Contrasting unitary transformations for the standard bipolaron model

The well known bipolaron prototype model [two sites, two electrons, two spi ns, single oscillator ("222 model")] is considered, involving a Frohlich-ty pe electron-phonon interaction and a Hubbard term. As in the one-electron c ase a Fulton-Gouterman transcription lends to a symmetry-adequate definitio n 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 w ithin the vibrational subspace. Several different combinations of these ope rators are used as generators. Comparing the optimized results with the res ults of an exact numerical diagonalization, it is found that one of these c ombinations, involving all three basic operators is the superior one in all coupling regions. Specifically it is found that in the intermediate and st rong coupling regimes the "reflection" operation is essential. A combinatio n of squeezing and displacement alone, as frequently used in literature, ca nnot reproduce the two-peaked nature of the vibrational wave functions. [S0 163-1829(99)01129-7].