Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz, Germany.
J Chem Phys. 2011 Aug 28;135(8):084114. doi: 10.1063/1.3624397.
We report the implementation of analytic energy gradients for the evaluation of first-order electrical properties and nuclear forces within the framework of the spin-free (SF) exact two-component (X2c) theory. In the scheme presented here, referred to in the following as SFX2c-1e, the decoupling of electronic and positronic solutions is performed for the one-electron Dirac Hamiltonian in its matrix representation using a single unitary transformation. The resulting two-component one-electron matrix Hamiltonian is combined with untransformed two-electron interactions for subsequent self-consistent-field and electron-correlated calculations. The "picture-change" effect in the calculation of properties is taken into account by considering the full derivative of the two-component Hamiltonian matrix with respect to the external perturbation. The applicability of the analytic-gradient scheme presented here is demonstrated in benchmark calculations. SFX2c-1e results for the dipole moments and electric-field gradients of the hydrogen halides are compared with those obtained from nonrelativistic, SF high-order Douglas-Kroll-Hess, and SF Dirac-Coulomb calculations. It is shown that the use of untransformed two-electron interactions introduces rather small errors for these properties. As a first application of the analytic geometrical gradient, we report the equilibrium geometry of methylcopper (CuCH(3)) determined at various levels of theory.
我们报告了在无自旋（SF）精确双组分（X2c）理论框架内评估一阶电性质和核力的分析能量梯度的实现。在本文提出的方案中，以下称为 SFX2c-1e，使用单个幺正变换对电子和正电子解的单电子狄拉克哈密顿量进行解耦，在其矩阵表示中。所得的双组分单电子矩阵哈密顿量与未经变换的双电子相互作用相结合，用于随后的自洽场和电子相关计算。通过考虑双组分哈密顿矩阵相对于外部微扰的全导数，考虑了计算性质中的“图像变化”效应。本文提出的分析梯度方案的适用性在基准计算中得到了证明。SFX2c-1e 对卤化氢的偶极矩和电场梯度的结果与非相对论、SF 高阶 Douglas-Kroll-Hess 和 SF 狄拉克-库仑计算的结果进行了比较。结果表明，对于这些性质，使用未经变换的双电子相互作用会引入相当小的误差。作为分析几何梯度的首次应用，我们报告了在不同理论水平下确定的甲基铜（CuCH(3)）的平衡几何形状。
