Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg [J. Chem. Phys. 107, 432 (1997)]. This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H2O)(6)](2+) and [Fe(NH3)(6)](2+) molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple-zeta basis set predicts the spin splittings of [Fe(H2O)(6)](2+) and [Fe(NH3)(6)](2+) to be -35.7 and -17.1 kcal mol(-1), respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples. Published under an exclusive license by AIP Publishing.

Automated summary

This study presents a spin-free formulation of the multireference driven similarity renormalization group based on ensemble normal ordering, which is used to compute constants of diatomic molecules and spin splittings of transition-metal complexes, demonstrating that third-order perturbative corrections are essential for achieving reasonably converged energetics. The results suggest good agreement with local CC theory, highlighting the importance of spin-free quantities in accurately predicting molecular properties.