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

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.