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.     

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（英文）

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.     

建立在群对称轨道(SMO)及特征组态(CD)基础上的线性分子SMO-CDCI方法

定义和讨论了线性分子的群对称轨道(SMO)及特征组态函数(CD),它能够对线性分子的分子轨道与组态函数进行简单而完全的对称分类.SMO－CDCI方法是一种高效的计算方法,大大节省了线性分子CI计算的机时与内存.     

确定等价双电子组态原子光谱项的简便方法

根据Pauli原理 ,即原子体系中完全波函数必须是反对称的要求 ,提出一种推测等价双电子组态原子光谱项的方法。以推测 (np) 2 ,(nd) 2 ,(nf) 2 组态光谱项为例 ,说明该方法是学习原子光谱项过程中容易理解、便于掌握的简便方法     

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.     

求解弱相互作用分子A-BC的振转能级和波函数的SCF-CI方法

给出了一种计A－BC型弱相互作用分子体系的分子间振转激发态的自洽场-组态相互作用(SCF－CI)方法. 首先使用SCF方法代化径向伸缩振动和弯曲振动的基函数,再用CI方法确定精确的振转激发态能级. 在求解-维的伸缩振动SCF方程时,采用Numerov－Johnson算法在给定区间上求解获得振动波函数的数值解. 具体计算了Ar－HCI和Ar－N₂体系的振转激发态的能级以验证该方法. 结果表明,本方法可用较少的组态就能获得可与其它大计算量的方法具有相比拟的精度的结果.     

稀土离子4fn-15d组态的配位场理论

基于配位场理论方法,以4f15d1组态为例,阐明了稀土离子4fn-15d组态的谱项、支谱项及其相应的波函数和能量的研究方案;推导出4fn-15d组态在S4点群对称晶体场作用下的配位场势函数和光谱跃迁选律;得出一些有关4fn-15d组态的能级能量的定性结论。     

建立在群对称轨道(SMO)及特征组态(CD)基础上的CI方法与程序发展

ISMO－CDCI方法点群理论，特别是不可约张量方法，在量子化学理论方法发展以及简化概念与计算方面，发挥了重要作用．但在国外的量子化学计算程序（如G94）中，在后自洽场（opt－SCF）计算方面，很少用到对称约化．在文献中，只见有关hbeltah群（DZh与它的子群）对称约化用于组态相关计算的报导．由于多重耦合系数的计算复杂，蜕化不可约表示多体问题的对称约化难于得到解决．我们提出了一个统一与普遍的方法，它能解决所有分子体系多体相关的点群对称约化问题［‘－6］，这个方法的核心是群对称轨道（SMO）概念的提出．SMO的基本特…     

多组态含时自旋非限制HartreeFock理论

基于自旋非限制HartreeFock理论,发展了自旋非限制多组态含时HartreeFock理论方法来研究激光场中的多电子相关动力学．自旋向上和自旋向下的自旋轨道分别在他们各自的子空间内传播;并通过约化密度矩阵和平均场算符相互作用．分别利用了自旋限制和非限制的多组态含时HartreeFock方法虚时和实时传播计算氦原子基态能量和电离几率．自旋非限制的计算结果与其他报道相吻合．     

超球坐标下原子、分子体系的变分计算：—氦原子和氢负离子基态

应用超球会标表示氦原子和氢负离子的薛定谔方程，将二电子原子在三维空间中的运动转化为单电子原子在六维空间中受广义库仑力作用的运动，我们给出了六维空间广义角动量算符的本征值与本征函数，并以此本征函数微基构造超球波函数，得到超球径微分方程，以广义Laguerre 多项式表示超球径波函数，运用密度矩阵和线性变分法得到非正交基下超球径波函数满足的久期方程，最后求得能量和波函数，计算结果与精确的计算符合良好。     

The vibrational fine structure of the 1A2g ← 1A1g polarized absorption band of trans-[Co(NH3)4(CN)2]+. The excited state geometry

The interpretation of configurational bases in the full reaction space depends on the type of FORS MOs from which they are generated. Configurations constructed from atom-adapted FORS MOs have the character of valence bond structures and can be transformed into antisymmetrized products of atomic state functions. Configurations based on natural FORS MOs can be used to advantage to generate that part of the full reaction space which dominates the orbital optimization. Configurational mixing in the full reaction space can be predicted using the minimal basis set of the free-atom SCF AOs. Illustrative examples are given. The FORS model can be improved through the intra-atomic correlation correction.     

Calculation of transition matrix elements by nonsingular orbital transformations

A general strategy is described for the evaluation of transition matrix elements between pairs of full class CI wave functions built up from mutually nonorthogonal molecular orbitals. A new method is proposed for the counter‐transformation of the linear expansion coefficients of a full CI wave function under a nonsingular transformation of the molecular‐orbital basis. The method, which consists in a straightforward application of the Cauchy–Binet formula to the definition of a Slater determinant, is shown to be simple and suitable for efficient implementation on current high‐performance computers. The new method appears mainly beneficial to the calculation of miscellaneous transition matrix elements among individually optimized CASSCF states and to the re‐evaluation of the CASCI expansion coefficients in Slater‐determinant bases formed from arbitrarily rotated (e.g., localized or, conversely, delocalized) active molecular orbitals. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Evolutionary algorithm based configuration interaction approach

A new evolutionary algorithm for stochastic configuration interaction (CI) method designed as an affordable approximation to full configuration interaction (FCI) has been described here. The key components of the algorithm are initiation, propagation, and termination steps taking inspiration from the genetic algorithm. The propagation step is performed with cloning (retention of a Slater determinant without change), mutation (single excitation/de‐excitation), and crossover (exchange of α and β strings between two Slater determinants) and termination is selection of few Slater determinants based on certain fitness function (measure of importance of a determinant in the CI space) and rejection of the rest. We find that the absolute value of the CI coefficients is a suitable fitness function when combined with a fixed selection scheme. We have tested its accuracy in 1D Hubbard problem and ground state potential energy surface (PES) has also been constructed for symmetric bond breaking of water molecule, where the errors are found to be around 10 mE_h with low non‐parallelity error, when retaining only a small fraction of the total number of Slater determinants in the final population. This shows that this method has the ability to capture both static and dynamic correlation. Performance and convergence properties of the algorithm are also tested for N₂ triple bond breaking problem. The algorithm opens up a promising way for stochastic sampling of the important determinants in the full Hilbert space.     

Computation of determinant expansion coefficients within the graphically contracted function method

Most electronic structure methods express the wavefunction as an expansion of N‐electron basis functions that are chosen to be either Slater determinants or configuration state functions. Although the expansion coefficient of a single determinant may be readily computed from configuration state function coefficients for small wavefunction expansions, traditional algorithms are impractical for systems with a large number of electrons and spatial orbitals. In this work, we describe an efficient algorithm for the evaluation of a single determinant expansion coefficient for wavefunctions expanded as a linear combination of graphically contracted functions. Each graphically contracted function has significant multiconfigurational character and depends on a relatively small number of variational parameters called arc factors. Because the graphically contracted function approach expresses the configuration state function coefficients as products of arc factors, a determinant expansion coefficient may be computed recursively more efficiently than with traditional configuration interaction methods. Although the cost of computing determinant coefficients scales exponentially with the number of spatial orbitals for traditional methods, the algorithm presented here exploits two levels of recursion and scales polynomially with system size. Hence, as demonstrated through applications to systems with hundreds of electrons and orbitals, it may readily be applied to very large systems. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Scaling the Coulomb interaction in calculations of electron spectra of transition metal complexes

A simple technique of scaling two-electron integrals in ab initio calculations of the electronically excited states of transition metal complexes is proposed. This technique uses the fact that one-center two-electron integrals depend linearly on the scaling factor when Slater type functions are subjected to scaling transformation. This leads to a linear dependence of the d—d transition energy on the “scale” of Coulomb interaction, which allows one to affect the calculation result by varying the Slater exponential. To test the technique, ab initio configuration interaction and full active space calculations of the low excited states of the CrF ₆ ^3- , MnF ₆ ^2- , and VF ₆ ^3- complexes are performed. For transition elements, a basis of Slater type effective functions chosen from the optical spectra of the atoms and ions of transition elements is used. It is shown that in the STO-6G basis with effective exponentials, experimental transitions are reproduced with an accuracy of about 2000 cm^-1 even with the use of small active space determined by the orbitals localized on the central atom of the complex.     

Large-scale parallel configuration interaction. I. Nonrelativistic and scalar-relativistic general active space implementation with application to (Rb-Ba)+

We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.     

Multi-overlap molecular dynamics methods for biomolecular systems

We propose a molecular dynamics method for the multi-overlap algorithm. By utilizing a non-Boltzmann weight factor, this method realizes a random walk in the overlap space at a constant temperature and explores widely in the configurational space, where the overlap of a configuration with respect to a reference state is a measure for structural similarity. We can obtain detailed information about the free-energy landscape and the transition states among any specific reference conformations at that temperature. We also introduce a multi-dimensional extension of the multi-overlap algorithm. Appling this multi-dimensional method to a penta peptide, Met-enkephalin, we demonstrate its effectiveness.     

PCILON. perturbative configuration interaction using localized orbitals and numerical integration. I. Numerical integration techniques for the calculation of Hamiltonian matrix elements between localized orbitals

Modern techniques for multidimensional numerical integration, Korobov's and Sobol's formulas namely, are used for the direct computation of matrix elements between the localized molecular orbitals needed for a configuration interaction calculation by a perturbation method. A minimal orbital basis of Slater functions is used for formaldehyde and ethylene taken as example. The resulting precision is satisfactory.