Accurate Complete Basis Set Extrapolation of Direct
Random Phase Correlation Energies
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Abstract
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-pV<i>X</i>Z split valence atomic basis set family. The cardinal number <i>X</i> controls the size of the basis set, and we use <i>X</i> = 3–6 in this study. It is known that even the
very expensive <i>X</i> = 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 CH<sub>4</sub> to
C<sub>6</sub>H<sub>6</sub>. 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 <i>X</i> = 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 <i>X</i> = 3 and
4 extrapolated dRPA energies for atoms or small molecules might be
inaccurate for larger molecules