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