Machine learning for a finite size correction in periodic coupled cluster theory calculations

Area of Science:

• Computational chemistry
• Materials science
• Condensed matter physics

Background:

• Coupled cluster singles and doubles (CCSD) calculations are essential for accurate electronic structure but suffer from finite size errors in periodic systems.
• Existing methods for finite size corrections, like those by Liao and Grüneis, and Mihm et al., utilize the transition structure factor.
• Efficiently converging CCSD calculations to the thermodynamic limit is crucial for reliable predictions in materials science.

Purpose of the Study:

• To introduce a novel Gaussian process regression (GPR) model for the transition structure factor in metal CCSD calculations.
• To develop a method, termed CCSD-FS-GPR, for correcting finite size errors in these calculations.
• To enable more accurate and efficient electronic structure predictions for metallic systems.

Main Methods:

• A straightforward Gaussian process regression (GPR) model is applied to the transition structure factor.
• The structure factor is fitted to a 1D function of momentum transfer (G).
• The fitted function is integrated over a k-point mesh to obtain extrapolated results, correcting for finite size effects.

Main Results:

• The CCSD-FS-GPR method is demonstrated to effectively correct for finite size errors in CCSD calculations.
• The model provides accurate comparisons with extrapolated results.
• The method is applied to lithium, sodium, and the uniform electron gas, showing its applicability to various metallic systems.

Conclusions:

• The developed GPR model offers a straightforward and effective approach for finite size corrections in metal CCSD.
• This method enhances the efficiency and accuracy of converging CCSD calculations to the thermodynamic limit.
• The CCSD-FS-GPR technique represents a valuable advancement for computational studies of metallic materials.