The Spin-Coupled Valence Bond Method

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]). 

P.C.H. Mitchell, G.M. Raos, P.B. Karadakov, J. Gerratt D.L. Cooper (1995). J. Chem. Soc. Faraday Trans., 91, 749-758. Catalytic chemistry of furan and thiophene—ab initio calculations, using the spin-coupled valence-bond method, of the interaction of furan and thiophene with a positively charged center. 

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. 

Cooper, D. L. Cerratt, J. Raimondi, M. Nature 1986,323,699 reported a spin-coupled valence bond method for calculation of molecular electronic structure and concluded that "our results suggest that the Kekule description of benzene, as expressed in the classic VB form, is in fact much closer in reality than is a description in terms of delocalized molecular orbitals."... 

It is not appropriate here to present a detailed account of the formalism of spin-coupled valence bond theory, and of its computational implementation. Instead, we provide a brief, almost entirely qualitative overview of our method, concentrating on the most interesting results for benzenoid aromatic molecules. Further details may be found in the literature cited and in various recent reviews [1,2,3]. 

We have indicated the ability of spin-coupled valence bond (SCVB) calculations to provide compact, though accurate, nonorthogonal configuration interaction expansions for ground and excited states. These wavefunctions can be made even more compact using the SCVB method, which starts from direct... 

Generalized valence bond perfect pairing (GVB/PP) and spin-coupled valence bond (SCVB) calculations for tri- and polyatomic molecules use multicentre, delocalized orbitals (i.e. 3-centre or many-centre orbitals) to accommodate the active space electrons. To quote Ref 27 The GVB/PP wavefimctions are antisymmetrized products of paired orbitals and represent a single valence bond structure.. .. The SC method is based on a single configuration in which each electron is described by a distinct orbital. The complete spin state is utilized. For example, a 4-electron 3-centre SC wavefunction involves four non-orthogonal 3-centre or-... 

Texts on alternative types of valence-bond theory include those of references 1 and 2. Reference 3 provides a review of modern ab initio methods and classical valence-bond approaches to electronic structure. References 4 and 5 provide reviews of generalised and spin-coupled valence-bond theory. Both of these theories can use delocalised orbitals that involve more than two atomic centres to accommodate the active-space electrons. In references 6-8, overviews are presented of aspects of increased-valence theory. 

Let us examine one-quarter occupancy of the valence band. The three-quarters case of (SN)x is similar, since the only difference is that electrons are replaced by holes. The solution with equal bond lengths is obviously the spin-coupled spin density wave (SDW) state seen at the top of Figure 18.20. The HOMO is shown in gray. A better analysis should include all the occupied orbitals. A complete analysis should be of an ab initio type and involve total energies. Here, the spin-coupled case was obtained by using the UHF method, which allows different spins on different atoms. In the solution, the bond order is equally distributed over the bond and therefore there are equal bond lengths. 

Other theoretical treatments which have been applied to considerations of antiaromaticity include spin-coupled theory, topological methods,and quantum statistical definitions. The relevance of spin-coupled theory has been described The comparison between the (spin-coupled) descriptions of cyclobutadiene, benzene, and cyclooctatetraene clearly indicates that the reason for the lower stability and higher reactivity of antiaromatic systems is due to a simultaneous unfavorable coupling of the spins of all valence orbitals to triplet pairs, which discourages bonding interactions and suggests diradical character. ... 

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... 

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