Contrasting unitary transformations for the standard bipolaron model

The well known bipolaron prototype model [two sites, two electrons, two spins, single oscillator ("222 model")] is considered, involving a Frohlich-type electron-phonon interaction and a Hubbard term. As in the one-electron case a Fulton-Gouterman transcription lends to a symmetry-adequate definition of the oscillatory companion functions of the two-electron base vectors. Trial expressions for these oscillatory functions are generated by means of three unitary operators ("displacive, squeezing, and reflective") acting within the vibrational subspace. Several different combinations of these operators are used as generators. Comparing the optimized results with the results of an exact numerical diagonalization, it is found that one of these combinations, involving all three basic operators is the superior one in all coupling regions. Specifically it is found that in the intermediate and strong coupling regimes the "reflection" operation is essential. A combination of squeezing and displacement alone, as frequently used in literature, cannot reproduce the two-peaked nature of the vibrational wave functions. [S0163-1829(99)01129-7].