Many chemical systems, notably those in condensed matter and in biology,
are characterized by the presence of multiple low energy states which
are separated by large barriers. The presence of these barriers prevents
exploration of all of configuration space during the relatively short timescales
accessible in molecular dynamics (MD) simulations. Typically this means
that only those configurations in a small, locally ergodic region in the vicinity
of the input structure are visited.
One trick that is commonly used to resolve this problem is to add a
simulation bias in order to force the interesting, rarer events to occur. This
simulation bias forces the value of some particularly interesting collective
variable (CV) to change more rapidly than it otherwise would. This is a very
good strategy when you have a reasonable understanding of what occurs during
your rare event and when you can encode what happens mathematically.
For instance, to study a process such as nucleation you simply have to find
a differentiable quantity that distinguishes between configurations where the
ions are distributed uniformly across the simulation cell from those in which
the ions are bunched together in a crystalline nucleus. To develop coordinates
for complicated problems such as these we are involved with the development
of a code called plumed 2.0. Already we are using this code to find new CVs
that can be used to study nucleation and to study how water molecules enter
the ionic channels in large protein molecules.
Contour plots showing the potential energy + the current bias at selected
points along a Reconnaissance Metadynamics trajectory for a particle diffusing about
a 2D potential energy surface. The black dots indicate the positions of the snapshots
accumulated from the trajectory while the red ellipses indicate the basins found using the
PPCA algorithm. Blue ellipses are those basins, found during previous PPCA analyses,
to which hills are being added.
We are also working on methods where you do not have an accurate
description of the rare events in advance. In particular, we have a method
called reconnaissance metadynamics  that finds CVs automatically and
have applied it to problems in protein folding , drug docking  and cluster
The locations of the various basins found during a reconnaissance metadynamics
simulation of the Lennard-Jones 7 cluster plotted as a function of the second and third
moments of the distribution of coordination numbers and the index of the atom with the
highest coordination number. Also shown is a free energy surface calculated using a well-
tempered metadynamics simulation that employed the second and third moments of the
distribution as collective coordinates. Each basin is represented by a circle with an area
that is proportional to the bias at its center.
The code we use to do these sorts of calculations can be downloaded from
 G. A. Tribello, M. Ceriotti and M. Parrinello. Proceedings of the National
Academy of Sciences, 107(41), 17509–17514 (2010).
 P. Soderhjelm, G. A. Tribello and M. Parrinello. Proceedings of the
National Academy of Sciences, 109(14), 5170–5175 (2012).
 G. A. Tribello, J. Cuny, H. Eshet and M. Parrinello. Journal of Chemical
Physics, 135(11), 114109 (2011).