Formulation to Include Phonon Effects in the Lattice-Statics Analysis of Electronic Defects and Polarons in Ionic Crystals

The Hamiltonian is derived for a dynamical crystal lattice of discrete ions with given ion-ion interaction, containing an excess-electron defect with nonharmonic lattice distortion. The electron-phonon part of the Hamiltonian turns out to include both linear and quadratic terms in the phonon variables. The contribution of the phonons to the energy of a defect such as an F center in its ground state is derived in terms of a variational electronic wave function, using simple perturbation theory, to illustrate how this contribution can be incorporated in the lattice-statics analysis of such a defect. The large- and small-polaron Hamiltonians arising in the model are also presented and briefly discussed.