Improved Ligand-Field Theory with Effect of Electron-Phonon Interaction

Abstract

Traditional ligand-field theory has to be improved by taking into account both "pure electronic" contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R1, R2, R 3 , R 2 , and R 1 lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG: Cr 3+ as well as thermal shifts of GSZFS, R1 line and R2 line of ruby have been calculated. The results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R1 line and R2 line of ruby, several conclusions have also been obtained.

Role of the plasmon-pole model in theGWapproximation

“…Table I summarizes the calculated E g of materials ranging from simple semiconductors and insulators to transition-metal oxide ZnO and molecular solid noble gas Ne. Compared with experimental data corrected by excluding the electron-phonon interactions, 41 which normally lead to a reduced band gap, [42][43][44][45][46] E g in AlN, GaAs, ZnO, and Ne have relatively large errors, requiring self-consistent GW computations 19,20 and/or more accurate DFT wave functions to construct G and W . 37,[47][48][49][50] Here we focus on the effects of the PPM on band structures, and our calculations suggest that for Si, Ge, and GaAs all four PPMs give very close E g values (within 0.1 eV) to those from numerical integration.…”

Pressure-Induced Shift of R-Line of MgO:Cr 3+ with Electron-Phonon Interaction Effect

“…According to the theory of PS of en-ergy spectra (e.g., see Refs. [2] and [5] and therein cited references), the expressions of B, C (Racah parameters), Dq (cubic-field parameter), ζ, and ζ (spin-orbit coupling parameters) as functions of χ (χ = R/R 0 , where R 0 and R are the local interionic distances around Cr 3+ at normal pressure and pressure P , respectively) are given as follows:…”

“…According to Refs. [3] and [4], the temperatureindependent contribution to i-state energy of the total system (i.e., the interaction system between localized delectronic states of a transition-metal ion and phonons of the lattice vibration) from EPI due to acoustic branches (i.e., the acoustic-branch term of i level in cm −1 unit) is…”

“…In Refs. [3] ∼ [5], it was demonstrated that traditional ligand-field theory has to be improved by taking into account both pure electronic contribution and EPI one. For PS of R-line, it consists of the two contributions, too.…”

“…Thus, it is necessary to carry out the theoretical calculation of R-line PS of MgO:Cr 3+ by using the improved ligand-field theory presented in Refs. [3] ∼ [5].…”