Electron Band Structure of Solid Methane:Ab InitioCalculations

The band structure of crystalline methane has been calculated in a linear-combination-of-molecular-orbitals approximation. In this molecular tight-binding method the Bloch sums are built up of Hartree-Fock orbitals of the free molecules. Interactions between the states of different molecules are calculated directly from molecular integrals without reducing the exchange interaction to an exchange potential. The approximations involved are shown to be well justified for a crystal made of closed-shell units. The band structure is obtained by solving secular equation in 400 points along the relevant symmetry lines. The calculated bands are relatively narrow, less than 2.5 eV wide, around the molecular levels. The band-to-band gap in solid methane is 24.5 eV. This value has the same order of magnitude as in solid rare gases.