Accelerating rare events

Laio A, Parrinello M (2006) Computing free energies and accelerating rare events with metadynamics. In Ferrario M, Ciccotti G, Binder K (eds) Computer simulations in condensed matter from materials to chemical biology, vol 1, Springer. Berlin, Heidelberg, New York, pp 315-347... 

Computing Free Energies and Accelerating Rare Events with Metadynamics... 

A. Laio and M. Parrinello Computing Free Energies and Accelerating Rare Events with Metadynamics, Lect. Notes Phys. 703, 315—347 (2006)... 

VandeVondele J, Rothlisberger U, Accelerating Rare Reactive Events by Means of a Finite Electronic Temperature, J Am Chem Soc, 124, 8163-8171 (2002)... 

Mosey NJ, Hu A, Woo TK, Ab initio molecular dynamics simulations with a HOMO-LUMO gap biasing potential to accelerate rare reaction events, Chem Phys Lett, 373, 498—505 (2003)... 

Directed evolution bypasses the bottleneck of rational design and mimics natural evolution in a test tube to evolve proteins without knowledge of their structures. What fundamentally differentiates directed evolution from natural evolution is its power to significantly accelerate the process of evolution. As shown in Fig. 1, directed evolution uses various methods to generate a collection of random protein variants, called a library, at the DNA level. Followed by screening/selection of the library, protein variants with improvement in desired phenotypes are obtained. Usually, the occurrence of these functionally improved protein variants is a rare event thus, this two-step procedure has to be iterated several rounds until the goal is achieved or no further improvement is possible. 

In this subsection we examine the mechanism of the very fast diffusion. In the bulk medium the vacancies and interstitial site play a primary role in accelerating the diffusion. However, these diffusion mechanisms are not relevant in microclusters. It is well known that the vacancies created inside the cluster are immediately pushed to the surface. Indeed in our simulation the creation of vacancies inside the cluster is a very rare event even at the temperature close to the melting temperature. Moreover, we cannot find any evidence that the interstitial deformation takes place inside the cluster, and therefore neither of them is responsible for the rapid diffusion into the cluster. The key feature of the cluster that distinguishes the cluster from the bulk medium is that it is surrounded by the surface beyond which no atoms exist. In other words, the outside of the cluster is occupied by vacancies. As a result, the atoms on the surface move very actively along the surface. Such an active movement along the surface will be responsible for the rapid diffusion in the radial direction of the cluster. We focus our attention to the details of the active diffusive motion along the surface of the cluster, and we present a direct evidence that the surface activity controls the radial diffusion. A direct measure of the surface motion is the diffusion rate of the surface atoms... 

In principle, the relativistic winds of newly born magnetars (neutron stars with surface magnetic fields about 1015 G) can directly accelerate particles up to 1021 eV [48], [49] but they are very rare events in the Galaxy. 

We have also developed a second hybrid EF/CG scheme for use when the Hessian is unavailable [82]. A variational approach is used to find the smallest eigenvalue and corresponding eigenvector [127] Voter has recently employed a similar method to accelerate molecular dynamics simulations of rare events in solids [128]. 

Maragliano, L., Vanden-Eijnden, E. A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations, Chem. Phys. Lett. 2006,426,168-75. 

Accelerated Method for Sampling Free Energy and Determining Reaction Pathways in Rare Events Simulations. 

One of the primary goals for the understanding of crystallization of liquids and amorphous materials is to gain a microscopic picture of the nucleation processes. MTD, which accelerates the occurrence of rare events, appears to be well suited for this purpose. 

L. Maragliano and E. Vanden-Eijnden, Ghent. Phys. Lett., 426,168-175 (2006). A Temperature Accelerated Method for Sampling Free Energy and Determining Reaction Pathways in Rare Events Simulations. 

Prominent among the methods for exploring the atomic scale dynamics of a system, including relaxation and rare events, are temperature-accelerated dynamics (TAD) [39], hyperdynamics [40] and parallel replica [41], all developed by Voter and coworkers. These techniques build on statistical mechanics principles for infrequent event systems, and as such do not make any prior assumptions regarding the atomistic mechanisms. They are designed to simply allow the system to evolve more quickly from state to state than they would in normal MD, provided that the barriers are relatively high compared to kT. 

---