Vibrational surprisals

To consider reaction out of specified mctant states it is necessary to modify slightly the definition of surinisal that was given in equation (28). Kaplan, Levine, and Manz consider the partially detailed rate constants for reaction from specified vibrational levels, the rotationaland translational d rees of freedom having thermal distributions defined by T. Now the (vibrational) surprisal is... 

In many cases, vibrational surprisals have been found to be linear functions of f (62). That is,... 

Figure 4. Vibrational surprisal plots for models I, 11, and III for F + CHsX reactions, taken from (31. Recent work suggests that the v = 3/v = 2 and v = 2/v = 1 ratios may be somewhat higher than those used in making this plot. The general conclusions (31) based upon the surprisal analyses would be unchanged but the —A.V values may be increased slightly.

Figure 5.17 CO vibrational state distribution following the highly exoergic 0( P) + CS CO + S( P) reaction. Dots experimental [adapted from G. Hancock, B. A. Ridley, and I. W. M. Smith, J. Chem. Soc. Faraday Trans 68, 2117 (1972)]. Open symbols trajectory computations for thermal (A) and translationally hot ( ) atoms [adapted from D. Summerfield at al., J. Chem. Phys. 108,1391 (1997)]. Dashed line a fit of the distribution by a linear vibrational surprisal as discussed in Section 6.4 [adapted from H. Kaplan, R. D. Levine, and J. Manz, Chem. Phys. 12, 447 (1976)].

In the light of our earlier discussion of microscopic reversibility, it should not be a surprise to learn that the information-theoretic analysis can be applied to the selective energy requirements for reaction, which are the primary concern of this chapter, as well as to the specificity of energy disposal. Now the vibrational surprisal may be defined as... 

So far we have concentrated on the analysis of detailed rate data, as distinct from their synthesis. It has been implied that vibrational surprisal plots are frequently linear because of some, qualitatively common, dynamic constraint, but this has not been identified. Bernstein and Levine have elegantly reviewed the statistical mechanical basis of the relationship between real distributions and the constraints which lead to them. The general principle is that a system will adopt the distribution with maximum entropy, which is also consistent with all the constraints. Consequently, a complete distribution could be synthesized if the constraints could be independently determined. Alternatively, it should be possible, in principle, to deduce the constraints by observing the distribution. 

Recently, Pollak has demonstrated that the linearity of vibrational surprisal plots is consistent with an exponential gap law for the detailed rate constants, k v v T), of the form ... 

The vibrational surprisal from F + HBr is linear with —Xy = 5.1. The individual HF distributions associated with the Br( Fi/2) and Br( P3,2) channels also give linear surprisal plots. The rather poor fit of the earV HF distribution from the F -I- HI reaction to a linear surprisal has been attributed to formation of /( Fi/2), as well as I Pzi however, recent direct experimental tests refute this. The more recently measured relative populations from F + HI give a better linear surprisal, although the deviation is still 10%. Some experimental error in the relative HF popula-... 

The vibrational energy disposal has been studied by the infrared chemiluminescence technique for a large number of polyatomic molecules (see Table 2.6) however, the interpretations are not as advanced as for the F + HR systems. The rotational energy disposal is somewhat less completely studied, but such data can be expected in the near future. With certain exceptions, the energy disposal generally resembles that of the H + Xa reactions with small , moderate , and nonlinear vibrational surprisals and failure of the HCl or KF product distribution to extend to the thcriiiO-chemical limit. The reactions with NOCl and the sulfur chlorides have been studied in greatest detail and the discussion will be focused on these reactions. 

Laser-induced fluorescence measurements were done only for i = 0 and 1. A linear vibrational surprisal was assumed to obtain the remainder of the distribution. A linear rotational surprisal was found for both i = 0 and 1 with Br = —4.0 this distribution was assumed for the other v levels to obtain . 

The NO vibrational distribution has been measured by infrared chemiluminescence under arrested relaxation conditions. The distribution is relatively flat from v = 1-7 and then decreases monotonically from 8 to 12 the value, assuming only 0( P) formation is 0.27. The break in the distribution occurs very close to the energy expected if the 0( D) channel is important. The vibrational surprisal also consists of two approximately linear regimes. The possibility of some contribution from N( P) reactions cannot be excluded and further work will be necessary to decide about the... 

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