VB exchange integral

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. 

We now want to understand the origin of the curious rhomboidal structure and the nature of the branching-space vectors Xj and X2. In the same fashion as for Eqn (3.4), in Eqn (3.5) we give the matrix elements between the VB structures in Figure 3.6 in terms of the exchange integrals. We also... 

We should stress at this point that the conditions in Eqn (3.8) are rigorous within the VB model that we have presented. The difficulty is that the exchange integrals are not easily extracted from an ab initio calculation, so the conditions are normally used in a quahtative way. As we have discussed previously for the 2 + 2 cycloaddition of two ethylenes, we have type interactions (i.e., the interactions Kx involve 13 a—it interactions) for which the exchange integrals behave quite differently. Nevertheless,... 

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