Quantum structural approach to high-Tcssuperconductivity theory: Herzberg-Teller, Renner-Teller, Jahn-Teller effects and intervalent geminal charge transfer

Abstract

We use quantum molecular structure and spectroscopic thoughts of various possible vibronic interactions for the position space of two-electron geminal orbitals with Bloch sums. Our geminals have different degeneracy from one-electron molecular orbitals and are different from the momentum space of BCS free electrons. Based on Herzberg-Teller expansions, our consideration of the aspect of the Renner-Teller effect for cyclic boundary crystals (instead of the usual linear molecules) involves first-order vibronic interaction with isotope effects different from the second-order electron-phonon energy of BCS theory, bipolaron theory, etc. Our consideration of the Jahn-Teller effect with equal-minimum double-well potential leads to the intervalent charge transfer between two degenerate vibrationally affected electronic structures. Our considerations of different style vibrations other than the antisymmetric vibration for the nearest neighbor (e.g., displaced oscillator, etc.) may possibly be related to the case of special chemical structures with special doping and special coherence length. Our simple structural illustrations of such different vibronic Renner-Teller, Jahn-Teller effects and intervalent charge transfer (of ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${\mathrm{CuO}}_{4}$ and ${\mathrm{YBa}}_{2}$ ${\mathrm{Cu}}_{3}$ ${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{x}}$ ) may promote some possible thoughts of quantum chemical structures compared and mixed with the physical treatments of special high-${\mathrm{T}}_{\mathrm{c}}$ superconductors.