The Born-Oppenheimer (BO) surface of triatomic silicon is investigated and accurately described using two- and three-body potentials. The topology of the BO surface is found to be unstable with respect to fluctuations in these potentials, indicating that it is nongeneric. Examination of the two- and three-body components shows that the topology of the three-body term is fundamentally different from that of potentials usually used to model crystalline silicon. A study was therefore made to determine under what conditions this topology could successfully reproduce the diamond cubic structure of crystalline silicon. Two limiting methods for applying these potentials in the bulk have been considered and appraised. One of them uses the exact two- and three-body terms, and approximates the effect of the remaining terms in the N-body expansion (the screening effect) with a four-body term. The other method consists of screening the two- and three-body terms directly. Both methods were unsuccessful in reproducing the diamond cubic structure, which indicates the importance of terms of order higher than 4.

• Received 23 August 1991

DOI:https://doi.org/10.1103/PhysRevB.46.2147