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

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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 3πu and 3πg states of Si2 is ambiguous. The ground state of Ge2 is here predicted to be 3πu with Re=2.29 Å, ke=2.65 mdyn/Å, le=16 mdyn/Å, and De=57 kcal (65 experimentally). For Sn2 the 3πu and 3Σg− states are close in binding energy (48.6 and 48.7 kcal vs 45.2 from experiment). The former has Re=2.65 Å, ke=2.25 mdyn/Å, le=15 mdyn/Å2, and the latter has Re=2.77 Å, ke=1.44 mdyn/Å, and le=8 mdyn/Å2. 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.

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