We give an overview of studies a bipolaron stability by variational method. For bipolaron formations, a relation is established between the variational principle and the virial theorem optimizing the electronic wave functions. We present a large number of qualitative and quantitative arguments, which indicate that the Landau-Pekar bipolaron is an axially-symmetrical formation. Much attention is paid to the analysis of the influence of the Coulomb electron-electron correlations on the stability of a large bipolaron. In detail we analyzed the criteria for determining the optimal wave functions. It is established that a step-by-step increase in the flexibility of the electronic wave function due to the electron correlations does not stabilize a one-center bipolaron. We show after into account of electron-electron correlations a singlet bipolaron retains spatial axially-symmetrical. At the same time, the electron-excited triplet states of Landau-Pekar bipolaron have spherical symmetry. The results of Kasirina and Lakhno are based on the one-center bipolaron model are incorrect. Presented evidence that the correct application of the variational method and correct account of electron-electron correlations only increase the binding energy of the bipolaron but symmetry of Hartree-Fock approximation can not change. We adduce proofs which point to methodological errors of one-center bipolaron model as well as arising from their calculations incorrect physical consequences. As illustrated in this review the axially symmetric Landau-Pekar bipolaron can correctly interpret the experimentally detected spectroscopic data.
We have established mathematically that the spatial symmetry of the singlet bipolaron Landau-Pekar is axial-symmetric. At the same time, triplet states of the bipolaron are spherically symmetric formations. Increasing the flexibility of the wave function does not change the spatial symmetry of the bipolaron. Knowledge of the bipolaron symmetry allows to correctly interpret experiment.
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