Tensor factorizations of local second-order M{\o}ller Plesset theory

TL;DR

This paper introduces tensor factorization techniques for local second-order Møller-Plesset theory, creating low-complexity wavefunction representations that improve computational efficiency while maintaining accuracy.

Contribution

It presents novel orbital specific virtual approximations that balance between existing methods, enhancing efficiency and accuracy in electronic structure calculations.

Findings

Favorable accuracy compared to Pulay-Saebø ansatz

Reduced computational times

Smooth potential energy curves

Abstract

Efficient electronic structure methods can be built around efficient tensor representations of the wavefunction. Here we describe a general view of tensor factorization for the compact representation of electronic wavefunctions. We use these ideas to construct low-complexity representations of the doubles amplitudes in local second order M{\o}ller-Plesset perturbation theory. We introduce two approximations - the direct orbital specific virtual approximation and the full orbital specific virtual approximation. In these approximations, each occupied orbital is associated with a small set of correlating virtual orbitals. Conceptually, the representation lies between the projected atomic orbital representation in Pulay-Saeb{\o} local correlation theories and pair natural orbital correlation theories. We have tested the orbital specific virtual approximations on a variety of systems and properties including total energies, reaction energies, and potential energy curves. Compared to the Pulay-Saeb{\o} ansatz, we find that these approximations exhibit favourable accuracy and computational times, while yielding smooth potential energy curves.