Li Zhendong, Xiao Yunlong, Liu Wenjian
Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China.
J Chem Phys. 2014 Aug 7;141(5):054111. doi: 10.1063/1.4891567.
The idea for separating the algebraic exact two-component (X2C) relativistic Hamiltonians into spin-free (sf) and spin-dependent terms [Z. Li, Y. Xiao, and W. Liu, J. Chem. Phys. 137, 154114 (2012)] is extended to both electric and magnetic molecular properties. Taking the spin-free terms (which are correct to infinite order in α ≈ 1/137) as zeroth order, the spin-dependent terms can be treated to any desired order via analytic derivative technique. This is further facilitated by unified Sylvester equations for the response of the decoupling and renormalization matrices to single or multiple perturbations. For practical purposes, explicit expressions of order α(2) in spin are also given for electric and magnetic properties, as well as two-electron spin-orbit couplings. At this order, the response of the decoupling and renormalization matrices is not required, such that the expressions are very compact and completely parallel to those based on the Breit-Pauli (BP) Hamiltonian. However, the former employ sf-X2C wave functions, whereas the latter can only use nonrelativistic wave functions. As the sf-X2C terms can readily be interfaced with any nonrelativistic program, the implementation of the O(α²) spin-orbit corrections to sf-X2C properties requires only marginal revisions of the routines for evaluating the BP type of corrections.
将代数精确双分量（X2C）相对论哈密顿量分离为无自旋（sf）项和自旋相关项的想法[Z. Li, Y. Xiao, and W. Liu, J. Chem. Phys. 137, 154114 (2012)]被扩展到电和磁分子性质。以无自旋项（在α≈1/137中精确到无穷阶）作为零阶，自旋相关项可通过解析导数技术处理到任意期望的阶数。解耦矩阵和重整化矩阵对单重或多重微扰响应的统一西尔维斯特方程进一步推动了这一过程。出于实际目的，还给出了自旋的α(2)阶电和磁性质以及双电子自旋 - 轨道耦合的显式表达式。在此阶数下，不需要解耦矩阵和重整化矩阵的响应，使得表达式非常简洁，并且与基于布赖特 - 泡利（BP）哈密顿量的表达式完全平行。然而，前者采用sf - X2C波函数，而后者只能使用非相对论波函数。由于sf - X2C项可以很容易地与任何非相对论程序对接，对sf - X2C性质进行O(α²)自旋 - 轨道修正的实现只需要对评估BP类型修正的例程进行少量修改。
