Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Direct random phase approximation (dRPA) offers improvements over semilocal density functionals.
• Standard dRPA calculations exhibit slow convergence with basis set size.
• Complete basis set extrapolation is crucial for accurate dRPA correlation energies.

Purpose of the Study:

• Investigate the basis set convergence of dRPA correlation energies.
• Evaluate different complete basis set extrapolation formulas.
• Develop improved extrapolation strategies for dRPA calculations.

Main Methods:

• Calculated dRPA correlation energies for 65 hydrocarbon isomers (CH4 to C6H6).
• Employed iterative density-fitted dRPA with an efficient CC-like algorithm.
• Tested inverse cubic, optimized exponential, and inverse power extrapolation formulas.
• Analyzed basis set convergence using Dunning's aug-cc-pVXZ basis sets (X=3-6).

Main Results:

• Optimized inverse power extrapolation yielded the most accurate dRPA correlation energies.
• Optimal extrapolation exponents depend on molecular structure.
• Two-point extrapolations (X=3, 4) can be enhanced by considering atomic composition and hybridization.
• Exponents accurate for small molecules may not be suitable for larger ones.

Conclusions:

• Optimized inverse power extrapolation is superior for dRPA correlation energies.
• Molecular structure-dependent exponents are necessary for accurate extrapolation.
• Accounting for atomic properties improves two-point extrapolation accuracy.
• Extrapolation strategies must be tailored to molecule size for reliable results.