Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies

摘要

The direct random phase approximation (dRPA) is a promising way to obtain improvements upon the standard semilocal density functional results in many aspects of computational chemistry. In this paper, we address the slow convergence of the calculated dRPA correlation energy with the increase of the quality and size of the popular Gaussian-type Dunning's correlation consistent aug-cc-pVXZ split valence atomic basis set family. The cardinal number X controls the size of the basis set, and we use X = 3-6 in this study. It is known that even the very expensive X = 6 basis sets lead to large errors for the dRPA correlation energy, and thus complete basis set extrapolation is necessary. We study the basis set convergence of the dRPA correlation energies on a set of 65 hydrocarbon isomers from CH4 to C6H6. We calculate the iterative density fitted dRPA correlation energies using an efficient algorithm based on the CC-like form of the equations using the self-consistent HF orbitals. We test the popular inverse cubic, the optimized exponential, and inverse power formulas for complete basis set extrapolation. We have found that the optimized inverse power based extrapolation delivers the best energies. Further analysis showed that the optimal exponent depends on the molecular structure, and the most efficient two-point energy extrapolations that use X = 3 and 4 can be improved considerably by considering the atomic composition and hybridization states of the atoms in the molecules. Our results also show that the optimized exponents that yield accurate X = 3 and 4 extrapolated dRPA energies for atoms or small molecules might be inaccurate for larger molecules.