Two-band model for halogen-bridged mixed-valence transition-metal complexes. II. Electron-electron correlations and quantum phonons

We study the effects of electron-electron interactions in halogen-bridged mixed-valence transition-metal linear-chain complexes (MX chains) applying a simple 3/4-filled two-band discrete tight-binding (extended) Peierls-Hubbard model with both on-site and intersite electron-phonon couplings. We employ a variety of methods: perturbation theory, Hartree-Fock approximation, and exact diagonalization in the limit of classical adiabatic phonons, and a variational approach allowing for a finite phonon frequency, i.e., quantum phonons and isotope effect. This variety of methods has proved necessary to obtain a complete picture, due to the structural richness of this model. We investigate the competition between the electron-electron and electron-phonon interactions in a wide range of parameter regimes for both ground and excited states. We focus on values relevant to the MX chains, probing the experimental variation as X and M are varied among X=Cl, Br, and I and M=Pt, Pd, and Ni (spanning electron-phonon-interaction-dominated to electron-electron-interaction-dominated materials).