The quantity 17(f) is the time-dependent friction kernel. It characterizes the dissipation effects of the solvent motion along the reaction coordinate. The dynamic solute-solvent interactions in the case of charge transfer are analogous to the transient solvation effects manifested in C(t) (see Section II). We assume that the underlying dynamics of the dielectric function for BA and other molecules are similar to the dynamics for the coumarins. Thus we quantify t](t) from the experimental C(t) values using the relationship discussed elsewhere [139], The solution to the GLE is in the form of p(z, t), the probability distribution function. [Pg.52]

A critical assumption in Eq. (2) is that the friction kernel y(t) is independent of the position s. However, it is now known from numerical simulations that for some reactions in solution this assumption is violated. [Pg.82]

Friction interactions, multiparticle collision dynamics, single-particle friction and diffusion, 114—118 Friction kernel, transition state trajectory, colored noise, 209 [Pg.280]

Fix the proton at some position s and run a MD simulation. The friction kernel is calculated from the force-force correlation function. [Pg.84]

In this equation, m. is the effective mass of the reaction coordinate, q(t -1 q ) is the friction kernel calculated with the reaction coordinate clamped at the barrier top, and 5 F(t) is the fluctuating force from all other degrees of freedom with the reaction coordinate so configured. The friction kernel and force fluctuations are related by the fluctuation-dissipation relation [Pg.889]

We should point out that Eq. (42) indicates that the function G(s) can be obtained from the value of the friction kernel at t = 0. This is a consequence of the fact that the friction kernel is calculated in the clamping approximation. In any case, Eq. (42) allows for the calculation of G(s) without the numerical difficulties that plague the long-time tail of molecular dynamics simulations. [Pg.83]

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely [Pg.852]

There are two primary associations that must be made between the polymer systems and the iGLE (i) the construction of the potential of mean force (PMF), and (ii) characterization of the nonstationary friction kernel by way of g(t). [Pg.106]

This phenomenological treatment, however, can be extended to include other quenching mechanisms. For example, living polymers are known to quench when the monomers are reacted to completion. In the context of the iGLE, a friction kernel that would simulate such a mechanism is the addition of the term. [Pg.107]

See also in sourсe #XX -- [ Pg.16 ]

See also in sourсe #XX -- [ Pg.388 ]

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