摘要
含碳官能基的聚硅氧烷除本身具有许多优良性能外,还可利用其官能基的反应活性,将聚硅氧烷引入其他聚合物,以形成具有特殊性能的各种聚合物,是一大类在许多领域发挥重大作用并迅速发展的有机硅聚合物,也是近来比较活跃的研究领域。然而,许多碳官能基的引入使得聚硅氧烷的热稳定性降低,影响了在某些方面的使用。研究搞清该类聚合物的热降解规律及其影响因素,对于控制热降解、更好的利用该类化合物以及改进和研制具有更优异性能的聚合物具有十分重要的意义。
本文使用密度泛函理论(DFT)和过渡态理论(TST),以含有2-4个硅氧链节的二甲基硅氧烷和羟烷基二甲基硅氧烷的低聚体为模型,在B3LYP/6-311++G(3df,3pd)//B3LYP/6-31G(d)水平上,首次对羟丙基聚二甲基硅氧烷、羟乙基聚二甲基硅氧烷和端羟基聚二甲基硅氧烷的热降解反应以及连结在不同原子上的甲基和苯基对热降解反应的影响进行了系统的理论研究。揭示了反应机理,进行了动力学和热力学分析。
主要成果有:
一、首次对α-硅醇的热重排反应进行了理论研究。结果表明:
1、硅基甲醇H_3SiCH_2OH在加热条件下可发生两种dyotropic重排反应。一种是Bro-ok重排反应,硅基由碳原子向氧原子迁移,同时氧上的氢原子向碳原子迁移,经由两个三元环构成的具有桥环结构的过渡态,生成甲氧基硅烷;另一种是羟基迁移反应,羟基由碳原子向硅原子迁移,同时硅上的一个氢原子向碳原子迁移,经由两个三元环构成的具有桥环结构的过渡态,生成甲基硅醇。两个反应过渡态中的硅均为五配位。在G3水平上两反应的活化能分别为344.5和236.8kJ/mol。动力学和热力学均有利于羟基重排反应。当硅基甲醇加热时,重排的主要产物是甲基硅醇。
2、连接在中心碳原子上的乙烯基可显著降低羟基迁移反应的活化能并增大反应速率,但是对Brook重排反应几乎没有影响。
3、连接在硅原子上的烃基可显著降低Brook重排反应的活化能并增大反应速率,对羟基迁移反应几乎没有影响。隧道效应对所研究反应的速率没有数量级水平的影响。
4、在MP2(full)/6-31G(d)、MP2(full)/6-311G(d,p)、B3LYP/6-31G(d)和B3LYP/6-311++G(3df,3pd)//B3LYP/6-31G(d)等理论计算模型中,B3LYP/6-311++G(3df,3pd)//B3LYP/6-31G(d)对反应活化能的预测值与G3水平的计算值最接近。
In spite of possessing a variety of unique and superior properties, carbofounctionalized polysiloxanes play important roles in modifitions of organic polymers, such as the copolymerization of polysiloxanes and organic polymers, with the aid of the reaction activity of the carbofunctional groups, to endow the organic polymers with the excellent properties of the polysiloxanes. However, because of the decomposition or rearrangement under certain conditions, their applications are limited to some extent. Understanding their rearrangement conditions and mechanisms will be of great important values for the control and application of these compounds.
In this dissertation, theoretical studies on thermal degradation or rearrangement reactions of hydroxylpropyl polydimethylsiloxanes, hydroxylethyl polydimethylsioxanes and hydroxyl-ended poly-dimethylsiloxanes and effects of methyl and phenyl attached to different atoms on the reactions were carried out by employing polydimethylsiloxane, hydroxylpropyl polydimethyl sioxane or hydroxylethyl polydimethylsioxanes oligomers containing three or four silicon atoms as model compounds. For all reactions under study, the reaction mechanisms were revealed through Density Functional Theory (DFT) and molecular orbital theory at the B3LYP/6-311++G(3df,3pd)//B3LYP/6-31G(d) level, and reaction rate constants were evaluated by using Transition State Theory (TST) with direct dynamic method. The important and valuable results are summarized as follows: 1. On the thermal rearrangement reactions of α-silylalcohols
(1) Two dyotropic reactions may occur when α-silylalcohols are heated. One is via the Brook rearrangement reaction, where the silyl group migrates from carbon atom to oxygen atom coupled with a simultaneous migration of a hydrogen atom from oxygen atom to carbon atom passing through a double three-membered ring transition state, forming alkyloxysilane. In the other rearrangement, the reactant undergoes a hydroxyl group migration from carbon atom to silicon atom coupled with a simultaneous migration of a hydrogen atom from silicon atom to carbon atom via a double three-membered ring transition state, forming alkylsilanol. The hydroxyl group migration reaction is preferred to the Brook rearrangement reaction both thermodynamically and kinetically.
引文
[1] Friedel C and Crafts J M, Compt Rend,56,592(1863)
[2] Kipping F S, Pro Chem Soc.London,20,15(1904)
[3] Rochow E G US Pat.2380995(1941)
[4] Warrick E L, et, al Rubber Chem Technol,52(3),437(1979)
[5] US Pat 2445794(1948)
[6] US Pat 2560498(1951)
[7] US Pat 2571039(1951)
[8] US Pat 2843555(1958)
[9] Donnet J C, Marechal E, Bull Soc Chim Fr,3561(1972)
[10] Willianms T C, US3234174(1965)
[11] Pierce O R, Kim Y K, J Elatoplast, 3,82(1971)
[12] Goldman G K, Marris L,US3531508(1970)
[13] Schroeder H G, Rubber Age,101,58(1969)
[14] Sasaki T, Ratner B D, Hoffman, Polym.Prepn 16(2),435(1973)
[15] General Electric Co., Brit.1067961(1967)
[16] Polmanteer K E, Falender J R, ACS Symp.Ser.260,117(1984)
[17] Saam J S, Gravier D, Baile M, Rubber Chem Technol,54,976(1981)
[18] 王坚平,冯圣玉,陈建华,聚硅氧烷接枝共聚物,有机硅材料及应用,1,7.10,1996
[19] 崔孟中,冯圣玉,含环氧基聚硅氧烷的研究进展,功能高分子学报,9(3)475,1996
[20] 吴拥中,冯圣玉等,含氨烷基聚硅氧烷的研究进展,材料工程,11,44-48,1998
[21] 吴明艳,冯圣玉等,含烃氧基聚硅氧烷的研究及应用,有机硅材料,16(5),26-29,2002
[22] 孙效华,王文忠,冯圣玉,氯丙基聚硅氧烷的合成进展,有机硅材料,2002,16(4),28-31
[23] 荣宇,冯圣玉,陈剑华,羟丙基封端聚硅氧烷的合成及性质,有机硅材料,2001.15(1),12—15
[24] 吴拥中,李红云,冯圣玉,新型含氨丙基聚硅氢烷基高温硫化硅橡胶的制备,材料科学与工程学报,2004,22(1),41-43
[25] Qingzeng Zhu, Shengyu Feng, Chen Zhang, J. Appl. Poly. Sci., 99,310-315(2003)
[26] Chuanjian Zhou, Ruifang Guan, Shengyu Feng, Eur. Poly. J., 40 (2004) 165-170
[27] 刘宗林,郝树萱等,高分子材料与工程学,1998,14:23
[28] 徐永祥,刘宗林,胡文军,等,有机硅材料,2001,15(6):12
[29] 许涌深,唐士立,反应性官能端基硅氧烷的合成与应用,化工进展,1,31-35,2001
[30] 雷艳秋,孙争光,黄士强,有机硅聚合物功能材料的研究与应用,有机硅材料,18(1),27-31,2004
[31] 孟勇,翁志学,黄志明,潘祖仁,有机硅侧链液晶研究进展,功能高分子学报,16(4)575-584,2003
[32] 侣庆法,范晓东,功能性有机聚硅氧烷的研究进展,高分子通报,1,21-29,2004
[33] 王绪荣,氨基改性聚硅氧烷及其乳液的研制,有机硅材料,2001,15(4),22-26
[34] 卿宁,田禾,张晓镭,周建华,俞从正,氨基聚硅氧烷的合成,功能高分子学报,2000,13(4),385-388
[35] 幸松民,氨烃基硅油的制法及其应用,有机硅材料及应用,1998,4,1-5
[36] 程建华,伍钦,汪晓军,氨烃基改性聚硅氧烷的合成及微乳化研究,印染助剂,2002,19(1),35-37
[37] 郑晓字,李平,丙二醇嵌段聚醚及其聚硅氢烷改性产物的界面性能和破乳性能,石油学报(石油加工),2004,20(2),5-12
[38] 吕伟,杨峰,α,ω-二羟基聚二甲基硅氧烷制备新工艺研究,吉化科技,1997,5(4),30-35
[39] 张建安,吴明元,吴庆云,杨建军,李英,含侧氨基聚二甲基硅氢烷齐聚物的合成,精细石油化工进展,2001,9,17-19
[40] Lewis RN. J Am Chem Soc 1948;70:1115.
[41] Andrianov KA. Vysokomol Soedin A 1971; 14:253.
[42] T.H. Thomas, T.C. Kendrcik, J. Polym. Sci. A-2 (7) (1969) 537.
[43] T.H. Thomas, T.C. Kendrcik, J. Polym. Sci. A-2 (8) (1970) 1823.
[44] Grassie N, MacFarlane J. Eur Polym J 1978;14:875.
[45] S.J. Clarson, J.A. Semlyen, Polymer 27 (1986) 1633.
[46] P.V. Wright, J.A. Semlyen, Polymer 11 (1970) 462.
[47] J.A. Semlyen, P.V. Wright, Polymer 10 (1969) 543.
[48] J.A. Semlyen, Adv. Polym. Sci. 21 (1976) 41.
[49] M.S. Beevers, J.A. Semlyen, Polymer 12 (1971) 373.
[50] S.J. Clarson, J.A. Semlyen, Polymer 27 (1986) 91.
[51] D.J. Orrah, J.A. Semlyen, K. Dodgson, S.B. Ross-Murphy, Polymer 28 (1987) 985.:229.
[52] M.K. Lee, D.J. Meier, Polymer 34 (23) (1993) 4882.
[53] a) G. Camino, S. M. Lomakin, M. Lazzari, Polymer,42(2001)2395-2402
b) G. Camino, S. M. Lomakin, M. Lazzari, Polymer,43(2002)2011-2015
[54] Kissinger H. E., Anal Chem 1959;29:1702.
[55] Ismail IMK, Rodgers SL. Carbon 1992;30
[56] 钟发春 宇航材料工艺 2003年第1期 29-32
[57] Grassie N. The thermal degradation of polysiloxanes. Part 4. poly ( dimethyl/diphenyl siloxane). European Polymer Journal, 1979; 15:415~420
[58] Durham LJ, Wurster CF, Mosher HS. JACS 1958;80:327, 332.
[59] KuceraM, L áníkováJ, and JelinekM. J Polym Sci, 1961, 53: 301.
[60] Thomas T H, Kendrick T C. J Polym Sci: Part A 22, 1969, 7: 537.
[61] Grassie N, M acfarlane I G. Euro Polym J, 1978, 14: 875.
[62] Grassie N, M acfarlane I G, F rancey K F. Euro.Polym.J, 1979, 15: 415.
[63] Grassie N, Francey KF, Macfarlane IG. Polym Degrad Stab 1980;2:67-83.
[64] Iskender YILGOR等Tr. J. of Chemistry 21 (1997),227-285
[65] E. Peter Maziarz Ⅲ, Gary A. Baker, and Troy D. Wood, Macromolecules 1999, 32, 4411-4418E.
[66] Huiping Chen, J Am Soe Mass Spectrom 2003, 14, 1039-1048
[67] Peter Maziarz, Ⅲ, X. Michael Liu, Edmond T. Quinn, Yu-Chin.Lai, Daniel M. Ammon, Jr., and George L. Grobe, Ⅲ, J Am Soc Mass Spectrom 2002, 13, 170-176
[68] Qingzeng Zhu, Ruifang Guan, Fanjun Meng, Shengyu Feng, Thermochimica Acta 402 (2003) 193-197
[69] 吴明艳,冯圣玉,山东大学硕士学位论文 2003年
[70] Bo Li Molecular Simulation of Gas Transport Properties and Chain Conformation of Polysilanes. Ph.D.dissertation,University of Cincinnati,2003
[71] Hua Sun, David Rigby Spectrochimica Acta Part A 53 (1997) 1301-1323
[72] R.D. Patil, J.E. Mark Computational and Theoretical Polymer Science 10 (2000) 189-195.
[73] Flory PJ. Statistical mechanics of chain molecules, New York/Cincinnati, OH: Interseience/Hanser Press, 1969 and 1989.
[74] Flory PJ. Macromolecules 1974;7:381.
[75] V. Van Speybroeck, Y. Martele, M. Waroquier, and E. Schacht, J. Am. Chem. Soc. 2001, 123, 10650-10657
[76] J. Katajisto et al. / Journal of Molecular Structure (Theochem) 634 (2003) 305-310
[77] James S. Smith, Oleg Borodin, and Grant D. Smith J. Phys. Chem., B 2004,
[78] D. G. Truhiar, M. S. Gordon, Science 1990, 249, 491. b) D.G Truhiar, A.D. lsaacson, B.C. Garret, Theory of Chemical Reaction Dynamics, M.Baer, ed., BocaRaton,CRC Press, 1985, p.65.
[79] D. G. Truhlar, M. S. Gordon, R. Steckler, Chem. Rev. 1987, 87, 217.
[80] J. C. Corchado, J. Espinosa-Garcia, W.PHu, I. Rossi, D.G Thuhlar, J.Phys. Chem. 1995, 99, 687.
[81] T. N. Truong, J. Chem. Phys. 1994, 100, 8014
[82] T. N. Truong,W Duncan, J. Phys. Chem. 1994, 101, 7408.
[83] D.G Truhlar, The Reaction Path in Chemistry, Current Approaches and Perspectives, Kluwer Academic, The Netherlands, 1995.
[84] S. Wang, M. Karplus, J. Am. Chem. Soc. 1973, 95, 8160.
[85] C. Leforestier, J.Chem. Phys. 1978, 68, 4406
[86].唐有棋,化学动力学和化学反应器原理,北京,科学出版社,1974.
[87].黄仲涛,基本有机化工理论基础,北京,化学工业出版社,1980.
[88].吉林大学等,物理化学(下册),人民教育出版社,1979.
[89].罗孝良,药学通报,1982,17,8.
[90] J. Warnatz, Combustion Chemistry, Springer-Verlag, New York, 1984.
[91] D. J. Hucknall, Chemistry of Hydrocarbons, Chapman and Hall, London, 1985.
[92] F. S. Rowland, M. J. Molina, Reviews of Geophysics and Space Physics, 1975, 13, 1.
[93] I. W. M. Smith, Kinetics and Dynamics of Elementary Gas reactions; Butterworths: Boston, 1980.
[94] M. Born, R. Oppenheimer, Zur Quantentheorie der Molekeln Ann. Phsik.(Quaritum Theory of the Molecules Ann. Phys.) 1927, 84, 457.
[95] (a)唐敖庆,杨忠志,李前树,量子化学,北京,科学出版社,1982.(b) 徐光宪,黎乐民,王德民,量子化学基本原理和从头计算法,北京,科学出版社,1985.
[96] 赵学庄,罗渝然,减雅茹,万学适著,《化学反应动力学原理》下册,高等教育出版社,1990.
[97] R. G. Parr and W. Yang, Density-Functional Theory of Atoms andMolecules, Oxford Univ. Press: Oxford, 1989.
[98] P. Hohenberg, W Kohn, Inhomogeneous Electron Gas, Phys. Rev. 1964,136, B864.
[99] W. Kohn, L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Efects,phys.Rev. 1965, 140,A1133.
[100] D.R.Salahub, M.C.Zemer, eds, The Challenge of d and f Electrons, ACS: Washington, D.C., 1989.
[101] J.K.Labanowski, J.W.Andzelm, eds, Density Functional Methods in Chemistry, Springer-Verlag: New York, 1991.
[102] J. S. Winn, Physical Chemistry, Harper Collins College Publishers,1995.
[103] P. W. Atkins, Physical Chemistry, WH. Freeman and Company, New York, 1990.
[104] G. D. Billing, K.V Mikkelsen, Introduction to Molecular Dynamics and Chemical Kinetics, John Wiley & Sons, Inc., New York, 1996.
[105] H. S. Johnston, Gas Phase Reaction Rate Theory, Ronald Press Company, New York, 1966.
[106] S. Glasstone, K. Laidler, H. Erying, Theory of Rate Processes, McGraw-Hill, New York, 1941.
[107] D. G. Thuhlar, A. D. lsaacson, B. C. Garreett, Generalized Transition State Theory, in The theory of Chemical Reaction Dynamics, edited by M. Baer, CRC Press, Boca Raton, FL, 1985, Vol. 4, pp.65-137.
[108] B. C. Garret, D. G. Truhlar, J Phys. Chem. 1979, 83, 1052
[109] B. C. Garrett, D.G Truhlar, J Chem. Phys. 1979, 70, 1593.
[110] W L. Hase, J Chem. Phys, 1976, 64, 2442.
[111] M. Quack, J. Troe, Ber. Bunsenges, Phys. Chem. 1977, 81,329.
[112] E. Wigner, Trans. Faraday Soc. 34, 29 (1938)
[113] K. Fukui, Variational Principles in a Chemical Reaction, Int. J Quantum Chem. 1981, 15, 633-642.
[114] K.Fukui,A.Tachibana, K.Yamashita, Toward Chemodynamics, Int. J.Quantum. Chem. 1981, 15, 621-632.
[115]Lowdin, P.O., Phys.Rev, 1955, 97, 1474.
[116] Reed, A. E., Larry A.Curtiss and Frank Weinhold, Chem.Rev.,1988,88,899.
[117] F. Jensen, Introduction to Computational Chemistry, JOHN WILEY&SONS, 1999,161.
[118] Almlof, J.and Taylor, P.R. Adv.Quantum Chem., 1991,22,301.
[119]Jensen, F.Introduction to Computational Chemistry,JOHN WILEY&SONS, 1999,229.
[120] Reed, A.E.&Weinhold, F. J.Chem.Phys.,1983,78(6),4061.
[121] Reed, A. E., Weinstock, R. B., Weinhold, F. J.Chem.Phys. 1985, 83(2), 735
[122] Carpenter, J.E., Weinhold, F. J.Mol.Struct.(Theochem), 1988,169,41.
[123] Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. P人ys. 1985, 83, 735-746.
[124] J. J. P. Stewart, J. Comp. Chem. 10, 209 (1989).
[125] J. J. P. Stewart, J. Comp. Chem. 10, 221 (1989).
[126] Brook, A. G. Acc. Chem. Res. 1974, 7, 77-84.
[127] Reich, H. J.; Holtan, R. C; Bolm, C. J. Am. Chem. Soc. 1990,112, 5609-5617.
[128] Dalton, J. C; Bourque, R. A. J. Am. Chem. Soc. 1981, 103, 699-700.
[129] Tsai, Y.-M.; Cherng, C.-D. Tetrahedron Lett. 1991, 32, 3515-3518.
[130] Chang, S.-Y; Jiaang, W.-T.; Cherng, C.-D.; Tang, K.; Hang, C.-H.; Tsai, Y.-M. J. Org. Chem. 1997, 62, 9089-9098.
[131] Robertson, J.; Burrow, J. N. Tetrahedron Lett. 1994, 35, 3777-3780.
[132] Paredes, M. D.; Alonso, R. Tetrahedron Lett. 1999,40, 3973-3976.
[133] Paredes, M. D.; Alonso, R. J. Org. Chem. 2000, 65, 2292-2304.
[134] Harris, J. M.; MacInnes, I.; Dalton, J. C; Maillard, B. J. Organomet.Chem. 1991,403, C25-C28.
[135] Wright, A.; West, R. J. Am. Chem. Soc. 1974,96, 3214-3222.
[136] Linderman, R. J.; Ghannam, A. J. Am. Chem. Soc. 1990,112,2392-2398
[137] Shuto, S.; Kanazaki, M.; Ichikawa, S.; Minakawa, N.; Matsuda, A. J. Org. Chem. 1998, 63,746-754.
[138] Antoniotti, P.; Tonachini, G. J. Org. Chem. 1993,58, 3622-3632.
[139] Antoniotti, P.; Canepa, C; Tonachini, G. J. Org. Chem. 1994, 59,3952-3959.
[140] Wang, Y.-G.; Dolg, M. Tetrahedron 1999, 55,12751-12756.
[141] Schiesser, C. H.; Styles, M. L. J. Chem. Soc, Perkin Trans. II 1997,2,2335-2340.
[142] a)Eyring, H. J. Chem. Phys. 1935, 3, 492. b) Evans, M. G.; Polanyi, M. Trans. Faraday, Soc. 1935, 31, 875; c) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1937, 33,448.
[143] (19) Ju, G.; Feng, D.; Deng, C. Acta Chim. Sin. 1985,43, 680.
[144] a) Foresman, J. B.; Frisch, A. Exploring Chemistry with Electronic Structure Methods, 2nd ed.; Gaussian, Inc. Pittsburgh, PA, 1996, p64. b) "Precomputed vibrational scaling factors", online available at http://srdata.nist.gov/cccbdb/vibscalejust.asp, Computational Chemistry Comparison and Benchmark Database (CCCBDB), released by National Institute of Standards and Technology (http://www.nist.gov).
[145] L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, and J. A. Pople, J. Chem Phys. 1998,109, 7764
[146] Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,M. A.; Cheeseman; Zakrzewski,V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C; Dapprich, S.; Millam, J. M.; Daniels,A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.;Mennucci, B.; Pomelli, C.; Adamo, C; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.;Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 03, Revision C.02,; Gaussian, Inc.: Wallingford CT, 2004.
[147] Manfred T. Reetz, Angew. Chem. internat. Edit., 1972, 11,129-131.
[148] (a) Ignat'ev, I. S.; Shchegolev, B. F. Phys. Chem. (Russian) 1987, 296 (1), 143-147.
(b) Grigoras, S.; Lane, T. H. J. Comput. Chem. 1987, 8, 84.
(c) Oberhammer, H.; Boggs, J. E. J. Am. Chem. Soc. 1980,102, 7241.
(d) Raghavachari, K.; Chandrasekhar, J.; Frisch, M. J. J. Am. Chem. Soc. 1982, 104, 3779.
[149] Yao-Yuan Chuang and Donald G. Truhlar, J. Chem. Phys., 2000,112,1221-1228]
[150] V. VAN Speybroeck; D. Van Neek; M. Waroquier. J. Phys. Chem. A, 2000,104. (46); 10939-10950.
[151] W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Chem. Phys. 51,2657 (1969).
[152] J. B. Collins, P. v. R. Schleyer, J. S. Binkley, and J. A. Pople, J. Chem. Phys. 64, 5142 (1976).
[153] Ju, G.; Feng, D.; Deng, C. Aria Chim. Sinica. 1985,43, 680.
[154] Baldrige, K. K.; Gordor, M. S.; Steckler, R.; Truhlar, D. G. J. Phys. Chem. 1989,93, 5107.
[155] Gonzalez-Lafont, A.; Truong, T. N.; Truhlar, D. G. J. Chem. Phys., 1991,95, 8875.
[156] Garrett B. C.; Truhlar, D. G. J. Phys. Chem., 1979, 83, 1052.
[157] R. Sumathi, William H. Green, Jr., Theor Chem Acc, 2002,108,187-213.
[158] R. Sumathi, William H Green, Jr., J. Phys. Chem. A, 2001,105,6910-6925.
[159] R. Sumathi, William H. Green, Jr., PCCP, 2003, 5, 3402-3417.
[160] Yu, Y.; Feng, S. J. Phys. Chem. A 2004, 108,7468-7472.
[161] Yu, Y.; Feng, S.; Feng, D. J. Phys. Chem. A 2005, 109, 3663-3668.
[162]Yu,Y.;Feng,S. In.t.J. Quantum Chem. 2007,107 (1), 105-115.