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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Data-driven kinetic energy density fitting for orbital-free DFT: Linear vs Gaussian process regression.

Sergei Manzhos¹, Pavlo Golub²

¹Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, 1650 Boulevard Lionel-Boulet, Varennes, Quebec J3X 1S2, Canada.

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Summary

This study explores kinetic energy densities (KEDs) in orbital-free density functional theory, finding weighted linear and Gaussian process regressions improve accuracy. Gaussian process regression offers superior KED fitting and energy-volume dependence.

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Area of Science:

Computational Physics
Materials Science
Quantum Chemistry

Background:

Kinetic energy density (KED) is crucial for orbital-free density functional theory (OF-DFT).
Accurate KED functionals are essential for predicting material properties.
Previous studies proposed density-dependent variables for KED approximations.

Purpose of the Study:

To investigate the dependence of KEDs on density-dependent variables.
To evaluate the impact of data distribution and regressor selection on KED fitting.
To compare linear and Gaussian process regression methods for KED approximation.

Main Methods:

Analysis of KEDs for light metals and a semiconductor.
Application of unweighted and weighted linear regression.
Implementation of unweighted and weighted Gaussian process regression.
Inclusion of effective potential as a descriptor.

Main Results:

Weighted linear regression, informed by KED histogram, yields good energy-volume dependence.
Gaussian process regression achieves excellent KED fit quality, surpassing linear methods.
Effective potential descriptor enhances linear KED fitting and Gaussian process energy-volume dependence.
Gaussian process regression performs well even without data weighting.

Conclusions:

Accurate KED approximations are achievable using density-dependent variables in OF-DFT.
Gaussian process regression provides a robust and accurate method for KED modeling.
Data weighting and descriptor selection significantly influence regression performance.