Analytical Forces for the Optimized Effective Potential Calculations
Analytical Forces for the Optimized Effective Potential Calculations
复制标题
用于优化有效势计算的分析力
DOI：
10.1021/acs.jctc.2c01208
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发表时间：
2023
影响因子：
5.5
通讯作者：
Huang, Chen
中科院分区：
文献类型：
--
作者：
Huang, Chen
优化有效势（OEP）方程在有限基组下是一个病态的线性方程组。如果不作任何特殊处理，所得到的交换关联势可能会出现非物理振荡。缓解这个问题的一种方法是正则化的解决方案;然而，正则化的XC势不是OEP方程的精确解。因此，系统的能量不再是相对于Kohn-Sham（KS）势的变分，并且分析力不能从Hellmann-Feynman定理导出。在这项工作中，我们开发了一个强大的和近黑盒OEP方法，以确保系统的能量是变化的KS潜力。其基本思想是在能量泛函中加入一个惩罚函数，使XC势正则化。然后可以根据赫尔曼-费曼定理推导出分析力。另一个关键的结果是，正则化的影响可以通过正则化XC势和近似XC势之间的差而不是正则化XC势来大大降低。数值试验表明，系统之间的力和能量差对正则化系数不敏感，这表明在实际应用中，不需要将正则化系数外推到零就可以得到精确的结构和电子性质。我们希望这种新方法被发现是有用的计算，采用先进的，基于轨道的泛函，特别是对于需要有效的力计算的应用程序。
The optimized effective potential (OEP) equation is an ill-conditioned linear system when using finite basis sets. Without any special treatment, the obtained exchange-correlation (XC) potential may have unphysical oscillations. One way to alleviate this problem is to regularize the solutions; however, a regularized XC potential is not the exact solution to the OEP equation. As a result, the system’s energy is no longer variational against the Kohn–Sham (KS) potential, and the analytical forces cannot be derived from the Hellmann–Feynman theorem. In this work, we develop a robust and nearly black-box OEP method to ensure that the system’s energy is variational against the KS potential. The basic idea is to add a penalty function that regularizes the XC potential to the energy functional. Analytical forces can then be derived based on the Hellmann–Feynman theorem. Another key result is that the impact of the regularization can be much reduced by regularizing the difference between the XC potential and an approximate XC potential rather than regularizing the XC potential. Numerical tests show that forces and the energy differences between systems are not sensitive to the regularization coefficient, which indicates that in practice accurate structural and electronic properties can be obtained without extrapolating the regularization coefficient to zero. We expect this new method to be found useful for calculations that employ advanced, orbital-based functionals, especially for applications that require efficient force calculations.