Evaluation of semiempirical quantum-chemical methods in solid-state applications. II. Cyclic-cluster calculations of silicon

The cyclic-cluster model has been used to compute properties of crystalline silicon. Semiempirical electronic-structure methods which neglect orbital overlap have been employed. These include the spectroscopic version of the complete neglect of differential overlap (CNDO/S), the modified intermediate neglect of differential overlap (MINDO/3), and the modified neglect of diatomic overlap (MNDO) methods. It is demonstrated that a 54-atom cyclic cluster provides a satisfactory approximation of the crystalline properties. Calculations with and without d orbitals show that they are required in order to reproduce the indirect band gap. Our results indicate that these semiempirical methods can describe most of the properties of a solid with good accuracy. The most important failure is the serious overestimation of the stability of s-like states, which is attributed to the neglect of overlap. Some consequences for defect calculations are also discussed.