Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators

TL;DR

This paper introduces a nonperturbative, numerically robust multireference theory called MR-LDSRG(2), which simplifies calculations while maintaining accuracy, effectively avoiding intruder states and ensuring size consistency.

Contribution

The paper develops the first nonperturbative MR-DSRG method truncated to one- and two-body operators, with a linearized recursive commutator approximation, improving numerical stability and computational efficiency.

Findings

Achieves accuracy comparable to established multireference methods.

Scales as O(N^2 N_P^2 N_H^2), suitable for larger systems.

Successfully applied to benchmark molecules, demonstrating robustness and reliability.

Abstract

The first nonperturbative version of the multireference driven similarity renormalization group (MR-DSRG) theory [C. Li and F. A. Evangelista, J. Chem. Theory Comput. $\mathbf{11}$, 2097 (2015)] is introduced. The renormalization group structure of the MR-DSRG equations ensures numerical robustness and avoidance of the intruder state problem, while the connected nature of the amplitude and energy equations guarantees size consistency and extensivity. We approximate the MR-DSRG equations by keeping only one- and two-body operators and using a linearized recursive commutator approximation of the Baker--Campbell--Hausdorff expansion [T. Yanai and G. K.-L. Chan, J. Chem. Phys. $\mathbf{124}$, 194106 (2006)]. The resulting MR-LDSRG(2) equations contain only 39 terms and scales as ${\cal O}(N^2 N_{\rm P}^2 N_{\rm H}^2)$ where $N_{\rm H}$, $N_{\rm P}$, and $N$ correspond to the number of hole, particle, and total orbitals, respectively. Benchmark MR-LDSRG(2) computations on the hydrogen fluoride and molecular nitrogen binding curves and the singlet-triplet splitting of $p$-benzyne yield results comparable in accuracy to those from multireference configuration interaction, Mukherjee multireference coupled cluster theory, and internally-contracted multireference coupled cluster theory.