多原子反应体系的高精度拟合势能面
|
摘要
本文介绍了近几年来我们组构建多原子反应体系的高精度拟合势能面的进展。我们基于神经网络(NN)方法,成功构建了多原子气相分子体系和气相分子在金属表面解离的一系列势能面。这些势能面的拟合精度相当高,并且经过了严格的量子动力学测试,能广泛应用到动力学研究中。我们还提出了一种新的置换不变势能面的拟合方法,即基本不变量神经网络方法(FI-NN)。基本不变量的使用极大地减少了神经网络输入层多项式的个数,有效提高了势能面的计算速度。
Over the past decade, significant progress has been made in theoretical and experimental research in the field of chemical reaction dynamics, moving from triatomic reactions to larger polyatomic reactions. This has challenged the theoretical and computational approaches to polyatomic reaction dynamics in two major areas: the potential energy surface and the dynamics. Highly accurate potential energy surfaces are essential for achieving accurate dynamical information in quantum dynamics calculations. The increased number of degrees of freedom in larger systems poses a significant challenge to the accurate construction of potential energy surfaces. Recently, there has been substantial progress in the development of potential energy surfaces for polyatomic reactive systems. In this article, we review the recent developments made by our group in constructing highly accurately fitted potential energy surfaces for polyatomic reactive systems, based on a neural network approach. A key advantage of the neural network approach is its more faithful representation of the ab initio points. We recently proposed a systematic procedure, based on neural network fitting, for the construction of accurate potential energy surfaces with very small root mean square errors. Based on the neural network approach, we successfully developed potential energy surfaces for polyatomic reactions in the gas phase, including the reactive systems OH_3, HOCO, and CH_5, and the dissociation of gas-phase molecules on metal surfaces, such as H_2O on the Cu(111) surface. These potential energy surfaces were fitted to an unprecedented level of accuracy, representing the most accurate potential energy surfaces calculated for these systems, and were rigorously tested using quantum dynamics calculations. The quantum dynamics calculations based on these potential energy surfaces produce accurate results, which are in good agreement with experiments. We have also proposed a new method for developing permutationally invariant potential energy surfaces, named fundamental-invariant neural networks. Mathematically, fundamental invariants are used to finitely generate the permutation-invariant polynomial ring; thus, fundamental-invariant neural networks can approximate any function to arbitrary accuracy. The use of fundamental invariants minimizes the size of the input permutation-invariant polynomials, which reduces the evaluation time for potential energy calculations, especially for polyatomic systems. Potential energy surfaces for OH_3 and CH_4 were constructed using fundamental-invariant neural networks, with their accuracies confirmed by full-dimensional quantum dynamics and bound-state calculations. These developments in the construction of highly accurate potential energy surfaces are expected to extend the theoretical study of reaction dynamics to larger and more complex systems.
Over the past decade, significant progress has been made in theoretical and experimental research in the field of chemical reaction dynamics, moving from triatomic reactions to larger polyatomic reactions. This has challenged the theoretical and computational approaches to polyatomic reaction dynamics in two major areas: the potential energy surface and the dynamics. Highly accurate potential energy surfaces are essential for achieving accurate dynamical information in quantum dynamics calculations. The increased number of degrees of freedom in larger systems poses a significant challenge to the accurate construction of potential energy surfaces. Recently, there has been substantial progress in the development of potential energy surfaces for polyatomic reactive systems. In this article, we review the recent developments made by our group in constructing highly accurately fitted potential energy surfaces for polyatomic reactive systems, based on a neural network approach. A key advantage of the neural network approach is its more faithful representation of the ab initio points. We recently proposed a systematic procedure, based on neural network fitting, for the construction of accurate potential energy surfaces with very small root mean square errors. Based on the neural network approach, we successfully developed potential energy surfaces for polyatomic reactions in the gas phase, including the reactive systems OH_3, HOCO, and CH_5, and the dissociation of gas-phase molecules on metal surfaces, such as H_2O on the Cu(111) surface. These potential energy surfaces were fitted to an unprecedented level of accuracy, representing the most accurate potential energy surfaces calculated for these systems, and were rigorously tested using quantum dynamics calculations. The quantum dynamics calculations based on these potential energy surfaces produce accurate results, which are in good agreement with experiments. We have also proposed a new method for developing permutationally invariant potential energy surfaces, named fundamental-invariant neural networks. Mathematically, fundamental invariants are used to finitely generate the permutation-invariant polynomial ring; thus, fundamental-invariant neural networks can approximate any function to arbitrary accuracy. The use of fundamental invariants minimizes the size of the input permutation-invariant polynomials, which reduces the evaluation time for potential energy calculations, especially for polyatomic systems. Potential energy surfaces for OH_3 and CH_4 were constructed using fundamental-invariant neural networks, with their accuracies confirmed by full-dimensional quantum dynamics and bound-state calculations. These developments in the construction of highly accurate potential energy surfaces are expected to extend the theoretical study of reaction dynamics to larger and more complex systems.
引文
(1)Bowman,J.M.;Schatz,G.C.Annu.Rev.Phys.Chem.1995,46,169.doi:10.1146/annurev.pc.46.100195.00112
(2)Zhang,J.Z.H.;Dai,J.;Zhu,W.J.Phys.Chem.A 1997,101,2746.doi:10.1021/jp9620734
(3)Miller,M.H.J.Chem.Soc.Faraday Trans.1997,93,685.doi:10.1039/A606858H
(4)Clary,D.C.Science 1998,279,1879.doi:10.1126/science.279.5358.1879
(5)Althorpe,S.C.;Clary,D.C.Annu.Rev.Phys.Chem.2003,54,493.doi:10.1146/annurev.physchem.54.011002.103750
(6)Balint-Kurti,G.G.Int.Rev.Phys.Chem.2008,27,507.doi:10.1080/01442350802102379
(7)Guo,H.Int.Rev.Phys.Chem.2012,31,1.doi:10.1080/0144235X.2011.649999
(8)Yarkony,D.R.Chem.Rev.2012,112,481.doi:10.1021/cr2001299
(9)Nyman,G.;Yu,H.-G.Int.Rev.Phys.Chem.2013,32,39.doi:10.1080/0144235X.2012.735863
(10)Otto,R.;Ma,J.;Ray,A.W.;Daluz,J.S.;Li,J.;Guo,H.;Continetti,R.E.Science 2014,343,396.doi:10.1126/science.1247424
(11)Liu,K.Annu.Rev.Phys.Chem.2001,52,139.doi:10.1146/annurev.physchem.52.1.139
(12)Fernandez-Alonso,F.;Zare,R.N.Annu.Rev.Phys.Chem.2002,53,67.doi:10.1146/annurev.physchem.53.091001.094554
(13)Balucani,N.;Capozza,G.;Leonori,F.;Segoloni,E.;Casavecchia,P.Int.Rev.Phys.Chem.2006,25,109.doi:10.1080/01442350600641305
(14)Yang,X.Annu.Rev.Phys.Chem.2007,58,433.doi:10.1146/annurev.physchem.58.032806.104632
(15)Crim,F.F.Proc.Natl.Acad.Sci.USA 2008,105,12654.doi:10.1073/pnas.0803010105
(16)Liu,K.Adv.Chem.Phys.2012,149,1.doi:10.1002/9781118180396.ch1
(17)Guo,H.;Liu,K.Chem.Sci.2016,7,3992.doi:10.1039/C6SC01066K
(18)Qiu,M.;Ren,Z.;Che,L.;Dai,D.;Harich,S.A.;Wang,X.;Yang,X.;Xu,C.;Xie,D.;Gustafsson,M.;et al.Science 2006,311,1440.doi:10.1126/science.1123452
(19)Che,L.;Ren,Z.;Wang,X.;Dong,W.;Dai,D.;Wang,X.;Zhang,D.H.;Yang,X.;Sheng,L.;Li,G.;et al.Science 2007,317,1061.doi:10.1126/science.1144984
(20)Wang,X.;Dong,W.;Xiao,C.;Che,L.;Ren,Z.;Dai,D.;Wang,X.;Casavecchia,P.;Yang,X.;Jiang,B.;et al.Science 2008,322,573.doi:10.1126/science.1163195
(21)Wang,T.;Chen,J.;Yang,T.;Xiao,C.;Sun,Z.;Huang,L.;Dai,D.;Yang,X.;Zhang,D.H.Science 2013,342,1499.doi:10.1126/science.1246546
(22)Yang,T.;Chen,J.;Huang,L.;Wang,T.;Xiao,C.;Sun,Z.;Dai,D.;Yang,X.;Zhang,D.H.Science 2015,347,60.doi:10.1126/science.1260527
(23)Xiao,C.;Xu,X.;Liu,S.;Wang,T.;Dong,W.;Yang,T.;Sun,Z.;Dai,D.;Xu,X.;Zhang,D.H.;et al.Science 2011,333,440.doi:10.1126/science.1205770
(24)Zhang,W.;Zhou,Y.;Wu,G.;Lu,Y.;Pan,H.;Fu,B.;Shuai,Q.;Liu,L.;Liu,S.;Zhang,L.;et al.Proc.Natl.Acad.Sci.USA 2010,107,12782.doi:10.1073/pnas.1006910107
(25)Zhang,D.H.;Guo,H.Annu.Rev.Phys.Chem.2016,67,135.doi:10.1146/annurev-physchem-040215-112016
(26)Zhang,Z.;Zhou,Y.;Zhang,D.H.;Czakó,G.;Bowman,J.M.J.Phys.Chem.Lett.2012,3,3416.doi:10.1021/jz301649w
(27)Liu,R.;Yang,M.;Czakó,G.;Bowman,J.M.;Li,J.;Guo,H.J.Phys.Chem.Lett.2012,3,3776.doi:10.1021/jz301735m
(28)Welsch,R.;Manthe,U.J.Phys.Chem.Lett.2015,6,338.doi:10.1021/jz502525p
(29)Zhao,Z.;Zhang,Z.;Liu,S.;Zhang,D.H.Nat.Commun.2017,8,14506.doi:10.1038/ncomms14506
(30)Fu,B.;Shan,X.;Zhang,D.H.;Clary,D.C.Chem.Soc.Rev.2017,46,7625.doi:10.1039/C7CS00526A
(31)Dawes,R.;Thompson,D.L.;Wagner,A.F.;Minkoff,M.J.Chem.Phys.2008,128,084107.doi:10.1063/1.2831790
(32)Collins,M.A.Theor.Chem.Acc.2002,108,313.doi:10.1007/s00214-002-0383-5
(33)Braams,B.J.;Bowman,J.M.Int.Rev.Phys.Chem.2009,13,577.doi:10.1080/01442350903234923
(34)Bowman,J.M.;Czakó,G.;Fu,B.Phys.Chem.Chem.Phys.2011,28,8094.doi:10.1039/C0CP02722G
(35)Raff,L.M.;Malshe,M.;Hagan,M.;Doughan,D.I.;Rockley,M.G.;Komanduri,R.J.Chem.Phys.2005,122,084104.doi:10.1063/1.1850458
(36)Chen,J.;Xu,X.;Xu,X.;Zhang,D.H.J.Chem.Phys.2013,138,154301.doi:10.1063/1.4801658
(37)Chen,J.;Xu,X.;Xu,X.;Zhang,D.H.J.Chem.Phys.2013,138,221104.doi:10.1063/1.4811109
(38)Jiang,B.;Guo,H.J.Chem.Phys.2013,139,054112.doi:10.1063/1.4817187
(39)Li,J.;Jiang,B.;Guo,H.J.Chem.Phys.2013,139,204103.doi:10.1063/1.4832697
(40)Shao,K.;Chen,J.;Zhao,Z.;Zhang,D.H.J.Chem.Phys.2016,145,071101.doi:10.1063/1.4961454
(41)Bartlett,R.J.;Musia?,M.Rev.Mod.Phys.2007,79,291.doi:10.1103/RevModPhys.79.291
(42)Werner,H.-J.Adv.Chem.Phys.1987,69,1.doi:10.1002/9780470142943.ch1
(43)Schatz,G.C.Rev.Mod.Phys.1989,61,669.doi:10.1103/RevModPhys.61.669
(44)Hollebeek,T.;Ho,T.S.;Rabitz,H.Annu.Rev.Phys.Chem.1999,50,537.doi:10.1146/annurev.physchem.50.1.537
(45)Zhou,Y.;Fu,B.;Wang,C.;Collins,M.A.;Zhang,D.H.J.Chem.Phys.2011,134,064323.doi:10.1063/1.3552088
(46)Fu,B.;Han,Y.;Bowman,J.M.;Angelucci,L.;Balucani,N.;Leonori,F.;Casavecchia,P.Proc.Natl.Acad.Sci.USA 2012,109,9733.doi:10.1073/pnas.1202672109
(47)Yang,J.;Shao,K.;Zhang,D.;Shuai,Q.;Fu,B.;Zhang,D.H.;Yang,X.J.Phys.Chem.Lett.2014,5,3106.doi:10.1021/jz5016923
(48)Raff,L.M.;Komanduri,R.;Hagan,M.;Bukkapatnam,S.Neural Networks in Chemical Reaction Dynamics;Oxford University Press:New York,NY,USA,2012.
(49)Blank,T.B.;Brown,S.D.;Calhoun,A.W.;Doren,D.J.J.Chem.Phys.1995,103,4129.doi:10.1063/1.469597
(50)Brown,D.F.R.;Gibbs,M.N.;Clary,D.C.J.Chem.Phys.1996,105,7597.doi:10.1063/1.472596
(51)Manzhos,S.;Wang,X.G.;Dawes,R.;Carrington,T.J.Phys.Chem.A 2006,110,5295.doi:10.1021/jp055253z
(52)Behler,J.;Parrinello,M.Phys.Rev.Lett.2007,98,146401.doi:10.1103/PhysRevLett.98.146401
(53)Pukrittayakamee,A.;Malshe,M.;Hagan,M.;Raff,L.M.;Narulkar,R.;Bukkapatnam,S.;Komanduri,R.J.Chem.Phys.2009,130,134101.doi:10.1063/1.3095491
(54)Handley,C.M.;Popelier,P.L.A.J.Phys.Chem.A 2010,114,3371.doi:10.1021/jp9105585
(55)Behler,J.Phys.Chem.Chem.Phys.2011,13,17930.doi:10.1039/C1CP21668F
(56)Xu,X.;Chen,J.;Zhang,D.H.Chin.J.Chem.Phys.2014,27,373.doi:10.1063/1674-0068/27/04/373-379
(57)Hagan,M.;Menhaj,M.IEEE Trans.Neural Networks 1994,5,989.doi:10.1109/72.329697
(58)Clary,D.C.Rate Coefficients in Astrochemistry;Millar,T.J.,Williams,D.A.,Eds.;Astrophysics and Space Science Library;Springer:The Netherlands,1988;Vol.146;Chapter 1,pp.1-16.
(59)Warnatz,J.Combustion Chemistry;Gardiner,W.,Ed.;SpringerVerlag:New York,NY,USA,1985;Chapter 5.
(60)Schatz,G.C.;Elgersma,H.Chem.Phys.Lett.1980,73,21.doi:10.1016/0009-2614(80)85193-1
(61)Ochoa de Aspuru,G.;Clary,D.C.J.Phys.Chem.A 1998,102,9631.doi:10.1021/jp982433i
(62)Pogrebnya,S.K.;Palma,J.;Clary,D.C.;Echave,J.Phys.Chem.Chem.Phys.2000,2,693.doi:10.1039/A908080E
(63)Wu,G.-S.;Schatz,G.C.;Lendvay,G.;Fang,D.-C.;Harding,L.B.J.Chem.Phys.2000,113,3150.doi:10.1063/1.1287329
(64)Yang,M.H.;Zhang,D.H.;Collins,M.A.;Lee,S.Y.J.Chem.Phys.2001,115,174.doi:10.1063/1.1372335
(65)Finlayson-Pitts,B.J.;Pitts,J.N.Chemistry of the Upper and Lower Atmosphere;Academic Press:San Diego,CA,USA,2000.
(66)Miller,J.A.;Kee,R.J.;Westbrook,C.K.Annu.Rev.Phys.Chem.1990,41,345.doi:10.1146/annurev.pc.41.100190.002021
(67)Kudla,K.;Schatz,G.C.;Wagner,A.F.J.Chem.Phys.1991,95,1635.doi:10.1063/1.461076
(68)Bradley,K.S.;Schatz,G.C.J.Chem.Phys.1997,106,8464.doi:10.1063/1.473923
(69)Yu,H.G.;Muckerman,J.T.;Sears,T.J.Chem.Phys.Lett.2001,349,547.doi:10.1016/S0009-2614(01)01238-6
(70)Lakin,M.J.;Troya,D.;Schatz,G.C.;Harding,L.B.J.Chem.Phys.2003,119,5848.doi:10.1063/1.1602061
(71)Valero,R.;van Hemert,M.C.;Kroes,G.J.Chem.Phys.Lett.2004,393,236.doi:10.1016/j.cplett.2004.06.036
(72)Li,J.;Wang,Y.;Jiang,B.;Ma,J.;Dawes,R.;Xie,D.;Bowman,J.M.;Guo,H.J.Chem.Phys.2012,136,041103.doi:10.1063/1.3680256
(73)Jordan,M.J.T.;Gilbert,R.G.J.Chem.Phys.1995,102,5669.doi:10.1063/1.469298
(74)Espinosa-García,J.;Corchado,J.C.J.Phys.Chem.1996,100,16561.doi:10.1021/jp961608q
(75)Wu,T.;Werner,H.-J.;Manthe,U.Science 2004,306,2227.doi:10.1126/science.1104085
(76)Zhang,X.;Braams,B.J.;Bowman,J.M.J.Chem.Phys.2006,124,021104.doi:10.1063/1.2162532
(77)Xie,Z.;Bowman,J.M.;Zhang,X.J.Chem.Phys.2006,125,133120.doi:10.1063/1.2238871
(78)Agrafiotis,D.K.;Cede?o,W.;Lobanov,V.S.J.Chem.Inform.Comput.Sci.2002,42,903.doi:10.1021/ci0203702
(79)Chorkendorff,I.;Niemantsverdriet,J.W.Concepts of Modern Catalysis and Kinetics;Wiley-VCH:Weinheim,Germany,2003.
(80)Jiang,B.;Xie,D.;Guo,H.Chem.Sci.2013,4,503.doi:10.1039/c2sc21393a
(81)Jiang,B.;Ren,X.;Xie,D.;Guo,H.Proc.Natl.Acad.Sci.USA 2012,109,10224.doi:10.1073/pnas.1203895109
(82)Ovesen,C.V.;Stoltze,P.;Norskov,J.K.;Campbell,C.T.J.Catal.1992,134,445.doi:10.1016/0021-9517(92)90334-E
(83)Liu,T.;Zhang,Z.;Fu,B.;Yang,X.;Zhang,D.H.Chem.Sci.2016,7,1840.doi:10.1039/c5sc03689e
(84)Zhang,Z.;Liu,T.;Fu,B.;Yang,X.;Zhang,D.H.Nat.Commun.2016,7,11953.doi:10.1038/ncomms11953
(85)Li,J.;Chen,J.;Zhang,D.H.;Guo,H.J.Chem.Phys.2014,140,044327.doi:10.1063/1.4863138
(86)Li,J.;Chen,J.;Zhao,Z.;Xie,D.;Zhang,D.H.;Guo,H.J.Chem.Phys.2015,142,204302.doi:10.1063/1.4921412
(87)Su,N.Q.;Chen,J.;Xu,X.;Zhang,D.H.Acta Phys.-Chim.Sin.2016,32,119.[苏乃强,陈俊,徐昕,张东辉.物理化学学报,2016,32,119.]doi:10.3866/PKU.WHXB201512011
(88)Su,N.Q.;Chen,J.;Sun,Z.;Zhang,D.H.;Xu,X.J.Chem.Phys.2015,142,084107.doi:10.1063/1.4913196
(89)Chen,J.;Su,N.Q.;Xu,X.;Zhang,D.H.J.Comput.Chem.2017,38,2326.doi:10.1002/jcc.24886
(90)Decker,W.;Greuel,G.-M.;Pfister,G.;Sch?nemann,H.Singular 4-0-2-A Computer Algebra System for Polynomial Computations.http://www.singular.uni-kl.de,2015.
(91)King,S.A.J.Symb.Comput.2013,48,101.doi:10.1016/j.jsc.2012.05.002
(92)Chen,J.;Zhang,D.H.Sci.China Chem.2015,45,1241.[陈俊,张东辉.中国科学:化学,2015,45,1241.]doi:10.1360/N032015-00148
(2)Zhang,J.Z.H.;Dai,J.;Zhu,W.J.Phys.Chem.A 1997,101,2746.doi:10.1021/jp9620734
(3)Miller,M.H.J.Chem.Soc.Faraday Trans.1997,93,685.doi:10.1039/A606858H
(4)Clary,D.C.Science 1998,279,1879.doi:10.1126/science.279.5358.1879
(5)Althorpe,S.C.;Clary,D.C.Annu.Rev.Phys.Chem.2003,54,493.doi:10.1146/annurev.physchem.54.011002.103750
(6)Balint-Kurti,G.G.Int.Rev.Phys.Chem.2008,27,507.doi:10.1080/01442350802102379
(7)Guo,H.Int.Rev.Phys.Chem.2012,31,1.doi:10.1080/0144235X.2011.649999
(8)Yarkony,D.R.Chem.Rev.2012,112,481.doi:10.1021/cr2001299
(9)Nyman,G.;Yu,H.-G.Int.Rev.Phys.Chem.2013,32,39.doi:10.1080/0144235X.2012.735863
(10)Otto,R.;Ma,J.;Ray,A.W.;Daluz,J.S.;Li,J.;Guo,H.;Continetti,R.E.Science 2014,343,396.doi:10.1126/science.1247424
(11)Liu,K.Annu.Rev.Phys.Chem.2001,52,139.doi:10.1146/annurev.physchem.52.1.139
(12)Fernandez-Alonso,F.;Zare,R.N.Annu.Rev.Phys.Chem.2002,53,67.doi:10.1146/annurev.physchem.53.091001.094554
(13)Balucani,N.;Capozza,G.;Leonori,F.;Segoloni,E.;Casavecchia,P.Int.Rev.Phys.Chem.2006,25,109.doi:10.1080/01442350600641305
(14)Yang,X.Annu.Rev.Phys.Chem.2007,58,433.doi:10.1146/annurev.physchem.58.032806.104632
(15)Crim,F.F.Proc.Natl.Acad.Sci.USA 2008,105,12654.doi:10.1073/pnas.0803010105
(16)Liu,K.Adv.Chem.Phys.2012,149,1.doi:10.1002/9781118180396.ch1
(17)Guo,H.;Liu,K.Chem.Sci.2016,7,3992.doi:10.1039/C6SC01066K
(18)Qiu,M.;Ren,Z.;Che,L.;Dai,D.;Harich,S.A.;Wang,X.;Yang,X.;Xu,C.;Xie,D.;Gustafsson,M.;et al.Science 2006,311,1440.doi:10.1126/science.1123452
(19)Che,L.;Ren,Z.;Wang,X.;Dong,W.;Dai,D.;Wang,X.;Zhang,D.H.;Yang,X.;Sheng,L.;Li,G.;et al.Science 2007,317,1061.doi:10.1126/science.1144984
(20)Wang,X.;Dong,W.;Xiao,C.;Che,L.;Ren,Z.;Dai,D.;Wang,X.;Casavecchia,P.;Yang,X.;Jiang,B.;et al.Science 2008,322,573.doi:10.1126/science.1163195
(21)Wang,T.;Chen,J.;Yang,T.;Xiao,C.;Sun,Z.;Huang,L.;Dai,D.;Yang,X.;Zhang,D.H.Science 2013,342,1499.doi:10.1126/science.1246546
(22)Yang,T.;Chen,J.;Huang,L.;Wang,T.;Xiao,C.;Sun,Z.;Dai,D.;Yang,X.;Zhang,D.H.Science 2015,347,60.doi:10.1126/science.1260527
(23)Xiao,C.;Xu,X.;Liu,S.;Wang,T.;Dong,W.;Yang,T.;Sun,Z.;Dai,D.;Xu,X.;Zhang,D.H.;et al.Science 2011,333,440.doi:10.1126/science.1205770
(24)Zhang,W.;Zhou,Y.;Wu,G.;Lu,Y.;Pan,H.;Fu,B.;Shuai,Q.;Liu,L.;Liu,S.;Zhang,L.;et al.Proc.Natl.Acad.Sci.USA 2010,107,12782.doi:10.1073/pnas.1006910107
(25)Zhang,D.H.;Guo,H.Annu.Rev.Phys.Chem.2016,67,135.doi:10.1146/annurev-physchem-040215-112016
(26)Zhang,Z.;Zhou,Y.;Zhang,D.H.;Czakó,G.;Bowman,J.M.J.Phys.Chem.Lett.2012,3,3416.doi:10.1021/jz301649w
(27)Liu,R.;Yang,M.;Czakó,G.;Bowman,J.M.;Li,J.;Guo,H.J.Phys.Chem.Lett.2012,3,3776.doi:10.1021/jz301735m
(28)Welsch,R.;Manthe,U.J.Phys.Chem.Lett.2015,6,338.doi:10.1021/jz502525p
(29)Zhao,Z.;Zhang,Z.;Liu,S.;Zhang,D.H.Nat.Commun.2017,8,14506.doi:10.1038/ncomms14506
(30)Fu,B.;Shan,X.;Zhang,D.H.;Clary,D.C.Chem.Soc.Rev.2017,46,7625.doi:10.1039/C7CS00526A
(31)Dawes,R.;Thompson,D.L.;Wagner,A.F.;Minkoff,M.J.Chem.Phys.2008,128,084107.doi:10.1063/1.2831790
(32)Collins,M.A.Theor.Chem.Acc.2002,108,313.doi:10.1007/s00214-002-0383-5
(33)Braams,B.J.;Bowman,J.M.Int.Rev.Phys.Chem.2009,13,577.doi:10.1080/01442350903234923
(34)Bowman,J.M.;Czakó,G.;Fu,B.Phys.Chem.Chem.Phys.2011,28,8094.doi:10.1039/C0CP02722G
(35)Raff,L.M.;Malshe,M.;Hagan,M.;Doughan,D.I.;Rockley,M.G.;Komanduri,R.J.Chem.Phys.2005,122,084104.doi:10.1063/1.1850458
(36)Chen,J.;Xu,X.;Xu,X.;Zhang,D.H.J.Chem.Phys.2013,138,154301.doi:10.1063/1.4801658
(37)Chen,J.;Xu,X.;Xu,X.;Zhang,D.H.J.Chem.Phys.2013,138,221104.doi:10.1063/1.4811109
(38)Jiang,B.;Guo,H.J.Chem.Phys.2013,139,054112.doi:10.1063/1.4817187
(39)Li,J.;Jiang,B.;Guo,H.J.Chem.Phys.2013,139,204103.doi:10.1063/1.4832697
(40)Shao,K.;Chen,J.;Zhao,Z.;Zhang,D.H.J.Chem.Phys.2016,145,071101.doi:10.1063/1.4961454
(41)Bartlett,R.J.;Musia?,M.Rev.Mod.Phys.2007,79,291.doi:10.1103/RevModPhys.79.291
(42)Werner,H.-J.Adv.Chem.Phys.1987,69,1.doi:10.1002/9780470142943.ch1
(43)Schatz,G.C.Rev.Mod.Phys.1989,61,669.doi:10.1103/RevModPhys.61.669
(44)Hollebeek,T.;Ho,T.S.;Rabitz,H.Annu.Rev.Phys.Chem.1999,50,537.doi:10.1146/annurev.physchem.50.1.537
(45)Zhou,Y.;Fu,B.;Wang,C.;Collins,M.A.;Zhang,D.H.J.Chem.Phys.2011,134,064323.doi:10.1063/1.3552088
(46)Fu,B.;Han,Y.;Bowman,J.M.;Angelucci,L.;Balucani,N.;Leonori,F.;Casavecchia,P.Proc.Natl.Acad.Sci.USA 2012,109,9733.doi:10.1073/pnas.1202672109
(47)Yang,J.;Shao,K.;Zhang,D.;Shuai,Q.;Fu,B.;Zhang,D.H.;Yang,X.J.Phys.Chem.Lett.2014,5,3106.doi:10.1021/jz5016923
(48)Raff,L.M.;Komanduri,R.;Hagan,M.;Bukkapatnam,S.Neural Networks in Chemical Reaction Dynamics;Oxford University Press:New York,NY,USA,2012.
(49)Blank,T.B.;Brown,S.D.;Calhoun,A.W.;Doren,D.J.J.Chem.Phys.1995,103,4129.doi:10.1063/1.469597
(50)Brown,D.F.R.;Gibbs,M.N.;Clary,D.C.J.Chem.Phys.1996,105,7597.doi:10.1063/1.472596
(51)Manzhos,S.;Wang,X.G.;Dawes,R.;Carrington,T.J.Phys.Chem.A 2006,110,5295.doi:10.1021/jp055253z
(52)Behler,J.;Parrinello,M.Phys.Rev.Lett.2007,98,146401.doi:10.1103/PhysRevLett.98.146401
(53)Pukrittayakamee,A.;Malshe,M.;Hagan,M.;Raff,L.M.;Narulkar,R.;Bukkapatnam,S.;Komanduri,R.J.Chem.Phys.2009,130,134101.doi:10.1063/1.3095491
(54)Handley,C.M.;Popelier,P.L.A.J.Phys.Chem.A 2010,114,3371.doi:10.1021/jp9105585
(55)Behler,J.Phys.Chem.Chem.Phys.2011,13,17930.doi:10.1039/C1CP21668F
(56)Xu,X.;Chen,J.;Zhang,D.H.Chin.J.Chem.Phys.2014,27,373.doi:10.1063/1674-0068/27/04/373-379
(57)Hagan,M.;Menhaj,M.IEEE Trans.Neural Networks 1994,5,989.doi:10.1109/72.329697
(58)Clary,D.C.Rate Coefficients in Astrochemistry;Millar,T.J.,Williams,D.A.,Eds.;Astrophysics and Space Science Library;Springer:The Netherlands,1988;Vol.146;Chapter 1,pp.1-16.
(59)Warnatz,J.Combustion Chemistry;Gardiner,W.,Ed.;SpringerVerlag:New York,NY,USA,1985;Chapter 5.
(60)Schatz,G.C.;Elgersma,H.Chem.Phys.Lett.1980,73,21.doi:10.1016/0009-2614(80)85193-1
(61)Ochoa de Aspuru,G.;Clary,D.C.J.Phys.Chem.A 1998,102,9631.doi:10.1021/jp982433i
(62)Pogrebnya,S.K.;Palma,J.;Clary,D.C.;Echave,J.Phys.Chem.Chem.Phys.2000,2,693.doi:10.1039/A908080E
(63)Wu,G.-S.;Schatz,G.C.;Lendvay,G.;Fang,D.-C.;Harding,L.B.J.Chem.Phys.2000,113,3150.doi:10.1063/1.1287329
(64)Yang,M.H.;Zhang,D.H.;Collins,M.A.;Lee,S.Y.J.Chem.Phys.2001,115,174.doi:10.1063/1.1372335
(65)Finlayson-Pitts,B.J.;Pitts,J.N.Chemistry of the Upper and Lower Atmosphere;Academic Press:San Diego,CA,USA,2000.
(66)Miller,J.A.;Kee,R.J.;Westbrook,C.K.Annu.Rev.Phys.Chem.1990,41,345.doi:10.1146/annurev.pc.41.100190.002021
(67)Kudla,K.;Schatz,G.C.;Wagner,A.F.J.Chem.Phys.1991,95,1635.doi:10.1063/1.461076
(68)Bradley,K.S.;Schatz,G.C.J.Chem.Phys.1997,106,8464.doi:10.1063/1.473923
(69)Yu,H.G.;Muckerman,J.T.;Sears,T.J.Chem.Phys.Lett.2001,349,547.doi:10.1016/S0009-2614(01)01238-6
(70)Lakin,M.J.;Troya,D.;Schatz,G.C.;Harding,L.B.J.Chem.Phys.2003,119,5848.doi:10.1063/1.1602061
(71)Valero,R.;van Hemert,M.C.;Kroes,G.J.Chem.Phys.Lett.2004,393,236.doi:10.1016/j.cplett.2004.06.036
(72)Li,J.;Wang,Y.;Jiang,B.;Ma,J.;Dawes,R.;Xie,D.;Bowman,J.M.;Guo,H.J.Chem.Phys.2012,136,041103.doi:10.1063/1.3680256
(73)Jordan,M.J.T.;Gilbert,R.G.J.Chem.Phys.1995,102,5669.doi:10.1063/1.469298
(74)Espinosa-García,J.;Corchado,J.C.J.Phys.Chem.1996,100,16561.doi:10.1021/jp961608q
(75)Wu,T.;Werner,H.-J.;Manthe,U.Science 2004,306,2227.doi:10.1126/science.1104085
(76)Zhang,X.;Braams,B.J.;Bowman,J.M.J.Chem.Phys.2006,124,021104.doi:10.1063/1.2162532
(77)Xie,Z.;Bowman,J.M.;Zhang,X.J.Chem.Phys.2006,125,133120.doi:10.1063/1.2238871
(78)Agrafiotis,D.K.;Cede?o,W.;Lobanov,V.S.J.Chem.Inform.Comput.Sci.2002,42,903.doi:10.1021/ci0203702
(79)Chorkendorff,I.;Niemantsverdriet,J.W.Concepts of Modern Catalysis and Kinetics;Wiley-VCH:Weinheim,Germany,2003.
(80)Jiang,B.;Xie,D.;Guo,H.Chem.Sci.2013,4,503.doi:10.1039/c2sc21393a
(81)Jiang,B.;Ren,X.;Xie,D.;Guo,H.Proc.Natl.Acad.Sci.USA 2012,109,10224.doi:10.1073/pnas.1203895109
(82)Ovesen,C.V.;Stoltze,P.;Norskov,J.K.;Campbell,C.T.J.Catal.1992,134,445.doi:10.1016/0021-9517(92)90334-E
(83)Liu,T.;Zhang,Z.;Fu,B.;Yang,X.;Zhang,D.H.Chem.Sci.2016,7,1840.doi:10.1039/c5sc03689e
(84)Zhang,Z.;Liu,T.;Fu,B.;Yang,X.;Zhang,D.H.Nat.Commun.2016,7,11953.doi:10.1038/ncomms11953
(85)Li,J.;Chen,J.;Zhang,D.H.;Guo,H.J.Chem.Phys.2014,140,044327.doi:10.1063/1.4863138
(86)Li,J.;Chen,J.;Zhao,Z.;Xie,D.;Zhang,D.H.;Guo,H.J.Chem.Phys.2015,142,204302.doi:10.1063/1.4921412
(87)Su,N.Q.;Chen,J.;Xu,X.;Zhang,D.H.Acta Phys.-Chim.Sin.2016,32,119.[苏乃强,陈俊,徐昕,张东辉.物理化学学报,2016,32,119.]doi:10.3866/PKU.WHXB201512011
(88)Su,N.Q.;Chen,J.;Sun,Z.;Zhang,D.H.;Xu,X.J.Chem.Phys.2015,142,084107.doi:10.1063/1.4913196
(89)Chen,J.;Su,N.Q.;Xu,X.;Zhang,D.H.J.Comput.Chem.2017,38,2326.doi:10.1002/jcc.24886
(90)Decker,W.;Greuel,G.-M.;Pfister,G.;Sch?nemann,H.Singular 4-0-2-A Computer Algebra System for Polynomial Computations.http://www.singular.uni-kl.de,2015.
(91)King,S.A.J.Symb.Comput.2013,48,101.doi:10.1016/j.jsc.2012.05.002
(92)Chen,J.;Zhang,D.H.Sci.China Chem.2015,45,1241.[陈俊,张东辉.中国科学:化学,2015,45,1241.]doi:10.1360/N032015-00148