Unimolecular decomposition, classical

This expression, and variations of it, have been used to fit classical anliamionic microcanonical k(E, J) for unimolecular decomposition [56]. 

A3.12.6 CLASSICAL DYNAMICS OF INTRAMOLECULAR MOTION AND UNIMOLECULAR DECOMPOSITION... 

Another classic example of a complex reaction is the decomposition of N2O5 which shows first order kinetics, but with the first order rate constant decreasing in value as the pressure is lowered. Superficially, this could be taken as evidence of a typical unimolecular decomposition. However, even a first glance at the stoichiometry of the reaction should suggest that it is unlikely that there is a simple one step breakdown of N2O5 into the products. 

B.M. Rice, D.L. Thompson, Classical Dynamics Studies of the Unimolecular Decomposition of Nitromethane, J. Chem. Phys., 93 (1990) 7986-8000. 

It is likely that theoretical methods, both ab initio and MD simulations, will be needed to resolve the complicated chemical decomposition of energetic materials. There are species and steps in the branching, sequential reactions that cannot be studied by extant experimental techniques. Even when experiments can provide some information it is often inferred or incomplete. The fate of methylene nitramine, a primary product observed by Zhao et al. [33] in their IRMPD/molecular beam experiments on RDX, is a prime example. Rice et al. [99, 100] performed extensive classical dynamics simulations of the unimolecular decomposition of methylene nitramine in an effort to help clarify its role in the mechanism for the gas-phase decomposition of RDX. 

Since the pressures in the experiments are in the region of the second-order limit, the observed first-order rate coefficients show a nearly linear pressure dependence and a strong temperature dependence in the Arrhenius activation energy. Using the classical Rice et al. model for unimolecular decomposition, s = 12 which is a surprisingly large value. 

By choosing the initial conditions for an ensemble of trajectories to represent a quantum mechanical state, trajectories may be used to investigate state-specific dynamics and some of the early studies actually probed the possibility of state specificity in unimolecular decay [330]. However, an initial condition studied by many classical trajectory simulations, but not realized in any experiment is that of a micro-canonical ensemble [331] which assumes each state of the energized reactant is populated statistically with an equal probability. The classical dynamics of this ensemble is of fundamental interest, because RRKM unimolecular rate theory assumes this ensemble is maintained for the reactant [6,332] as it decomposes. As a result, RRKM theory rules-out the possibility of state-specific unimolecular decomposition. The relationship between the classical dynamics of a micro-canonical ensemble and RRKM theory is the first topic considered here. 

A classical diffusion theory model has been proposed to calculate the rate of IVR between the reaction coordinate and the remaining bath modes of the molecule [345]. Following work by Bunker [324], the unimolecular dynamics will be non-ergodic (intrinsically non-RRKM) if A rrkm fciVR. For such a situation, the unimolecular decomposition will be exponential and occur with a rate constant equal to /sivr- The rate of IVR is modeled by assuming a random force between the bath modes and the reaction coordinate. The model was used to successfully analyze the intrinsic non-RRKM dynamics for Si2He -> 2SiH3 dissociation [345]. 

A reaction-path based method is described to obtain information from ab initio quantum chemistry calculations about the dynamics of energy disposal in exothermic unimolecular reactions important in the initiation of detonation in energetic materials. Such detailed information at the microscopic level may be used directly or as input for molecular dynamics simulations to gain insight relevant for the macroscopic processes. The semiclassical method, whieh uses potential energy surface information in the broad vicinity of the steepest descent reaction path, treats a reaction coordinate classically and the vibrational motions perpendicular to the reaction path quantum mechanically. Solution of the time-dependent Schroedinger equation leads to detailed predictions about the energy disposal in exothermic chemical reactions. The method is described and applied to the unimolecular decomposition of methylene nitramine. 

The conclusion one reaches is that quantum RRKM theory is an incomplete model for unimolecular decomposition. It does not describe fluctuations in state-specific resonance rates, which arise from the nature of the couplings between the resonance states and the continuum. It also predicts steps in k E), which appear to be inconsistent with the actual quantum dynamics as determined from computational chemistry. However, for molecules whose classical unimolecular dynamics is ergodic and intrinsically RRKM and/or whose resonance rates are statistical state specific (see Section 15.2.4), the quantum RRKM k E) gives an accurate average rate constant for an energy interval E E + AE [47]. 

The first classical trajectory study of unimolecular decomposition and intramolecular motion for realistic anharmonic molecular Hamiltonians was performed by Bunker [12,13]. Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,17,30,M,65,66 and 62] from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3.12.7. Chaotic vibrational motion is not regular as predicted by the normal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9]. For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is formed and the probability of decomposition becomes that of RRKM theory. 

The random lifetime assumption is perhaps most easily tested by classical trajectory calculations (Bunker, 1962 1964 Bunker and Hase, 1973). Initial momenta and coordinates for the Hamiltonian of an excited molecule can be selected randomly, so that a microcanonical ensemble of states is selected. Solving Hamilton s equations of motion, Eq. (2.9), for an initial condition gives the time required for the system to reach the transition state. If the unimolecular dynamics of the molecule are in accord with RRKM theory, the decomposition probability of the molecule versus time, determined on the basis of many initial conditions, will be exponential with the RRKM rate constant. That is, the decay is proportional to exp[-k( )t]. The observation of such an exponential distribution of lifetimes has been identified as intrinsic RRKM behavior. If a microcanonical ensemble is not maintained during the unimolecular decomposition (i.e., IVR is slower than decomposition), the decomposition probability will be nonexponential, or exponential with a rate constant that differs from that predicted by RRKM theory. The implication of such trajectory studies to experiments and their relationship to quantum dynamics is discussed in detail in chapter 8. 

Anharmonic corrections have also been determined for unimolecular rate constants using classical mechanics. In a classical trajectory (Bunker, 1962, 1964) or a classical Monte Carlo simulation (Nyman et al., 1990 Schranz et al., 1991) of the unimolecular decomposition of a microcanonical ensemble of states for an energized molecule, the initial decomposition rate constant is that of RRKM theory, regardless of the molecule s intramolecular dynamics (Bunker, 1962 Bunker, 1964). This is because a... 

Classical trajectory studies of unimolecular decomposition have helped define what is meant by RRKM and non-RRKM behavior (Bunker, 1962, 1964 Bunker and Hase, 1973 Hase, 1976, 1981). RRKM theory assumes that the phase space density of a decomposing molecule is uniform. A microcanonical ensemble exists at t = 0 and rapid intramolecular processes maintain its existence during the decomposition [fig. 8.9(a), (b)]. The lifetime distribution, Eq. (8.35a), is then... 

Intrinsic non-RRKM behavior occurs when an initial microcanonical ensemble decays nonexponentially or exponentially with a rate constant different from that of RRKM theory. The former occurs when there is a bottleneck (or bottlenecks) in the classical phase space so that transitions between different regions of phase space are less probable than that for crossing the transition state [fig. 8.9(e)]. Thus, a micro-canonical ensemble is not maintained during the unimolecular decomposition. A limiting case for intrinsic non-RRKM behavior occurs when the reactant molecule s phase space is metrically decomposable into two parts, for example, one part consisting of chaotic trajectories which can decompose and the other of quasiperiodic trajectories which are trapped in the reactant phase space (Hase et al., 1983). If the chaotic motion gives rise to a uniform distribution in the chaotic part of phase space, the unimolecular decay will be exponential with a rate constant k given by... 

The classical mechanical model of unimolecular decomposition developed by Slater (1959) is based on the normal mode harmonic oscillator Hamiltonian, Eq. (2.47). 

Table 8.5. Classical Trajectory Studies Identifying Intrinsic RRKM and non-RRKM Unimolecular Decomposition.

Kassel s quantum-theory treatment of unimolecular decomposition [6] is probably more realistic than the corresponding classical theory. It has the disadvantage, however, of having an additional adjustable parameter. 

The energy disposal and effective upper state lifetimes have been reproduced using classical trajectory calculations a quasi-diatomic assumption was made to determine the slope of the section through the upper potential energy surface along the N—a bond from the shape of the u.v. absorption profile. The only adjustable parameter was the assumption of a parallel transition in the quasi-diatomic molecule. In contrast, a statistical adiabatic channel model which assumed dissociation via unimolecular decomposition out of vibrationally and rotationally excited level in the ground electronic state (following internal con-... 

An analysis of the specificity of unimolecular decompositions and of intramolecular vibrational relaxation can be developed by starting with some simple models for coupled oscillators, for which different modes and (transitions among them) have been well characterized, both in classical and in quantum mechanics. 

A theory encompassing k, V3, and V4 would be a theory for exothermic binary reactions. While no such comprehensive theory exists, it has nevertheless been possible to make some useful qualitative predictions on very simple grounds. The determination of v can be related to the classical problem of unimolecular decomposition. No exact solution to this problem is possible, but approximate expressions for simplified models are well known and these give the correct qualitative dependence of the complex lifetime on the various controlling parameters. The simplest such expression, derived for a simple statistical model consisting of s coupled oscillators of the same frequency, is... 

Unimolecular decomposition is a classic instance where theory demonstrates that a mechanism is more complex than the stoichiometry suggests. Another instance is in the atomic recombination reaction... 

Molecular Collisions Classical Treatment. 2 Unimolecular Decomposition 403... 

Since classical mechanics allows C2H4F dissociation to occur without zero-point energy in the TS s vibrational modes, the energy distribution of the C2Fi3F + FI products is expected to agree with experiment only at the high-energy limit. If it is correct to assume the unimolecular decomposition... 

E. R. Grant and D. L. Bunker, Dynamical effects in unimolecular decomposition A classical trajectory study of the dissociation of C2He, J. Chem. Phys. 68 628 (1978). 

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