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Time correlation function approach to vibrational energy relaxation in liquids: Revised results for monatomic solvents and a comparison with the isolated binary collision model
1.The experimental study and theoretical analysis of liquid phase vibrational energy relaxation (VER) commenced with the ultrasonic absorption studies of Herzfeid, Litovitz, and co-workers. See K. F. Herzfeid and T. A. Litovitz, Absorption and Dispersion of Ultrasonic Waves (Academic, New York, 1959);
1.T. A. Litovitz, J. Acoust. Soc. Am. 26, 469 (1956);
1.W. M. Madigosky and T. A. Litovitz, J. Chem. Phys. 34, 489 (1961).
2.For early laser spectroscopic studies of liquid phase VER see, for example, W. G. Callaway and G. E. Ewing, J. Chem. Phys. 63, 2942 (1975);
2.S. R. J. Brueck and R. M. Osgood, Jr., Chem. Phys. Lett. 39, 568 (1976);
2.N. Legay-Sommaire and F. Legay, Chem. Phys. Lett. 52, 213 (1977); , Chem. Phys. Lett.
2.S. R. J. Brueck and R. M. Osgood, Jr., J. Chem. Phys. 68, 4911 (1978);
2.C. Manzanares and G. E. Ewing, J. Chem. Phys. 69, 1418, 2803 (1978); , J. Chem. Phys.
2.S. F. Brueck, T. F. Deutsch, and R. M. Osgood, Jr., Chem. Phys. Lett. 51, 339 (1977) and 60, 242 (1979);
2.D. W. Chandler and G. E. Ewing, J. Chem. Phys. 73, 4904 (1980).
3.Extensive laser spectroscopic studies of the density and temperature dependence of VER for and its isotopes and are available. See, for example, C. Delalande and G. M. Gale, Chem. Phys. Lett. 50, 339 (1977);
3.G. M. Gale and C. Delalande, Chem. Phys. 34, 205 (1978);
3.M. Chateau, C. Delalande, R. Frey, G. M. Gale, and F. Pradtere, J. Chem. Phys. 71, 4799 (1979);
3.C. Delalande and G. M. Gale, Chem. Phys. Lett. 71, 264 (1980);
3.C. Delalande and G. M. Gale, J. Chem. Phys. 73, 1918 (1980);
3.M. Chatelet, B. Oksengorn, G. Widenlocher, and Ph. Marteau, J. Chem. Phys. 75, 2347 (1981); , J. Chem. Phys.
3.M. Chatelet, J. Kieffer, and B. Oksengorn, Chem. Phys. 79, 413 (1983).
4.For spectroscopic studies of VER of other small molecules, especially and the hydrogen halides, see for example, R. Protz and M. Maier, Chem. Phys. Lett. 64, 27 (1979);
4.B. Faltermeier, R. Protz, and M. Maier, Chem. Phys. Lett. 74, 425 (1980); , Chem. Phys. Lett.
4.B. Faltermeier, R. Protz, and M. Maier, Chem. Phys. 62, 877 (1981);
4.J. Chesnoy and D. Ricard, Chem. Phys. Lett. 73, 433 (1980);
4.J. Chesnoy and D. Ricard, Chem. Phys. 67, 347 (1982);
4.J. Chesnoy and D. Ricard, Chem. Phys. Lett. 91, 130 (1982) and 92, 449 (1982).
5.Extensive studies of VER of small molecules which are particularly illuminating since they involve the comparison of gas phase measurements, liquid phase measurements in rare gas solution, and gas phase collisional calculations have been performed by Simpson and co-workers. For the liquid phase work, see for example, M. R. Buckingham, H. T. Williams, R. S. Pennington, C. J. S. M. Simpson, and M. Matti Maricq, Chem. Phys. 98, 197 (1985);
5.H. T. Williams, M. H. Purvis, and C. J. S. M. Simpson, Chem. Phys. 115, 7 (1987); , Chem. Phys.
5.H. T. Williams, S. V. Gwynn, and C. J. S. M. Simpson, Chem. Phys. 136, 95 (1987); , Chem. Phys.
5.H. T. Williams, M. H. Purvis, M. R. Buckingham, and C. J. S. M. Simpson, Chem. Phys. 119, 171 (1988).
6.There is considerable theoretical literature which consists of critiques of the isolated binary collision (IBC) model and attempts to justify its assumptions. See, for example, M. Fixman, J. Chem. Phys. 34, 369 (1961);
6.R. Zwanzig, J. Chem. Phys. 34, 1931 (1961); , J. Chem. Phys.
6.K. F. Herzfeid, J. Chem. Phys. 36, 3305 (1962);
6.H. K. Shin and J. Keizer, Chem. Phys. Lett. 27, 611 (1974);
6.S. Velsko and D. W. Oxtoby, J. Chem. Phys. 72, 2260 (1980);
6.P. S. Dardi and R. I. Cukier, J. Chem. Phys. 86, 2264, 6893 (1987) and 89, 459, 4145 (1988)., J. Chem. Phys.
7.P. K. Davis and I. Oppenheim, J. Chem. Phys. 57, 505 (1972).
8.G. Delalande and G. M. Gale, J. Chem. Phys. 71, 4804 (1979).
9.For extensions of the IBC model to include the effects of soft cores and anisotropic forces see J. Chesnoy, Chem. Phys. 83, 283 (1984);
9.P. A. Madden and F. Van Swol, Chem. Phys. 112, 43 (1987).
10.A comprehensive review of IBC theory and its applications is given by J. Chesnoy and G. M. Gale, Ann. Phys. Fr. 9, 893 (1984).
11.For other reviews of liquid phase VER see, for example, D. W. Oxtoby, Adv. Chem. Phys. 47, 487 (1981);
11.D. W. Oxtoby, Ann. Rev. Phys. Chem. 32, 77, 101 (1981);
11.C. B. Harris, D. E. Smith, and D. J. Russell, Chem. Rev. 90, 481 (1990).
12.(a) S. A. Adelman and R. H. Stote, J. Chem. Phys. 88, 4397 (1988);
12.(b) R. H. Stote and S. A. Adelman, J. Chem. Phys. 88, 4415 (1988). Reference 12(b) requires three corrections, (i) The values of the solute liquid phase frequencies quoted in Ref. 12(b) differ significantly from the gas phase frequencies. This is an error. The correct values of the frequencies, which are given in this paper, were however used in the computations of Ref. 12(b). (ii) It was implied [see Figs. 3 and 5 of Ref. 12(b)] that the density dependence of VER rates arises from the density dependence of the normalized frequency spectrum while in fact it arises mainly from the density dependence of (iii) It was stated that certain approximations of Ref. 12(a) amounted to neglect of vibrational dephasing contributions. A more accurate statement is that the approximations amount to a neglect of the effects of solvent fluctuations on VER., J. Chem. Phys.
13.For a rigorous development of our theory of liquid phase chemical reaction dynamics see S. A. Adelman, Adv. Chem. Phys. 53, 61 (1983).
14.For a detailed review of the physical concepts of our theory see S. A. Adelman, Rev. Chem. Intermed. 8, 321 (1987).
14.For other reviews see S. A. Adelman, J. Stat. Phys. 42, 37 (1986);
14.S. A. Adelman, J. Mol. Liquids 39, 265 (1988);
14.F. Patron and S. A. Adelman, Chem. Phys. 152, 121 (1991).
15.For applications to molecular iodine photolysis see C. L. Brooks III, M. W. Balk, and S. A. Adelman, J. Chem. Phys. 79, 784 (1983)
15.and M. W. Balk, C. L. Brooks III, and S. A. Adelman, J. Chem. Phys. 79, 804 (1983)., J. Chem. Phys.
16.For applications to activated barrier crossing and superionic conduction see M. Olson and S. A. Adelman, J. Chem. Phys. 83, 1865 (1985).
17.For extension to molecular solvents see S. A. Adelman and M. W. Balk, J. Chem. Phys. 82, 4641 (1985) and 84, 1752 (1986).
18.The partial champing theory which is the basis of the work in this paper is developed for monatomic solvents in S. A. Adelman, J. Chem. Phys. 81, 2776 (1984).
18.The theory is refined and extended to molecular solvents in S. A. Adelman, Int. J. Quantum Chem. Symp. 21, 199 (1987).
19.For an application of our theory to the rate constant for liquid phase activated barrier crossing see S. A. Adelman and R. Muralidhar, J. Chem. Phys. (in press).
20.H. Metiu, D. W. Oxtoby, and K. F. Freed, Phys. Rev. A 15, 361 (1977). Also see Eq. (5.7) of the first of Ref. 11.
21.S. A. Adelman, R. H. Stote, and R. Muralidhar, Theory of Vibrational Energy Relaxation in Liquids: Construction of the Equation of Motion for Solute Vibrational Dynamics in Molecular Solvents, Translational-Rotational Energy Transfer (in preparation).
22.The exact result is On physical grounds one expects (see Ref. 13) hence Eq. (2.16).
23.M. J. Gillan, Mol. Phys. 38, 1781 (1979).
24.M. Balk, Mol. Phys. 46, 577 (1982).
25.We use the IMSL 10 double precision subroutines DBSNAK, DBSINT, and DBSCPP. These subroutines are documented in the IMSL Math Library User’s Manual, IMSL Corporation, Houston 1989.
26.To avoid spurious contributions to the integrals from small solute-solvent internuclear separations the pair correlation functions are set to zero for all where
27.As discussed in Refs. 12 may be decomposed into the components etc.
28.J. J. Andrew, A. P. Harriss, D. C. McDermott, H. T. Williams, P. A. Madden, and C. J. S. M. Simpson, The Breakdown of the Isolated Binary Collision Hypothesis for Near Resonant V Vprocesses in Liquid Argon, Chem. Phys. (to be published).
29.J. Chesnoy and J. J. Weis, J. Chem. Phys. 84, 5378 (1986).
30.G. C. Maitland, M. Rigby, E. B. Smith, and W. A. Wakeham, Intermolecular Forces Their Determination and Origin (Clarendon, Oxford, 1981).
31.J. E. Straub, M. Borkovec, and B. J. Berne, J. Chem. Phys. 89, 4833 (1988).
32.J. D. Kelley and M. Wolfsberg, J. Chem. Phys. 44, 324 (1966).
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