Spin Coupled Valence Bond

The final description, either in terms of a Cl wave function written as a linear combination of two determinants built from delocalized MOs (eq. (7.4)), or as a VB wave function written in terms of two VB-HL structures composed of AOs (eq. (7.7)), is identical. 

For the H2 system, the amount of ionic HL structures determined by the variational principle is 44%, close to the MO-HF value of 50%. The need for including large atnounts of ionic structures in the VB formalism is due to the fact that pure atomic orbitals are used. 

Consider now a covalent VB function build from atomic orbitals which are allowed to distort from the pure atomic shape. 

Such a VB function is known as a Coulson-Fischer (CF) type. The c constant is fairly small (for H2 c 0.04), but by allowing the VB orbitals to adopt the optimum shape, the need for ionic VB stractures is strongly reduced. Note that the two VB orbitals in eq. (7.8) are not orthogonal, the overlap is given by 

Compared to the overlap of the undistorted atomic orbitals used in the HL wave function, which is just 5ab. it is seen that the overlap is increased (c is positive), i.e. the orbitals distort so that they overlap better in order to make a bond. Although the distortion is fairly small (a few %) this effectively eliminates the need for including ionic VB terms. When c is variationally optimized, the MO-CI, VB-HL and VB-CF wave functions (eqs. (7.4), (7.7) and (7.8)) are all completely equivalent. The MO approach incorporates the flexibility in terms of an excited determinant, the VB-FIL in terms of ionic structures, and the VB-CF in terms of distorted atomic orbitals. 

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Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

T orbital for benzene obtained from spin-coupled valence bond theory. (Figure redrawn from Gerratt ], D L oer, P B Karadakov and M Raimondi 1997. Modem valence bond theory. Chemical Society Reviews 87 100.) figure also shows the two Kekule and three Dewar benzene forms which contribute to the overall wavefunction Kekuleform contributes approximately 40.5% and each Dewar form approximately 6.4%. 

The generalization of a Coulson-Fischer type wave function to the molecular case with an arbitrary size basis set is known as Spin Coupled Valence Bond (SCVB) theory. ... 

Cooper, D. L., Gerratt, J., and Raimondi, M. The Spin-Coupled Valence Bond Description of Benzenoid Aromatic Molecules. 153, 41-56 (1990). 

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]). 

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. 

Resonance between three 7t-complex structures might lead to stabilization of 1 in the sense of 7t-aromatic stabilization involving the six CC bond electrons. Therefore, Dewar8 has discussed the stability of 1 in terms of a u-aromatic stabilization (Section V). However, spin-coupled valence bond theory clearly shows that 1 cannot be considered as the aromatic benzene51. The 7t-complex description of 1 is a (very formal) model description, which should be discarded as soon as it leads to conflicting descriptions of the properties of 1. This will be discussed in Section V. 

FIGURE 17. Schematic representation of the symmetry-unique spin-coupling patterns in cyclopropane (above) and benzene (below). In the case of cyclopropane, carbon hybrid orbitals and, in the case of benzene, carbon p n orbitals are shown. For each structure, Gallup-Norbeck occupation numbers as determined by spin-coupled valence bond theory are given. All data from Reference 51... 

SCVB spin-coupled valence bond method... 

The Spin-Coupled Valence Bond Description of Benzenoid Aromatic Molecules... 

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]. 

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