A new theory for symmetry orbital and tensor (II)

The symmetry orbital-symmetry orbital tensor methtd is applied to the evaluation of molecular integrals (one-electron) and two-electron integrals) and the symmetry-orbital-tensor and self-consistent-field (SOT-SCF) calculations. A calculation sheme is proposed to simplify the evaluation of integrals and a key equation is derived to reduce the computation efforts in SCF iterations. According to the key equation, compared with the traditional SCF method, the computation efficiencies including CPU timing and external disk (or internal memory) requirement increase in the magnitude of the square of the order of a point group. The new SOT method is expected to be useful in the theoretical calculations of large molecular systems of high point group symmetries. Projcct supported by the National Natural Science Foundation of China (Grant No. 29473119).     

A new theory for symmetry orbital and tensor (Ⅱ)——Symmetric reduction of molecular integrals and self-consistent field calculations

The symmetry orbital-symmetry orbital tensor method is applied to the evaluation of molecular integrals (one-electron and two-electron integrals) and the symmetry-orbital-tensor and self-consistent-field (SOT-SCF) calculations. A calculation scheme is proposed to simplify the evaluation of integrals and a key equation is derived to reduce the computation efforts in SCF iterations. According to the key equation, compared with the traditional SCF method, the computation efficiencies including CPU timing and external disk (or internal memory) requirement increase in the magnitude of the square of the order of a point group. The new SOT method is expected to be useful in the theoretical calculations of large molecular systems of high point group symmetries.     

Colle-Salvetti-type correction for electron-nucleus correlation in the nuclear orbital plus molecular orbital theory

A Colle-Salvetti (CS)-type electron-nucleus correction in the nuclear orbital plus molecular orbital theory is proposed. The CS-type correction is designed to satisfy the cusp condition for the electron-nucleus interaction. Since the CS-type correction is expressed in terms of the electron and nucleus densities, its evaluation is computationally feasible. Numerical assessment confirms that the CS-type correction performs well for the small G2 set.     

Products of arbitrary class-sums in the symmetric group

An algorithm for the evaluation of products of arbitrary conjugacy class-sums in the symmetric group is conjectured. This algorithm generalizes a procedure presented sometime ago, which deals with products in which at least one of the class-sums involved consists of a single cycle (and an appropriate number of fixed points). Let the support size of a conjugacy class be the number of indices that are not fixed points. The algorithm proposed implies that the coefficient of the class-sum C in the product of the class-sums A and B is given in terms of a well-defined enumeration problem within the symmetric group S_p, where p is the smallest of the support sizes of A, B, and C. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 429–440, 1998     

Iterative diagonalization for orbital optimization in natural orbital functional theory

A challenging task in natural orbital functional theory is to find an efficient procedure for doing orbital optimization. Procedures based on diagonalization techniques have confirmed its practical value since the resulting orbitals are automatically orthogonal. In this work, a new procedure is introduced, which yields the natural orbitals by iterative diagonalization of a Hermitian matrix F . The off‐diagonal elements of the latter are determined explicitly from the hermiticity of the matrix of the Lagrange multipliers. An expression for diagonal elements is absent so a generalized Fockian is undefined in the conventional sense, nevertheless, they may be determined from an aufbau principle. Thus, the diagonal elements are obtained iteratively considering as starting values those coming from a single diagonalization of the matrix of the Lagrange multipliers calculated with the Hartree‐Fock orbitals after the occupation numbers have been optimized. The method has been tested on the G2/97 set of molecules for the Piris natural orbital functional. To help the convergence, we have implemented a variable scaling factor which avoids large values of the off‐diagonal elements of F . The elapsed times of the computations required by the proposed procedure are compared with a full sequential quadratic programming optimization, so that the efficiency of the method presented here is demonstrated. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

General method for symmetry orbitals and tensors in electronic structure calculations

The symmetry orbital tensor (SOT) method, which makes full use of symmetries in all point groups and can be applied to the self-consistent field (SCF) and post-SCF calculations, is introduced. The principal feature of this method is the definition of the symmetry orbitals (SOs). Any element in a molecular point group will transform one SO to another equivalent SO or simply to itself, and no mixture among SOs exists. Thus, although the SOs for non-Abelian point groups may adapt to reducible representations, their transformation properties are much simpler than in conventional treatments. This article also presents a general scheme to generate SOs for all point groups. The direct products of N SOs form an Nth-rank SOT group, and each matrix element between SOTs is the product of a physical factor and a geometric factor. Compared with the canonical molecular orbitals, the use of SOs can noticeably reduce the computation efforts by decreasing the number of integrals needed in the SCF calculations or the number of configurations needed in the configuration interaction (CI) calculations. The SOT-SCF and SOT-CI approaches are formulated and a preliminary SOT-SCF program is written. Pilot calculations demonstrate the value of the SOT approach, at least at the closed-shell Hartree–Fock level. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 305–321, 1999     

A scalable optimization approach for fitting canonical tensor decompositions

Tensor decompositions are higher‐order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as CANDECOMP/PARAFAC (CP), which expresses a tensor as the sum of component rank‐one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience and web analysis. The task of computing CP, however, can be difficult. The typical approach is based on alternating least‐squares (ALS) optimization, but it is not accurate in the case of overfactoring. High accuracy can be obtained by using nonlinear least‐squares (NLS) methods; the disadvantage is that NLS methods are much slower than ALS. In this paper, we propose the use of gradient‐based optimization methods. We discuss the mathematical calculation of the derivatives and show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient‐based optimization methods are more accurate than ALS and faster than NLS in terms of total computation time. Copyright © 2011 John Wiley & Sons, Ltd.     

Semiempirical molecular orbital theory in carcinogenesis research

It is generally believed that most chemical carcinogens exert their effects through covalent modification of the nucleic acid base sites. Significant clarification of the underlying chemistry involved in these early and critical events is available through the techniques of computational chemistry. The role of semiempirical molecular orbital theory in this area is reviewed using examples focusing on

1. (i) the conversion of precarcinogens to reactive electrophiles,

2. (ii) the regiochemistry of nucleic acid adduct formation,

3. (iii) the chemical and physical consequences of nucleic acid base modification, and

4. (iv) empirical structure activity relationships.

The symbiotic relationship that can exist between the semiempirical and ab initio molecular orbital procedures is emphasized, as is the continuing niche for the semiempirical methodology in the study of systems that are too large, or in situations that are insufficiently cost effective, for the application of ab initio methods.     

Third-order energy derivative corrections to the Kohn-Sham orbital hardness tensor

The third term in the Taylor expansion of the total energy functional around the number of electronsN is evaluated as the second-order derivative of orbital Kohn-Sham energies with respect to orbital occupancy. Present approach is an extension of an efficient algorithm to compute densityfunctional based orbital reactivity indices. Various energy derivatives used to approximate orbital reactivity indices are defined within the space spanned by the orbital occupation numbers and the Kohn-Sham one-electron energies. The third-order energy functional derivative has to be considered for singular hardness tensor ([η]). On the contrary, this term has negligible influence on the reactivity index values for atomic or molecular systems with positively defined hardness tensors. In this context, stability of a system in equilibrium state estimated through the eigenvalues of [η] is discussed. Numerical illustration of the Kohn-Sham energy functional derivatives in orbital resolution up to the third order is shown for benchmark molecules such as H₂O, H₂S, and OH⁻.     

A new method for partition of interaction energy. Relation between stabilization energy and orbital mixing

A new method for partition of interaction energy is proposed. The scheme given here easily connects the calculated stabilization energy with the orbital mixing in analyzing orbital interactions of molecules. The method can reveal the relation between the change of electron distribution and stabilization energy. As an example, orbital interaction energies are estimated for diazocompounds, diazomethane and diazirine.     

A comparative analysis of Hartree-Fock and Kohn-Sham orbital energies

Hartree-Fock and Kohn-Sham orbital energies, the latter computed with several different exchange/correlation functionals, are compared and analyzed for 12 molecules. The Kohn-Sham energies differ significantly from experimental ionization energies, but by amounts that are, for a given molecule and exchange/correlation functional, roughly the same for all of the valence orbitals. With the exchange/correlation functionals used, the energy of the highest occupied Kohn-Sham orbital does not approximate the corresponding ionization potential any better than do the other orbital energies. Received: 24 October 1997 / Accepted 31 October 1997     

THE STUDY OF MANY-BODY THEORY OF VALENCE-ELECTRON STRUCTURE OF METAL COMPLEX

An irreducible tensor method based on M. O. theory for solving many-body Schrodinger equation of valence-electron system of metal complexes has been proposed. Electronic structures of several typical octahedral transition metal complexes have been studied by means of this method. Calculated excitation energies agree with observed ones within several kcm-1.     

价键方法中的非活性轨道优化新算法

本文通过引进一组正交的辅助非活性轨道和与它正交的辅助活性轨道,将价键理论方法中的冻核近似推广到轨道非正交的情形,得到了体系能量及其对非活性轨道的梯度解析表达式,简化了价键自洽场方法中非正交轨道能量梯度的计算．该方法的标度为（Na＋1）m^4,其中Na和m分别是活性轨道和基函数的个数．分析表明,与现有的其他算法相比较,该方法具有更低的计算标度,因而计算效率更高．     

Generalized spin orbital GW theory for spin‐frustrated and spin‐degenerate systems

We proposed the ab initio linear combination of Gaussian type orbital (LCGTO) generalized spin orbital GW (GSO–GW) method and calculated triangular hydrogen molecules as models of the noncolinear magnetic clusters. A remarkable improvement of ionized potentials (IPs) by the GW procedure for GHFS solutions is observed in comparison with calculational results by full CI. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 369–374, 2001     

A new algorithm for inactive orbital optimization in valence bond theory

This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field (VBSCF) method with non-orthogonal orbitals. The frozen core approximation method is extended to the case of non-orthogonal orbitals. The expressions for the total energy and its gradients are presented by introducing auxiliary orbitals, where inactive orbitals are orthogonal, while active orbitals are non-orthogonal themselves but orthogonal to inactive orbitals. It is shown that our new algorithm has a low scaling of (N _a + 1)m ⁴, where N _a and m are the numbers of the active orbitals and basis functions, respectively, and is more efficient than the existing VBSCF algorithms.     

Products of class sums of the symmetric group: Rules of partial elimination

Progress in the formulation of a procedure for the combinatorial evaluation of the product of a single-cycle and an arbitrary class sum in the symmetric group algebra is presented. The procedure consists of a “global conjecture” concerning the representation of the product [(p)]_n·[*]_n in terms of a set of operators referred to as reduced class sums, and of an (incomplete) set of rules for the evaluation of the (n-independent!) coefficients of these operators. Two new types of index elimination rules are suggested, and some properties of the formalism are explored. These include useful sum rules as well as a certain “detailed balance” property that sheds some light on a combinatorial aspect of the global conjecture. The present results account for several new types of reduced class coefficients and suggest some feasible further developments. Some outstanding open problems are pointed out. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 961–979, 1997     

Reactive orbital energy theory serving a theoretical foundation for the electronic theory of organic chemistry

It is established that the reactive orbital energy theory (ROET) theoretically reproduces the rule-based electronic theory diagrams of organic chemistry by a comparative study on the charge transfer natures of typical organic carbon–carbon and carbon–heteroatom bond formation reactions: aldol, Mannich, α-aminooxylation, and isogyric reactions. The ROET, which is an expansion of the reaction electronic theories (e.g., the frontier orbital theory) in terms of orbital energies, elucidates the reactive orbitals driving reactions and the charge transferability indices of the reactions. Performing the ROET analyses of these reactions shows that the charge transfer directions given in the rule-based diagrams of the electronic theory are reproduced even for the functional groups of charge transfer destinations in all but only two processes for 38 reaction processes. The ROET analyses also make clear the detailed orbital-based pictures of these bond formation reactions: that is, the use of the out-of-plane antibonding π orbitals in acidic conditions (enol-mode) and in-plane antibonding π orbitals in basic conditions (enolate-mode), which explain the experimentally assumed mechanisms such as the π-bond formations in acidic conditions and σ-bond formations at α-carbons in basic conditions. Furthermore, the ROET analyses explicate that the methyl group initially accepts electrons and then donates them to the bond formations in the target reactions. It is, consequently, suggested that the ROET serves a theoretical foundation for the electronic theory of organic chemistry.     

键能的分子轨道理论研究 1: 理论公式

从LCAO-MO出发, 给出了一个计算键能的近似方法, 即EAB(i)-∑∑CaiSabCbiεi为第i个占据分子轨道(MO)中的一对电子对A-B键键能的贡献。对所有分子轨道求和即为该键的键能: EAB=∑EAB(i)。按该方法, 不仅可以计算各种不同分子中每两个相键连原子间的键能, 还可以从MO及AO角度分析每一具体键, 如σ, π, δ键的键能以及各AO对键能的贡献。该方法虽有别于求键焓和平衡离解能De, 但计算结果和De的实验值甚相符合。通过对键能的分析研究, 能较好地揭示原子间的相互作用关系及化学键的强弱, 从而可进一步探讨化学反应活性, 反应速率等化学性质。