We present a benchmark study on equilibrium structures optimized with subsystem density functional theory (sDFT) employing a new analytical gradient implementation in the program SERENITY. Geometry optimizations are performed on all complexes of the S22 [Jurečka et al. Phys. Chem. Chem. Phys.2006, 8, 1985–1993] and A24 [Řezáč and Hobza. J. Chem. Theory Comput.2013, 9, 2151–2155] test sets. While some combinations of approximate exchange-correlation (XC) and nonadditive kinetic-energy functionals (e.g., LDA/Thomas–Fermi or PW91/PW91k) more or less successfully mimic the effect of medium-range dispersion in these complexes, we also include the combination of BP86/LLP91. This functional reproduces the dispersion problem of the corresponding BP86 Kohn–Sham (KS-)DFT calculations and can hence successfully be corrected by empirical dispersion corrections developed for KS-DFT. We propose this as a robust and accurate strategy for sDFT geometry optimizations, which appears to be preferable over the previously used strategy relying on error cancellation between XC and nonadditive kinetic-energy functionals. In fact, the best results in our benchmark are obtained from BP86/LLP91 together with a D3-type dispersion correction. We also discuss the difference between our Gaussian-type orbital implementation in SERENITY and a Slater-type orbital based implementation in the Amsterdam density functional (ADF) program but only find small differences in most cases.

中文翻译：

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子系统密度泛函理论形式主义中的几何优化：一项基准研究

我们提出了一项对平衡结构的基准研究，该平衡结构通过子系统密度泛函理论（sDFT）在SERENITY程序中采用了新的解析梯度实现进行了优化。对S22的所有配合物进行几何优化[Jurečka等。物理 化学 化学 物理 2006年，8，1985-1993]和A24 [雷扎克和Hobza。J.化学。理论计算。2013年，9，2151–2155]测试集。虽然近似交换相关（XC）和非相加动能功能（例如LDA / Thomas-Fermi或PW91 / PW91k）的某些组合或多或少成功地模仿了这些复合物中的中程分散效应，但我们也包括了BP86 / LLP91的组合。此函数再现了相应的BP86 Kohn-Sham（KS-）DFT计算的色散问题，因此可以通过为KS-DFT开发的经验色散校正成功地进行校正。我们建议将其作为sDFT几何优化的可靠且准确的策略，这似乎比以前使用的依赖XC和非相加动能功能之间的误差消除的策略更为可取。实际上，从BP86 / LLP91以及D3型色散校正中获得了我们基准测试中的最佳结果。我们还讨论了SERENITY中的高斯型轨道实现与Amsterdam密度函数（ADF）程序中基于Slater型轨道的实现之间的区别，但在大多数情况下只发现了很小的区别。