Unimolecular Systems

Tardy D C and Rabinovitch B S 1977 Intermolecular vibrational energy transfer in thermal unimolecular systems Chem. Rev. 77 369-408... 

The details of these short-time calculations, made for the case that U(r) = 0, are given elsewhere (28). Searching for the inverted effect in unimolecular systems (reactants linked to each other) would also be very desirable since their rates would not be diffusion limited. 

For unimolecular reaction systems described by mass-action kinetics, the kinetic equations are always linear. Hence they are called linear reaction systems. For stochastic unimolecular systems, the key is to understand the multi-state kinetics of a single molecule, as we have seen. If N is the number of states of amolecule, and there are M number of identical, independent molecules, then the probability of having... 

T. L. Hill. Studies in irreversible thermodynamics IV. Diagrammatic representation of steady state fluxes for unimolecular systems. J. Theor. Biol., 10 442 159,... 

A RRKM unimolecular system obeys the ergodic principle of statistical mechanics [337]. A quantity of more utility than N t), for analyzing the classical dynamics of a micro-canonical ensemble, is the lifetime distribution Pc t), which is defined by... 

The simplest approach [338] to describe a non-ergodic unimolecular system is to assume that the reactant s phase space only consists of quasi-periodic and chaotic trajectories, whose numbers are ATqp and Nch- If a micro-canonical ensemble is prepared at t = 0 and if it is assumed that a restricted micro-canonical ensemble is maintained within the chaotic region, while no trajectory dissociates from the quasi-periodic region, the number of reactant molecules versus time is... 

A strength of direct dynamics is that it allows one to determine the classical dynamics for a particular level of electronic structure theory, without the need for an intermediate analytic PES fit. In addition, since it is difficult to develop analytic PES s for many-atom systems, direct dynamics greatly expands the range of unimolecular systems whose dynamics may be investigated by classical trajectories. However, a limitation of direct dynamics, is the large computer time needed to calculate the trajecto-... 

We performed several series of spectroscopic measurements in acetonitrile solutions containing equimolar solutions of 3 and 4 and a lower concentration of host 14+ and determined the complex concentrations as variable amounts of TFA and pyridine were added to control the extent of protonation of the benzidine derivative 3 [9]. Typical results, obtained with a solution initially containing 2.0 mM of 3, 2.0 mM of 4, and 1.0 mM of 14+, are shown in Fig. 1. Clearly, protonation of 3 leads to dissociation of its complex with 14+ and a modest increase of the concentration of complex 4 14+. To compare in more quantitative terms this switching behavior to that observed with the unimolecular system (rotaxane 24+), it is useful to focus on the molar... 

A RRKM unimolecular system obeys the ergodic principle of statistical mechanics[JT],... 

For a RRKM calculation without any approximations, the complete vibrational/rotational Hamiltonian for the unimolecular system is used to calculate the reactant density and transition state s sum of states. No approximations are made regarding the coupling between vibration and rotation. However, for many molecules the exact nature of the coupling between vibration and rotation is uncertain, particularly at high energies, and a model in which rotation and vibration are assumed separable is widely used to calculate the quantum RRKM k(E, J) [4,16]. To illustrate this model, first consider a linear polyatomic molecule which decomposes via a linear transition state. The rotational energy for the reactant is assumed to be that for a rigid rotor, i.e. 

The Link Atom Problem. - As mentioned earlier, the question of how to describe the boundary between the quantum and classical regions is hotly debated. Following the example given by Bakowies and Thiel,142 consider a bimolecular system X+ + Y The question of how to partition this system is trivial. X+ may be treated quantum mechanically and Y may be treated classically, or vice versa. However the partitioning of a covalently bonded, unimolecular system, X-Y, is more difficult as none of the obvious fragments, X+ + Y, X + Y or X- + Y+ accurately describe the electron distribution of either X or Y as part of the whole system X-Y. 

This model has been applied to the unimolecular systems O3, CINO, NOz. CH4, CiHc, CD4, and Putting a == c in equation (45), one obtains... 

We shall now first consider (for reactions similar to those mentioned above) molecular beam, chemiluminescence, and related techniques, in which the metastable molecules may be considered to be essentially isolated during their lifetime, and which allow for a detailed determination of the product quantum states after decomposition. We shall then shortly review bulk investigations on unimolecular systems with chranical activation and photoactivation, which continue to provide a wealth of information. 

We may conclude this section with the hope that more detailed e q)erimental information on unimolecular systems, together with a refined theoretical evaluation, will provide in future a deeper understanding of the dynamics. Oearly, the various statistical models can describe only limiting situations. Although the experimental material so far appears to be not yet sufficient to delimit the cases where these limiting situations are well approximated, this should become possible in the near future. In this respect, molecular beam experiments similar to the classical bulk chemical activation experiments by Rynbrandt and Rabinovitch on the cyclopropanes would be most desirable. ... 

Taking everything together, this reaction system can be considered to be quite well understood over a uniquely large temperature range. The earlier discrepancies between theory and experiments have been removed, mainly due to improvement of the theory and some extension of the experiments. It would be most helpful to have more unimolecular systems with similarly complete experimental and theoretical data in the future. 

This appendix provides a set of self-contained computer programs for the calculation of rate constants in thermal unimolecular systems. Most of them were written by Andrew Yau [78.Y2], and have now stood up to five years, or so, of continual use. They may run into trouble occasionally if anharmonicity values in the range 0.005-0.006 are used for several oscillators at the same time, or if other unusual molecular parameters are tried but, by and large, they perform acceptably in normal circumstances. Some effort has been expended in trying to make the repetitive segments of the calculations efficient, but there is no pretence at elegance - a contradiction in terms when one is constrained to use FORTRAN [72.D3],... 

The reduction technique works best for linear (such as unimolecular) systems, or weakly coupled nonlinear systems. Coupled nonlinear reactions will cause degeneracies and erroneously identify fast species in the above procedure. In these cases, condition C.l will not be satisfied, even after the described transformation of variables. 

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