Valence Bond Wave Functions with Semilocalized AOs

2 Valence Bond Wave Functions with Semilocalized AOs 

One inconvenience of the expression of FvB-fuii (Eq. 3.4) is its relative complexity compared to the simple Heitler—London function (Eq. 3.2). 

a and b are purely localized AOs, while pa and pfc are slightly delocalized or semilocalized . In fact, experience shows that the Coulson—Fischer orbitals pa and cp which result from the optimization of the coefficient e by energy minimization, are generally not very delocalized (e 1), and as such they can be viewed as distorted orbitals that remain atomic-like in nature. However, minor as this may look, the slight delocalization renders the Coulson—Fischer wave function equivalent to the VB-full wave function (Eq. 3.4a) with the three classical structures. A straightforward expansion of the Coulson—Fischer wave function leads to the linear combination of the classical structures in Equation 3.6. 

the Coulson—Fischer representation keeps the simplicity of the covalent picture while treating the covalent—ionic balance by embedding the effect of the ionic terms in a variational way, through the delocalization tails. The Coulson—Fischer idea was subsequently generalized to polyatomic molecules and gave rise to the GVB and SC methods, which were mentioned in Chapter 1 and will be discussed later. 

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