多参考驱动的相似性重整化群的无自旋表述：第一排双原子分子和自旋交叉能量学的基准研究
Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics
摘要：
利用Mukherjee和Kutzelnigg [W. Kutzelnigg和D. Mukherjee，J.Chem.Phys.107，432（1997）]。对于给定的总自旋量子数，这个系综平均了所有的微观态，因此，它对于SU（2）变换是不变的。因此，所有的方程可以重新制定的自旋自由量，他们非常类似的自旋自适应闭壳耦合集团（CC）理论。目前的实施是用来评估各种截断MR-DSRG方法（微扰理论高达三阶和迭代方法与单，双激发）在计算33个第一行双原子分子的常数的准确性。这些第一行的精确度趋势与我们以前的一个小子集的闭壳双原子分子的基准一致。通过计算[Fe（H $_2$ O）$_6$ ] $^{2+}$和[Fe（NH $_3$）$_6$ ] $^{2+}$分子的自旋劈裂，首次提出了MR-DSRG在过渡金属配合物上的应用。焦点分析（FPA）表明，三阶微扰修正是必不可少的，以实现合理收敛的能量。基于线性化的MR-DSRG理论，采用一体和二体算符以及高达五元的$ζ$基组，（H $_2$ O）PDMATHAMN] $^{2+}$和[Fe（NH $_3$）$_6$ ] $^{2+}$为$-35.7$且$-17.1$千卡/摩尔$^{-1}$，分别显示出良好的协议与本地CC理论的结果与单打，双打，和微扰三重。
英文摘要：
We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) by employing the ensemble normal ordering of Mukherjee and Kutzelnigg [W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997)]. This ensemble averages over all microstates for 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 thirty-three 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(H$_2$O)$_6$]$^{2+}$ and [Fe(NH$_3$)$_6$]$^{2+}$ molecules. Focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. A 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(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 CC theory with singles, doubles, and perturbative triples.
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