异核双原子分子势能函数的变分研究
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摘要
本文详细地介绍了孙卫国和冯灏运用二阶微扰理论所导出的高阶振动力常数的求解公式、能量自洽法(energy consistent method-ECM)、ECM势能函数的定义以及用能量自洽法计算稳定双原子分子体系势能函数的具体步骤，并将ECM方法推广应用于CIF、CH、BH、XeO、LaF、~7LiD、Na~7Li、NaRb和KRb等九种异核双原子分子的十二个电子基态和激发态的势能函数。通过把获得的ECM势与Morse势、HMS(Huxley-Murrell-Sorbie)势、RKR(Rydberg-Klein-Rees)值或IPA(Inverted-Perturbation-Approach)值比较表明：Morse势和HMS势等一些常用的解析势能函数往往在长程区和渐近区出现较大、甚至很大的偏差，HMS势还可能出现物理上错误的结构；而ECM势能函数不仅能满足正确的物理性质，并且在核间距变化的全程区域都能得到比较准确的势能。本文的结果还说明，ECM势不仅很好地适用于同核双原子分子，也能很好地适用于异核双原子分子的全程势能。这些进一步说明了ECM势能函数是比Morse势和HMS势等一些常用的解析势能函数更为优秀的势能函数。本文对ECM方法的应用进一步验证了ECM势能函数的正确性和广泛性，同时也为需要分子渐近区和离解区的正确势能数据的研究工作提供了可靠的物理数据。
This study introduces the energy consistent method(ECM), the ECM potential function, and the new formulae of vibrational force constants which are proposed by
Weiguo Sun and Hao Feng[45,46] recently. The ECM is applied to study the diatomic potential functions for some electronic ground states and excited states of GIF, CH, BH, XeO, LaF, 7LiD, Na7Li, NaRb and KRb molecules. The ECM potentials are compared with the experimental based RKR (Rydberg-Klein-Rees) potentials, IPA(Inverted-Perturbation-Approach) potentials, analytical Morse potentials, and HMS(Huxley-Murrell-Sorbie) potentials. It is shown that the ECM potentials have better or much better agreement with RKR and IPA data than the widely used Morse and HMS potentials especially in the molecular asympototic and dissociation region, and that the ECM potentials can be not only well applied to homonuclear diatomic molecules, but also to heteronuclear diatomic molecules. The ECM potentials are particularly usefull to generate correct potential data in molecular asymptotic and dissociation region for some diatomic molecular states which may be difficult to obtain experimrntly or theoretically
This study introduces the energy consistent method(ECM), the ECM potential function, and the new formulae of vibrational force constants which are proposed by
Weiguo Sun and Hao Feng[45,46] recently. The ECM is applied to study the diatomic potential functions for some electronic ground states and excited states of GIF, CH, BH, XeO, LaF, 7LiD, Na7Li, NaRb and KRb molecules. The ECM potentials are compared with the experimental based RKR (Rydberg-Klein-Rees) potentials, IPA(Inverted-Perturbation-Approach) potentials, analytical Morse potentials, and HMS(Huxley-Murrell-Sorbie) potentials. It is shown that the ECM potentials have better or much better agreement with RKR and IPA data than the widely used Morse and HMS potentials especially in the molecular asympototic and dissociation region, and that the ECM potentials can be not only well applied to homonuclear diatomic molecules, but also to heteronuclear diatomic molecules. The ECM potentials are particularly usefull to generate correct potential data in molecular asymptotic and dissociation region for some diatomic molecular states which may be difficult to obtain experimrntly or theoretically
引文
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[3]．金家俊，分子化学反应动态学，上海交通大学出版社，1988
[4]．朱正和，原子分子反应静力学，科学出版社，1996
[5]．M.Orchin,H.H.Jaffé著，徐广智译，对称性、轨道和光谱，科学出版社，1980
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[8]．徐光宪，黎乐民，王德民，量子化学基本原理和从头计算法(中册)，科学出版社，1999
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[11]．曾谨言，量子力学(卷Ⅱ)，科学出版社，1999
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[47]．文静，孙卫国，冯灏，物理学报，2000．49．2352
[48]．文静，冯灏，孙卫国，山东师大学报，2000．15．29
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[58]. W. Kuchle, M. Dolg and H. Stoll, J. Phys. Chem. A., 1997. 101. 7128
[59]．陈林红，桑斌，项金根，尚仁成，原子与分子物理学报，2001．18(4)．399
[60]. Y. C. Chan, D. R. Harding and W. C. Stwalley, J. Chem. Phys., 1986. 85. 2436
[61]．G. Herzberg．著，王鼎昌译，分子光谱与分子结构(第一卷 双原子分子光谱)，科学出版社，1983
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[65]. C. Amiot, J. Mol. Spectrosc., 2000. 203. 126
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[67]. K. P. Huber and G. Herzberg, "Constants of Diatomic Molecules," Van Nostrand-Reinhold, New York, 1979
[68]. T Heurlinger and E. Hulthen, Z. Wiss. Photogr. Photophys. Photochem., 1919. 18. 241
[69]. R. F. Barrow, M. W. Bastin, D. L. G. Moore, et al.., Nature., 1967. 215. 1072
[70]. H. Schall, C. Linton, W. R. Field, J. Mol. Spectrosc., 1983. 100.437
[71]. J. Verges, C. Effantin, J. D'incan, A. Bernard and Shenyavskaya, J. Mol. Spectrosc., 1999. 198. 196
[72]. A. Bernard, C. Effantin, J. D'incan and J. Verges, J. Mol. Spectrosc.,2000. 202. 163
[73]. A. Bernard, C. Effantin, J. D'incan and J. Verges, J. Mol. Spectrosc., 2000. 204. 55
[74]. K. A. Leonid, K. L. Alexey and H. C. Michael, J. Mol. Spectrosc., 1997. 182. 50
[75]．刘启能，冯灏，孙卫国，李绚，四川大学学报(自然科学版)，2001．38．688
[2]. G. Herzberg, Molecular spectra and Molecular Structure I. Spectra of Diatomic Molecules, (D. Van Nostrand Company, Inc, 1950)
[3]．金家俊，分子化学反应动态学，上海交通大学出版社，1988
[4]．朱正和，原子分子反应静力学，科学出版社，1996
[5]．M.Orchin,H.H.Jaffé著，徐广智译，对称性、轨道和光谱，科学出版社，1980
[6]．徐克尊，高等原子分子物理学，科学出版社，2000
[7]. M. A. Morrison and Sun weiguo, Computational Methods for Electron-Molecule Collisions Edited by Huo W and Gianturco F (New York: Plenum, 1995)
[8]．徐光宪，黎乐民，王德民，量子化学基本原理和从头计算法(中册)，科学出版社，1999
[9]. Born and Oppenheimer,Ann.Physik,1927.84.457
[10]．[美]Ira N.Levine著，宁世光，佘敬曾，刘尚长译，量子化学，人民教育出版社，1980
[11]．曾谨言，量子力学(卷Ⅱ)，科学出版社，1999
[12]．封继康，基础量子化学原理，高等教育出版社，1987
[13]. H. F. Schaefer Ⅲ, Methods of Electronic Structure Theory, (Plenum Press, New York and London, 1977)
[14]. H. F. Schaefer Ⅲ, Applications of Electronic Structure Theory, (Plenum Press, New York and London, 1977)
[15]. W. Meyer and P. Rosmus, J. Chem. Phys., 1975, 63, 2356
[16]．[美]物理学评述委员会编，伍烈尧，陈凌冰译，原子、分子物理学和光学，科学出版社，1993
[17]. W. Kolos and L. Wolniewicz, J. Chem. Phys., 1965. 43. 2429
[18]. W. Kolos and L. Wolniewicz, J. Chem. Phys., 1968. 48. 3672
[19]. W. Kolos and L. Wolniewicz, J. Chem. Phys., 1968. 49. 404
[20]. W. Kolos and L. Wolniewicz, J. Chem. Phys.,1974.24. 457
[21]. W. Kolos and L. Wolniewicz, J. Chem. Phys.,1993.98. 3960
[22]. R. Rydberg, Z. Physik, 1931.73. 376
[23]. O. Klein, Z. Physik, 1932.76. 226
[24]. J. N. Huffaker, J. Mol. Spectrosc., 1977. 65. 1
[25]. S. M. Kirschner and J. K. G. Watson, J. Mol. Spectrosc., 1973. 47. 234
[26]. A. L. G Rees, Proc. Phys. Soc., 1947. 59. 998
[27]. W. M. Kozman and J. J. Hinze, J. Mol. Spectrosc., 1975. 56. 93
[28]. C. R. Vidal and H. Scheingraber, J. Mol. Spectrosc., 1977. 65. 46
[29]. C. R. Vidal, Comments At. Mol. Phys., 1986. 17. 173
[30]. P. M. Morse, Phys. Rev., 1929. 34. 57
[31]. R. Rydberg, Z. phys., 1931. 73. 376
[32]. H. M. Hulbert and J. O. Hirschfelder, J. Chem. Phys., 1941. 9. 61
[33]. W. N. Whitton and P. J. Kuntz, J. Chem. Phys., 1976. 64. 3624
[34]. J. N. Murrell and K. S. Sorbic, J. Chem. Soc. Faraday. Trans. Ⅱ, 1974. 70. 1552
[35]. P. Huxley and J. N. Murrell, J. Chem. Soc. Faraday. Trans. Ⅱ, 1983. 79. 323
[36]. J. E. Lennard-Jones, Proc. Roy. Soc., 1924. A106. 463
[37]. K. T. Tang and J. P. Toennies, J. Chem. Phys., 1984. 80. 3726
[38]. K. T. Tang, J. P. Toennies and Meyer, J. Chem. Phys., 1991. 95. 1144
[39]. M. L. Sage, J. Chem. Phys., 1984. 87. 431
[40]. P. E. Siska, J. Chem. Phys., 1986. 85. 7497
[41]. A. J. C. Varandas, Mol. Phys., 1984. 53. 1303
[42]. A. J. C. Varandas and J. D. da silva, J. Chem. Soc. Faraday Trans. Ⅱ, 1986. 82. 593
[43]. A. J. C. Varandas and J. D. da silva, J. Chem. Soc. Faraday Trans. Ⅱ, 1992. 88. 941
[44]. Weiguo Sun, Mol. Phys., 1997. 92. 105
[45]. Weiguo Sun and Hao Feng, J. Phys. B: At. Mol. Opt. Phys., 1999. 32. 5109
[46]. Hao Feng, Weiguo Sun and Qineng Liu, J. Mol. Spectroscopy 2000. 80. 204
[47]．文静，孙卫国，冯灏，物理学报，2000．49．2352
[48]．文静，冯灏，孙卫国，山东师大学报，2000．15．29
[49]. J. L. Dunham, Phys. Rev., 1932. 41. 721
[50]. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, "Numerical Recipes in FORTRAN", Chap. 9, (Cambridge Univ. Press, New York, 1992)
[51]. B. R. Johnson, J. Phys. Chem., 1977. 67. 4086
[52]. I. S. Mcdermid, J. Chem. Soc. Faraday. Trans. Ⅱ., 1981. 77. 519
[53]. V. A. Alekseev, D. W. Setser and J. Tellinghuisen, J. Mol. Spectrosc., 1999. 195. 162
[54]. P. F. Bernath, J. Chem. Phys., 1987. 86. 4838
[55]. F. S. Pianalto, L. C. O'Brien, P. C. Keller and P F. Bernath, J. Mol. Spectrosc., 1988. 129. 348
[56]. J. D. Simmons, A. G. Maki and J. T. Hougen, J. Mol. Spectrosc., 1979. 74. 70
[57]. A. Bernard, C. Effantin, J. D'incan and J. Verges, J. Mol. Spectrosc. Note., 2000. 202. 163
[58]. W. Kuchle, M. Dolg and H. Stoll, J. Phys. Chem. A., 1997. 101. 7128
[59]．陈林红，桑斌，项金根，尚仁成，原子与分子物理学报，2001．18(4)．399
[60]. Y. C. Chan, D. R. Harding and W. C. Stwalley, J. Chem. Phys., 1986. 85. 2436
[61]．G. Herzberg．著，王鼎昌译，分子光谱与分子结构(第一卷 双原子分子光谱)，科学出版社，1983
[62]. C. E. Fellows, J. Mol. Spectrosc., 1989. 136. 369
[63]. S. Kasahara, T. Ebi, M. Tanimura, H. Ikoma, K. Matsubara, M. Baba and H. Kato, J. Chem. Phys., 1996. 105. 1341
[64]. W. T. Zemke and W. C. Stwalley, J. Chem. Phys., 2001. 114(24). 10811
[65]. C. Amiot, J. Mol. Spectrosc., 2000. 203. 126
[66]. S. Kasahara, C. Fujiwara, N. Okada, H. Kato and M. Bara, J. Chem. Phys., 1999. 111. 8857
[67]. K. P. Huber and G. Herzberg, "Constants of Diatomic Molecules," Van Nostrand-Reinhold, New York, 1979
[68]. T Heurlinger and E. Hulthen, Z. Wiss. Photogr. Photophys. Photochem., 1919. 18. 241
[69]. R. F. Barrow, M. W. Bastin, D. L. G. Moore, et al.., Nature., 1967. 215. 1072
[70]. H. Schall, C. Linton, W. R. Field, J. Mol. Spectrosc., 1983. 100.437
[71]. J. Verges, C. Effantin, J. D'incan, A. Bernard and Shenyavskaya, J. Mol. Spectrosc., 1999. 198. 196
[72]. A. Bernard, C. Effantin, J. D'incan and J. Verges, J. Mol. Spectrosc.,2000. 202. 163
[73]. A. Bernard, C. Effantin, J. D'incan and J. Verges, J. Mol. Spectrosc., 2000. 204. 55
[74]. K. A. Leonid, K. L. Alexey and H. C. Michael, J. Mol. Spectrosc., 1997. 182. 50
[75]．刘启能，冯灏，孙卫国，李绚，四川大学学报(自然科学版)，2001．38．688