Rigorous ab initio quantum embedding for quantum chemistry using Green's function theory: screened interaction, non-local self-energy relaxation, orbital basis, and chemical accuracy

TL;DR

This paper discusses self-energy embedding theory (SEET), a quantum embedding method that accurately describes strongly correlated subsystems within molecules, achieving chemical accuracy through practical implementation strategies.

Contribution

It provides a detailed, practical framework for implementing SEET in quantum chemistry, enabling accurate treatment of strongly correlated orbitals with manageable computational cost.

Findings

SEET achieves chemical accuracy on molecular examples.

The method is systematically improvable and comparable to wavefunction methods.

Practical guidelines for orbital basis and impurity solver selection are provided.

Abstract

We present a detailed discussion of self-energy embedding theory (SEET) which is a quantum embedding scheme allowing us to describe a chosen subsystem very accurately while keeping the description of the environment at a lower cost. We apply SEET to molecular examples where commonly our chosen subsystem is made out of a set of strongly correlated orbitals while the weakly correlated orbitals constitute an environment. Such a self-energy separation is very general and to make this procedure applicable to multiple systems a detailed and practical procedure for the evaluation of the system and environment self-energy is necessary. We list all the intricacies for one of the possible procedures while focusing our discussion on many practical implementation aspects such as the choice of best orbital basis, impurity solver, and many steps necessary to reach chemical accuracy. Finally, on a set of carefully chosen molecular examples, we demonstrate that SEET which is a controlled, systematically improvable Green's function method can be as accurate as established wavefunction quantum chemistry methods.