Explicitly correlated local second-order perturbation theory with a frozen geminal correlation factor

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Traditional correlated methods face challenges with slow basis set convergence and computational cost.
• Explicitly correlated methods (e.g., R12 methods) incorporate interelectronic distances to accelerate convergence.
• Localized approximations and density fitting are crucial for reducing computational scaling in quantum chemistry.

Purpose of the Study:

• To modify and improve existing localized explicitly correlated methods (MP2-R122*A(loc) and LMP2-R122*A(loc)).
• To enhance the efficiency and accuracy of calculating second-order correlation energies.
• To enable the application of these methods to larger molecular systems.

Main Methods:

• Modification of MP2-R122*A(loc) and LMP2-R122*A(loc) using a short-range correlation factor.
• Expansion of the correlation factor using a fixed linear combination of Gaussian geminals.
• Implementation of density fitting for integral evaluation and local approximations for improved computational scaling.

Main Results:

• The modified MP2-F122*A(loc) method demonstrates very rapid convergence of correlation energies with respect to basis set size.
• Correlation energies computed with the aug-cc-pVTZ basis set are within 0.5% of the basis set limit for 21 small molecules.
• The short-range correlation factor improves resolution of the identity convergence and mitigates long-range errors in density fitting.

Conclusions:

• The developed DF-LMP2-F122*A(loc) method significantly accelerates the convergence of correlated calculations.
• This approach provides accurate correlation energies with smaller basis sets, reducing computational cost.
• The method is successfully applied to molecules up to 49 atoms, demonstrating its scalability and utility for larger systems.