Multireference equation-of-motion driven similarity renormalization group: theoretical foundations and applications to ionized states

TL;DR

This paper introduces an equation-of-motion extension of the multireference driven similarity renormalization group method for calculating ionization potentials, providing accurate results for strongly correlated systems with efficient scaling.

Contribution

It develops and benchmarks a new IP-EOM-DSRG formalism with multiple truncation schemes, outperforming existing multireference methods in accuracy and efficiency.

Findings

Accurately reproduces ionization potentials and spectroscopic constants.

Outperforms several state-of-the-art multireference methods.

Efficiently computes properties with $O(N^5)$ scaling.

Abstract

We present a formulation and implementation of an equation-of-motion (EOM) extension of the multireference driven similarity renormalization group (MR-DSRG) formalism for ionization potentials (IP-EOM-DSRG). The IP-EOM-DSRG formalism results in a Hermitian generalized eigenvalue problem, delivering accurate ionization potentials for systems with strongly correlated ground and excited states. The EOM step scales as $O(N^5)$ with the basis set size $N$, allowing for efficient calculation of spectroscopic properties, such as transition energies and intensities. The IP-EOM-DSRG formalism is combined with three truncation schemes of the parent MR-DSRG theory: an iterative nonperturbative method with up to two-body excitations [MR-LDSRG(2)] and second- and third-order perturbative approximations [DSRG-MRPT2/3]. We benchmark these variants by computing 1) the vertical valence ionization potentials of a series of small molecules at both equilibrium and stretched geometries; 2) the spectroscopic constants of several low-lying electronic states of the OH, CN, N2+, and CO+ radicals; and 3) the binding curves of low-lying electronic states of the CN radical. A comparison with experimental data and theoretical results shows that all three IP-EOM-DSRG methods accurately reproduce the vertical ionization potentials and spectroscopic constants of these systems. Notably, the DSRG-MRPT3 and MR-LDSRG(2) versions outperform several state-of-the-art multireference methods of comparable or higher cost.