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Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method.

Sandeep Sharma¹, Alec F White², Gregory Beylkin³

¹Department of Chemistry, University of Colorado Boulder, Boulder, Colorado80309, United States.

Journal of Chemical Theory and Computation

|November 23, 2022

Summary

This summary is machine-generated.

This study introduces a new algorithm for efficiently calculating the exchange matrix in periodic systems, significantly reducing computational cost without sacrificing accuracy. The method optimizes calculations for Gaussian basis sets and pseudopotentials.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Materials Science

Background:

Evaluating the exchange matrix in periodic systems using Gaussian basis sets with pseudopotentials typically involves computationally expensive O(N^2) Fast Fourier Transforms (FFTs).
Existing methods face limitations in computational efficiency due to the scaling of FFTs with system size.

Purpose of the Study:

To develop and present an efficient algorithm for evaluating the exchange matrix in periodic systems.
To significantly reduce the computational prefactor in exchange matrix calculations while maintaining cubic scaling.
To improve the efficiency of electronic structure calculations for periodic systems.

Main Methods:

Introduced an algorithm that represents products of Gaussian basis functions using a linear combination of an auxiliary basis.
Employed a robust pseudospectral method with a limited number of auxiliary basis functions for high accuracy.
Utilized the occ-RI exchange method to avoid constructing the full exchange matrix.
Integrated the (interpolative separable density fitting) ISDF algorithm to construct auxiliary basis sets.

Main Results:

The new algorithm retains cubic scaling but significantly reduces the computational prefactor by eliminating the need for intermediate FFTs.
The method achieves high accuracy, with errors in the final energy decreasing exponentially with the number of auxiliary functions.
The algorithm offers a more computationally tractable approach for electronic structure calculations in periodic systems.

Conclusions:

The developed algorithm provides an efficient and accurate method for evaluating the exchange matrix in periodic systems.
The combination of pseudospectral methods, occ-RI exchange, and ISDF offers a significant improvement over traditional approaches.
This advancement has the potential to accelerate computational studies in various fields of chemistry and materials science.