Generalized valence bond

Generalized valence bond

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.citation | author = Goddard, W. A., Dunning, T. H., Hunt, W. J. and Hay, P. J. | year = 1973 | journal = Accounts of Chemical Research | volume = 6 | pages = 368 | doi = 10.1021/ar50071a002 ] cite journal |author=Goodgame MM, Goddard WA |title=Modified generalized valence-bond method: A simple correction for the electron correlation missing in generalized valence-bond wave functions; Prediction of double-well states for Cr2 and Mo2 |journal=Phys. Rev. Lett. |volume=54 |issue=7 |pages=661–664 |year=1985 |month=February |pmid=10031583 |doi= |url=http://link.aps.org/abstract/PRL/v54/p661]

Theory

The generalised Coulson-Fisher for the hydrogen molecule, discussed in Modern valence bond theory is generalised to describe every electron pair in a molecule. The pair of 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), can also be used to do a variety of restricted open-shell Hartree-Fock calculations,citation | author = Muller, Richard P. | year = 1994 | title = A generalized direct inversion in the iterative subspace approach for generalized valence bond wave functions | journal = The Journal of Chemical Physics | volume = 100 | pages = 1226 | doi = 10.1063/1.466653 ] 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.

References


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