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结合机器学习算法提高从头算方法对HF/HBr/H35Cl/Na35Cl振动能谱的预测性能

杨章章 刘丽 万致涛 付佳 樊群超 谢锋 张燚 马杰

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结合机器学习算法提高从头算方法对HF/HBr/H35Cl/Na35Cl振动能谱的预测性能

杨章章, 刘丽, 万致涛, 付佳, 樊群超, 谢锋, 张燚, 马杰

Combining machine learning algorithm to improve prediction performance of ab initio method for vibrational energy spectra of HF/HBr/H35Cl/Na35Cl

Yang Zhang-Zhang, Liu Li, Wan Zhi-Tao, Fu Jia, Fan Qun-Chao, Xie Feng, Zhang Yi, Ma Jie
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  • 高精度振动能谱蕴含着分子体系的大量量子特征, 是人们认识和操控分子的重要基础数据. 目前, 从头算方法在计算分子的振动能谱方面取得了大量成果, 但是仍然面临着精度和计算量上的挑战. 本文提出了一种综合从头算方法与机器学习算法进行能谱预测的新方法, 在提高振动能级精度的同时大幅降低了计算量. 针对HF、HBr、H35Cl和Na35Cl等卤素分子的研究结果表明, 相较于单独的CCSD(T)/cc-pV5Z计算方法, 新方法将误差减少了50%以上, 同时将计算量降低了一个数量级.
    Halides play an important role in atmospheric chemistry, corrosion of steel, and also in controlling the abundance of O3. Moreover high-precision vibrational energy spectra contain a large amount of quantum information of molecular system and are basic data for people to understand and manipulate molecules. At present, ab-initio methods have achieved many calculation results of the potential energy surfaces and corresponding vibrational energy of molecules, but they still face challenges in terms of accuracy and computational cost. Recently, data-driven machine learning methods have demonstrated very strong capability of extracting high-dimensional functional relationships from massive data and have been widely used in spectrum studies. ​Therefore, a theoretical approach to combining ab-initio method and machine learning algorithm is presented here to predict the vibrational energy of diatomic systems, which improves the accuracy and simultaneously reduces the computational cost. Firstly, the vibrational energy levels of 42 diatomic molecules are obtained by using different CCSD(T) methods to calculate the configurations from simple to complex and the corresponding experimental results are also collected. ​A machine learning algorithm is then used to learn the difference between the CCSD(T) method calculated vibrational results and the experimental vibrational results, and a high-dimensional error function is finally constructed to improve the original CCSD(T) computational accuracy. The results for HF, HBr, H35Cl and Na35Cl (they did not appear in the training set) and other halogen molecules show that compared with the CCSD(T)/cc-pV5Z calculation method alone, the present method reduces the prediction error by more than 50% and the computational cost by nearly one order of magnitude. It is worth noting that the method proposed in this paper is not only limited to the energy level prediction of diatomic systems, but also applicable in other fields where data can be obtained by ab initio methods and experimental methods simultaneously, such as the energy spectrum properties of macromolecular systems.
      通信作者: 付佳, fujiayouxiang@126.com ; 樊群超, fanqunchao@sina.com
    • 基金项目: 国家自然科学基金(批准号: 11904295)、四川省科学技术计划(批准号: 2021ZYD0050) 和极端光学协同创新中心开放研究基金项目(批准号: KF2020003)资助的课题.
      Corresponding author: Fu Jia, fujiayouxiang@126.com ; Fan Qun-Chao, fanqunchao@sina.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11904295), the Program of Science and Technology of Sichuan Province of China (Grant No. 2021ZYD0050), and the Open Research Found Program of Collaborative Innovation Center of Extreme Optics (Grant No. KF2020003).
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  • 图 1  RFRA结构图

    Fig. 1.  Architecture of RFRA.

    图 2  CCSD(T)/cc-pVQZ的误差趋势图

    Fig. 2.  Error trend figure of CCSD(T)/cc-pVQZ.

    图 3  新方法的预测能级误差与CCSD(T)/cc-pV5 Z的误差对比 (a) HF; (b) HBr; (c) H35Cl; (d) Na35Cl

    Fig. 3.  Comparison of the errors of the new method and CCSD(T)/cc-pV5 Z: (a) HF; (b) HBr; (c) H35Cl; (d) Na35Cl.

    图 4  新方法与CCSD(T)/cc-pV5 Z的平均相对误差对比

    Fig. 4.  Comparison of the average relative errors of the new method and CCSD(T)/cc-pV5 Z.

    表 1  基态分子的部分实验振动能级 (cm–1)

    Table 1.  Partial experimental vibrational energy levels of molecules in the ground state (cm–1).

    $ \nu $H2HFDFH35ClLiHLi2
    02179.692050.771490.301483.88705.08175.032
    16341.756012.194396.974369.862078.45521.26
    210268.409801.577212.127151.863406.08862.26
    313694.5413423.609937.669830.664688.811198.00
    417433.2216882.4512575.3312406.715927.551528.41
    ${\text{H}}{}^{{\text{79}}}{\text{Br}}$N2BFClFNOCN
    01314.651175.77742.00191.77948.501031.20
    13873.573505.692208.00573.062824.503073.60
    26341.995806.933651.00951.354627.305089.70
    38719.918079.475072.001326.606491.907079.50
    411007.0110323.286470.001698.908283.509042.80
    Br2BClCPCSSiClO2
    0162.38416.83618.19709.00267.25664.69
    1485.531242.631844.322117.00798.542326.53
    2806.512058.803056.763515.001325.503968.09
    31125.292865.494255.534902.001847.505589.60
    41441.883662.855440.626278.002365.507191.32
    12C16O13C16O14C16O12C17O13C17O14C17O
    01081.771057.721036.741068.031043.661022.39
    13225.043153.793091.613184.323112.113049.05
    26341.835224.545122.155274.815155.925052.07
    37432.217270.047128.447339.547175.147031.50
    49496.249290.359110.529378.609169.838987.38
    SOSiCSiN24Mg16ONa35ClNaLi
    0576.94475.47574.06391.14181.90127.83
    11740.421416.671712.461165.88543.05381.22
    22916.752344.872837.851930.32900.70631.10
    34105.983260.073950.202684.161254.89877.79
    45308.164162.275049.473427.111605.651121.12
    MgHAlOAlFAl ClSiOBH
    0739.11488.00394.60246.60619.201171.06
    12171.091453.401180.00734.101848.903440.30
    23539.792404.761956.101217.303066.505614.11
    34841.143342.192722.301698.004272.307694.16
    46070.504265.423480.202175.205466.109684.16
    下载: 导出CSV

    表 2  Li2的输入数据与预测数据 (cm–1)

    Table 2.  Input data and predicted data of Li2 (cm–1).

    输入变量$X$目标变量$\hat Y:{E_\nu }$文献[59]$E_\nu ^{{\text{this work}}}$
    $ E_\nu ^{\text{T}} $$ E_\nu ^{\text{Q}} $
    171.702172.1623175.03174.059178.903
    511.410513.631521.26518.255531.853
    846.059849.982862.26857.832878.969
    1175.5991181.1771198.001191.3971173.096
    1499.9871507.1691528.411519.3301496.133
    1819.1611827.9061853.461841.9911906.993
    2133.0632143.3282173.072159.8522106.362
    2441.6202453.3682487.192471.9912438.853
    2744.7532757.9542795.742778.3342693.961
    3042.3683057.0023090.643072.7033102.89
    3334.3773350.4213395.803373.9203369.871
    3620.6693638.1083687.113663.1593630.759
    3901.1263919.9513972.433946.6184009.308
    4175.6194195.9274251.734223.9974297.662
    4444.0034465.5974524.784495.2704487.998
    4706.1264729.1134791.434760.6104530.406
    4961.8054986.2105051.535018.5594962.152
    5210.8585236.7065304.935270.2685225.061
    5453.0745480.4025551.45514.8315506.045
    5688.2245717.0816790.715753.5395701.189
    5916.0595946.5036022.665983.9596022.425
    注: 文献[59]的数据和$E_\nu ^{{\text{this work}}}$不作为输入数据.
    下载: 导出CSV

    表 3  HF/HBr/H35Cl/Na35Cl的预测振动能级( cm–1)

    Table 3.  Predicted vibrational energy levels of HF/HBr/H35Cl/Na35Cl (cm–1).

    HF$ \nu $${E_\nu }$${\delta _{{\text{this work}}}}$$E_\nu ^{{\text{this work}}}$$\delta _\nu ^{\text{Q}}$$E_\nu ^{\text{Q}} $
    02050.7710.040932134.7140.012002075.378
    16012.1940.054856341.9830.015626106.099
    29801.5660.0304410099.8840.016949967.644
    313423.6030.00116613407.9500.0179713664.780
    416882.4480.00408316951.3830.0189317202.024
    520181.8240.000571020193.3470.0199020583.515
    623324.6200.00811823135.2670.0209323812.920
    726313.1460.0163725882.4230.0220526893.357
    829148.9270.0143528730.6900.0232729827.322
    931832.3670.0196331207.4350.0246432616.648
    1034362.9090.00439734211.8060.0261835262.441
    1136738.4050.0171436108.5270.0279437764.995
    1238954.9430.0176938265.6580.0300040123.716
    1341006.5930.0148740396.7990.0324442337.026
    1442884.4430.0148342248.5440.0353944402.227
    1544576.0050.0126444012.5080.0390246315.354
    1646064.2070.00942845629.9210.0435748071.083
    1747325.6630.00623447030.6440.0493849662.648
    1848328.5410.000346348311.8070.0569751081.932
    1949026.5080.00545949294.1460.0671752319.807
    HBr$ \nu $${E_\nu }$${\delta _{{\text{this work}}}}$$E_\nu ^{{\text{this work}}}$$\delta _\nu ^{\text{Q}}$$E_\nu ^{\text{Q}}$
    01314.6530.020801341.9930.013141331.929
    13873.5660.066014129.2430.017623941.805
    26341.9900.011306413.8680.019356464.682
    38719.9130.011048816.2070.020938902.436
    411007.0120.0131611151.8880.0225911255.684
    513202.5850.0138713385.7000.0243713524.341
    615305.4710.0179515580.1460.0263015707.958
    717313.9700.00226817274.7040.0284117805.806
    H35Cl $ \nu $${E_\nu }$${\delta _{{\text{this work}}}}$$E_\nu ^{{\text{this work}}}$$\delta _\nu ^{\text{Q}}$$E_\nu ^{\text{Q}}$
    01483.8810.010521468.2760.010501468.294
    14369.8570.010094413.9520.0032994384.273
    27151.8640.0092097217.7240.0066377199.330
    39830.6580.0191010018.4620.0085669914.869
    412406.7100.00474812465.6160.0102812534.187
    514880.1560.00270614839.8920.0125015066.200
    617250.7460.00246117208.2840.0156317520.446
    719517.7780.00309819457.3200.0190619889.759
    821680.0030.0152921348.5160.0223122163.716
    923735.5170.0130623425.5790.0256124343.381
    1025681.6080.00511925813.0720.0287126418.895
    1127514.6090.00939227256.1800.0315428382.336
    1229229.6479.641 E-0529226.8290.0337830217.072
    1330820.2910.00859130555.5090.0350731901.224
    1432278.1440.00405232408.9300.0347633400.117
    Na35Cl $ \nu $${E_\nu }$${\delta _{{\text{this work}}}}$$E_\nu ^{{\text{this work}}}$$\delta _\nu ^{\text{Q}}$$E_\nu ^{\text{Q}}$
    0181.8990.008954180.2700.04204174.252
    1543.0500.01550534.6330.03299525.138
    2900.7020.007215894.2040.03107872.718
    31254.8900.011441240.5380.030141217.063
    41605.6490.0055731596.7000.029551558.204
    51953.0130.0081201937.1550.029121896.150
    62297.0160.0052332284.9950.028772230.937
    72637.6920.0011722640.7840.028472562.592
    82975.0750.010922942.5740.028212891.142
    93309.1980.0011953305.2430.027983216.614
    103640.0930.010843600.6530.027763539.057
    113967.7950.0019663959.9920.027553858.485
    124292.3340.0021714283.0170.027354174.918
    下载: 导出CSV

    表 3 (续)  HF/HBr/H35Cl/Na35Cl的预测振动能级( cm–1)

    Table 3 (续).  Predicted vibrational energy levels of HF/HBr/H35Cl/Na35Cl (cm–1).

    Na35Cl $ \nu $${E_\nu }$${\delta _{{\text{this work}}}}$$E_\nu ^{{\text{this work}}}$$\delta _\nu ^{\text{Q}}$$E_\nu ^{\text{Q}}$
    134613.7430.010774564.0700.027174488.398
    144932.0540.0026174919.1470.026994798.950
    155247.2980.012745180.4280.026815106.596
    165559.5060.0099775504.0420.026655411.364
    175868.7100.021195744.3390.026485713.289
    186174.9400.0037476198.0780.026326012.398
    196478.2260.0076596428.6120.026176308.719
    206778.5990.00083966772.9140.026016602.272
    下载: 导出CSV
  • [1]

    Ye Y W, Jiang Z L, Zou Y J, Chen H, Guo S D, Yang Q M, Chen L Y 2020 J. Mater. Sci. Technol. 43 144Google Scholar

    [2]

    Wick C D 2017 J. Chem. Phys. 147 161703Google Scholar

    [3]

    Devlin J P, Farnik M, Suhm M A, Buch V 2005 J. Phys. Chem. A. 109 955Google Scholar

    [4]

    Delval C, Fluckiger B, Rossi M J 2003 Atmos. Chem. Phys. 3 1131Google Scholar

    [5]

    Barone S B, Zondlo M A, Tolbert M A 1999 J. Phys. Chem. A. 103 9717Google Scholar

    [6]

    Smart R S C, Sheppard N 1971 Proc. R. Soc. Lond. A. 320 417Google Scholar

    [7]

    Blass P M, Jackson R C, Polanyi J C, Weiss H 1991 J. Chem. Phys. 94 7003Google Scholar

    [8]

    Giorgi J B, Kuhnemuth R, Polanyi J C, Wang J X 1997 J. Chem. Phys. 106 3129Google Scholar

    [9]

    Carvalho A, Hancock G, Saunders M, 2006 Phys. Chem. Chem. Phys. 8 4337Google Scholar

    [10]

    Sun Q 2012 Vib. Spectros. 62 110Google Scholar

    [11]

    Weiss P S, Mestdagh J M, Covinsky M H, Balko B A, Lee Y T 1988 Chem. Phys. 126 93Google Scholar

    [12]

    Rubio L, Samoudi B, Santos M, Diaz L 2012 J. Photoch. Photobio. A. 237 1Google Scholar

    [13]

    Reiser C, Lussier F M, Jensen C C, Steinfeld J I 1979 J. Am. Chem. Soc. 101 350Google Scholar

    [14]

    Rauhut G, Knizia G, Werner H J 2009 J. Chem. Phys. 130 054105Google Scholar

    [15]

    Neff M, Hrenar T, Oschetzki D, Rauhut G 2011 J. Chem. Phys. 134 064105Google Scholar

    [16]

    Kowalski K, Piecuch P 2000 J. Chem. Phys. 113 18Google Scholar

    [17]

    张瑶, 张云波, 陈立 2021 物理学报 70 168702Google Scholar

    Zhang Y, Zhang Y B, Chen L 2021 Acta Phys. Sin. 70 168702Google Scholar

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出版历程
  • 收稿日期:  2022-10-13
  • 修回日期:  2022-12-29
  • 上网日期:  2023-02-17
  • 刊出日期:  2023-04-05

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