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Related Experiment Video

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: June 8, 2018

Discrete variable representation in electronic structure theory: quadrature grids for least-squares tensor

Robert M Parrish¹, Edward G Hohenstein, Todd J Martínez

¹Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, USA.

The Journal of Chemical Physics

|May 24, 2013

Summary

This study explores molecular quadratures using Becke grids and discrete variable representation (DVR) techniques for electron repulsion integral (ERI) tensor calculations. Findings show DVR methods offer comparable accuracy with fewer computational points for efficient quantum chemistry.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Theoretical Chemistry

Background:

The least-squares tensor hypercontraction (LS-THC) method offers an efficient representation of the electron repulsion integral (ERI) tensor.
The accuracy and efficiency of LS-THC depend on the choice of molecular quadrature grids.
Standard Becke-type grids and discrete variable representation (DVR) techniques are potential candidates for LS-THC grid generation.

Purpose of the Study:

To investigate the application of molecular quadratures from Becke-type grids and DVR techniques to the LS-THC representation of the ERI tensor.
To develop and compare algorithms for generating quadrature grids suitable for LS-THC.
To evaluate the performance of different grid types in the context of LS-THC-DF-MP2 calculations.

Main Methods:

Applying standard Becke-type grids to LS-THC.
Developing and applying radial discrete variable representation (R-DVR) grids.
Developing and applying full discrete variable representation (F-DVR) grids.
Comparing the accuracy and efficiency of Becke, R-DVR, and F-DVR grids within the LS-THC-DF-MP2 framework.

Main Results:

Becke grids and R-DVR grids provide similar accuracy and efficiency for LS-THC.
R-DVR grids are constructed using basis set information, potentially guiding future grid development.
F-DVR grids achieve reasonable accuracy with significantly fewer grid points compared to Becke and R-DVR.
LS-THC-DF-MP2 calculations demonstrate the performance differences between the grid types.

Conclusions:

Both Becke and R-DVR grids are effective for LS-THC calculations, with R-DVR offering basis-set specific advantages.
F-DVR presents a promising approach for achieving high accuracy with reduced computational cost.
The choice of quadrature grid significantly impacts the efficiency and accuracy of LS-THC ERI tensor calculations.