Improving the efficiency of the multireference driven similarity renormalization group via sequential transformation, density fitting, and the non-interacting virtual orbital approximation

Abstract: This study examines several techniques to improve the efficiency of the linearized multireference driven similarity renormalization group truncated to one- and two-body operators [MR-LDSRG(2)]. We propose a sequential MR-LDSRG(2) [sq-MR-LDSRG(2)] approach, in which one-body rotations are folded exactly into the Hamiltonian. This new approach is combined with density fitting (DF) to reduce the storage cost of two-electron integrals. To further avoid the storage of large four-index intermediates, we propose a non-interacting virtual orbit (NIVO) approximation in which tensor blocks labeled by three and four virtual indices are neglected. The NIVO approximation reduces the computational cost prefactor of the MR-LDSRG(2) bringing it closer to that of coupled cluster with singles and doubles (CCSD). We test the effect of the DF and NIVO approximations on the MR-LDSRG(2) and sq-MR-LDSRG(2) methods by computing properties of eight diatomic molecules. The diatomic constants obtained by DF-sq-MR-LDSRG(2)+NIVO are found to be as accurate as those from the original MR-LDSRG(2) and coupled cluster theory with singles, doubles, and perturbative triples. Finally, we demonstrate that the DF-sq-MR-LDSRG(2)+NIVO scheme can be applied to chemical systems with more than 550 basis functions by computing the automerization energy of cyclobutadiene with a quintuple-zeta basis set. The predicted automerization energy is found similar to the values computed with Mukherjee's state-specific multireference coupled cluster theory with singles and doubles.