Electronic structures of endohedral complexes theory

Before embarking upon sophisticated quantum-chemical calculations, it is desirable to shed some light on the electronic structures of endohedral complexes using approximate techniques. An approach that is particularly suitable for such a purpose is based on a mixed variational-perturbative expression for the wavefunction of an inclusion complex HG in its electronic ground state 

In the above equation, A is the antisymmetrizer, f (H) stands for the unperturbed wavefunctions of the host, and 1(G) is the wavefunction of the guest species that is determined variationally. On the other hand, the linear combination coefficients in Eq.(16) and the corresponding ground state energy are calculated using perturbation theory. The matrix elements of the relevant electronic Hamiltonian that includes the energy of the nuclear-nuclear repulsion read 

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