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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).
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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).
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FORTRAN 5 (CDC)
Lines of Code: 4287
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