Clifford algebra and unitary group formulations of the many-electron problem

An essential role of Clifford algebras for quantum-chemical finite-dimensional orbital models of many-electron systems is pointed out. The relationship between Clifford algebra matric units, the generators of the unitary group approach (UGA) and the higher order replacement or excitation operators, as well as between their first and second quantized realizations, is elucidated. The usefulness of higher order replacement operators in the spin-adaptation of various many-body theories is briefly outlined and illustrated on the orthogonally spin-adapted coupled-pair approach. A natural connection with the Clifford algebra UGA is explored and new possibilities for its exploitation in large scale configuration interaction calculations are suggested.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayKillam Research Fellow 1987–8     

Freeon unitary group formulation of Hartree-Fock theory

Summary Hartree—Fock theory was a major topic in Professor Löwdin's famous 1955Physical Review papers. His development was based on fermion orbitals and the Slater determinant. Since that time there has been developed, at the University of Texas, the freeon, unitary-group formulation of quantum chemistry as a viable alternative to the fermionic formulations of nonrelativistic quantum chemistry. We wish to express our appreciation to Professor Löwdin for his strong support of our freeon studies and for many helpful conversations.     

Use of a unitary wavefunction in the calculation of static electronic properties

A unitary coupled cluster method is advocated in this paper for the calculation of static properties. Corresponding to the perturbed Hamiltonian H() including the relevant static property, a suitable unitary wavefunction is envisaged. It is shown that a specific nonvariational model of calculating various order static properties utilising this unitary ansatz results in simplifications compared to the previous Coupled Cluster Theories using only hole-particle excitation parameters formulated for this purpose.NCL Communications No. 3533     

The computation of the representation matrices of the generators of the unitary group

A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.Taken in part from a thesis submitted to the University of London in partial fulfilment of the requirements for the degree of PhD.     

On the structure of the Clifford algebra unitary group adapted states in the many‐electron correlation problem

An attempt has been made to understand the structure of the Clifford algebra unitary group adapted many‐particle states from the conventional symmetric group point of view. Emphasizing the symmetric group result that the consideration of the spin‐independent Hamiltonian matrix over the many‐particle configuration functions (CFs) entails a particular subspace of their spatial parts only, attention is confined entirely in this subspace. Question of adapting the functions therein to the unitary group subduction chain is then shown to bring out an interesting lead to the Clifford algebra unitary group approach (CAUGA) states, thus underlining the motive and the essential gains of the CAUGA formulation. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 607–614, 2000     

配体场强场近似的酉群计算及程序化

以立方体场为例,介绍了配体场强场近似中的酉群计算方法.按这一方法设计的计算机程序需输入内存的数据少,计算速度快.最后产生的本征函数可用于配合物磁学性质的计算.     

Efficient method for computation of representation matrices of the unitary group generators

The representation matrices of the unitary group generators E_k1 are equivalent to the representation matrices of cyclic permutations (k, k ± l, …, l ? 1, l). A method is presented for simultaneous computation of matrices corresponding to all different generators at a cost of less than one multiplication per nonzero element. The number of operations necessary for calculation of individual matrices for single generators or for products of two generators is at most proportional to the number of matrix elements of the final matrix. This approach eliminates the need to store the representation matrices in CI calculations.     

量子化学酉群方法(UGA)的新算法——Wey1基图解法

本文是作者在近二年中创立的酉群计算新方法——weyl基图解法的一个系统介绍和总结。具体介绍了处理量子化学中多电子体系组态相互作用问题(包括与自旋无关和与自旋有关的哈密顿体系)的方法和公式。     

The direct configuration interaction method for general multireference expansions: Symmetric group approach

A computer implementation of the direct configuration interaction method formulated within the symmetric group approach is discussed. The formulation allows for an open-shell as well as for a multiconfigurational reference state. The number of all necessary formulas, derived by a computer for each integral type rather than for the individual integrals, is lower than in the currently existing techniques, including the unitary group approach. The logical structure of a general program for singly and doubly excited configurations is outlined. The efficiency of the symmetric group approach is demonstrated on a recently developed program, restricted to one reference state only.     

Estimation of the Gibbs energy of C60 fullerene solution in organic solvents based on the additive group method

The literature data on the Gibbs energy of C₆₀ fullerene dissolution in organic solvents of different classes are analyzed. The contributions of the functional groups (-CH₃,-CH₂-, >CH-, >C<,-OH,-Ph,-Napht, etc.) of solvent molecules to the Gibbs energy of C₆₀ fullerene solution were calculated based on the additive group model. The effects of different functional groups on the solution process are discussed.     

Theoretical modeling of the heme group with a hybrid QM/MM method

The quality of the results obtained in calculations with the hybrid QM/MM method IMOMM on systems where the heme group is partitioned in QM and MM regions is evaluated through the performance of calculations on the 4‐coordinate [Fe(P)] (P = porphyrin), the 5‐coordinate [Fe(P)(1−(Me)Im)] (Im = imidazole) and the 6‐coordinate [Fe(P)(1−(Me)Im)(O₂)] systems. The results are compared with those obtained from much more expensive pure quantum mechanics calculations on model systems. Three different properties are analyzed—namely, the optimized geometries, the binding energies of the axial ligands to the heme group, and the energy cost of the biochemically relevant out‐of‐plane displacement of the iron atom. Agreement is especially good in the case of optimized geometries and energy cost of out‐of‐plane displacements, with larger discrepancies in the case of binding energies. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 282–294, 2000     

青霉素基团性质的分析

以密度泛函理论和电负性均衡原理为基础,应用修正的电负性均衡方法,并自编程序,用最小二乘法,拟合确定了H,C,O,N,F和Cl以及S等各种类型原子的价态电负性、价态硬度和能量的相关参数;从电负性均衡原理的观点,利用这些参数确定了一些青霉素基团的电负性和电荷分布,并进行了讨论.     

Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S2 eigenfunctions

We present an implementation of the spin‐dependent unitary group approach to calculate spin densities for configuration interaction calculations in a basis of spin symmetry‐adapted functions. Using S² eigenfunctions helps to reduce the size of configuration space and is beneficial in studies of the systems where selection of states of specific spin symmetry is crucial. To achieve this, we combine the method to calculate U(n) generator matrix elements developed by Downward and Robb (Theor. Chim. Acta 1977, 46, 129) with the approach of Battle and Gould to calculate U(2n) generator matrix elements (Chem. Phys. Lett. 1993, 201, 284). We also compare and contrast the spin density formulated in terms of the spin‐independent unitary generators arising from the group theory formalism and equivalent formulation of the spin density representation in terms of the one‐ and two‐electron charge densities.     

A flexible correlation group table (CGT) method for the relativistic configuration interaction wavefunctions

A generalized correlation group table (CGT) method is described for the relativistic configuration interaction (RCI) wavefunctions of molecules containing heavy atoms. In this method first four keywords are defined and two properties are discussed in terms of spectroscopic states and double group theory. These definitions and properties are then used to summarize six principles to stipulate the relationship among relativistic states, nonrelativistic states, as well as RCI configurations. The definitions, properties, and principles comprise the generalized CGT method, which facilitates the classification and assignment of the RCI wavefunctions, and thus, provide a general technique for complex systems containing several open shells. Finally, the techniques are exemplified with a few computational models.     

丙酮-二正丁胺滴定法测定聚氨酯中的异氰酸酯基

采用丙酮代替甲苯和异丙醇作溶剂, 采用二正丁胺滴定法测定聚氨酯中的异氰酸酯基. 用改进方法对样品测定结果的相对标准偏差为0.35%～0.48%, 加标回收率为95.07%～102.30%. FTIR跟踪实验表明, 丙酮作为溶剂可以在体系中稳定存在至少1 d以上, 完全可以满足相关分析的需要. 与传统的甲苯-二正丁胺滴定法的对比实验表明, 本方法准确、简便, 有效降低了实验成本.     

预测烷烃密度的新方法: 基团键贡献法

根据分子结构的特点,通过用染色矩阵和邻接矩阵对分子结构进行矩阵化表征,发展了一种根据分子结构信息烷烃密度的新方法---基团键贡献法。该方法有机地将基团贡献法和化学键贡献法结合在一起,既考虑了分子中基团的特性,又考虑了基团之间的连接性(化学键),具有基团贡献法和化学键贡献法的特点。对658种烷烃的计算结果表明,密度预测值十分接近实验值,平均误差0.245%,进一步外推对聚乙烯、聚丙烯和聚1-丁烯等聚合物的密度进行预测,也取得了令人满意的结果。     

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

The graphical unitary group approach has been applied in an efficient implementation of a general multireference configuration interaction (MRCI) method for use with small active molecular orbital spaces in a semiempirical framework. Gradients can be computed analytically for molecular orbitals from a closed-shell or a half-electron open-shell Hartree-Fock calculation. CPU times for single point energy and gradient calculations are reported. The code allows MRCI geometry optimizations of large molecules, as illustrated for the singlet ground state and the four lowest triplet states of fullerene C(76).     

The combinatorics of graphical unitary group approach to many electron correlation

The combinatorics of Gel'fand states which are useful in the graphical unitary group approach to many electron correlation problem and spin free quantum chemistry is considered. Using operator theoretic methods it is shown that the generators of Gel'fand states are S-functions.     

Matrix element factorization in the unitary group approach for configuration interaction calculations

Techniques of diagrammatic spin algebra are employed to derive segment factorization formulas for spin-adapted matrix elements of one- and two-electron excitation operators. The spin-adapted basis is formed by the Yamanouchi–;Kotani geneological coupling method, and therefore constitutes an irreducible basis of the unitary group U(N), as prescribed by Gel'fand and Tsetlin. Several features distinguish this paper from similar work that has recently been published. First, intermediate steps in the derivation of each segment factor are fully documented. Comprehensive tables list the spin diagrams and phases that contribute to the possible segment factors. Second, a special effort has been made to distinguish between those parts of a segment factor that can be ascribed to a spin diagram and those parts which arise from the orbitals. The results of this paper should thus be useful for those who wish to extend diagrammatic spin algebra to evaluation of matrix elements for states built from nonorthogonal orbitals. Third, a novel graphical method has been introduced to keep track of phase changes that are induced by line up permutations of creation and annihilation operators. This technique may be useful for extension of our analysis to higher excitations. The necessary concepts of second quantization and diagrammatic spin algebra are developed in situ, so the present derivation should be accessible to those who have little prior knowledge of such methods.     

Freeon tensor product states and the unitary group formulation of the many-electron problem

The freeon tensor product basis provides a rapid method for the evaluation of matrix elements in the unitary group formulation of quantum chemistry. The method employs fast transformations between the Gel'fand and freeon tensor product basis.