Correlation eects and Pekar bipolaron

Buimistrov-Pekar method of canonical transformation was used to calculate the energies of the lowest singlet and triplet terms of bipolarons in crystals with ion binding. An arbitrary electron-phonon interaction described by Frohlich Hamilto-nian was considered. It was shown that in the whole parametric range of electron-phonon interaction, the value of the free bipolaron ground state energy obtained by Buimistrov-Pekar method is the lowest than those found in the framework of direct variational approaches [1] and only slightly exceed (relative error < 0:3%) the ones obtained by integration over trajectories for 7 [2]. The calculations have shown that any metastable triplet states corresponding to the lowest triplet term of a bipolaron are absent for all the parameters of the electron-phonon interaction, the results being in complete analogy with Hill's theorem about the absence of any bound excited states for an H ion [3]. The study of the wave function of a more general form has demonstrated that a two-center bipolaron is energetically less advantageous than a one-center one for all the parameters of the electron-phonon interaction. Control calculations performed with the system of functions used in the paper have yielded 1:173 a.u. for the hydrogen molecule energy which is in good agreement with the experimental value.