Theoretical analysis of hole self-trapping in ionic solids: Application to the KCl crystal.

Abstract

A method for the calculation of the hole self-trapping (ST) energy in ionic crystals is proposed. It combines model-Hamiltonian and quantum-chemical approaches. An artificial path for the ST process has been suggested containing (a) a free hole not interacting with the lattice vibrations; (b) a free-hole wave packet localized in a small crystal volume in the form of the real ST state, all crystal ions being in their perfect lattice positions; (c) the final ST state of the hole, accompanied with a corresponding lattice relaxation, including strong displacements of ions belonging to the hole region. Some intermediate states might be adopted between (a) and (b) in order to simplify the calculations. The first step (a\ensuremath{\rightarrow}b) is calculated with the use of a simple model Hamiltonian taking into account inertial-free crystal polarization; the latter is calculated by means of Toyazawa's electronic polaron model. Quantum-chemical calculations are used for the last (b\ensuremath{\rightarrow}c) and all intermediate (if any) steps, and are made by means of the embedded-molecular-cluster model combined wtih a self-consistent treatment of both the crystal polarization and the electronic structure. In order to illustrate the method, a ST hole in the form of the ${\mathit{V}}_{\mathit{k}}$ center (${\mathit{X}}_{2}^{\mathrm{\ensuremath{-}}}$ quasimolecular ion) in the KCl crystal is considered and the ST energy is calculated as carefully as possible. In particular, the semiempirical intermediate neglect of the differential overlap modification of the unrestricted Hartree-Fock-Roothaan method is employed for actual calculations. The hole ST energy in the KCl crystal is found to be near -2.4 eV.