Comments to a series of works by V.K. Mukhomorov on the theory of a continuum polaron and two-center bipolaron (axially symmetrical quasimolecular dimer)

TL;DR

This paper critically examines Mukhomorov's work on polarons and bipolarons, clarifying misconceptions about the minimization approach and confirming the virial theorem's applicability in strong coupling regimes.

Contribution

It refutes Mukhomorov's claim that constrained minimization is necessary and demonstrates the virial theorem's validity for bipolaron states with interelectronic correlations.

Findings

V.K. Mukhomorov's minimization approach is incorrect.

The virial theorem holds for bipolaron states in strong coupling.

Two-center bipolaron minima are due to limited variational functions.

Abstract

Some critical remarks are made regarding a series of works by V.K. Mukhomorov dealing with polarons and oscillatory and rotational spectrum of a large-radius bipolaron near a subsidiary minimum corresponding to its two-center configuration. It is shown that V.K. Mukhomorov's conclusion that by varying the bipolaron functional one should look for a constrained rather than absolute minimum is erroneous. Consideration of interelectronic correlations corresponding to a direct dependence of the wave function of the studied system on the distance between the electrons does not break the virial theorem. In the strong coupling limit the virial theorem holds true for both one-center and two-center bipolaron states, the latter representing a subsidiary minimum which arises due to a choice of an insufficiently versatile variation function.