Efficient HF exchange evaluation through Fourier convolution in Cartesian grid for orbital-dependent density...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate computation of Hartree-Fock (HF) exchange is crucial for HF and density functional theory (DFT) models.
• Existing methods often face computational bottlenecks, particularly in evaluating electrostatic potentials.

Purpose of the Study:

• To develop a purely numerical, Cartesian grid-based approach for efficient HF exchange computation.
• To extend this method to global hybrid functionals and compare its performance with existing algorithms.

Main Methods:

• Utilizes the Fourier convolution theorem with a range-separated Coulomb interaction kernel.
• Employs an LCAO-MO ansatz in a Cartesian grid for global hybrid functionals.
• A parallel semi-numerical approach using the Obara-Saika recursion algorithm was developed for comparison.

Main Results:

• The proposed numerical scheme achieves logarithmic scaling with molecular size.
• Excellent agreement was found between the numerical and semi-numerical approaches for total and orbital energies.
• The method was successfully extended to global hybrid functionals like B3LYP, PBE0, and BHLYP.

Conclusions:

• The developed numerical approach provides a highly efficient and competitive method for calculating HF exchange.
• This work paves the way for further development of optimally tuned range-separated hybrid and hyper functionals.