Generalized valence bond wavefunctions

A. F. Voter, W. A. Goddard, III, Chem. Phys. 57, 253 (1981). A Method for Describing Resonance between Generalized Valence Bond Wavefunctions. 

J.H. van Lenthe and G.G. Balint-Kurti, VBSCF The optimisation of non-orthogonal orbitals in a general (Valence Bond) wavefunction, in 5th seminar on Computational Methods in Quantum Chemistry (Groningen, 1981). 

Basis-set optimization is thus the hallmark of the present author s approach. Nevertheless, GMCSC wavefunctions can otherwise be viewed as more flexible versions of Resonating Generalized Valence Bond (R-GVB) wavefunctions [9]. The extra flexibility arises from GMCSC s freedom from the constraint of... 

It can be seen that the first two terms are the same as the valence bond wavefunction, and there are an additional two terms. The first two are commonly called the covalent terms because each has the electrons associated with both centers. The final two are known as ionic terms because each places two electrons at one center (i.e. H+ H and H H ). Valence bond theory generally neglects ionic terms of this type, whereas in MO theory the covalent and ionic terms are treated equally. 

In certain Instances it may be appropriate to determine the ground state wavefunction using the generalized valence-bond (GVB) technique (21). This is especially true for closed shell anions where the pair of electrons in the highest occupied molecular orbital (HOMO) may be described by the wavefunction... 

One popular wavefunction of this form is the generalized valence bond (GVB) expansion " . With this method an N-electron molecule is described in terms of N non-orthogonal orbitals and an energy-optimized spin function as... 

Intermediate between the spin-coupled expansion in N orthonormal sets and the MO expansion in a single set is an expansion in just two distinct sets. The first term of (17) now becomes the electron-pair wavefunction of Hurley, Lennard-Jones and Pople " , in which pairs of orbitals (i/ i,i/ 2X (i/ j, 1/ 4),..., overlap with each other, but different pairs are (strongly) orthogonal. Much work has been carried out on this model by Goddard and coworkers under the nomenclature generalized valence bond (GVB) wavefunction . ... 

The generalized valence bond (GVB) method developed by Gaddard and coworkers does not employ a full Cl in the valence shell, but includes only the configurations needed to describe proper dissociation of a chemical bond. As will be demonstrated later, such a wavefunction represents a restricted form of the CASSCF wavefunction, where the active subspace is partitioned into subsets with a fixed number of electrons occupying the orbitals in each subset (acutally the GVB function is further restricted by allowing only specific spin couplings within each subset). 

A rapid development of the field was initiated by the formulation of the AIMD by Car and Parrinello based on a DF procedure employing a plane wave expansion of the electronic wavefunction. Related approaches based on the rigorous BO approximation for separation of nuclear and electronic degrees of freedom have been proposed. At the same time other AIMD procedures have been developed in the framework of the HF (AIMD-HF) (cf. Ref. 17 and references therein), the generalized valence bond, and recently the nonlocal density functional (AlMD-B-LYP) methods. All these approaches employ Gaussian basis sets localized at the nuclei. 

---