Barrier crossing

Kramers solution of the barrier crossing problem [45] is discussed at length in chapter A3.8 dealing with condensed-phase reaction dynamics. As the starting point to derive its simplest version one may use the Langevin equation, a stochastic differential equation for the time evolution of a slow variable, the reaction coordinate r, subject to a rapidly statistically fluctuating force F caused by microscopic solute-solvent interactions under the influence of an external force field generated by the PES F for the reaction... 

The key quantity in barrier crossing processes in tiiis respect is the barrier curvature Mg which sets the time window for possible influences of the dynamic solvent response. A sharp barrier entails short barrier passage times during which the memory of the solvent environment may be partially maintained. This non-Markov situation may be expressed by a generalized Langevin equation including a time-dependent friction kernel y(t) [ ]... 

As a multidimensional PES for the reaction from quantum chemical calculations is not available at present, one does not know the reason for the surprismg barrier effect in excited tran.s-stilbene. One could suspect diat tran.s-stilbene possesses already a significant amount of zwitterionic character in the confomiation at the barrier top, implying a fairly Tate barrier along the reaction path towards the twisted perpendicular structure. On the other hand, it could also be possible that die effective barrier changes with viscosity as a result of a multidimensional barrier crossing process along a curved reaction path. 

Schroeder J and Troe J 1993 Soivent effects in the dynamics of dissociation, recombination and isomerization reactions Activated Barrier Crossing ed G R Fieming and P Hanggi (Singapore Worid Scientific) p 206... 

Larson R S 1986 Simulation of two-dimensional diffusive barrier crossing with a curved reaction path Physica A 137 295-305... 

Agmon N and Kosloff R 1987 Dynamics of two-dimensional diffusional barrier crossing J. Phys. Chem. 91 1988-96... 

Mohrschladt R, Schroeder J, Troe J, Vdhringer P and Votsmeier M 1994 Solvent influence on barrier crossing in the S. -state of c/s- and trans- st ff stiibene Ultrafast Phenomena /Xed P F Barbara et al (New York Springer) pp 499-503... 

Fleming G and Hanggi P (eds) 993 Activated Barrier Crossing (New Jersey World Scientific)... 

Haynes G R, Voth G A and Poliak E 1994 A theory for the activated barrier crossing rate constant in systems influenced by space and time dependent friction J. Chem. Phys. 101 7811... 

Haynes G R and Voth G A 1995 Reaction coordinate dependent friction in classical activated barrier crossing dynamics when it matters and when it doesn t J. Chem. Phys. 103 10 176... 

Borkovec M and Berne B J 1987 Activated barrier crossing for many degrees of freedom corrections to the low friction result J. Chem. Phys. 86 2444... 

Gershinsky G and Berne B J 1999 The rate constant for activated barrier crossing the competition between IVR and energy transfer to the bath J. Chem. Phys. 110 1053... 

Ruiz-Montero M J, Frenkel D and Brey J J 1997 Efficient schemes to compute diffusive barrier crossing rates Mol. Phys. 90 925-41... 

Transition State Theory for Rates of Barrier Crossing... 

The time for classical simulated annealing increases exponentially as a function of the ratio of the energy scales /AU. However, for 5 > 1 the situation is qualitatively different. As a result of the weak temperature dependence in the barrier crossing times, the time for simulated annealing increases only weakly as a power law. 

In HMC the momenta are constantly being refreshed with the consequence that the accompanying dynamics will generate a spatial diffusion process superposed on the ini rtial dynamics, as in BGK or Smoluchowski dynamics. It is well known from the theory of barrier crossing that this added spatial... 

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