Semi-empirical Parametrization of the VB Hamiltonian

The VB potential surfaces 1E and 3 7s can be approximated by analytical Morse and anti-Morse functions  

The parameters D and a can be obtained by fitting 1E to the actual ground state of the given molecule (D is determined by the observed bond dissociation energy and a is determined by the vibrational force constant). This allows one to express J and K in terms of available experimental information. That is, from eqs. (1.47), (1.49), and (1.52) we obtain 

The covalent nature of the chemical bond changes significantly when the 

The potential surfaces Eg, Hn, and H22 of the HF molecule are described in Fig. 1.6. These potential surfaces provide an instructive example for further considerations of our semiempirical strategy (Ref. 5). That is, we would like to exploit the fact that Hn and H22 represent the energies of electronic configurations that have clear physical meanings (which can be easily described by empirical functions), to obtain an analytical expression for the off-diagonal matrix element H12. To accomplish this task we represent Hn, H22, and Eg by the analytical functions 

With the approximated functions for e1 and e2 and with a Morse potential, M, that describes the observed properties of Eg we can solve eq. (1.56) and obtain 

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