The unrestricted Hartree-Fock method is applied to tetrahedrally coordinated ${\mathrm{Si}}_5$${\mathrm{H}}_{12}$ clusters as a function of several different Si-H "saturator" bond lengths. Ground-state and excited-state configurations, representative of the initial and final states of a low-energy optical transition, are studied analyzing the energetics, symmetries, and charge densities. The determination of the "cluster band gap" by Koopmans' theorem versus $\Delta \mathrm{SCF}$ (self-consistent-field) calculations shows electronic relaxation to be significant compared to the expected transition-energy range. The cluster band gap and other energetic properties are shown to change appreciably for the various Si-H bond lengths, yet the charge densities in the Si-Si bond regions remain similar, exemplifying a minimal environmental effect on the central bonding region. The charge densities obtained are comparable to experimental x-ray and theoretical pseudopotential calculations describing bulk silicon. The adequacy of using an ab initio effective core potential for the five silicon atoms is established by comparison to a calculation allowing relaxation of the core on the one central silicon atom. The concepts underlying cluster simulation of condensed matter are discussed with particular emphasis on the environmental models. The usefulness and formal limitations of the self-consistent saturator environmental model are addressed.

• Received 6 October 1980

DOI:https://doi.org/10.1103/PhysRevB.23.2897