Energy surfaces forSi3andC3: A comparative study

Abstract

Density-functional calculations have been performed for the energy surface of the ${}_{}{}^1{}_{}{}^{}\mathrm{A}_1^{}{}_{}{}^{}$ state of ${\mathrm{Si}}_3$ and for vertical excitation energies of low-lying excited states. In contrast to the results for ${\mathrm{C}}_3$ and the predictions of Walsh’s rules for triatomic molecules with twelve valence electrons, the equilibrium geometry is found to be nonlinear (${\alpha }_{\mathrm{Si}\mathrm{?}\left(\mathrm{h}\mathrm{y}\mathrm{S}\mathrm{i}\mathrm{?}\right(\mathrm{h}\mathrm{y}\mathrm{S}\mathrm{i}\mathrm{\sim }85}$°). The relative importance of d functions in silicon contributes to this and other differences between the energy surfaces of ${\mathrm{C}}_3$ and ${\mathrm{Si}}_3$. The trends in bond lengths and bond angles are discussed for dimers, trimers, and bulk systems of carbon and silicon. The energy surface for the lowest ${}_{}{}^3{}_{}{}^{}\mathrm{B}_2^{}{}_{}{}^{}$ state shows a minimum for α=60° which is almost degenerate with the ${}_{}{}^1{}_{}{}^{}\mathrm{A}_1^{}{}_{}{}^{}$ minimum.