GVB method

When most quantum ohemists were pursuing improvements in the moleoular orbital method, he returned to the valenoe bond theory and developed the so-oalled GVB methods that allow eleotron oorrelation to be inoluded within a valenoe bond framework... 

One widely used valence bond theory is the generalised valence bond (GVB) method of Goddard and co-workers [Bobrowicz and Goddard 1977]. In the simple Heitler-London treatment of the hydrogen molecule the two orbitals are the non-orthogonal atomic orbitals on the two hydrogen atoms. In the GVB theory the analogous wavefunction is written ... 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

Localized molecular orbital/generalized valence bond (LMO/GVB) method, direct molecular dynamics, ab initio multiple spawning (AIMS), 413-414 Longuet-Higgins phase-change rule conical intersections ... 

When atomic orbitals are derived for each carbon of the rr-electron system of benzene by the GVB method, they are somewhat more spread out than simple carbon p orbitals (Figure 21-12). Use of these orbitals in VB calculations... 

One more example of the CASSCF procedure will be outlined calculating the barrier to rotation around the CC double bond in ethene. Step 2, orbital localization, showed nicely localized orbitals when NBO localization was used, but the orbitals were harder to identify with Boys localization. For a CAS(2,2)/6-31G optimization the active orbitals chosen were the n and 7t MOs, and for a CAS(4,4)/6-31G optimization the n, n, cr and cr MOs. The input structures were the normal planar ethene and perpendicular (90° twisted) ethene. Optimization and frequency calculations gave a minimum for the planar and a transition state for the perpendicular structures. The energies (without ZPE, for comparison with those calculated with the GVB method by Wang and Poirier [71]) were ... 

The generalized valence bond (GVB) method was the earliest important generalization of the Coulson—Fischer idea to polyatomic molecules (13,14). The method uses OEOs that are free to delocalize over the whole molecule during orbital optimization. Despite its general formulation, the GVB method is usually used in its restricted form, referred to as GVB SOPP, which introduces two simplifications. The first one is the perfect-pairing (PP) approximation, in which only one VB structure is generated in the calculation. The wave function may then be expressed in the simple form of Equation 9.1, as a product of so-called geminal two-electron functions ... 

The GVB and SC methods provide wave functions that are, of course, much more compact than the corresponding valence—CASSCF one (e.g., only 14 spin-coupling modes for methane with the SC method, and a single one with the GVB method). Owing to this difference in size, the GVB and SC methods cannot be expected to include the totality of the nondynamical correlation, even if these two methods treat well, by definition, the left—right correlation for each bond of the molecule. Physically, this is because the various local ionic... 

Other than the GVB method that is now implemented in many packages, here we offer brief descriptions of the main VB softwares that we are aware of and with which we had some experience to varying degrees. 

The BDEs provided by the various VB methods are displayed in Table 10.2. Inspection of the first four entries shows that the HF method has a large negative BDE, while the CAS and GVB methods lead to positive BDEs. The full valence-CASSCF energy, in the second entry, is lower than... 

Although the emphasis in ab initio calculations in recent years has been on calculations using the MO approach, alternative methods have not been neglected, particularly Valence Bond (VB) methods of various types. Particularly promising has been the work of Goddard and co-workers with the so-called Generalized Valence Bond (GVB) method.13... 

The GVB method avoids a major deficiency of the HF method, namely the incorrect dissociation behaviour of the wavefunction, by taking the wavefunction to be of the form (6),108 where GJ is a group operator that simultaneously takes care of... 

BH has been extensively studied by Goddard during the development of the GVB methods. Early calculations were reported both with (SOGI) and without spin optimization (GI).163 154 Contributions from other spin functions than the usual VB function (13) are negligible, and the SOGI and GVB calculations give very similar... 

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