Efficient adiabatic connection approach for strongly correlated systems. Application to singlet-triplet gaps of biradicals

TL;DR

This paper introduces a new efficient adiabatic connection method that accurately captures dynamic electron correlation in strongly correlated systems, demonstrated on singlet-triplet gaps of biradicals.

Contribution

The paper proposes the AC$_{ m n}$ method, a size-consistent, stable, and efficient approach based on adiabatic connection and multireference RPA for dynamic correlation.

Findings

AC$_{ m n}$ accurately predicts singlet-triplet gaps in biradicals.

Method is computationally efficient, scaling with the fifth power of system size.

Provides a new tool for studying large strongly correlated systems.

Abstract

Strong correlation can be essentially captured with multireference wavefunction methods such as complete active space self-consistent field (CASSCF) or density matrix renormalization group (DMRG). Still, an accurate description of the electronic structure of strongly correlated systems requires accounting for the dynamic electron correlation, which CASSCF and DMRG largely miss. In this work a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The AC$_{\rm n}$ method accounts for terms up to the desired order n in the coupling constant, is rigorously size-consistent, free from instabilities and intruder states. It employs the particle-hole multireference random phase approximation and the Cholesky decomposition technique, which leads to a computational cost growing with the fifth power of the system size. Thanks to AC$_{\rm n}$ depending solely on one- and two-electron CAS reduced density matrix, the method is much more efficient than existing ab initio dynamic correlation methods for strong correlation. AC$_{\rm n}$ affords excellent results for singlet-triplet gaps of challenging organic biradicals. Development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.