Maximum overlap symmetry orbitals

Based on the principle of maximum overlap, a new simple method is suggested for constructing the symmetry orbitals of arbitrary molecules and the delocalized molecular orbitals of molecules that do not involve the rings with an odd number of atoms. All these orbitals, called “maximum overlap symmetry orbitals,” are determined by an extended maximum overlap criterion and form the bases for the irreducible representations of the molecular point symmetry group. The theoretical analysis and the numerical results show that the obtained molecular orbitals are close to those obtained from the customary LCAO method, and calculation by the proposed method requires less computing time than does the LCAO method, thus illustrating a fact that the method is not only a reasonable approximation of the LCAO method, but simpler and feasible in large molecular systems.     

Maximum overlap symmetry molecular orbital model

This paper provides a brief and systematic presentation of the basic principle and method of the maximum overlap symmetry molecular orbital (MOSMO ) model and its application to simplification of molecular orbital calculation and to calculation of molecular structures and properties, together with some new results about the MOSMO calculation and new insights concerning the further extension of the principle and method. It has been shown that the theoretical method of the MOSMO model is very simple, reliable, and useful and can be employed to study the structure–property relation in even very large molecular systems. The numerical results obtained from the MOSMO calculation on various semiempirical molecular orbital approximation levels show that when the same parametrization, such as one of those employed in EHMO , CNDO /2, and HMO methods, is adopted, the MOSMOS are very close to the canonical molecular orbitals obtained from the customary LCAO method and the MOSMO calculation requires less computing time than does the LCAO method. The MOSMO calculation can be used for rapidly obtaining reasonably good molecular geometries, vibrational frequencies, and other properties of molecules by employing a simple improved semiempirical parametrization. Equilibrium geometries, vibrational frequencies, and other results are in good agreement with the experimental data and the results obtained from ab initio molecular orbital calculation. The basic calculational procedure of the MOSMO model can be extended further and has been employed to give some new results, to propose some new theoretical schemes and principles, and to introduce some new interesting theoretical problems that deserve to be studied further.     

Disjoint molecular orbitals in nonalternant conjugated diradical hydrocarbons

The concept of disjoint NBMOs in diradical alternant hydrocarbons (AHs) is reviewed and extended to diradical nonalternant hydrocarbons (nonAHs). A valence-bond (VB) method for recognizing disjoint versus nondisjoint NBMOs (nonbonding molecular orbitals) in diradicals is presented. When circumscribed with hexagonal rings, disjoint diradicals produce nonradical polycyclic successors and nondisjoint diradicals produce diradical polycyclic successors. The interconnection between the topological VB terms of cross-conjugated, disjoint NBMOs, and essentially disconnected polycyclic hydrocarbons is delineated.     

Calculating overlap intergals with slater-type orbitals in the molecular coordinate system

Kirov Azerbaidzhan University. Translated from Zhurnal Strukturnoi Khimii, Vol. 28, No. 5, pp. 148–149, September–October, 1987.     

Hybrid molecular orbitals for reacting systems

A method of describing the interactions between two systems in terms of coupled hybrid molecular orbitals of fragments is discussed and is applied to simple interacting systems to provide information on the processes of bond formation.     

分子轨道图形理论中对称轴定理

本文试图以浅显明确的形式描述对称轴定理，使之能与对称面定理相媲美，并对对称轴定理作一定的扩展，给出分子轨道构造定理。     

Continuous symmetry measures of irreducible representations: application to molecular orbitals

The formalism of continuous symmetry measures is extended to describe the extent to which a function, such as a molecular orbital, transforms under the symmetry operations of a given point group according to each irreducible representation of this group. For distorted molecules we are able to calculate the degree to which any molecular orbital transforms with respect to the irreducible representations of the pseudosymmetry group that is valid for a higher symmetry, idealized geometry, showing which irreducible representations participate in each molecular orbital upon symmetry loss in the geometry of the nuclear framework.     

Double coset for symmetry orbitals

In this paper it is shown that, by use of the double coset decompositions of the point symmetry group and permutation group, the related symmetry coefficients and Clebsch–Gordan coefficients can be given in close formulas.     

Maximum bond order hybrid orbitals

Summary Based on the simplified calculation scheme of the maximum bond order principle and the basic idea of the maximum overlap symmetry orbital method, a simple procedure is suggested for constructing systematically the bonding hybrid orbitals, called maximum bond order hybrid orbitals, for a given molecule from the first-order density matrix obtained from a molecular orbital calculation. As an example, the proposed procedure is performed for some typical small molecules by use of the density matrix obtained from CNDO/2 calculation. It is shown that the bonding hybrid orbitals constructed by using the procedure are extremely close to those by using the natural hybrid orbital procedure and in good agreement with chemical intuition, and that the proposed procedure can be performed more easily than the natural hybrid orbital procedure and can given simultaneously the values of the maximum bond order for all bonds in molecules.The project was supported by National Natural Science Foundation of China and also supported partly by Foundation of Hubei Education Commission     

Cluster molecular orbitals and an orbital symmetry view of solid phase transitions in perovskites

The molecular orbitals, normalization constants and energies of the M₈(O_h), M₄(T_d) and M₆(O_h) clusters are derived and tabulated through the d-atomic orbitals. A vector method, adapted to computer application, is devised to compute s, p and d overlap between variously oriented orbitals at atoms that do not have co-directional local axes. Mixing of σ, π and δ orbitals to give the same irreducible representation is also included. As illustrations, the orbitals of Sr₈, La₈, TiO₆ and AlO₆ clusters are computed by the Mulliken—Wolfsberg and Helmholz approximations. During solid phase transitions in the perovskite structures of SrTiO₃ and LaAlO₃, the TiO₆ octahedron rotates about the C₄ axis whereas the AlO₆ octahedron rotates about the C₃ axis. This difference is explained qualitatively in terms of the relative symmetries of the cluster HOMOs and LUMOs using the second-order Jahn—Teller effect. Allusions are made to the application of this cluster symmetry approach to other systems.     

Treatment of symmetry in MO calculations. II. Numerical projection operators for molecular orbitals

This article describes the numerical application of projection operators to restore the symmetry of molecular orbitals in self-consistent field (SCF) calculations when the symmetry is lost because of degeneracy or near degeneracy. The application of projection operators is particularly useful in cases of near degeneracies of three or more molecular orbitals, where it is difficult to find an effective algorithm for restoring the symmetry of molecular orbitals by orthonormal transformations.     

Computer-generated formulas for overlap integrals of slater-type orbitals

Using a modified form of Sharma's method for the expansion of a Slater-type orbital in spherical harmonics about a displaced center, a general expression for the overlap integral between two orbitals is derived that is equivalent to that given by Sharma. By use of a simple kind of “computer algebra” this expression is developed here into a formula that is equivalent to earlier known ones and may have computational advantages when the generated formula coefficients are stored. This method is capable of extension to more complicated integrals.     

Evaluation of two-center overlap integrals using slater type orbitals in terms of bessel type orbitals

Using the definition of STOs in terms of BTOs, we have presented analytical formula for two-center overlap integrals. The obtained formula contains generalized binomial coefficients and Mulliken integrals A_k and B_k. Taking into account the recent advances on the efficient calculation of Mulliken integrals (Harris, Int. J. Quantum Chem., 100 (2004) 142), we have obtained many more satisfactory results for two-center overlap integrals, for arbitrary quantum numbers, scaling parameters, and location of atomic orbitals.PACS No: 31.15.+qAMS Subject Classification: 81V55, 81–08     

Molecular equilibrium geometries and vibrational frequencies by maximum overlap symmetry molecular orbital method

It is demonstrated that the maximum overlap symmetry molecular orbital method can be used for optimization of molecular geometries and calculation of vibrational frequencies by adding a two-body repulsive energy term and a modification of the Wolfsberg–Helmholz formula. The obtained equilibrium geometries and vibrational frequencies are on the whole in good accordance with experimental data, which shows that the basic idea using the method to optimize molecular geometries and to calculate vibrational frequencies is reasonable.     

An overlap criterion for selection of core orbitals

 An overlap criterion is defined that connects the identification of core orbitals in a molecular system, which can be problematic, to that in isolated atoms, which is well defined. This approach has been tested on a variety of troublesome systems that have been identified in the literature, including molecules containing third-row main-group elements, and is shown to remove errors of up to 100 kcal/mol arising from an inconsistent treatment of core orbitals at different locations on a potential-energy surface. For some systems and choices of core orbitals, errors as large as 19 kcal/mol can be introduced even when consistent sets of orbitals are frozen, and the new method is shown to identify these cases of substantial core–valence mixing. Finally, even when there is limited core–valence mixing, the frozen-core approximation can introduce errors of more than 5 kcal/mol, which is much larger than the presumed accuracy of models such as G2 and CBS-QB3. The source of these errors includes interatomic core–core and core–valence dispersion forces. Received: 31 August 2001 / Accepted: 11 October 2001 / Published online: 9 January 2002