Molecular electronic excitations calculated from a solid-state approach: Methodology and numerics

We investigate the applicability and accuracy of a solid-state approach, which was developed originally for the relatively homogeneous electron gas, to describe electronic single-particle and electron-hole pair excitations in molecules. Thereby we start from the determination of the molecular ground state within the local density functional theory using repeated supercells and pseudopotentials for the electron-ion interaction. The electronic spectra are obtained from the Green's function formalism. The exchange-correlation self-energy Sigma is linearly expanded in the screened Coulomb interaction, i.e., the GW approximation is used. Optical spectra are obtained from the Bethe-Salpeter equation for the irreducible polarization propagator. The numerical implementation and possible pitfalls of this methodology are discussed using silane, disilane, and water molecules as examples. In particular the influence of the dynamics of the screening, the supercell size, and the number of empty states are studied. The resulting single- and two-particle excitation energies are compared with experiment and previous theoretical work.