Institut für Physikalische Chemie, Universität Mainz, Mainz, Germany.
J Chem Phys. 2011 Dec 28;135(24):244104. doi: 10.1063/1.3667202.
The formulation and implementation of the spin-free (SF) exact two-component (X2c) theory at the one-electron level (SFX2c-1e) is extended in the present work to the analytic evaluation of second derivatives of the energy. In the X2c-1e scheme, the four-component one-electron Dirac Hamiltonian is block diagonalized in its matrix representation and the resulting "electrons-only" two-component Hamiltonian is then used together with untransformed two-electron interactions. The derivatives of the two-component Hamiltonian can thus be obtained by means of simple manipulations of the parent four-component Hamiltonian integrals and derivative integrals. The SF version of X2c-1e can furthermore exploit available nonrelativistic quantum-chemical codes in a straightforward manner. As a first application of analytic SFX2c-1e second derivatives, we report a systematic study of the equilibrium geometry and vibrational frequencies for the bent ground state of the copper hydroxide (CuOH) molecule. Scalar-relativistic, electron-correlation, and basis-set effects on these properties are carefully assessed.
在本文中，我们将自旋无（SF）精确双组分（X2c）理论在单电子水平上的公式和实施（SFX2c-1e）扩展到了能量二阶导数的解析评估中。在 X2c-1e 方案中，四分量单电子 Dirac 哈密顿量在其矩阵表示中被块对角化，得到的“仅电子”双分量哈密顿量然后与未变换的双电子相互作用一起使用。因此，可以通过对原始四分量哈密顿量积分和导数积分进行简单的操作来获得双分量哈密顿量的导数。SF 版本的 X2c-1e 还可以以直接的方式利用现有的非相对论量子化学代码。作为解析 SFX2c-1e 二阶导数的第一个应用，我们报告了对弯曲基态的平衡几何形状和振动频率的系统研究铜氢氧化物（CuOH）分子。仔细评估了这些性质的标量相对论、电子相关和基组效应。
