Dimensional perturbation theory for vibration-rotation spectra of linear triatomic molecules

Journal of Chemical Physics

Volumn 107, Issue 11, 1997, Pages 4099-4111

  Suvernev, Andrei A ^a   Goodson, David Z ^a  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CARBON DIOXIDE; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; ELECTRONIC DENSITY OF STATES; HARMONIC ANALYSIS; MATRIX ALGEBRA; MOLECULAR DYNAMICS; MOLECULAR VIBRATIONS; NITROGEN COMPOUNDS; PERTURBATION TECHNIQUES; VARIATIONAL TECHNIQUES;

DIMENSIONAL PERTURBATION THEORY; KINETIC ENERGY OPERATOR; LINEAR TRIATOMIC MOLECULES; PERTURBATION EXPANSIONS; VIBRATION ROTATION SPECTRA;

MOLECULAR SPECTROSCOPY;

EID: 0031572024     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.474802     Document Type: Article

References (77)

1. C-L. Chen, B. Maessen, and M. Wolfsberg, J. Chem. Phys. 83, 1795 (1985).
2. J. Tennyson and B. T. Sutcliffe, Mol. Phys. 58, 1067 (1986).
3. Z. Bačić and J. C. Light, Annu, Rev. Phys. Chem. 40, 469 (1989), and references therein.
4. J. Tennyson and J. R. Henderson, J. Chem. Phys. 91, 3815 (1989).
5. S. Tennyson, S. Miller, J. R. Henderson, and B. T. Sutcliffe, Phil. Trans. R. Soc. London Ser. A 332, 329 (1990).
6. J. Cižek, V. Špirko, and O. Bludský, J. Chem. Phys. 99, 7331 (1993).
7. A. A. Suvernev and D. Z. Goodson, J. Chem. Phys. 106, 2681 (1997).
8. S. Kais and D. R. Herschbach, J. Chem. Phys. 98, 3990 (1993).
9. Dimensional Sealing in Chemical Physics, edited by D. R. Herschbach, J. Avery, and O. Goscinski (Kluwer Academic, Dordrecht, 1993).
10. New Methods in Quantum Theory, edited by C. A. Tsipis, J. Avery and D. R. Herschbach (Kluwer Academic, Dordrecht, 1996).
11. L. G. Yaffe, Rev. Mod. Phys. 54, 407 (1982), and references therein.
12. A. Chatterjee, Phys. Rep. 186, 249 (1990), and references therein.
13. D. R. Herschbach, Int. J. Quantum Chem. 57, 295 (1996).
14. J. G. Loeser, J. Chem. Phys. 86, 5635 (1987).
15. V. M. Vaǐnberg, V. D. Mur, V. S. Popov, A. V. Sergeev, and A. V. Shcheblykin, Teor. Mat. Fiz. 74, 399 (1988) [Theor. Math. Phys. 74, 269 (1988)].
16. V. M. Vaǐnberg, V. D. Mur, V. S. Popov, A. V. Sergeev, and A. V. Shcheblykin, Teor. Mat. Fiz. 74, 399 (1988) [Theor. Math. Phys. 74, 269 (1988)].
17. M. Dunn, T. C. Germann, D. Z. Goodson, C. A. Traynor, J. D. Morgan, III, D. K. Watson, and D. R. Herschbach, J. Chem. Phys. 101, 5987 (1994).
18. D. Z. Goodson and D. R. Herschbach, Phys. Rev. A 46, 5428 (1992); D. Z. Goodson and D. K. Watson, ibid. 48, 2668 (1993); D. Z. Goodson, M. López-Cabrera, D. R. Herschbach, and J. D. Morgan, III, J. Chem. Phys. 97, 8481 (1992).
19. D. Z. Goodson and D. R. Herschbach, Phys. Rev. A 46, 5428 (1992); D. Z. Goodson and D. K. Watson, ibid. 48, 2668 (1993); D. Z. Goodson, M. López-Cabrera, D. R. Herschbach, and J. D. Morgan, III, J. Chem. Phys. 97, 8481 (1992).
20. D. Z. Goodson and D. R. Herschbach, Phys. Rev. A 46, 5428 (1992); D. Z. Goodson and D. K. Watson, ibid. 48, 2668 (1993); D. Z. Goodson, M. López-Cabrera, D. R. Herschbach, and J. D. Morgan, III, J. Chem. Phys. 97, 8481 (1992).
21. D. Z. Goodson, Phys. Rev. A. 55, 4155 (1997).
22. M. López-Cabrera, D. Z. Goodson, D. R. Herschbach, and J. D. Morgan, III, Phys. Rev. Lett. 68, 1992 (1992).
23. D. D. Frantz and D. R. Herschbach, Chem. Phys. 126, 59 (1988).
24. J. M. Cohen and D. Z. Goodson, Int. J. Quantum Chem. 59, 445 (1996).
25. A. A. Belov and Yu. E. Lozovik, Zh. Éksp. Teor. Fiz. 94, 38 (1988) [Sov. Phys. JETP 67, 2413 (1988)]; A. A. Belov, Yu. E. Lozovik, and V. A. Mandel' shtam, ibid. 98, 25 (1990) [ibid. 71, 12 (1990)]; A. Gonzalez and D. Leal, J. Phys. B 26, 1253 (1993).
26. A. A. Belov and Yu. E. Lozovik, Zh. Éksp. Teor. Fiz. 94, 38 (1988) [Sov. Phys. JETP 67, 2413 (1988)]; A. A. Belov, Yu. E. Lozovik, and V. A. Mandel' shtam, ibid. 98, 25 (1990) [ibid. 71, 12 (1990)]; A. Gonzalez and D. Leal, J. Phys. B 26, 1253 (1993).
27. A. A. Belov and Yu. E. Lozovik, Zh. Éksp. Teor. Fiz. 94, 38 (1988) [Sov. Phys. JETP 67, 2413 (1988)]; A. A. Belov, Yu. E. Lozovik, and V. A. Mandel' shtam, ibid. 98, 25 (1990) [ibid. 71, 12 (1990)]; A. Gonzalez and D. Leal, J. Phys. B 26, 1253 (1993).
28. A. A. Belov and Yu. E. Lozovik, Zh. Éksp. Teor. Fiz. 94, 38 (1988) [Sov. Phys. JETP 67, 2413 (1988)]; A. A. Belov, Yu. E. Lozovik, and V. A. Mandel' shtam, ibid. 98, 25 (1990) [ibid. 71, 12 (1990)]; A. Gonzalez and D. Leal, J. Phys. B 26, 1253 (1993).
29. A. A. Belov and Yu. E. Lozovik, Zh. Éksp. Teor. Fiz. 94, 38 (1988) [Sov. Phys. JETP 67, 2413 (1988)]; A. A. Belov, Yu. E. Lozovik, and V. A. Mandel' shtam, ibid. 98, 25 (1990) [ibid. 71, 12 (1990)]; A. Gonzalez and D. Leal, J. Phys. B 26, 1253 (1993).
30. D. A. Morales, Chem. Phys. Lett. 161, 253 (1989).
31. T. C. Germann and S. Kais, J. Chem. Phys. 99, 7739 (1993).
32. J. Louck, J. Mol. Spectrosc. 3, 673 (1960).
33. D. R. Herschbach, in Dimensional Scaling in Chemical Physics, edited by D. R. Herschbach, J. Avery, and O. Goscinski (Kluwer Academic, Dordrecht, 1993), pp. 61-80.
34. D. R. Herrick and F. H. Stillinger, Phys. Rev. A 11, 42 (1975).
35. L. D. Mlodinow, in Progress in Particle and Nuclear Physics, edited by D. Wilkinson (Pergamon, Oxford, 1982), Vol. 8, pp. 387-399; L. D. Mlodinow and M. P. Shatz, J. Math. Phys. 25, 943 (1984).
36. L. D. Mlodinow, in Progress in Particle and Nuclear Physics, edited by D. Wilkinson (Pergamon, Oxford, 1982), Vol. 8, pp. 387-399; L. D. Mlodinow and M. P. Shatz, J. Math. Phys. 25, 943 (1984).
37. D. K. Watson and D. Z. Goodson, Phys. Rev. A 51, R5 (1995).
38. J. G. Loeser and D. R. Herschbach, in New Methods in Quantum Theory, edited by C. A. Tsipis, J. Avery, and D. R. Herschbach (Kluwer Academic, Dordrecht, 1996), pp. 33-54; S. Kais and R. Bleil, ibid., pp. 55-70.
39. J. G. Loeser and D. R. Herschbach, in New Methods in Quantum Theory, edited by C. A. Tsipis, J. Avery, and D. R. Herschbach (Kluwer Academic, Dordrecht, 1996), pp. 33-54; S. Kais and R. Bleil, ibid., pp. 55-70.
40. it is possible to carry out the separation of variables for arbitrary D, and that would be an alternative to the approach developed here. See M. Dunn and D. K. Watson, Ann. Phys. (N.Y.) 251, 266 (1996).
41. A. A. Suvernev and D. Z. Goodson, Chem. Phys. Lett. 269, 177 (1997).
42. 2).
43. H. C. Allen, Jr. and P. C. Cross, Molecular Vib-Rotors (Wiley, New York, 1963), pp. 51-53.
44. (n,j,k,σ) is not normalized to unity. This must be taken into account if the wave-function perturbation expansion is to be used directly to compute expectation values of operators. See Ref. 16 for a discussion of this point.
45. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith. D. Chris Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, J. Quant. Spectrosc. Radiat. Transfer 48, 469 (1992).
46. G. Herzberg, Molecular Spectra and Molecular Structure: II. Infrared and Raman Spectra of Polyatomic Molecules (van Nostrand, New York, 1966), pp. 276 and 395.
47. A. Chedin, J. Mol. Spectrosc. 76, 430 (1979).
48. C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (McGraw-Hill, New York, 1955), pp. 624, 641.
49. W. Hückel, Structural Chemistry of Inorganic Compounds, (Elsevier, New York, 1950), Vol. 1, p. 432.
50. E. B. Wilson, Jr. and J. B. Howard, J. Chem. Phys. 4, 262 (1936); D. Kivelson and E. B. Wilson, Jr., ibid. 20, 1575 (1952).
51. E. B. Wilson, Jr. and J. B. Howard, J. Chem. Phys. 4, 262 (1936); D. Kivelson and E. B. Wilson, Jr., ibid. 20, 1575 (1952).
52. H. H. Nielsen, Rev. Mod. Phys. 23, 90 (1951).
53. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), pp. 89-90.
54. J. Chang, N. Moiseyev, and R. E. Wyatt, J. Chem. Phys. 84, 4997 (1986).
55. It does not have to be the case that the energy calculated with perturbation theory will be less accurate. Since the perturbation theory is not variational, it is conceivable that with sufficiently optimized dimensional continuation and summation methods the convergence of the energy expansion would be so rapid that it would give a value for the energy that is more accurate than the variational result even for the same basis set.
56. B. N. Parlett, The Symmetric Eigenvalue Problem (Prentice-Hall, Englewood Cliffs, NJ, 1980), p. 119.
57. V. S. Popov, A. V. Sergeev, and A. V. Shcheblykin, Zh. Eksp. Teor. Fiz 102 (1992) [Sov. Phys. JETP 75, 787 (1992)]; V. S. Popov and A. V. Sergeev, Phys. Lett. A 193, 165 (1994).
58. V. S. Popov, A. V. Sergeev, and A. V. Shcheblykin, Zh. Eksp. Teor. Fiz 102 (1992) [Sov. Phys. JETP 75, 787 (1992)]; V. S. Popov and A. V. Sergeev, Phys. Lett. A 193, 165 (1994).
59. V. S. Popov, A. V. Sergeev, and A. V. Shcheblykin, Zh. Eksp. Teor. Fiz 102 (1992) [Sov. Phys. JETP 75, 787 (1992)]; V. S. Popov and A. V. Sergeev, Phys. Lett. A 193, 165 (1994).
60. C. M. Bender and T. T. Wu, Phys. Rev. D 7, 1620 (1973).
61. J. Killingbeck, J. Phys. A 14, 1005 (1981).
62. A. Nauts and R. E. Wyatt, Phys. Rev. A 30, 872 (1984).
63. E. L. Sibert III, J. Chem. Phys. 88, 4378 (1988).
64. J. M. Bowman and B. Gazdy, J. Chem. Phys. 94, 454 (1991).
65. V. M. Vaǐnberg, V. D. Mur. V. S. Popov, and A. V. Sergeev, Pis'ma Zh. Eksp. Teor. Fiz. 44, 9 (1986) [JETP Lett. 44, 9 (1986)].
66. V. M. Vaǐnberg, V. D. Mur. V. S. Popov, and A. V. Sergeev, Pis'ma Zh. Eksp. Teor. Fiz. 44, 9 (1986) [JETP Lett. 44, 9 (1986)].
67. 54J. M. Bowman, J. Chem. Phys. 68, 608 (1978); G. D. Carney, L. I. Sprandel, and C. W. Kern, Adv. Chem. Phys. 37, 305 (1978); R. B. Gerber and M. A. Ratner, ibid. 70, 97 (1988).
68. 54J. M. Bowman, J. Chem. Phys. 68, 608 (1978); G. D. Carney, L. I. Sprandel, and C. W. Kern, Adv. Chem. Phys. 37, 305 (1978); R. B. Gerber and M. A. Ratner, ibid. 70, 97 (1988).
69. 54J. M. Bowman, J. Chem. Phys. 68, 608 (1978); G. D. Carney, L. I. Sprandel, and C. W. Kern, Adv. Chem. Phys. 37, 305 (1978); R. B. Gerber and M. A. Ratner, ibid. 70, 97 (1988).
70. M. Dunn, D. K. Watson, J. R. Walkup, and T. C. Germann, J. Chem. Phys. 104, 9870 (1996).
71. B. T. Sutcliffe, in Current Aspects of Quantum Chemistry 1981, edited by R. Carbó (Elsevier, Amsterdam, 1982), pp. 99-125; S. Carter, N. C. Handy, and B. T. Sutcliffe, Mol. Phys. 49, 745 (1983).
72. B. T. Sutcliffe, in Current Aspects of Quantum Chemistry 1981, edited by R. Carbó (Elsevier, Amsterdam, 1982), pp. 99-125; S. Carter, N. C. Handy, and B. T. Sutcliffe, Mol. Phys. 49, 745 (1983).
73. D. Estes and D. Secrest, Mol. Phys. 59, 569 (1986).
74. N. C. Handy, Mol. Phys. 61, 207 (1987).
75. 59 For a detailed description of the properties of Wigner functions and Clebsch-Gordan coefficients, see D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988), Chaps. 4 and 8.
76. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957), p. 62.
77. T. C. Germann, D. R. Herschbach, and B. M. Boghosian, Comput. Phys. 8, 712 (1994).