Chang-Guo Zhan

An improved iterative maximum overlap approximation method

Abstract A new formula for calculating bond energy has been suggested in order to improve the iterative maximum overlap approximation method and to describe clearly the physical picture determining molecular geometry according to the principle of hybridization. By use of this formula, one can directly work out the equilibrium internuclear distances on the condition that the sum of bond energies in a molecule is maximum. The improved method has been examined by being applied to some alkanes and silanes, the agreement with experimental results indicates that the idea stated in this paper is reasonable.

Construction of the symmetry orbitals in large molecular systems

Abstract It is shown that the procedures for constructing the symmetry orbitals proposed in preceding papers can be extended and simplified, and may be employed to construct the symmetry orbitals in very large molecular systems by partitioning the atomic orbitals into many sets.

Construction of orthogonalized maximum overlap symmetry orbitals

Abstract Based on the extended maximum-overlap criterion proposed previously, a set of generalized equations were obtained for constructing the orthogonalized maximum overlap symmetry orbitais of an arbitrary molecule. Particularly for molecules which do not involve rings with an odd number of atoms, the orthogonalized maximum overlap symmetry orbitais obtained can be used not only to block diagonalize the Fock matrix, but also as the initial molecular orbitais in the self-consistent-field calculation.

The canonical orthogonalization of AO basis set and block diagonalization of the hamiltonian matrix

Abstract On the basis of a general conclusion expressed in the Appendix, in this paper, we firstly discuss the symmetry properties of the orthogonalized AO basis set obtained by use of the canonical orthogonalization, then suggest a simple and systematic method for constructing a set of ortho-normalized symmetry orbitais which are fully classified according to the basis vectors for the rows of the irreducible representations of the corresponding molecular point symmetry group. By use of the orbitais obtained, the Hamiltonian or Fock matrix can be fully block diagonalized according to the rows of the irreducible representations.

Maximum overlap population principle and direct calculation of bond order, valence and atomic charge

Abstract A maximum overlap population principle is introduced to give a very simple approximate scheme for calculating bond order, atomic valence and atomic charge directly from the eigenvectors of the AO overlap matrix without performing the ordinary molecular orbital calculation. The calculated results are close to or on the whole coincident with those obtained from the canonical molecular orbitals constructed by use of the ab initie calculation, which shows that the calculation scheme suggested in this paper is feasible.

Maximum overlap symmetry molecular orbitals in conjugated systems

Abstract The application of the maximum overlap symmetry orbital (MOSO) method to conjugated systems is discussed briefly. The MOSO method can be employed to construct not only the symmetry orbitals and the molecular orbitais in alternant conjugated systems, but also the symmetry orbitais in non-alternant systems. It is shown that under the Huckel approximation the matrix MM+ can be written out directly from the molecular skeleton and may be treated by using chemical graph theory. Because the matrix MM+ of a system can be regarded as the Huckel matrix of a smaller system, the maximum overlap symmetry molecular orbital (MOSMO) calculation results can be easily obtained from those of the smaller systems. For homonuclear conjugated systems and for systems in which two kinds of atom appear altemantly, the MOSMOs and the corresponding molecular orbital (MO) energies obtained by the MOSMO calculation are the same as the MOs and the MO energies calculated by the Huckel molecular orbital method.

The maximum overlap symmetry orbital method and the group overlap method

Abstract The relationship between the maximum overlap symmetry orbital (MOSO) method and the group overlap method is briefly discussed. It is shown that one of the equations in the MOSO method can become the basic equation in the group overlap method by making use of the simple maximum overlap approximation, and can be regarded as a generalized equation for constructing the covariant basis vectors. The procedure for constructing the generator orbitals can be simplified by use of a generalized eigenvalue equation in the MOSO method, instead of by calculating the transformation coefficients between the basis vectors for the irreducible representations of the SO(3) group and those of the molecular point symmetry group.

Maximum bond order hybrid orbital calculations of CO bond stretching vibrational frequencies

Abstract A generalized relationship, which includes contributions of the s-characters of C O bond and the net atomic charges, is employed to elucidate C O bond stretching vibrational frequencies based on the maximum bond order hybrid orbital calculations at ab initio HF/6-31G∗ level of theory. It is demonstrated that the change of the s-characters is the most important factor for determining the change of C O stretching frequencies. The C O stretching frequencies calculated by using the explicit relationship obtained are in good agreement with the corresponding experimental frequencies.

Band structures by the maximum overlap symmetry molecular orbital method

Abstract It is shown that the maximum overlap symmetry molecular orbital (MOSMO) procedure can be employed to construct the crystal orbitals and study the band structures by using the Bloch function basis set. The concrete MOSMO calculations on the extended Hiickel molecular orbital (EHMO) approximation level using Bloch functions for some organic polymers and graphite show that the calculated band gaps are close to those worked out by using the ordinary linear combination of atomic orbitals (LCAO) method if the same parameterization is adopted. Because the MOSMO procedure is more easily performed than the ordinary LCAO procedure, the MOSMO calculation using Bloch functions may be feasible in large systems.

Ab initio calculation of natural hybrid orbitals

Abstract The natural hybrid orbital (NHO) procedure is tested at the ab initio level by use of the density matrix in a Lowdin orthogonalized atomic orbital basis. The direct NHO calculation based on the whole density matrix also includes the hybridization of the inner atomic orbitals, and the NHO calculation employing the valence orbital part of the density matrix considers only the hybridization of the valence atomic orbitals. The numerical results obtained by using the NHO calculation based on the ab initio calculation with an STO-3G basis show that the components of the s atomic orbitals in the NHOs obtained from the two kinds of NHO calculations are very close to each other, and that the two kinds of NHOs have excellent correlations with the nuclear spin-spin coupling constants.