Bridging the Time Scale Gap with Transition Path Sampling Christoph Dellago 1 and David Chandler 2 1 Department of Chemistry, University of Rochester, Rochester, New York 14627, USA 2 Department of Chemistry, University of California, Berkeley, California 94720, USA Abstract Transition path sampling is a methodology which overcomes both the long timescale problem and the lack of prior knowledge about transition mecha- nisms. Here we briefly review the basic principles of transition path sampling, illustrate its application using autoionization in liquid water, and emphasize the capabilities and limitations of the methodology. 1 Why transition path sampling is needed Many interesting processes in nature are characterized by the presence of differ- ent relevant time scales. In a chemical reaction, for instance, the reaction time can be many orders of magnitudes longer than the molecular vibration period usually measured in units of femtoseconds [1]. Such a separation of time scales creates serious problems for the computer simulation: on one hand the resolution in time needs to be fine enough to capture the properties of fast motions (such as molecular oscillations) and on the other hand the simulation must be extended to times longer then the longest relevant time scale in order to observe the events of interest (such as chemical reactions). This is the notorious time scale gap prob- lem addressed in this conference. It is not only a problem in chemical physics. For example some comets exhibit rapid transitions between heliocentric orbits inside and outside the orbit of Jupiter [2]. While the transition, during which the comet transiently orbits Jupiter for a few periods, is swift, many revolutions of the comet around the sun can occur between transition. Often, widely separated time scales are caused by energy (or free energy) barriers preventing the system from quickly visiting a representative sample of pertinent configurations. In the past, many efficient computer simulation tech- niques [3] such as umbrella sampling [4], the multiple histogram method [5], and, most recently, the Laio-Parrinello approach [6], to mention just a few, have been developed to overcome such barriers and sample the free energy surface for a specified control parameter (or order parameter). While biasing schemes of this sort can be used to determine structural quantities such as chemical potentials and equilibrium constants, they are of limited use if one wishes to study the