A practical guide to density matrix embedding theory in quantum chemistry

TL;DR

This paper provides a practical guide to density matrix embedding theory (DMET), detailing its numerical implementation, self-consistent optimization procedures, and demonstrating its application to various molecular systems.

Contribution

It offers an explicit, practical description of DMET formulation and self-consistent optimization, with application examples in molecular systems.

Findings

Successful application of DMET to hydrogen and beryllium rings.

Comparison of embedding strategies with and without self-consistency.

Provision of source code for reproducibility.

Abstract

Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample S$_{\text{N}}$2 reaction. The source code for the calculations in this work can be obtained from \url{https://github.com/sebwouters/qc-dmet}.