Wave functions ionic terms, inclusion

Therefore, the principal role of the inclusion of the ionic term in the wave function is the reduction of the kinetic energy from the value in the purely covalent wave function. Thus, this is the delocalization effect alluded to above. We saw in the last section that the bonding in H2 could be attributed principally to the much larger size of the exchange integral compared to the Coulomb integral. Since the electrical effects are contained in the covalent function, they may be considered a first order effect. The smaller added stabilization due to the delocalization when ionic terms are included is of higher order in VB wave functions. 

As pointed out in a 1996 review of the importance of dynamic electron correlation [le], in general, addition of correlation between the active and inactive electrons stabihzes the ionic terms in the CASSCF wave functions for the active electrons. Not only in the Cope TS, but also in the TSs for other Woodward-Hoffmann-allowed, pericyclic reactions [3], the ionic terms in the RHF configuration benefit from this type of stabilization. Consequently, with the inclusion of dynamic electron correlation, the weight of the RHF configuration in the wave function for the TS increases and the energy of the TS is lowered, relative to that of the reactants and products. It is for this reason that calculations which include dynamic electron correlation usually give much lower activation enthalpies for allowed pericychc reactions than either RHF or CASSCF calculations do [le,21]. 

A valence-bond wave function like that of Eq. (20.3-7) or Eq. (20.3-20) corresponds to equally shared electrons. Inclusion of both of the two ionic terms in Eq. (20.3-10) does not correspond to ionic bonding, because one ionic term corresponds to bond polarity in one direction and the other to bond polarity in the opposite direction. For a polar molecule such as LiH a modified valence-bond wave function can be constructed by including only one ionic term ... 

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