VB configuration mixing

L. Eberson, R. Gonzalez-Luque, M. Merchan, F. Radner, B. O. Roos, S. Shaik, J. Chem. Soc., Perkin Trans 2, 463 (1997). Radical Cations of Non-Alternant Systems as Probes of the Shaik-Pross VB Configuration Mixing Model. 

Soc. Perkin Trans. 2, 463 (1997). Radical Cations of Non-Alternant Systems as Probes of the Shaik-Pross VB Configuration Mixing Model. 

BEP = Bell-Evans-Polanyi BOVB = breathing orbital VB FMVB = fragments in molecules based VB HL structure = Heitler-London structure PRS = perfectly resonating state VBCM = VB configuration mixing VBSCD = VB state correlation diagram VBSCF = self-consistent field VB. 

This section illustrates therefore that both ground and excited states of the R—X bond may be simply described by either VB or MO configurations. These configurations are mutually related and an improved wave-function may be obtained through configuration mixing. 

An analysis in terms of VB structures (see exercise 3) shows that this configurational mixing corresponds to approximately 40% diradical character in the wave function for ozone. The RHF wave function, on the other hand, contains only 12% of the diradical VB structure (the result was obtained using Hiickel values for the coefficients of the orbitals (2 11)). It is clear from these considerations that a correct treatment of the electronic structure for the ozone molecule must be based on a multiconfigurational wave function. 

Note that the triplet MO configuration is equal to the triplet VB structure and that in the case of nonpolar bonds the singly excited MO configuration is equal to the zwitterionic VB structure (xl - )d)/V5. Configuration mixing provides a better description of the states G = 4 - A 4>2 and D = d, + A 4> , whose ionic character can vary from purely covalent to purely ionic as the value of A changes. A transformation to standard VB theory based on non-orthogonal AOs is also possible but is more complicated (Michl and BonaCid-Koutecky, 1990 Section 4.1). 

Fig. 10. A mixing diagram for the VB configurations which make up the radical anion, (R1X) . Reprinted from reference 5 a with permission of Acta Chemica Scandinavica...

Curves involving variational mixing of all the VB configurations in the basis set. Diabatic VB curves correspond to variational mixing of a subset of VB configurations which describe the bonding motif of the reactants or of the products. BEP principle... 

The SCD involves diabatic state curves of mixed character. Sometimes, however, the mixed character of the curves will conceal important information which can be revealed by looking at the VB configurations individually. Figures 5(a) versus 5(b) shows the HL and triple ionic structures for Sn2 reactions on carbon versus silicon. It is seen that the Si case is favored over the C case by having a much more stable triple ionic structure as well as a larger covalent-ionic VB mixing. Consequently, the Sn2(C) is typified by a TS and a barrier, while the Sn2(S1) case by a stable pentacoordinated species, (SiHsXa) . 

Thus, the PRS corresponds to a VB mixture of the ionic configuration (mixing coefficient A.) with the resonating HL state in which the two HL configurations contribute to the... 

It is dear, therefore, that as the atoms are pulled apart the Hartree-Fock MO solution does not go over to that of two neutral-free atoms H°H°, but instead goes over to a mixed configuration, schematically represented by [2H°H° + H+H" + H H+]. Since the energy cost for the ionic configuration is / — A = (13.6 — 0.8) eV = 12.8 eV, the Hartree-Fock MO solution dissociates incorrectly to +6.4 eV rather than zero (We have assumed the Hartree-Fock treatment of H is exact.) The Heitler-London VB solution avoids this problem by working with only the covalent configurations in the first square bracket of eqn (3.37), so that it dissodates correctly. 

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