And phase space theory

The modified thermal and phase space theories reproduce most three body association data equally well, including the inverse temperature dependence of the rate coefficient (Herbst 1981 Adams and Smith 1981), and are capable of reproducing experimental rate coefficients to within an order of magnitude (Bates 1983 Bass, Chesnavich, and Bowers 1979 Herbst 1985b). They should therefore be this accurate for radiative association rate coefficients if kr is treated correctly. 

It must be emphasized that such phenomena are to be expected for a statistical system only in the regime of low level densities. Theories like RRKM and phase space theory (PST) (Pechukas and Light 1965) are applicable when such quantum fluctuations are absent for example, due to a large density of states and/or averaging over experimental parameter such as parent rotational levels in the case of incomplete expansion-cooling and/or the laser linewidth in ultrafast experiments. However, in the present case, it is unlikely that such phenomena can be invoked to explain why different rates are obtained when using ultrafast pump-probe methods that differ only in experimental detail. 

In Section VII we conclude our results and discuss several issues arising from our proposals. We revisit our original motivation—that is, to find a simple model, in the sense of dynamical systems, that captures several common aspects of slow dynamics in liquid water, or more generally supercooled liquids or glasses. Our attempt is to make clear the relation and compatibility between the potential energy landscape picture and phase space theories in the Hamiltonian dynamics. Importance of heterogeneity of the system is discussed in several respects. Unclarified and unsolved points that still remain but should be considered as crucial issues in slow dynamics in molecular systems are listed. 

Figure 5. Comparison of the observed product rotational state distributions (solid bars) and the results of two statistical models the statistical adiabatic channel model (SACM, open bars) and phase space theory (PST, hatched bars). The distributions are an average of those observed, or those calculated, at several excitation wavelengths in the region of (a) the 5tbu main band, (b) the 5voh combination band, (c) the 6vOH main band, and (d) the 6v0H combination band of HOOH. (Reproduced with permission from Ref. 41.)...

Degrees of Freedom in the Prior and Phase Space Theories... 

The remarkably complicated kinetic behavior of reaction (viii) is reviewed in Section 4.5.1 and phase-space theory cannot begin to provide... 

For the theoretician, clusters are also convenient model systems to evaluate the performance of dissociation rate theories. By comparing the results of numerically exact molecular dynamics (MD) trajectories to the predictions of rate theories, the various approximations inherent to these theories can be unambiguously tested and possibly improved upon. Previous authors have critically discussed how the Rice-Ramsperger-Kassel (RRK), ° Weisskopf, and Phase Space Theory of Light and Pechukas, Nikitin, Klots, Chesnavich and Bowers respectively compare for the thermal evaporation of atomic clusters. This work was subsequently extended by the present authors to rotating and molecular clusters. From these efforts it was concluded that phase space theory (PST), in its orbiting transition state version, was quantitatively able to describe statistical dissociation. This chapter is not devoted to a detailed presentation of phase space theory and the reader is encouraged to consult the cited work. 

Energy Constrained and Quantum Anharmonic Rice-Ramsperger-Kassel-Marcus and Phase Space Theory Rate Constants For AI3 Dissociation. 

Since the observation made in study of the formation HeH+ indicated that this product was not formed by reaction of He + with H2, it had been assumed that the exothermic heat of reaction of He+ ions with H2 is probably deposited in the product HeH + as internal energy, decomposing the product into H+ and He. This idea was cited by Light (16) in his phase space theory of ion-molecule reactions to account for the failure to observe HeH+ from reactions with He+ ions. The experimental difficulty in the mass spectrometric investigation of this process is that H + formed by electron impact tends to obscure the ion-molecule-produced H+ so that a sensitive quantitative cross-section measurement is difficult. 

Rosenstock (55) pointed out that the initial formulation of the theory failed to consider the effect of angular momentum on the decomposition of the complex. The products of reaction must surmount a potential barrier in order to separate, which is exactly analogous to the potential barrier to complex formation. Such considerations are implicit in the phase space theory of Light and co-workers (34, 36, 37). These restrictions limit the population of a given output channel of the reaction com-... 

The phase space theory in its present form suffers from the usual computational difficulties and from the fact it has thus far been developed only for treating three-body processes and a limited number of output channels. Further, to treat dissociation as occurring only through excitation of rotational levels beyond a critical value for bound vibrational states is rather artificial. Nevertheless, it is a useful framework for discussing ion-molecule reaction rates and a powerful incentive for further work. 

The association rate data determined in this study can be used to make quite a precise binding energy estimate for the aluminum ion-benzene complex. The relation between the association rate constant and the binding energy was made with use of phase space theory (PST) to calculate as a function of E, with a convolution over the Boltzmann distribution of energies and angular momenta of the reactants (see Section VI). PST should be quite a reasonable approximation for... 

Phase space theory (PST) has been widely used for estimation of rates and energy partitioning for ion dissociations. It can be considered within the framework of transition-state theory as the limiting case of a loose transition state, in which all product degrees of freedom are statistically fully accessible at the transition state. As such, it is expected to give an upper limit for dissociation rates and to be best suited to barrierless dissociations involving reaction coordinates with simple bond cleavage character. 

Figure 3. Thermal rate constants for capture of HC1 by H3 (PST locked-dipole capture corresponding to phase-space theory, Eq. (16) SACM statistical adiabatic channel model, Eqs. (26)-(34) [15] SACMci classical SACM, Eqs. (28H31) [15] CT classical trajectories, Eqs. (26) and (27) [1]).

Figure 6. Number of open channels for the interaction between H3 and HC1 (SACM calculations from Ref. IS PST phase-space theory full curves permanent + induced dipole dashed smoothed curves permanent dipole J total angular momentum of H3-HCI complex).

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