定标谐波频率计算的模型化学建议：基准研究
Model Chemistry Recommendations for Scaled Harmonic Frequency Calculations: A Benchmark Study
摘要：
尽管定标谐波频率计算在化学中很受欢迎，但稀疏基准测试可用于指导用户选择适当的理论水平和基组（模型化学）。在这里，我们评估了600多个模型化学在缩放谐波频率计算中的性能，评估了不同的缩放因子类型。我们可以将我们的结果总结为三个主要发现：（1）使用针对三个不同频率区域优化的模型化学特定比例因子（低（低于1，000 cm-1），中（1，000 -2，000 cm-1），高（高于2, 000 cm-1））相比于其他选择，在定标谐波和实验频率之间产生更好的一致性;（2）更大的基组和更稳健的理论水平通常导致更好的性能;然而，特定的模型化学选择很重要;以及（3）在常规计算中应该预期离群值。就具体建议而言，总体而言，最高精度的模型化学是具有非Pople增强三重zeta基组的双杂交泛函，其可以产生低至7.6cm-1的中值频率误差（DSD-PBEP 86/def 2-TZVPD），接近谐波近似的误差。双zeta基组不应与双杂交泛函一起使用，因为与杂交泛函相比没有改进。注意，6- 311 G * 和6-311+G* 碱基对于振动频率表现为类似于双ζ基组。在标度后，所有研究的混合泛函与非Pople三重zeta基集将产生小于15 cm-1的中位误差，与B 97 -1/def 2-TZVPD的最佳结果为9.9 cm-1。双zeta基组与混合泛函的适当匹配可以产生高质量的结果。建议使用B 97 -1、TPSS 0-D3（BJ）或wB 97 X-D混合泛函，6- 31 G *、pc-1或pcseg-1进行快速常规计算，所有计算的中位误差均为11- 12 cm-1。
英文摘要：
Despite the popularity of scaled harmonic frequency calculations in chemistry, sparse benchmarking is available to guide users on appropriate level of theory and basis set choices (model chemistry). Here, we assess the performance of over 600 model chemistries in scaled harmonic frequencies calculations evaluating different scaling factors types. We can summarise our results into three main findings: (1) using model chemistry-specific scaling factors optimised for three different frequency regions (low (below 1,000cm-1), mid (1,000-2,000cm-1), and high (above 2,000cm-1)) results in better agreement between the scaled harmonic and experimental frequencies compared to other choices; (2) larger basis sets and more robust levels of theory generally lead to superior performance; however, the particular model chemistry choice matters; and (3) outliers should be expected in routine calculations. In terms of specific recommendations, overall, the highest accuracy model chemistries are double-hybrid functionals with non-Pople augmented triple-zeta basis sets, which can produce median frequency errors of down to 7.6cm-1 (DSD-PBEP86/def2-TZVPD) lying close to the error in the harmonic approximation. Double-zeta basis sets should not be used with double-hybrid functionals as there is no improvement compared to hybrid functionals. Note that the 6-311G* and 6-311+G* bases perform like double-zeta basis sets for vibrational frequencies. After scaling, all studied hybrid functionals with non-Pople triple-zeta basis sets will produce median errors of less than 15cm-1, with the best result of 9.9cm-1 with B97-1/def2-TZVPD. Appropriate matching of double-zeta basis sets with hybrid functionals can produce high quality results. The B97-1, TPSS0-D3(BJ) or wB97X-D hybrid functionals with 6-31G*, pc-1 or pcseg-1 are recommended for fast routine calculations, all delivering median errors of 11-12cm-1.
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