Random Phase Approximation for Periodic Systems Employing Direct Coulomb Lattice Summation

A method
to compute ground state correlation energies from the
random phase approximation (RPA) is presented for molecular and periodic
systems on an equal footing. The supermatrix representation of the
Hartree kernel in canonical orbitals is translation-symmetry adapted
and factorized by the resolution of the identity (RI) approximation.
Orbital expansion and RI factorization employ atom-centered Gaussian-type
basis functions. Long ranging Coulomb lattice sums are evaluated in
direct space with a revised recursive multipole method that works
also for irreducible representations different from Γ. The computational
cost of this RI-RPA method scales as O­(N4) with the
system size in direct space, N, and as O­(Nk2) with the number of sampled k-points in reciprocal
space, Nk. For chain
and film models, the exploration of translation symmetry with 10 k-points along each periodic direction reduces the computational
cost by a factor of around 10–100 compared to equivalent Γ-point
supercell calculations.