开壳层微扰理论的性能研究

采用一系列开壳层分子来检验我们最近提出的开壳层微扰理论(J Chem Theory Comput,2009,5:931―936,简称OSPT)的有效性.我们首先采用双重态分子NH2来讨论OSPT的收敛性.微扰能量计算至400阶.基函数为6-13G.选择这个基函数是为了易于进行完全组态相互作用计算(简称FCI),以及和FCI结果比较.几何结构有3种:(1)N-H键长为平衡键长,(2)N-H键长为平衡键长的1.5倍,(3)N-H键长为平衡键长的2.0倍.在这3种情况下,键角∠HNH均为103.2°.在第一种情况,NH2完全为单参考态分子.随着N-H键长逐渐偏离平衡键长,NH2波函数开始显示出多参考态性质.从微扰量能的角度来看,在第一种情况,微扰能量很快就单调收敛至完全组态相互作用(简称FCI)的计算结果.第二种情况,微扰能量稍微有一点振荡,但也很快收敛至FCI的结果.第三种情况对单参考态微扰理论是一种考验,微扰能量振荡比较明显,收敛较慢.在这3种情况下,我们提出的OSPT微扰方法均比文献中报道的ZAPT(the Z-averaged perturbation theory)方法和RMP方法(restricted ...     

空穴-粒子对称的图形酉群方法在多参考态组态相互作用中的应用

空穴-粒子对称的图形酉群方法(graphic unitary group approach,GUGA)被用于发展高效的多参考态组态相互作用(multi-reference configuration interaction,MRCI)程序.通过将轨道空间划分为双占据轨道、活性轨道和外轨道空间分别处理,耦合系数可以写为三个空间片段因子的乘积.由于仅需搜索和保存活性空间的片段因子,其余两个空间的片段因子可以根据图形类型直接确定,从而避免了部分耦合系数随内空间增大无法保存的难题,使MRCI可被用于超过32个内轨道的计算.空穴一粒子对称允许我们将MRCI的组态空间按照双占据空间空穴数和外空间电子数自然划分为子组态空间,内收缩函数可以分别定义在子组态空间中.在此基础上,我们提出了基于GUGA的内收缩MRCI新方案并程序化.测试表明,未收缩组态空间超过10亿的MRCI已成为可以在普通工作站上完成的常规计算.     

组态相互作用中的特征波函数

提出了完全活性空间组态相互作用方法中对称化算符、本征基、特征矩阵、特征波函数等概念和将多电子波函救按空间与自旋对称分类的统一方法。按此法对称化算符并作用在特征波函数上,再按等价权空间求和即得全组态波函数。因对称性使组态函数中物理因子与几何因子完全分离,可消除了变分求解中多余的变量。特征基化学概念明确,直接对应给定的价键结构。     

多参考态微扰理论大小一致性的数值研究

采用由H2、He 和LiH分别组成的三个超分子系列, 从数值的角度研究了多参考态微扰理论和单双重激发的多参考态组态相互作用(MRSDCI)的大小一致性. 首先在模型空间中进行一个小的完全组态相互作用计算, 然后进行多参考态微扰计算. 数值结果显示, 对这三个模型体系, 我们以前提出的多参考态二级微扰公式是完全大小一致的. 和MRSDCI结果比较, 我们也对它的计算精度进行了讨论. 另外, 还对两组多参考态微扰理论的二级和三级计算结果以及MRSDCI的计算结果的大小一致性误差进行了研究和比较.     

Re_2(edt)_4的电子结构和电子吸收光谱的从头算研究

用密度泛函理论中的B3LYP/CEP-4G方法对Re2（edt）4进行了结构优化和自然键轨道计算,并用单电子激发组态相互作用方法（CIS）计算了Re2（edt）4的分子轨道和激发态。结果表明Re-Re之间不存在明显的三重键,进而很好地解释了Re2（edt）4分子的电子吸收光谱。     

环芳类化合物分子轨道相互作用的研究

建立模型分子描述环芳类分子中二苯环、二乙炔的π轨道间的相互作用,应用多重散主射Ｘα自洽场方法对模型分子的电子结构进行计算,得到分子轨道通过空间相互作用的大小随二苯环、二乙炔间距离的增加呈指数下降,在环芳类经合物分子电子结构研究基础上,分析了分子轨道通过键的相互作用,表明,分子轨道通过空间相互作用与通过键相互作用相互抵消,采用过滤态方法计算环芳类化合物分子前线分子轨道电离能,与实验符合较好。     

基于完全活性空间自洽场的杂化多组态密度泛函方法λ-DFCAS

提出了一种杂化多组态密度泛函新方法——λ-DFCAS. 在λ-DFCAS方法中, 电子相关能被分为静态和动态相关能. 静态相关能由多组态波函数方法完全活性空间自洽场(CASSCF)得到, 而动态相关能由密度泛函理论方法描述. 两种相关能的杂化比例由一个可调节的参数λ控制. 参数λ的取值取决于分子体系的多组态特性, 在0~1之间变化, 从而使得λ-DFCAS可以应用于各种强相关分子体系. 该方法能够以与CASSCF相当的计算代价获得接近完全活性空间二阶微扰(CASPT2)的计算精度, 并具备了大小一致性.     

激发态1，2-二硫环丁烯去活性和异构化机理的理论研究

运用完全活性空间多组态CASSCF方法研究了激发态1,2-二硫环丁烯（1,2-Dithiete）势能面交叉机理．自旋．轨道耦合（SOC）常数采用完全Pauli-Breit旋轨耦合算符（包括单电子和双电子项）进行计算,其强度为198．37或211．35cm^-1,对不同自旋态跃迂起着重要作用．研究结果表明：光激发1,3-dithiol-2-one导致形成主要产物trans—dithioglyoxal（Trans-MinS0）和次级产物thiolthioketene．计算与实验观察结果一致．     

猪胰岛素的活力位置的电子结构分析

本文采用负因子计数方法对猪胰岛素分子作了完整分子的量子化学计算,其中对矩阵元的计算采用EHMO方法。我们将前线轨道的概念推广为靠近Fermi能级的能量区域中的分子轨道,将局域于少数氨基酸残基上的前线轨道简称为活性轨道。计算结果表明,猪胰岛素70％的活力敏感位置上局域有活性轨道。对全部结果的分析说明猪胰岛素的活性轨道和生物活力之间存在某些内在联系,但不是一一对应关系;猪胰岛素的三级构象的变化可以引起电子结构的变化;相同种类的氨基酸残基在分子的不同位置上可以有不同的活性轨道能级和轨道分布。     

马来腈二硫纶·邻菲咯啉镍(Ⅱ)配合物的电子光谱和理论研究

测量了标题配合物Ni(mnt)(phen)在多种介质中的电子吸收光谱和发射光谱,使用密度泛函理论的B3LYP方法和分子轨道理论的PM3方法研究了其气态分子几何构型、电子结构和成键,用ZINDO／S方法通过多组态的组态相互作用(CI)计算解释了实验光谱．结果表明：该配合物分子为平面结构,对称性属于点群C2v,基态为自旋三重态,配位键Ni-N和Ni-S为典型的共价结合,Ni的3d电子反馈效应较显著;可见区的吸收带和发射带(对应于基态电子组态到较低能量激发态组态的跃迁)本质上属于配体phen到mnt^2-的荷移跃迁(LL'CT),紫外区的吸收带本质上属于配体的π→π*跃迁。     

Ab initio study of AmCl(+): f-f spectroscopy and chemical binding

A valence full configuration interaction study with a polarized double-zeta quality basis set has been carried out for the lowest 49 electronic states of AmCl(+). The calculations use a pseudopotential treatment for the core electrons and incorporate a one-electron spin-orbit interaction operator. Electrons in the valence s, p, d, and f subshells were included in the active space. The resulting electronic potential energy curves are largely repulsive. The chemical bonding is ionic in character with negligible participation of 5f electrons. The molecular f-f spectroscopy of AmCl(+) arises essentially from an in situ Am(2+) core with states slightly redshifted by the presence of chloride ion. Am(+)+Cl asymptotes which give rise to the few attractive potential energy curves can be predicted by analysis of the f-f spectroscopy of isolated Am(+) and Am(2+). The attractive curves have substantial binding energies, on the order of 75-80 kcal/mol, and are noticeably lower than recent indirect measurements on the isovalent EuCl(+). An independent empirical correlation supports the predicted reduction in AmCl(+) binding energy. The energies of the repulsive curves are strongly dependent on the selection of the underlying atomic orbitals while the energies of the attractive curves do not display this sensitivity. The calculations were carried out using our recently developed parallel spin-orbit configuration interaction software.     

A quantum chemical calculation on Fe(CO)5 revealing the operation of the Dewar–Chatt–Duncanson model

A nonstandard computational scheme has been applied to calculate Fe(CO)₅ with the aim to illustrate the operation of the Dewar–Chatt–Duncanson model by computation. A full configuration interaction (CI) calculation in an active space has been performed. The active space is built from naturally localized molecular orbitals (NLMOs) localized in bond regions or forming lone pairs. For selecting this active space, Weinhold's perturbation theory formulated in the natural bond orbital (NBO) space has been applied. Bonding, lone pair, and antibond NBOs exhibiting large interaction energies serve to define the active space. The actually applied active space, however, comprises NLMOs that are close in shape to the NBOs indicated by perturbation theory. Thus, a CI calculation with localized orbitals has been performed meeting the classical reasoning of chemists that is often based on local bonding concepts. The computational scheme yields the Lewis structure for Fe(CO)₅ whose energy is identical to the Hartree–Fock energy. The Lewis energy comprises CO → Fe σ‐electron transfer (ET) and CO ← Fe electron back donation (BD). This Lewis energy gets lowered by localized correlation energy contributions caused by ET processes where electrons are back donated from the Fe d‐lone pairs into the CO ligands. Thus, electron correlation within the selected active space is dominated by electron BD. Energies and electron populations of the NBOs support the notion that electrons are preferentially back donated into the equatorial CO ligands. Weights of local Slater determinants, determining the correlation energy, also point to a predominant BD into the equatorial CO ligands. Correlation energy increments resulting from electron BD into single antibond orbitals of the CO ligands have been calculated. These energy quantities also demonstrate that BD into the equatorial CO ligands is more energy lowering than BD into the axial CO ligands. © 2012 Wiley Periodicals, Inc.     

Optimization of virtual orbitals in the framework of a multiconfiguration spin-coupled wave function

A new method is introduced for the optimization of nonorthogonal virtual orbitals for use in general multiconfiguration spin-coupled wave functions. The use of a number of highly effective approximations greatly reduces the computational effort involved, the most important being the use of a second-order perturbation expression for the energy and an approximate expression for the elements of the Hessian. As a result, the overall scheme scales very favourably with respect to the numbers of active electrons and of basis functions, making it suitable for the accurate study of large systems. Benchmark calculations are presented for the dissociation of LiH(X¹Σ⁺) and Li₂(X¹Σ⁺ _g ) using a highly compact four-configuration wave function. Standard spin-coupled valence bond expansions in the same virtual space are required to be significantly larger before equivalent results are obtained. The results are shown to compare very favourably with full valence complete active space self-consistent field calculations using an identical basis, and binding energies are within 4% of the values obtained from full configuration interaction calculations in the same basis set. Received: 10 June 1997 / Accepted: 7 October 1997     

A theoretical study of the excited states of AmO2n+, n=1,2,3

The ground and excited states of the AmO(2) (+), AmO(2) (2+), and AmO(2) (3+) ions have been studied using the four-component configuration interaction singles doubles, spin-orbit complete active space self-consistent field, and spin-orbit complete active space-order perturbation theory methods. The roles of scalar relativistic effects and spin-orbit coupling are analyzed; results with different methods are carefully compared by a precise analysis of the wave functions. A molecular spinor diagram is used in relation to the four-component calculations while a ligand field model is used for the two-step method. States with the same number of electrons in the four nonbonding orbitals are in very good agreement with the two methods while ligand field and charge transfer states do not have the same excitation energies.     

Quasi-degenerate perturbation theory with general multiconfiguration self-consistent field reference functions

The quasi-degenerate perturbation theory (QDPT) with complete active space (CAS) self-consistent field (SCF) reference functions is extended to the general multiconfiguration (MC) SCF references functions case. A computational scheme that utilizes both diagrammatic and sum-over-states approaches is presented. The second-order effective Hamiltonian is computed for the external intermediate configurations (including virtual or/and core orbitals) by the diagrammatic approach and for internal intermediate configurations (including only active orbitals) by the configuration interaction matrix-based sum-over-states approach. The method is tested on the calculations of excitation energies of H(2)O, potential energy curves of LiF, and valence excitation energies of H(2)CO. The results show that the present method yields very close results to the corresponding CAS-SCF reference QDPT results and the available experimental values. The deviations from CAS-SCF reference QDPT values are less than 0.1 eV on the average for the excitation energies of H(2)O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H(2)CO, the maximum deviation from available experimental values is 0.28 eV.     

HX体系电子对内、对间相关研究

在6-311+G^*基组水平上用CISD（configurationinteractionwithsinglyanddoublyexcitedconfigurations)方法研究HX(X=Li-F,HBe)体系电子对内、对间的相关能。计算结果表明不同元素形成的HX(X=Li-F,HBe^+,HBe)体系,其价层电子对内、对间相关能的变化较大,它们之间存在着轨道差别,不宜将其相关贡献归为简单的常数。在使用相同理论方法和相同质量基组的前提下,电子数将直接影响到电子对间相关能的大小。对于多电子体系,电子对间相关在总相关中占有优势,若将其忽略会引起较大误差。     

The unrestricted natural orbital-restricted active space method: methodology and implementation

The full configuration interaction method in the space of fractionally occupied unrestricted natural orbitals (UNO-CAS method) is extended to excited states as well as to strongly correlated and reactive systems with large active spaces. This is accomplished by␣using restricted active space (RAS) wave functions introduced by Olsen et al. [(1988) J Chem Phys 89: 2185] and using the UNOs without the expensive orbital optimization step. In RAS, the space of active orbitals is subdivided into three groups: a group with essentially doubly occupied orbitals (RAS1), the usual CAS space (RAS2), and a space with weakly occupied active orbitals (RAS3). We select these spaces on the basis of the occupation numbers of the UNOs. All possible electron distributions are allowed in the usual CAS space, but the number of vacancies is limited in RAS1 and the number of electrons is limited in RAS3. We discuss an efficient algorithm for generating a RAS wave function. This is based on the Handy-Knowles determinantal expansion with an addressing scheme adopted for the restricted expansion. Results for both ground and excited states of azulene and free base porphyrin are presented. Received: 16 July 1998 / Accepted: 7 August 1998 / Published online: 19 October 1998     

On the stability of Be3: a benchmark complete active space self-consistent field + averaged quadratic coupled cluster study

The optimized geometries and binding energies for the linear and triangular isomers of the beryllium trimer have been obtained through benchmark multireference averaged quadratic coupled cluster (AQCC) calculations using very large complete active space SCF (CASSCF) references (12 active electrons in 13 and 14 orbitals). Geometries were optimized with the cc-pV5Z basis, while the binding energies (including counterpoise correction) were obtained with the significantly larger aug-cc-pV5Z basis set. The binding energies (27.3 and 16.3 kcal/mol for the equilateral and linear isomers, respectively) are larger than the previous full CI benchmark values, while the corresponding Be-Be equilibrium distances of 4.101 and 4.088 a.u. are smaller. In view of the near-size consistency character of the CASSCF + AQCC method, the fact that all 12 electrons are fully correlated, the active reference space includes 14 orbitals, and the very large basis set used here, we propose to consider these results as reference data for Be(3). Using the electron pair localization function obtained at the CASSCF(12,15) level, it is clearly illustrated that the 2p orbitals lying in the molecular plane play a dominant role in the bonding pattern for the equilateral isomer.     

Coupled-cluster with active space selected higher amplitudes: performance of seminatural orbitals for ground and excited state calculations

The active space approach for coupled-cluster models is generalized using the general active space concept and implemented in a string-based general coupled-cluster code. Particular attention is devoted to the choice of orbitals on which the subspace division is based. Seminatural orbitals are proposed for that purpose. These orbitals are obtained by diagonalizing only the hole-hole and particle-particle block of the one-electron density of a lower-order method. The seminatural orbitals are shown to be a good replacement for complete active space self-consistent field orbitals and avoid the ambiguities with respect to the reference determinant introduced by the latter orbitals. The seminatural orbitals also perform well in excited state calculations, including excited states with strong double excitation contributions, which usually are difficult to describe with standard coupled-cluster methods. A set of vertical excitation energies is obtained and benchmarked against full configuration interaction calculations, and alternative hierarchies of active space coupled-cluster models are proposed. As a simple application the spectroscopic constants of the C(2) B (1)Delta(g) and B(') (1)Sigma(g) (+) states are calculated using active space coupled-cluster methods and basis sets up to quadruple-zeta quality in connection with extrapolation and additivity schemes.