Generalized valence bond
Encyclopedia
The generalized valence bond (GVB) method is one of the simplest and oldest valence bond
method that uses flexible orbitals in the general way used by modern valence bond theory
. The method was developed by the group of William A. Goddard, III
around 1970.
, is used to describe every electron pair in a molecule. The orbitals for each electron pair are expanded in terms of the full basis set and are non-orthogonal. Orbitals from different pairs are forced to be orthogonal - the strong orthogonality condition. This condition simplifies the calculation but can lead to some difficulties.
, can also be used to do a variety of restricted open-shell Hartree-Fock
calculations, such as those with one or three electrons in two pi-electron molecular orbitals while retaining the degeneracy of the orbitals. This wave function is essentially a two-determinant function, rather than the one-determinant function of the restricted Hartree-Fock method.
Valence bond theory
In chemistry, valence bond theory is one of two basic theories, along with molecular orbital theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds...
method that uses flexible orbitals in the general way used by modern valence bond theory
Modern valence bond theory
Modern valence bond theory is the term used to describe applications of valence bond theory with computer programs that are competitive in accuracy and economy with programs for the Hartree-Fock method and other molecular orbital based methods. The latter methods dominated quantum chemistry from...
. The method was developed by the group of William A. Goddard, III
William A. Goddard, III
William Andrew Goddard III is the Charles and Mary Ferkel Professor of Chemistry and Applied Physics, and Director, Materials and Process Simulation Center at the California Institute of Technology. He obtained his B.S. from the University of California, Los Angeles, in 1960 and his Ph.D...
around 1970.
Theory
The generalized Coulson-Fisher for the hydrogen molecule, discussed in Modern valence bond theoryModern valence bond theory
Modern valence bond theory is the term used to describe applications of valence bond theory with computer programs that are competitive in accuracy and economy with programs for the Hartree-Fock method and other molecular orbital based methods. The latter methods dominated quantum chemistry from...
, is used to describe every electron pair in a molecule. The orbitals for each electron pair are expanded in terms of the full basis set and are non-orthogonal. Orbitals from different pairs are forced to be orthogonal - the strong orthogonality condition. This condition simplifies the calculation but can lead to some difficulties.
Calculations
GVB code in some programs, particularly GAMESS (US)GAMESS (US)
GAMESS is a computational chemistry software program that stands for General Atomic and Molecular Electronic Structure System. The original code started on October 1, 1977 as a National Resources for Computations in Chemistry project. In 1981, the code base split into GAMESS and GAMESS variants,...
, can also be used to do a variety of restricted open-shell Hartree-Fock
Hartree-Fock
In computational physics and chemistry, the Hartree–Fock method is an approximate method for the determination of the ground-state wave function and ground-state energy of a quantum many-body system....
calculations, such as those with one or three electrons in two pi-electron molecular orbitals while retaining the degeneracy of the orbitals. This wave function is essentially a two-determinant function, rather than the one-determinant function of the restricted Hartree-Fock method.