Inoue Nobuki, Watanabe Yoshihiro, Nakano Haruyuki
Department of Chemistry, Graduate School of Science, Kyushu University, Fukuoka, Japan.
J Comput Chem. 2024 Apr 5;45(9):523-535. doi: 10.1002/jcc.27251. Epub 2023 Nov 23.
The generalized Foldy-Wouthuysen (GFW) transformation was proposed as a generic form that unifies four types of transformations in relativistic two-component methods: unnormalized GFW(UN), and normalized form 1, form 2, and form 3 (GFW(N1), GFW(N2), and GFW(N3)). The GFW transformation covers a wide range of transformations beyond the simple unitary transformation of the Dirac Hamiltonian, allowing for the systematic classification of all existing two-component methods. New two-component methods were also systematically derived based on the GFW transformation. These various two-component methods were applied to hydrogen-like and helium-like ions. Numerical errors in energy were evaluated and classified into four types: the one-electron Hamiltonian approximation, the two-electron operator approximation, the newly defined "picture difference error (PDE)," and the error in determining the transformation, and errors in multi-electron systems were discussed based on this classification.
广义福尔德-伍思胡森（GFW）变换被提出作为一种通用形式，它统一了相对论性双分量方法中的四种变换类型：未归一化的GFW（UN）以及归一化形式1、形式2和形式3（GFW（N1）、GFW（N2）和GFW（N3））。GFW变换涵盖了超出狄拉克哈密顿量简单酉变换的广泛变换范围，从而能够对所有现有的双分量方法进行系统分类。基于GFW变换还系统地推导了新的双分量方法。这些各种双分量方法被应用于类氢离子和类氦离子。评估了能量中的数值误差并将其分为四种类型：单电子哈密顿量近似、双电子算符近似、新定义的“图像差异误差（PDE）”以及确定变换时的误差，并基于此分类讨论了多电子系统中的误差。
