Correlation effects and Pekar bipolaron (arbitrary electron–phonon interaction)

Abstract The Buimistrov–Pekar method of canonical transformation was used to calculate the energies of the lowest singlet and triplet terms of bipolarons in crystals with ionic binding. An arbitrary electron–phonon interaction described by the Fröhlich Hamiltonian 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 the Buimistrov–Pekar method is lower than all those found by Adamowski and Bednarek in the framework of direct variational approaches, and only slightly exceeds (relative error <0.3%) those obtained by Verbist, Peeters, and Devreese by integration over trajectories for α ≤ 7. 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. Study of a wave function of 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 this paper have yielded 1.173 a.u. for the hydrogen molecule energy, which is in good agreement with the experimental value.

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