Calculation of anharmonic phonon couplings in C, Si, and Ge

Frozen-phonon total-energy calculations are used to extract anharmonic phonon couplings for the tetrahedral elements C, Si, and Ge. The local-density approximation is employed, with a localized-orbital basis used for C and a plane-wave expansion used for Si and Ge. The bare interactions between optical phonons are completely determined through fourth order at the Brillouin-zone center. These are used to compute renormalized couplings, in which a vertex is screened by virtual phonons. The renormalized couplings are found to have the wrong sign to allow formation of a proposed two-phonon bound state in diamond.