Vibrational potentials and structures in molecular and solid carbon, silicon, germanium, and tin

Abstract

Using a molecular orbital method presented recently [J. Chem. Phys. 62, 1187 (1975)], a study is made of equilibrium distances, force constants, and binding energies for several states of diatomic Group IV A molecules. Close agreement exists with experiment for low‐lying states of C₂. The agreement between calculated and experimental properties for the ³π_u and ³π_g states of Si₂ is ambiguous. The ground state of Ge₂ is here predicted to be ³π_u with R_e=2.29 Å, k_e=2.65 mdyn/Å, l_e=16 mdyn/Å, and D_e=57 kcal (65 experimentally). For Sn₂ the ³π_u and ³Σ_g⁻ states are close in binding energy (48.6 and 48.7 kcal vs 45.2 from experiment). The former has R_e=2.65 Å, k_e=2.25 mdyn/Å, l_e=15 mdyn/Ų, and the latter has R_e=2.77 Å, k_e=1.44 mdyn/Å, and l_e=8 mdyn/Ų. A quantitative study of five atom tetrahedral clusters of these atoms leads to accurate determinations of bulk lattice parameters and stretching force constants. The origin of forces important to binding and interaction force constants is discussed. Structures and binding energies for three, four, and five atom clusters of tin are calculated. The binding energies follow experimental trends. The introduction of d orbitals to the basis set significantly improves binding energies for the larger clusters, but has little effect on calculated structures.