PES of coordination compound as derived from DMM

Now we can turn to deriving a true mechanistic (MM-like) model for CCs of nontransition element by excluding the ESVs V. Inserting eq. (4.49) in eq. (4.47) we get for the energy  

This expression contains in a condensed form all the results which are obtained in detail in [41], namely the theory of ligand influence which can be considered as one describing a response of molecular geometry to the chemical substitution. For example, optimizing the above expression with respect to 6q) yields the response of the complex geometry to the substitution of the ligands. One easily gets the close expression for it  

The MM-like model of complexes of nontransition elements requires even less than is given by eq. (4.50) only the first and the second term in the first row. They represent the bare harmonic dependence of the energy on the nuclear shifts and the renormalizations of the respective harmonic constants due to adjustment of the electronic structure to these shifts  

As mentioned previously, the specifics of the central atoms in CCs are determined by the structure of the supermatrix II, which is in its turn predefined by the structure of the carrier space of the CLS group and by the number of electrons in it. Indeed, the supermatrix II of the polarization propagator is particularly simple in the basis of the eigenstates of the Fock operator Fq. Its matrix elements then are  

The simplest approximate description of II corresponds to what is known as the frontier orbitals approximation, where only the highest occupied and lowest unoccupied MOs (HOMO and LUMO, respectively) are involved. Within it one gets  

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