On non-RRKM unimolecular kinetics: Molecules in general, and CH3NC in particular

In this work, we investigate the possibility of describing gas phase atomic cluster dissociation by means of variational transition state theory ͑vTST͒ in the microcanonical ensemble. A particular emphasis is placed on benchmarking the accuracy of vTST in predicting the dissociation rate and kinetic energy release of a fragmentation event as a function of the cluster size and internal energy. The results for three Lennard-Jones clusters ͑LJ n , n =8,14,19͒ indicate that variational transition state theory is capable of providing results of accuracy comparable to molecular dynamics simulations at a reduced computational cost. Possible simplifications of the master equation formalism used to model a dissociation cascade are also suggested starting from molecular dynamics results. In particular, it is found that the dissociation rate is only weakly dependent on the cluster total angular momentum J for the three cluster sizes considered. This would allow one to partially neglect the J-dependency of the kinetic coefficients, leading to a substantial decrease in the computational effort needed for the complete description of the cascade process. The impact of this investigation on the modeling of the nucleation process is discussed.

Section: B Comparison Between -Vtst and MD Dissociation Ratesmentioning

confidence: 99%

On possible simplifications in the theoretical description of gas phase atomic cluster dissociation

Mella¹

2009

“…In the present paper we consider the problem of defining and evaluating theoretical unimolecular reaction rates in light of the penetrating analyses of Thiele, 32 Bunker and Hase, 37 Dumont and Brumer, 49 and DeLeon and co-workers, 97,98 the classical spectral theorem, 55,56 and the recent developments in phase space transition state theory 148,149,153-159 mentioned above. The particular reaction chosen for study is the isomerization HCN CNH, 155,156,[168][169][170][171][172][173][174][175][176] for which several relevant theoretical quantities have recently been computed for a ͑classical͒ model of the HCN molecule at fixed energy.…”

Section: Introductionmentioning

confidence: 99%

“…As we show below, Thiele's work has proved to be remarkably prescient in terms of its identification of the appropriate phase space structures involved in unimolecular reaction dynamics. Following Thiele's work, 32,33 and the pioneering contributions of Bunker and co-workers, 11,[34][35][36][37] a large number of computational ͑trajectory͒ investigations of gap time and reactant lifetime distributions have been undertaken ͑see, for example, Refs. 38-48͒.…”

Section: Introductionmentioning

confidence: 99%

Microcanonical rates, gap times, and phase space dividing surfaces

Ezra

Waalkens

Wiggins

2009

112

The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. Key concepts, such as the phase space dividing surface separating reactants from products, the average gap time, and the volume of phase space associated with reactive trajectories, are both rigorously defined and readily computed within the phase space approach. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerization reaction HCN CNH, previously studied using the methods of phase space transition state theory. Both algebraic ͑power law͒ and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Correcting the RRKM estimate to account for the measure of the reactant phase space region occupied by trapped trajectories results in a drastic overestimate of the isomerization rate. Compensating but as yet not fully understood trapping mechanisms in the reactant region serve to slow the escape rate sufficiently that the uncorrected RRKM estimate turns out to be reasonably accurate, at least at the particular energy studied. Examination of the decay properties of subensembles of trajectories that exit the HCN well through either of two available symmetry related product channels shows that the complete trajectory ensemble effectively attains the full symmetry of the system phase space on a short time scale t Շ 0.5 ps, after which the product branching ratio is 1:1, the "statistical" value. At intermediate times, this statistical product ratio is accompanied by nonexponential ͑nonstatistical͒ decay. We point out close parallels between the dynamical behavior inferred from the gap time distribution for HCN and nonstatistical behavior recently identified in reactions of some organic molecules.

“…The importance of obtaining the correct trajectory is emphasized by a recent direct dynamics simulation by Bach et al 62 in which ϳ20% of the trajectories for a microcanonical ensemble of highly excited C 2 H 5 radicals consisted of regular-type trajectories, an intrinsic non-RiceRamsperger-Kassel-Marcus result. 63 On the other hand, if the ensemble of trajectories has only irregular/chaotic motion, this strict requirement of obtaining the correct trajectory is unnecessary, since the noisy chaotic trajectories map onto each other. 64,65 In future work, several extensions can be made to the work presented here.…”

Section: Discussionmentioning

confidence: 99%

Direct dynamics simulations using Hessian-based predictor-corrector integration algorithms

Lourderaj

Song²,

Windus³

et al. 2007

In previous research [ J. Chem. Phys.111, 3800 (1999)] a Hessian-based integration algorithm was derived for performing direct dynamics simulations. In the work presented here, improvements to this algorithm are described. The algorithm has a predictor step based on a local second-order Taylor expansion of the potential in Cartesian coordinates, within a trust radius, and a fifth-order correction to this predicted trajectory. The current algorithm determines the predicted trajectory in Cartesian coordinates, instead of the instantaneous normal mode coordinates used previously, to ensure angular momentumconservation. For the previous algorithm the corrected step was evaluated in rotated Cartesian coordinates. Since the local potential expanded in Cartesian coordinates is not invariant to rotation, the constants of motion are not necessarily conserved during the corrector step. An approximate correction to this shortcoming was made by projecting translation and rotation out of the rotated coordinates. For the current algorithm unrotated Cartesian coordinates are used for the corrected step to assure the constants of motion are conserved. An algorithm is proposed for updating the trust radius to enhance the accuracy and efficiency of the numerical integration. This modified Hessian-based integration algorithm, with its new components, has been implemented into the VENUS/NWChem software package and compared with the velocity-Verlet algorithm for the H2CO→H2+CO, O3+C3H6, and F−+CH3OOH chemical reactions. KeywordsInterpolation, Ab initio calculations, Trajectory models, Electronic structure, Angular momentum Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 126 (2007) In previous research ͓J. Chem. Phys. 111, 3800 ͑1999͔͒ a Hessian-based integration algorithm was derived for performing direct dynamics simulations. In the work presented here, improvements to this algorithm are described. The algorithm has a predictor step based on a local second-order Taylor expansion of the potential in Cartesian coordinates, within a trust radius, and a fifth-order correction to this predicted trajectory. The current algorithm determines the predicted trajectory in Cartesian coordinates, instead of the instantaneous normal mode coordinates used previously, to ensure angular momentum conservation. For the previous algorithm the corrected step was evaluated in rotated Cartesian coordinates. Since the local potential expanded in Cartesian coordinates is not invariant to rotation, the constants of motion are not necessarily conserved during the corrector step. An approximate correction to this shortcoming was made by projecting translation and rotation out of the rotated coordinates. For the current algorithm unrotated Cartesian coordinates are used for the corrected step to assure the constants of motion are conserved. An algorithm is proposed for updating the trust radius to enhance the accuracy and efficiency of the numerical integration. This modified Hessian-based integration algorit...