  Many enhanced sampling techniques rely on the identification of a number of
collective variables that describe all the slow modes of the system. By
constructing a bias potential in this reduced space one is then able to sample
efficiently and reconstruct the free energy landscape. In methods like
metadynamics, the quality of these collective variables plays a key role in
convergence efficiency. Unfortunately in many systems of interest it is not
possible to identify an optimal collective variable, and one must deal with the
non-ideal situation of a system in which some slow modes are not accelerated.
  We propose a two-step approach in which, by taking into account the residual
multiscale nature of the problem, one is able to significantly speed up
convergence. To do so, we combine an exploratory metadynamics run with an
optimization of the free energy difference between metastable states, based on
the recently proposed variationally enhanced sampling method. This new method
is well parallelizable and is especially suited for complex systems, because of
its simplicity and clear underlying physical picture.
