Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan.
Waseda Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan.
J Chem Phys. 2018 Mar 21;148(11):114109. doi: 10.1063/1.5016581.
This article proposes a gauge-origin independent formalism of the nuclear magnetic shielding constant in the two-component relativistic framework based on the unitary transformation. The proposed scheme introduces the gauge factor and the unitary transformation into the atomic orbitals. The two-component relativistic equation is formulated by block-diagonalizing the Dirac Hamiltonian together with gauge factors. This formulation is available for arbitrary relativistic unitary transformations. Then, the infinite-order Douglas-Kroll-Hess (IODKH) transformation is applied to the present formulation. Next, the analytical derivatives of the IODKH Hamiltonian for the evaluation of the nuclear magnetic shielding constant are derived. Results obtained from the numerical assessments demonstrate that the present formulation removes the gauge-origin dependence completely. Furthermore, the formulation with the IODKH transformation gives results that are close to those in four-component and other two-component relativistic schemes.
本文提出了一种基于幺正变换的两分量相对论框架下核磁感应常数的规范原点无关形式。该方案将规范因子和幺正变换引入原子轨道。通过将狄拉克哈密顿量与规范因子一起对角化，得到了两分量相对论方程的形式。这种形式适用于任意的相对论幺正变换。然后，将无限阶道格拉斯-克罗尔-赫斯（IODKH）变换应用于本形式。接下来，推导出用于评估核磁感应常数的 IODKH 哈密顿量的解析导数。数值评估的结果表明，本形式完全消除了规范原点的依赖性。此外，带有 IODKH 变换的形式给出的结果与四分量和其他两分量相对论方案非常接近。
