Communications: Explicitly correlated second-order Møller-Plesset perturbation method for extended systems

A formalism for the second-order Møller-Plesset perturbation method employing basis functions that depend explicitly on electron-electron distances (the MP2-R12 or F12 method) is derived and implemented into computer codes for extended systems periodic in one dimension. The excitation amplitudes on these functions are held fixed at values that satisfy the first-order cusp condition. Necessary many-electron integrals over Gaussian-type functions involving Slater-type geminals are evaluated by means of the resolution-of-the-identity approximation with a complementary auxiliary basis set. These integrals and thus the final correlation energy are shown to have the correct size dependence. The valence MP2 correlation energy of polyethylene near the complete basis-set limit is obtained and shown to be considerably greater in magnitude than the value obtained without the R12 treatment.