Chapter 22 - Data-driven acceleration of coupled-cluster and perturbation theory methods

Abstract

Molecular electronic structure theory refers to the study of the electron motion in molecules and it has become an important computational tool in chemical research. An exact solution to the full electronic Hamiltonian in the Born-Oppenheimer approximation can be obtained only for hydrogenic atoms or molecular species with one electron. A variety of powerful approximate theories (configuration interaction theory, perturbation theory, and coupled-cluster theory) have been developed since the dawn of quantum mechanics. These wave function-based methods are often described as post-Hartree-Fock methods since a Hartree-Fock wave function is typically used as their starting point. However, significant computational resources are required for reaching the expected high accuracy due to exponential scaling with respect to the system size. Machine learning has been utilized as a powerful alternative for the acceleration of the convergence of the underlying equations of post-Hartree-Fock methods. Here, the recent advances in the acceleration of the coupled-cluster iterative solver through machine learning are presented. Wave function properties obtained from computationally less demanding calculations are used as input for machine learning. The data-driven coupled-cluster scheme provides the exact coupled-cluster energy because the actual iterative coupled-cluster equations are solved. Alternatively, accurate energetics can also be obtained by bypassing the explicit solution of the coupled-cluster projected equations. Our results show that remarkable speedups are achieved, especially when the physics of the electron correlation are encoded and used for training ML models. Finally, an extension of these data-driven approaches to other quantum chemical methods, such as the complete active space second-order perturbation theory (CASPT2), is presented. Comprehensive examples as case studies are provided at the end of the chapter for both methods.