Charge and Orbital Ordering and Spin State Transition Driven by Structural Distortion in YB

涡旋光束拓扑荷值的干涉测量方法周洋;李新忠;王静鸽;王辉;李贺贺【摘要】基于平面波或球面波与拉盖尔-高斯(Laguerre-Gaussian,LG)涡旋光束的干涉特性,提出了一种LG涡旋光束拓扑荷值的测量方法.利用改进的马赫-曾德尔干涉光路对LG涡旋光束的拓扑荷值进行测量,其中,干涉光路中的一支为平面波或球面波,另一支为LG光束.然后,通过干涉亮条纹中的分叉数(平面波干涉时)或螺旋线嵌套数(球面波干涉时)来确定LG涡旋光束的拓扑荷值.拓扑荷值的符号,通过分叉向上还是向下(平面波干涉时)或螺旋线为顺时针还是逆时针(球面波干涉时)来判断其正负.数值模拟和试验结果表明:该方法能有效测量LG涡旋光束的拓扑荷值和符号,并且具有快速、简洁的特点.【期刊名称】《河南科技大学学报（自然科学版）》【年(卷),期】2016(037)003【总页数】5页(P95-99)【关键词】涡旋光束;拓扑荷值;平面波;球面波;干涉【作者】周洋;李新忠;王静鸽;王辉;李贺贺【作者单位】河南科技大学物理工程学院,河南洛阳471023;河南科技大学物理工程学院,河南洛阳471023;河南科技大学物理工程学院,河南洛阳471023;河南科技大学物理工程学院,河南洛阳471023;河南科技大学物理工程学院,河南洛阳471023【正文语种】中文【中图分类】O436;O438.1涡旋光束是一种具有螺旋形相位波前且中心光强为0的暗中空光束[1]，其表达式中含有exp(imθ)的相位因子，其中，m是涡旋光束的拓扑荷值，每个光子携带mћ的轨道角动量。

近年来，涡旋光束在量子信息编码[2-3]、光学扳手、粒子旋转与操纵[4-5]和图像处理[6-7]等方面获得了广泛的应用。

而在这些应用中，涡旋光束的拓扑荷值是一个关键参数。

因此，如何快速准确地对拓扑荷值进行测量是该领域研究中首要解决的问题。

从目前研究来看，涡旋光束拓扑荷值的测量方法主要分为干涉测量[8-10]和衍射测量[11-12]两种。

a r X i v :c o n d -m a t /0301048v 1 [c o n d -m a t .s t r -e l ] 6 J a n 2003Magnetic,orbital and charge ordering in the electron-doped manganitesTulika Maitra ∗1and A.Taraphder †2∗Max-Planck-Institut f¨u r Physik Komplexer Systeme N¨o thnitzer Str.3801187Dresden,Germany †Department of Physics &Meteorology and Centre for Theoretical Studies,Indian Institute of Technology,Kharagpur 721302India Abstract The three dimensional perovskite manganites R 1−x A x MnO 3in the range of hole-doping x >0.5are studied in detail using a double exchange model with degenerate e g orbitals including intra-and inter-orbital correlations and near-neighbour Coulomb repulsion.We show that such a model captures the observed phase diagram and orbital-ordering in the intermediate to large band-width regime.It is argued that the Jahn-Teller effect,considered to be crucial for the region x <0.5,does not play a major role in this region,particularly for systems with moderate to large band-width.The anisotropic hopping across the degenerate e g orbitals are crucial in understanding the ground state phases of this region,an observation emphasized earlier by Brink and Khomskii.Based on calculations using a realistic limit of finite Hund’s coupling,we show that the inclusion of interactions stabilizes the C-phase,the antiferromagnetic metallic A-phase moves closer to x =0.5while the ferromagnetic phase shrinks in agreement with recent observations.The charge ordering close to x =0.5and the effect of reduction of band-width are also outlined.The effect of disorder and the possibility of inhomogeneous mixture of competing states have been discussed.PACS Nos.75.30.Et,75.47.Lx,75.47.Gk I.Introduction The colossal magnetoresistive manganites have been investigated with renewed vigour inthe recent past mainly because of their technological import.It was soon realized that these systems have a rich variety of unusual electronic and magnetic properties involving almost all the known degrees of freedom in a solid,viz.,the charge,spin,orbital and lattice degrees of freedom[1,2,3].Of particular interest have been the systems R 1−x A x MnO 3,where Rand A stand for trivalent rare-earth(e.g.,La,Nd,Pr,Sm)and divalent alkaline-earth ions (Ca,Sr,Ba,Pb etc.)respectively.Around the region0.17<x<0.4,electrical transport properties of these systems generically show extreme sensitivity towards external magnetic field with a concomitant paramagnetic insulator(or poor metal)to ferromagnetic metal transition at fairly high temperatures[5,6,7].For a long time the dominant paradigm in the theory of this unusual magneticfield-dependence of transport has been the idea of double exchange(DE)[8]involving the localized core spins(the three t2g electrons at each Mn site)coupled to the itinerant electrons in the Jahn-Teller split e g level via strong Hund’s exchange.It has been realized recently that such a simplifying theoretical framework may not be adequate in explaining several other related features involving transport,electronic and magnetic properties[9,10,11,12,13].It was already known that the observed structural distortions and magnetic and orbital orders in these systems in the region x≃0.5require interactions not included in the DE model[14,15,16].Owing to the observation of colossal magnetoresistance(CMR)in the region x<0.5in the relatively narrow band-width materials[6]at high temperatures,much of the attention was centred around this region.Only in the last few years CMR effect has been observed in the larger band-width materials like Nd1−x Sr x MnO3[17,18]and Pr1−x Sr x MnO3[19,20] in the region x>0.5.If one counts the doping from the side x=1in R1−x A x MnO3where all Mn ions are in+4state,then doping by R y(y=1−x)introduces Mn+3ions carrying one electron in the e g orbitals.This region,therefore,is also called the electron-doped region. The charge,magnetic and orbital structures of the manganites in the electron-doped regime have already been found to be quite rich[2,4,21,22,23]and the coupling between all these degrees lead to stimulating physics[24].In the framework of the conventional DE model with one e g orbital,one would expect qualitatively similar physics for x∼0and x∼1[25].On the contrary,experiments reveal a very different and assymetric picture for the phase diagram between the regions x<0.5andx>0.5.The lack of symmetry about x=0.5manifests itself most clearly in the magnetic phase diagram of these manganites.It has now been shown quite distinctly[18,32,27,34] that the systems Nd1−x Sr x MnO3,Pr1−x Sr x MnO3,La1−x Sr x MnO3are antiferromagnetically ordered beyond x=0.5while one observes either a metallic ferromagnetic state[7]ora charge ordered state with staggered charge-ordering[29,30]in the approximate range0.25<x<0.5.This charge ordered insulating state can be transformed into a ferromagnetic metallic state[19,31]by the application of magneticfields.There are several different types of AFM phases with their characteristic dimensionality of spin ordering observed in this 1−x Sr x MnO3shows A-type antiferromagnetic ground state(in which ferromagnetically aligned xy-planes are coupled antiferromagnetically)in the range0.52<x<0.58.It also shows a sliver of FM phase[27]immediately above x=0.5. In Nd1−x Sr x MnO3[34,18],the A-type spin structure appears at x=0.5and is stable upto x=0.62while in Pr1−x Sr x MnO3[19,26],this region extends from x=0.48to x=0.6.In all these cases,the phase that abuts the A-type antiferromagnet(AFM)in the region of higher hole-doping(x)is the C-type AFM state,in which antiferromagnetically aligned planes are coupled ferromagnetically.The C-type AFM phase occupies largest part of the phase diagram in this region.For even larger x,the C-phase gives way to the three dimensional antiferromagnetic G-phase.The systematics of the phase diagram changes considerably(except close to x=1)in these systems as a function of the bandwidth.Recently Kajimoto et al.[28]have quite succinctly summarized the phase diagrams of various manganites of varying bandwidths across the entire range of doping.Their phase diagram is reproduced infig.1.The phase diagram changes considerably with changing bandwidth as shown in thefigure.We note that the narrow bandwidth compounds like Pr1−x Ca x MnO3,La1−x Ca x MnO3etc.exhibit a wide region of CE-type insulating charge-ordered state around x=0.5whereas the inter-mediate bandwidth material Nd1−x Sr x MnO3shows a conducting A-type antiferromagneticphase around x=0.5.As one moves towards the larger bandwidth compounds such as Pr1−x Sr x MnO3,La1−x Sr x MnO3,a small strip of ferromagnetic(F)metallic phase appears at x=0.5[27,28]followed by the A-type AFM state.In contrast with the narrow band-width manganites,the relatively wider bandwidth manganites generally show the following sequence of spin/charge ordering upon hole doping(in the entire range0≤x≤1):insulating A-type AFM→metallic FM→metallic A-type AFM→insulating C-type AFM andfinally insulating G-type AFM states.Clearly,the most important feature here is the absence of CE-type spin/charge ordering and the presence of a metallic A-type AFM state in these wider band-width compounds in the region close to x=0.5.It appears that the physics involved in the CE-type charge/spin ordering,important for the low band-width systems,is not quite as relevant in this case.In addition,it is also observed in the neutron diffraction studies that the metallic A-type AFM state is orbitally ordered[32,34]with predominant occupation of d x2−y2orbitals.The importance of orbital-ordering has been emphasized pre-viously in several other experimental[18,35,39,40]and theoretical[33,41,42,43,44,45,46] investigations.The crucial role of the e g orbitals and inter-orbital Coulomb interaction has been underlined by Takahashi and Shiba[50]from a study of the optical absorption spectra in the ferromagnetic metallic phase of the doped manganite La1−x Sr x MnO3.They point out that it is imperative to consider the transition between nearly degenerate and moder-ately interacting e g orbitals even in the hole-doped region in order to interpret the optical absorption spectra in La1−x Sr x MnO3.In a detailed observation carried out by Akimoto et al.[27]the electronic and magnetic properties of a heavily doped manganite R1−x Sr x MnO3with R=La1−z Nd z are studied by continuously changing the band-width.In this novel procedure they were able to control the band-width chemically by changing the average ionic radius by manipulating the ratio of La and Nd(i.e.,changing z).Substitution of the smaller Nd+3ions for the larger La+3 ions effectively reduces the one-electron band-width.By increasing z chemically,they wereable to go continuously from the large band-width system La1−x Sr x MnO3down to the intermediate band-width system Nd1−x Sr x MnO3.For z<0.5,there is a metallic FM phase in the region0.5<x<0.52.From x≥0.54to about x=0.58the ground state is A-type antiferromagnetic metallic irrespective of the value of z,i.e.from La1−x Sr x MnO3 (z=0)all the way down to Nd1−x Sr x MnO3(z=1).They believe that the key factor that stabilizes the A-type AFM metallic state in a wide range of z is the structure of the two e g orbitals(d x2−y2and d3z2−r2)and the anisotropic hopping integral between them.There is no signature of charge-ordering or CE-type ordering below z=0.5for any x.The charge-ordered(CO)insulating state appears above z=0.5and around x=0.5primarily due to the commensuration(between the lattice periodicity and hole concentration)effect in the low band-width systems.The ground state phase diagram for doped manganites in x−z plane(i.e.,doping versus band-width plane)is shown infig.2after Akimoto et al.[27].The general inferences from all these measurements are that the physics of the electron-doped region is very different from the hole-doped region.In this region,with decreasing band-width starting from La1−x Sr x MnO3down to Nd1−x Sr x MnO3,the F-phase shrinks,the A-phase and C-phase remain nearly unaffected.The A-phase disappears and the C-phase shrinks(with the possible growth of incommesurate charge order region as infig.1)rapidly in the low band-width systems like La1−x Ca x MnO3and Pr1−x Ca x MnO3.The G-phase at the low electron-doping region seems to remain unaffected all through.It has been seen [27,34,35]that the gradual build up of the AFM correlations in the electron-doped region is pre-empted by the orbital ordering in the A-and C-phases.The e g orbitals and the anisotropic hopping of electrons between them[16,63],must indeed play a significant role given the presence of orbital ordering in much of the phase diagram beyond x=0.5.It is also realized that the effect of lattice could be ignored in thefirst approximation for these moderate to large band-width systems in this region of doping.All these point to the fact that the interactions that play a dominant role in the elctron-doped region are different[36,37,38]from the ones that are considered crucial in the hole-doped side.There has been a large number of reports of charge ordering and inhomogeneous states [17,18,19,47,48,49,52,53]in the region x≃0.5.These states are quite abundant in the low band-width materials.The inhomogeneous states result primarily from the competing ground states[54](charge ordered/AFM and FM in this case)that lead to1st.order phase transitions with a discontinuity in the density as the chemical potential is varied.Such transitions are known to lead to phase separation in the canonical ensemble.Phase separation in this context has been dicussed in the literature for quite some time[51,55,56,57,58,61]. Such macroscopic phase separations are not stable against long range Coulomb interactions and tend to break up into microscopic inhomogeneities[55,59,60].There is also the well-known CE-type charge and spin ordering that has been seen at x=0.5in most of these systems[14,15,47]with low band-width.In both Nd1−x Sr x MnO3and P r1−x Sr x MnO3Kawano et al.[32]and Kajimoto et al. [28,34]have seenfinite temperature(T≃150K)first order transitions at x=0.5from a ferromagnetic metal to an antiferromagnetic A-phase which is insulating but has quite low resistivity(immediately away from x=0.5it becomes A-type metal).In a neutron diffraction study Kajimoto et al.[28]have also observed that close to the boundary of the FM and A-type AFM metallic phases of P r1−x Sr x MnO3,an unusual stripe-like charge-order appears along with this weaklyfirst order transition.This stripe-like charge-order is distinctly different from the staggered charge-ordering of the CE-type state.Very recently,an inhomegeneous mixture of micron-size antiferromagnetic grains(possibly charge-ordered)and similar sized ferromagnetic grains has been seen in electron diffraction and dark-field imaging in the low band-width system La1−x Ca x MnO3at x=0.5[62]without any evidence of the long-range CE or any other macroscopic ordering. The ground state energies of these different phases seem to be very close[67]in this region leading to a possiblefirst order phase transition and consequent phase seggregation.Apossible nanoscale phase separation between A-type AFM and ferromagnetic regions has recently been reported by Jirac et al.,[81]in the cintered ceramic samples of Pr0.44Sr56MnO3 doped with Cr(upto8percent).It is also observed that although both the ferromagnetic domains and A-type AFM host are independently metallic(though anisotropic for A-AFM), the resultant inhomohgeneous state is non-metallic.Almost all the experiments discussed above consider orbital ordering as the underlying reason for the various magnetic orders observed in the electron-doped regime.The anisotropy of the two e g orbitals and the nature of overlap integral between them[16,63]make the electronic bands low dimensional.Such anisotropic conduction in turn leads to anisotropic spin exchanges and different magnetic structures.In the A-phase the kinetic energy gain of the electrons is maximum when the orbitals form a2D band in the xy-plane and maximize the in-plane ferromagnetic exchange interaction.However,in the z-direction AFM super-exchange interaction dominates due to the negligible overlap of d x2−y2and d3z2−r2orbitals. In addition,the presence of charge ordering and inhomegeneous or phase separated states, particularly around the commensurate densities,are suggestive of the vital role of Coulomb interactions in the manganites.The absence of CE-phase in the moderate to large band-width materials imply that the role of Jahn-Teller or static lattice distortions may not be as crucial in the electron-doped regime even in the region close to x=0.5.A model,for the electron-doped systems,therefore,should have as its primary ingredients,the two e g orbitals at each Mn site and the anisotropy of hopping between them.In addition,the Coulomb interactions are present,and their effects on the charge,orbital and magnetic order are important[9,38,41,46,67].In the next section,we motivate a model recently proposed by Brink and Khomskii[36]for the electron-doped manganites and later extended by us [38]in order to take into account the effects of local Coulomb interactions present in these systems.We extend this model further in the present work,study the magnetic and orbital orders in more detail,investigate the possibility of charge-ordering and phase separation anddiscuss their consequences.In sections II and III we present our calculations and results and compare them with experimental literature.We conclude with a brief discussion on the implications of our results.II.a.Degenerate Double-Exchange ModelEvidently the physics of the region x>0.5is quite different from that in the x<0.5 for the manganites and one has to look at the electron-doped manganites from a different perspective.In order to pay due heed to the compelling experimental and theoretical evidence in support of the vital role of the orbitals,Brink and Khomskii[36](hereafter referred to as BK)have proposed a model for the electron-doped manganites that incorporates the e g orbitals and the anisotropic hopping between them.In the undoped LaMnO3compound each Mn ion has one electron and acts as a Jahn-Teller centre,the e g orbitals are split and the system is orbitally ordered.Thus for the lightly(hole-)doped system one can at the first approxmation ignore the orbital degree of freedom and apply a single band model like the conventional double exchange(DE)model to describe it.If,however,one proceeds from the opposite end and starts,for example,from the insulating CaMnO3compound where the empty e g orbitals of Mn+4ions are degenerate,then doping trivalent(La,Nd,Pr etc.)ions into CaMnO3results in adding electrons into the doubly degenerate e g manifold.In the doped manganites R1−x A x MnO3there are y=1−x number of electrons in the e g orbitals at each Mn site.Since each site has two e g orbitals,four electrons can be accommodated per site and hence the actualfilling(electron density)is y[we restrict ourselves to the region0.5≤x≤1.0(0.5≥y≥0) 8in the foregoing].Due to this low electron concentration and hence very few Jahn-Teller centres the e g band is mostly degenerate and the Jahn-Teller effect is negligible to a leadingapproximation.The neglect of Jahn-Teller effect is also justified from the experimental evidence presented above.The usual charge and spin dynamics of the conventional DE model then operate here too,albeit with an additional degree of freedom coming from the degenerate set of e g orbitals.This process has been described by BK as double exchange via degenerate orbitals.In order to capture the magnetic phases properly,the model has,in addition to the usual double exchange term,orbital degeneracy and the superexchange(SE)coupling between neighbouring t2g spins.At x=1(or y=0)end the e g band is completely empty and the physics is governed entirely by the antiferromagnetic exchange(superexchange)between the t2g spins at neighbouring sites.On doping,the band begins tofill up,the kinetic energy of electrons in the degenerate e g levels along with the attendant Hund’s coupling between t2g and e g spins begin to compete with the antiferromagnetic superexchange interaction leading to a rich variety of magnetic and orbital structures.The model used to describe the ground state properties of the electron-doped manganites contains the following termsH=J AF<ij>S i.S j−J HiS i.s i−<ij>σ,α,βtαβi,j c†i,α,σc j,β,σ(1)Thefirst term is the usual AF superexchange between t2g spins at nearest-neighbour sites,the second term represents the Hund’s exchange coupling between t2g and e g spins at each site and the third term stands for the hopping of electrons between the two orbitals [16,63,64](α,βtake values1and2for d x2−y2and d3z2−r2orbitals,corresponding to the choice of the phaseξi=0in Ref.[65]).The hopping matrix elements are determined by the symmetry of e g orbitals[16,63].Although similar in appearance to the conventional DE model the presence of orbital degeneracy together with the very anisotropic hopping matrix elements tαβij makes this model and its outcome very different from the conventional DE model of Zener[8,25,68,69]with a single non-degenerate orbital.In the manner often used in literature[8]BK treated the t2g spins quasi-classically andthe Hund’s coupling was set to infinity.At each site the spins were allowed to cant in the xz-plane leading to the effective hopping matrix elements[8]t xy=tcos(θxy/2)and t z=tcos(θz/2).Hereθxy is the angle between nearest neighbour t2g spins in the xy−plane andθz is the same in the z−direction.The superexchange energy per state then becomesE SE=J AF S20√3t xy(cosk x+cosk y)−83(cosk x+cosk y)−4t z3(cosk x+cosk y)−4t z3(cosk x−cosk y)2)1we have plotted the bands for the A-phase in the presence of a small canting infig.3a.Note that even in the presence of canting,there is almost no dispersion in the z-direction(Γ-Z and M-L directions).In the canted C-phase as well the band disperses little in the x and y directions and remains almost indistinguishable from the pure phase.The total energy is then obtained for a particularfilling by adding the superexchange contribution to the band energy.It is evident that the energy spectrum obtained depends on the underlying magnetic structure as well as the orbital-dependent(anisotropic)hopping ma-trix elements.This will lead to different anisotropic magnetic structures at different doping. The magnetic phase diagram in the(electron)doping y-t/J AF plane is then calculated by minimizing the total energy with respect toθxy andθz.The sequence of phases follows from the nature of the DOS modulated by the anisotropic overlap of orbitals as well as the DE mechanism.At very low doping(x∼1)BK get a stable A-type(canted)antiferromagnetic phase and on increasing the doping the systemfirst enters the C-phase and then depending on the value of t/J AF directly gets into the ferromagnetic phase or reenters the A-phase before becoming ferromagnetic at large doping.The presence of ferromagnetic phase at large doping and C-type antiferromagnetic order at the intermediate electron doping range is rightly captured in their model.Such a sequence of phases is indeed seen in the experimen-tal phase diagram in these systems.Quite remarkably the phase diagram has almost all the magnetic phases except the G-type antiferromagnetic one that is observed experimentally in these systems at low electron doping.The phase diagram of BK,unfortunately,has two major shortcomings in it.At very low electron-doping a canted A-type antiferromagnetic phase is obtained which is stable for all values of J AF whereas experimentally G-type anti-ferromagnetic phase is observed at this end.The stability of the G-phase around x→1is quite naturally expected on physial grounds.At the y=0(x=1)end there are no electrons in the e g band,the only interaction is the antiferromagnetic exchange between neighbouring t2g spins which should lead to the three dimensional G-type antiferromagnetic order.Theother problem is that of the limiting behaviour.When the antiferromagnetic exchange in-teraction is zero or very close to zero(i.e.t/J AF→∞)the system should be completely ferromagnetic,a feature which is also missed out in their phase diagram.It appears that the designation of the A-type ordering by BK was somewhat ambiguous and that might have led to the absence of the G-phase around x=1in their phase diagram. This is particularly relevant as the typical values of canting obtained by BK in their A-phase are quite large.In their convention for different spin ordering,they chose to designate A-phase whenθxy<θz.It is apparent,therefore,that by this convention,a spin ordering with both the anglesθxy andθz close toπbutθxy<θz,could be designated as a canted A-phase.On the other hand,from the structure of spin arrangements,it should be more appropriately called a canted G-phase.Although G-phase with such large canting has not been seen experimentally(there is hardly any evidence of significant canting in the region close to x=1).This ambiguity is easily resolved if in addition one considers orbital ordering which,however,was not included in their treatment.We discuss this in more detail later on with reference to our calculations.The limit of infinite Hund’s coupling which BK worked with is unphysical for the man-ganites considered[3,9,65,67].Typical values reported in the experiments[3,4,23]and various model studies[9,41,65]and LDA calculations[67,70]do not suggest the spin spilit-tings of the e g band in various manganites to be very large.These are typically comparable to(or slightly larger than)the e g band-width.The scale of Coulomb correlations are most likely to be even higher[3,9].The other serious consequence of using such large values of Hund’s coupling is that the predictions about low energy excitations(like optical spectra, specific heat,spinfluctuation energy scales)are going to be inaccurate.BK’s calculation, though,serves as a starting point for improved theories.Based on their phase diagram BK argue that the degeneracy of orbitals and the anisotropy of hopping are crucial and the lattice(including Jahn-Teller(JT)effect)is of secondaryimportance for the physics of electron-doped manganites.This was borne out by a more refined calculation by Pai.In a more realistic treatment of the spin degrees of freedom,Pai [37]considered the limit offinite J H in the same model and succeeded in recovering the G-and F-phases.II.b.Double exchange and correlationWe mentioned earlier that by all estimates the Coulomb correlations in these systems are large[24,73,70]and it is not obvious,therefore,that the phase diagram obtained by BK will survive once these are introduced in the model.Neither of the treatments of BK or Pai includes the interactions present in the system,namely the inter-and intra-orbital Coulomb interactions as well as the longer-range Coulomb interactions.Although for low doping the local correlations are expected to be ineffective,with increase in doping they preferentially enhance the orbital ordering[38].This affects the F-phase and alters the relative stability of the A-and C-phases.The longer-range part of the interactions would tend to localize the carriers and lead to charge ordering.It is,therefore,necessary to include them in the Hamiltonian and look for their effects on the phase diagram.In the present work we have incorporated the onsite inter-and intra-orbital as well as the nearest neighbour Coulomb interactions in the model Hamiltonian and studied how these terms affect the nature of magnetic phase diagram,orbital ordering and other properties of electron doped manganites.We also set out from the double exchange model with degenerate e g orbitals and the superexchange interaction between the neighbouring t2g spins.The addition of the correlation terms makes the model very different from the ones considered by BK and Pai. Besides,the physics of charge ordering is beyond the scope of the models earlier considered.The model Hamiltonian we consider consists of two parts,thefirst part is the same as the Hamiltonian in eqn.(1)we discussed in the previous section.The second part,which is the interaction part,has onsite inter-and intra-orbital interaction and the nearest neighbourCoulomb interaction terms in it.The total Hamiltonian is thereforeH=H1+H intH1is the same as in eqn.(1)andH int=Uiαˆn iα↑ˆn iα↓+U′iσσ′ˆn i1σˆn i2σ′+V<ij>ˆn iˆn j.(5)In the above U,U′and V are the intra-and inter-orbital and the nearest neighbour Coulomb interaction strengths respectively.We treat the t2g spin subsystem quasi-classically as in BK(this is the usual practice in many of the treatments of the double exchange model [8,9,68]),but we choose to work with the more realistic limit offinite values of the Hund’s coupling.In an uncanted homogeneous ground state we choose S=S0exp(i Q.r)where the choice of Q determines the different spin arrangements for the core(t2g)spins.For example,Q=(0,0,0)would be the pure ferromagnetic phase,Q=(π,π,π)gives the G-type antiferromagnetic phase,Q=(π,π,0)is for C-type antiferromagnetic phase and finally Q=(0,0,π)reproduces A-type antiferromagnetic phase.In the infinite J H limit, the e g electron spins are forced to follow the t2g spins leading to the freezing of their spin degrees of freedom.Atfinite J H,however,the quantum nature of the transport allows for fluctuations and the e g spin degrees of freedom,along with anisotropic hopping across the two orbitals,play a central role.For canted magnetic structures where the angle between two nearest-neighbour t2g spins is different from that of the pure phases,S i is given by S i=S0(sinθi,0,cosθi)withθi taking all values between0andπ.The t2g spins are allowed to cant only in the xz−plane(this does not cause any loss of generality in the treatments that follow).We will discuss the canted structures at length in the foregoing.We begin our discussion by considering the model without the interaction terms U,U′and V.The interactions and their effects will be dealt with in detail later.。

Actinium(Ac) 锕 Aluminium(Al) 铝 Americium(Am) 镅 Antimony(Sb) 锑Argon(Ar) 氩Arsenic(As) 砷Astatine(At) 砹Barium(Ba) 钡Berkelium(Bk) 锫 Beryllium(Be) 铍 Bismuth(Bi) 铋Boron(B) 硼Bromine(Br) 溴Cadmium(Cd) 镉Caesium(Cs) 铯Calcium(Ca) 钙Californium(Cf) 锎 Carbon(C) 碳Cerium(Ce) 铈Chlorine(Cl) 氯Chromium(Cr) 铬Cobalt(Co) 钴Copper(Cu) 铜Curium(Cm) 锔Dysprosium(Dy) 镝 Einsteinium(Es) 锿 Erbium(Er) 铒Europium(Eu) 铕Fermium(Fm) 镄Fluorine(F) 氟Francium(Fr) 钫Gadolinium(Gd) 钆 Gallium(Ga) 镓Germanium(Ge) 锗 Gold(Au) 金Hafnium(Hf) 铪Helium(He) 氦Holmium(Ho) 钬Hydrogen(H) 氢Indium(In) 铟Iodine(I) 碘Iridium(Ir) 铱Iron(Fe) 铁Krypton(Kr) 氪Lanthanum(La) 镧 Lawrencium(Lr) 铹 Lead(Pb) 铅Lithium(Li) 锂Lutetium(Lu) 镥Magnesium(Mg) 镁Manganese(Mn) 锰Mendelevium(Md) 钔Mercury(Hg) 汞Molybdenum(Mo) 钼Neodymium(Nd) 钕Neon(Ne) 氖Neptunium(Np) 镎Nickel(Ni) 镍Niobium(Nb) 铌Nitrogen(N) 氮Nobelium(No) 锘Osmium(Os) 锇Oxygen(O) 氧Palladium(Pd) 钯Phosphorus(P) 磷Platinum(Pt) 铂Plutonium(Pu) 钚Polonium(Po) 钋Potassium(K) 钾Praseodymium(Pr) 镨Promethium(Pm) 钷Protactinium(Pa) 镤Radium(Ra) 镭Radon(Rn) 氡Rhenium(Re) 铼Rhodium(Rh) 铑Rubidium(Rb) 铷Ruthenium(Ru) 钌Samarium(Sm) 钐Scandium(Sc) 钪Selenium(Se) 硒Silicon(Si) 硅Silver(Ag) 银Sodium(Na) 钠Strontium(Sr) 锶Sulphur(S) 锍Tantalum(Ta) 钽Technetium(Tc) 锝Tellurium(Te) 碲Terbium(Tb) 铽Thallium(Tl) 铊Thorium(Th) 钍Tin(Sn) 锡Thulium(Tm) 铥Titanium(Ti) 钛Tungsten(W) 钨Uranium(U) 铀Vanadium(V) 钒Xenon(Xe) 氙Ytterbium(Yb) 镱Yttrium(Y) 钇Zinc(Zn) 锌Zirconium(Zr) 锆Bunsen burner 本生灯product 化学反应产物flask 烧瓶apparatus 设备PH indicator PH值指示剂,氢离子(浓度的)负指数指示剂matrass 卵形瓶litmus 石蕊litmus paper 石蕊试纸graduate, graduated flask 量筒,量杯reagent 试剂test tube 试管burette 滴定管retort 曲颈甑still 蒸馏釜cupel 烤钵crucible pot, melting pot 坩埚pipette 吸液管filter 滤管stirring rod 搅拌棒element 元素body 物体compound 化合物atom 原子gram atom 克原子atomic weight 原子量atomic number 原子数atomic mass 原子质量molecule 分子electrolyte 电解质ion 离子anion 阴离子cation 阳离子electron 电子isotope 同位素isomer 同分异物现象polymer 聚合物symbol 复合radical 基structural formula 分子式valence, valency 价monovalent 单价bivalent 二价halogen 成盐元素bond 原子的聚合mixture 混合combination 合成作用compound 合成物alloy 合金organic chemistry 有机化学 inorganic chemistry 无机化学 derivative 衍生物series 系列acid 酸hydrochloric acid 盐酸sulphuric acid 硫酸nitric acid 硝酸aqua fortis 王水fatty acid 脂肪酸organic acid 有机酸hydrosulphuric acid 氢硫酸 hydrogen sulfide 氢化硫alkali 碱,强碱ammonia 氨base 碱hydrate 水合物hydroxide 氢氧化物,羟化物hydracid 氢酸hydrocarbon 碳氢化合物,羟anhydride 酐alkaloid 生物碱aldehyde 醛oxide 氧化物phosphate 磷酸盐acetate 醋酸盐methane 甲烷,沼气butane 丁烷salt 盐potassium carbonate 碳酸钾 soda 苏打sodium carbonate 碳酸钠caustic potash 苛性钾caustic soda 苛性钠ester 酯 gel 凝胶体analysis 分解fractionation 分馏endothermic reaction 吸热反应exothermic reaction 放热反应precipitation 沉淀to precipitate 沉淀to distil, to distill 蒸馏distillation 蒸馏to calcine 煅烧to oxidize 氧化alkalinization 碱化to oxygenate, to oxidize脱氧,氧化to neutralize 中和to hydrogenate 氢化to hydrate 水合,水化to dehydrate 脱水fermentation 发酵solution 溶解combustion 燃烧fusion, melting 熔解alkalinity 碱性isomerism, isomery同分异物现象hydrolysis 水解electrolysis 电解electrode 电极anode 阳极,正极cathode 阴极,负极catalyst 催化剂catalysis 催化作用oxidization, oxidation 氧化reducer 还原剂dissolution 分解synthesis 合成reversible 可逆的氨 ammonia氨基酸 amino acid铵盐 ammonium salt饱和链烃saturated aliphatic hydrocarbon苯 benzene变性 denaturation不饱和烃unsaturated hydrocarbon超导材料superconductive material臭氧 ozone醇 alcohol次氯酸钾potassium hypochlorite醋酸钠 sodium acetate蛋白质 protein氮族元素nitrogen group element碘化钾 potassium iodide碘化钠 sodium iodide电化学腐蚀electrochemical corrosion电解质 electrolyte电离平衡 ionization equilibriu电子云 electron cloud淀粉 starch淀粉碘化钾试纸starch potassium iodide paper二氧化氮 nitrogen dioxide二氧化硅 silicon dioxide二氧化硫 sulphur dioxide二氧化锰 manganese dioxide芳香烃 arene放热反应 exothermic reaction非极性分子 non-polar molecule非极性键 non-polar bond肥皂 soap分馏 fractional distillation酚 phenol复合材料 composite干电池 dry cell干馏 dry distillation甘油 glycerol高分子化合物 polymer共价键 covalent bond官能团 functional group光化学烟雾 photochemical fog过氧化氢 hydrogen peroxide合成材料 synthetic material合成纤维 synthetic fiber合成橡胶 synthetic rubber核电荷数 nuclear charge number核素 nuclide化学电源 chemical power source化学反应速率chemical reaction rate化学键 chemical bond化学平衡 chemical equilibrium 还原剂 reducing agent磺化反应 sulfonation reaction 霍尔槽 Hull Cell极性分子 polar molecule极性键 polar bond加成反应 addition reaction加聚反应addition polymerization甲烷 methane碱金属 alkali metal碱石灰 soda lime结构式 structural formula聚合反应 po1ymerization可逆反应 reversible reaction 空气污染指数air pollution index勒夏特列原理Le Chatelier&#39;s principle离子反应 ionic reaction离子方程式 ionic equation离子键 ionic bond锂电池 lithium cell两性氢氧化物amphoteric hydroxide两性氧化物amphoteric oxide裂化 cracking裂解 pyrolysis硫氰化钾potassium thiocyanate硫酸钠 sodium sulphide氯化铵 ammonium chloride氯化钡 barium chloride氯化钾 potassium chloride氯化铝 aluminium chloride氯化镁 magnesium chloride氯化氢 hydrogen chloride氯化铁 iron (III) chloride氯水 chlorine water麦芽糖 maltose煤 coal酶 enzyme摩尔 mole摩尔质量 molar mass 品红 magenta或fuchsine葡萄糖 glucose气体摩尔体积molar volume of gas铅蓄电池lead storage battery强电解质 strong electrolyte氢氟酸 hydrogen chloride氢氧化铝aluminium hydroxide取代反应substitution reaction醛 aldehyde炔烃 alkyne燃料电池 fuel cell弱电解质 weak electrolyte石油 Petroleum水解反应hydrolysis reaction四氯化碳carbon tetrachloride塑料 plastic塑料的降解 plastic degradation塑料的老化 plastic ageing酸碱中和滴定acid-base neutralization titration酸雨 acid rain羧酸 carboxylic acid碳酸钠 sodium carbonate碳酸氢铵ammonium bicarbonate碳酸氢钠 sodium bicarbonate糖类 carbohydrate烃 hydrocarbon烃的衍生物derivative of hydrocarbon烃基 hydrocarbonyl同分异构体 isomer同素异形体 allotrope同位素 isotope同系物 homo1og涂料 coating烷烃 alkane物质的量amount of substance物质的量浓度amount-of-substanceconcentration of B烯烃 alkene洗涤剂 detergent纤维素 cellulose相对分子质量relative molecular mass相对原子质量relative atomic mass消去反应elimination reaction硝化反应 nitratlon reaction硝酸钡 barium nitrate硝酸银 silver nitrate溴的四氯化碳溶液solution of bromine in carbontetrachloride溴化钠 sodium bromide溴水 bromine water溴水 bromine water盐类的水解 hydrolysis of salts盐析 salting-out焰色反应 flame test氧化剂 oxidizing agent氧化铝 aluminium oxide氧化铁 iron (III) oxide乙醇 ethanol乙醛 ethana1乙炔 ethyne乙酸 ethanoic acid乙酸乙酯 ethyl acetate乙烯 ethene银镜反应 silver mirror reactio硬脂酸 stearic acid油脂 oils and fats有机化合物 organic compound元素周期表periodic table of elements元素周期律periodic law of elements原电池 primary battery原子序数 atomic number皂化反应 saponification粘合剂 adhesive蔗糖 sucrose指示剂 Indicator酯 ester酯化反应 esterification周期 period族 group（主族：main group）基础化学常用英语词汇380条1. The Ideal-Gas Equation 理想气体状态方程2. Partial Pressures 分压3. Real Gases: Deviation from Ideal Beh***ior 真实气体：对理想气体行为的偏离4. The van der Waals Equation范德华方程5. System and Surroundings系统与环境6. State and State Functions状态与状态函数7. Process 过程8. Phase 相9. The First Law of Thermodynamics 热力学第一定律10. Heat and Work 热与功11. Endothermic and Exothermic Processes 吸热与发热过程12. Enthalpies of Reactions反应热13. Hess’s Law 盖斯定律14. Enthalpies of Formation生成焓15. Reaction Rates 反应速率16. Reaction Order 反应级数17. Rate Constants 速率常数18. Activation Energy 活化能19. The Arrhenius Equation阿累尼乌斯方程20. Reaction Mechanisms 反应机理21. Homogeneous Catalysis 均相催化剂22. Heterogeneous Catalysis非均相催化剂23. Enzymes 酶24. The Equilibrium Constant平衡常数25. the Direction of Reaction反应方向26. Le Chatelier’s Principle列·沙特列原理27. Effects of Volume,Pressure, TemperatureChanges and Catalystsi. 体积，压力，温度变化以及催化剂的影响28. Spontaneous Processes 自发过程29. Entropy (StandardEntropy) 熵（标准熵）30. The Second Law ofThermodynamics 热力学第二定律31. Entropy Changes 熵变32. Standard Free-EnergyChanges 标准自由能变33. Acid-Bases 酸碱34. The Dissociation of Water水离解35. The Proton in Water 水合质子36. The pH Scales pH值37. Bronsted-Lowry Acids andBases Bronsted-Lowry 酸和碱38. Proton-TransferReactions 质子转移反应39. Conjugate Acid-BasePairs 共轭酸碱对40. Relative Strength ofAcids and Bases 酸碱的相对强度41. Lewis Acids and Bases 路易斯酸碱42. Hydrolysis of Metal Ions金属离子的水解43. Buffer Solutions 缓冲溶液44. The Common-Ion Effects同离子效应45. Buffer Capacity 缓冲容量46. Formation of Complex Ions配离子的形成47. Solubility 溶解度48. The Solubility-ProductConstant Ksp 溶度积常数49. Precipitation and separation of Ions 离子的沉淀与分离50. Selective Precipitation of Ions 离子的选择沉淀51. Oxidation-Reduction Reactions 氧化还原反应52. Oxidation Number 氧化数53. Balancing Oxidation-Reduction Equations 氧化还原反应方程的配平54. Half-Reaction 半反应55. Galvani Cell 原电池56. Voltaic Cell 伏特电池57. Cell EMF 电池电动势58. Standard Electrode Potentials 标准电极电势59. Oxidizing and Reducing Agents 氧化剂和还原剂60. The Nernst Equation 能斯特方程61. Electrolysis 电解62. The W***e Beh***ior of Electrons 电子的波动性63. Bohr’s Model of The Hydrogen Atom 氢原子的波尔模型64. Line Spectra 线光谱65. Quantum Numbers 量子数66. Electron Spin 电子自旋67. Atomic Orbital 原子轨道68. The s (p, d, f) Orbital s（p，d，f）轨道69. Many-Electron Atoms 多电子原子70. Energies of Orbital 轨道能量71. The Pauli ExclusionPrinciple 泡林不相容原理72. Electron Configurations电子构型73. The Periodic Table 周期表74. Row 行75. Group 族76. Isotopes, Atomic Numbers,and Mass Numbers 同位素，原子数，质量数77. Periodic Properties ofthe Elements 元素的周期律78. Radius of Atoms 原子半径79. Ionization Energy 电离能80. Electronegativity 电负性81. Effective Nuclear Charge有效核电荷82. Electron Affinities 亲电性83. Metals 金属84. Nonmetals 非金属85. Valence Bond Theory 价键理论86. Covalence Bond 共价键87. Orbital Overlap 轨道重叠88. Multiple Bonds 重键89. Hybrid Orbital 杂化轨道90. The VSEPR Model 价层电子对互斥理论91. Molecular Geometries 分子空间构型92. Molecular Orbital 分子轨道93. Diatomic Molecules 双原子分子94. Bond Length 键长95. Bond Order 键级96. Bond Angles 键角97. Bond Enthalpies 键能98. Bond Polarity 键矩99. Dipole Moments 偶极矩100. Polarity Molecules 极性分子101. Polyatomic Molecules 多原子分子102. Crystal Structure 晶体结构103. Non-Crystal 非晶体104. Close Packing of Spheres球密堆积105. Metallic Solids 金属晶体106. Metallic Bond 金属键107. Alloys 合金108. Ionic Solids 离子晶体109. Ion-Dipole Forces 离子偶极力110. Molecular Forces 分子间力111. Intermolecular Forces 分子间作用力112. Hydrogen Bonding 氢键113. Covalent-Network Solids 原子晶体114. Compounds 化合物115. The Nomenclature, Composition and Structure of Complexes 配合物的命名，组成和结构116. Charges, Coordination Numbers, and Geometries 电荷数、配位数、及几何构型117. Chelates 螯合物118. Isomerism 异构现象119. Structural Isomerism 结构异构120. Stereoisomerism 立体异构121. Magnetism 磁性122. Electron Configurations in Octahedral Complexes 八面体构型配合物的电子分布123. Tetrahedral andSquare-planar Complexes 四面体和平面四边形配合物124. General Characteristics共性125. s-Block Elements s区元素126. Alkali Metals 碱金属127. Alkaline Earth Metals碱土金属128. Hydrides 氢化物129. Oxides 氧化物130. Peroxides andSuperoxides 过氧化物和超氧化物131. Hydroxides 氢氧化物132. Salts 盐133. p-Block Elements p区元素134. Boron Group (Boron,Aluminium, Gallium, Indium,Thallium) 硼族（硼，铝，镓，铟，铊）135. Borane 硼烷136. Carbon Group (Carbon,Silicon, Germanium, Tin,Lead) 碳族（碳，硅，锗，锡，铅）137. Graphite, CarbonMonoxide, Carbon Dioxide 石墨，一氧化碳，二氧化碳138. Carbonic Acid,Carbonates and Carbides 碳酸，碳酸盐，碳化物139. Occurrence andPreparation of Silicon 硅的存在和制备140. Silicic Acid，Silicates硅酸，硅酸盐141. Nitrogen Group(Phosphorus, Arsenic,Antimony, and Bismuth) 氮族（磷，砷，锑，铋）142. Ammonia, Nitric Acid,Phosphoric Acid 氨，硝酸，磷酸143. Phosphorates,phosphorus Halides 磷酸盐，卤化磷144. Oxygen Group (Oxygen,Sulfur, Selenium, andTellurium) 氧族元素（氧，硫，硒，碲）145. Ozone, HydrogenPeroxide 臭氧，过氧化氢146. Sulfides 硫化物147. Halogens (Fluorine,Chlorine, Bromine, Iodine)卤素（氟，氯，溴，碘）148. Halides, Chloride 卤化物，氯化物149. The Noble Gases 稀有气体150. Noble-Gas Compounds 稀有气体化合物151. d-Block elements d区元素152. Transition Metals 过渡金属153. Potassium Dichromate 重铬酸钾154. Potassium Permanganate 高锰酸钾155. Iron Copper Zinc Mercury 铁，铜，锌，汞156. f-Block Elements f区元素157. Lanthanides 镧系元素158. Radioactivity 放射性159. Nuclear Chemistry 核化学160. Nuclear Fission 核裂变161. Nuclear Fusion 核聚变162. analytical chemistry 分析化学163. qualitative analysis 定性分析164. quantitative analysis 定量分析165. chemical analysis 化学分析166. instrumental analysis 仪器分析167. titrimetry 滴定分析168. gr***imetric analysis 重量分析法169. regent 试剂170. chromatographicanalysis 色谱分析171. product 产物172. electrochemicalanalysis 电化学分析173. on-line analysis 在线分析174. macro analysis 常量分析175. characteristic 表征176. micro analysis 微量分析177. deformation analysis 形态分析178. semimicro analysis 半微量分析179. systematical error 系统误差180. routine analysis 常规分析181. random error 偶然误差182. arbitration analysis 仲裁分析183. gross error 过失误差184. normal distribution 正态分布185. accuracy 准确度186. deviation偏差187. precision精密度188. relative standarddeviation 相对标准偏差（RSD）189. coefficient variation变异系数（CV）190. confidence level置信水平191. confidence interval置信区间192. significant test显著性检验193. significant figure有效数字194. standard solution标准溶液195. titration滴定196. stoichiometric point化学计量点197. end point滴定终点198. titration error滴定误差199. primary standard基准物质200. amount of substance物质的量201. standardization标定202. chemical reaction化学反应203. concentration浓度204. chemical equilibrium 化学平衡205. titer 滴定度206. general equation for a chemical reaction 化学反应的通式207. proton theory of acid-base 酸碱质子理论208. acid-base titration 酸碱滴定法209. dissociation constant 解离常数210. conjugate acid-base pair 共轭酸碱对211. acetic acid 乙酸212. hydronium ion 水合氢离子213. electrolyte 电解质214. ion-product constant of water 水的离子积215. ionization 电离216. proton condition 质子平衡217. zero level 零水准218. buffer solution 缓冲溶液219. methyl orange甲基橙220. acid-base indicator酸碱指示剂221. phenolphthalein酚酞222. coordination compound配位化合物223. center ion中心离子224. cumulative stabilityconstant 累积稳定常数225. alpha coefficient酸效应系数226. overall stabilityconstant 总稳定常数227. ligand配位体228. ethylenediaminetetraacetic acid 乙二胺四乙酸229. side reactioncoefficient副反应系数230. coordination atom配位原子231. coordination number配位数232. lone pair electron孤对电子233. chelate compound螯合物234. metal indicator金属指示剂235. chelating agent螯合剂236. masking掩蔽237. demasking解蔽238. electron电子239. catalysis催化240. oxidation氧化241. catalyst催化剂242. reduction还原243. catalytic reaction催化反应244. reaction rate反应速率245. electrode potential电极电势246. activation energy反应的活化能247. redox couple氧化还原电对248. potassium permanganate高锰酸钾249. iodimetry碘量法250. potassium dichromate 重铬酸钾251. cerimetry 铈量法252. redox indicator 氧化还原指示253. oxygen consuming 耗氧量（OC）254. chemical oxygen demanded 化学需氧量(COD)255. dissolved oxygen 溶解氧(DO)256. precipitation 沉淀反应257. argentimetry 银量法258. heterogeneous equilibrium of ions 多相离子平衡259. aging 陈化260. postprecipitation 继沉淀261. coprecipitation 共沉淀262. ignition 灼烧263. fitration 过滤264. decantation 倾泻法265. chemical factor 化学因数266. spectrophotometry分光光度法267. colorimetry比色分析268. transmittance透光率269. absorptivity吸光率270. calibration curve校正曲线271. standard curve标准曲线272. monochromator单色器273. source光源274. w***elength dispersion色散275. absorption cell吸收池276. detector检测系统277. bathochromic shift红移278. Molar absorptivity摩尔吸光系数279. hypochromic shift紫移280. acetylene 乙炔281. ethylene 乙烯282. acetylating agent 乙酰化剂283. acetic acid 乙酸284. adiethyl ether 乙醚285. ethyl alcohol 乙醇286. acetaldehtde 乙醛287. β-dicarbontl compoundβ–二羰基化合物288. bimolecular elimination双分子消除反应289. bimolecularnucleophilic substitution双分子亲核取代反应290. open chain compound 开链族化合物291. molecular orbitaltheory 分子轨道理论292. chiral molecule 手性分子293. tautomerism 互变异构现象294. reaction mechanism 反应历程295. chemical shift 化学位移296. Walden inversio 瓦尔登反转n297. Enantiomorph 对映体298. addition rea ction 加成反应299. dextro- 右旋300. levo- 左旋301. stereochemistry 立体化学302. stereo isomer 立体异构体303. Lucas reagent 卢卡斯试剂304. covalent bond 共价键305. conjugated diene 共轭二烯烃306. conjugated double bond 共轭双键307. conjugated system 共轭体系308. conjugated effect 共轭效应309. isomer 同分异构体310. isomerism 同分异构现象311. organic chemistry 有机化学312. hybridization 杂化313. hybrid orbital 杂化轨道314. heterocyclic compound 杂环化合物315. peroxide effect 过氧化物效应t316. valence bond theory 价键理论317. sequence rule 次序规则318. electron-attracting grou p 吸电子基319. Huckel rule 休克尔规则320. Hinsberg test 兴斯堡试验321. infrared spectrum 红外光谱322. Michael reacton 麦克尔反应323. halogenated hydrocarbon卤代烃324. haloform reaction 卤仿反应325. systematic nomenclatur系统命名法e326. Newman projection 纽曼投影式327. aromatic compound 芳香族化合物328. aromatic character 芳香性r329. Claisen condensationreaction克莱森酯缩合反应330. Claisen rearrangement克莱森重排331. Diels-Alder reation 狄尔斯-阿尔得反应332. Clemmensen reduction 克莱门森还原333. Cannizzaro reaction 坎尼扎罗反应334. positional isomers 位置异构体335. unimolecularelimination reaction 单分子消除反应336. unimolecularnucleophilic substitution单分子亲核取代反应337. benzene 苯338. functional grou 官能团p339. configuration 构型340. conformation 构象341. confomational isome 构象异构体342. electrophilic addition亲电加成343. electrophilic reagent亲电试剂344. nucleophilic addition亲核加成345. nucleophilic reagent 亲核试剂346. nucleophilicsubstitution reaction亲核取代反应347. active intermediate 活性中间体348. Saytzeff rule 查依采夫规则349. cis-trans isomerism 顺反异构350. inductive effect 诱导效应 t351. Fehling’s reagent 费林试剂352. phase transfer catalysis 相转移催化作用353. aliphatic compound 脂肪族化合物354. elimination reaction 消除反应355. Grignard reagent 格利雅试剂356. nuclear magnetic resonance 核磁共振357. alkene 烯烃358. allyl cation 烯丙基正离子359. le***ing group 离去基团360. optical activity 旋光性361. boat confomation 船型构象362. silver mirror reaction 银镜反应363. Fischer projection 菲舍尔投影式364. Kekule structure 凯库勒结构式365. Friedel-Crafts reaction 傅列德尔-克拉夫茨反应366. Ketone 酮367. carboxylic acid 羧酸368. carboxylic acid derivative 羧酸衍生物369. hydroboration 硼氢化反应370. bond oength 键长371. bond energy 键能372. bond angle 键角373. carbohydrate 碳水化合物374. carbocation 碳正离子375. carbanion 碳负离子376. alcohol 醇377. Gofmann rule 霍夫曼规则378. Aldehyde 醛379. Ether 醚380. Polymer 聚合物欢迎您的下载，资料仅供参考！致力为企业和个人提供合同协议，策划案计划书，学习资料等等打造全网一站式需求。

9
(1) The electrons in a molecule move in the field of fixed nuclei. Thus, the kinetic energy of the nuclei can be neglected and the internuclear repulsion can be considered to be constant.
Physical quantity Conversion factor X
Length Mass Charge Energy
Angular momentum
a 0
m e
e
a(a.u.)
Value of X (in SI)
5.2918 1011 m 9.1095 1031 kg 1.6022 1019 C 4.3598 1018 J
A1 B A
A1
R 2M AB
A
11
Thus, the nuclear Schrödinger equation which describes the vibration,
rotation, and translation of a molecule is: H E with
nucl nucl
nucl
M
E R z z H nucl 2M R A1
1
A
2
A
{ elec
MM
A}
A1 B A
AB AB
M
1
2 A
U
{RA}
2M A1 A
U {RA} constitutes a potential energy surface,
which provides a potential for nuclear motion.