Molecular aspects of superconductivity: The role of the one-particle term at the gap formation

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.