Efficient Computation of Exchange Energy Density with Gaussian Basis Functions

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• Density Functional Theory (DFT) is a cornerstone in computational chemistry and physics.
• Standard DFT struggles with systems exhibiting significant nondynamic correlation.
• Existing DFT functionals addressing nondynamic correlation often rely on exact exchange energy density, posing computational challenges.

Purpose of the Study:

• To present an efficient seminumerical algorithm for calculating Hartree-Fock (HF) exchange energy density.
• To address the computational bottleneck associated with advanced DFT functionals.
• To improve the accuracy and efficiency of DFT for challenging quantum chemical systems.

Main Methods:

• Implementation of an efficient seminumerical algorithm for HF exchange energy density calculation.
• Quadratic scaling of the method with respect to molecular and basis set size.
• Utilizing standard atom-centered grids for HF exchange energy and matrix computation.

Main Results:

• The seminumerical algorithm achieves quadratic scaling, offering significant speedups.
• Demonstrated competitiveness with conventional analytical methods and previous approximate schemes.
• Achieved up to six times faster calculations for large basis sets (e.g., aug-cc-pvtz) on alanine peptides.
• Validated practicality through local hybrid self-consistent calculations on the acenes-20 molecule.

Conclusions:

• The developed seminumerical algorithm effectively resolves the computational bottleneck in advanced DFT functionals.
• The method provides an accurate and efficient approach for handling nondynamic correlation in quantum chemical calculations.
• This advancement enables more reliable and feasible simulations of complex molecular systems using DFT.