The electron-vibrational problem of the general nonadiabatic molecular systems has been solved by means of the quasi-particle transformations. The SCF ab initio solution of the nonadiabatic fermion Hamiltonian yields stabilization of the electronic ground-state energy due to electron-phonon interaction and it also gives the corrections to the one-and two-particle terms. Two two-particle correction yields effective attractive electron-electron interaction, but in the form different from Frolich's effective electron-electron interaction term. In contrast to the standard electron-phonon Hamiltonian of solid-state physics that does not take into account the possible effects of nonadiabaticity of a system, the presented nonadiabatic theory yields also one-particle corrections. The presence of this term in the Hamiltonian might play a crucial role in the theory of superconductivity since the superconductors are nonadiabatic systems. Since the quasi-particle theory of vibrational energy calculations for nonadiabatic molecules is extremely extensive and will be published elsewhere [lo], we restrict ourselves only to the schematic way of derivation, with the focus being placed on the fermion part of the nonadiabatic e1.-vibr. Hamiltonian.

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An exact solution for the electron-vibrational problem of the nonadiabatic molecular system has been obtained. By the quasi-particle transformation technique, the fermionic Hamiltonian has been derived and solved at the ab initio level. Results clearly and unambiguously show that the gap formation due to nonadiabatic electron-phonon coupling is mediated by the one-particle electron-phonon interaction term, whereas the two-particle one represents just a correction to the correlation energy. The temperature dependence of the gap and electronic specific heat connected with the electron-phonon coupling have also been derived.

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AbSttSdThe partitioning of the vibrational-electronic Hamiltonian is presented. This partitioning is based on a new quasiparticle transformation that is constructed in such a way that the adiabatic approximation is included into the unperturbed Hamiltonian; nonadiabacity, anharmonicity, and electron correlation are treated as perturbations. We also present the second quantization treatment for bosons. The many body perturbation theory expansion for the vibrational-electronic Hamiltonian is suggested. A comparison of this approach is made with gradient techniques.