Rotation rotational state dependence

Even at room temperature, the sum over the angular momentum may include hundreds of rotational states, depending on the rotational constants. Thus, the temperature and pressure dependent unimolecular rate includes averaging over a very large number of resonance states and therefore a reasonable question is to which extent the quantum mechanical fluctuations can survive this averaging. As was shown by Miller [288], the rate k ni, T) is actually related to the micro-canonical rate constant averaged over the distribution of resonance widths Q k), k v, introduced in Eq. (51),... 

In this analysis and in that of the next section, the vibrational motion effects presume a field source that is rotating with the molecule, such as when the electrical perturbation is due to a weakly complexed partner molecule. A freely rotating molecule in a laboratory-fixed field source, however, is different, and then evaluations of electrical properties should account for rotational state dependence as well [114, 115]. 

Levine R.D. and Bernstein, R.B. (1986) Rotational state dependence of the reactivity of oriented symmetric top molecules. Chem. Phys. Lett. 132, 11-15. 

Figure 35, (a) Variation of the initial sticking coeiiicient with initial normal kinetic energy (circles represent experimental results from Hamza and Madix (1985) while triangles and squares represent classical GLE calculations at incident angles of 0° and 45°, respectively) (b) calculated number density of scattered Hj vs. final polar angle (c) calculated initial rotational state dependence of the dissociation probability. The plots are from Kara and DePristo (1989). 

Figure 41. Initial rotational state dependence of the dissociative chemisorption probability of Nj on W(llO). The figure is reprinted with permission from Kara and DePristo (1988c).

Anthony, E.B., Bastian, M.J., Bierbaum, V.M., Leone, S.R., Laser probing of rotational-state-dependent velocity distributions of NJ (v" = 0, /) drifted in He. J. Chem. Phys. 

Because they lend themselves to studies using both photochemical and chemical activation, bimolecular reactions of vibrationally excited hydrogen halides have been more throughly investigated than any other family of reactions. The rate constants in Table 1.3 have been obtained by the laser-induced vibrational fluorescence technique and correspond to the sum of rate constants for reactive and inelastic processes. The main problem is to establish the atomic concentrations accurately. This is usually accomplished by gas-phase titration in a discharge-flow system, although photolysis methods have also been employed. To find the ratio of reaction to non-reactlve relaxation, product concentrations have to be observed. This has been done in relatively few cases. Some systems have also been studied using the infrared chemiluminescence depletion technique (see Section 1.5.1). These experiments supply relative rate data for removal from several vibrational levels, and, in favorable cases, also provide some information about the rotational-state dependence of these rates. 

The strong dependence of the PES on molecular orientation also leads to strong coupling between rotational states, and hence rotational excitation/de-excitation in the scattering. This has been observed experimentally for H2 scattering from Cu surfaces. Recent work has shown that for H2 the changes m rotational state occur almost exclusively when the molecular bond is extended, that is, longer than the gas-phase equilibrium value [ ]. 

The site specificity of reaction can also be a state-dependent site specificity, that is, molecules incident in different quantum states react more readily at different sites. This has recently been demonstrated by Kroes and co-workers for the Fl2/Cu(100) system [66]. Additionally, we can find reactivity dominated by certain sites, while inelastic collisions leading to changes in the rotational or vibrational states of the scattering molecules occur primarily at other sites. This spatial separation of the active site according to the change of state occurring (dissociation, vibrational excitation etc) is a very surface specific phenomenon. 

RRKM theory assumes a microcanonical ensemble of A vibrational/rotational states within the energy interval E E + dE, so that each of these states is populated statistically with an equal probability [4]. This assumption of a microcanonical distribution means that the unimolecular rate constant for A only depends on energy, and not on the maimer in which A is energized. If N(0) is the number of A molecules excited at / =... 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

Spectral lines are fiirther broadened by collisions. To a first approximation, collisions can be drought of as just reducing the lifetime of the excited state. For example, collisions of molecules will connnonly change the rotational state. That will reduce the lifetime of a given state. Even if die state is not changed, the collision will cause a phase shift in the light wave being absorbed or emitted and that will have a similar effect. The line shapes of collisionally broadened lines are similar to the natural line shape of equation (B1.1.20) with a lifetime related to the mean time between collisions. The details will depend on the nature of the intemrolecular forces. We will not pursue the subject fiirther here. 

The Time Dependent Processes Seetion uses time-dependent perturbation theory, eombined with the elassieal eleetrie and magnetie fields that arise due to the interaetion of photons with the nuelei and eleetrons of a moleeule, to derive expressions for the rates of transitions among atomie or moleeular eleetronie, vibrational, and rotational states indueed by photon absorption or emission. Sourees of line broadening and time eorrelation funetion treatments of absorption lineshapes are briefly introdueed. Finally, transitions indueed by eollisions rather than by eleetromagnetie fields are briefly treated to provide an introduetion to the subjeet of theoretieal ehemieal dynamies. 

The tools of time-dependent perturbation theory can be applied to transitions among electronic, vibrational, and rotational states of molecules. 

Here, I(co) is the Fourier transform of the above C(t) and AEq f is the adiabatic electronic energy difference (i.e., the energy difference between the v = 0 level in the final electronic state and the v = 0 level in the initial electronic state) for the electronic transition of interest. The above C(t) clearly contains Franck-Condon factors as well as time dependence exp(icOfvjvt + iAEi ft/h) that produces 5-function spikes at each electronic-vibrational transition frequency and rotational time dependence contained in the time correlation function quantity <5ir Eg ii,f(Re) Eg ii,f(Re,t)... 

The dependence of Av, the frequency spread, on results in a much larger value for an excited electronic state, typically 30 MHz, than for an excited rotational state, typically 10 Hz, because of the much greater v for an excited electronic state. 

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