Pokhilko Pavel, Epifanovsky Evgeny, Krylov Anna I
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA.
Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA.
J Chem Phys. 2019 Jul 21;151(3):034106. doi: 10.1063/1.5108762.
Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., M = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.
非相对论激发态计算的标准实现方式仅计算自旋多重态的一个分量（即 (M = 0) 的三重态）；然而，对于推导与自旋相关的实验可观测量而言，所有分量的矩阵元都是必需的。维格纳 - 埃卡特定理使人们能够规避对所有多重态分量进行显式计算。我们通过将维格纳 - 埃卡特定理应用于为单个多重态分量计算的约化单粒子跃迁密度矩阵，来生成所有其他自旋 - 轨道矩阵元。除了计算效率外，这种方法还解决了在玻恩 - 奥本海默核与电子自由度分离中出现的相位问题。本文提出了一种通用形式体系及其在使用运动方程耦合簇波函数计算自旋 - 轨道耦合中的应用。通过平均场自旋 - 轨道处理包含双电子贡献。讨论了为开壳层参考构建自旋 - 轨道平均场算符的内在问题，并提出了一种解决方案。该方法通过使用几个自由基和双自由基进行了基准测试。通过计算高自旋三（吡咯基甲基）胺铁（II）配合物中自旋反转的势垒，说明了该方法的优点。
