|
460. FALLOFF: Calculation of Fall-Off Curves for
Unimolecular and Termolecula Reactions
by Robert G. Gilbert, Department of Theroretical Chemistry, University of Sydney, N.S.W. 2006, Australia This FORTRAN 5 program package calculates rate coefficients for unimolecular reactions in the fall- off, high pressure and low pressure regimes. The input required consists of RRKM parameters (frequencies of reactant molecule and of activated complex, and the critical energy for reaction, EO) and average (downward) collisional energy transfer. It may be used to fit experimental rate data in the fall-off regime (taking proper account of weak collisional effects) or to generate rate coefficients at any pressure and temperature from a set of RRKM and collisional energy transfer parameters. This enables one to fit or predict rate data in the fall-off or low pressure regime without recourse to the strong collision approximation (which is often used as an additional approximation in RRKM calculations); it is well known (see, e.g., Ref. 1.) that the strong collision approximation can give rise to large errors in data interpretation and prediction. A particular use is the fitting of fall-off data to enable one to obtain high pressure rate parameters (activation energy and frequency factor). Termolecular rate coefficients can be calculated from the unimolecular coefficients for the reverse reaction using microscopic reversibility. The program is written to run on a CDC installation. However, no difficulty has been experienced in transfer to other machines (although double precision may be required on IBM computers) except for slight changes in FORMAT and PROGRAM statements. The RRKM calculation is carried out using a conventional direct count method. The fall-off and low pressure rate coefficients are computed from a solution of the master equation. If the program is to be used to generate rate coefficients at any required pressure and temperature, with a given bath gas, using tabulated RRKM parameters, the requisite value of the remaining parameter (the downward energy transfer, < Edown >) can be estimated from tabulated values for analogous collision partners in, for example, Ref. 4. If the program is to be used to fit fall-off data to obtain RRKM parameters and the downward energy transfer (and hence high pressure rate parameters), one first estimates the frequencies of the reactant molecule and of the activated complex, and the critical energy, using the techniques of Ref. 5, and estimates < Edown > using Ref. 4, and then refines the initial values of (i) the critical energy, (ii) of the lowest few frequencies of the activated complex, and (iii) of < Edown > to bring about agreement with the experimental data. It has been shown (Ref. 1) that this procedure gives reliable results. Note that one must distinguish here between the overall energy transfer and the downward energy transfer in this context (Ref. 6). __________ References: 1. R. G. Gilbert, K. Luther and J. Troe, Ber. Bunsenges. Phys. Chem., 87, 169-177 (1983). 2. R. G. Gilbert and K. D. King, Chem. Phys., 49, 367 (1980). 3. B. J. Gaynor, R. G. Gilbert and K. D. King, Chem. Phys. Letters, 55, 40 (1978). 4. General Reviews of the Master Equation in Unimolecular Reactions: D. C. Tardy and B. S. Rabinowitch, Chem. Rev., 77, 369 (1977); M. Quack and J. Throe, Gas Kinetics and Energy Transfer, Volume 2, eds. P. G. Ashmore and R. J. Donovan (London: The Chemical Society, 1977), p. 175. 5. S. W. Benson, Thermochemical Kinetics, Second Edition (New York: John Wiley & Sons, 1976). 6. R. G. Gilbert, Chem. Phys. Letters, 96, 259 (1983). 7. P. J. Robinson and K. A. Holbrook, Unimolecular Reactions (London: John Wiley & Sons, 1972). _________ FORTRAN 5 (CDC) Lines of Code: 4287 |