Chemical reaction heat bath dynamics

The main problem of elementary chemical reaction dynamics is to find the rate constant of the transition in the reaction complex interacting with its environment. This problem, in principle, is close to the general problem of statistical mechanics of irreversible processes (see, e.g., Blum [1981], Kubo et al. [1985]) about the relaxation of initially nonequilibrium state of a particle in the presence of a reservoir (heat bath). If the particle is coupled to the reservoir weakly enough, then the properties of the latter are fully determined by the spectral characteristics of its susceptibility coefficients. 

This section is organized as follows in subsection A the approaches based on the assumption of heat bath statistical equilibrium and those which use the generalized Langevin equation are reviewed for the case of a bounded one-dimensional Brownian particle. A detailed analysis of the activation dynamics in both schemes is carried out by adopting AEP and CFP techniques. In subsection B we shall consider a case where the non-Markovian eharacter of the variable velocity stems from the finite duration of the coherence time of the light used to activate the chemical reaction process itself. 

Molecular dynamics with periodic boundary conditions is presently the most widely used approach for studying the equilibrium and dynamic properties of pure bulk solvent,97 as well as solvated systems. However, periodic boundary conditions have their limitations. They introduce errors in the time development of equilibrium properties for times greater than that required for a sound wave to traverse the central cell. This is because the periodicity of information flow across the boundaries interferes with the time development of other processes. The velocity of sound through water at a density of 1 g/cm3 and 300 K is 15 A/ps for a cubic cell with a dimension of 45 A, the cycle time is only 3 ps and the time development of all properties beyond this time may be affected. Also, conventional periodic boundary methods are of less use for studies of chemical reactions involving enzyme and substrate molecules because there is no means for such a system to relax back to thermal equilibrium. This is not the case when alternative ensembles of the constant-temperature variety are employed. However, in these models it is not clear that the somewhat arbitrary coupling to a constant temperature heat bath does not influence the rate of reequilibration from a thermally perturbed... 

For biochemically driven reactions, embedding heat bath provides the source of stochastic dynamics. The stochastic model, in the form of the chemical master equation, is an infinite system of mathematically coupled ordinary differential equations (Vellela and Qian, 2009). Assuming that tia and b are the number of substrate molecules, which are fixed for a fixed volume, and p (f) is the probability of having nX molecule at time t. The stochastic model equations are... 

In atomic scale simulations, there is often a clear separation of timescales. The rate of rare events, e.g., chemical reactions, in a system coupled to a heat bath can be estimated by evaluating the free energy barriers for the transitions. Transition State Theory (TST) [9] is the foundation for this approach. Due to the large difference in time scale between atomic vibrations and typical thermally induced processes such as chemical reactions or diffusion, this would require immense computational power to directly simulate dynamical trajectories for a sufficient period of time to include these rare events. Identification of transition states is often the critical step in assessing rates of chemical reactions and path techniques like the nudged elastic band method is often used to identify these states [10-12,109]. 

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