Machine-learned electron correlation model based on correlation energy density at complete basis set limit.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Machine learning in quantum mechanics

Background:

• Accurate calculation of electron correlation is crucial in quantum chemistry.
• Density Functional Theory (DFT) methods rely on approximations for exchange-correlation functionals.
• Coupled Cluster Singles, Doubles, and Perturbative Triples (CCSD(T)) provides highly accurate correlation energies.

Purpose of the Study:

• To develop a novel machine-learned model for predicting correlation energy density.
• To utilize readily available density variables as input for the machine learning model.
• To achieve accurate and efficient estimation of correlation energy at the complete basis set (CBS) limit.

Main Methods:

• Machine learning regression model trained on density variables.
• Derivation of correlation energy density from coupled cluster singles, doubles, and perturbative triples (CCSD(T)) calculations.
• Estimation of complete basis set (CBS) limit using composite methods.
• Inclusion of Hartree-Fock (HF) exchange energy density and fractional electron density as explanatory variables.

Main Results:

• The correlation energy density at the CCSD(T)/CBS level was identified as a suitable response variable for machine learning.
• The developed model demonstrated high accuracy and efficiency in predicting correlation energy density.
• Numerical assessments confirmed the reliability of the machine-learned correlation model.

Conclusions:

• A computationally efficient machine-learned correlation model was successfully developed.
• The protocol enables accurate prediction of CCSD(T)/CBS correlation energy density using Hartree-Fock (HF) calculations with small basis sets.
• This approach offers a promising avenue for accelerating quantum chemical calculations.