Pair density functional theory by means of the correlated wave function

物理化学学报(Wuli Huaxue Xuebao)August Acta Phys.鄄Chim.Sin.,2006,22(8)：937~941B28N28笼的稳定性及笼中四元环间键联类型对笼稳定性的影响田欣欣张富强冯瑞娟武海顺*(山西师范大学化学与材料科学学院,山西临汾041004)摘要采用密度泛函方法对四、六元环组成的所有可能的的23个笼状B28N28结构进行了理论计算和拓扑学特性研究,用三个指标N4x4(x=0,1,2)来描述相邻四元环间的键联类型,结果发现B28N28笼的相对能量随N4x4值的增大而增大,且N404对稳定性的影响起主导作用.这一简单的拓扑学标准可以给出所有四六结构B28N28异构体的大致能量顺序,并从ISR结构中挑选出能量较低的结构,因此有望用于挑选大尺寸氮化硼团簇的热力学稳定结构.关键词：氮化硼,稳定性,拓扑学,密度泛函理论中图分类号：O641Stability of B28N28Alternant Cages and Their Dependence on Bondsbetween SquaresTIAN,Xin⁃Xin ZHANG,Fu⁃Qiang FENG,Rui⁃Juan WU,Hai⁃Shun*(School of Chemistry and Material Science,Shanxi Normal University,Linfen041004,P.R.China) Abstract The structures and stabilities of twenty⁃three B28N28alternant structures have been investigated at the B3LYP/ 6⁃31G*level of density functional theory.It is found that stability index of all the isomers obey a simple N4x4(x=0, 1,2)topological rule characterizing the number of bonds between squares.The relative energies show an increasing tendency with the rising of x in N4x4(x=0,1,2),in which N404is dominant.The present study provides a simple topological criterion that can be used to sort an approximate stability order of all the isomers and select the more stable candidate from the ISR(isolated square rule)structures.The simple filtering scheme is ideally suited for prescreening the thermodynamically viable structures of large boron nitride clusters.Keywords:Boron nitride,Stability,Topology,Density functional theoryAs the isoelectronic analogues to carbon fullerene,boron nitride nanomaterials with a band⁃gap energy of~6eV and non⁃magnetism are also expected to show various electronic,optical and magnetic properties such as Coulomb blockade,photo luminescence,and super paramagnetism[1].Up to now,extensive studies have been reported on the structure and stability of boron nitrides(BN)n as nanotubes[2]and cages[3].Experimentally, Stéphan et al.[4]synthesized the small singer⁃layer and nested BN cages under electron irradiation of nanotubes and bulk material. More recently,Oku et al.[5]synthesized and detected the B24N24and B28N28clusters by means of an arc⁃melting method and laser desorption time⁃of⁃flight mass putationally,it has been found that the small molecules(BN)x(x=3~10)favor ring structures while those with x>10prefer forming cages[6].As for the caged BN structures,there exist two major classes[7]that ex⁃hibit quite different structural features,i.e.,fullerene⁃like struc tures consisting of pentagons and hexagons,and alternant struc⁃tures consisting of squares and hexagons.Fowler and co⁃wor⁃kers[8]suggested that the fullerene⁃like class was systematically more stable than the alternant class over the entire range of[Article]Received：December12,2005；Revised：March6,2006.*Correspondent,E⁃mail：wuhs@；Tel：+86357⁃2052468.国家自然科学基金(20471034)和山西省青年基金(20051011)资助项目鬁Editorial office of Acta Physico⁃Chimica Sinica937Acta Phys.鄄Chim.Sin.(Wuli Huaxue Xuebao ),2006Vol.22molecule size.Conversely,other theoretical studies conclude that alternant class would be preferred [2d,7],and these findings agreed with the more recent study of Strout [9]on B 13N 13,B 14N 14,and B 16N 16.Interestingly,our previous studies showed that the medi ⁃umsized structures [10]comprising octagons also exhibited com ⁃parable stability.However,the traditional square ⁃hexagon systems were still more stable for the large cages [11].By now we know that the stability of carbon fullerenes obeys the isolated pentagon rule(IPR)[12]and the stability of alternant boron nitrides is dominated by the isolated square rule(ISR)[13].Besides,a theoretical study of the even subset [14]of isomers up to 70atoms has verified that isolated ⁃pentagon ⁃pair(IPP)B x N x +4cages are especially stable.Furthermore,it is noteworthy that the number of possible isomers of (BN)x is an increasing function of x ,and systematic calculations performed on all of the isomers are difficult and time ⁃consuming.The filtering principles must therefore be used.The well ⁃known ISR has helped to filter out a large number of less stable isomers,however,the calculations are still expensive for the large ⁃sized structure.For the BN alternant class,does it exist any other useful filtering principles for the large ⁃sized isomers?In this article,a study of density functional theory at B3LYP/6⁃31G *level on the structures and energies of all the possible isomers of the B 28N 28is presented.It is found that the most stable isomer always has all the least number of N 4x 4(x =0,1,2)which topologically characterize the bonds between squares.And with increased number of the N 4x 4,the relative energiesinr ease consistently.The result provides useful information to experimentalists on the formation of other BN clusters.1Computational detailsAll structures of the B 28N 28isomers were optimized at the B3LYP/6⁃31G *level of density functional theory,and the corre ⁃spond ing vibrational frequency calculations at the same level were used to characterize the optimized structure to be energy minima without imaginary frequencies.Single ⁃point energies at B3LYP/6⁃311G *level of are used for discussion.The vertical ionization potentials are calculated to aid experimental study.All neutral cages were treated as closed ⁃shell singlet configura ⁃tions by using the Gaussian 03program [15].2Results and discussion2.1StructuresAll the isomers of B 28N 28were generated based on the fullerene spiral algorithms [16],and the total number was 23.Each isomer has 84B —N bonds without direct B —B and N —N conn ections.Topologically,these neutral cages can be viewed as polyhedra containing squares (f 4)and hexagons (f 6),and all of them have 6f 4and 24f 6.For simplicity,only the more stable 10optimized structures are shown in Fig.1.In order to get the location of f 4in an easy way,a N 4x 4(x =0,1,2)nomenclature is introduced to characterize bonds between f 4,in which N 404is the number of shared square B —N bonds among fused f 4,N 414is the number of B —N bonds that connectedFig.1B3LYP/6鄄31G *optimized B 28N 28isomers (1~10)vNo.8WU,Hai ⁃Shun et al .：Stability of B 28N 28Alternant Cages and Their Dependence on Bonds between Squarestwo isolated f 4,and N 424is the number of B —N —B and N —B —N linker that bridged two isolated f 4(Fig.2).The nomenclature can characterize different isomers very well.For example,isomer 1in T symmetry is an octahedron ⁃liked structure with all the f 4and f 6arranged in the most sym ⁃metric way.There are no fused f 4(N 404=0)in the structure and the numbers of B —N bonds that connected any two ⁃neighbored f 4are all 3(N 414=0,N 424=0).Isomers 3and 4are both tube ⁃liked with all the f 4dispersed averagely in the two caps.In each cap,3f 4are separated by 3fused f 6(N 404=0,N 414=0),all the 3f 4in each cap are bridged by B —N —B and N —B —N (N 424=12).Isomer 10is an oblate structure with C s symmetry,in which 2fused f 4(N 404=1)locate at one side of the cage,2B —N bridged f 4(N 414=1)locate at another side,and the left 2f 4are well isolated (N 424=0).The nomenclature for other structures is given in Table 1.2.2StabilityThe B3LYP/6⁃311G*single ⁃point energies of all structuresand their relative energies are summarized in Table 1.The vertical ionization energies (VIP)are also listed to aid experimental study.Isomer 1in T symmetry with N 404=0is the most stable B 28N 28not only in this study but also in literature [11a].The least stable isomer 23with N 404=6is higher in energy than isomer 1by 3368.67kJ ·mol -1.It can be seen clearly that the most stable structure has the minimal value of N 404while the least stable isomer has the ma ⁃ximum N 404.Additionally,considering all isomers with N 404=0,almost all of them have lower energies than those isomers with N 404逸1.The result is satisfied with the simple rule of thumb ISR [13],namely,the most stable isomer at any given N is one thatminimizes the number of square adjacencies.Examination of the full set of optimized geometries shows that the relative energies of the B 28N 28isomers increase steadily and considerably with rising of N 404.For example,among those structures with N 404=1,isomer 8is the most stable one that is Table 1B3LYP/6⁃311G *single ⁃point energies E T ,relative energies E rel ,ZPE,vertical ionization energy(E VIP ),energy gapsE g and the topological nomenclature (N 4x 4)number of B 28N 28B 28N 28Sym.E T (a.u.)E rel /(kJ ·mol -1)ZPE (kJ ·mol -1)E VIP /(kJ ·mol -1)E g /eV N 404N 414N 4241T -2232.128450.00820.3237.15 6.840002C 1-2232.08464115.02819.2737.24 6.540043C 3v -2232.06334170.95818.1436.61 5.5100124C 3v -2232.06124176.46817.8536.61 5.5100125C 1-2232.04317223.90817.5536.65 6.160146C 1-2232.03620242.20816.7636.48 6.070247C 2-2232.02092282.32816.4237.20 6.540088C 1-2232.02358275.34813.7937.11 5.771049C 1-2232.00740317.82816.1336.94 5.8511010C S -2231.97233409.89815.5036.78 5.9011011C 1-2231.97109413.15814.1636.40 5.8611212C 3-2231.95583453.21814.3736.74 5.8003013C 1-2231.94816473.35813.4536.57 5.7511214C 1-2231.92389537.07812.2036.69 5.6920015C 1-2231.91552559.05812.0336.40 5.4720016C 1-2231.90262592.92811.1536.44 5.4420017C 1-2231.90101597.14811.0336.69 5.4320018C 1-2231.84597741.65809.7336.19 5.8420419C i -2231.83400773.08808.8136.11 5.8120420C 3-2231.83376773.71805.2136.74 5.8330021C 1-2231.74823998.27808.6835.61 4.9422222S 4-2231.303192166.72786.1335.02 5.5240023C 3v-2230.845393368.67766.3835.312.616Fig.2Structure motifs of the nomenclature N 4x 4(x =0,1,2)939Acta Phys.鄄Chim.Sin.(Wuli Huaxue Xuebao ),2006Vol.22275.34kJ ·mol -1higher than isomer 1;while isomer 14,the most stable structure of those with N 404=2,is 537.07kJ ·mol -1higher than isomer 1and 261.73kJ ·mol -1higher than isomer 8.The similar behavior is also found in other isomers.It is also not claimed that all isomers with less N 404value will have lower ener ⁃gies than all isomers with high N 404value.As the energy range spanned when the number of isomers grow,some overlaps occur.However,most of them obey this rule and the most stable isomers can be surely included and selected.Thus,we can get a few likely stable isomers based on the N 404number of all isomers of a given size alternant BN cluster.Additionally,we studied the other two merits N 414and N 424in detail.For all the isomers with [a ,b ,c ](a ,b ,c in [a ,b ,c ]denotes N 404,N 414,N 424respectively),the isomers 5[0,1,4],6[0,2,4],12[0,3,0]is higher in energy than ismer 1[0,0,0]by 223.90,242.20,and 453.21kJ ·mol -1,respectively,demonstrating an inc reasing tendency of relative energy with increasing of N 414.The similar trend is also found in other isomers sharing the same N 404number but different N 414numbers,e.g.,isomer 9with [1,1,0]is 42.48kJ ·mol -1higher than isomer 8with [1,0,4];isomer 21[2,2,2]is higher in energy than the isomer 14with [2,0,0]by 461.20kJ ·mol -1.This result can help us to reduce the likely candidates again from the sorted ISR structures,and can also give a mainly picture of all isomers ′relative stability order.Furthermore,the merit N 424can provide more detailed in ⁃formation when isomers have the same N 404and N 414values.As shown in Table 1,the first four likely isomers all have [0,0,c]nomenclature.Among of them,isomers 3and 4that sharing the same nomenclature [0,0,12]are both in C 3v symmetry and very close in energy.The observed stability order is [0,0,12](isomers3,4)<[0,0,4](isomer 2)<[0,0,0](isomer 1).The same tendency can be found in other isomers with the same N 404and N 414but different N 424,such as [1,1,2](isomer 11)>[1,1,0](isomers 9,10),[2,0,4](isomers 18,19)<[2,0,0](isomers 14⁃17).It should be noted that the isomer 7with [0,0,8]in C 2sym ⁃metry is higher in energy than the two [0,0,12]isomers 3and 4.As shown in Fig.1,isomers 3and 4are both tube ⁃liked,however,isomer 7is oblate.The 6f 4of isomers 3and 4are all dispersed in the two caps while the f 4of isomer 7are all located in the belt and make the cage very flat with large strain in the structure.These energetic differences are very similar to those of fullerenes obeying the isolated pentagons rule (IPR)[17],and the relative stability of BN cages reflects the intimate interplay be ⁃tween strains of individual rings,conjugations and curvatures of the cages.For the similar reason,isomers 5[0,1,4]and 6[0,2,4]with N 414of 1and 2are also lower in energy than isomer 7.Based on the discussion above,it can be concluded that,in general,relative energies show an increasing tendency with N 4x 4(x =0,1,2)nomenclature.And the penalty caused by N 404is larger than those caused by N 414and N 424.To make the tendency clearer and more visible,Fig.3shows the variation of relative energies with numbers of topological merit N 4x 4(x =0,1,2).From the gradient of N 4x 4(x =0,1,2)against the relative energy,it can be found that,the relative order of the three kinds of gradients is N 404>N 414>N 424,i.e.,the penalty caused by N 404,N 414,and N 424decreases gradually.Therefore,N 404is further confirmed to be dominant in affecting the relative energies of isomers.3ConclusionIn summary,the topological properties and stabilities of all 23B 28N 28alternant cages have been investigated at the B3LYP level systemically.It is found that relative energies show a ten ⁃dency to rise with N 4x 4(x =0,1,2).The most stable isomer has the least number of N 4x 4(x =0,1,2).N 404is dominant in affecting the relative energies of isomers,but the influences of the N 414and N 424are also significant.The present study suggests a simple topological criterion that can be used to select the ISR isomers and choose the more stable candidate from the sorted ISR structures.The simple filtering scheme is ideally suited for prescreening the thermodynamically viable structures of large boron nitride clus ⁃ters.It may also give us a guideline for designing and synthesis of the BN clusters.Fig.3Variation of relative energy with number of N 4x 4(x =0,1,2)nomenclatureN 4x 4940No.8WU,Hai⁃Shun et al.：Stability of B28N28Alternant Cages and Their Dependence on Bonds between SquaresReferences1Oku,T.;Kuno,M.;Kitahara,H.;Nartia,I.Int.J.Inorg.Mater., 2001,3:5972(a)Saito,Y.;Maida,M.J.Phys.Chem.A,1999,103(10):129(b)Kongsted,J.;Osted,A.;Jensen,L.;Åstrand,P.O.;Mikkelsen.K.V.J.Phys.Chem.B,2001,105:10243(c)Ma,R.;Bando,Y.;Sato,T.;Kurashima,K.Chem.Mater.,2001,13:2965(d)Wu,H.S.;Xu,X.H.;Zhang,F.Q.;Jiao,H.J.J.Phys.Chem.A,2003,107:6609(e)Xu,H.;Ma,J.;Chen,X.;Hu,Z.;Huo,K.F.;Chen,Y.J.Phys.Chem.B,2004,108:40243(a)Alexandre,S.S.;Nunes,R.W.;Chacham,H.Phys.Rev.B, 2002,66:085406(b)Oku,T.;Kuno,M.;Nartia,I.Diamond Relat.Mater.,2002,11:940(c)Oku,T.;Nishiwaki,A.;Nartia,I.Physica B,2004,351:184(d)Zope,R.R.;Baruah,T.;Pederson,M.R.;Dunlap,B.I.Chem.Phys.Lett.,2004,393:3004Stéphan,O.;Bando,Y.;Loiseau,A.;Willaime,F.;Shramchenko, N.;Tamiya,T.;Sato,T.Appl.Phys.A,1998,67:1075(a)Oku,T.;Nishiwaki,A.;Nartia,I.;Gonda,M.Chem.Phys.Lett., 2003,380:620(b)Oku,T.;Nishiwaki,A.;Nartia,I.Solid State Comm.,2004,130:1716(a)Martin,J.M.L.;El⁃Yazal,J.;Francois,J.P.;Gijbels,R.Chem.Phys.Lett.,1995,232:289(b)Martin,J.M.L.;El⁃Yazal,J.Chem.Phys.Lett.,1996,248:95(c)Strout,D.L.J.Phys.Chem.A,2001,105:261(d)Jia,J.F.;Wu,H.S.;Jiao,H.J.Acta Chim.Sin.,2003,61(5):653[贾建峰,武海顺,焦海军.化学学报(Huaxue Xuebao),2003,61(5):653]7(a)Sun,M.L.;Slanina,Z.;Lee,S.L.Chem.Phys.Lett.,1995, 233:279(b)Slanina,Z.;Sun,M.L.;Lee,S.L.Nanostruct.Mater.,1997,8:6238Rogers,K.M.;Fowler,P.W.;Seifert,G.Chem.Phys.Lett.,2000, 332:439Strout,D.L.Chem.Phys.Lett.,2004,383:9510(a)Wu,H.S.;Jiao,H.J.Chem.Phys.Lett.,2004,386:369(b)Wu,H.S.;Xu,X.H.;Jia,J.F.Acta Chim.Sin.,2004,62(1):28[武海顺,许小红,贾建峰.化学学报(Huaxue Xuebao),2004,62(1):28](c)Cui,X.Y.;Wu,H.S.Chin.J.Chem.,2005,23:11711(a)Wu,H.S.;Cui,X.Y.;Qin,X.F.;Jiao,H.J.J.Mol.Struct.(THEOCHEM),2004,714:153(b)Wu,H.S.;Cui,X.Y.;Xu,X.H.J.Mol.Struct.(THEOCHEM),2005,717:10712(a)Kroto,H.W.Nature,1987,329:529(b)Schmalz,T.G.;Seitz,W.A.;Klein,D.J.;Hite,G.E.J.Am.Chem.Soc.,1988,110:111313Fowler,P.W.;Heine,T.;Mitchell,D.;Schmidt,R.;Seifert,G.J.Chem.Soc.Faraday Trans.,1996,92(12):219714Fowler,P.W.;Rogers,K.M.;Seifert,G.;Terrones,M.;Terrones.H.Chem.Phys.Lett.,1999,299:35915Frisch,M.J.；Trucks,G.W.；Schlegel,H.B.;et al.Gaussian03, Revision A.I.Pittsburgh PA：Gaussian Inc.,200316(a)Manolopoulos,D.E.;May,J.C.;Down,S.E.Chem.Phys.Lett.,1991,181:105(b)Fowler,P.W.;Manolopoulos,D.E.An atalas of fullerenes.Oxford：Oxford University Press,199517Cioslowski,J.;Rao,N.;Moncrieff,D.J.Am.Chem.Soc.,2000, 122:8265941。

（完整版）化学毕业论文范文中文摘要：乙酰甲喹是一种广谱，高效，低毒的兽药，受到人们的广泛应用。

其在动物体内的主要代谢产物为和，这是一对同分异构体。

为了更加透彻的了解乙酰甲喹在动物体内的代谢作用情况，我们就要研究其主要代谢产物。

在合成1-单氧乙酰甲喹和4-单氧乙酰甲喹后，得到RF 值不同的两个代谢产物，由于其是同分异构体，难以区分。

本文就以为理论基础，利用根据Balandina （Tetrahedron Letters 45 (2004) 4003–4007）及Timmons （J. Org. Chem. 2008, 73, 9168–9170）等人的研究，应用化学软件计算1-单氧乙酰甲喹和4-单氧乙酰甲喹的核磁数据，并与实验值进行比较分析，得到区分这一对单氧乙酰甲喹的方法。

关键字：1-单氧乙酰甲喹4-单氧乙酰甲喹同分异构体计算化学Gaussian 03 核磁英文摘要：Mequindox is a broad spectrum, vivo and the major metabolite, which is a pair of isomers. For more thorough understanding of Mequindox metabolism in vivo situation, we will study the major metabolite. In the synthesis of 1 - desoxymaquindox and 4 - desoxymaquindox, got two different RF values of metabolites, because of its isomers is difficult to distinguish. In this paper, that the theoretical basis for the studies of Balandina (Tetrahedron Letters 45 (2004)) and Timmons (J. Org. Chem. 2008, 73,), application of chemical software to the calculate 1 - desoxymaquindox and 4 - desoxymaquindox NMR data, and compared with experimental data analysis, to assigned the approach that distinguish this couple of desoxymaquindoxes.目录中文摘要(Ⅰ)英文摘要(Ⅱ)目录……………………………………………………………Ⅲ前言 (1)1．乙酰甲喹药物用途1.1理化性质1.2抗菌作用及其机理1.3临床应用2．计算化学2.1计算化学的产生2.2计算化学的发展2.3 计算化学的现状2.4计算方法3．应用软件——Gaussian 033.1 Gaussian 03的应用3.2基组的选择4.核磁4.1NMR理论计算研究方法概述4.2化学位移概述4.3计算方法及细节5合成与计算5.1试剂与仪器5.2合成步骤5.3计算方法分析与结论参考文献 (115)致谢……………………………………………………………118 附录…………………………………………………………………前言1．乙酰甲喹药物用途1.1理化性质乙酰甲喹，化学名为3-甲基-2-乙酰基喹噁啉-N-1，4-二氧化物。

Mg掺杂GaN结构及电子结构的理论研究王海燕;李旭升;李丹;姚彦文【摘要】采用基于密度泛函理论的赝势平面波方法研究了金属元素Mg掺杂GaN 的结构及电子结构性质.计算金属Mg分别替换Ga和N原子后体系的结合能,得到Mg原子更容易替换Ga原子,与他人的结果一致.掺杂后晶格常数a和c反而略有增大,并且高压下的情况是类似的.Mg掺杂后GaN电子结构显示掺杂使得GaN带隙略有增加,压强从0增加到20GPa,掺杂前后带隙值分别增大约39.1％和38.4％.%The structure and electronic structure properties of GaN doped with Mg are studied by planewave pseudopotential density functional theory method.By calculating the binding energy of systems with Mg replacing the Ga and N atoms respectively,it is easier for Mg atoms to replace the Ga atoms,which is consistent with the results of others.The lattice constants a and c are slightly increased after doping,and the case under high pressure is similar.With the pressure increasing from 0 to 20 GPa,the band gaps of the GaN and the doped-GaN increase by about 39.1％and 38.4％,respectively.【期刊名称】《四川大学学报（自然科学版）》【年(卷),期】2017(054)005【总页数】4页(P997-1000)【关键词】掺杂;高压;带隙;第一性原理【作者】王海燕;李旭升;李丹;姚彦文【作者单位】河南理工大学材料科学与工程学院,焦作454003;河南理工大学材料科学与工程学院,焦作454003;攀枝花学院材料工程学院,攀枝花617000;河南理工大学材料科学与工程学院,焦作454003【正文语种】中文【中图分类】O521+.2以氮化镓(GaN)为代表的宽禁带材料，是继Si和GaAs之后的第三代半导体,是研制微电子器件、光电子器件的新型半导体材料. 它具有宽的直接带隙、强的原子键、化学稳定性好(几乎不被任何酸腐蚀)、高热导率、难压缩和强的抗辐照能力等特性，被认为是最有前途的宽带隙半导体材料[1].掺杂被认为是改善半导体性能的一种有效途径[2, 3]. 理论计算发现金属元素Mn，Cr或V掺杂有可能使得GaN的居里温度(TC)高于室温[4-7]，这一预言引起了人们的广泛关注.对理想半导体掺杂可以使其性能得到更好的应用，比如金属Al掺杂到GaN晶体中可使得光学带隙在3.42～6.20 eV (300 K时)范围变化，使得其发射波长覆盖整个可见光区及部分紫外线区；金属Mg掺杂到GaN晶体中可得到p 型GaN，p型GaN的实现解决了制造GaN发光器件的一个难题. 实际上，金属元素掺杂GaN，不论在实验上还是在理论上都有大量的研究. 邢等人[8]利用广义梯度近似(GGA)研究了Mn掺杂GaN的电子结构和光学性能，结果表明，Mn掺杂GaN使得Mn3d与N2p轨道杂化，产生自旋极化杂质带，材料表现为半金属性，非常适于自旋注入，说明该种材料是实现自旋电子器件的理想材料. 孙等人[9]采用同样的方法研究了Zn掺杂GaN电子结构及光学性能.实验上发现通过Mg掺杂可以提高样品中空穴的迁移率. 然而至今如何获得高掺杂浓度和高质量的p型GaN，搞清楚Mg掺杂对GaN性质影响的微观机制，仍是热点问题. 微观上Mg掺杂的占位问题，以及掺杂对GaN结构及电子结构性质的影响等相关研究报道较少，这些问题有助于我们更好地分析实验结果. 因此，本文利用基于密度泛函理论的第一性原理方法，对Mg掺杂纤锌矿结构的GaN进行了研究，详细分析了Mg掺杂占位，掺杂体系的结构性质，以及能带结构. 对Mg掺杂后影响GaN的结构和电学性质进行了理论解释，为实验提供了理论依据.文中计算采用基于密度泛函理论的赝势平面波方法，平面波截断能为350 eV，交换关联能采用广义梯度近似(GGA)，交换关联势取 Perdew Burke Ernzerhof (PBE)[10]形式. 采用超软赝势[11]， Ga和N的价电子分别取为3d104s24p1和2s22p3，其他轨道电子视为芯电子. 布里渊区采用9×9×6 Monkhorst-Pack[12] 形式的特殊K点，自洽计算时总能量收敛设为1.0×10-6 eV/atom.3.1 计算模型通常来讲，晶格取代和间隙填充是掺杂原子在掺杂体系中的两种位置. 在此研究过程中，由于掺杂原子Mg半径较大，较难形成间隙填充，所以通常是以晶格取代形式为主的掺杂. 为了判断掺杂原子Mg是优先占据GaN体系中Ga原子还是N原子的位置，我们分别计算两种掺杂体系的结合能，结合能的差值(Eb 可以反映掺杂原子的占位情况. (Eb如下式：(Eb=Eb(GaN→Ga8N7Mg)- Eb(GaN→Ga7N8Mg)=[Etot(G a8N7Mg)-Etot(Ga8N8)-[Etot(Ga7N8Mg)-Etot(Ga8N8)+Etot(Ga)-Etot(N)]=Etot(Ga8N7Mg)-Etot(Ga7N8Mg)-Etot(Ga)+Etot(N)下标b和tot分别表示体系的结合能和总能，Etot(Ga)，Etot(N)和Etot(Mg)分别表示独立Ga，N原子和掺杂Mg原子的能量. 我们分别计算Ga和N原子被掺杂原子Mg取代的体系总能量以及独立原子的能量，从而可以得到两种掺杂体系的结合能差值约为17.37 eV，也就是说掺杂原子替换Ga原子时的结合能更低，即掺杂原子更容易占据Ga原子的位置，这与理论计算和实验结果一致[13, 14]. 因此，选择用Mg原子替换Ga原子的掺杂模型进行计算.掺杂体系为(2×2×1)超晶胞，对应的掺杂浓度为6.25%.3.2 掺杂体系的结构性质为了研究掺杂对GaN结构性质的影响，计算了不同压力下掺杂前后体系的晶格常数a和c，如图1(a)和图1(b)所示. 出现这一反常现象的主要原因是形成Mg-N 键键长(0.206 nm)和远离Mg的Ga-N键键长(0.198 nm)都比Ga-N键的平均值(0.196 nm)长，高压下的情况是类似的. 此外，Mg2+替代Ga3+造成了晶格畸变，从而导致残余应力的产生，使得掺杂体系的能量升高，体积增大，所以它的晶胞参数稍微有些增大.3.3 掺杂体系的微观电子结构图2给出了零压下金属元素Mg掺杂前后GaN晶体的能带结构图. 从图2(a)中可以看出，掺杂前GaN是直接带隙半导体，导带底与价带顶都位于布里渊区的G点上，禁带宽度为1.61 eV，均小于实验值3.39 eV，与邢海英[15] 和Pugh[16]等人的计算结果一致. 由于在计算中采用的密度泛函理论是基态理论，而能隙属于激发态，因此，带隙结果偏低是采用该理论计算时普遍存在的现象.图2(b)是零压下金属Mg掺杂浓度为6.25%的GaN体系的能带结构图. 与图2(a)中掺杂前GaN的能带结构图相比，掺杂金属元素Mg后，晶体的价带、导带的数量明显增多、变密，导带底和价带顶都位于G点，仍然为直接带隙半导体. 带隙宽度为1.742 eV，掺杂后带隙变大.图3给出了不同压力下掺杂前后GaN体系的带隙值. 由图可以看出，Mg掺杂GaN后使得带隙变大，并且带隙均随着压强的增大而增大，压强从0增加到20 GPa，掺杂前后带隙值分别增大约39.1%和38.4%. 说明压强使得GaN晶体的绝缘性增强. 带隙随着压强的增大而增大，主要由于晶体材料中原子间距离减小，电子云重叠程度增大，电荷之间的相互作用增强，导致晶体材料中的原子之间由离子键向共价键转变，带隙变大，绝缘性增强[17].采用基于密度泛函理论的赝势平面波方法研究了金属元素Mg掺杂对GaN性质的影响. 晶格取代和间隙填充是掺杂原子在掺杂体系中的两种位置，由于掺杂原子Mg半径较大，较难形成间隙填充，所以通常是以晶格取代的形式掺杂. 通过计算金属Mg掺杂分别替换Ga和N原子后体系结合能的变化，得到Mg原子更容易替换Ga原子，与他人的结果一致.计算了不同压力下掺杂前后体系的晶格常数a和c，掺杂后晶格常数a和c略有增大，并且高压下的情况是类似的，这主要是由掺杂后形成Mg-N键键长比掺杂前原子之间的平均键长长导致的. 另外，掺杂造成了晶格畸变，使得掺杂体系的能量升高，体积增大. 通过对Mg掺杂前后GaN电子结构的计算发现，掺杂使得GaN 带隙略有增加，且带隙均随着压强的增大而增大，压强从0增加到20 GPa，掺杂前后带隙值分别增大约39.1%和38.4%.【相关文献】[1] 谢长坤, 徐法强, 邓锐, 等. GaN(0001)表面的电子结构研究[J]. 物理学报, 2002, 51: 2606.[2] 周殿凤, 陈红霞, 庄国策. C掺杂ZnS纳米线电子性质和磁性质[J]. 四川大学学报: 自然科学版, 2016, 53: 1307.[3] 张春红, 张忠政, 邓永荣, 等. 稀土(Sc、Y、La)掺杂CdS光电性质的第一性原理研究[J].四川大学学报: 自然科学版, 2017, 54: 108.[4] Dietl T, Ohno H, Matsukura F, et al. Zener model description of ferro-magnetism in zinc-blende magdnetic semiconductors [J]. Science, 2000, 287: 1019.[5] Dietl T, Ohno H, Matsukura F. Hole-mediated ferromagnetism in tetrahedrally coordinated semiconductors [J]. Phys Rev B, 2001, 63: 195205.[6] Crooker S A, Furis M, Lou X, et al. Imaging spin transport in lateralferromagnet/semiconductor structures [J]. Science, 2005, 309: 2191.[7] Van Schilfgaarde M, Mryasov O N. Anomalous exchange interactions in Ⅲ-Ⅴ dilute magnetic semiconductors [J]. Phys Rev B, 2001, 63: 233205.[8] 邢海英, 范广涵, 赵德刚, 等. Mn 掺杂GaN 电子结构和光学性质研究[J]. 物理学报, 2008, 57:6513.[9] 孙美玉, 曾江斌, 张伟, 等. Zn掺杂GaN电子结构及光学性质的第一性原理研究[J]. 鲁东大学学报, 2012, 28: 322.[10] Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple [J]. Phys Rev Lett, 1996, 77: 3865.[11] Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism [J]. Phys Rev B, 1990, 41: 7892.[12] Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations [J]. Phys Rev B, 1976, 13: 5188.[13] Larson P, Lambrecht W, Chantis A, et al．Electronic structure of rare-earth nitrides using the LSDA+ U approach: importance of allowing 4f orbitals to break the cubic crystal symmetry [J]．Phys Rev B, 2007, 75: 045114.[14] 李倩倩, 郝秋艳, 李英, 等．稀土元素(Ce，Pr)掺杂GaN的电子结构和光学性质的理论研究[J]．物理学报, 2013, 62: 017103．[15] Xing H Y, Fan G H, Zhang Y, et al．First principle study of Mg, Si and Mn co-doped GaN [J]．Acta Phys Sin, 2009, 58: 450.[16] Push S K, Dugdale D J, Brand S, et al．Electronic structure calculations on nitride semiconductors [J]. Semicond Sci Technol, 1999, 14: 23.[17] Ramzan M，Hussain T，Ahuja R. High pressure phase determination and electronic properties of lithiumamidoborane [J]. Appl Phys Lett, 2012, 101: 111902.。

密度泛函理论-定理介绍点击查看大图Density functional theory (DFT)密度泛函理论是一种研究多电子体系电子结构的量子力学方法。

密度泛函理论在物理和化学上都有广泛的应用，特别是用来研究分子和凝聚态的性质，是凝聚态物理和计算化学领域最常用的方法之一。

电子结构理论的经典方法，特别是Hartree-Fock方法和后Hartree-Fock 方法，是基于复杂的多电子波函数的。

密度泛函理论的主要目标就是用电子密度取代波函数做为研究的基本量。

因为多电子波函数有 3N 个变量（N 为电子数，每个电子包含三个空间变量），而电子密度仅是三个变量的函数，无论在概念上还是实际上都更方便处理。

虽然密度泛函理论的概念起源于Thomas-Fermi模型，但直到Hohenberg-Kohn定理提出之后才有了坚实的理论依据。

Hohenberg-Kohn第一定理指出体系的基态能量仅仅是电子密度的泛函。

Hohenberg-Kohn第二定理证明了以基态密度为变量，将体系能量最小化之后就得到了基态能量。

最初的HK理论只适用于没有磁场存在的基态，虽然现在已经被推广了。

最初的Hohenberg-Kohn定理仅仅指出了一一对应关系的存在，但是没有提供任何这种精确的对应关系。

正是在这些精确的对应关系中存在着近似（这个理论可以被推广到时间相关领域，从而用来计算激发态的性质[6]）。

密度泛函理论最普遍的应用是通过Kohn-Sham方法实现的。

在Kohn-Sham DFT的框架中，最难处理的多体问题（由于处在一个外部静电势中的电子相互作用而产生的）被简化成了一个没有相互作用的电子在有效势场中运动的问题。

这个有效势场包括了外部势场以及电子间库仑相互作用的影响，例如，交换和相关作用。

处理交换相关作用是KS DFT中的难点。

目前并没有精确求解交换相关能 EXC 的方法。

最简单的近似求解方法为局域密度近似(LDA)。

LDA近似使用均匀电子气来计算体系的交换能（均匀电子气的交换能是可以精确求解的），而相关能部分则采用对自由电子气进行拟合的方法来处理。

色散校正密度泛函
色散校正密度泛函
(Dispersion-correcteddensityfunctionaltheory)是一种基于密度
泛函理论的计算方法，可以用于研究分子间相互作用力的非共价成分，例如范德华力。

在传统的密度泛函理论中，范德华力常常被忽略或者只是通过经验修正来处理。

然而，范德华力在很多分子间相互作用中发挥着重要作用，因此研究它们的特性对于分子结构、反应性质等方面的理解具有重要意义。

色散校正密度泛函通过引入包含范德华力的修正项来提高计算
精度。

这些修正项可以基于经验或者理论模型，例如Grimme方法和TS方法等。

此外，也可以将色散校正与其他密度泛函理论方法相结合，例如自洽场双重杂化方法 (Self-consistent field double hybrid method)。

色散校正密度泛函方法在计算化学、材料科学、生物化学等领域中得到了广泛应用，可以用于研究吸附、光电性质、分子动力学等方面的问题。

它为理解分子间相互作用提供了一种新的视角和工具，为探索分子结构和反应机制提供了有力支持。

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