Rate constants master equation dynamics

The time scales of the structural transitions in (NaCl)35Cl mean that it is impossible to use conventional molecular dynamics to investigate the interfunnel dynamics. Instead we use the master equation method outlined in Section III.D. To reduce the computational expense and numerical difficulties we recursively removed from our sample those minima that are only connected to one other minimum—these dead-end minima do not contribute directly to the probability flow between different regions of the PES. The resulting pruned sample had 1624 minima and 2639 transition states. RRKM theory in the harmonic approximation was used to model the individual rate constants,. ... 

Cracial to the simulations presented here is the inclusion of surface reconstmction, together with correct time-dependence of the reactions. As such, the method provides an extension of earlier important computer simulations of CO oxidation on Pt surfaces " . A dynamic Monte Carlo method is used based on the solution of the master equation of the reaction system. The reaction system consists of a regular grid with periodic boundary conditions. The largest grid used in our simulations contained ca. eight million reaction sites. A short description of the model is presented in Fig. 3 and in Table I, that shows the parameters of the rate constants considered. 

Figure 9.11. Time evolution of (a) nonequilibrium rate constant k 12(f)and (b) electronic population in the donor state Pi(t) for V= 120cm . The parameter Icijlt) was obtained from the molecular dynamics simulation data for the model back ET reaction in a rigid collinear triatomic molecule with equivalent donor and acceptor sites separated by a neutral spacer in a polar solvent. The parameter Pfi) is a result of solution of the master equation. (Reproduced from [62c] with permission. Copyright (1996) by the American Institute of Physics.)...

Networks of coupled chemical reactions in a dilute solution should be described by a chemical master equation whenever fluctuations are relevant due to small numbers of at least one of the involved species. The master equation contains the rate constants of all possible reactions. The solution of the chemical master equation gives the dynamics of the probability of flnding a certain number of molecules of each species at a given time for a given initial condition. This leads to the stochastic trajectory of the network by recording the time at which each particular reaction took place with its concomitant change of the number of molecules. 

Proton transport in the gA channel was also simulated with a kinetic model (see section 16.3.5.3). " Each H2O molecule was allowed to take six orientations and each HsO molecule, four orientations, so that the chain of eleven H2O molecules could take 10 states. Three types of transitions were allowed rotation of H2O and HsO" proton transfer from HsO to a neighbouring H2O molecule when they form a hydrogen bond and proton uptake and release for water molecules located at the channel ends. The rate constants were taken of the TST type, with Ag values calculated by continuum electrostatics or deduced from data about proton transfer in water. For the proton uptake and release steps, the Ag value depended explicitly on the pH. The master equation was solved by a sequential dynamical Monte Carlo algorithm and the PMF was deduced from the probability of occupancy of the various sites. When no voltage was applied, the PMF was a symmetrical barrier with a maximum at 3.4 kcal mol . Stationary proton ffuxes calculated for various pH and voltages values were in reasonable agreement with the conductance data. Despite the simplified description of electrostatic interactions and the questionable... 

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