Tensor Hypercontraction Error Correction Using Regression.

Area of Science:

• Quantum chemistry
• Computational chemistry
• Electronic structure theory

Background:

• Wavefunction-based quantum methods accurately predict molecular electronic structure, accounting for dynamical electron correlation.
• High-level methods including dynamical correlation are computationally expensive for large molecules.
• Approximations like tensor hyper-contraction (THC) reduce computational cost but introduce errors.

Purpose of the Study:

• To correct errors in THC-approximated quantum chemistry methods using machine learning.
• To apply machine learning to THC-approximated third-order Møller-Plesset theory (MP3) as a model for coupled cluster methods.
• To evaluate the effectiveness of regression techniques for improving accuracy.

Main Methods:

• Applied tensor hyper-contraction (THC) to third-order Møller-Plesset theory (MP3).
• Trained multiple linear regression and Kernel Ridge regression models on THC errors from the Main Group Chemistry Database (MGCDB84).
• Investigated absolute and relative correction procedures for molecular and reaction energies.

Main Results:

• Nonlinear regression models reduced root mean squared errors between THC-MP3 and canonical MP3 by 6-9× for total molecular energies.
• Nonlinear regression models reduced root mean squared errors by 2-3× for reaction energies.
• Identified optimal regression techniques based on accuracy compared to canonical MP3.

Conclusions:

• Machine learning, particularly nonlinear regression, effectively corrects errors in THC-approximated quantum chemical calculations.
• This approach enhances the feasibility of accurate electronic structure analysis for larger molecular systems.
• Regression techniques offer a promising avenue for improving the accuracy of computationally efficient quantum methods.