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We report a spin-free formulation of the multireference (MR) drivensimilarity renormalization group (DSRG) by employing the ensemble normalordering of Mukherjee and Kutzelnigg [W. Kutzelnigg and D. Mukherjee, J. Chem.Phys. 107, 432 (1997)]. This ensemble averages over all microstates for a giventotal spin quantum number and, therefore, it is invariant with respect to SU(2)transformations. As such, all equations may be reformulated in terms ofspin-free quantities and they closely resemble those of spin-adaptedclosed-shell coupled cluster (CC) theory. The current implementation is used toassess the accuracy of various truncated MR-DSRG methods (perturbation theoryup to third order and iterative methods with single and double excitations) incomputing the constants of thirty-three first-row diatomic molecules. Theaccuracy trends for these first-row diatomics are consistent with our previousbenchmark on a small subset of closed-shell diatomic molecules. We then presentthe first MR-DSRG application on transition-metal complexes by computing thespin splittings of the [Fe(H$_2$O)$_6$]$^{2+}$ and [Fe(NH$_3$)$_6$]$^{2+}$molecules. Focal point analysis (FPA) shows that third-order perturbativecorrections are essential to achieve reasonably converged energetics. A FPAbased on the linearized MR-DSRG theory with one- and two-body operators and upto a quintuple-$\zeta$ basis set predicts the spin splittings of[Fe(H$_2$O)$_6$]$^{2+}$ and [Fe(NH$_3$)$_6$]$^{2+}$ to be $-35.7$ and $-17.1$kcal mol$^{-1}$, respectively, showing good agreement with results of local CCtheory with singles, doubles, and perturbative triples.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

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