Department of Chemistry, University of California, Berkeley, Berkeley, CA 94720, USA.
Phys Chem Chem Phys. 2011 Nov 21;13(43):19325-37. doi: 10.1039/c1cp21635j. Epub 2011 Sep 28.
Many of the most promising new density functionals have improved the treatment of non-local exchange effects with the help of semi-empirical information and more sophisticated recipes for combining Hartree-Fock and local exchange approximations. In order to quantify recent advancements and identify directions for improvement, we have examined a broad spectrum of test problems. We evaluate the performance of several new hybrid density functionals (ωB97, ωB97X, ωB97X-D, LRC-ωPBEh, M06, M06-2X, and M06-HF) on a variety of chemical problems, some sensitive to the treatment of exact exchange (which we have hoped to systematically improve) and some which require a balanced treatment of correlation. Since all of the functionals under consideration are parameterized with ground-state thermochemical data, the benchmark aims to determine the applicability of the new density functionals to cases that have not been considered in the optimization of the semi-empirical parameters. The first class of benchmarks includes the excitation energies of 21 molecules (83 states) primarily from a recent benchmark conducted by Tozer and co-workers, with some additional references from data made available from the groups of Thiel and Truhlar. We briefly examine the conformational preferences of a small peptide and complete our study with two recently published sets of data that have shown large, systematic errors in simple alkane thermochemistry. While our results indicate that the more general hybrids currently under development perform well for problems outside of their parameterization and improve over the standard hybrid density functionals in an essentially systematic way, there is still a significant self-interaction error in the more difficult cases. Functionals based on a range-separation of exchange and functionals depending on the kinetic-energy density both perform comparably, and there is evidence for complementary strengths.
许多最有前途的新密度泛函在半经验信息和更复杂的组合哈特ree-fock 和局域交换近似的方法的帮助下，改善了非局域交换效应的处理。为了量化最近的进展并确定改进的方向，我们检查了广泛的测试问题。我们评估了几种新的混合密度泛函（ωB97、ωB97X、ωB97X-D、LRC-ωPBEh、M06、M06-2X 和 M06-HF）在各种化学问题上的性能，其中一些对精确交换的处理敏感（我们希望系统地改进），而另一些则需要对相关性进行平衡处理。由于所有考虑的泛函都是用基态热化学数据参数化的，基准的目的是确定新密度泛函在优化半经验参数时未考虑的情况下的适用性。第一类基准包括 21 个分子（83 个态）的激发能，主要来自 Tozer 及其同事最近进行的基准测试，还有一些来自 Thiel 和 Truhlar 小组提供的数据的参考文献。我们简要地研究了一个小肽的构象偏好，并完成了我们的研究，包括两个最近发表的数据集，它们在简单烷烃热化学方面显示出了大的、系统的误差。虽然我们的结果表明，目前正在开发的更通用的混合泛函在其参数化之外的问题上表现良好，并以基本系统的方式改进了标准混合密度泛函，但在更困难的情况下仍然存在显著的自相互作用误差。基于交换的范围分离的泛函和依赖于动能密度的泛函的性能相当，并且有互补优势的证据。
