  The ability of widely used sampling methods, such as molecular dynamics or
Monte Carlo, to explore complex free energy landscapes is severely hampered by
the presence of kinetic bottlenecks. A large number of solutions have been
proposed to alleviate this problem. Many are based on the introduction of a
bias potential which is a function of a small number of collective variable.
However constructing such a bias is not simple. Here we introduce a functional
of the bias potential and an associated variational principle. The bias that
minimizes the functional relates in a simple way to the free energy surface.
This variational principle can be turned into a practical, efficient and
flexible sampling method. A number of numerical examples are presented which
include the determination of a three dimensional free energy surface. We argue
that, beside being numerically advantageous, our variational approach provides
a convenient standpoint for looking with novel eyes at the sampling problem.
