  We develop an efficient sampling and free energy calculation technique within
the adaptive biasing potential (ABP) framework. By mollifying the density of
states we obtain an approximate free energy and an adaptive bias potential that
is computed directly from the population along the coordinates of the free
energy. Because of the mollifier, the bias potential is "nonlocal" and its
gradient admits a simple analytic expression. A single observation of the
reaction coordinate can thus be used to update the approximate free energy at
every point within a neighborhood of the observation. This greatly reduces the
equilibration time of the adaptive bias potential. This approximation
introduces two parameters: strength of mollification and the zero of energy of
the bias potential. While we observe that the approximate free energy is a very
good estimate of the actual free energy for a large range of mollification
strength, we demonstrate that the errors associated with the mollification may
be removed via deconvolution. The zero of energy of the bias potential, which
is easy to choose, influences the speed of convergence but not the limiting
accuracy. This method is simple to apply to free energy or mean force
computation in multiple dimensions and does not involve second derivatives of
the reaction coordinates, matrix manipulations nor on-the-fly adaptation of
parameters. For the alanine dipeptide test case, the new method is found to
gain as much as a factor of ten in efficiency as compared to two common
adaptive biasing force formulations and it is shown to be as efficient as
well-tempered metadynamics with the post-process deconvolution giving a clear
advantage to the mollified density of states method.
