  This paper is committed to investigate an extension of the classical adaptive
biasing force method, which is used to compute the free energy related to the
Boltzmann-Gibbs measure and a reaction coordinate function. The issue of this
technique is that the approximated gradient of the free energy, called biasing
force, is not a gradient. The commitment to this field is to project the
estimated biasing force on a gradient using the Helmholtz decomposition. The
variance of the biasing force is reduced using this technique, which makes the
algorithm more efficient than the standard ABF method. We prove exponential
convergence to equilibrium of the estimated free energy, with a precise rate of
convergence in function of Logarithmic Sobolev inequality constants.
