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Scientific Report 2007-2009<br />
Condensed matter physics and biophysics<br />
C22. Computer simulation of rare events and non-equilibrium<br />
phenomena<br />
Computational physics, in particular molecular dynamics<br />
(MD), adopts an atomistic representation of matter,<br />
with model or ab initio interaction potentials, and<br />
solves numerically the evolution equations of the system.<br />
Statistical mechanics links the microscopic evolution to<br />
macroscopic properties and provides the framework to<br />
employ simulations to understand and control materials<br />
by acting at the nano-scale. Our group develops<br />
methods to make simulations more effective theoretical<br />
tools and applies them to investigate condensed matter.<br />
Two important areas of research are rare events and nonequilibrium<br />
MD.<br />
Rare events are characterized by time-scales much<br />
longer than those accessible by brute force MD. In an<br />
appropriate set of collective variables, they can be described<br />
as transitions, over barriers higher than the thermal<br />
energy of the system, among metastable states of<br />
the free energy landscape. Chemical reactions, phase<br />
transformations, nucleation processes, and conformational<br />
changes related to the functionality of proteins<br />
are just a few examples of rare events. In collaboration<br />
with Eric Vanden-Eijnden (Courant Institute for Mathematical<br />
Studies), our group has contributed to establishing<br />
a set of methods that, appropriately combined,<br />
determine the most relevant aspects of rare events: free<br />
energy landscape, rate, mechanism. Recently, we used<br />
these methods to characterize the short-range diffusion<br />
of hydrogen in sodium alanates [1], prototypical materials<br />
for building safe and cost-effective storage devices for<br />
using hydrogen to fuel sustainable vehicles. The same<br />
kinetics of phase transitions in the Ising model [2].<br />
Non-equilibrium MD. Perturbing a system from<br />
equilibrium is a common experimental method to study<br />
its properties. Transport coefficients (shear and bulk<br />
viscosity, thermal conductivities etc.) are often measured<br />
by creating a flow (of momentum, energy, etc.)<br />
in the material. Standard MD cannot be used directly<br />
to simulate a system in non-equilibrium conditions. A<br />
few years ago, we introduced a method, the dynamical<br />
approach to non-equilibrium (D-NEMD), that allows<br />
to obtain rigorous ensemble averages for properties of<br />
a non-stationary system out of equilibrium via MD<br />
trajectories. D-NEMD can be used to study both the<br />
steady state and the transient evolution of a system<br />
out of an initial stationary state and it can be applied<br />
also in the presence of a time-dependent perturbation<br />
that takes the system to a non-equilibrium final state.<br />
Calculations of the bulk viscosity of the triple point<br />
Lennard-Jounes fluid were performed [3] to prove the<br />
accuracy of the method compared with Green-Kubo<br />
estimates. More recently, the method has been applied<br />
Figure 2: Snapshots of the velocity field in the 2d fluid at<br />
successive times during the D-NEMD simulation [4]. The<br />
development of the velocity roll in panel (d) reflects the response<br />
of the system, initially in a steady state under the<br />
effect of a thermal gradient (panel (a)), to the ignition of<br />
gravity. The system here is heated from below.<br />
to study the transient leading to the formation of a<br />
convective cell which appears in a two dimensional fluid<br />
under the combined action of a thermal gradient and of<br />
gravity[4].<br />
Figure 1: CO diffusion in myoglobin. The yellow curves are<br />
the most likely migration paths, while the arrows locate CO<br />
exits to the solvent. The white and black spheres indicate,<br />
respectively, the free energy barriers and minima along the<br />
pathways. The protein backbone is represented as ribbons<br />
and the heme as sticks.<br />
methods were employed to map the exit pathways and<br />
the binding sites of CO in myoglobin and to study the<br />
References<br />
1. M. Monteferrante et al., Sc. Model. Sim. 35, 187 (2008).<br />
2. M. Venturoli et al., J. Math. Chem. 45, 188 (2009).<br />
3. P. L. Palla et al., Phys. Rev. E 78, 021204 (2008).<br />
4. M. L. Mugnai et al., J. Chem. Phys. 131, 064106 (2009).<br />
Authors<br />
G. Ciccotti 7 , S. Caprara, S. Bonella 7 , M. Monteferrante<br />
http://abaddon.phys.uniroma1.it/<br />
<strong>Sapienza</strong> Università di Roma 75 Dipartimento di Fisica