁄hyperconjugation in acrolein results the increase of conjugation in molecule what leads to the increase of the rotation barrier (Table2).4.ConclusionsResults of quantum-chemical calculations demonstrate the structure of acrolein does not correspond to conventional views about influence of the polarization of p-system by the oxygen atom.According to classic viewpoint this effect should lead to in-crease of conjugation between double bonds and shortening of central single C–C bond as compared to butadiene.However,anal-ysis of intramolecular interactions shows that the geometry of acrolein is determined by counteraction of p–p conjugation and n?r⁄hyperconjugation.The energies of these interactions are very close but ones influence on the C–C bond lengths in opposite directions.Conjugation promotes the shortening of the central sin-gle bond due to the overlapping of the p-orbitals of two double bonds.In the contrary the n?r⁄hyperconjugation causes the elongation of the C–C bond due to the population of its antibonding orbital.The absence of conjugation in the transition state for the rotation about the C–C bond process results in the elongation of the single bond in conjugated system.In turn the shielding of n?r⁄hyperconjugation by the formation of dative bond between lone pair of oxygen atom and vacant orbital of Lewis acid causes the shortening of the C–C bond in acrolein.The C–C bond length correlates well with the difference between two strong intramolec-ular interactions.The absence of both interactions does not almost change the C–C bond length.Thus,these data clearly indicate that molecular structure of conjugated systems containing heteroatoms is determined by not only p–p conjugation but also by n?r⁄hyperconjugation.References[1]F.A Carey,R.J.Sundberg,Advanced Organic Chemistry.Part A:Structure 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DOI: 10.1126/science.1257570, 763 (2014);346 Science et al.Bernhard Misof Phylogenomics resolves the timing and pattern of insect evolutionThis copy is for your personal, non-commercial use only.clicking here.colleagues, clients, or customers by , you can order high-quality copies for your If you wish to distribute this article to othershere.following the guidelines can be obtained by Permission to republish or repurpose articles or portions of articles): November 6, 2014 (this information is current as of The following resources related to this article are available online at/content/346/6210/763.full.html version of this article at:including high-resolution figures, can be found in the online Updated information and services, /content/suppl/2014/11/05/346.6210.763.DC1.html can be found at:Supporting Online Material /content/346/6210/763.full.html#ref-list-1, 58 of which can be accessed free:cites 161 articles This article/cgi/collection/evolution Evolutionsubject collections:This article appears in the following registered trademark of AAAS.is a Science 2014 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. 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J.Jin,L.Agosto,T.Wang,R.B.Altman,and M.R.Wasserman for assistance;C.Walsh,J.Binely,A.Trkola,and M.Krystal for reagents;and members of the Structural Biology Section,Vaccine Research Center,for critically reading the manuscript.We thank I.Wilson and J.Sodroski for encouraging us to extend our approach to a R5-tropic Env.The data presented in this paper are tabulated in the main paper and in the supplementary materials.This work wassupported by NIH grants R21AI100696to W.M.and S.C.B;P0156550to W.M.,S.C.B.,and A.B.S.;and R01GM098859to S.C.B.;by the Irvington Fellows Program of the Cancer Research Institute to J.B.M;by a fellowship from the China Scholarship Council-Yale World Scholars to X.M.;by grants from the International AIDS Vaccine Initiative ’s (IAVI)Neutralizing Antibody Consortium to D.R.B.,W.C.K.,and P.D.K.;and by funding from the NIH Intramural Research Program (Vaccine Research Center)to P.D.K.IAVI's work is made possible by generous support from many donors including:the Bill &Melinda Gates Foundation and the U.S.Agency for International Development (USAID).This study is made possible by the generous support of the American people through USAID.The contents are the responsibility of the authors and do not necessarily reflect the views of USAID or the ernment.Reagents from the NIH are subject to nonrestrictive material transferagreements.Patent applications pertaining to this work are the U.S.and World Application US2009/006049and WO/2010/053583,Synthesis of JRC-II-191(A.B.S.,J.R.C.),U.S.Patent Application 13/202,351,Methods and Compositions for Altering Photopysical Properties of Fluorophores via Proximal Quenching (S.C.B.,Z.Z.);U.S.Patent Application 14/373,402Dye Compositions,Methods of Preparation,Conjugates Thereof,and Methods of Use (S.C.B.,Z.Z.);and International and US Patent Application PCT/US13/42249Reagents and Methods for Identifying Anti-HIV CompoundsSUPPLEMENTARY MATERIALS/content/346/6210/759/suppl/DC1Materials and Methods Figs.S1to S15Tables S1to S3References (46–56)4April 2014;accepted 15September 2014Published online 8October 2014;colonize and exploit terrestrial and freshwa-ter ecosystems.They have shaped Earth ’s biota,exhibiting coevolved relationships with many groups,from flowering plants to hu-mans.They were the first to master flight and establish social societies.However,many as-pects of insect evolution are still poorly under-stood (2).The oldest known fossil insects are from the Early Devonian [~412million years ago (Ma)],which has led to the hypothesis that in-sects originated in the Late Silurian with the earliest terrestrial ecosystems (3).MolecularEarly Ordovician origin (4),which implies that early diversification of insects occurred in marine or coastal environments.Because of the absence of insect fossils from the Cambrian to the Silurian,these conclusions remain highly controversial.Fur-thermore,the phylogenetic relationships among major clades of polyneopteran insect orders —including grasshoppers and crickets (Orthoptera),cockroaches (Blattodea),and termites (Isoptera)—have remained elusive,as has the phylogenetic position of the enigmatic Zoraptera.Even the closest extant relatives of Holometabola (e.g.,SCIENCE 7NOVEMBER 2014•VOL 346ISSUE 6210763RESEARCH |REPORTSbeetles,moths and butterflies,flies,sawflies,wasps,ants,and bees)are unknown.Thus,in order to understand the origins of physiological and mor-phological innovations in insects (e.g.,wings andmetamorphosis),it is important to reliably re-construct the tempo and mode of insect diversifi-cation.We therefore conducted a phylogenomic study on 1478single-copy nuclear genes obtained from genomes and transcriptomes representing key taxa from all extant insect orders and other arthropods (144taxa)and estimated divergence dates with a validated set of 37fossils (5).Phylogenomic analyses of transcriptome and genome sequence data (6)can be compromised by sparsely populated data matrices,gene paral-ogy,sequence misalignment,and deviations from the underlying assumptions of applied evolution-ary models,which may result in biased statistical confidence in phylogenetic relationships and tem-poral inferences.We addressed these obstacles by removing confounding factors in our analysis (5)(fig.S2).We sequenced more than 2.5gigabases (Gb)of cDNA from each of 103insect species,which represented all extant insect orders (5).Addition-ally,we included published transcript sequence data that met our standards (table S2)and offi-cial gene sets of 14arthropods with sequenced draft genomes (5),of which 12served as refer-ences during orthology prediction of transcripts (tables S2and S4).Comparative analysis of the reference species'official gene sets identified 1478single-copy nuclear genes present in all these species (tables S3and S4).Functional annotation of these genes revealed that many serve basic cellular functions (tables S14and S15and figs.S4to S6).A graph-based approach using the best reciprocal genome-and transcriptome-wide hit criterion identified,on average,98%of these genes in the 103de novo sequenced transcriptomes,but only 79%and 62%in the previously published transcriptomes of in-and out-group taxa,respec-tively (tables S12and S13).After transcripts had been assigned and aligned to the 1478single-copy nuclear-encoded genes,we checked for highly divergent,putatively misaligned transcripts.Of the 196,027aligned transcripts,2033(1%)were classified as highly divergent.Of these,716were satisfactorily re-aligned with an automated refinement.How-ever,alignments of 1317transcripts could not be improved,and these transcripts were excluded from our analyses (supplementary data file S5,/10.5061/dryad.3c0f1).Nonrandom distribution of missing data among taxa can inflate statistical support for incorrect tree topologies (7).Because we detected a non-random distribution of missing data,we only considered data blocks if they contained infor-mation from at least one representative of each of the 39predefined taxonomic groups of un-disputed monophyly (table S6).In this represent-ative data set,the extent of missing data was still between 5and 97.7%in pairwise sequence com-parisons,with high percentages primarily because of the data scarcity in some previously published out-group taxa (table S19and figs.S7to S10).We inferred maximum-likelihood phylogenetic trees (Fig.1)with both nucleotide (second-codon positions only and applying a site-specific rate model)and amino acid –sequence data (applying a protein domain –based partitioning scheme to improve the biological realism of the applied evolutionary models)from the representative data set (5)(figs.S21,S22,and S23,A and D).Trees from both data sets were fully congruent.The absence of taxa that cannot be robustly placed on the tree (rogue taxa)in the amino acid –sequence data set and the presence of a few rogue taxa that did not bias tree inference in the nucleotide sequence data set (5)indicated a suf-ficiently representative taxonomic sampling.To detect confounding signal derived from nonrandom data coverage,we randomized ami-no acids within taxa,while preserving the dis-tribution of data coverage in the representative data set (5).This approach revealed no evidence of biased node support that could be attributed to nonrandom data coverage (5)(figs.S11and S12and table S20).Phylogenomic data may violate the assumption of time-reversible evolu-tionary processes,irrespective of what partition scheme one applies,which could lead to in-correct tree estimates and biased node support.Because sections in the amino acid –sequence alignments of the representative data set violat-ing these assumptions were present,we tested whether the observed compositional heteroge-neity across taxa biased node support but found no evidence for this (5)(fig.S20).We next dis-carded data strongly violating the assumption of time-reversible evolutionary processes (tables S21and S22,data files S6to S8,and figs.S13to S19).Results from phylogenetic analysis of this filtered data set (5)were fully congruent with those obtained from analyzing the unfiltered representative data set.The nucleotide sequence data of the representative data set containing also first and third codon positions strongly violated the assumption of time-reversible evolutionary processes,but still supported largely congruent topologies (fig.S23,B to D).In summary,our phylogenetic inferences are unlikely to be biased by any of the above-mentioned confounding factors.Our phylogenomic study suggests an Early Ordovician origin of insects (Hexapoda)at ~479Ma [confidence interval (CI),509to 452Ma]and a radiation of ectognathous insects in the Early Silurian ~441Ma (CI 465to 421Ma)(Figs.1and 2).These estimates imply that insects colonized land at roughly the same time as plants (8),in agreement with divergence date estimates on the basis of other molecular data (4).The early diversification pattern of insects has remained unclear (2,7,9).We received support for a monophyly of insects,including Collembola and Protura as closest relatives (10),and Diplura as closest extant relatives of bristletails (Archae-ognatha),silverfish (Zygentoma),and winged in-sects (Pterygota)(Fig.1).Furthermore,our analyses corroborate Remipedia,cave-dwelling crustaceans,as the closest extant relatives of insects (11,12).A close phylogenetic relationship of bristletails to a clade uniting silverfish and winged insects (Dicondylia)is generally accepted.However,the monophyly of silverfish has been questioned,with the relict Tricholepidion gertschi considered more distantly related to winged insects than7647NOVEMBER 2014•VOL 346ISSUE 6210 SCIENCE1Zoologisches Forschungsmuseum Alexander Koenig (ZFMK)/Zentrum für Molekulare Biodiversitätsforschung (ZMB),Bonn,Germany.2China National GeneBank,BGI-Shenzhen,China.3BGI-Shenzhen,China.4Australian National Insect Collection,Commonwealth Scientific and Industrial Research Organization (Australia)(CSIRO),National Research Collections Australia,Canberra,ACT,Australia.5Abteilung Arthropoda,Zoologisches Forschungsmuseum Alexander Koenig (ZFMK),Bonn,Germany.6Department of Entomology,Rutgers University,New Brunswick,NJ 08854,USA.7Department of Biological Sciences,Rutgers University,Newark,NJ 08854,USA.8Scientific Computing,Heidelberg Institute for Theoretical Studies (HITS),Heidelberg,Germany.9Institut für Spezielle Zoologie undEvolutionsbiologie mit Phyletischem Museum Jena,FSU Jena,Germany.10Steinmann-Institut,Bereich Paläontologie,Universität Bonn,Germany.112.Zoologische Abteilung(Insekten),Naturhistorisches Museum Wien,Vienna,Austria.12Department of Integrative Zoology,Universität Wien,Vienna,Austria.13Institut für Spezifische Prophylaxe und Tropenmedizin,Medizinische Parasitologie,Medizinische Universität Wien (MUW),Vienna,Austria.14Manaaki Whenua Landcare Research,Auckland,New Zealand.15Center for Advanced Modeling,Emergency Medicine Department,Johns Hopkins University,Baltimore,MD 21209,USA.16Biozentrum Grindel und Zoologisches Museum,Universität Hamburg,Hamburg,Germany.17Evolutionary Morphology Laboratory,Graduate School of Science and Engineering,EhimeUniversity,Japan.18Sugadaira Montane Research Center/Hexapod Comparative Embryology Laboratory,University of Tsukuba,Japan.19Land and Water Flagship,CSIRO,Canberra,ACT,Australia.20Florida Museum of Natural History,University of Florida,Gainesville,FL 32611,USA.21Entomology,Staatliches Museum für Naturkunde Stuttgart (SMNS),Germany.22Ecology Evolution and Genetics,Research School of Biology,Australian National University,Canberra,ACT,Australia.23National Evolutionary Synthesis Center,Durham,NC 27705,USA.24Department of Biological Sciences,Macquarie University,Sydney,Australia.25Department für Botanik und Biodiversitätsforschung,Universität Wien,Vienna,Austria.26Natural History Museum of Crete,University of Crete,Post Office Box 2208,Gr-71409,Iraklio,and Biology Department,University of Crete,Iraklio,Crete,Greece.27Department of Biological Sciences and Feinstone Center for Genomic Research,University of Memphis,Memphis,TN 38152,USA.28Centro Universitario de Ciencias Biólogicas y Agropecuarias,Centro de Estudios en Zoología,Universidad de Guadalajara,Zapopan,Jalisco,México.29Leibniz Supercomputing Centre of the Bavarian Academy of Sciences and Humanities,Garching,Germany.30Institute of Evolutionary Biology and Ecology,Zoology and Evolutionary Biology,University of Bonn,Bonn,Germany.31Department of Life Sciences,The Natural History Museum London,London,UK.32Abteilung Entomologie,Biozentrum Grindel und Zoologisches Museum,Universität Hamburg,Hamburg,Germany.33Fakultät für Informatik,Karlsruher Institut für Technologie,Karlsruhe,Germany.34California Academy of Sciences,San Francisco,CA 94118,USA.35Department of Entomology,College of Natural Resources and Environment,South ChinaAgricultural University,China.36Yokosuka City Museum,Yokosuka,Kanagawa,Japan.37Department of Entomology,North Carolina State University,Raleigh,NC 27695,USA.38Systematic Entomology,Hokkaido University,Sapporo,Japan.39Department of Biology,University of Copenhagen,Copenhagen,Denmark.40Princess Al Jawhara Center of Excellence in the Research of Hereditary Disorders,King Abdulaziz University,Jeddah,Saudi Arabia.41MacauUniversity of Science and Technology,Avenida Wai Long,Taipa,Macau,China.42Department of Medicine,University of Hong Kong,Hong Kong.43Department of Ecology,Evolution,and Natural Resources,Rutgers University,New Brunswick,NJ 08854,USA.*Major contributors.†Corresponding author.E-mail:xinzhou@ (X.Z.),b.misof.zfmk@uni-bonn.de (B.M.),kjer@ (K.M.K),wangj@ (J.W.)RESEARCH |REPORTSRESEARCH|REPORTSrelationships.maximum-likelihoodoptimized and sampledare labeled indicateorigin of events.SCIENCE 7NOVEMBER2014•VOL346ISSUE6210765estimates.correspondrange estimatesare Additionally,separatelybarsthe inferredcommon course,bewithRESEARCH|REPORTSother silverfish (13).We find that silverfish are monophyletic,consistent with recently published morphological studies (14),and estimate that Tricholepidion diverged from other silverfish in the Late Triassic (~214Ma)(Figs.1and 2).This result implies parallel and independent loss of the ligamentous head endoskeleton,abdominal styli,and coxal vesicles in winged insects and silverfish (5).The diversification of insects is undoubtedly related to the evolution of flight.Fossil winged insects exist from the Late Mississippian (~324Ma)(15),which implies a pre-Carboniferous origin of insect flight.The description of †Rhyniognatha (~412Ma)from a mandible,potentially indicative of a winged insect,suggested an Early Devonian to Late Silurian origin of winged insects (3).Our results corroborate an origin of winged insect lineages during this time period (16)(Figs.1and 2),which implies that the ability to fly emerged after the establishment of complex terrestrial ecosystems.Ephemeroptera and Odonata are,according to our analyses,derived from a common ancestor.However,node support is low for Palaeoptera (Ephemeroptera +Odonata)and for a sister group relationship of Palaeoptera to modern winged in-sects (Neoptera),which indicates that additional evidence,including extensive taxon sampling and the analysis of genomic meta-characters (17),will be necessary to corroborate these relationships.We find strong support for the monophyly of Polyneoptera,a group that comprises earwigs,stone-flies,grasshoppers,crickets,katydids (Orthoptera),Embioptera,Phasmatodea,Mantophasmatodea,Grylloblattodea,cockroaches,mantids,termites,and Zoraptera (18–20).We estimated the origin of the polyneopteran lineages at ~302Ma (CI 377to 231Ma)in the Pennsylvanian (Figs.1and 2),con-sistent with the idea that at least part of the rich Carboniferous neopteran insect fauna was of poly-neopteran origin.Finally,our analyses suggest that the major diversity within living cockroaches,man-tids,termites,and stick insects evolved after the Permian mass extinction.Given that the oldest known fossil hemipterans date to the Middle Pennsylvanian (~310Ma)(21),it had been thought that the stylet marks on liv-erworts from the Late Devonian (~380Ma)(22)could not have been of hemipteran origin.Our study indicates that true bugs (Hemiptera)and their sister lineage,thrips (Thysanoptera),all of which possess piercing-sucking mouthparts,orig-inated ~373Ma (CI 401to 346Ma),which gives support to the possibility of a hemipteroid origin of Early Paleozoic stylet marks.True bugs,thrips,bark lice (Psocoptera),and true lice (Phthiraptera)(together called Acercaria)were thought to be the closest extant relatives of Holometabola (Acercaria +Holometabola =Eumetabola)(10).However,convincing morpho-logical features and fossil intermediates support-ing a monophyly of Acercaria are lacking (13).We recovered bark and true lice (Psocodea)as likely closest extant relatives of Holometabola (5),which suggests that both groups started to diverge in the Devonian-Mississippian ~362Ma (CI 390to 334Ma)(Figs.1and 2).However,this result did not receive support in all statistical tests and,therefore,should be further investigated in future studies that embrace additional types of characters (17).We estimated that the radiation of parasitic lice occurred ~53Ma (CI 67to 46Ma),which implies that they diversified well after the emer-gence of their avian and mammalian hosts in the Late Cretaceous –Early Eocene and contradicts the hypothesis that parasitic lice originated on fea-thered theropod dinosaurs ~130Ma (23).Within Holometabola,our study recovered phylogenetic relationships fully congruent with those suggested in recent studies (2,24,25).Although we estimated the origin of stem lineages of many holometabolous insect orders in the Late Carboniferous,we dated the spectacular diver-sifications within Hymenoptera,Diptera,and Lepidoptera to the Early Cretaceous,contem-porary with the radiation of flowering plants (21,26).The almost linear increase in interordinal insect diversity suggests that the process of di-versification of extant insects may not have been severely affected by the Permian and Cretaceous biodiversity crises (Fig.2).With this study,we have provided a robust phylogenetic backbone tree and reliable time estimates of insect evolution.These data and analyses establish a framework for future com-parative analyses on insects,their genomes,and their morphology.REFERENCES AND NOTES1.The term “insects ”is used here in a broad sense andsynonymous to Hexapoda (including the ancestrally wingless Protura,Collembola,and Diplura).2.M.D.Trautwein,B.M.Wiegmann,R.Beutel,K.M.Kjer,D.K.Yeates,Annu.Rev.Entomol.57,449–468(2012).3.M.S.Engel,D.A.Grimaldi,Nature 427,627–630(2004).4.O.Rota-Stabelli et al.,Curr.Biol.23,392–398(2013).5.Materials and methods are available as supplementarymaterial on Science Online.6.Transcriptome refers to the sequencing of all of the mRNAs ofan individual or many individuals present at the time of preservation.7. E.Dell ’Ampio et al .,Mol.Biol.Evol.31,239–249(2014).8. bandeira,Arthro Syst.Phylo.64,53–94(2006).9.K.Meusemann et al .,Mol.Biol.Evol.27,2451–2464(2010).10.W.Hennig,Die Stammesgeschichte der Insekten(Kramer,Frankfurt am Main,1969).11.With the notable exception of Cephalocarida,for which RNA-sequencing data were unavailable to us.12.B.M.von Reumont et al .,Mol.Biol.Evol.29,1031–1045(2012).13.N.P.Kristensen,Annu.Rev.Entomol.26,135–157(1981).14.A.Blanke,M.Koch,B.Wipfler,F.Wilde,B.Misof,Front.Zool.11,16(2014).15.J.Prokop,A.Nel,I.Hoch,Geobios 38,383–387(2005).16.These estimates are robust whether or not †Rhyniognatha(Pragian stage,~412Ma)is used as a calibration point.17.O.Niehuis et al .,Curr.Biol.22,1309–1313(2012).18.H.Letsch,S.Simon,Syst.Entomol.38,783–793(2013).19.K.Ishiwata,G.Sasaki,J.Ogawa,T.Miyata,Z.-H.Su,Mol.Phylogenet.Evol.58,169–180(2011).20.K.Yoshizawa,Syst.Entomol.36,377–394(2011).21.A.Nel et al .,Nature 503,257–261(2013).bandeira,S.L.Tremblay,K.E.Bartowski,L.VanAllerHernick,New Phytol.202,247–258(2014).23.V.S.Smith et al .,Biol.Lett.7,782–785(2011).24.R.G.Beutel et al .,Cladistics 27,341–355(2011).25.B.M.Wiegmann et al .,BMC Biol.7,34(2009).26.J.A.Doyle,Annu.Rev.Earth Planet.Sci.40,301–326(2012).ACKNOWLEDGMENTSThe data reported in this paper are tabulated in the supplementary materials and archived at National Center for BiotechnologyInformation,NIH,under the Umbrella BioProject ID PRJNA183205(“The 1KITE project:evolution of insects ”).Supplementary files are archived at the Dryad Digital Repository /10.5061/dryad.3c0f1.Funding support:China National GeneBank and BGI-Shenzhen,China;German Research Foundation (NI 1387/1-1;MI 649/6,MI 649/10,RE 345/1-2,BE1789/8-1,BE 1789/10-1,STA 860/4,Heisenberg grant WA 1496/8-1);Austria Science Fund FWF;NSF (DEB 0816865);Ministry of Education,Culture,Sports,Science and Technology of Japan Grant-in-Aid forYoung Scientists (B 22770090);Japan Society for the Promotion of Science (P14071);Deutsches Elektronen-Synchrotron (I-20120065);Paul Scherrer Institute (20110069);SchlingerEndowment to CSIRO Ecosystem Sciences;Heidelberg Institute for Theoretical Studies;University of Memphis-FedEx Institute ofTechnology;and Rutgers University.The authors declare no conflicts of interest.SUPPLEMENTARY MATERIALS/content/346/6210/763/suppl/DC1Materials and Methods Supplementary Text Figs.S1to S27Tables S1to S26Data File Captions S1to S14References (27–187)17June 2014;accepted 23September 201410.1126/science.1257570SCIENCE 7NOVEMBER 2014•VOL 346ISSUE 6210767RESEARCH |REPORTS。
Remnant PbI2, an unforeseen necessity in high-efficiency hybrid perovskite-based solar cells?a)Duyen H. Cao, Constantinos C. Stoumpos, Christos D. Malliakas, Michael J. Katz, Omar K. Farha, Joseph T. Hupp, and Mercouri G. KanatzidisCitation: APL Materials 2, 091101 (2014); doi: 10.1063/1.4895038View online: /10.1063/1.4895038View Table of Contents: /content/aip/journal/aplmater/2/9?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inParameters influencing the deposition of methylammonium lead halide iodide in hole conductor free perovskite-based solar cellsAPL Mat. 2, 081502 (2014); 10.1063/1.4885548Air stability of TiO2/PbS colloidal nanoparticle solar cells and its impact on power efficiencyAppl. Phys. Lett. 99, 063512 (2011); 10.1063/1.3617469High efficiency mesoporous titanium oxide PbS quantum dot solar cells at low temperatureAppl. Phys. 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Phys. 101, 114503 (2007); 10.1063/1.2737977APL MATERIALS2,091101(2014)Remnant PbI2,an unforeseen necessity in high-efficiency hybrid perovskite-based solar cells?aDuyen H.Cao,1Constantinos C.Stoumpos,1Christos D.Malliakas,1Michael J.Katz,1Omar K.Farha,1,2Joseph T.Hupp,1,band Mercouri G.Kanatzidis1,b1Department of Chemistry,and Argonne-Northwestern Solar Energy Research(ANSER)Center,Northwestern University,2145Sheridan Road,Evanston,Illinois60208,USA2Department of Chemistry,Faculty of Science,King Abdulaziz University,Jeddah,Saudi Arabia(Received2May2014;accepted26August2014;published online18September2014)Perovskite-containing solar cells were fabricated in a two-step procedure in whichPbI2is deposited via spin-coating and subsequently converted to the CH3NH3PbI3perovskite by dipping in a solution of CH3NH3I.By varying the dipping time from5s to2h,we observe that the device performance shows an unexpectedly remark-able trend.At dipping times below15min the current density and voltage of thedevice are enhanced from10.1mA/cm2and933mV(5s)to15.1mA/cm2and1036mV(15min).However,upon further conversion,the current density decreases to9.7mA/cm2and846mV after2h.Based on X-ray diffraction data,we determinedthat remnant PbI2is always present in these devices.Work function and dark currentmeasurements showed that the remnant PbI2has a beneficial effect and acts as ablocking layer between the TiO2semiconductor and the perovskite itself reducingthe probability of back electron transfer(charge recombination).Furthermore,wefind that increased dipping time leads to an increase in the size of perovskite crys-tals at the perovskite-hole-transporting material interface.Overall,approximately15min dipping time(∼2%unconverted PbI2)is necessary for achieving optimaldevice efficiency.©2014Author(s).All article content,except where otherwisenoted,is licensed under a Creative Commons Attribution3.0Unported License.[/10.1063/1.4895038]With the global growth in energy demand and with compelling climate-related environmental concerns,alternatives to the use of non-renewable and noxious fossil fuels are needed.1One such alternative energy resource,and arguably the only legitimate long-term solution,is solar energy. Photovoltaic devices which are capable of converting the photonflux to electricity are one such device.2Over the last2years,halide hybrid perovskite-based solar cells with high efficiency have engendered enormous interest in the photovoltaic community.3,4Among the perovskite choices, methylammonium lead iodide(MAPbI3)has become the archetypal light absorber.Recently,how-ever,Sn-based perovskites have been successfully implemented in functional solar cells.5,6MAPbI3 is an attractive light absorber due to its extraordinary absorption coefficient of1.5×104cm−1 at550nm;7it would take roughly1μm of material to absorb99%of theflux at550nm.Further-more,with a band gap of1.55eV(800nm),assuming an external quantum efficiency of90%,a maximum current density of ca.23mA/cm2is attainable with MAPbI3.Recent reports have commented on the variability in device performance as a function of perovskite layer fabrication.8In our laboratory,we too have observed that seemingly identicalfilmsa Invited for the Perovskite Solar Cells special topic.b Authors to whom correspondence should be addressed.Electronic addresses:j-hupp@ and m-kanatzidis@2,091101-12166-532X/2014/2(9)/091101/7©Author(s)2014FIG.1.X-ray diffraction patterns of CH3NH3PbI3films with increasing dipping time(%composition of PbI2was determined by Rietveld analysis(see Sec.S3of the supplementary material for the Rietveld analysis details).have markedly different device performance.For example,when ourfilms of PbI2are exposed to MAI for several seconds(ca.60s),then a light brown coloredfilm is obtained rather than the black color commonly observed for bulk MAPbI3(see Sec.S2of the supplementary material for the optical band gap of bulk MAPbI3).23This brown color suggests only partial conversion to MAPbI3and yields solar cells exhibiting a J sc of13.4mA/cm2and a V oc of960mV;these values are significantly below the21.3mA/cm2and1000mV obtained by others.4Under the hypothesis that fully converted films will achieve optimal light harvesting efficiency,we increased the conversion time from seconds to2h.Unexpectedly,the2-h dipping device did not show an improved photovoltaic response(J sc =9.7mA/cm2,V oc=846mV)even though conversion to MAPbI3appeared to be complete.With the only obvious difference between these two devices being the dipping time,we hypothesized that the degree of conversion of PbI2to the MAPbI3perovskite is an important parameter in obtaining optimal device performance.We thus set out to understand the correlation between the method of fabrication of the MAPbI3layer,the precise chemical compositions,and both the physical and photo-physical properties of thefilm.We report here that remnant PbI2is crucial in forming a barrier layer to electron interception/recombination leading to optimized J sc and V oc in these hybrid perovskite-based solar cells.We constructed perovskite-containing devices using a two-step deposition method according to a reported procedure with some modifications.4(see Sec.S1of the supplementary material for the experimental details).23MAPbI3-containing photo-anodes were made by varying the dipping time of the PbI2-coated photo-anode in MAI solution.In order to minimize the effects from unforeseen variables,care was taken to ensure that allfilms were prepared in an identical manner.The composi-tions offinal MAPbI3-containingfilms were monitored by X-ray diffraction(XRD).Independently of the dipping times,only theβ-phase of the MAPbI3is formed(Figure1).9However,in addition to theβ-phase,allfilms also showed the presence of unconverted PbI2(Figure1,marked with*) which can be most easily observed via the(001)and(003)reflections at2θ=12.56◦and38.54◦respectively.As the dipping time is increased,the intensities of PbI2reflections decrease with a concomitant increase in the MAPbI3intensities.In addition to the decrease in peak intensities of PbI2,the peak width increases as the dipping time increases indicating that the size of the PbI2 crystallites is decreasing,as expected,and the converse is observed for the MAPbI3reflections.This observation suggests that the conversion process begins from the surface of the PbI2crystallites and proceeds toward the center where the crystallite domain size of the MAPbI3phase increases and that of PbI2diminishes.Interestingly,the remnant PbI2phase can be seen in the data of other reports, but has not been identified as a primary source of variability in cell performance.8,10 Considering that the perovskite is the primary light absorber within the device,we wantedto further investigate how the optical absorption of thefilm changes with increasing dipping timeFIG.2.Absorption spectra of CH3NH3PbI3films as a function of unconverted PbI2phase fraction.FIG.3.(a)J-V curves and(b)EQE of CH3NH3PbI3-based devices as a function of unconverted PbI2phase fraction.(Figure2).11,12The pure PbI2film shows a band gap of2.40eV,consistent with the yellow color of PbI2.As the PbI2film is gradually converted to the perovskite,the band gap is progressively shifted toward1.60eV.The deviation of MAPbI3’s band gap(1.60eV)from that of the bulk MAPbI3 material(1.55eV)could be explained by quantum confinement effects related with the sizes of TiO2and MAPbI3crystallites and their interfacial interaction.13,14Interestingly,we also noticed the presence of a second absorption in the light absorber layer,in which the gap gradually red shifts from1.90eV to1.50eV as the PbI2concentration is decreased from9.5%to0.3%(Figure2—blue arrow).Having established the chemical compositions and optical properties of the light absorberfilms, we proceeded to examine the photo-physical responses of the corresponding functional devices in order to determine how the remnant PbI2affects device performance.The pure PbI2based device remarkably achieved a0.4%efficiency with a J sc of2.1mA/cm2and a V oc of564mV (Figure3(a)).Upon progressive conversion of the PbI2layer to MAPbI3,we observe two different regions(Figure4,Table I).In thefirst region,the expected behavior is observed;as more PbI2is converted to MAPbI3,the trend is toward higher photovoltaic efficiency,due both to J sc and V oc, until1.7%PbI2is reached.The increase in J sc is attributable,at least in part,to increasing absorption of light by the perovskite.We speculate that progressive elimination of PbI2,present as a layer between TiO2and the perovskite,also leads to higher net yields for electron injection into TiO2and therefore,higher J values.For a sufficiently thick PbI2spacer layer,electron injection would occur instepwise fashion,i.e.,perovskite→PbI2→TiO2.Finally,the photovoltage increase is attributable toFIG.4.Summary of J-V data vs.PbI2concentration of CH3NH3PbI3-based devices(Region1:0to15min dipping time, Region2:15min to2h dipping time).TABLE I.Photovoltaic performance of CH3NH3PbI3-based devices as a function of unconverted PbI2fraction.Dipping time PbI2concentration a J sc(mA/cm2)V oc(V)Fill factor(%)Efficiency(%) 0s100% 2.10.564320.45s9.5%10.10.93352 4.960s7.2%13.40.96052 6.72min 5.3%14.00.964557.45min 3.7%14.70.995578.315min 1.7%15.1 1.036629.730min0.8%13.60.968648.51h0.4%12.40.938657.62h0.3%9.70.84668 5.5a Determined from the Rietveld analysis of X-ray diffraction data.the positive shift in TiO2’s quasi-Fermi level as the population of photo-injected electrons is higher with increased concentration of MAPbI3.The second region yields a notably different trend;surprisingly,below a concentration of2% PbI2,J sc,V oc,and ultimatelyηdecrease.Considering that the light-harvesting efficiency would increase when the remaining2%PbI2is converted to MAPbI3(albeit to only a small degree),then the remnant PbI2must have some other role.We posit that remnant PbI2serves to inhibit detrimental electron-transfer processes(Figure5).Two such processes are back electron transfer from TiO2to holes in the valence band of the perovskite(charge-recombination)or to the holes in the HOMO of the HTM(charge-interception).This retardation of electron interception/recombination observation is reminiscent of the behavior of atomic layer deposited Al2O3/ZrO2layers that have been employed in dye-sensitized solar cells.15–18It is conceivable that the conversion of PbI2to MAPbI3occurs from the solution interface toward the TiO2/PbI2interface and thus would leave sandwiched between TiO2and MAPbI3a blocking layer of PbI2that inhibits charge-interception/recombination.For this hypothesis to be correct,it is crucial that the conduction-band-edge energy(E cb)of the PbI2be higher than the E cb of the TiO2.19–21 The work function of PbI2was measured by ultraviolet photoelectron spectroscopy(UPS)and was observed to be at6.35eV vs.vacuum level,which is0.9eV lower than the valence-band-edge energy(E vb)of MAPbI3(see Sec.S7of the supplementary material23for the work function of PbI2);the E cb(4.05eV)was calculated by subtracting the work function from the band gap(2.30eV).solar cell.FIG.6.Dark current of CH3NH3PbI3-based devices as a function of unconverted PbI2phase fraction.The E cb of PbI2is0.26eV higher than the E cb of TiO2and thus PbI2satisfies the conditions of a charge-recombination/interception barrier layer.In order to probe the hypothesis that PbI2acts as a charge-interception barrier,dark current measurements,in which electronsflow from TiO2to the HOMO of the HTM,were made.Consistent with our hypothesis,Figure6illustrates that the onset of the dark current occurs at lower potentials as the PbI2concentration decreases.In the absence of other effects,the increasing dark current with increasing fraction of perovskite(and decreasing fraction of PbI2)should result in progressively lower open-circuit photovoltages.Instead,the photocurrent density and the open-circuit photovoltage bothincrease,at least until to PbI2fraction reaches1.7%.As discussed above,thinning of a PbI2-basedFIG.7.Cross-sectional SEM images of CH3NH3PbI3film with different dipping time.sandwich layer should lead to higher net injection yields,but excessive thinning would diminish the effectiveness of PbI2as a barrier layer for back electron transfer reactions.Given the surprising role of remnant PbI2in these devices,we further probed the two-step conversion process by using scanning-electron microscopy(SEM)(Figure7).Two domains of lead-containing materials(PbI2and MAPbI3)are present.Thefirst domain is sited within the mesoporous TiO2network(area1)while the second grows on top of the network(area2).Area2initially contains 200nm crystals.As the dipping time is increased,the crystals show marked changes in size and morphology.The formation of bigger perovskite crystals is likely the result of the thermodynamically driven Ostwald ripening process,i.e.,smaller perovskite crystals dissolves and re-deposits onto larger perovskite crystals.22The rate of charge-interception,as measured via dark current,is proportional to the contact area between the perovskite and the HTM.Thus,the eventual formation of large, high-aspect-ratio crystals,as shown in Figure7,may well lead to increases in contact area and thereby contributes to the dark-current in Figure6.Regardless,we found that the formation of large perovskite crystals greatly decreased our success rate in constructing high-functioning,non-shorting solar cells.In summary,residual PbI2appears to play an important role in boosting overall efficiencies for CH3NH3PbI3-containing photovoltaics.PbI2’s role appears to be that of a TiO2-supported blocking layer,thereby slowing rates of electron(TiO2)/hole(perovskite)recombination,as well as decreasing rates of electron interception by the hole-transporting material.Optimal performance for energy conversion is observed when ca.98%of the initially present PbI2has been converted to the perovskite. Conversion to this extent requires about15min.Pushing beyond98%(and beyond15min of reaction time)diminishes cell performance and diminishes the success rate in constructing non-shorting cells.The latter problem is evidently a consequence of conversion of small and more-or-less uniformly packed perovskite crystallites to larger,poorly packed crystallites of varying shape and size.Finally,the essential,but previously unrecognized,role played by remnant PbI2 provides an additional explanation for why cells prepared dissolving and then depositing pre-formed CH3NH3PbI3generally under-perform those prepared via the intermediacy of PbI2.We thank Prof.Tobin Marks for use of the solar simulator and EQE measurement system. Electron microscopy was done at the Electron Probe Instrumentation Center(EPIC)at Northwestern University.Ultraviolet Photoemission Spectroscopy was done at the Keck Interdisciplinary SurfaceScience facility(Keck-II)at Northwestern University.This research was supported as part of theANSER Center,an Energy Frontier Research Center funded by the U.S Department of Energy, Office of Science,Office of Basic Energy Sciences,under Award No.DE-SC0001059.1R.Monastersky,Nature(London)497(7447),13(2013).2H.J.Snaith,J.Phys.Chem.Lett.4(21),3623(2013).3M.M.Lee,J.Teuscher,T.Miyasaka,T.N.Murakami,and H.J.Snaith,Science338(6107),643(2012).4J.Burschka,N.Pellet,S.J.Moon,R.Humphry-Baker,P.Gao,M.K.Nazeeruddin,and M.Gratzel,Nature(London) 499(7458),316(2013).5F.Hao,C.C.Stoumpos,D.H.Cao,R.P.H.Chang,and M.G.Kanatzidis,Nat.Photonics8(6),489(2014);F.Hao,C.C. Stoumpos,R.P.H.Chang,and M.G.Kanatzidis,J.Am.Chem.Soc.136,8094–8099(2014).6N.K.Noel,S.D.Stranks,A.Abate,C.Wehrenfennig,S.Guarnera,A.Haghighirad,A.Sadhanala,G.E.Eperon,M.B. Johnston,A.M.Petrozza,L.M.Herz,and H.J.Snaith,Energy Environ.Sci.7,3061(2014).7H.S.Kim,C.R.Lee,J.H.Im,K.B.Lee,T.Moehl,A.Marchioro,S.J.Moon,R.Humphry-Baker,J.H.Yum,J.E.Moser, M.Gratzel,and N.G.Park,Sci.Rep.2,591(2012).8D.Y.Liu and T.L.Kelly,Nat.Photonics8(2),133(2014).9C.C.Stoumpos,C.D.Malliakas,and M.G.Kanatzidis,Inorg.Chem.52(15),9019(2013).10J.H.Noh,S.H.Im,J.H.Heo,T.N.Mandal,and S.I.Seok,Nano Lett.13(4),1764(2013).11Diffuse reflectance measurements of MAPbI3films were converted to absorption spectra using the Kubelka-Munk equation,α/S=(1-R)2/2R,where R is the percentage of reflected light,andαand S are the absorption and scattering coefficients, respectively.The band gap values are the energy value at the intersection point of the absorption spectrum’s tangent line and the energy axis.12L.F.Gate,Appl.Opt.13(2),236(1974).13O.V oskoboynikov,C.P.Lee,and I.Tretyak,Phys.Rev.B63(16),165306(2001).14X.X.Xue,W.Ji,Z.Mao,H.J.Mao,Y.Wang,X.Wang,W.D.Ruan,B.Zhao,and J.R.Lombardi,J.Phys.Chem.C 116(15),8792(2012).15E.Palomares,J.N.Clifford,S.A.Haque,T.Lutz,and J.R.Durrant,J.Am.Chem.Soc.125(2),475(2003).16C.Prasittichai,J.R.Avila,O.K.Farha,and J.T.Hupp,J.Am.Chem.Soc.135(44),16328(2013).17A.K.Chandiran,M.K.Nazeeruddin,and M.Gratzel,Adv.Funct.Mater.24(11),1615(2014).18M.J.Katz,M.J.D.Vermeer,O.K.Farha,M.J.Pellin,and J.T.Hupp,Langmuir29(2),806(2013).19M.J.DeVries,M.J.Pellin,and J.T.Hupp,Langmuir26(11),9082(2010).20C.Prasittichai and J.T.Hupp,J.Phys.Chem.Lett.1(10),1611(2010).21F.Fabregat-Santiago,J.Garcia-Canadas,E.Palomares,J.N.Clifford,S.A.Haque,J.R.Durrant,G.Garcia-Belmonte, and J.Bisquert,J.Appl.Phys.96(11),6903(2004).22Alan D.McNaught and Andrew Wilkinson,IUPAC Compendium of Chemical Terminology(Blackwell Scientific Publica-tions,Oxford,1997).23See supplementary material at /10.1063/1.4895038for experimental details,absorption spectrum of bulk CH3NH3PbI3,fraction,size,absorption spectrum,work function of unconverted PbI2,and average photovoltaic perfor-mance.。
Subcategory ISSN Abbreviated Journal Title中科院分区2013年10月发TotalCitesACOUSTICS0960-7692ULTRASOUND OBST GYN2区 8490 ACOUSTICS1350-4177ULTRASON SONOCHEM2区 5008 ACOUSTICS0301-5629ULTRASOUND MED BIOL2区 7839 ACOUSTICS0041-624XULTRASONICS2区 3651 ACOUSTICS1077-5463J VIB CONTROL2区 1649 ACOUSTICS0885-3010IEEE T ULTRASON FERR3区 7469 ACOUSTICS1558-7916IEEE T AUDIO SPEECH3区 2251 ACOUSTICS0001-4966J ACOUST SOC AM3区 35754 ACOUSTICS0022-460XJ SOUND VIB3区 19012 ACOUSTICS0161-7346ULTRASONIC IMAGING3区 890 ACOUSTICS0165-2125WAVE MOTION3区 1367 ACOUSTICS0278-4297J ULTRAS MED3区 3907 ACOUSTICS0167-6393SPEECH COMMUN3区 1982 ACOUSTICS1048-9002J VIB ACOUST3区 1825 ACOUSTICS0003-682XAPPL ACOUST4区 1975 ACOUSTICS1549-4950J AUDIO ENG SOC4区 832 ACOUSTICS0137-5075ARCH ACOUST4区 242 ACOUSTICS1610-1928ACTA ACUST UNITED AC4区 1808 ACOUSTICS0091-2751J CLIN ULTRASOUND4区 1642 ACOUSTICS0031-8388PHONETICA4区 570 ACOUSTICS0218-396XJ COMPUT ACOUST4区 328 ACOUSTICS1687-4722EURASIP J AUDIO SPEE4区 59 ACOUSTICS1475-472XINT J AEROACOUST4区 190 ACOUSTICS1070-9622SHOCK VIB4区 320 ACOUSTICS1063-7710ACOUST PHYS+4区 600 ACOUSTICS1027-5851INT J ACOUST VIB4区 57 ACOUSTICS0736-2501NOISE CONTROL ENG J4区 273 ACOUSTICS0814-6039ACOUST AUST4区 49 ACOUSTICS0263-0923J LOW FREQ NOISE V A4区 79 ACOUSTICS1541-0161SOUND VIB4区 195 AGRICULTURAL ECON0306-9192FOOD POLICY2区 1736 AGRICULTURAL ECON0165-1587EUR REV AGRIC ECON2区 744 AGRICULTURAL ECON2040-5790APPL ECON PERSPECT P3区 101 AGRICULTURAL ECON0021-857XJ AGR ECON3区 829 AGRICULTURAL ECON1364-985XAUST J AGR RESOUR EC3区 473 AGRICULTURAL ECON0169-5150AGR ECON-BLACKWELL3区 1284 AGRICULTURAL ECON0002-9092AM J AGR ECON4区 4462 AGRICULTURAL ECON0008-3976CAN J AGR ECON4区 378 AGRICULTURAL ECON1068-5502J AGR RESOUR ECON4区 534 AGRICULTURAL ECON1756-137XCHINA AGR ECON REV4区 43 AGRICULTURAL ECON1559-2448INT FOOD AGRIBUS MAN4区 199 AGRICULTURAL ECON1699-6887ITEA-INF TEC ECON AG4区 54 AGRICULTURAL ECON0303-1853AGREKON4区 104 AGRICULTURAL ECON1808-2882CUST AGRONEGOCIO4区 3 AGRICULTURAL ENGIN0960-8524BIORESOURCE 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SCIENCE1025-3890STRESS3区 1631 BEHAVIORAL SCIENCEBEHAVIORAL SCIENCE0379-864XCHEM SENSES3区 37981045-2249BEHAV ECOL3区 7392 BEHAVIORAL SCIENCE0065-3454ADV STUD BEHAV3区 1119 BEHAVIORAL SCIENCEBEHAVIORAL SCIENCE0031-9384PHYSIOL BEHAV3区 170030003-3472ANIM BEHAV3区 21716 BEHAVIORAL SCIENCE0006-8977BRAIN BEHAV EVOLUT3区 2315 BEHAVIORAL SCIENCE1744-9081BEHAV BRAIN FUNCT3区 1055 BEHAVIORAL SCIENCE0340-5443BEHAV ECOL SOCIOBIOL3区 10205 BEHAVIORAL SCIENCE1435-9448ANIM COGN3区 1820 BEHAVIORAL SCIENCE0735-7044BEHAV NEUROSCI4区 8038 BEHAVIORAL SCIENCE0091-3057PHARMACOL BIOCHEM BE4区 12961 BEHAVIORAL SCIENCE0001-8244BEHAV GENET4区 3356 BEHAVIORAL SCIENCE0195-6663APPETITE4区 6200 BEHAVIORAL SCIENCE0097-7403J EXP PSYCHOL ANIM B4区 2311 BEHAVIORAL SCIENCE0955-8810BEHAV PHARMACOL4区 2896 BEHAVIORAL SCIENCE0096-140XAGGRESSIVE BEHAV4区 2025 BEHAVIORAL SCIENCE0179-1613ETHOLOGY4区 3596 BEHAVIORAL SCIENCE0735-7036J COMP PSYCHOL4区 2517 BEHAVIORAL SCIENCE1543-4494LEARN BEHAV4区 654 BEHAVIORAL SCIENCEBEHAVIORAL SCIENCE0340-7594J COMP PHYSIOL A4区 50301525-5050EPILEPSY BEHAV4区 4765 BEHAVIORAL SCIENCE0196-206XJ DEV BEHAV PEDIATR4区 2669 BEHAVIORAL SCIENCEBEHAVIORAL SCIENCE1095-0680J ECT4区 9040005-7959BEHAVIOUR4区 4666 BEHAVIORAL SCIENCE1558-7878J VET BEHAV4区 303 BEHAVIORAL SCIENCE0376-6357BEHAV PROCESS4区 2669 BEHAVIORAL SCIENCE0168-1591APPL ANIM BEHAV SCI4区 5989 BEHAVIORAL SCIENCE1543-3633COGN BEHAV NEUROL4区 634 BEHAVIORAL SCIENCE0018-7208HUM FACTORS4区 2872 BEHAVIORAL SCIENCE0873-9749ACTA ETHOL4区 240 BEHAVIORAL SCIENCE0394-9370ETHOL ECOL EVOL4区 631 BEHAVIORAL SCIENCE0022-5002J EXP ANAL BEHAV4区 2483 BEHAVIORAL SCIENCE0896-4289BEHAV MED4区 503 BEHAVIORAL SCIENCE0289-0771J ETHOL4区 600 BEHAVIORAL SCIENCEBIOCHEMICAL RESEA1548-7091NAT METHODS1区 19241 BIOCHEMICAL RESEA0907-4449ACTA CRYSTALLOGR D1区 12453 BIOCHEMICAL RESEA1754-2189NAT PROTOC1区 16922 BIOCHEMICAL RESEA0958-1669CURR OPIN BIOTECH2区 9501 BIOCHEMICAL RESEA1535-9476MOL CELL PROTEOMICS2区 14201 BIOCHEMICAL RESEA1473-0197LAB CHIP2区 16485 BIOCHEMICAL 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Experimental Vibrational Zero-Point Energies:Diatomic MoleculesKarl K.Irikura a…Physical and Chemical Properties Division,National Institute of Standards and Technology,Gaithersburg,Maryland20899-8380͑Received23August2006;revised manuscript received18December2006;accepted22December2006;published online18April2007͒Vibrational zero-point energies͑ZPEs͒,as determined from published spectroscopicconstants,are derived for85diatomic molecules.Standard uncertainties are also pro-vided,including estimated contributions from bias as well as the statistical uncertaintiespropagated from those reported in the spectroscopy literature.This compilation will behelpful for validating theoretical procedures for predicting ZPEs,which is a necessarystep in the ab initio prediction of molecular energetics.©2007by the U.S.Secretary ofCommerce on behalf of the United States.All rights reserved..͓DOI:10.1063/1.2436891͔Key words:molecular energetics;uncertainty;vibrational spectroscopy;zero-point energy.CONTENTS1.Introduction (389)2.Definition of Zero-Point Energy (389)3.Selection of Molecules (390)4.Contributions to Uncertainties (390)5.Analyses for Individual Molecules (394)6.Results and Discussion (396)7.Acknowledgments (396)8.References (396)List of Tables1.Spectroscopic constants for selected diatomicmolecules (391)2.Derivatives of ZPE with respect tospectroscopic constants,c (392)3.Estimated standard uncertainties associatedwith some diatomic ZPEs͑cm−1units͒asdetermined using the full͓Eq.͑6͔͒,diagonal͓Eq.͑7͔͒,and pessimistic͓Eq.͑8͔͒approximations (393)4.Truncation bias with respect to sextic diatomicvibrational model (394)5.Experimental vibrational zero-point energies͑cm−1͒for selected diatomic molecules (395)1.IntroductionOne of the most popular uses of computational quantum chemistry models is to predict molecular energetics,which is required for applications such as thermochemistry and reac-tion kinetics.As a result of steady progress in electronic structure theory and computational efficiency,the precision of ab initio molecular energetics has improved by a factor of about10every10years.With the advent of basis-set ex-trapolation methods and highly correlated theories,the ener-getics of small molecules can now be computed to high pre-cision almost routinely.1As the uncertainties in electronic energy fall away,other sources of uncertainty become in-creasingly noticeable.Vibrational zero-point energy͑ZPE͒has emerged as one of the principal remaining sources of uncertainty in calculations of molecular energetics.In careful work,it is necessary to go beyond the harmonic approxima-tion to obtain a reliable ZPE.2–5However,the most common practice is simply to scale the computed harmonic ZPE by a multiplicative correction factor.The empirical scaling factor carries uncertainty.We have recently quantified the uncer-tainties associated with scaling factors for fundamental vi-brational frequencies.6The uncertainties associated with the experimental vibrational frequencies were required in the analysis,although in the end their contribution was small enough to be neglected.Similar work is underway to provide scaling factors,with their associated uncertainties,appropri-ate for routine predictions of ZPE.Unfortunately,we have been unable to locate any recent compilations of experimen-tally derived ZPEs,or compilations of any age that include uncertainties.Moreover,existing compilations include few data for polyatomic molecules.We are now working tofill this gap by providing benchmark,experimental ZPEs along with the associated uncertainties.The present list,restricted to diatomic molecules,is not intended to be exhaustive.Nev-ertheless,it is the largest such list yet assembled,thefirst to employ spectroscopic data more recent than those compiled by Huber and Herzberg,7and thefirst to include uncertainties.2.Definition of Zero-Point EnergyIn quantum chemistry,the Born-Oppenheimer approxima-tion͑BOA͒is almost8always accepted.Thus,the most com-mon definition of the molecular ZPE is the energy difference between the vibrational ground state and the lowest point on the Born-Oppenheimer potential energy surface.Unfortu-a͒karl.irikura@©2007by the U.S.Secretary of Commerce on behalf of the United States.All rights reserved..0047-2689/2007/36…2…/389/9/$42.00J.Phys.Chem.Ref.Data,Vol.36,No.2,2007389nately,this definition is not convenient for experimentalZPEs,as the BOA is never adopted by real molecules.Ex-perimental spectra are generally analyzed,however,as if theBOA were followed by real molecules;explicit Born-Oppenheimer corrections are only made when simulta-neouslyfitting different isotopologs to the same effective po-tential.Thus,in the present compilation,the experimentalZPE is defined as the difference between the molecularground state and the lowest point on its isotope-specific ef-fective potential.The small difference between this definitionand that used by quantum chemists must be absorbed by theempirical scaling factor that is typically applied to theoreti-cally determined ZPEs.The ZPE cannot be measured directly since no moleculecan be observed below its ground state.Instead,the term“experimental ZPE”describes a value that is usually͑but notnecessarily9͒derived by combining experimental spectro-scopic constants with standard theoretical or empirical mod-els for anharmonic oscillators.Thus,“experimental”ZPEvalues are actually hybrids of experiment and theoreticalmodeling.Most available experimental ZPEs are for diatomic mol-ecules,because far fewer spectroscopic constants are neededfor diatomic molecules than for polyatomic molecules.Al-though thefield of molecular spectroscopy is home tocrowds of molecular constants,among nonspecialists themost common expression for the vibrational energy levels ofa diatomic molecule,relative to the minimum on the poten-tial energy curve,isG͑v͒=e͑v+12͒−e x e͑v+12͒2.͑1͒In Eq.͑1͒,e ande x e are the harmonic frequency and the first anharmonicity constant,respectively,and v is the vibra-tional quantum number,which can assume nonnegative inte-ger values.10Note that the symbole x e represents a single constant,not a product.Thus,the most popular expression for diatomic ZPE is,to second order in͑v+12͒,ZPE=G͑0͒=12e−14e x e.͑2͒This expression is derived by extrapolating Eq.͑1͒to v i=−1 2,which corresponds to the lowest point on the effectivepotential,to a good approximation.11Contributions from higher-order anharmonicities are generally negligible͑e.g., 0.1cm−1for H2,0.07cm−1for OH,and0.0013cm−1for CO͒.Unfortunately,as has been pointed out recently,2–5the popular expression is incorrect.In addition to the linear and quadratic terms in Eq.͑1͒, there is a constant term that is usually overlooked.This was demonstrated by Dunham in his classic power-series analysis.12The resulting energy levels,to second order,are given byG͑v͒=Y00+Y10͑v+12͒+Y20͑v+12͒2,͑3͒where Y10Ϸe and Y20Ϸ−e x e to good approximations.The constant Y00does not influence the line positions͑i.e.,energy intervals͒in a spectrum but contributes to the ZPE.In this paper we include Y00and even the third-order term͑second anharmonicity constant͒when available.Thus,ZPEs of di-atomic molecules are taken to beZPE=G͑0͒=Y00+12e−14e x e+18e y e,͑4͒where Y30Ϸe y e.To a good approximation,Y00can be ex-pressed in terms of conventional spectroscopic constants as13Y00ϷB e4+␣ee12B e+␣e2e2144B e3−e x e4.͑5͒The Dunham constants that correspond to the conventional rotational constants here are Y01ϷB e and Y11Ϸ−␣e.The value of Y00is largest for H2͑Y00=8.9cm−1͒,smaller for hydrides such as OH͑Y00=3.0cm−1͒,and less than one wavenumber for nonhydrides such as CO͑Y00=0.2cm−1͒.3.Selection of MoleculesAn initial list of molecules and associated ground-state spectroscopic constants was culled from the classic compila-tion by Huber and Herzberg7and from the NIST Diatomic Spectral Database.14For compatibility with the NIST Com-putational Chemistry Comparison and Benchmark Database,15only molecules composed of elements lighter than argon͑i.e.,atomic number ZϽ18͒were included.More recent values of constants were taken from the spectroscopic literature as available.Since our goal is a list of reliable ZPEs,diatomic molecules were excluded if their ZPEs obvi-ously͑upon cursory analysis͒had standard uncertainties of about0.5cm−1or more.Ourfinal list of diatomic molecules, with their spectroscopic constants,is provided in Table1.͑In Table1,and throughout this paper,H refers specifically to protium and D to deuterium.͒Standard uncertainties are listed in the spectroscopic style.For example,the quantity 12.345±0.067would be written12.345͑67͒.When the ground state is classically degenerate͑usually2⌸͒,averaged constants are used,as reported in the experimental sources cited.This choice was made for convenient comparison with conventional,non-relativistic quantum chemistry calcula-tions.For Cl2+,only separate constants for2⌸3/2and1⌸3/2 were reported.74.Contributions to UncertaintiesThe spectroscopic constants have both statistical uncer-tainty͑i.e.,uncertainty from random effects͒and bias͑i.e., systematic error͒.As we are interested in the ZPE,it is nec-essary to determine how the uncertainties in the constants contribute to the uncertainty in the corresponding ZPE.For this purpose,we accept the common linearized propagation of uncertainties16given byy2Ϸ͚iii͑ץy/ץx i͒2+2͚iϽjij͑ץy/ץx i͒͑ץy/ץx j͒,͑6͒for a quantity y=f͑x1,x2,...,x i,...͒,wherey2is the esti-mated variance of y andij=͗͑x i−x¯i͒͑x j−x¯j͒͘is the element of the covariance matrix that corresponds to the pair of vari-390K.K.IRIKURA J.Phys.Chem.Ref.Data,Vol.36,No.2,2007EXPERIMENTAL VIBRATIONAL ZERO-POINT ENERGIES391 T ABLE1.Spectroscopic constants for selected diatomic molecules.Standard uncertainties͑1͒are between parentheses and refer to the least significant digits. Values are in wavenumber units͑cm−1͒.Moleculeee x ee y e B e␣e ReferenceFirst-row elements onlyH24401.213͑18͒121.336͑18͒0.8129͑18͒60.8530͑18͒ 3.0622͑18͒7HD3813.15͑18͒91.65͑9͒0.723͑9͒45.655͑9͒ 1.986͑9͒7D23115.50͑9͒61.82͑9͒0.562͑9͒30.4436͑18͒ 1.0786͑9͒7Second-row elementsBeH2061.235͑15͒37.327͑22͒0.084͑17͒10.31992͑5͒0.3084͑2͒22BeD1529.986͑11͒20.557͑12͒0.035͑7͒ 5.68830͑3͒0.1261͑1͒22Be18O1457.09͑22͒11.311͑74͒0.0143͑83͒ 1.5847͑5͒0.01784͑15͒33BF1402.15865͑26͒11.82106͑15͒0.051595͑35͒ 1.51674399͑21͒0.01904848͑22͒23BH2366.7296͑16͒49.33983͑99͒0.362͑10͒12.025755͑45͒0.421565͑22͒34BO1885.286͑41͒11.694͑11͒−0.00952͑83͒ 1.781110͑31͒0.016516͑17͒35C21855.0663͑63͒13.6007͑54͒−0.116͑2͒ 1.820053͑11͒0.0179143͑44͒36C2−1781.189͑18͒11.6717͑48͒0.009981͑28͒ 1.74666͑32͒0.01651͑46͒37CF1307.93͑37͒11.08͑12͒0.093͑15͒ 1.41626͑48͒0.01844͑17͒38CH2860.7508͑98͒64.4387͑85͒0.3634͑27͒14.45988͑20͒0.53654͑33͒39CD2101.05193͑55͒34.72785͑58͒0.14147͑10͒7.8079823͑55͒0.212240͑11͒40CN2068.648͑11͒13.0971͑68͒−0.0124͑17͒ 1.89978316͑67͒0.0173720͑12͒41CO2169.75589͑8͒13.28803͑2͒0.0104109͑14͒ 1.9316023͑7͒0.01750513͑14͒42CO+2214.127͑35͒15.094͑21͒−0.0117͑34͒ 1.976941͑39͒0.018943͑34͒43and44F2916.929͑10͒11.3221͑10͒−0.10572͑67͒0.889294͑11͒0.0125952͑24͒45HF4138.3850͑7͒89.9432͑7͒0.92449͑31͒20.953712͑2͒0.7933704͑65͒46Li2351.4066͑10͒ 2.58324͑41͒−0.00583͑7͒0.6725297͑50͒0.0070461͑16͒47and48 LiF910.57272͑10͒8.207956͑46͒0.569166͑82͒ 1.34525715͑57͒0.02028749͑19͒49LiH1405.49805͑76͒23.1679͑7͒0.17093͑28͒7.5137315͑9͒0.2163911͑24͒50LiD1054.93973͑32͒13.05777͑21͒0.075478͑50͒ 4.23308131͑46͒0.09149428͑84͒50LiO814.62͑15͒7.78͑15͒NA 1.21282948͑11͒0.0178990͑25͒27N22358.57͑9͒14.324͑9͒−0.00226͑9͒ 1.998241͑18͒0.017318͑9͒7N2+2207.0115͑60͒16.0616͑23͒−0.04289͑25͒ 1.93176͑9͒0.01881͑9͒vib,51rot7 NF1141.37͑9͒8.99͑9͒NA 1.205679͑53͒0.014889͑53͒vib,7rot52 NH3282.72͑10͒79.04͑8͒0.367͑23͒16.66792͑6͒0.65038͑17͒53ND2399.126͑30͒42.106͑21͒0.1203͑54͒8.90867͑15͒0.25457͑19͒54NO1904.1346͑18͒14.08836͑89͒0.01005͑20͒ 1.7048885͑21͒0.0175416͑14͒55NO+2376.72͑11͒16.255͑18͒−0.01562͑92͒ 1.997195͑89͒0.018790͑69͒56O21580.161͑9͒11.95127͑9͒0.0458489͑9͒ 1.44562͑9͒0.0159305͑9͒57O2+1905.892͑82͒16.489͑13͒0.02057͑90͒ 1.689824͑91͒0.019363͑37͒58FO1053.0138͑12͒9.9194͑13͒−0.06096͑59͒ 1.05870763͑81͒0.0132951͑23͒59OH3737.761͑18͒84.8813͑18͒0.5409͑18͒18.9108͑18͒0.7242͑9͒7OD+2271.80͑9͒44.235͑9͒0.4267͑18͒8.9116͑18͒0.2896͑9͒7Third-row elementsAlCl481.77466͑20͒ 2.101811͑88͒0.006638͑15͒0.243930066͑12͒0.001611082͑12͒60AlF802.32447͑11͒ 4.849915͑44͒0.0195738͑68͒0.552480208͑65͒0.004984261͑44͒23AlH1682.37474͑31͒29.05098͑29͒0.24762͑12͒ 6.3937842͑17͒0.1870527͑15͒61AlD1211.77402͑15͒15.06477͑11͒0.09244͑4͒ 3.3183929͑8͒0.0698773͑4͒61AlO979.4852͑50͒7.0121͑32͒−0.00206͑56͒0.6413856͑54͒0.0057796͑8͒62AlS617.1169͑33͒ 3.3310͑19͒−0.00924͑32͒0.2800368͑33͒0.00178225͑55͒63BCl840.29472͑63͒ 5.49170͑33͒0.02995͑7͒0.684282͑12͒0.0068124͑14͒17BeS997.94͑9͒ 6.137͑9͒NA0.79059͑9͒0.00664͑9͒7BS1179.91͑3͒ 6.25͑3͒−0.0083͑58͒0.79478͑5͒0.00578͑4͒64CCl876.89749͑69͒ 5.44698͑54͒0.02607͑15͒0.697137͑34͒0.00685277͑45͒25Cl2559.751͑20͒ 2.69427͑20͒−0.003325͑2͒0.24415͑20͒0.001516͑20͒65Cl2+645.61͑9͒ 3.015͑9͒0.007͑9͒0.26950͑18͒0.00164͑9͒7͑⍀=1/2͒644.77͑9͒ 2.988͑9͒NA0.2697͑9͒0.00167͑9͒7ClF783.4534͑24͒ 4.9487͑6͒−0.0176͑1͒0.5164805͑31͒0.0043385͑8͒66ClO853.64268͑13͒ 5.51828͑6͒−0.01256͑30͒0.62345797͑4͒0.0059357͑1͒28CP1239.79924͑8͒ 6.833769͑46͒−0.001377͑7͒0.79886775͑8͒0.00596933͑19͒67CS1285.15464͑10͒ 6.502605͑53͒0.003887͑9͒0.82004356͑4͒0.00591835͑5͒68HCl2990.9248͑15͒52.8000͑15͒0.21803͑55͒10.5933002͑13͒0.3069985͑41͒69J.Phys.Chem.Ref.Data,Vol.36,No.2,2007ables x i and x j.For the problem at hand,y is the ZPE and the x i are generic spectroscopic constants.The required deriva-tives,summarized in Table2,are straightforward but do not appear to have been compiled previously.Typically,only the diagonal elements,ii,of the covari-ance matrix͑i.e.,the variances of thefitting constants͒are reported and available to us.Omitting the off-diagonal con-tributions in Eq.͑6͒yields the estimatey2Ϸ͚ii2͑ץy/ץx i͒2,͑7͒where the standard uncertainties of the x i arei=ͱii.This diagonal approximation introduces a bias in the estimated uncertainty,which will be different for different molecules. To estimate the magnitude of the bias,we consider the situ-ation for BCl,for which the covariance matrix has been published.17Using the derivatives in Table2and the param-eter values and statistical uncertainties from Table1,the standard uncertainty͑i.e.,the square root of the variance͒for the ZPE is0.00065cm−1.When only the diagonal terms are included,the resulting standard uncertainty is only slightly smaller,0.00057cm−1.Given only the variances,the most pessimistic scenario for the correlation coefficients r ij͑−1Յr ijϵij/ijՅ1͒leads to the upper boundT ABLE1.Spectroscopic constants for selected diatomic molecules.Standard uncertainties͑1͒are between parentheses and refer to the least significant digits. Values are in wavenumber units͑cm−1͒.—ContinuedMoleculeee x ee y e B e␣e ReferenceDCl2145.1326͑11͒27.1593͑7͒0.07993͑20͒ 5.4487838͑6͒0.1132345͑15͒69HCl+2673.69͑9͒52.537͑9͒NA9.95661͑18͒0.32716͑18͒7LiCl642.95453͑93͒ 4.47253͑40͒0.020118͑49͒0.70652247͑20͒0.00801019͑32͒70NaLi256.5412͑19͒ 1.62271͑96͒−0.00495͑22͒0.3758620͑89͒0.0031465͑15͒30Mg251.121͑18͒ 1.645͑9͒0.01624͑18͒0.09287͑9͒0.003776͑18͒7MgH1492.7763͑36͒29.847͑4͒−0.3048͑20͒ 5.8255229͑41͒0.177298͑14͒71MgD1077.2976͑26͒15.521͑2͒−0.1184͑7͒ 3.0343436͑21͒0.066607͑5͒71MgO785.2183͑6͒ 5.1327͑3͒0.01649͑7͒0.5748414͑3͒0.0053223͑3͒72MgS528.74͑9͒ 2.704͑9͒NA0.26797͑9͒0.00176͑9͒7Na2159.08548͑44͒0.70866͑29͒−0.004632͑77͒0.15473537͑29͒0.00086375͑11͒29NaCl364.6842͑4͒ 1.7761͑2͒0.005937͑35͒0.21806302͑8͒0.00162479͑6͒73NaF535.65805͑21͒ 3.57523͑13͒0.018453͑34͒0.43690153͑7͒0.00455918͑7͒74NaH1171.968͑12͒19.703͑10͒0.175͑2͒ 4.90327͑13͒0.1370͑4͒75NCl827.95767͑75͒ 5.30015͑61͒−0.00480͑19͒0.649767390͑85͒0.00641432͑20͒76P2780.77͑9͒ 2.835͑18͒−0.00462͑9͒0.30362͑9͒0.00149͑9͒7P2+672.20͑9͒ 2.74͑9͒NA0.27600͑18͒0.00151͑9͒7PF846.75͑9͒ 4.489͑9͒0.019͑9͒0.5667427͑35͒0.00456͑9͒7but B e77 PH2363.774͑36͒43.907͑27͒0.1059͑73͒8.53904͑19͒0.25339͑28͒54PN1336.948͑20͒ 6.8958͑57͒−0.00605͑48͒0.7864844͑28͒0.0055337͑36͒78PO1233.34͑9͒ 6.56͑9͒NA0.733223657͑22͒0.005466162͑50͒vib,7rot79S2725.7102͑97͒ 2.8582͑25͒NA0.29539516͑30͒0.00159754͑59͒80SF837.6418͑5͒ 4.46953͑18͒NA0.555173͑4͒0.004459͑10͒81SH2696.2475͑58͒48.7420͑28͒0.1124͑6͒9.600247͑51͒0.27990͑10͒82Si2510.98͑9͒ 2.02͑9͒NA0.2390͑9͒0.00135͑18͒7SiCl535.59͑2͒ 2.1757͑50͒0.00604͑36͒0.256103͑14͒0.0015817͑72͒83SiF837.32507͑22͒ 4.83419͑9͒0.019807͑16͒0.58125735͑21͒0.00503859͑39͒84SiH2042.5229͑8͒36.0552͑5͒0.1254͑1͒7.503898͑30͒0.21814͑2͒85SiH+2157.17͑9͒34.24͑9͒NA7.6603͑9͒0.2096͑9͒7SiN1151.284͑43͒ 6.455͑21͒−0.0069͑20͒0.730927͑15͒0.005685͑30͒86bute y e87 SiO1241.54388͑7͒ 5.97437͑2͒0.006090͑3͒0.72675206͑2͒0.00503784͑1͒88SiS749.64559͑7͒ 2.58623͑4͒0.001048͑9͒0.303527856͑6͒0.001473130͑3͒88SO1150.7913͑10͒ 6.4096͑5͒0.01306͑11͒0.72082210͑2͒0.00575080͑2͒vib,89rot90T ABLE2.Derivatives of ZPE with respect to spectroscopic constants,c.cץ͑ZPE͒/ץcZPE=e2−e x e2+e y e8+B e4+␣ee12B e+␣e2e2144B e3e1/2+B ee s͑2s+1͒,where sϵ␣ee12B ee x e−1/2e y e1/8B e1/4−s͑3s+1͒␣e B e␣e s͑2s+1͒392K.K.IRIKURA J.Phys.Chem.Ref.Data,Vol.36,No.2,2007yՅ͚ii͉ץy/ץx i͉,͑8͒oryՅ0.00098cm−1for the BCl example.This is50% larger than the result from Eq.͑6͒and appears inferior to the diagonal approximation.These various estimates are summa-rized in Table3,along with analogous estimates for three other diatomic molecules,based upon unpublishedfitting data generously provided by Dr.F.J.Lovas.Based upon the data for these four molecules,the diagonal approximation appears reasonable and in this paper we use Eq.͑7͒to esti-mate the statistical contribution to the standard uncertainty of the diatomic ZPEs.Most of the standard uncertainties presented in Table1are from the experimental papers in which the constants were reported.In some cases,uncertainties were reported but not described;they have been assumed to represent standard un-certainties͑1͒.When uncertainties have been described as 95%confidence intervals,they have been divided by2to estimate standard uncertainties.Other special cases are de-scribed in Sec.5.The uncertainties associated with spectroscopic constants only reflect the statistical uncertainties resulting fromfitting the observed line positions to a model Hamiltonian.In this context,a Hamiltonian is a physically motivatedfitting func-tion involving selected spectroscopic constants and various quantum numbers.In some cases,the uncertainties were propagated from v-dependentfitting constants or from esti-mated͓type B͑Ref.18͔͒uncertainties in line positions.In addition to the statistical uncertainties,there are sources of bias͑“systematic error”͒which may dominate the com-bined uncertainties.True bias cannot be known,since that requires knowledge of true values.When ancillary informa-tion is available about the possible values of bias,we can make a correction for bias,as recommended in the Guide to the Expression of Uncertainty in Measurement,published by the International Organization for Standardization.19There is uncertainty associated with the correction for bias,corre-sponding to the uncertainty of the ancillary information.If we have no information,we choose the value of the correc-tion to be zero,but there is still an uncertainty associated with this͑null͒value.This uncertainty is combined with the statistical uncertainties to obtain the combined uncertainty. One source of bias derives from the truncation in Taylor-series expansions such as Eq.͑1͒.Such model-dependent uncertainties are seldom discussed.20–22Thefitted values of low-order constants are affected when higher-order constants are included in thefitting procedure.Further,our ZPE com-putation͓Eq.͑4͔͒includes terms only through third order. For diatomic molecules,we estimate the uncertainty due to truncation using the simplified analytical model described in the following paragraph.Assume,for this approximate model,that the diatomic vi-brational energy levels are perfectly described by the sextic polynomialG͑v͒=͚i=06b i͑v+12͒i,͑9͒where v is the quantum number,G͑v͒is the energy of the associated level,and the b i are constants.The exact zero-point energy within this model isZPE=b0+12b1+14b2+18b3+116b4+132b5+164b6.͑10͒Also suppose that n transition frequencies,y j=G͑j͒−G͑0͒, are observed and arefitted to the empirical expressionG͑v͒Ϸ͚i=0na i͑v+12͒i,͑11͒where a i=Y i0or the equivalent conventional constant and n Յ6.This is an exactfit because we have assumed,for math-ematical convenience,that the number of free parameters is equal to the number of data.Then the apparent zero-point energy isZPE app=a0+12a1+14a2+18a3.͑12͒ZPE app depends upon the number,n,offitted constants even though the higher-order constants are not explicit in Eq.͑12͒. The difference͑ZPE app−ZPE͒,determined from Eqs.͑10͒and͑12͒,is the truncation bias in this simple model;its ab-solute value is an estimate for the uncertainty arising from truncation of the spectroscopic Hamiltonian.The biases in the cubic approximation͑12͒,for different orders n of the fitting polynomial͑11͒,are listed in the second column of Table4.The value for n=2uses the more severely truncatedquadratic expression ZPE app=a0+12a1+14a2instead of Eq.͑12͒,because a3is undefined.The differences͑a0−b0͒, which appear in the expressions for estimated bias,require evaluation.If we identify a0and b0with Y00,we can use Eq.͑5͒to estimate that͑a0−b0͒Ϸ١Y00·͑a−b͒=␣e12B eͩ1+␣e6B e2eͪ͑a1−b1͒−14͑a2−b2͒.͑13͒The expressions for͑a1−b1͒and for͑a2−b2͒are given in the last two columns of Table4.To obtain numerical values for the uncertainty arising from truncation for a particular di-atomic molecule,we determine n based upon the order of the experimentalfit,choose b iϷY i0,and combine Eq.͑13͒with the expressions in Table4.However,frequently the higherT ABLE3.Estimated standard uncertainties associated with some diatomicZPEs͑cm−1units͒as determined using the full͓Eq.͑6͔͒,diagonal͓Eq.͑7͔͒,and pessimistic͓Eq.͑8͔͒approximations.Molecule Full Diagonal a PessimisticBCl0.000650.00057͑−12%͒0.00098͑+51%͒CS0.000440.00045͑+2%͒0.00050͑+14%͒SiO0.000330.00052͑+58%͒0.00082͑+148%͒SiS0.000360.00037͑+3%͒0.00041͑+14%͒a Percentage deviation from“full”value given between parentheses.EXPERIMENTAL VIBRATIONAL ZERO-POINT ENERGIES393J.Phys.Chem.Ref.Data,Vol.36,No.2,2007Y i0are unknown.As typically͉Y i+1,0͉Ͻ͉Y i0͉,we estimate the missing Y i0crudely by geometric extrapolation from the two highest measured Y i0.As pointed out by a referee,Y i0and Y i+1,0usually differ in sign.Thus,an alternating sign is as-sumed in the present work.However,for about one-third of the data at hand,the sign does not change,i.e.,Y i0Y i−1,0Ͼ0͑for iϾ3͒.To test the sensitivity of the results to the choice of sign,we consider a positive sign in the extrapolation.This changes the magnitude of͑ZPE app−ZPE͒by a mean factor of 1.8͑standard deviationϭ1.5͒.Thus,we multiply the trunca-tion bias values by1.8to reflect the uncertainty of the ex-trapolation.Among the remaining sources of uncertainty,the most im-portant is probably that Dunham’s canonical treatment is it-self an approximation that leads to bias.In particular,any perturbations from electronically or vibrationally excited states will displace some rovibrational levels,skewing the values of thefitting constants.These effects are specific to individual molecules.We do not attempt to quantify the as-sociated uncertainties.However,they are probably small for the ground states of diatomic molecules.Dunham’s analysis is also for non-degenerate electronic states͑1⌺͒and must be considered more approximate in other cases.To illustrate the current procedure,consider BF as an ex-ample.Constants from Table1are substituted into Eq.͑5͒to obtain Y00=0.3111cm−1.Applying Eq.͑4͒yields ZPE =698.4416cm−1,as listed in Table5.The associated uncer-tainty is computed by propagating the uncertainties in the spectroscopic constants,estimating the uncertainty associ-ated with the͑null͒correction for truncation bias,and com-bining these two quantities to obtain a combined standard uncertainty.To propagate uncertainties,substitute values from Table1into the formulas in Table2to obtain the partial derivativesץ͑ZPE͒/ץ͑e͒=0.50307,ץ͑ZPE͒/ץ͑e x e͒=−0.5,ץ͑ZPE͒/ץ͑e y e͒=0.125,ץ͑ZPE͒/ץ͑B e͒=−3.5257,and ץ͑ZPE͒/ץ͑␣e͒=226.11.The intermediate quantity s =0.96750͑Table2͒.The standard uncertainties for the spec-troscopic constants,from Table1,are combined with thesederivatives according to Eq.͑7͒to obtain the estimated sta-tistical contribution to the variance of the ZPE.Taking thesquare root gives u statϷ0.000159cm−1,as listed in Table5͑rounded to two digits͒.To estimate the uncertainty associ-ated with the͑null correction for͒truncation bias,check theliterature͑Zhang et al.23͒tofind the available Dunham con-stants Y n0.In this case,Y40=0.0003464cm−1and no higher constants are available.Thus,the appropriate row in Table4 is that for n=4.Values of b j in Table4are approximated as b jϷY j0.The missing constants are estimated by geometric extrapolation with sign alternation as Y i+1,0Ϸ−͉Y i,02/Y i−1,0͉͑Y i,0/͉Y i,0͉͒,so Y50Ϸ−2.33ϫ10−6cm−1and Y60Ϸ1.56ϫ10−8cm−1.Then from the third column of Table 4,͑a1−b1͒=0.000225cm−1and from the fourth column of Table4,͑a2−b2͒=−0.000255cm−1.Substituting these val-ues into Eq.͑13͒then gives͑a0−b0͒=6.435ϫ10−5cm−1.Fi-nally the expression in the second column of Table4evalu-ates to͑ZPE app−ZPE͒=0.000107cm−1.Multiplying by1.8 to account for sensitivity to guessed Y i0values,and taking the absolute value,u truncϷ0.000193cm−1.Thefinal,esti-mated,combined standard uncertainty is then=͑u stat2 +u trunc2͒1/2=0.000250cm−1,which is rounded to a single digit in Table5.5.Analyses for Individual MoleculesIn their classic compilation,Huber and Herzberg͑H&H͒did not attempt to estimate the uncertainties associated withthe reported spectroscopic constants.7Instead,they providedthe following guidance.“…we hope that the number of dig-its quoted may serve as a very rough indication of the esti-mated order of magnitude of the error,generally±9units ofthe last decimal place.Where the last digit is given as asubscript,we expect that the uncertainty may considerablyT ABLE4.Truncation bias with respect to sextic diatomic vibrational model͓Eqs.͑9͒–͑13͔͒.The order of thefitting polynomial is n. n ZPE app−ZPE͑a1−b1͒͑a2−b2͒60005͑a0−b0͒−116b4−132b5+6794b648818b6−1213916b64͑a0−b0͒−116b4−48516b5−600516b6−168916b5−1290b64754b5+2206116b63͑a0−b0͒+10516b4+1052b5+892532b622b4+271116b5+17652b6−432b4−150b5−1190916b62͑a0−b0͒−158b3−13516b4−43516b5−247532b6−234b3−24b4−119916b5−210b692b3+292b4+1654b5+177116b6394K.K.IRIKURA J.Phys.Chem.Ref.Data,Vol.36,No.2,2007。
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SRIM –The stopping and range of ions in matter (2010)James F.Ziegler a,*,M.D.Ziegler b ,J.P.Biersack caUnited States Naval Academy,Physics Dept.,Annapolis,MD 21402,USA bUniversity of California at Los Angeles,Los Angeles,CA 90066,USA cBerlin,Germanya r t i c l e i n f o Article history:Available online 26February 2010Keywords:SRIMIon stopping Stopping power Stopping force Ion rangea b s t r a c tSRIM is a software package concerning the S topping and R ange of I ons in M atter.Since its introduction in 1985,major upgrades are made about every six years.Currently,more than 700scientific citations are made to SRIM every year.For SRIM-2010,the following major improvements have been made:(1)About 2800new experimental stopping powers were added to the database,increasing it to over 28,000stop-ping values.(2)Improved corrections were made for the stopping of ions in compounds.(3)New heavy ion stopping calculations have led to significant improvements on SRIM stopping accuracy.(4)A self-con-tained SRIM module has been included to allow SRIM stopping and range values to be controlled and read by other software applications.(5)Individual interatomic potentials have been included for all ion/atom collisions,and these potentials are now included in the SRIM package.A full catalog of stopping power plots can be downloaded at .Over 500plots show the accuracy of the stopping and ranges produced by SRIM along with 27,000experimental data points.References to the citations which reported the experimental data are included.Published by Elsevier B.V.1.IntroductionSRIM is a software package concerning the S topping and R ange of I ons in M atter.It has been continuously upgraded since its intro-duction in 1985[1].A recent textbook ‘‘SRIM –The Stopping and Range of Ions in Matter ”describes in detail the fundamental phys-ics of the software [2].Since this time,corrections have been made based on new experimental data [3].Major changes occur in SRIM about every six years.The last major changes were in 1995and 1998and 2003.In 1995a complete overhaul was made of the stop-ping of relativistic light ions with energies above 1MeV/u.In 1998,special attention was made to the Barkas Effect and the theoretical stopping of Li ions.In 2010,significant changes were made to cor-rect the stopping of ions in compounds.All the figures in this paper are also available on the SRIM website,in considerably more detail.2.SRIM-2010stopping accuracyShown in Table 1are the statistical improvements in SRIM’s stopping power accuracy when compared to experimental data and also compared to SRIM-1998.The right two columns show the percentage of data points within 5%and within 10%of the SRIM calculation.The experimental stopping powers for heavy ions contain far more scatter than for light ions,hence there are larger errors for heavy ions,Be–U.The accuracy of SRIM-2010for individual ions or targets can be reviewed by viewing plots which compare experimental values and the equivalent SRIM calculations.Fig.1shows a typical com-parison for a light ion,He,in Ag.Fig.2shows a similar plot for all heavy ions,Be(4)–U(92)in Ag.Here,the various ion stopping powers have been normalized to the stopping of Al ions in Al,(nor-malization means that for any ion,the relative error of its experi-mental value to that calculated by SRIM is plotted with a similar displacement from the stopping of Al ions in Ag).Note that the scatter of data points is much higher than for the case of He ions in Ag,which increases the perceived error of SRIM.Higher resolu-tion figures for each heavy ion and all elemental targets are avail-able at .3.Stopping of ions in compoundsBragg and Kleeman,in 1903,conducted stopping experiments with a radium source in organic gases such as methyl bromide and methyl iodide to find how alpha stopping depended on the atomic weight of the target.They also calculated the stopping contribution of hydrogen and carbon atoms in hydrocarbon target gases by assuming a linear addition based on the chemical composition of H and C atoms in the targets.The concept that the stopping power of a compound may be estimated by the linear combination of the stopping powers of its individual elements has come to be known as Bragg’s Rule [4].This rule is reasonably accurate,and the measured stopping of ions in compounds usually deviates less than 20%from that0168-583X/$-see front matter Published by Elsevier B.V.doi:10.1016/j.nimb.2010.02.091*Corresponding author.E-mail address:Ziegler@ (J.F.Ziegler).Nuclear Instruments and Methods in Physics Research B 268(2010)1818–1823Contents lists available at ScienceDirectNuclear Instruments and Methods in Physics Research Bjournal homepage:www.els ev i e r.c o m /l o c a t e /n i mbpredicted by Bragg’s rule.The accuracy of Bragg’s rule is limited be-cause the energy loss to the electrons in any material depends on the detailed orbital and excitation structure of the matter,and any differences between bonding in elemental materials and in compounds will cause Bragg’s rule to become inaccurate.Further,bonding changes may also alter the charge state of the transitionTable 1Accuracy of SRIM stopping calculations.Approx.data pts.SRIM-1998(%)SRIM-2010(%)SRIM-2010(within 5%)SRIM-2010(within 10%)H ions 9000 4.5 3.968%85%He ions 6800 4.6 3.570%87%Li ions 1700 6.4 4.668%81%Be–U Ions10,6008.1 5.655%78%Overall accuracy28,1006.14.364%85%Notes to Table 1:The above table compares all 28,000data points to SRIM calculations.If wacko points are omitted (those differing from SRIM by more than 25%)then most of the above heavy ion accuracy numbers would be reduced by about 25%.The overall accuracy of SRIM-2010then reduces to 3.9%instead of 4.3%.Approx.data points :Current total data points used in SRIM plots.SRIM-1998:Comparison of SRIM-1998stopping to experimental data.SRIM-1998was the last major change in SRIM stopping powers.SRIM-2010:Current stopping power calculation.SRIM-2010(within 5%):Percentage of experimental data within 5%of the SRIM values.SRIM-2010(within 10%):Percentage of experimental data within 10%of the SRIMvalues.Fig.1.The stopping of He ions in Ag targets.The plot shows experimental values of He ion stopping in Ag targets.It shows the actual stopping,in units of eV/(1015atoms/cm 2).At the right is a listing of the original data citations.As noted,there is a total of 439data points taken from 44papers,and they vary from SRIM calculations by an average of 3.9%.Also noted is the mean ionization potential used for Al (<I >=488eV)and the Fermi velocity ratio for Ag,V /V F =1.254.The <I >value is only used for high energy stopping (>1MeV/u),while the Fermi velocity is important for lower velocities.A higher resolution plot is available at .Fig.2.The stopping of heavy ions in Ag targets.The plot shows experimental stopping values of heavy ions (atomic numbers 4–92)in Ag targets.The plot is organized similar to that of Fig.1.There are 930experimental data points taken from 131citations,and the mean error of SRIM is 4.5%.Ag targets are easy to make and these targets tend to have small grains without texture and contain few contaminants.So the accuracy of SRIM is better than normal when compared to experimental heavy ion data due to the consistency of the targets.A higher resolution plot is available at .J.F.Ziegler et al./Nuclear Instruments and Methods in Physics Research B 268(2010)1818–18231819ion,thus changing the strength of its interaction with the target medium.Detailed experimental studies of Bragg’s rule started in the 1960’s,and wide discrepancies were found from simple additivity of stopping powers.A classic example is shown in Fig.3for targets containing H and C atoms,which show non-additivity of stopping in simple hydrocarbons[5].In thisfigure,the stopping of He ions in various hydrocarbons was measured for pairs of compounds,and the relative contribution of H and C was extracted for each pair (solving two equations with two unknowns).It was found that the relative stopping contributions of H and C differ by almost 2Âover the range of compounds.Similar work studied more com-plex hydrocarbons but instead of adding H and C bonds,they added extra hydrocarbon molecules.In this study,it was found that by adding identical molecules to hydrocarbon strings, stopping linearity returned[6].Adding new molecules to a target just scaled the stopping by the extra number of atoms.These results showed that atomic bonding had large effects on stopping powers in simple molecular targets,while extra agglomeration of molecules to the target compounds had a small stopping effect.Since these early experiments,theorists have shown that extensive calculations can predict the stopping of light ions (usually protons)in hydrocarbon compounds.Much of this work has been based on a seminal paper by Peter Sigmund that devel-oped methods to account for detailed internal motion within a medium[7].This theory allows for arbitrary electronic configura-tions in the target.Sabin and collaborators used this approach to calculate stopping powers for protons in hydrocarbons with good success[8].Sabin’s calculation follows what is sometimes called the‘‘Köln Core and Bond”(CAB)approach which is discussed in detail below.The Core and Bond(CAB)approach suggested that stopping powers in compounds can be predicted using the superposition of stopping by atomic‘‘cores”and then adding the stopping corre-sponding to the bonding electrons[9].The core stopping would simply follow Bragg’s rule for the atoms of the compound,where we linearly add the stopping from each of the atoms in the com-pounds.The chemical bonds of the compound would then contain the necessary stopping correction.They would be evaluated depending on the simple chemical nature of the compound.For example,for hydrocarbons,carbon in C–C,C@C and C…C struc-tures would have different bonding contributions(C@C indicates a double-bond structure and C…C is a triple bond).SRIM uses this CAB approach to generate corrections between Bragg’s rule and compounds containing the common elements in compounds:H,C,N,O,F,S and Cl.These light atoms have the larg-est bonding effect on stopping powers.Heavier atoms are assumed not to contribute anomalously to stopping because of their bonds (discussed later in Stopping of High Energy Heavy Ions).When you use SRIM,you have the option to use the Compound Dictionary which contains the chemical bonding information for about150 common compounds.The compounds with available corrections are shown with a Star symbol,q,next to the name.When these compounds are selected,SRIM shows the chemical bonding dia-gram and calculates the best stopping correction.The correction is a variation from unity(1.0=no correction).Some corrections are quite big:carbon atoms have almost a4Âchange in stopping power from single bonds to triple bonds.This large change indi-cates the importance of making some sort of correction for the stopping of ions in compounds.The CAB corrections that SRIM uses have been extracted from the stopping of H,He and Li ions in more than100compounds, from162experiments.The details of applying this correction are described in Ref.[10].SRIM correctly predicts the stopping of H and He ions in compounds with an accuracy of better than2%at the peak of their stopping power curve,$125keV/u.An example of a large correction for compound targets is the9% correction necessary for a target of water,H2O,see Fig.4.The stop-ping of He ions in gaseous H2and O2is shown with the lower two dotted lines.The stopping in gaseous water vapor is essentially the Bragg’s Rule sum since its bonding correction is only1%,see the upper dotted line.However,for solid water(ice),the sum of stop-ping in H2O is shown as the upper solid line.With the H2O phase correction,which reduces the stopping by9%at the peak,SRIM shows good agreement between predicted stopping and the data from the ten experimental reports[11].The limitations of the CAB approach should be mentioned.A.The most important limitation might be that of the targetband-gap.Experiments on insulating targets dominate the experimental results that we use.For compounds which are conducting,there might be an error with thecalculatedFig.3.Accuracy of Bragg’s Rule in hydrocarbon compounds.In thisfigure,the stopping of He ions(at500keV)in various hydrocarbons is shown for pairs of compounds,with the relative contributions of stopping in H and C extracted assuming Bragg’s Rule and solving using two unknowns[5].This classic paper shows with clarity the errors associated with Bragg’s Rule.The units of the ordinate and abscissa are reduced stopping units,e[18].It is found that the various determinations of stopping by H and C atoms differ by almost2Âover the range of compounds.The result is a clear indication of the importance of including bonding corrections in stopping powers.(Figure from Ref.[5]). 1820J.F.Ziegler et al./Nuclear Instruments and Methods in Physics Research B268(2010)1818–1823stopping correction being too small.Theoretically,band-gap materials are expected to have lower stopping powers than equivalent conductors because the small energy transfers to target electrons are not available in insulators.It is not clear what the magnitude of this effect is,but about 50papers have discussed the stopping of ions in metals and their oxides,e.g.targets of Fe,Fe 2O 3and Fe 3O 4.These exper-iments evaluated similar materials with and without band-gaps.No significant differences were found that could be attributed to the band-gap.Measurements have also been made of the stopping of H and He ions into ice (solid water)with various dopings of salt (NaCl).No change of energy loss was observed for up to 6orders of magnitude change in resistivity of the ice [11].B.The scaling of ion stopping from H to He to Li ions is assumed to be independent of target material.This assump-tion has been evaluated with 27targets which have been measured for two of the three ions (at the same ion velocity)and 6of these targets have been measured for all three ions (see listings in Ref.[11]).In all cases,the stopping scaled identically within 4%.That is,for H (125keV)and He (500keV)and Li (875keV)the scaling of stopping powers was 1:2.7:4.7for the 27targets (average error was <4%).(For those unfamiliar with stopping theory,the primary parameter for the scaling of stopping powers is the ion velocity,which reduces to scaling in units of keV/a.).C.The light elements of He and Ne are missing from the above list of target bonding atoms.No comparative experiments have been done on the stopping into elemental He in solid/gas phases.However studies of stopping into targets of Ne and Ar have been conducted in both gas and solid form.These papers show no significant difference between the stopping in gas and solid phases.It appears that the Van der Waals forces,which hold noble gases together in frozen form,are too weak to effect the energy loss of ions.Of particular note is the extensive work done in a PhD paper by Besenbacher.[12].D.The light target atoms of Li,Be and B are missing from the list of bonding atoms with corrections.This is a serious defect.The number of papers that have looked at com-pounds which contain significant amounts of these three elements is too limited to allow their evaluation.Target atoms of these three elements are considered by SRIM to have no bonding correction,which is clearly not true.But without experimental data,there is no reliable way to eval-uate the contribution of their bonds in compounds.E.Bragg’s Rule and Heavy Target Elements.We have concen-trated on the analysis of the stopping of ions in compounds made up of light elements.For compounds with heavier atoms,many experiments have shown that deviations from Bragg’s rule disappear.In Table 2are shown representative examples of ion stopping in various compounds containing heavy elements.None show measurable deviations from Bragg’s rule.These and other similar results were reviewed in the 1980s [13,14].4.Stopping of high energy heavy ionsThe stopping powers of high energy (E >1MeV/u)heavy ions (Z >3)have two separate components.First is the charge state of these ions,which is traditionally addressed by using the Brandt–Kitagawa approximation,and then the many high velocity effects are combined into modern Bethe–Bloch theory.The Brandt–Kitagawa (BK)theory [15]is easiest to understand relative to the Bohr theory of the average charge state of heavy ions [16].Bohr suggested the simple picture that the energetic heavy ion would lose any of its electrons whose classical velocity was slower than the ion’s velocity.This concept lasted for more than 30years,with remarkable success.The concept was then improved by the suggestion of BK that one should consider instead the loss of any electrons whose velocity was slower than the relative velocity of the ion to the target medium.This lowered the charge state of heavy ions since the relative velocity of the ion was always lower than its absolute velocity.BK then presented a simple method of calculating this relative velocity based on considering the target to be a perfect Fermi conductor.This significantly improved the calculation of stopping powers [1].Modern approaches to Bethe–Bloch stopping equation have been reviewed in detail in Ref.[17].In Bethe–Bloch,twolargeFig.4.Corrections for stopping in compounds:He ions in water.The effects on stopping of target phase are illustrated in the figure for the stopping of He ions in water (solid and gaseous).Data from 14citations are shown.The special bonding of H–O in water is approximately the same for H–H and O–O bonds,so the stopping in the gaseous H 2O is almost the same as found using Bragg’s Rule.However,a large 9%phase correction must be applied to calculate the stopping of H 2O in solid forms,ice and water (see text).A higher resolution plot is available at .J.F.Ziegler et al./Nuclear Instruments and Methods in Physics Research B 268(2010)1818–18231821components are not well described by pure theoretical consider-ations:(1)the mean ionization energy of the target,commonly symbolized using<I>,and(2)the shell corrections for the target, called C/Z2.The<I>value for a target corrects for the quantized en-ergy levels of the target electrons and also any band-gap and target phase correction.The C/Z2term corrects for the Bethe–Bloch assumption that the ion velocity is much larger than the target electron velocities.This term is usually calculated by detailed accounting of the particle’s interaction with each electronic orbit in various elements.Since both of these terms are only dependent on the target,they are assumed to be the same for heavy ions and lighter ions.An example of SRIM’s stopping accuracy for heavy ions is shown in Fig.5.It shows the ratio of experimental stopping values to SRIM calculation for heavy ions in Al targets.(Al targets seem to be the most reliable target to make,since the data scatter about an aver-age value is the least of that for any solid).The data shown are from 135papers,and represents720data points for ion energies over 1MeV/u.There are several heavy ion data points at about 100MeV/u which show about5%higher experimental values than SRIM values.This is of the order of the estimated nuclear reaction losses,and is always a problem with very high energy ions (>10MeV/u).5.Anomalous heavy Ion stopping valuesSRIM uses several different stopping theories to evaluate the accuracy of experimental stopping powers.Specifically,calcula-tions are made for all ions in individual targets(which eliminates common difficulties with target dependent quantities such as shell corrections and mean ionization potentials,discussed above).Cal-culations are also made of one heavy ion in all solids,which elim-inates some of the difficulties with ion dependent quantities such as the degree of ion stripping.Also,calculations are made from fun-damental theories like the Brandt–Kitagawa theory and LSS theory [18].If the experimental values are within reasonable agreement with this set of theoretical calculations,then the experimental val-ues are weighted with the theoretical values to obtainfinal values. However,at times,significant errors occur in experimental stop-ping values and they deviate so far from theoretical values that they are totally ignored.Table2Bragg’s rule accuracy in heavy compounds.Compound Deviation from Bragg’s rule(%)Compound Deviation from Bragg’s rule(%)Compound Deviation from Bragg’s rule(%)Al2O3<1HfSi2<2Si3N4<2Au–Ag alloys<1NbC<2Ta2O5<1Au–Cu alloys<2NbN<2TiO2<1BaCl2<2Nb2O5<1W2N3<2BaF2<2RhSi<2WO3<2Fe2O3<1SiC<2ZnO<1Fe3O4<1Note:For compounds which contain elements with atomic numbers greater than12,it is possible to combine the CAB approach with Bragg’s rule.The CAB approach can beused for the small atomic number cores and bonds,and these can be combined with the normal stopping contribution of the other components of thecompound.Fig.5.Stopping of high energy heavy ions in aluminum.Thefigure shows the ratio of experimental stopping to SRIM calculation for high energy(>1MeV/u)ions in aluminum.The data shown is from135papers,and represents720data points over1MeV/u.The mean error is2.7%.There are several heavy ion data points at about 100MeV/u which show about5%higher experimental values than SRIM values.This is of the order of estimated nuclear reaction losses,and is always a problem with very high energy ions(>10MeV/u).A higher resolution plot is available at .1822J.F.Ziegler et al./Nuclear Instruments and Methods in Physics Research B268(2010)1818–1823Shown in Fig.6is the stopping of Mg ions in all solids.Note the large number of experimental data points below 100keV/u,which diverge from the SRIM stopping by up to 200%.For Mg ions,SRIM has an average accuracy of about 9%,the worst for any ion.Almost lost by the large number of data points which disagree with SRIM are those from seven citations which showed values almost identi-cal to SRIM.All of the deviant experimental stopping values were deter-mined by a technique called ‘‘Inverted Doppler Shift Attenuation ”,IDSA [19].This technique relies on the knowledge of the life-time of an excited nuclear state and is fraught with potential errors.The technique requires a nuclear reaction to occur in the target,result-ing in an emitted gamma ray.The gamma ray energy may be shifted due to motion of the recoiling particle.A particular source of error occurs if the differential of the particle energy loss with ion velocity changes much while the particle is slowing down.Note that in the energy range of 10–100keV/u,the energy loss is chang-ing rapidly with ion velocity,and this is where the maximum devi-ation occurs between IDSA stopping values and SRIM.As also shown,SRIM agrees well with 7papers which measured stopping using other methods.The advantage of the IDSA technique is that it can be used to determine stopping in difficult targets such as liquids and also to evaluate bonding effects in compounds.However,it is often used without full consideration of its sensitivity to non-linear effects.6.SRIM sub-routine moduleA ‘‘module”has been made so that the stopping and ranges of SRIM may be run as a batch sub-program for other applications [20].This allows the user to use SRIM as a sub-routine of another application that needs stopping powers and ranges.The user cre-ates a control file and executes the file ‘‘SRModule.exe”which will generate an output table similar to those normally made by SRIM.The user can generate the standard file (with stopping and ranges)or can generate a file which contains stopping powers for a specific list of energies.AcknowledgementsThe author is particularly indebted to the many users of SRIM who helped debug the first twenty five years of SRIM,leading to SRIM-2010.Without your significant help and enthusiasm,SRIM would not be the robust and versatile program that it is.References[1]J.F.Ziegler,J.Biersack,U.Littmark,‘‘The Stopping and Range of Ions in Matter”,Pergamon Press,1985.[2]J.F.Ziegler,J.P.Biersack,M.D.Ziegler,SRIM –The Stopping and Range of Ions inMatter”,Ion Implantation Press,2008./content/1524197.[3]See .More than 500plots are included showing more than28,000experimental data points as compared to SRIM calculations.[4]W.H.Bragg,R.Kleeman,Phil.Mag.10(1905)318.[5]A.S.Lodhi,D.Powers,Phys.Rev.A10(1974)2131.[6]D.Powers,Acc.Chem.Res.13(1980)433.[7]P.Sigmund,Phys.Rev.A26(1982)2497.[8]J.R.Sabin,J.Oddershede,Nucl.Instrum.Methods B27(1987)280.[9]G.Both,R.Krotz,K.Lohman,W.Neuwirth,Phys.Rev.A28(1983)3212.[10]The most recent core and bond values used in SRIM are shown at: n SRIM n CompoundsCABTheory.htm .The modeling technique used to extract these values was originally described in:J.F.Ziegler,J.M.Manoyan,Nucl.Instrum.Methods,B35(1988)215.[11]The data plotted in Fig.4are from papers listed at: n SRIM n Compounds.htm .This website also describes in detail how corrections are made for target phase changes (solid or gas phases)and for target compound binding.Also,citations are listed for compounds containing heavy atoms,and also the effects of variations of the target band-gap on stopping powers.[12]F.Besenbacher,J.Bottiger,O.Graversen,J.Hanse,H.Sorensen,Nucl.Instrum.Methods 188(1981)657–667.[13]D.I.Thwaites,Nucl.Instrum.Methods B12(1985)84.[14]D.I.Thwaites,Nucl.Instrum.Methods B27(1987)293.[15]W.Brandt,M.Kitagawa,Phys.Rev.25B (1982)5631.[16]N.Bohr,Mat.-Fys.Medd.K.Dan.Selse 18(1948)1.[17]J.F.Ziegler,Applied physics reviews,J.Appl.Phys.85(1999)1249–1272.[18]J.Lindhard,M.Scharff,H.E.Schiott,Kgl.Danske Vid.Sels.Mat.-Fys.Medd.33(1963)1.[19]P.Petkova, A.Dewaldb,P.von Brentano,‘‘A new procedure for lifetimedetermination using the Doppler-shift attenuation method”,Nucl.Instrum.Methods A-560(2006)564–570.[20]Details of using the Stopping and Range module are included in the SRIM-2010package.See the SRIM directory,.../SR Module/HELP SRModule.rtf.Fig.6.The stopping of Mg ions in all solids.The plot shows experimental stopping values for Mg ions in all solids.This plot shows a considerable number of data points which differ from SRIM calculations,especially for low energy ions (<100keV/u).The variation arises from the use of ‘‘Inverted Doppler Shift Attenuation”,IDSA,as a method to measure stopping powers.This technique is quite complex and relies on the knowledge of the life-time of an excited nuclear state (see text)and is fraught with potential errors.As shown,SRIM calculations are in serious disagreement with the lower energy Mg values of which were determined by IDSA,however it agrees with 7papers which measured stopping at the same energies,using other methods.A higher resolution plot is available at .J.F.Ziegler et al./Nuclear Instruments and Methods in Physics Research B 268(2010)1818–18231823。
第 21 卷 第 12 期2023 年 12 月Vol.21，No.12Dec.，2023太赫兹科学与电子信息学报Journal of Terahertz Science and Electronic Information Technology新型太赫兹光子晶体OAM光纤设计杨婧翾1，李巍2，成利敏1(1.廊坊师范学院电子信息工程学院，河北廊坊065000；2.北华航天工业学院电子与控制工程学院，河北廊坊065000)摘要：太赫兹通信兼具微波通信和光波通信的优势，是解决通信容量紧缺难题的最有效技术手段之一。
针对太赫兹波段吸收损耗严重及抗外在扰动差，难以支持长距传输问题，设计了一种基于环形光子晶体光纤(PCF)结构的新型太赫兹光纤。
以现有常见材料作为光纤基底材质，通过创新光纤结构中空气孔排布方式，抵消材料高吸收损耗，以支持高性能轨道角动量(OAM)模式传输。
选择最优参数，实现6个OAM模式群的高模式质量、低限制损耗和宽带宽的稳定传输。
在0.2~0.9 THz宽波段内，实现模式纯度超过88.9%，限制损耗小于10-7 dB/m。
通过软件仿真实验设计，解决了太赫兹与OAM技术相结合的关键问题，为模分复用(MDM)技术在太赫兹通信系统的应用奠定了理论研究基础。
关键词：轨道角动量；太赫兹通信；光子晶体光纤；模分复用中图分类号：TN914 文献标志码：A doi：10.11805/TKYDA2023089Design of new terahertz photonic crystal fiber forOrbital Angular Momentum modes transmissionYANG Jingxuan1，LI Wei2，CHENG Limin1(1.School of Electrical Information Engineering，Langfang Normal University，Langfang Hebei 065000，China；2.School of Electronic and Control Engineering，North China Institute of Aerospace Engineering，Langfang Hebei 065000，China)AbstractAbstract：：Terahertz communication has the advantages of both microwave communication and optical communication, which is one of the most effective technical means to solve the problem ofcommunication capacity shortage. In order to solve the problems of serious absorption loss and poorexternal disturbance resistance in terahertz band, a new terahertz fiber based on circular PhotonicCrystal Fiber(PCF) structure is designed to support high performance Orbital Angular Momentum(OAM)modes transmission. The existing common materials are used as the fiber base material, and the highabsorption loss of materials is offset by the innovation of hollow porosity arrangement in the fiberstructure. The optimal parameters are selected to realize the stable transmission of six OAM mode groupswith high mode quality, low confinement loss and wide bandwidth. The mode purity is above 88.9% andthe confinement loss is below 10-7 dB/m in the 0.2~0.9 THz band. Through simulation, the key problemof combining terahertz and OAM technology is solved, which lays a theoretical foundation for theapplication of Mode Division Multiplexing(MDM) technology in terahertz communication system.KeywordsKeywords：：Orbital Angular Momentum；terahertz communication；Photonic Crystal Fiber；Mode Division Multiplexing随着信息互联网技术创新的快速发展，人工智能、高清视频、直播等新的应用方式受到了社会各界的广泛关注[1-3]。
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BIOPHYS1382-3256EMPIR SOFTW ENG0885-6125MACH LEARN0149-1423AAPG BULL0273-2289APPL BIOCHEM BIOTECH0379-5721FOOD NUTR BULL1559-128X APPL OPTICS1566-2535INFORM FUSION0142-9418POLYM TEST0043-1648WEAR0022-3115J NUCL MATER1752-1416IET RENEW POWER GEN1042-7147POLYM ADVAN TECHNOL0098-9886INT J CIRC THEOR APP0968-090X TRANSPORT RES C-EMER0018-9316IEEE T BROADCAST0950-7051KNOWL-BASED SYST0016-0032J FRANKLIN I0022-2461J MATER SCI1424-8220SENSORS-BASEL0255-2701CHEM ENG PROCESS1531-1309IEEE MICROW WIREL CO382 383384 385 386387 388389390 391392 393 394395 396397 398399 400 401 402 403 404 405 406407 408IEEE TRANCIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORYAND APPLICATJOUMICROENCAPSULATIONDigesNanomaterials andMODESIMULATION IN MATERIALSSCIENCE ANDENGINEERINGJOURNALMANAGEMENTAd HoEUROPEALIPID SCIENCE ANDMacromolEngineeringCIRPMANUFACTURINGTECHNOLOGYJOURNALSPRAY TECHNOLOGYIEEE TRANDEVICE AND MATERIALSRELIABILITYACM TRANSOFTWARE ENGINEERINGAND METHODOLOGYJOURNSCIENCEAPPLIEDMATERIALS SCIENCE &COMPSTRUCTURESMEXPERIMEINTERNATIOF HUMAN-COMPUTERCurrentJOUMICROSCOPY-OXFORDIEEE TRANINFORMATIONTECHNOLOGY INBIOMEDICINEMETIEEE SIEEE TRANCONTROL SYSTEMSTECHNOLOGYANNUALCONTROLBIOTECHNOMACRORESEARCH3333333333333333333333333330265-2048J MICROENCAPSUL1530-4388IEEE T DEVICE MAT RE1049-331X ACM T SOFTW ENG METH0007-8506CIRP ANN-MANUF TECHN0022-1147J FOOD SCI0947-8396APPL PHYS A-MATER1549-8328IEEE T CIRCUITS-I1059-9630J THERM SPRAY TECHN1996-1944MATERIALS1842-3582DIG J NANOMATER BIOS1063-8016J DATABASE MANAGE1570-8705AD HOC NETW0740-7459IEEE SOFTWARE0965-0393MODEL SIMUL MATER SC1438-7697EUR J LIPID SCI TECH1862-832X MACROMOL REACT ENG0045-7949COMPUT STRUCT1063-6536IEEE T CONTR SYST T1367-5788ANNU REV CONTROL0141-5492BIOTECHNOL LETT1089-7771IEEE T INF TECHNOL B0026-1394METROLOGIA1071-5819INT J HUM-COMPUT ST1573-4137CURR NANOSCI0022-2720J MICROSC-OXFORD1598-5032MACROMOL RES0723-4864EXP FLUIDS409410 411412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430431432433 434 435 436TRIBOLOJOURNALINTELLIGENCE RESEARCHTRIINTERNATIONALMJournal of thof Chemical EngineersDATA & KENGINEERINGDRYING TCOMPUTFORUMMACROTHEORY AND SIMULATIONSCONTROLPRACTICENanoscaleThermophysical EngineeringMETALLUMATERIALSTRANSACTIONS A-PHYSICAL METALLURGYAND MATERIALAUTONOMAND MULTI-AGENTWINDINTERNATIOF REFRACTORY METALS& HARD MATERIALSIEEE TraComputational Intelligence andBIOLOGICAIEEE TransSpeech and LanguageJOURNAELECTROCHEMISTRYIEEE CGRAPHICS ANDJOURNAL OREASONINGCERAMICSLETTERMICROBIOLOGYIEEE TRANVEHICULAR TECHNOLOGYAPPLIED SIEEE TRANULTRASONICSFERROELECTRICS ANDFREQUENCY CONTROLINTERNATIOF ROBUST ANDNONLINEAR CONTROLINTERNATIOF FATIGUE33333333333333333333333333330737-3937DRY TECHNOL0167-7055COMPUT GRAPH FORUM1076-9757J ARTIF INTELL RES0301-679X TRIBOL INT1556-7265NANOSC MICROSC THERM1073-5623METALL MATER TRANS A1022-1344MACROMOL THEOR SIMUL0968-4328MICRON1387-2532AUTON AGENT MULTI-AG1095-4244WIND ENERGY1023-8883TRIBOL LETT0967-0661CONTROL ENG PRACT0018-9545IEEE T VEH 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PHYSICAL REVIEW B84,104112(2011)High-pressure vibrational and optical study of Bi2Te3R.Vilaplana,1,*O.Gomis,1F.J.Manj´o n,2A.Segura,3E.P´e rez-Gonz´a lez,4P.Rodr´ıguez-Hern´a ndez,4A.Mu˜n oz,4 J.Gonz´a lez,5,6V.Mar´ın-Borr´a s,3V.Mu˜n oz-Sanjos´e,3C.Drasar,7and V.Kucek71Centro de Tecnolog´ıas F´ısicas,MALTA Consolider Team,Universitat Polit`e cnica de Val`e ncia,46022Valencia,Spain 2Instituto de Dise˜n o para la Fabricaci´o n y Producci´o n Automatizada,MALTA Consolider Team,Universitat Polit`e cnica de Val`e ncia,46022Valencia,Spain3Instituto de Ciencia de Materiales de la Universidad de Valencia—MALTA Consolider Team—Departamento de F´ısica Aplicada,Universitatde Val`e ncia,46100Burjassot,Valencia,Spain4MALTA Consolider Team—Departamento de F´ısica Fundamental II and Instituto Universitario de Materiales y Nanotecnolog´ıa,Universidad de La Laguna,La Laguna,Tenerife,Spain5DCITIMAC,MALTA Consolider Team,Universidad de Cantabria,Avda.de Los Castros s/n,39005Santander,Spain6Centro de Estudios de Semiconductores,Universidad de los Andes,M´e rida5201,Venezuela7Faculty of Chemical Technology,University of Pardubice,Studentsk´a95,53210-Pardubice,Czech Republic(Received8June2011;revised manuscript received25July2011;published9September2011)We report an experimental and theoretical lattice dynamics study of bismuth telluride(Bi2Te3)up to23GPa together with an experimental and theoretical study of the optical absorption and reflection up to10GPa.The indirect bandgap of the low-pressure rhombohedral(R-3m)phase(α-Bi2Te3)was observed to decrease withpressure at a rate of−6meV/GPa.In regard to lattice dynamics,Raman-active modes ofα-Bi2Te3were observedup to7.4GPa.The pressure dependence of their frequency and width provides evidence of the presence of anelectronic-topological transition around4.0GPa.Above7.4GPa a phase transition is detected to the C2/mstructure.On further increasing pressure two additional phase transitions,attributed to the C2/c and disorderedbcc(Im-3m)phases,have been observed near15.5and21.6GPa in good agreement with the structures recentlyobserved by means of x-ray diffraction at high pressures in Bi2Te3.After release of pressure the sample reverts backto the original rhombohedral phase after considerable hysteresis.Raman-and IR-mode symmetries,frequencies,and pressure coefficients in the different phases are reported and discussed.DOI:10.1103/PhysRevB.84.104112PACS number(s):61.50.Ks,62.50.−p,78.20.Ci,78.30.−jI.INTRODUCTIONBismuth telluride(Bi2Te3)is a layered chalcogenide with a tremendous impact for thermoelectric applications.1The thermoelectric properties of Bi2Te3and their alloys have been extensively studied due to their promising operation in the temperature range of300–400K.In fact Bi2Te3is the material with the best thermoelectric performance at ambient temperature.2,3Recently,it has been shown that Bi2Te3can be exfoliated like graphene and that a single layer exhibits high electrical conductivity and low thermal conductivity so that a new nanostructure route can be envisaged to improve dramatically the thermoelectrical properties of this compound by means of either charge-carrier confinement or acoustic-phonon confinement.4,5Bi2Te3is a narrow bandgap semiconductor with tetradymite crystal structure[R-3m,space group(S.G.)166,Z=3].6 This rhombohedral-layered structure is formed by layers, which containfive hexagonal close-packed atomic sublayers (Te-Bi-Te-Bi-Te)and is named a quintuple linked by van der Waals forces.The same layered structure is common to other narrow bandgap semiconductor chalcogenides,like Bi2Se3and Sb2Te3,and has been found in As2Te3at high pressures.7 Bi2Te3,as well as Bi2Se3and Sb2Te3,has been recently predicted to behave as a topological insulator8;i.e.,a new class of materials that behave as insulators in the bulk but conduct electrical current in the surface.The topological insulators are characterized by the presence of a strong spin-orbit(SO) coupling that leads to the opening of a narrow bandgap and causes certain topological invariants in the bulk to differ from their values in vacuum.The sudden change of invariants at the interface results in metallic,time-reversal invariant-surface states whose properties are useful for applications in spintronics and quantum computation.9,10Therefore,in recent years a number of papers have been devoted to the search of the 3D-topological insulators among Sb2Te3,Bi2Te3,and Bi2Se3, and different works observed the features of the topological nature of the band structure in the three compounds.11–13 High-pressure studies are very useful to understand mate-rials properties and design new materials because the increase in pressure allows us to reduce the interatomic distances and tofinely tune the materials properties.It has been verified that the thermoelectric properties of semiconductor chalcogenides improve with increasing pressure,and that the study of the properties of these materials could help in the design of better thermoelectric materials by substituting external pressure by chemical pressure.14–18Therefore,the electrical and thermoelectric properties of Sb2Te3,Bi2Te3,and Bi2Se3, as well as their electronic-band structure,have been studied at high pressures.19–27In fact a decrease of the bandgap energy with increasing pressure was found in Bi2Te3.19,20 Furthermore,recent high-pressure studies in these compounds have shown a pressure-induced superconductivity28,29that has further stimulated high-pressure studies.30However,the pressure dependence of many properties of these layered chalcogenides is still not known.In particular the determi-nation of the crystalline structures of these materials at high pressures has been a long puzzle15,23,31,32and the space groups of the high-pressure phases of Bi2Te3have been elucidatedR.VILAPLANA et al.PHYSICAL REVIEW B84,104112(2011)only recently by powder x-ray diffraction measurements at synchrotron-radiation sources33,34specially with the use of particle-swarm optimization algorithms for crystal-structure prediction.34Recent high-pressure powder x-ray diffraction measure-ments have evidenced a pressure-induced electronic topolog-ical transition(ETT)in Bi2Te3around3.2GPa as a changein compressibility.29,31,32,35,36An ETT or Lifshitz transitionoccurs when an extreme of the electronic-band structure,whichis associated to a Van Hove singularity in the density of states,crosses the Fermi-energy level.37This crossing,which canbe driven by pressure,temperature,doping,etc.,results in achange in the topology of the Fermi surface that changes theelectronic density of states near the Fermi energy.An ETTis a2.5transition in the Ehrenfest description of the phasetransitions so no discontinuity of the volume(first derivativeof the Gibbs free energy)but a change in the compressibility(second derivative of the Gibbs free energy)is expected inthe vicinity of the ETT.Anomalies in the phonon spectrumare also expected for materials undergoing an ETT38,39andhave been observed in a number of materials40,41as well as inSb1.5Bi0.5Te3.31The lattice dynamics of Bi2Te3have been studied ex-perimentally at room pressure42–44and a recent study sug-gests that Raman spectroscopy can be used to monitorthe number of single quintuple layers in nanostructuredBi2Te3,as in graphene.45Theoretical studies of the lat-tice dynamics of Bi2Te3at room pressure have also beenperformed;46–49however,Raman measurements at high pres-sures have only been reported up to0.5GPa,50and to ourknowledge there is no theoretical study of the lattice dynamicsproperties of Bi2Te3under high pressure.As a part of oursystematic study of the structural stability and the vibrationalproperties of the semiconductor chalcogenide family,wereport in this work room-temperature Raman-scattering mea-surements in Bi2Te3up to23GPa together with total-energyand lattice-dynamical ab initio calculations at different pres-sures.We discuss the recent observation of a pressure-inducedETT in the rhombohedral phase ofα-Bi2Te3and study whetherthe Raman-scattering signal of the Bi2Te3at pressures above7.4GPa match with the proposed high-pressure phases recentlyreported for this compound33,34and which have also beenfound in Sb2Te3at high pressures.51II.EXPERIMENTAL DETAILSWe have used single crystals of p-type Bi2Te3that weregrown using a modified Bridgman technique.A polycrystallineingot was synthesized by the reaction of stoichiometricquantities of the constituting elements(5N).Afterward,thepolycrystalline material was annealed and submitted to thegrowth process in a vertical Bridgman furnace.Preliminaryroom-temperature measurements on single crystalline samples(15mm×4mm×0.3mm)yield in-plane electrical resistivityρ⊥c=1.7·10−5 m and Hall coefficient R H(B c)= g0.52cm3C−1.Following the calculation presented in Ref.52,the latter gives hole concentration of7.2·1018cm−3andminority electron concentration of2.1·1017cm−3.A smallflake of the single crystal(100μm×100μm×5μm)was inserted in a membrane-type diamond anvil cell(DAC)with a4:1methanol-ethanol mixture as pressure-transmitting medium,which ensures hydrostatic con-ditions up to10GPa and quasihydrostatic conditions between 10and23GPa.53,54Pressure was determined by the ruby luminescence method.55Unpolarized room-temperature Raman-scattering measure-ments at high pressures were performed in backscattering geometry using two setups:(i)A Horiba Jobin Yvon LabRAM HR microspectrometer equipped with a TE-cooled multichan-nel CCD detector and a spectral resolution below2cm−1. HeNe laser(6328˚A line)was used for excitation.(ii)A Horiba Jobin Yvon T64000triple-axis spectrometer with resolution of1cm−1.In this case an Ar+laser(6470˚A line)was used for excitation.In order not to burn the sample,power levels below2mW were used inside the DAC.This power is higher than that used in Raman measurements at room pressure due to superior cooling of the sample in direct contact with the pressure-transmitting media and the diamonds.Optical transmission and reflection measurements under pressure were performed by putting the DAC in a home-built Fourier Transform infrared(FTIR)setup operating in the mid-IR region(400–4000cm−1).The pressure-transmitting medium was KBr.The setup consists of a commercial TEO-400FTIR interferometer by ScienceTech S.L.,which includes a Globar thermal-infrared source and a Michelson interferome-ter,and a liquid-nitrogen cooled Mercury-Cadmium-Telluride (MCT)detector with wavelength cutoff at25μm(400cm−1) from IR Associates Inc.A gold-coated parabolic mirror focuses the collimated IR beam onto a calibrated iris of1 to3mm diameter.A gold-coated X15Cassegrain microscope objective focuses the IR beam inside the DAC to a size of70–200μm.A second Cassegrain microscope objective collects the transmitted IR beam and sends it to the detector after being focused by another parabolic mirror.In the reflection configuration,aflat gold mirror is placed at45◦before the focusing Cassegrain objective,blocking half of the IR beam. The half-beam let into the DAC is reflected by the sample, then by theflat gold mirror,andfinally focused on the MCT detector by another parabolic mirror.III.AB INITIO CALCULATIONSTwo recent works have reported the structures of the high-pressure phases of Bi2Te3up to52GPa.33,34The rhombohedral(R-3m)structure(α-Bi2Te3)is suggested to transform to the C2/m(β-Bi2Te3,S.G.12,Z=4)and the C2/c (γ-Bi2Te3,S.G.15,Z=4)structures above8.2and13.4GPa, respectively.34Furthermore,a fourth phase(δ-Bi2Te3)has been found above14.5GPa and assigned to a disordered bcc structure(Im-3m,S.G.229,Z=1).33,34In order to explore the relative stability of these phases in Bi2Te3we have performed ab initio total-energy calculations within the density functional theory(DFT)56using the plane-wave method and the pseudopotential theory with the Vienna ab initio simulation package(V ASP)57We have used the projector-augmented wave scheme(PAW)58implemented in this package.Ba-sis set,including plane waves up to an energy cutoff of 320eV,were used in order to achieve highly converged results and accurate descriptions of the electronic properties. We have used the generalized gradient approximation(GGA)HIGH-PRESSURE VIBRATIONAL AND OPTICAL STUDY...PHYSICAL REVIEW B84,104112(2011)for the description of the exchange-correlation energy with the PBEsol59exchange-correlation prescription.Dense special k-points sampling for the Brillouin zone(BZ)integration were performed in order to obtain very well-converged energies and forces.At each selected volume,the structures were fully relaxed to their equilibrium configuration through the calculation of the forces on atoms and the stress tensor.In the relaxed equilibrium configuration,the forces on the atoms are less than0.002eV/˚A and the deviation of the stress tensor from a diagonal hydrostatic form is less than1kbar(0.1GPa). Since the calculation of the disordered bcc phase was not possible to do,we have attempted to perform calculations for the bcc-like monoclinic C2/m structure proposed in Ref.34. The application of DFT-based total-energy calculations to the study of semiconductors properties under high pressure has been reviewed in Ref.60,showing that the phase stability, electronic and dynamical properties of compounds under pressure are well describe by DFT.Furthermore,since the calculation of the disordered bcc phase is not possible to do with the V ASP code,we have attempted to perform calculations for the bcc-like mono-clinic C2/m structure proposed in Ref.34.Also,because the thermodynamic-phase transition between two structures occurs when the Gibbs free energy(G)is the same for both phases,we have obtained the Gibbs free energy of the different phases using a quasiharmonic Debye model61that allows obtaining G at room temperature from calculations performed for T=0K in order to discuss the relative stability of the different phases proposed in the present work.In order to fully confirm whether the experimentally mea-sured Raman scattering of the high-pressure phases of Bi2Te3 agree with theoretical estimates for these phases,we have also performed lattice-dynamics calculations of the phonon modes in the R-3m,C2/m,and C2/c phases at the zone center ( point)of the BZ.Our theoretical results enable us to assign the Raman modes observed for the different phases of Bi2Te3. Furthermore,the calculations also provide information about the symmetry of the modes and polarization vectors,which is not readily accessible in the present experiment.Highly converged results on forces are required for the calculation of the dynamical matrix.We use the direct-force constant approach(or supercell method).62Highly converged results on forces are required for the calculation of the dynamical matrix. The construction of the dynamical matrix at the point of the BZ is particularly simple and involves separate calculations of the forces in which afixed displacement from the equilibrium configuration of the atoms within the primitive unit cell is considered.Symmetry aids by reducing the number of such independent displacements,reducing the computational effort in the study of the analyzed structures considered in this work.Diagonalization of the dynamical matrix provides both the frequencies of the normal modes and their polarization vectors.It allows to us to identify the irreducible representation and the character of the phonon’s modes at the point.In this work we provide and discuss the calculated frequencies and pressure coefficients of the Raman-active modes for the three calculated phases of Bi2Te3.The theoretical results obtained for infrared-active modes for the three calculated phases of Bi2Te3are given as supplementary material of this article.63Finally,we want to mention that we have also checked the effect of the SO coupling in the structural stability and the phonon frequencies of the different phases.We have found that the effect of the SO coupling is very small and did not affect our present results(small differences of1–3cm−1in the phonon frequencies at the point)but increased substantially the computer time so that the cost of the computation was very high for the more complex monoclinic high-pressure phases, as already discussed in Ref.34.Therefore,all the theoretical values corresponding to lattice-dynamics calculations in the present paper do not include the SO coupling.In order to test our calculations,we show in Table I the calculated lattice parameters in the different phases of Bi2Te3at different pressures.For the sake of comparison we show in Table I other theoretical calculations and experimental results available.As far as the R-3m phase is concerned,our calculated lattice parameters are in relatively good agreement with experimental values from Refs.6and36.Our calculations with GGA-PBEsol give values which are intermediate between those calculated with GGA-PBE and local density approximation (LDA),as it is generally known.Additionally,we give the calculated lattice parameters of Bi2Te3in the monoclinic C2/m and C2/c structures at7.7and15.5GPa,respectively,for comparison with experimental data.Note that in Table I the a and b lattice parameters of the C2/m and C2/c structures at7.7and15.5GPa are very similar to those reported by Zhu et al.;34however,the c lattice parameter andβangle for monoclinic C2/m and C2/c structures differ from those obtained by Zhu et al.34The reason is the results of our ab initio calculations are given in the standard setting for the monoclinic structures,in contrast with Ref.34,for a better comparison to future experiments since many experimentalists use the standard setting.IV.RESULTS AND DISCUSSIONA.Optical absorption ofα-Bi2Te3under pressureIt is known thatα-Bi2Te3has an indirect forbidden bandgap, E gap,between130and170meV.19,64–66Figure1shows the optical transmittance of ourα-Bi2Te3sample in the mid-IR region at room pressure outside the DAC.The spectrum near the fundamental absorption edge is dominated by large interferences.The large amplitude of the interference fringe pattern in the transparent region is a result of the high value of the refractive index,that is larger than9.42,65,66The sample transmittance and the interference-fringe amplitude decreases at low-photon energy due to the onset of free-carrier absorption and to high energies due to the fundamental absorption edge caused by band-to-band absorption.The absorption coefficient can be accurately determined from the transmittance spectrum only in a small photon energy range between the end of the interference pattern and the photon energy at which the transmitted intensity merges into noise.In this interval the absorption coefficient exhibits an exponential dependence on the photon energy.This prevents a detailed analysis of the absorption edge shape.Consequently,the optical bandgap has been determined byfitting a calculated transmittance to the experimental one.We calculate the transmittance by assumingR.VILAPLANA et al.PHYSICAL REVIEW B 84,104112(2011)TABLE I.Calculated (th.)and experimental (exp.)lattice parameters,bulk modulus (B 0),and its derivative (B 0 )of Bi 2Te 3in the R -3m structure at ambient pressure and calculated lattice parameters of Bi 2Te 3in the C 2/m and C 2/c structures at 8.4and 15.5GPa,respectively.a(˚A)b(˚A)c(˚A)β(∞)B 0(GPa)B 0 Ref.α-Bi 2Te 3(0GPa)th.(GGA-PBEsol)4.38029.98241.924.89This work th.(GGA-PBESol)a 4.37530.16741.614.68This workth.(GGA-PBE)4.4531.6349th.(GGA-PBE)a 4.4731.1249th.(LDA)a 4.3630.3847exp.4.38530.4976exp.4.38330.38032.5b 10.1b 3640.9c3.2c β-Bi 2Te 3(8.4GPa)th.(GGA-PBESol)14.8834.0669.12189.7341.254.06This workth.(GGA-PBE)d 14.8654.05617.468148.3934exp.d14.6454.09617.251148.4834γ-Bi 2Te 3(15.5GPa)th.(GGA-PBESol)9.8956.9627.70970.3045.283.57This workth.(GGA-PBE)e 9.9567.14610.415134.8634exp.e10.2336.95510.503136.034a Calculations including the SO coupling.bAt room pressure.cAbove 3.2GPa.dAround 12-12.6GPa.eAround 14-14.4GPa.an absorption coefficient with two termsα(E )=A E 2+Be−E gap −E (1)where the first one corresponds to the free-carrier contribution and the second one corresponds to the Urbach tail of the fundamental absorption edge.Equation (1)was used to fit the calculated transmittance spectra to the experimental ones.The dotted line in Fig.1was calculated with Equation (1)by using only A and E gap as fitting parameters,where E gap =159meV at roompressure.FIG.1.(Color online)Experimental transmittance of a 7-μm-thick α-Bi 2Te 3sample at room pressure outside the DAC (solid line).Dotted line indicates the fit of the experimental spectrum.Figure 2shows the Bi 2Te 3transmittance spectrum for several pressures up to 5.5GPa.Above that pressure the signal-to-noise ratio is too low to determine the optical bandgap energy.Figure 3shows the pressure dependence of the optical bandgap of Bi 2Te 3,as determined from the previously described procedure.The pressure coefficient turns out to be −6.4±0.6meV /GPa.This pressure coefficient of the optical bandgap is close to the value we obtained for the pressure dependence of the indirect bandgap from ab initio calculations (−10meV /GPa).From this result it appears that,even if the sample becomes opaque at 5.5GPa,Bi 2Te 3still has a finite bandgap of some 120meV.FIG.2.(Color online)Experimental transmittance of α-Bi 2Te 3at different pressures up to 5.5.GPa.A shift of the absorption edge to low energies is observed with increasing pressure.HIGH-PRESSURE VIBRATIONAL AND OPTICAL STUDY...PHYSICAL REVIEW B84,104112(2011)FIG.3.(Color online)Pressure dependence of the optical bandgap ofα-Bi2Te3according to reflectance(red squares)and to transmittance(black circles)measurements.Sample opacity above5.5GPa seems to be then a result of the free-carrier absorption tail shifting to higher energies as the carrier concentration increases.Consequently,the sample opacity is likely caused by the overlap of the free-carrier absorption tail with the fundamental-absorption tail rather than a real closure of the bandgap.We have to note that our pressure coefficient of the optical bandgap is somewhat smaller in module than the pressure coefficient previously reported for the indirect bandgap:−22meV/GPa19;−12meV/GPa below3GPa;and−60meV/GPa above3GPa.20We have to consider that the estimation of these pressure coefficients in Refs.19and20were indirectly obtained from the pressure dependence of the electrical conductivity and those estimations suffer considerable errors since they assume that the change in resistivity is only due to the change of the indirect bandgap energy,which is not a well-founded assumption in extrinsic degenerate semiconductors.In order to confirm our results on optical absorption we have performed high-pressure reflectance measurements in a3-μm-thick sample whose results are shown in Fig.4.The reflectance spectrum also exhibits a large interference fringe pattern in the transparency region,with amplitude decreasing to lowand high photon energies.The reflectance spectrum at6GPaFIG.4.(Color online)Experimental reflectance ofα-Bi2Te3at different pressures.shows that the sample exhibits a clear onset of the fundamental absorption edge at around120meV and also that the free-carrier absorption edge,even if it has shifted to higher energies, has not overlapped the fundamental absorption.Therefore our reflectance measurements allow us to confirm the results obtained from absorption measurements.Furthermore,the bandgap pressure coefficient,as determined from the shift of the photon energy at which interferences disappear,agrees with the one determined from the transmission spectra.At 7GPa,a clear change in the reflectance occurs,with a large increase of the reflectance by80%in the low-energy range.A large reflectance minimum(not shown here)appears at some 4000cm−1(500meV),suggesting a phase transition to a metallic phase.The metallic nature of the high-pressure phases is in good agreement with previously reported resistivity measurements.17,21,28–30If the reflectance minimum is taken as an estimation of the plasma frequency of the high-pressure phase above7GPa,the carrier concentration would be larger than1021cm−3(assuming the same dielectric constant as in the rhombohedral phase).If the dielectric constant inβphase is much smaller,the carrier concentration should be close to1022cm−3,which is more consistent with the observed superconducting behavior.28–30The shift of the free-carrier absorption tail follows the in-crease of the free-carrier plasma frequency.Then the pressure dependence of the plasma frequency can be estimated from the shift of the photon energy at which the free-carrier absorption tail quenches the interference fringe pattern.Reflectance measurements outside the cell show that the plasma frequency at ambient pressure is below50meV,consistently with the hole concentration that is of the order of7·1018cm−3,as measured by Hall effect.At4.3GPa interference fringes are observed down to some60meV(560cm−1).This upper limit to the plasma frequency would correspond to hole concentration of lower than1019cm−3,typical of a degenerate semiconductor.This increase in the hole concentration should result in a Burstein-Moss positive contribution to the optical bandgap, which explains the discrepancy between the experimental and theoretical value of the bandgap pressure coefficient.The bandgap around5GPa is in fact smaller than the measured optical gap.Given the band structure of Bi2Te3,67with six equivalent minima in the valence band,the density of states is very large and the hole concentration per minimum would be only of some1.5×1018cm−3,which would lead to a Burstein-Moss shift of some50meV for a hole effective mass of0.09m0.68Then even taking into account the Burstein-Moss shift,Bi2Te3at5GPa would still be a low-gap semiconductor. In fact this estimation of the Burstein-Moss shift is based on the ambient-pressure electronic structure.At pressures above the ETT transition the density of states in the valence-band maximum is expected to be much larger as the ellipsoids merge into a thoroidal ring,as proposed by Istkevitch et al.69 Consequently,the Burstein-Moss shift above the ETT should be much lower than50meV.Finally,we must note that our analysis of the optical absorption edge in Bi2Te3have not allowed us to detect any change in the pressure dependence of the indirect bandgap around3GPa to confirm the presence of an ETT as observed in other works.20,29,31,32,35,36The very small change in the pressure coefficient of the indirect bandgap seems not toR.VILAPLANA et al.PHYSICAL REVIEW B 84,104112(2011)FIG.5.Experimental Raman spectra of α-Bi 2Te 3at pressures between room pressure and 7.4GPa.be affected by the ETT since there is no change in volume but in volume compressibility,and the change is very subtle to be measured in our transmission or reflection spectra in comparison with the drastic effects observed in transport measurements or even in the parameters of the Raman modes (as will be discussed in the next section).B.Raman scattering of α-Bi 2Te 3under pressureThe rhombohedral structure of α-Bi 2Te 3is a centrosym-metric structure that has a primitive cell with one Te atom located in a 3a Wyckoff position and the remaining Bi(2)and Te(2)atoms occupying 6c Wyckoff sites.Therefore,group theory allows 10zone-center modes,which decompose in the irreducible representations as follows 70:10=2A 1g +3A 2u +2E g +3E u .(2)The two acoustic branches come from one A 2u and a doubly degenerated E u mode,while the rest correspond to optic modes.Gerade (g)modes are Raman active while ungerade (u)modes are infrared (IR)active.Therefore,there are four Raman-active modes (2A 1g +2E g )and four IR-active modes (2A 2u +2E u ).The E g modes correspond to atomic vibrations in the plane of the layers,while the A 1g modes correspond to vibrations along the c axis perpendicular to the layers.42–44,50Figure 5shows the experimental Raman spectra of α-Bi 2Te 3at different pressures up to 7.4GPa.We have observed and followed under pressure three out of the four Raman-active modes.The E g mode calculated to be close to 40cm −1has not been observed in our experiments as it was also not seen in previous Raman-scattering measurements at room and high pressures.42,50,71–73Figure 6(a)shows the experimental-pressure dependence of the frequencies of the three first-orderRaman modes measured in α-Bi 2Te 3,and Table II summarizes our experimental and theoretical first-order Raman-mode frequencies and pressure coefficients in the rhombohedral phase.Our experimental frequencies at room pressure are in good agreement with those already measured in Ref.42and Ref.50and with those recently measured in Refs.45and 71–73.On the other hand our theoretical frequencies at room pressure are also in good agreement with those reported in Ref.49without SO coupling (see Table II )and are slightly larger than those calculated including SO coupling (see Ref.49).In Fig.6(a)it can be observed that all the measured Raman modes exhibit a hardening with increasing pressure.The experimental values of the pressure coefficients of the Raman-mode frequencies are in a general good agreement with our theoretical calculations and with the values reported in Ref.50up to 0.5GPa;however,a decrease of the pressure coefficient of two modes around 4.0GPa should be noted [see dashed lines in Fig.6(b)].We have attributed the less positive pressure coefficient of these two Raman modes to the pressure-induced ETT observed in Sb 2Te 3and Bi 2Te 3.20,29,31,32,35,36In fact in a previous study in Sb 2Te 3under pressure we have found a change in the pressure coefficient of the frequency of all modes measured.51In order to support our hypothesis we also plot as Fig.6(b)the pressure dependence of the full width at half maximum (FWHM)of the three measured Raman modes.Curiously,it is observed that the FWHM changes its slope around 4GPa thus confirming an anomaly related to the ETT.Therefore,both our results of the pressure dependence of the frequency and linewidth give support to the observation of the ETT around 4.0GPa in α-Bi 2Te 3similarly to the case of α-Sb 2Te 3.51As previously commented,anomalies in the phonon spec-trum are also expected for materials undergoing a ETT and have been observed in Sb 1.5Bi 0.5Te 3.15In the latter work the high-frequency A 1g mode was not altered near the ETT in good agreement with our measurements;however,we have noted a change both in the lower A 1g and the higher-frequency E g modes.Since A 1g modes are polarized in the direction perpendicular to the layers while the E g modes are polarized along the layers,our observation of a less positive pressure coefficient at 4.0GPa of both modes in α-Bi 2Te 3suggests that the ETT in Bi 2Te 3is related to a change of the structural compressibility of both the direction perpendicular to the layers and the direction along the layers.This seems not to be in agreement with Polian et al.’s observations,which suggest that the ETT in Bi 2Te 3only affects the plane of the layers.36Consequently,more work is needed to understand the mechanism of the ETT in this material.To conclude this section regarding the rhombohedral structure of α-Bi 2Te 3,we want to make a comment on the pressure coefficients of the Raman modes of this structure in comparison to those recently measured in α-Sb 2Te 3.51It is known that in chalcogenide laminar materials,the two lowest frequency E and A modes are usually related to shear vibrations between adjacent layers along the a -b plane and to vibrations of one layer against the others along the c axis,respectively.It has been commented that the E mode displays the smallest pressure coefficient due to the weak bending force constant between the interlayer distances (in our case,Te-Te distances)while。
Spin-chargeseparationinthesingle-hole-dopedMottantiferromagnetZ.Y.Weng,1V.N.Muthukumar,2D.N.Sheng,1,3andC.S.Ting11TexasCenterforSuperconductivity,UniversityofHouston,Houston,Texas77204-5506
2JosephHenryLaboratoriesofPhysics,PrincetonUniversity,Princeton,NewJersey08544
3DepartmentofPhysicsandAstronomy,CaliforniaStateUniversity,Northridge,California91330
͑Received23August2000;published16January2001͒
ThemotionofasingleholeinaMottantiferromagnetisinvestigatedbasedonthet-Jmodel.Anexactexpressionoftheenergyspectrumisobtained,inwhichtheirreparablephasestringeffect͓Phys.Rev.Lett.77,5102͑1996͔͒isexplicitlypresent.Byidentifyingthephasestringeffectwithspinbackflow,wepointoutthatspin-chargeseparationmustexistinsuchasystem:thedopedholehastodecayintoaneutralspinonandaspinlessholon,togetherwiththephasestring.Weshowthatwhilethespinonremainscoherent,theholonmotionisdeterredbythephasestring,resultinginitslocalizationinspace.Wecalculatetheelectronspectralfunctionwhichexplainsthelineshapeofthespectralfunctionaswellasthe‘‘quasiparticle’’spectrumobservedinangle-resolvedphotoemissionexperiments.Otheranalyticandnumericalapproachesarediscussedbasedonthepresentframework.
DOI:10.1103/PhysRevB.63.075102PACSnumber͑s͒:71.27.ϩa,74.20.Mn,74.72.Ϫh
I.INTRODUCTIONSincethediscoveryofhigh-Tcsuperconductivity,therehasbeenmuchefforttoelucidatethepropertiesofdopedMottinsulators.Inthiscontext,thespecificcaseofoneholeinaMottinsulatingantiferromagnet͑half-filledband͒hasbeenthesubjectofextensivetheoreticalandexperimentalinvestigation.Thesestudiesaddressthebasicquestionofwhetherthemotionofaholeintheantiferromagnetcanpos-siblybedescribedwithinaquasiparticleapproach.Photo-emissionspectroscopyprovidesvaluableinformationthatcanhelpresolvethisissue.Experimentalresultsfromangle-resolvedphotoemissionspectroscopy͑ARPES͒arenowavailableforSr2CuO2Cl2aswellasforCa2CuO2Cl2.
1–5
BoththesematerialsareMottinsulatorsandareparentcom-poundsofthehigh-Tccuprates.TheresultsfromARPEScan
besummarizedasfollows:͑i͒thespectralfeaturesobservedarenotsharpatall.Quitetothecontrary,anintrinsicbroadfeatureextendingtoenergiesoftheorderof1.5eVbeforemergingintothemainvalencebandisseen.Thisistobecontrastedwithsharpspectralfeaturesthatoneexpectsinaquasiparticlescenario;͑ii͒theobserveddispersionisisotro-picaroundk0ϭ(/2,/2);͑iii͒themeasurementsofRon-
ningetal.3revealthepresenceofaso-calledremnantFermisurfaceofthemomentumstructureintheenergy-integratedspectralfunction.ThebroadspectralfeaturesseeninARPESstronglysug-gestthebreakdownofthequasiparticlepicture.Basedonsuchconsiderations,Laughlin6conjecturedthefailureof
quasiparticletheoryinthesematerials,andfurtherproposedthattheobservedisotropicdispersionhasitsoriginsinanunderlyingspinonspectrum.Thispictureenvisagesspin-chargeseparationwiththescaleoftheobserveddispersiondeterminedbythesuperexchangeJ.Anentirelydifferentpictureispresentedbytheself-consistentBornapproximation͑SCBA͒approach.7–10
Thoughthisschemeisbasedonthet-Jmodel,itdepictsaspin-polaronpictureforthesingleholecasewherethedopedholebehavesnotverydifferentfromaquasiparticleinthe
Landau-Fermiliquidtheory.TheSCBAresultshavealsobeensupportedbyexactnumericalcalculationsonfinitelattices11upto32sites12aswellasvariationalcalculations
onlargerlattices.13Here,theconsistencyamongdifferent
numericalmethodsmostlyconcernsthespectrum⑀k,usuallydefinedastheminimumenergyforagivenmomentumk.Thespectrumisanisotropicaroundthe‘‘Fermipoints’’k0
ϭ(Ϯ/2,Ϯ/2)inallthesecalculations.Itiscalleda‘‘qua-
siparticle’’spectrumsinceasharppeakinthespectralfunc-tionusuallyappearsat⑀kinboththeSCBAaswellasresults
fromexactdiagonalization.NotethattheseresultsarenotconsistentwithARPESwhichexhibitsanisotropicdisper-sionaroundk0,andratherbroadspectralfeatures.Thus,to
accountfortheformer,theinclusionofsecond(tЈ)andthird(tЉ)nearest-neighborhoppingstothet-Jmodelhavebeenproposedintheliterature.2,14–16However,thisapproachis
meaningfulonlywhenthequasiparticledescriptionholds,i.e.,onlyifasharpquasiparticlepeakexistsat⑀kinthet-J
model.AsillustratedinFig.1,ifinthethermodynamiclimit,thespectralfunctionforagivenmomentumkdoesnotshowasharpquasiparticlepeak,then,notwithstandinghowaccu-rately⑀kisdeterminedbyvarioustheoreticalmethods,ithas
noexperimentalimplication.For,inthiscase,thehigherenergy⑀k
Јatthebroad‘‘peak’’inFig.1,whichisobservable
experimentally,mayhavenothingtodowiththeanisotropic⑀k.
Onmoregeneralgrounds,thebreakdownoftheLandau-FermiquasiparticlepicturehasbeendiscussedbyAndersonforadopedMottinsulatorinthepresenceofanupperHub-bardband.17HearguesthatthequasiparticleweightZvan-ishesduetounrenormalizableFermi-surfacephaseshiftsin-ducedwhenaparticleisinjectedintotheMottinsulator.Indeed,basedonarigorousformulationofthesingle-electronGreen’sfunctionintheone-holecaseusingthet-Jmodel,ithasbeendemonstrated18,19thatthequasiparticle
