Nascent product excitations in unimolecular reactions: The separate statistical ensembles method

Abstract

The unimolecular reaction of a vibrationally excited molecule having low rotational excitation often leads to nascent products in which the vibrational degrees of freedom appear ‘‘hotter’’ than the rotation, translation (R,T) degrees of freedom. We show that this can derive from parent vibrations being ‘‘hot’’ while parent rotations remain ‘‘cold,’’ since the parentage of product vibration is parent vibration, while product R,T excitations are obtained from parent vibration as well as rotation. Calculations are performed for reactions having loose transition states and no reverse barriers, in which an ensemble of 3N–6 degrees of freedom are used to equilibrate parent vibrations, thereby providing a statistical distribution of product vibrational excitations. For each set of product vibrational states, all R,T excitations are then apportioned statistically using the phase space theory of unimolecular reactions (PST). The results indicate that for those energies above reaction threshold (E‡) which exceed the lowest product vibrational energies, product vibrations are more excited than with PST, while product R,T excitations are less than with PST. These differences increase with E‡, and rotational distributions obtained using the separate statistical ensembles (SSE) method peak at low N″ relative to PST. When product vibrations are energetically inaccessible, SSE and PST are identical. The calculations are compared to nascent distributions from the unimolecular dissociation of monoenergetic NCNO, and the agreement is excellent.

Ultrafast Molecular Reaction Dynamics in Real-Time: Progress Over a Decade

“…The different versions of statistical theories (25)(26)(27)(28)(29)(30)(31) [RRKM and its variational modification for flexible states, phase space theory (PST), the statistical adiabatic channel model (SACM), the separate statistical ensemble (SSE)] differ in the details of the constraints assumed. We do not attempt a review of the theories here and refer the interested reader to several textbooks (93, 94), reviews (2,3,24,(95)(96)(97), and the original articles (25-31) on these topics.…”

“…Under these conditions, the reaction is said to be statistical (see e.g. 24) and statistical theories of reaction rates (25)(26)(27)(28)(29)(30)(31) may be applied; a reaction rate constant can be directly obtained from the exponential loss of population in the initial state or buildup in any product state. On the other hand, if the rate of reaction is intrinsically faster than the rate of energy redistribution, then one would expect the outcome of the reaction to be deterministic--initial state influences both rate and product distributions.…”

Photodissociation dynamics of acetone studied by time-resolved ion imaging and photofragment excitation spectroscopy

“…The calculations model CH3 and HCO as oblate and prolate symmetric tops, respectively, and used the rotational and vibrational constants reported by de Wit et al 46 PST and SEE weight the product vibrational state distributions differently, based on the number of disappearing vibrational modes, although the distributions are almost indistinguishable. 64,65 The ET distributions calculated using PST and SSE are shown in Figure 4 alongside the experimental data. The ET distributions predicted by PST and SSE peak near zero and reproduce the observed slow component at both 317 and 320 nm reasonably well, consistent with unimolecular dissociation on the S0 surface.…”

“…31 Phase Space Theory (PST) 62,63 and Separate Statistical Ensembles (SSE) 64 calculations have been performed using EAVL = 2300 cm -1 and 2600 cm -1 , equivalent to excitation at 320 nm and 317 nm. The calculations model CH3 and HCO as oblate and prolate symmetric tops, respectively, and used the rotational and vibrational constants reported by de Wit et al 46 PST and SEE weight the product vibrational state distributions differently, based on the number of disappearing vibrational modes, although the distributions are almost indistinguishable.…”

Vibrational overtone initiated unimolecular dissociation of HOCH2OOH and HOCD2OOH: Evidence for mode selective behavior

“…This trend likely reflects the breakdown in the applicability of PST for states substantially above the dissociation threshold, where the critical configuration no longer corresponds to a loose transition state and vibrationally excited products can form. 28 …”