Analytic energy gradients with respect to nuclear coordinates for an exact exchange-only (EXX) Kohn–Sham method are presented. In the underlying EXX method, the exact exchange potential is obtained as the electrostatic potential of an exchange charge density, which is determined via the optimized effective potential method. Parts of the presented calculation of analytic EXX energy gradients can be reused for analytic energy gradients in self-consistent Kohn–Sham methods treating correlation via the adiabatic-connection fluctuation–dissipation theorem, e.g., methods relying on the random phase approximation. A version of the analytic EXX energy gradients that uses density-fitting is shown to be highly efficient. The accuracy of the analytic energy gradients is tested by comparison with numerically calculated gradients.

中文翻译：

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精确交换Kohn-Sham方法的解析能量梯度

提出了一种仅用于精确交换（EXX）Kohn-Sham方法的相对于核坐标的解析能量梯度。在基本的EXX方法中，将获得精确的交换电势作为交换电荷密度的静电电势，该静电电势是通过优化的有效电势方法确定的。可以通过绝热连接波动耗散定理（例如，依赖于随机相位近似的方法），在自洽的Kohn-Sham方法中使用相关的分析EXX能量梯度的计算方法来重现分析能量梯度。使用密度拟合的EXX解析能量梯度版本显示出很高的效率。通过与数值计算的梯度进行比较来测试分析能量梯度的准确性。