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-ζ 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.

中文翻译：

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多参考驱动相似重整化组的无自旋公式：第一行双原子分子和自旋交叉能量学的基准研究

我们报告了基于 Mukherjee 和 Kutzelnigg [J. 化学 物理。107, 432 (1997)]。该系综对给定总自旋量子数的所有微观状态求平均值，因此，它对于 SU(2) 变换是不变的。因此，所有方程都可以根据无自旋量重新表述，并且它们非常类似于自旋适应闭壳耦合簇 (CC) 理论中的方程。当前的实现用于评估各种截断 MR-DSRG 方法（高达三阶的微扰理论和具有单和双激发的迭代方法）在计算 33 个第一行双原子分子的常数时的准确性。这些第一排双原子的准确性趋势与我们之前对一小部分闭壳双原子分子进行的基准测试一致。然后，我们通过计算 [Fe(H₂ O) ₆ ] ²⁺和[Fe(NH ₃ ) ₆ ] ²⁺分子。焦点分析 (FPA) 表明，三阶微扰校正对于实现合理收敛的能量学至关重要。基于线性化 MR-DSRG 理论的 FPA 具有一体和二体算子以及多达五重ζ基组，预测 [Fe(H ₂ O) ₆ ] ²⁺和 [Fe(NH ₃ )的自旋分裂₆ ] ²⁺为 -35.7 和 -17.1 kcal mol ^-1，分别与局部 CC 理论的单、双和微扰三元组的结果非常吻合。