Generalized valence bond

The generalized valence bond (GVB) is a method in valence bond theory 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.^[1]^[2]

Theory

The generalized Coulson–Fischer theory for the hydrogen molecule, discussed in Modern valence bond theory, 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), can also be used to do a variety of restricted open-shell Hartree–Fock calculations,^[3] 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

^ Goddard, W. A., Dunning, T. H., Hunt, W. J. and Hay, P. J. (1973), "Generalized valence bond description of bonding in low-lying states of molecules", Accounts of Chemical Research, 6 (11): 368, doi:10.1021/ar50071a002{{citation}}: CS1 maint: multiple names: authors list (link)
^ Goodgame MM, Goddard WA (February 1985), "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", Physical Review Letters, 54 (7): 661–664, Bibcode:1985PhRvL..54..661G, doi:10.1103/PhysRevLett.54.661, PMID 10031583.
^ Muller, Richard P.; Langlois, Jean-Marc; Ringnalda, Murco N.; Friesner, Richard A.; Goddard, William A. (1994), "A generalized direct inversion in the iterative subspace approach for generalized valence bond wave functions", The Journal of Chemical Physics, 100 (2): 1226, Bibcode:1994JChPh.100.1226M, doi:10.1063/1.466653

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[Goddard1973-1] Goddard, W. A., Dunning, T. H., Hunt, W. J. and Hay, P. J. (1973), "Generalized valence bond description of bonding in low-lying states of molecules", Accounts of Chemical Research, 6 (11): 368, doi:10.1021/ar50071a002{{citation}}: CS1 maint: multiple names: authors list (link)

[pmid10031583-2] Goodgame MM, Goddard WA (February 1985), "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", Physical Review Letters, 54 (7): 661–664, Bibcode:1985PhRvL..54..661G, doi:10.1103/PhysRevLett.54.661, PMID 10031583.

[Muller1994-3] Muller, Richard P.; Langlois, Jean-Marc; Ringnalda, Murco N.; Friesner, Richard A.; Goddard, William A. (1994), "A generalized direct inversion in the iterative subspace approach for generalized valence bond wave functions", The Journal of Chemical Physics, 100 (2): 1226, Bibcode:1994JChPh.100.1226M, doi:10.1063/1.466653

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