Troe theory

R.G. Gilbert, K. Luther, and J. Troe. Theory of Thermal Unimolecular Reactions in the Fall-Off Range. 2. Weak Collision Rate Constants. Ber. Bunsenges. Phys. Chem., 87 169-177,1983. 

J. Troe, Theory of multichannel thermal unimolecular reactions. 2. Application to the thermal dissociation of formaldehyde, /. Phys. Chem. A109 (37) (2(X)5) 8320-8328. 

Lindemann-Hinshelwood theory makes the assumption that a single collision with a bath gas molecule M is sufficient to deactivate AB to AB. In reality, each collision removes only a fraction of the energy. To account for the fact that not all collisions are fully deactivating, Troe (1983) developed a modification to the Lindemann-Hinshelwood rate expression. In the Troe theory, the right-hand side of... 

Actual experimental data on the pressure variation of the pseudo-second-order rate constant k do not conform with (3.71). The reason is that the elementary rate constants k , and should have been defined for each individual quantized vibrational level of AB, and the individual rates summed to give the total rate. Also, vibrations and rotations can interconvert in the newly formed molecule. A widely used modification of the treatment of pressure-dependent reactions is due to Troe (1983). In the Troe theory, the right-hand side of (3.71) is multiplied by a broadening factor F that is itself a function of ko/k. ... 

J. Troe, Theory of thermal unimolecular reactions at low pressures. I. Solutions of the master equation, J. Chem. Phys. 66 4745 (1977). 

Figure A3.4.7. Sunnnary of statistical theories of gas kinetics with emphasis on complex fomiing reactions (m the figure A.M. is the angular momentum, after Quack and Troe [27, 36, 74]). The indices refer to the following references (a) [75, 76 and 77] (b) [78] (c) [79, and M] (d) [31, 31 and M] (e) [, 31 and...

Gilbert R G, Luther K and Troe J 1983 Theory of thermal unimolecular reactions in the fall-off range. II. Weak collision rate constants Ber. Bunsenges. Phys. Chem. 87 169-77... 

Troe J 1992 Statisticai aspects of ion-moiecuie reactions State-Selected and State-to-State Ion-Molecule Reaction Dynamics Theory ed M Baer M and C-Y Ng (New York Wiiey)... 

Troe J 1975 Unimolecular reactions experiments and theories Kinetics of Gas Reactions ed W dost (New York Academic) p 835... 

Troe J 1977 Theory of thermal unimoleoular reaotions at low pressures. Applioations J. Chem. Rhys. 66 4758-75... 

Troe, J., Predictive Possibilities of Unimolecular Rate Theory, J. Phys. Chem., 83, 114-126 (1979). 

E. Poliak In relation to the point discussed by Profs. Troe and Marcus, we have shown that those cases considered as saddle-point avoidance are consistent with variational transition-state theory (VTST). If one includes solvent modes in the VTST, one finds that the variational transition state moves away from the saddle point the bottleneck is simply no longer at the saddle point. 

J. Troe, in State-Selected and State-to-Slale Ion-Molecule Reaction Dynamics, Part 2 Theory, M. Bear and C. Y. Ng, Eds., Wiley, New York, 1992. 

Prof. Troe has presented to us the capture cross sections for two colliding particles, for example, an induced dipole with a permanent dipole interacting via the potential V(r,0) = ctq/2rA - ocos 0/r2 (see Recent Advances in Statistical Adiabatic Channel Calculations of State-Specific Dissociation Dynamics, this volume). The results have been evaluated using classical trajectories or SAC theory. But quantum mechanically, a colliding pair of an induced dipole and a permanent dipole could never be captured because ultimately they have to dissociate after forming some sort of a collision complex. I would therefore like to ask for the definition of the capture cross section. ... 

Quack, M. and Troe, J. (1981). Statistical methods in scattering, in Theoretical Chemistry, Vol. 6b Theory of Scattering, ed. D. Henderson (Academic Press, New York). 

At low temperature the classical approximation fails, but a quantum generalization of the long-range-force-law collision theories has been provided by Clary (1984,1985,1990). His capture-rate approximation (called adiabatic capture centrifugal sudden approximation or ACCSA) is closely related to the statistical adiabatic channel model of Quack and Troe (1975). Both theories calculate the capture rate from vibrationally and rotationally adiabatic potentials, but these are obtained by interpolation in the earlier work (Quack and Troe 1975) and by quantum mechanical sudden approximations in the later work (Clary 1984, 1985). 

Statistical methods represent a background for, e.g., the theory of the activated complex (239), the RRKM theory of unimolecular decay (240), the quasi-equilibrium theory of mass spectra (241), and the phase space theory of reaction kinetics (242). These theories yield results in terms of the total reaction cross-sections or detailed macroscopic rate constants. The RRKM and the phase space theory can be obtained as special cases of the single adiabatic channel model (SACM) developed by Quack and Troe (243). The SACM of unimolecular decay provides information on the distribution of the relative kinetic energy of the products released as well as on their angular distributions. 

The strong collision correction factor Fsc is a function of two further parameters that arise in Kassel theory (see Section 3). These are the number of effective oscillators, S, and B = Eg/kT, a measure of the relative magnitudes of the threshold energy and thermal energy. Troe used an energy criterion to obtain the number of effective oscillators. 

Cf. R. A. Marcus, J. Chem. Phys. 45,2630 (1966). This paper contains this criterion (p. 2635), but mistakenly ascribes it to Bunker, who actually uses, instead, a minimized density of states criterion [D. L. Bunker and M. Pattengill, J. Chem. Phys. 48, 772 (1968)]. This minimum number of states criterion has been used by various authors, for example, W. L. Hase, J. Chem. Phys. 57, 730 (1972) 64, 2442 (1976) M. Quack and J. Troe (Ref. 21) B. C. Garrett and D. G. Truhlar, J. Chem. Phys. 70, 1593 (1979). The transition state theory utilizing it is now frequently termed microcanonical variational transition state theory (/iVTST). A recent review of /tVTST and of canonical VTST is given in D. G. Truhlar and B. C. Garrett, Ann. Rev. Phys. Chem. 35,159 (1984). 

Troe, J., Predictive possibilities of unimolecular rate theory. J Phys Chem 83, 114, 1979. 

Troe, J. Statistical aspects of ion-molecule reactions. In State-selected and state-to-state ion-molecule reaction dynamics theory Baer, M., Ng, C.-Y., Eds. John Wiley New York, 1992, 485. 

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