Estimation of vibrational frequencies and vibrational densities of states in isotopically substituted nonlinear triatomic molecules

Journal of Physical Chemistry A

Volumn 105, Issue 23, 2001, Pages 5586-5589

  Hathorn, B C ^a   Marcus, R A ^b  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FREQUENCIES; ISOTOPES; MATRIX ALGEBRA; PERTURBATION TECHNIQUES;

VIBRATIONAL DENSITIES;

MOLECULAR DYNAMICS;

EID: 0035859408     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp003849a     Document Type: Article

References (27)

1. Hathorn, B. C.; Marcus, R. A. J. Chem. Phys. 1999, 111, 4087.
2. (b) Hathorn B. C.; Marcus, R. A. J. Chem. Phys. 2000, 113, 9497.
3. Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific Publications: Boston, 1990 and references therein.
4. Whitten, L. Z.; Rabinovitch, B. S. J. Chem. Phys. 1963, 38, 3462.
5. Whitten, L. Z.; Rabinovitch, B. S. J. Chem. Phys. 1964, 41, 1883.
6. Baer, T.; Hase, W. Unimolecular Reaction Dynamics: Theory and Experiments; Oxford University Press: New York, 1996 and references therein.
7. Holbrook, K. A.; Pilling, M. J.; Robertson, S. H. Unimolecular Reactions; Wiley: New York, 1996 and references cited therein.
8. Teller, E., as quoted in Angus, W. R.; Bailey, C. R.; Hale, J. B.; Ingold, C. K.; Leckie, A. H.; Raisin, C. G.; Thompson, J. W.; Wilson, C. L. J. Chem. Soc. 1936, 971.
9. Redlich, O. Z. Physik. Chem. B. 1935, 28, 371. It is described in ref 11 below, p 183ff.
10. (a) For example, Hedberg, L.; Mills, I. M. J. Mol. Spectrosc. 1993, 160, 117 for ASYM 20;
11. Hedberg, L.; Mills, I. M. J. Mol. Spectrosc. 2000, 203, 82 for ASYM 40.
12. (b) Mills, I. M. private communication.
13. (a) Califano, S. Vibrational States; John Wiley: New York, 1976.
14. (b) Califano, S. Vibrational States; ibid; p 214.
15. (c) Califano, S. Vibrational States; ibid; p 216.
16. (d) Califano, S. Vibrational States; ibid; pp 222-3.
17. (e) Califano, S. Vibrational States; ibid; p 243.
18. (f) Califano, S. Vibrational States; ibid p 242.
19. 33 from the expression for the secular determinant.
20. Steinfeld, J. I.; Alder-Golden, S. M.; J. W. Gallagher, J. W. J. Phys. Chem. Ref. Data. 1987, 16, 911.
21. Ivanov, S. V.; Panchenko, V. Y. Phys.-Uspekhi, 1994, 37, 667.
22. Flaud, J.; Bacis, R. Spectrochim. Acta A 1998, 54, 3 and references therein.
23. (a) Wu, T.-Y. Vibrational Spectra and Structure of Polyatomic Molecules, National University of Peking: Kun-ming, China, 1939; revised edition: J. W. Edwards, Ann Arbor, 1946. (b) p 163, eqs 29-30 in Chapter V. 1B of 1939 edition.
24. (a) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1955; Dover Publications: New York 1980, (b) pp. 64-65.
25. For first-order perturbation theory, we use the result in eq 35, p 190 of ref 11 with a cyclic permutation. For the second-order expression, we use the rarely cited result of Edgell, W. F., J. Chem. Phys. 1945, 13, 539,
26. but introducing the type of manipulation which led from eq 32 in ref 11, p 190 to eq 35 there. Explicit second-order expressions for the G-matrix are rare in the literature and are not given, for example, in Wilson et al.'s ref 11, Califano's ref 8, or in Herzberg, G. Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand: New York, 1945.
27. A discussion is given in Marcus, R. A. J. Phys. Chem. A 2001, 105, 2612.