Transition pathway

Chandler D 1998 Finding transition pathways throwing ropes over rough mountain passes, in the dark Classical and Quantum Dynamics In Condensed Phase Simulations (Singapore World Scientific) pp 51-66... 

How can the continuous transition pathway l(r) be represented by a computer for a complex molecular system l(r) can be approximately represented as a set of configurations of the system rj,. ... 

This discretized path allows us to represent the transition pathway numerically as a set of discrete configurations of the system. 

Pratt [43] made the innovative suggestion that transition pathways could be determined by maximizing the cumulative transition probability connecting the known reactant and product states. That is, the most probable transition pathways would be expected to be those with the largest conditional probability. 

In many cases, it is also helpful to have the path repel itself so that the transition pathway is self-avoiding. An acmal dynamic trajectory may oscillate about a minimum energy configuration prior to an activated transition. In the computed restrained, selfavoiding path, there will be no clusters of intermediates isolated in potential energy minima and no loops or redundant segments. The self-avoidance restraint reduces the wasted effort in the search for a characteristic reaction pathway. The constraints and restraints are essential components of the computational protocol. 

Figure 8 An accurate estimate of the barrier height can be found by adding a sufficient number of intermediate points in the discretized transition pathways. The solid line in the graph represents the energy profile for a reaction path described by 11 intermediate configurations of the system. The dashed line shows a coarse pathway described by only two intermediate configurations. The latter path underestimates the true energy ban ier.

Start from a straight line path as the first guess at the transition pathway connecting known reactant and product structures. 

Make that lowest energy point a permanent intermediate point on the transition pathway. 

Figure 9 The refinement of an initial straight line path to a smooth transition pathway using the conjugate peak refinement algorithm. The initial guess is a straight line path. That path is refined by the addition of an intermediate point (the long-stemmed arrow). Two additional intermediates are added to create a path of three intermediates before four more intermediates are inserted. The process can be continued until the desired level of smoothness m the transition pathway is obtained.

Weinan, E. Vanden-Eijnden, E., in Multiscale Modelling and Simulation, LNCSE 39, 2004 (chapter Metastability, conformation dynamics, and transition pathways in complex systems)... 

Csajka, F. S. Chandler, D., Transition pathways in a many-body system application to hydrogen-bond breaking in water, J. Chem. Phys. 1998,109, 1125-1133... 

The overall objective of these studies is to unravel mechanisms of interfacial PT. This requires identification of collective coordinates (or reaction coordinates) and transition pathways of transferring protons. Differences in activation energies and rates of corresponding mechanism due to distinct polymer constituents, acid head groups, side chain lengths, side chain densities, and levels of hydration have to be examined. Comparison with experimental... 

A problem that has become more evident in recent years, however, is that for many systems of interest there is a complexity that makes it difficult, if not impossible, to determine all the relevant reaction paths to which TST should be applied. This is a serious issue, as omitted transition pathways can have uncontrollable consequences on the simulated long-time kinetics. 

Sato, K., et al. 1993. Generation and transit pathway of H+ is critical for inhibition of palmar sweating by iontophoresis in water. J Appl Physiol 75 2258. 

Tang M, Carter WC, Belak JF, Chiang Y-M. Modeling the competing phase transition pathways in nanoscale olivine electrodes. Electrochim Acta. 2010 56 969-76. 

FIGURE 8.3 Energy levels for a two-spin system, /, S, showing the six possible transition pathways. 

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