Analysis of covalent effects on the multiplet structure of ruby based on first-principles cluster calculations

A general method to calculate multiplet structures in distorted molecular orbitals has been developed, in which the matrix elements of the electron-electron interaction are calculated numerically using the molecular orbitals obtained by cluster calculations. The multiplet structure of chromium-doped alumina (ruby) has been calculated from first principles using model clusters consisting of 7 to 41 atoms with or without cubic approximation. By comparing the results, it was discovered that the energy of the E-2 state is sensitive to the trigonal distortion of the impurity-state wave functions and that the energies of the T-2(1) and T-2(2) states are sensitive to spatial extension of these wave functions over aluminum ions. The present calculation is an effective method not only for the first-principles calculation of multiplet structures beyond cubic or tetragonal approximations but also for analysis of the effects of covalency on multiplet structures.