  Determining the kinetic bottlenecks that make transitions between metastable
states difficult is key to understanding important physical problems like
crystallization, chemical reactions, or protein folding. In all these
phenomena, the system spends a considerable amount of time in one metastable
state before making a rare but important transition to a new state. The rarity
of these events makes their direct simulation challenging, if not impossible.
We propose a method to explore the distribution of configurations that the
system passes as it translocates from one metastable basin to another. We shall
refer to this set of configurations as the transition state ensemble. We base
our method on the committor function and the variational principle to which it
obeys. We find the minimum of the variational principle via a self-consistent
procedure that does not require any input besides the knowledge of the initial
and final state. Right from the start, our procedure focuses on sampling the
transition state ensemble and allows harnessing a large number of such
configurations. With the help of the variational principle, we perform a
detailed analysis of the transition state ensemble, ranking quantitatively the
degrees of freedom mostly involved in the transition and opening the way for a
systematic approach for the interpretation of simulation results and the
construction of collective variables.
