Machine-learned electron correlation model based on frozen core approximation.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Machine Learning in Science

Background:

• The machine-learned electron correlation (ML-EC) model approximates electron correlation energy density using a regression model.
• Previous ML-EC models relied on computationally expensive all-electron calculations with core polarization functions.

Purpose of the Study:

• To reduce the computational cost of developing ML-EC models by applying the frozen core approximation (FCA).
• To assess the suitability of FCA-derived correlation energy densities as a response variable for machine learning.

Main Methods:

• Calculated coupled cluster singles, doubles, and perturbative triples [CCSD(T)] correlation energy density using FCA and correlation-consistent basis sets.
• Determined the complete basis set (CBS) limit using extrapolation and composite schemes.
• Constructed the ML-EC model using a large dataset (5,662,500 points) from 30 molecules based on the density-to-density relationship.

Main Results:

• FCA significantly reduced computational time, particularly for heavy elements.
• CCSD(T)/CBS correlation energy densities showed appropriate behavior for use as a response variable.
• The ML-EC model constructed using FCA demonstrated good agreement with reference values for valence-electron and reaction energies.
• The ML-EC model outperformed 71 existing exchange-correlation functionals in accuracy for reaction energies.

Conclusions:

• The frozen core approximation is a viable and effective strategy for reducing the computational cost of constructing ML-EC models.
• The developed ML-EC model offers a versatile and accurate alternative to traditional density functional methods for electronic structure calculations.