Tackling the time-scale problem in molecular dynamics simulations of rare events: the temperature-accelerated dynamics method

Francesco Montalenti
Università di Milano - Bicocca
Dipartimento di Scienza dei Materiali

1L-NESS, CNR/INFM, and Dipartimento di Scienza dei Materiali, Università di Milano-
Bicocca, Milan (Italy).

A wide variety of fundamental phenomena in physics, chemistry and materials science is determined by a sequence of rare events. A typical example is given by diffusion and growth at solid surfaces, where ad-atoms spend most of their time vibrating around equilibrium positions before finally jumping to a nearby site. Under rather typical experimental conditions, the time scale of the diffusion events can be as long as 10??3-100 s, i.e. at least 5-8 orders of magnitude larger than the time scale achieved by classical molecular dynamics simulations. The problem is well recognized by the atomistic-simulation community and in the last few years several possible ways for overcoming this problem were proposed (for a review see [1]). In this talk, I should describe the perhaps most promising accelerated molecular dynamics method, called temperature-accelerated dynamics (TAD). The method, whose only requirement is the validity of the harmonic approximation to the transition state theory, allows one to simulate rare-events based evolution at low temperatures at the typical experimental time scale. No a priori knowledge of the microscopic diffusion mechanisms is required. After presenting the most important aspects of TAD, I shall show how further acceleration in the dynamics can be gained if an estimate of the minimum possible barrier is available in a given state.

The application of the method to metals' thin-Film growth phenomena [2] and to radiation damage in MgO [3] revealed the importance of unexpected many-atom diffusion mechanisms, which will be illustrated in detail. While most of the applications of the TAD method, so far, have been based on the use of classical semi-empirical potentials, encouraging preliminary results were recently obtained within a more refined tight-binding approach [4].

[1] A.F. Voter, F. Montalenti, and T.C. Germann, Ann. Rev. Mater. Res 32, 321 (2002).
[2] F. Montalenti, M.R. Sørensen, and A.F. Voter, Phys. Rev. Lett. 87, 126101 (2001).
[3] B. P. Uberuaga et al, Phys. Rev. Lett. 92, 115505 (2004).
[4] M. Cogoni et al, Phys. Rev. B 71, 121203 (2005).

Back to Workshop II: Multiscale Modeling in Condensed Matter and Materials Sciences, including Mini-Workshop: Time Acceleration Methods in Atomistic Simulations