Valence-bond method generalized

Ionova I V and Carter E A 1995 Crbital-based direct inversion in the iterative subspace for the generalized valence bond method J. Chem. Phys. 102 1251... 

Most of the commonly used electronic-structure methods are based upon Hartree-Fock theory, with electron correlation sometimes included in various ways (Slater, 1974). Typically one begins with a many-electron wave function comprised of one or several Slater determinants and takes the one-electron wave functions to be molecular orbitals (MO s) in the form of linear combinations of atomic orbitals (LCAO s) (An alternative approach, the generalized valence-bond method (see, for example, Schultz and Messmer, 1986), has been used in a few cases but has not been widely applied to defect problems.)... 

The precise quantum cluster calculations of the electronic structure of SC ceramics were performed in Refs. [13,17,21]. Guo et al. [13] used the generalized valence bond method, Martin and Saxe [17] and Yamamoto et al. [21] performed calculations at the configuration interaction level. But in these studies the calculations were carried out for isolated clusters, the second aspect of the ECM scheme, see above, was not fulfilled. The influence of crystal surrounding may considerably change the results obtained. 

Another, quite independent theoretical assessment, based on ab initio calculations and the generalized valence bond method, found that the barrier height for cis,trans isomerization of cyclopropane is essentially the same (calculated value, 60.5 kcal mol-1) whether one or both of the thermal CH2 groups are rotated after opening of the CC bond 243. Thus, in 1972, there seemed to be general agreement among theoreticians that the stereomutations of cyclopropane should take place with k, about equal to kl2. 

RGVB resonating generalized valence bond method... 

Generalized Valence Bond method with one pair of correlated orbitals... 

Goodgame, M. M., and W. A. Goddard III (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 Crj and Moj. Phys. Rev. Lett. 54, 661-64. 

The generalized valence bond method [55] can be considered as a special APSG technique, where each geminal consists only of two spatial orbitals. 

The choice of reference space for MRCI calculations is a complex problem. First, a multieonfigurational Hartree-Fock (MCSCF) approach must be chosen. Common among these are the generalized valence-bond method (GVB) and the complete active space SCF (CASSCF) method. The latter actually involves a full Cl calculation in a subspace of the MO space—the active space. As a consequence of this full Cl, the number of CSFs can become large, and this can create very long Cl expansions if all the CASSCF CSFs are used as reference CSFs. This problem is exacerbated when it becomes necessary to correlate valence electrons in the Cl that were excluded from the CASSCF active space. It is very common to select reference CSFs, usually by their weight in the CASSCF wave function. Even more elaborate than the use of a CASSCF wave function as the reference space is the seeond-order Cl, in which the only restriction on the CSFs is that no more than two electrons occupy orbitals empty in the CASSCF wave function. Such expansions are usually too long for practical calculations, and they seldom produce results different from a CAS reference space MRCI. 

In order to gain both a more local and a more accurate description of the bonding in SF we introduced intra-pair correlations via the perfect pairing generalized valence bond method (GVB-PP) (35). The valence electrons are described by generalized Heitler-London pairs,... 

Table 11.2. Cationic Metal-Hydride and Metal-Methyl Bond Dissociation Energies (heal mol ) Calculated by a Generalized Valence Bond Method (References 34 and 35) ...

Chapter 4 discusses configuration interaction (Cl) and is the first of the four chapters that deal with approaches incorporating electron correlation. One-electron density matrices, natural orbitals, the multiconfiguration self-consistent-field approximation, and the generalized valence bond method are... 

---