Franco de Carvalho Felipe, Curchod Basile F E, Penfold Thomas J, Tavernelli Ivano
Laboratory of Computational Chemistry and Biochemistry, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Switzerland.
SwissFEL, Paul Scherrer Inst, CH-5232 Villigen, Switzerland.
J Chem Phys. 2014 Apr 14;140(14):144103. doi: 10.1063/1.4870010.
Using an approach based upon a set of auxiliary many-electron wavefunctions we present a rigorous derivation of spin-orbit coupling (SOC) within the framework of linear-response time-dependent density functional theory (LR-TDDFT). Our method is based on a perturbative correction of the non-relativistic collinear TDDFT equations using a Breit-Pauli spin-orbit Hamiltonian. The derivation, which is performed within both the Casida and Sternheimer formulations of LR-TDDFT, is valid for any basis set. The requirement of spin noncollinearity for the treatment of spin-flip transitions is also discussed and a possible alternative solution for the description of these transitions in the collinear case is also proposed. Our results are validated by computing the SOC matrix elements between singlet and triplet states of two molecules, formaldehyde and acetone. In both cases, we find excellent agreement with benchmark calculations performed with a high level correlated wavefunction method.
我们采用基于一组辅助多电子波函数的方法，在线性响应含时密度泛函理论（LR - TDDFT）框架内给出了自旋 - 轨道耦合（SOC）的严格推导。我们的方法基于使用Breit - Pauli自旋 - 轨道哈密顿量对非相对论共线TDDFT方程进行微扰修正。该推导在LR - TDDFT的Casida和Sternheimer形式体系内进行，对任何基组均有效。还讨论了处理自旋翻转跃迁时自旋非共线性的要求，并提出了在共线情况下描述这些跃迁的一种可能替代解决方案。通过计算甲醛和丙酮这两种分子的单重态和三重态之间的SOC矩阵元，验证了我们的结果。在这两种情况下，我们发现与使用高水平相关波函数方法进行的基准计算结果非常吻合。
