ANALYSIS OF COVALENT EFFECTS ON THE MULTIPLET STRUCTURE OF RUBY BASEDON FIRST-PRINCIPLES CLUSTER CALCULATIONS

A general method to calculate multiplet structures in distorted molecu lar orbitals has been developed, in which the matrix elements of the e lectron-electron interaction are calculated numerically using the mole cular orbitals obtained by cluster calculations. The multiplet structu re of chromium-doped alumina (ruby) has been calculated from first pri nciples using model clusters consisting of 7 to 41 atoms with or witho ut cubic approximation. By comparing the results, it was discovered th at 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 str uctures beyond cubic or tetragonal approximations but also for analysi s of the effects of covalency on multiplet structures.