Variational band theory of vibronic polarons in crystals. II. Extending Merrifield's Ansatz

Merrifield’s Variational Ansatz is extended so as to cover the case of two electronic bands mixed by an Einstein phonon. The Hamiltonian is composed of the local and kinetic (hopping) energies in the absence of vibrations, the vibrational energy, and a mixing band-off-diagonal part linear in the electron-phonon coupling, all expressed in second quantization terms. The variational eigenstate is a linear combination of Merrifield states for either electronic band. We derive equations for the phonon Fourier amplitudes and for the fractional contribution of either electronic band.