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.     

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     

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.     

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     

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.     

过渡金属络合物荷移光谱的研究

在配位场近似下,用不可约张量方法对具有O_4对称性的FeCl_6~(3-)及与其结构相似的过渡金属络合物的Hamilton矩阵进行了矩阵分割,得到了一种计算荷移光谱的简单方法.在计算中采用方案,考虑了纯组态内部的Coulomb作用和旋轨作用,忽略了不同组态间的Coulomb作用.并采取冻结轨道近似.计算结果与实验光谱数据符合较好.     

Ab-initio molecular orbital studies on a new mechanism for the interconversion of monomethylnitrosamine and methyldiazohydroxide

Monomethylnitrosamine and methyldiazohydroxide are two proposed N-nitrosamine metabolites, which are formally related by an N O 1,3-proton shift. Their possible interconversion is an important reaction to investigate in elucidating the pathways involved in the decomposition of carcinogenic N-nitrosamines. Self-consistent field molecular orbital studies using a 4-21G basis set, in which solvation is treated using the supermolcule approach, have led to the proposal of a new low energy pathway for their interconversion; this mechanism involves protonation and the implicit involvement of at least two molecules of water.     

Optimal group symmetric localized molecular orbitals

Summary The concept and generating method of optimum group symmetric localized molecular orbitals (OSLMOs) are proposed. The OSLMOs have strong points of orthogonality, equivalence and symmetry, and they are simultaneously as close to the classical VB structure as possible. By using the OSLMOs as one-electron orbitals the multiconfigurational correlation calculations are reduced. The scheme is also a valuable popularization and development to hybridization theory.     

A new approach to the molecular orbital theory of bonding

The Moffitt atoms in Molecules approach [8] and the Mulliken approximation [11] to two-centre integrals have been applied to M. O. Theory to give a simple equation for the energy of a diatomic molecule in terms of atomic spectral parameters and nuclear attraction integrals.The equation has been used to calculate the potential energy curves of 24 electronic states of the diatomic hydrides of second row elements and 24 states of the corresponding iso-electronic singly charged positive molecular ions. The agreement between the calculated and experimental values of the energies, the equilibrium internuclear separations, the force constants and the dipole moments is satisfactory.

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Zusammenfassung Die Moffittsche Näherung der Atome in Molekülen [8] und die Mullikensche Näherung für Zweizentrenintegrale [11] wurden auf die MO-Theorie angewandt, um eine einfache Gleichung für die Energie eines zweiatomigen Moleküls mit Termen aus atomaren Spektralparametern sowie Kernwechselwirkungsintegralen zu erhalten.Diese Gleichung wurde benutzt, um Potentialkurven für 24 elektronische Zustände zweiatomarer Hydride von Elementen der zweiten Hauptreihe zu berechnen sowie 24 Zustände der korrespondierenden isoelektronischen, positiv einfach geladenen Ionenmoleküle zu bestimmen. Die Übereinstimmung zwischen berechneten und experimentellen Werten der Energie, der Gleichgewichtsabstände, der Kraftkonstanten und der Dipolmomente ist befriedigend.

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Résumé L'approximation de Moffitt «atomes en molécules» [8] et l'approximation de Mulliken pour les intégrales bicentriques [11] sont utilisées dans la méthode des O. M. pour obtenir une équation simple pour l'énergie d'une molécule diatomique, contenant des termes en fonction de données de spectroscopie atomique et des intégrales d'attraction nucléaire.Cette équation est utilisée pour l'évaluation des courbes d'énergie potentielle pour 24 états électroniques des hydrures diatomiques des éléments de la deuxième période et de 24 états des mono-cations moléculaires correspondants isoélectroniques. L'agrément est satisfaisant entre les résultats calculés et les données expérimentales de l'énergie, des distances internucléaires d'équilibre, des constantes de force et des moments dipolaires.

     

Kinetics and molecular orbital calculations of desulfonation of strong acid cation-exchange resin

This paper deals with the desulfonation properties of some strong acid cation-exchange resins. The sulfate concentration in solution is continuously increased when a strong acid cation-exchange resin is mixed with water. The leaching of sulfate results from the desulfonation of the fixed group, and the amount of leached sulfate depends on the counter ion charge, the crosslinking degree and the exchanger matrix. The effects of the counter ion charge on the desulfonation rate suggested that the counter ion induces the nucleophilic attack of a water molecule on the sulfo group. This interpretation was supported by semiempirical molecular orbital calculations for the C₆H₅SO₃⁻M^m+ (M^m+ = Na⁺, Mg²⁺ and Al³⁺) systems, and the transition state of the Na⁺ system was successfully predicted by DFT calculations. The crosslinking degree influenced the desulfonation rate, which can be related to the decreasing hydration number of each counter ion in the resin phase with the increasing crosslinking degree. Furthermore, different exchanger matrices produced the differences in the rates, which may be derived from the electron-density donation from the exchanger matrix to the sulfo group. The desulfonation is governed by the electron-density of the sulfur atom and the water activity in the solid phase.     

Systematic approach to extended even-tempered orbital bases for atomic and molecular calculations

Explicit formulas are established for simply generating arbitrarily large basis sets of optimal even-tempered Gaussian primitives which systematically approach complete bases for the entire function space. These bases, moreover, reproduce the corresponding optimal atomic SCF wavefunctions extremely closely and permit an extrapolation of the SCF energies to the Hartree-Fock limit. On the basis of the detailed quantitative information available from these calculations a simple general procedure is formulated for generating optimal even-tempered basis sets for molecular calculations.Dedicated to Professor Dr. Hermann Hartmann on the occasion of his 65th birthday.     

GPGPU for orbital function evaluation with a new updating scheme

We have accelerated an ab initio quantum Monte Carlo electronic structure calculation using general purpose computing on graphical processing units (GPGPU). The part of the code causing the bottleneck for extended systems is replaced by Compute Unified Device Architecture‐GPGPU subroutine kernels which build up spline basis set expansions of electronic orbital functions at each Monte Carlo step. We have achieved a speedup of a factor of 30 for the bottleneck for a simulation of solid TiO₂ with 1536 electrons. To improve the performance with GPGPU we propose a new updating scheme for Monte Carlo sampling, quasi‐simultaneous updating, which is intermediate between configuration‐by‐configuration updating and the widely used particle‐by‐particle updating. The error in the energy due to by the single precision treatment and the new updating scheme is found to be within the required accuracy of ～10^?3 hartree per primitive cell. © 2012 Wiley Periodicals, Inc.     

Efficient algorithm for the spin-free valence bond theory. I. New strategy and primary expressions

A new algorithm for nonorthogonal valence bond (VB) method is presented by using symmetric group approach. In the present algorithm, a new function, called paired-permanent-determinant (PPD), is defined, which is an algebrant and has the same symmetry of a corresponding VB structure. The evaluation of a PPD is carried out by using a recursion formula similar to the Laplace expansion method for determinants. An overlap matrix element in the spin-free VB method may be obtained by evaluating a corresponding PPD, while the Hamiltonian matrix element is expressed in terms of the products of electronic integrals and sub-PPDs. In the present work, some important properties of PPDs are discussed, and the primary procedure for the evaluation of PPD is deduced. Furthermore, the expressions for evaluating both the overlap and Hamiltonian matrix elements are also given in details, which are essential to develop an efficient algorithm for nonorthogonal VB calculations. In the present study, some further effective technical considerations will be adopted, and a new ab initio VB program will be introduced. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 287–297, 1998