Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions

TL;DR

This paper introduces dynamical configuration interaction, a quantum embedding method that combines wave functions and Green's functions to accurately describe static and dynamic electron correlation with low computational cost.

Contribution

The paper develops a novel quantum embedding approach integrating CI and Green's functions, enabling efficient and accurate treatment of static and dynamic correlations.

Findings

Accurately reproduces dimer dissociation curves for H₂ and N₂

Excited state energies of N₂ and C₂ match benchmark results

Achieves balanced correlation treatment in a systematic, ab-initio framework

Abstract

We present the concept, derivation, and implementation of dynamical configuration interaction, a quantum embedding theory that combines Green's function methodology with the many-body wave function. In a strongly-correlated active space, we use full configuration interaction (CI) to describe static correlation exactly. We add energy dependent corrections to the CI Hamiltonian which, in principle, include all remaining correlation derived from the bath space surrounding the active space. Next, we replace the exact Hamiltonian in the bath with one of excitations defined over a correlated ground state. This transformation is naturally suited to the methodology of many-body Green's functions. In this space, we use a modified $GW$/Bethe-Salpeter equation procedure to calculate excitation energies. Combined with an estimate of the ground state energy in the bath, we can efficiently compute the energy dependent corrections, which correlate the full set of orbitals, for very low computational cost. We present dimer dissociation curves for H$_2$ and N$_2$ in good agreement with exact results. Additionally, excited states of N$_2$ and C$_2$ are in excellent agreement with benchmark theory and experiment. By combining the strengths of two disciplines, we achieve a balanced description of static and dynamic correlation in a fully ab-initio, systematically improvable framework.