Doubly-Colored Graphs as Graphical Models for Subductions of Coset Representations, Double Cosets, and Unit Subduced Cycle Indices

The concept of doubly-colored graphs is proposed to model subductions of coset representations, double cosets, and unit subduced cycle indices, which have been mathematically formulated in coset algebraic theory developed by Fujita (Symmetry and Combinatorial Enumeration in Chemistry, Springer-Verlag, Berlin, 1991).     

Efficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfaces

The spin‐Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics—valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge‐transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin‐Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step‐by‐step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin‐Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

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     

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).     

A method to fast determine the coupling coefficients in CI calculation

A new algorithm for evaluating the coupling coefficients and the addresses of molecular integrals in configuration interaction (CI) calculations is presented, which leads to an improved CI calculation program CGUGA. The validity and efficiency of the new code are compared with other programs, such as MELD and GAUSSIAN-94.     

Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications

We present here a comprehensive account of the formulation and pilot applications of the second‐order perturbative analogue of the recently proposed unitary group adapted state‐specific multireference coupled cluster theory (UGA‐SSMRCC), which we call as the UGA‐SSMRPT2. We also discuss the essential similarities and differences between the UGA‐SSMRPT2 and the allied SA‐SSMRPT2. Our theory, like its parent UGA‐SSMRCC formalism, is size‐extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size‐consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low‐lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis‐a‐vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size‐consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA‐SSMRPT2 results. The striking aspect of the size‐consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin‐multiplicities, which are obtained as the asymptotic limit of super‐molecules with different coupled spins. © 2015 Wiley Periodicals, Inc.     

整体都市主义：重构被金钱化的微观心理氛围—情境主义国际思潮研究

情境主义国际的革命情境建构不仅仅是理论讨论,而且是对资产阶级日常生活世界（环境）的直接干预。他们并不直接关注资本主义生产方式、经济关系和政治法权关系的制度,而是转向这些制度通过日常生活中的吃喝穿住小事情对象化结果,即微观社会批判。在黑格尔看到宏观“市民社会”的地方,情境主义者看到了原子化个人活动被入序于金钱化都市关系中的微观生活细节,这种细节化的“氛围”不是由人主动构序和塑形的,而是由景观操控的。整体都市主义,正是针对资产阶级都市主义这种景观控制下的城市生活的微观伪场境,同样从建筑和城市生活建构的场境入手,试图重构日常生活的诗意情境。     

Multinomial Combinatorial Group Representations of the Octahedral and Cubic Symmetries

We consider the full multinomial combinatorics of all irreducible representations of the octahedral (cubic) symmetry as a function of partitions for vertex, face and edge colorings. Full combinatorial tables for all irreducible representations and all multinomial partitions are constructed. These enumerations constitute multinomial expansions of character-based cycle index polynomials, and grow in combinatorial complexity as a function of edge or vertex coloring partitions.     

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.     

Application of Angular Momentum Theory to Constructing Basis Functions of Irreducible Representations of Icosahedral Group

A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e. , coefficients S, are the components of the eigenvectors of some Hermitian matrices, and can be made as real numbers for all pure rotation point groups. The general formula for coefficient S was deduced, and applied to constructing the basis functions of single-valued irreducible representations of icosahedral group from the spherical harmonics with angular momentum j≤7.     

A multireference direct CI program based on the symmetric group graphical approach

Specific features of an SGGA-based multireference direct CI program working in large internal spaces are discussed. In particular, advantages resulting from the explicit separation of the orbital and the spin spaces are explored. Concepts allowing for the efficient creation of a flexible and symmetry-adapted CI basis, for the high-speed generation of the coupling coefficients and for structuring a simple permutation driven algorithm to handle the orbital space are briefly discussed.Alexander von Humboldt Fellow 1985/87     

对取代苯Ph一X（X＝F，OH，NH_2）的价键理论研究

采用键表酉群方法对Ｃ６Ｈ５Ｆ、Ｃ６Ｈ５ＯＨ和Ｃ６Ｈ５ＮＨ２中的电子离域现象进行了计算和分析，讨论了取代苯的价键描述特性，并计算了取代基的π电子离域能．结果表明离子结构成分与离域能有直接关系，即离子成分越多，电子离域能越大．／６－３１Ｇ基组及“分子中的原子”方法将电荷密度分区积分得到各原子上的电荷集居数，并将此结果与取代苯的反应性能进行了比较。为在价键意义上分析和理解取代基对苯环电子结构及其反应性能的影响，本文对３个典型的取代苯Ｐｈ－Ｘ（Ｘ＝Ｆ，ＯＨ，ＮＨ２）进行了初步的价键计算和讨论．１计算方法及构型在键表酉群方法中［５］，体系的一个共振结构可用一个价键结构函数即键表ψ（ｋ）来描述，相应的体系总波函数Ψ可表示为Ｍ个正则键表的线性组合：式（１）便构成了键表相互作用（ＢＴＩ）计算方法［６］的基础．键表对体系的结构贡献定义为：原子轨道ｑ上的电荷集居数定义为：式中ｍｑ（ｋ）可取０、１或２，分别对应于键表ψ（ｋ）中原子轨道ｑ出现０、１或２次．为简比计算，我们将取代苯的σ骨架用ＨＦ分子轨道固定［７］，这样仅需考虑π电子及轨道．原子轨道积分及ＨＦ－ＳＣＦ计算采用Ｇａｕｓｓｉａｎ８０程序．联系人及第一作者：莫亦荣，男，２９     

有机化学主要章节内容的图示总结

以图示方式归纳总结有机化学中烯烃、炔烃、单环芳烃、卤代烷、醇、酚、醛、酮、羧酸及其衍生物、β-二羰基化合物、胺及重氮盐的化学性质、重要反应及其相关应用,将有机化学反应的知识系统化,帮助学生形成脉络清晰的知识体系。     

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.     

TB-curve, a New 2-D Graphical Representation of DNA Sequences

Based on the classifications of the four nucleic acid bases, we introduce a new 2-D method of DNA representation: TB-curve, which avoids loss of information accompanying alternative 2-D representation in which the curve standing for DNA overlaps and intersects itself. The method is illustrated on the coding sequence of the first exon of human beta-globin gene.     

Global Forcing Number of Benzenoid Graphs

A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons.     

Comparison of Reliability of log P Values Calculated from a Group Contribution Approach and from the Autocorrelation Method

Abstract

The values of log P (n-octanol/water partition coefficient) for 1449 chemicals were calculated from the fragmental/regression model of Klopman and co-workers (J. Chem. Inf. Comput. Sci. 1994, 34, 752-781) and from the autocorrelation/backpropagation neural network model implemented in AUTOLOGP_TM (Version 4.0). Both models provided good simulation results but the superiority of the latter was demonstrated.     

Graphical method for the determination of the complex NMR shift and equilibrium constant for a hetero-association accompanying self-associations

We describe a novel graphical method which, in conjunction with the previously proposed graphical determination of monomer shift, dimer shift, and dimerization constant for self-association, allows us to determine the complex shift and equilibrium constant for a hetero-association, A + B ⇌ AB, accompanying self-associations, A + A ⇌ A₂, and B + B ⇌ B₂. The merit of the new method includes the removal of the restrictions imposed on the conventional Benesi-Hildebrand (B-H) plot: (1) that the concentration of one component must be much less than that of the other; (2) that there be no accompanying self-association. The simultaneous equilibrium of the self-association of 2-pyrrolidone (A) and that of 4-methyl-α-pyrrolidone (B) and the hetero-association between A and B in acetonitrile-d₃ at 25‡C is studied. The inappropriateness of the B-H plot in dealing with this case is also pointed out.     

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.     

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