Generalized valence bond

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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]

Contents

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.

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Per-Olov Löwdin was a Swedish physicist, professor at the University of Uppsala from 1960 to 1983, and in parallel at the University of Florida until 1993.

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Modern valence bond theory is the application of valence bond theory [ VBT ] with computer programs that are competitive in accuracy and economy with programs for the Hartree–Fock or post-Hartree-Fock methods. The latter methods dominated quantum chemistry from the advent of digital computers because they were easier to program. The early popularity of valence bond methods thus declined. It is only recently that the programming of valence bond methods has improved. These developments are due to and described by Gerratt, Cooper, Karadakov and Raimondi (1997); Li and McWeeny (2002); Joop H. van Lenthe and co-workers (2002); Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004)

Valence bond (VB) computer programs for modern valence bond calculations:-

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Restricted open-shell Hartree–Fock (ROHF) is a variant of Hartree–Fock method for open shell molecules. It uses doubly occupied molecular orbitals as far as possible and then singly occupied orbitals for the unpaired electrons. This is the simple picture for open shell molecules but it is difficult to implement. The foundations of the ROHF method were first formulated by Clemens C. J. Roothaan in a celebrated paper and then extended by various authors, see e.g. for in-depth discussions.

Jaguar is a computer software package used for ab initio quantum chemistry calculations for both gas and solution phases. It is commercial software marketed by the company Schrödinger. The program was originated in research groups of Richard Friesner and William Goddard and was initially called PS-GVB.

Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term ab initio was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene. The background is described by Parr. Ab initio means "from first principles" or "from the beginning", implying that the only inputs into an ab initio calculation are physical constants. Ab initio quantum chemistry methods attempt to solve the electronic Schrödinger equation given the positions of the nuclei and the number of electrons in order to yield useful information such as electron densities, energies and other properties of the system. The ability to run these calculations has enabled theoretical chemists to solve a range of problems and their importance is highlighted by the awarding of the Nobel prize to John Pople and Walter Kohn.

In computational chemistry, spin contamination is the artificial mixing of different electronic spin-states. This can occur when an approximate orbital-based wave function is represented in an unrestricted form – that is, when the spatial parts of α and β spin-orbitals are permitted to differ. Approximate wave functions with a high degree of spin contamination are undesirable. In particular, they are not eigenfunctions of the total spin-squared operator, Ŝ2, but can formally be expanded in terms of pure spin states of higher multiplicities.

References

  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)
  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.
  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