Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany.
J Phys Chem A. 2012 Nov 8;116(44):10864-9. doi: 10.1021/jp308916s. Epub 2012 Oct 30.
We have derived and implemented analytical gradients for broken-symmetry unrestricted density functional calculations (BS-UDFT) with removal of spin contamination by Yamaguchi's approximate spin projection method. Geometry optimizations with these analytical gradients (AGAP-opt) yield results consistent with those obtained with the previously available numerical gradients (NAP-opt). The AGAP-opt approach is found to be more precise, efficient, and robust than NAP-opt. It allows full geometry optimizations for large open-shell systems. We report results for three types of organic diradicals and for a binuclear vanadium(II) complex to demonstrate the merits of removing the spin contamination effects during geometry optimization (AGAP-opt vs BS-UDFT) and to illustrate the superior performance of the analytical gradients (AGAP-opt vs NAP-opt). The results for the vanadium(II) complex indicate that the AGAP-opt method is capable of handling pronounced spin contamination effects in large binuclear transition metal complexes with two magnetic centers.
我们已经推导出并实现了通过 Yamaguchi 近似自旋投影方法去除自旋污染的非对称限制密度泛函计算（BS-UDFT）的解析梯度。使用这些解析梯度（AGAP-opt）进行几何优化的结果与先前可用的数值梯度（NAP-opt）的结果一致。AGAP-opt 方法比 NAP-opt 更精确、高效和稳健。它允许对大型开壳系统进行完整的几何优化。我们报告了三种类型的有机双自由基和双核钒（II）配合物的结果，以证明在几何优化期间去除自旋污染效应（AGAP-opt 与 BS-UDFT）的优点，并说明解析梯度的优越性能（AGAP-opt 与 NAP-opt）。对于钒（II）配合物的结果表明，AGAP-opt 方法能够处理带有两个磁心的大型双核过渡金属配合物中明显的自旋污染效应。
