Furche Filipp, Perdew John P
Institut für Physikalische Chemie, Universität Karlsruhe, Kaiserstrasse 12, 76128 Karlsruhe, Germany.
J Chem Phys. 2006 Jan 28;124(4):044103. doi: 10.1063/1.2162161.
We investigate the performance of contemporary semilocal and hybrid density functionals for bond energetics, structures, dipole moments, and harmonic frequencies of 3d transition-metal (TM) compounds by comparison with gas-phase experiments. Special attention is given to the nonempirical metageneralized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], which has been implemented in TURBOMOLE for the present work. Trends and error patterns for classes of homologous compounds are analyzed, including dimers, monohydrides, mononitrides, monoxides, monofluorides, polyatomic oxides and halogenides, carbonyls, and complexes with organic pi ligands such as benzene and cyclopentadienyl. Weakly bound systems such as Ca(2), Mn(2), and Zn(2) are discussed. We propose a reference set of reaction energies for benchmark purposes. Our all-electron results with quadruple zeta valence basis sets validate semilocal density-functional theory as the workhorse of computational TM chemistry. Typical errors in bond energies are substantially larger than in (organic) main group chemistry, however. The Becke-Perdew'86 [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 33, 8822 (1986)] GGA and the TPSS meta-GGA have the best price/performance ratio, while the TPSS hybrid functional achieves a slightly lower mean absolute error in bond energies. The popular Becke three-parameter hybrid B3LYP underbinds significantly and tends to overestimate bond distances; we give a possible explanation for this. We further show that hybrid mixing does not reduce the width of the error distribution on our reference set. The error of a functional for the s-d transfer energy of a TM atom does not predict its error for TM bond energies and bond lengths. For semilocal functionals, self-interaction error in one- and three-electron bonds appears to be a major source of error in TM reaction energies. Nevertheless, TPSS predicts the correct ground-state symmetry in the vast majority of cases and rarely fails qualitatively. This further confirms TPSS as a general purpose functional that works throughout the periodic table. We also give workstation timing comparisons for the 645-atom protein crambin.
我们通过与气相实验进行比较，研究了当代半局域和杂化密度泛函对3d过渡金属（TM）化合物的键能、结构、偶极矩和谐波频率的性能。特别关注了陶、佩德韦、斯塔罗沃罗夫和斯库塞里亚（TPSS）提出的非经验元广义梯度近似（meta-GGA）[《物理评论快报》91, 146401 (2003)]，在本工作中已在TURBOMOLE中实现了该近似。分析了同源化合物类别的趋势和误差模式，包括二聚体、一氢化物、一氮化物、一氧化物、一氟化物、多原子氧化物和卤化物、羰基化合物以及与有机π配体（如苯和环戊二烯基）形成的配合物。讨论了弱束缚体系，如Ca(2)、Mn(2)和Zn(2)。我们提出了一组用于基准测试的反应能量参考值。我们使用四重ζ价基组的全电子结果验证了半局域密度泛函理论作为计算TM化学的主要工具。然而，键能中的典型误差比（有机）主族化学中的误差大得多。Becke-Perdew'86 [《物理评论A》38, 3098 (1988); 《物理评论B》33, 8822 (1986)]广义梯度近似（GGA）和TPSS元-GGA具有最佳的性价比，而TPSS杂化泛函在键能方面实现了略低的平均绝对误差。流行的Becke三参数杂化泛函B3LYP明显结合不足，并且往往高估键长；我们对此给出了一个可能的解释。我们进一步表明，杂化混合并没有减小我们参考集上误差分布的宽度。一个泛函对TM原子的s-d转移能量的误差并不能预测其对TM键能和键长的误差。对于半局域泛函，单电子键和三电子键中的自相互作用误差似乎是TM反应能量误差的主要来源。然而，TPSS在绝大多数情况下预测了正确的基态对称性，并且很少在定性上失败。这进一步证实了TPSS作为一种适用于整个周期表的通用泛函。我们还给出了645个原子的蛋白质胰蛋白酶抑制剂的工作站计时比较。
