APPEARANCE POTENTIALS AND MASSSPECTRA OF FLUORINATED ETHYLENES
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Appearance Potentials and Mass Spectra of Fluorinated Ethylenes. 111. Calculations Based on the Statistical Theory of Mass Spectral
by Chava Lifshitz and F. A. Long Departmmt of Chemistry, Corn& UniversUy, Ithaca, New York (Received April 7, 1986)
Calculations based upon the statistical theory of mass spectra have been carried out for three parallel primary reactions in the spectrum of difluoroethylene. Theoretical expressions derived by Marcus are utilized for computation of the unimolecular rate constants for the processes at near threshold energies. These are compared with the reciprocal of the parent ion residence time in the ion source of the mass spectrometer. The dependence of relative rates of the three processes upon the internal energy of the active molecule ion is also computed. The much faster increase with energy of the rate constant for a reaction possessing a “loose” activated complex relative to that for one which has a “rigid” complex is demonstrated. It is further shown that for a high activation energy process to compete effectively enough with a low activation energy one to be detected in the mass spectrometer, it is not enough for the rate constant of the former to be comparable to the reciprocal of the residence time; rather, it has to be a certain fraction of the rate constant of the faster process. I n all of these calculations exact sums of states were computed for the activated complexes, while the approximation formula due to Whitten and Rabinovitch was used for the active molecule. For some processes, qualitative agreement between theory and experiment can be obtained by plausible assignment of molecular parameters. I n other cases there are various difficulties, in particular for the relative yields of carbonfluorine and carbon-hydrogen bond breakages.
Introduction The statistical theory of mass spectra assumes that the mass spectrum of a polyatomic molecule is due to parallel and successive unimolecular decompositions of vibrationally excited ions. It was first developed by Rosenstock, et aL12and has been used to compare computed and experimental mass spectra of hydrocarbons, in particular those of propane and b ~ t a n e . One ~ of the reasonsforundertakinga study of the mass spectra of fluorocarbons416was that these compounds permit different sorts of comparisons to be made with the theory. I n this paper attention is focused on the application of theory to the spectra of fluorinated ethylenes. The major ion yields in the spectra of the fluorinated ethylenes result from primary decomposition processes of the parent molecule ion. The processes have quite differing energy requirements ; some involve simple bond breakages while others are rearrangement proc-
esses or four-centered reactions. In spite of these differences, the ion yields are roughly comparable. It is .thus of interest to see whether calculat,ions from theory can reproduce the relative rates of these competing processes as a function of the internal excitation energy of the parent molecule ion. Such calculations are similar in character to those suggested by Wolfsberge; however, results will be presented up to higher excitation energies. The Computing Procedure. The formulas developed (1) Work supported by the Advanced Research Projects Agency through the Materials Science Center. (2) H. M. Rosenstock, M. B. Wallenstein, A. L. Wahrhaftig, and H. Eyring, Proc. Nail. Acad. Sci. U.S., 38, 667 (1952). (3) M. Vestal, A. L. Wahraftig, and W. H. Johnston, Aeronautical Research Laboratories, Report ARL 62-426, Sept. 1962. (4) C. Lifshita and F. A. Long, J. Phys. Chem., 67, 2463 (1963). (6) C.Lifshita and F. A. Long, ibid., 69,3731 (1965). (6) M.Wolfsberg, J. Chem. Phys., 36, 1072 (1962).
Volunts 69, Number 12 November 1066
CHAVALIFSHITZAND F. A. LONG
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in the unimolecular reaction rate theory of Marcus' were used for computing reaction rates for decomposition reactions of the polyatomic molecule ion. The general expression for the rate constant for reaction of an excited molecule is8
(1) where E, is the activation energy, E is the internal energy of active molecule, E+ is the internal energy of activated complex, such that E = E, E+, P(E,) is the number of vibrational states of an activated complex whose nonfixed vibrational energy is E,, N*(E) is the number of quantum states per unit energy of active molecule, r is the number of active internal rotations in activated complex, and I d is the moment of inertia of ith rotation. A Fortran program was set up for the CDC 1604 computer to obtain P(E,) by exact summation a t
+
Ev6E'
low energies. This is virtually the same procedure as that of Whitten and R a b i n o ~ i t c hLe., , ~ counting all lattice points in an energy phase space for vibrational energy levels (assumed harmonic). It has been shown recently that anharmonicities play only a minor role in changing the sum of states for molecules of the size that we are dealing with.1° We have verified this for even smaller molecules, specifically methane and acetylene for which anharmonicity constants are .known and the summations may thus be carried out rigorously. In particular, for methane even a t 4.5 e.v. internal energy, the number of states considering anharmonicity is only twice as large as the number obtained when assuming harmonic vibrations." At high nonfixed energies and, in particular, in the case of the active molecule, the approximation for P(E,) due to Whitten and Rabinovitchg was used. Ev
