Calculation of multiplet structure of ruby using explicit effective Hamiltonian

Recently, we have carried out a first-principles calculation of the multiplet structure of ruby, using the discrete variational-multielectron (DV-ME) method, and the effects of covalency and distortion of the wave functions on the multiplet structure of ruby have been analyzed quantitatively. In these calculations, however, the matrix elements of the many-electron Hamiltonian were calculated by the Fazzio's method. Although the Fazzio's method enables one to calculate the matrix elements of the many-electron Hamiltonian without knowing the explicit form of the effective single-electron Hamiltonian, the Slater determinants should be classified into several electronic configurations and there is some ambiguity in the way of classification when the distortion of the wave function is relatively large. In the present paper, we carried out a more direct calculation of the multiplet structure of ruby using the explicit form of the effective single-electron Hamiltonian obtained by Watanabe and Kamimura. In the calculated results of the present method, the degeneracy of each state is considerably improved and the trigonal-field split of each state is also qualitatively reproduced. However, the energies of quartet states are considerably overestimated, indicating that the present method requires a larger number of basis functions than the Fazzio's method.