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物理化学学报  2017, Vol. 33 Issue (6): 1149-1159    DOI: 10.3866/PKU.WHXB201703291
论文     
B972-PFD:一种高精度的色散校正密度泛函方法
何禹1,2,王一波1,2,*()
1 贵州省高性能计算化学重点实验室,贵阳550025
2 贵州大学网络与信息中心,贵阳550025
B972-PFD: A High Accuracy Density Functional Method for Dispersion Correction
Yu HE1,2,Yi-Bo WANG1,2,*()
1 Key Laboratory of High Performance Computational Chemistry, Guiyang 550025, P. R. China
2 Network and Information Center of Guizhou University, Guiyang 550025, P. R. China
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摘要:

发现一种与球原子经验色散模型SAM深度契合的杂化泛函B972,组合成高精度的色散校正密度泛函B972-PFD。采用S66、S66x8和S22标准数据集以及大气氢键团簇、Adenine-Thymine的ππ堆叠、Watson-Crick氢键复合物和甲烷结合(H2O)20水簇等体系测试了B972-PFD的性能。测试结果显示:对于S66数据集B972-PFD方法的精度与Head-Gordon研究组的三个新泛函ωB97X-V、B97M-V和ωB97M-V处于同一水平,相对于CCSD(T)/CBS金质标准,结合能的RMSD小于1 kJ·mol-1;在其它数据集的测试中,B972-PFD方法也表现出很好的计算精度。通过研究基函数效应,我们推荐Pople的6-311++G(2dp)作为B972-PFD方法的最优性价比基组。

关键词: 分子间相互作用密度泛函色散校正球原子色散模型B972-PFD    
Abstract:

A novel DFT-D method, B972-PFD, has been found by combining the B972 hybrid density functional with the empirical dispersion correction based on the spherical atom model (SAM). The performance of the B972-PFD method is assessed on the S66, S66x8, and S22 standard data sets, atmospheric hydrogen-bonded clusters, the Adenine-Thymine ππ stacked, Watson-Crick hydrogen-bonded complexes, and the methane to (H2O)20 water cluster. The benchmark results of the S66 test set show that B972-PFD and three recently developed density functionals, ωB97X-V, B97M-V, and ωB97M-V developed by the Head-Gordon group, are at the same level of accuracy, and have an root-mean-square deviation (RMSD) of binding energies less than 1 kJ·mol-1 relative to the CCSD(T)/CBS gold standard. The B972-PFD method also showed excellent accuracy in other data set tests. The basis set effect of the B972-PFD method has been benchmarked, and we recommend that the favorable price/performance ratios basis set is Pople's 6-311++G(2d, p).

Key words: Intermolecular Interaction    DFT-D    Spherical atom model for dispersion correction    B972-PFD
收稿日期: 2017-01-10 出版日期: 2017-03-29
中图分类号:  O641  
基金资助: 国家自然科学基金(41165007);贵州省自然科学基金(20082116)
通讯作者: 王一波     E-mail: ybw@gzu.edu.cn
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引用本文:

何禹,王一波. B972-PFD:一种高精度的色散校正密度泛函方法[J]. 物理化学学报, 2017, 33(6): 1149-1159.

Yu HE,Yi-Bo WANG. B972-PFD: A High Accuracy Density Functional Method for Dispersion Correction. Acta Physico-Chimica Sinca, 2017, 33(6): 1149-1159.

链接本文:

http://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201703291        http://www.whxb.pku.edu.cn/CN/Y2017/V33/I6/1149

图1  S66测试集各类泛函计算精度范围
Method
with PFD
MD/
(kJ?mol?1)
MAD/
(kJ?mol?1)
RMSD/
(kJ?mol?1)
MAX/
(kJ?mol?1)
Method
without PFD
MD/
(kJ?mol?1)
MAD/
(kJ?mol?1)
RMSD/
(kJ?mol?1)
MAX/
(kJ?mol?1)
B972-PFD0.290.710.962.97B97214.6214.6216.6939.78
B3LYP-PFD?0.631.261.766.44B3LYP13.7113.7116.1738.11
TPSS-PFD?1.431.521.946.85TPSS12.9012.9015.2637.86
B973-PFD?1.261.512.056.9B97313.0513.0514.7334.92
B3PW91-PFD1.511.842.224.69B3PW9115.8215.8218.1141.66
APF-PFD?2.802.803.269.25APF11.5311.5613.7833.42
X3LYP-PFD?3.133.193.709.77X3LYP11.2011.2213.6933.22
BLYP-PFD3.313.393.856.69BLYP17.6417.6420.1346.68
B97-PFD?4.564.564.8511.3B979.789.8511.9030.53
PBE-PFD?5.235.235.5611.51PBE9.099.2611.4430.32
B97-K-PFD?4.444.525.8219.66B97-K9.879.9210.9822.17
PBE0-PFD?5.825.826.2314.18PBE08.528.6910.8327.65
B971-PFD?6.286.286.6914.9B9718.038.2010.0726.94
ωB97X-PFD?13.9713.9715.1533.51ωB97X0.332.092.798.32
ωB97-PFD?15.2315.2316.6537.99ωB97?0.891.582.168.89
表1  筛选泛函DFT-PFD/6-311++G(2d, p)和DFT/6-311++G(2d, p)以CCSD(T)/CBS为基准的S66数据集误差分析
图2  筛选泛函DFT-PFD/6-311++G(2d, p)以CCSD(T)/CBS为基准的S66数据集误差分析
图3  B97系列泛函DFT-PFD/6-311++G(2d, p)以CCSD(T)/CBS为基准的S66数据集误差分析
Basis setMDMADRMSDMAX
6-311G(2d, p)0.461.051.303.18
6-311++G(2d, p)0.290.710.962.97
6-311++G(2df, 2p)0.440.750.993.08
6-311++G(3df, 3pd)0.460.791.083.75
cc-pVDZ0.961.261.634.44
aug-cc-pVDZ0.500.791.053.14
cc-pVTZ0.590.921.264.18
aug-cc-pVTZ0.460.841.133.89
cc-pVQZ0.450.841.164.42
aug-cc-pVQZ0.390.801.124.30
def2-TZVP0.380.791.053.18
def2-TZVPP0.460.791.134.18
def2-QZVPP0.400.791.124.30
表2  B972-PFD泛函基于S66数据集的基函数效应分析(kJ?mol?1)
MethodBasis setMDMADRMSDMAX
B972-PFD6-311++G(2d, p)0.290.710.962.97
APF-PFD*6-311++G(2d, p)?0.791.211.767.32
ωB97X-D6-311++G(3df, 3pd)?1.261.381.886.44
ωB97X-D36-311++G(3df, 3pd)?0.961.011.244.03
B3LYP-D3(BJ)def2-QZVP?0.920.961.515.77
ωB97X-Vaug-cc-pVDZ0.180.340.471.80
ωB97X-Vaug-cc-pVTZ0.130.410.572.69
B97M-Vaug-cc-pVDZ0.650.780.931.97
B97M-Vaug-cc-pVTZ0.390.630.771.96
ωB97M-Vaug-cc-pVDZ?0.300.500.752.08
ωB97M-Vaug-cc-pVTZ?0.070.370.532.19
XYG36-311+G(3df, 2p)0.141.301.614.49
XYGJ-OS6-311+G(3df, 2p)0.461.461.794.73
ωB97X-2cc-pV(T/Q)Z1.181.341.775.71
PBE0-26-311++G(3df, 3pd)2.772.793.408.09
表3  B972-PFD与其它泛函基于S66数据以CCSD(T)/CBS为基准误差分析(kJ?mol?1)
图4  B972-PFD与其他DFT-D泛函方法基于S66数据集的计算精度比较
MethodBasis setMDMADRMSDMAXRef.
XYG36-311+G(3df, 2p)?0.460.791.052.517
ωB97X-D36-311++G(3df, 3pd)?0.330.751.053.4345
ωB97X-D6-311++G(3df, 3pd)?0.590.791.052.4345
B972-PFD6-311++G(2d, p)0.421.051.342.68this work
B972-PFD6-311++G(2df, 2p)0.541.051.302.43this work
B972-PFD6-311++G(3df, 3pd)0.521.071.353.10this work
APF-PFD*6-311++G(2d, p)?1.091.341.976.53this work
APF-PFD6-311++G(2d, p)?3.413.414.261.55this work
B3LYP-D3(BJ)def2-QZVP?1.131.171.805.02this work
ωB97X-Vaug-cc-pVDZ0.750.891.253.06this work
ωB97X-Vaug-cc-pVTZ0.690.961.272.79this work
B97M-Vaug-cc-pVDZ1.391.391.794.08this work
B97M-Vaug-cc-pVTZ0.991.041.363.23this work
ωB97M-Vaug-cc-pVDZ?0.131.041.453.25this work
ωB97M-Vaug-cc-pVTZ0.230.861.183.05this work
表4  B972-PFD与其它泛函基于S22测试集以CCSD(T)/CBS为基准误差分析(kJ?mol?1)
Method/ComplexRef.37B972-PFD
BS1
B972-PFD
BS2
XYG3
BS3
M062X
BS3
ωB97X-D
BS3
ωB97X-V
BS3
B97M-V
BS3
ωB97M-V-V
BS3
(H2SO4)(H2O)?58.032.182.470.87?2.760.130.491.070.14
(H2SO4)(NH3)?84.77?0.59?0.590.78?2.59?0.75?0.022.761.50
(H2SO4)(CH3NH2)?396.770.59?0.210.20?1.975.27?4.1810.893.34
(H2SO4)((CH3)2NH)?459.110.29?0.211.08?1.345.56?7.0715.932.07
(H2SO4)((CH3)3N)?367.271.171.091.740.004.35?1.4317.726.01
(H2SO4)(H2N(CH3)2NH2)?388.02?2.38?2.721.06?4.272.22?3.749.412.83
(H2SO4)(HCOOH)?90.960.67?0.841.49?2.09?1.00?1.181.78?0.72
(H2SO4)(CH3COOH)?97.110.13?1.421.61?1.92?1.13?1.271.44?0.81
(H2SO4)(HCO3H)?80.292.431.092.10?2.51?0.29?0.461.25?0.91
(H2SO4)(CH3CO3H)?86.941.670.332.40?2.30?0.50?0.590.93?1.07
(H2SO4)2?88.743.140.252.17?1.21?1.46?0.502.82?0.76
MD0.84?0.071.41?2.091.13?1.816.001.06
MAD1.381.021.412.092.061.906.001.83
MAX3.142.722.404.275.567.0717.726.01
RMSD1.691.321.552.322.832.828.532.44
表5  B972-PFD与其它泛函基于大气化学强氢键数据集使用CCSD(T)/CBS基准所得误差分析(kJ?mol?1)
Intermolecular distanceMDMADRMSDMAX
0.901.722.092.647.03
0.950.841.131.464.48
1.000.290.670.922.93
1.05?0.080.630.843.14
1.10?0.330.710.923.64
1.25?0.840.921.094.06
1.50?0.880.880.963.01
2.00?0.330.330.420.92
表6  S66x8测试集B972-PFD/6-311++G(2d, p)以CCSD(T)/CBS为基准误差分析(kJ?mol?1)
MethodMD allRMSD allRMSD H-bondsRMSD π stacksRMSD LondonRMSD mixed
B972-PFDa0.041.130.921.671.001.05
M06b?3.224.063.476.233.393.64
M06-2Xb1.211.881.592.302.381.59
M06Lb2.893.353.314.142.473.60
B97Db?0.542.132.851.722.261.00
PBE0-D3(BJ)b0.501.461.921.631.050.88
TPSS0-D3(BJ)b0.041.261.511.171.340.84
B3LYP-D3(BJ)b0.210.841.170.790.540.17
B3PW91-D3(BJ)b?0.171.301.461.840.920.84
PW6B95-D3(BJ)b?0.421.421.881.461.050.96
CAM-B3LYP-D3(BJ)b?0.311.792.382.311.050.85
ωB97X-D3b?0.331.340.671.422.380.71
LC-wPBE-D3(BJ)b0.131.051.261.090.790.88
TPSS-D3(BJ)b?0.251.421.211.921.761.09
PBE-D3(BJ)b0.381.511.632.301.340.88
BP86-D3(BJ)b0.962.432.014.482.011.55
BLYP-D3(BJ)b?0.460.961.091.050.710.96
B97D3b0.001.551.971.721.341.00
ωB97X-Vb?0.330.960.841.550.750.79
表7  B972-PFD与其它18种DFT-D泛函基于S66x8数据集以CCSD(T)/CBS为基准的误差分析(kJ?mol?1)
图5  Adenine-Thymine π-π与Adenine?Thymine Watson-Crick复合物在CCSD(T)与B972-PFD方法中的势能曲线
MethodBinding energyRef.
QMC?22.15 ± 2.0947
B972-PFD/6-311++G(2d, p)?19.56this work
B972-PFD/aug-cc-pVTZ?20.48this work
B972-PFD/aug-cc-pVQZ?20.61this work
APF-PFD/6-311++G(2d, p)?24.91this work
APF-PFD/aug-cc-pVTZ?25.83this work
APF-PFD*/6-311++G(2d, p)?19.60this work
APF-PFD*/aug-cc-pVTZ?20.52this work
MP2/CBS?21.0748
MP2C-F12/aug-cc-pVTZ?19.2347
att-MP2/aug-cc-pVTZ?16.7648
ωB97X-V/aug-cc-pVTZ?26.2948
B97M-V/aug-cc-pVTZ?21.23this work
ωB97M-V/aug-cc-pVTZ?22.95this work
ωB97X-D/ aug-cc-pVTZ?26.7148
ωB97X-D3/6-311++G(3df, 3pd)?29.37this work
LC-VV10/aug-cc-pVTZ?4.8948
XYG3/aug-cc-pVTZ(UCP)?18.62this work
XYGJ-OS/aug-cc-pVTZ(UCP)?20.03this work
B3LYP-D3(BJ)/aug-cc-pVTZ?27.92this work
B2PLYP/aug-cc-pVTZ?4.5648
B2PLYP-D3(zero)/ aug-cc-pVTZ?25.2548
M06-2X/aug-cc-pVTZ?25.5448
M06-2X-D3(zero)/ aug-cc-pVTZ?30.6048
DFT-SAPT/aug-cc-pVTZ?16.2247
XSAPT(KS)+D3/hpTZVPP?14.5548
表8  CH4与(H2O)20作用能计算(kJ?mol?1)
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