Abstract
The subject of unimolecular dynamics deals with the intermolecular and intramolecular microscopic details of unimolecular reactions. Theories of unimolecular dynamics are concerned with molecular motion over potential energy surfaces and the behavior of molecular coordinates as a function of time. Most studies of unimolecular reactions have involved measurements and predictions of the rate at which an energized molecule will undergo a uni-molecular reaction. The basic postulate of all unimolecular theories is the rapidity of intramolecular vibrational energy relaxation. Experimentalists were awarded a rare opportunity to test two conflicting assumptions regarding this postulate by the simultaneous advent of the Slater(1) and Rice-Ramsperger-Kassel-Marcus (RRKM)(2) theories in the 1950s. Slater’s theory, which is dynamical, pictures a molecule as an assembly of harmonic oscillators. Within this framework vibrational energy relaxation between the normal modes is forbidden, and reaction occurs only when some coordinate, the reaction coordinate, reaches a critical extension by superposition of the various normal modes. In contrast, the RRKM theory, which is an extension by R. A. Marcus of the statistical theory developed by O. K. Rice, H. C. Ramsperger, and L. S. Kassel, assumes rapid relaxation of vibrational energy. The experimental tests overwhelmingly endorsed the RRKM theory, and the controversy involving intramolecular vibrational energy relaxation was seemingly laid to rest. It also appeared as though dynamical treatments of unimolecular reactions were unnecessary.
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References
N. B. Slater, Theory of Unimolecular Reactions, Cornell University Press, Ithaca, N.Y. (1959).
R. A. Marcus, Unimolecular dissociations and free radical recombination reactions, J. Chem. Phys 20, 359–364 (1952).
J. M. Parson and Y. T. Lee, Crossed molecular beam study of F + C2H4, C2D4, J. Chem. Phys 56, 4658–4666 (1972).
J. M. Parson, K. Shobatake, Y. T. Lee, and S. A. Rice, Unimolecular decomposition of the long-lived complex formed in the reaction F + C4H8, J. Chem. Phys 59, 1402–1415 (1973).
K. Shobatake, J. M. Parson, Y. T. Lee, and S. A. Rice, Unimolecular decomposition of long-lived complexes of fluorine and substituted mono-elfins, cyclic olefins, and dienes. J. Chem. Phys 59, 1416–1426 (1973).
K. Shobatake, J. M. Parson, Y. T. Lee, and S. A. Rice, Laboratory angular dependence and the recoil-energy spectrum of the products of the reaction F+C6D6→D+C6D5F, J. Chem. Phys 59, 1427–1434 (1973).
K. Shobatake, Y. T. Lee, and S. A. Rice, Reactions of F atoms and aromatic and heterocyclic molecules: Energy distribution in the reaction complex, J. Chem. Phys 59, 1435–1448 (1973).
K. Shobatake, Y. T. Lee, and S. A. Rice, Crossed molecular beams study of the reaction F+(C2H2Cl2)→Cl+(C2H2CIF), J. Chem. Phys 59, 6104–6111 (1973).
J. M. Parson, K. Shobatake, Y. T. Lee, and S. A. Rice, Substitution reactions of fluorine atoms with unsaturated hydrocarbons: Crossed molecular beam studies of unimolecular decomposition, Discuss. Faraday Soc 55, 344–356 (1973).
P. N. Clough, J. C. Polanyi, and R. T. Taguchi, Vibrational energy distribution in HF formed by elimination from activated CH3CF3 and CH2CF2, Can. J. Chem 48, 2919–2930 (1970).
H. W. Chang, D. W. Setser, and M. J. Perona, Comparison of energy partitioning from three-centered processes. Bimolecular transfer and unimolecular elimination reactions, J. Phys. Chem 75, 2070–2072 (1971).
J. G. Moehlmann and J. D. McDonald, Vibrational energy distribution of chemically activated cycloactanone, J. Chem. Phys 59, 6683–6684 (1973).
J. G. Moehlmann, J. T. Gleaves, J. W. Hudgens, and J. D. McDonald, Infrared chemiluminescence studies of the reaction of fluorine atoms with monosubstituted ethylene compounds, J. Chem. Phys 60, 4790–4799 (1974).
J. T. Gleaves and J. D. McDonald, Infrared chemiluninescence studies of hydrogen halide elimination reactions, J. Chem. Phys 62, 1582–1583 (1975).
D. L. Bunker and W. L. Hase, On non-RRKM unimolecular kinetics: Molecules in general, and CH3NC in particular, J. Chem. Phys 59, 4621–4632 (1973).
J. D. Rynbrandt and B. S. Rabinovitch, Intramolecular energy relaxation. Nonrandom decomposition of hexafluorobicyclopropyl, J. Phys. Chem 75, 2164–2171 (1971).
J. F. Meagher, K. J. Chao, J. R. Barker, and B. S. Rabinovitch, Intramolecular vibrational energy relaxation. Decomposition of a series of chemically activated fluoralkyl cyclopropanes, J. Phys. Chem 78, 2535–2543 (1974).
R. A. Marcus, Dissociation and isomerization of vibrationally excited species. III, J. Chem. Phys 43, 2658–2661 (1965).
D. L. Bunker and M. Pattengill, Monte Carlo calculations. VI. A re-evaluation of the RRKM theory of unimolecular reaction rates, J. Chem. Phys 48, 772–776 (1968).
E. V. Waage and B. S. Rabinovitch, Centrifugal effects in reaction rate theory, Chem. Rev 70, 377–387 (1970).
D. L. Bunker, RRKM theory, the CH3NC paradox, and the decomposition of hot-atom substitution products, J. Chem. Phys 57, 332–335 (1972).
D. L. Bunker, Theory of Elementary Gas Reaction Rates, Pergamon Press, Inc., Elmsford, N.Y. (1966).
K. J. Laidler, Theories of Chemical Reaction Rates, McGraw-Hill Book Company, New York (1969).
D. W. Setser, in: MTP International Review of Sciences, Physical Chemistry (J. Polanyi, ed.), Vol. 9, pp. 1–43, University Park Press, Baltimore (1972).
P. J. Robinson and K. A. Holbrook, Unimolecular Reactions, John Wiley and Sons, Inc. ( Interscience Division ), New York (1972).
W. Forst, Theory of Unimolecular Reactions, Academic Press, Inc., New York (1973).
S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes, McGraw-Hill Book Company, New York (1941).
W. Forst, Methods for calculating energy level densities, Chem. Rev 71, 339–356 (1971).
D. C. Tardy, B. S. Rabinovitch, and G. Z. Whitten, Vibration-rotation energy-level density calculations, J. Chem. Phys 48, 1427–1429 (1968).
W. L. Hase, Theoretical configuration for ethane decorposition and methyl radical recombination, J. Chem. Phys 57, 730–733 (1972).
W. H. Wong and R. A. Marcus, Concept of minimum state density in the activated complex theory of bimolecular reactions, J. Chem. Phys 55, 5625–5629 (1971).
H. S. Johnston, Gas Phase Reaction Rate Theory, The Ronald Press Company, New York (1966).
M. Quack and J. Troe, Specific rate constants of unimolecular processes. II. Adiabatic channel model, Ber. Bunsenges. Phys. Chem 78, 240–252 (1974).
R. C. Baetzold and D. J. Wilson, Classical unimolecular rate theory. II. Effect of the distribution of initial conditions, J. Phys. Chem 68, 3141–3145 (1964).
E. V. Waage and B. S. Rabinovitch, Simple and accurate approximation for the centrifugal factor in RRKM theory, J. Chem. Phys 52, 5581–5584 (1970).
H. S. Johnston and P. Goldfinger, Theoretical interpretation of reactions occuring in photoclorination, J. Chem. Phys 37, 700–709 (1962).
K. J. Mintz and R. J. Cvetanovic, Arrhenius A factors of unimolecular decomposition of alcohols formed by insertion of O(D2) atoms into the C-H bonds of paraffins, Can. J. Chem 51, 3386–3393 (1973).
W. L. Hase, R. L. Johnson, and J. W. Simons, The decomposition of chemically activated n-butane, isopentane, neohexane, and n-pentane and the correlation of their decomposition rates with radical recombination rates, Int. J. Chem. Kinet 4, 1–35 (1972).
F. B. Growcock, W. L. Hase, and J. W. Simons, Kinetics of chemically activated ethane, Int. J. Chem. Kinet 5, 77–92 (1973).
W. L. Hase, C. J. Mazac, and J. W. Simons, Decomposition kinetics of chemically activated dimethylsilane and ethylsilane, J. Am. Chem. Soc 95, 3454–3459 (1973).
H. O. Pritchard, R. G. Sowden, and A. F. Trotman-Dickenson, Studies in energy transfer. II. The isomerization of cyclopropane—A quasi-unimolecular reaction, Proc. R. Soc. London Ser. A 217, 563–571 (1953).
T. S. Chambers and G. B. Kistiakowsky, Kinetics of the thermal isomerization of cyclopropane, J. Am. Chem. Soc. 56, 399–405 (1934)
M. C. Lin and K. J. Laidler, Fall-off behavior and kinetic isotope-effects in reactions of cyclic hydrocarbons, Trans. Faraday Soc 64, 927–944 (1968).
P. Jeffers, D. Lewis, and M. Sarr, Cyclopropane structural isomerization in shock waves, J. Phys. Chem 77, 3037–3041 (1973).
F. W. Schneider and B. S. Rabinovitch, The thermal unimolecular isomerization of methyl isocyanide. Fall-off behavior, J. Am. Chem. Soc 84, 4215–4230 (1962).
F. W. Schneider and B. S. Rabinovitch, The unimolecular isomerization of methyl-d3 isocyanide. Statistical-weight inverse secondary intermolecular kinetic isotope effects in nonequilibrium thermal systems, J. Am. Chem. Soc 85, 2365–2370 (1963).
B. S. Rabinovitch, P. W. Gilderson, and F. W. Schneider, The thermal unimolecular isomerization of methyl-d1 isocyanide. Fall-off and inverse isotope effect, J. Am. Chem. Soc 87, 158–160 (1965).
K. M. Maloney and B. S. Rabinovitch, The thermal isomerization of isocyanide. Variation of molecular parameters, Ethyl isocyanide, J. Phys. Chem. 73, 1652–1666 (1969).
K. M. Maloney, S. P. Pavlou, and B. S. Rabinovitch, Kinetic isotope effects in nonequilibrium thermal unimolecular systems. Ethyl isocyanide-d5, J. Phys. Chem 73, 2756–2760 (1969).
J. V. Michael and G. N. Suess, Application of RRKM theory to the chemical and thermal activation of ethyl radicals, J. Chem. Phys 58, 2807–2812 (1973).
K. J. Laidler and J. C. Polanyi, Theories of the kinetics of bimolecular reactions, in: Progress in Reaction Kinetics (G. Porter, ed.), Vol. 3, pp. 1–61, Pergamon Press, Inc., Elmsford, N.Y. (1965).
E. Tschuikow-Roux, Critical bond length in radical combination and unimolecular dissociation reactions, J. Phys. Chem 72, 1009–1011 (1968).
C. W. Larson and B. S. Rabinovitch, Competitive unimolecular decomposition of alkyl radicals. Tertiary butyl rupture, J. Chem. Phys 52, 5181–5183 (1970).
K. Dees, D. W. Setser, and W. G. Clark, The reactions of methylene with 1,2-dichloroethane and nonequilibrium unimolecular HCI elimination from 1,3-dichloropropane, 1,4dichlorobutane, and 1-chloropropane, J. Phys. Chem 75, 2231–2240 (1971).
K. C. Kim and D. W. Setser, Unimolecular reactions and energy partitioning. Three-and four-centered elimination reactions of chemically activated 1,1,2-trichloroethane-do-d1 and d2, J. Phys. Chem 78, 2166–2179 (1974).
F. S. Rowland, in: MTPlnternational Review of Sciences, Physical Chemistry (J. Polanyi, ed.), Vol. 9, pp. 109–133, University Park Press, Baltimore (1972).
K. A. Krohn, N. J. Parks, and J. W. Root, Chemistry of nuclear recoil 18F atoms. VI. Approximate energetics and molecular dynamics in CH3CF3, J. Chem. Phys 55, 5785–5794 (1971).
C. C. Chou and W. L. Hase, Rice—Ramsperger—Kassel—Marcus theory applied to decomposition of hot atom substitution products. c-C4H7T and c-C4D7T, J. Phys. Chem 78, 2309–2315 (1974).
J. N. Butler and G. B. Kistiakowsky, Reactions of methylene. IV. Propylene and cyclopropane, J. Am. Chem. Soc 82, 759–765 (1960).
A. F. Trotman-Dickenson, Gas Kinetics, Butterworths, London (1955).
S. C. Chan, B. S. Rabinovitch, J. T. Bryant, L. D. Spicer, T. Fujimoto, Y. N. Lin, and S. P. Pavlou, Energy transfer in thermal methyl isocyanide isomerization. A comprehensive investigation, J. Phys. Chem 74, 3160–3176 (1970).
W. G. Valance and E. W. Schlag, Nonequilibrium effects in unimolecular reaction theory, J. Chem. Phys 45, 4280–4288 (1966).
V. J. Troe and H. G. Wagner, Unimolecular reactions in thermal systems, Ber. Bunsenges. Phys. Chem 71, 937–979 (1967).
D. C. Tardy and B. S. Rabinovitch, Collisional energy transfer in thermal unimolecular systems. Dilution effects and fall-off region, J. Chem. Phys 48, 1282–1301 (1968).
S. P. Pavlou and B. S. Rabinovitch, Energy transfer in thermal isocyanide isomerization. Noble gases in the ethyl isocyanide system, J. Phys. Chem 75, 1366–1374 (1971).
M. Hoare, Steady state unimolecular processes in multilevel systems, J. Chem. Phys 38, 1630–1635 (1963).
H. W. Chang, N. L. Craig, and D. W. Setser, Nonequilibrium unimolecular reactions and collisional deactivation of chemically activated fluoroethane and 1,1,1-trifluoroethane, J. Phys. Chem 76, 954–963 (1972).
J. D. Rynbrandt and B. S. Rabinovitch, Collisional transition probability distributions for deactivation of vibrationally excited dimethylcyclopropane, J. Phys. Chem 74, 1679–1685 (1970).
J. H. Georgakakos and B. S. Rabinovitch, Collision transfer of vibrational energy from highly excited polyatomics. Transfer probabilities and cross sections for inefficient bath gases, J. Chem. Phys 56, 5921–5930 (1972).
D. W. Setser and E. E. Siefert, Vibrational energy transfer probabilities of highly vibration-ally excited dichloroethane with argon, krypton, xenon, and sulfur hexafluoride, J. Chem. Phys 57, 3623–3628 (1972).
Von S. H. Luu and J. Troe, Photoisomerization of cycloheptatriene, II. Temperature dependence of collisional energy transfer, Ber. Bunsenges. Phys. Chem 78, 766–773 (1974).
Y. N. Lin and B. S. Rabinovitch, A simple quasi-accommodation model of vibrational energy transfer. Low pressure thermal methyl isocyanide isomerization, J. Phys. Chem 74, 3151–3159 (1970).
M. L. Dutton, D. L. Bunker, and H. H. Harris, Two familiar gas reactions at suprahigh pressure, J. Phys. Chem 76, 2614–2617 (1972).
J. Aspen, N. A. Khawaja, J. Reardon, and D. J. Wilson, Pyrolysis of ethylcyclobutane in the gas phase at high pressures, J. Am. Chem. Soc 91, 7580–7582 (1969).
R. E. Harrington, B. S. Rabinovitch, and H. M. Frey, Decomposition of activated sec-butyl radicals from different sources and unimolecular reaction theory, J. Chem. Phys 33, 1271–1272(1960).
I. Oref, D. Schuetzle, and B. S. Rabinovitch, Unimolecular decomposition and intramolecular energy relaxation in the suprahigh-pressure region, J. Chem. Phys 54, 575–578 (1971).
E. Thiele and D. J. Wilson, Anharmonicity in unimolecular reactions, J. Chem. Phys 35, 1256–1263 (1961).
R. J. Harter, E. B. Alterman, and D. J. Wilson, Anharmonic effects in unimolecular rate theory. Vibrations and collisions of simple polyatomic systems, J. Chem. Phys 40, 2137–2145 (1964).
N. C. Hung and D. J. Wilson, Anharmonic effects in unimolecular rate theory. Dynamics of a rotating anharmonic triatomic molecule, J. Chem. Phys 38, 828–831 (1963).
N. C. Hung, Rotational-vibrational energy transfer. Dynamics of a rotating anharmonic four-atom molecule, J. Chem. Phys 57, 5202–5215 (1972).
R. C. Baetzold and D. J. Wilson, Classical unimolecular rate theory. III. Effect of initial conditions on lifetime-distributions, J. Chem. Phys 43, 4299–4303 (1965).
D. L. Bunker, Monte Carlo calculations. IV. Further studies of unimolecular decomposition, J. Chem. Phys 40, 1946–1957 (1964).
H. H. Harris and D. L. Bunker, Methyl isocyanide is probably a non-RRKM molecule, Chem. Phys. Lett 11, 433–436 (1971).
D. H. Loskiw, C. F. Bender, and H. F. Schaefer III, Some features of the CH3NC→CH3CN potential surface, J. Chem. Phys 57, 4509–4511 (1972).
W. L. Hase and Da-Fei Feng, Classical trajectory study of the unimolecular decomposition of H-C=C-Cl, H-C=C-H and Cl-C-C-Cl, J. Chem. Phys 61, 4690–4699 (1974).
K. Evans, R. Scheps, S. A. Rice, and D. Heller, Primary photochemical and photophysical processes in chloro-and bromoacetylene, Chem. Soc. Faraday Trans 269, 856–880 (1973).
C. E. Klots, Quasi-equilibrium theory of ionic fragmentation: Further considerations, Z. Naturforsch. Teil A 27, 553–561 (1972).
S. A. Safron, N. D. Weinstein, D. R. Herschbach, and J. C. Tully, Transition state theory for collision complexes: Product translational energy distributions, Chem. Phys. Lett 12, 564–568 (1972).
R. A. Marcus, On the theory of energy distributions of products of molecular beam reactions involving transient complexes, J. Chem. Phys 62, 1372–1384 (1975).
E. L. Spotz, W. A. Seitz, and J. L. Franklin, Translational energy of fragments of ion decomposition and totality of states functions, J. Chem. Phys 51, 5142–5148 (1969).
K. C. Kim, J. H. Beynon, and R. G. Cooks, Energy partitioning by mass spectrometry: chloroalkanes and chloroalkenes, J. Chem. Phys 61, 1305–1314 (1974).
E. Fermi, J. Pasta, and S. Ulam, Studies of non linear problems, in: Enrico Fermi: Collected Papers, Vol. II, pp. 978–988, University of Chicago Press, Chicago (1965).
G. H. Walker and J. Ford, Amplitude instability and ergodic behavior for conservative nonlinear oscillator systems, Phys. Rev. A 188, 416–432 (1969).
B. Barbanis, On the isolating character of the third integral in a resonance case, Astron. J 71, 415–424 (1966).
M. Henon and C. Heiles, The applicability of the third integral of motion: Some numerical experiments, Astron. J 69, 73–79 (1964).
K. C. Mo, Theoretical prediction for the onset of widespread instability in conservative nonlinear oscillator systems, Physica 57, 445–454 (1972).
K. S. J. Nordholm and S. A. Rice, Quantum ergodicity and vibrational relaxation in isolated molecules, J. Chem. Phys 61, 203–223 (1974).
S. Nordholm and S. A. Rice, Quantum ergodicity and vibrational relaxation in isolated molecules. II.,l-Independent effects and relaxation to the asymptotic limit, J. Chem. Phys 61, 768–779 (1974).
J. W. Brauner and D. J. Wilson, Intramolecular energy transfer in unimolecular reactions. II. A weakly-coupled-oscillators model, J. Phys. Chem 67, 1134–1138 (1963).
W. M. Gelbart, S. A. Rice, and K. F. Freed, Stochastic theory of vibrational relaxation and dissociation, J. Chem. Phys 52, 5718–5732 (1970).
W. M. Gelbart, S. A. Rice, and K. F. Freed. Random matrix theory and the master equation for finite systems, J. Chem. Phys 57, 4699–4712 (1972).
K. G. Kay, Theory of vibrational relaxation in isolated molecules, J. Chem. Phys 61, 5205–5220 (1974).
W. H. Miller, The semiclassical nature of atomic and molecular collisions, Acc. Chem. Res 4, 161–167 (1971).
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Hase, W.L. (1976). Dynamics of Unimolecular Reactions. In: Miller, W.H. (eds) Dynamics of Molecular Collisions. Modern Theoretical Chemistry, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0644-4_3
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