Valence bond calculations, spin-coupled

Special attention has been dedicated to the study of the basis set superposition error (BSSE). The SCF-Ml algorithm which excludes the BSSE from the SCF function was employed. A multi configuration version of it, particularly suited to study proton transfer effects, has been formulated. The use of these techniques has led to binding energy values which show a better stability against variation of the basis set, when compared with standard SCF results. For a more complete evaluation of the advantages of the a priori strategy to avoid BSSE see references [47-50], where applications to the study of the water properties are reported, and reference [51], where the Spin Coupled Valence Bond calculations for the He-LiH system are presented. 

According to the relationship between three-membered rings and 7r-complexes, cyclopropane can be considered as a resonance hybrid of three equivalent methylene-ethene n-complexes Of course, such Ti-complexes do not exist but this is also true in the case of the two cyclohexatriene resonance structures normally used to present benzene. Spin-coupled valence bond calculations of Karadakov and coworkers reveal that there is a small but significant contribution of 3.7% to the electronic structure of 1 resulting from 7r-com-plex structures (see Section V. E). This indicates that the Ti-complex description of is not totally unreasonable and, although seldom used, helps to unravel some of the peculiarities of bonding in 1 ... 

Estimation of resonance energy by spin-coupled valence bond calculations [129] and the application of newly developed aromaticity indices considering the cyclic x-electron delocalization [142, 143] have confirmed that [3]- and [6]radialene are nonaromatic. As far as the magnetic criterion for aromaticity of conjugated... 

As far as the molecular calculation is concerned, the use of an ab initio method is necessary for an adequate representation of the open-shell metastable N (ls2s) + He system with four outer electrons. The CIPSI configuration interaction method used in this calculations leads to the same rate of accuracy as the spin-coupled valence bond method (cf. the work on by Cooper et al. [19] or on NH" + by Zygelman et al. [37]). 

The combination of modem valence bond theory, in its spin-coupled (SC) form, and intrinsic reaction coordinate calculations utilizing a complete-active-space self-consistent field (CASSCF) wavefunction, is demonstrated to provide quantitative and yet very easy-to-visualize models for the electronic mechanisms of three gas-phase six-electron pericyclic reactions, namely the Diels-Alder reaction between butadiene and ethene, the 1,3-dipolar cycloaddition of fulminic acid to ethyne, and the disrotatory electrocyclic ringopening of cyclohexadiene. 

Calculations of nuclear spin-spin couplings by Karplus and co-workers (60) using valence bond functions have been gratifyingly successful. It was to be expected that valence bond functions would be more accurate than LCAO MO functions for this purpose since the former include explicitly effects of spin correlation. For interactions between nonbonded nuclei such as occur, for example, between the hydrogen atoms of CH4 or NH4+, structures of the forms (61)... 

The latter was developed as a single-configuration method, complemented by non-orthogonal configuration-interaction calculations exploiting virtual orbitals in the Spin-Coupled Valence Bond (SCVB) approach [5] (for a review, see e.g. Ref. [6]). More recently, the use of perturbative virtuals has been introduced, giving rise to the SCVB variant of the method [7] [8]. There are further accounts of SCVB in this volume. 

There are many texts that make the point very clearly that the bonding in a molecule such as SFfi has very little to do with the availability of d atomic orbitals, but this is normally done in the context of MO theory, whereas the general ideas of utilizing d orbitals are much more closely allied with the ideas of classical valence bond theory. This, perhaps, is one of the reasons for the continued survival of such models. The purpose of this Chapter is to describe various calculations which have been performed using modern valence bond theory, in its spin-coupled form, resulting in a useful aide memoire which we term the democracy principle. We argue that there are no significant qualitative differences between the hypercoordinate nature of first-row, second-row and noble gas atoms in appropriate chemical environments. 

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