Drift-oscillatory steering with the forward-reverse method for calculating the potential of mean force

We present a method that enables the use of the forward-reverse (FR) method of Kosztin et al. on a broader range of problems in soft matter physics. Our method, which we call the oscillating forward-reverse (OFR) method, adds an oscillatory steering potential to the constant velocity steering potential of the FR method. This enables the calculation of the potential of mean force (PMF) in a single unidirectional oscillatory drift, rather than multiple drifts in both directions as required by the FR method. By following small forward perturbations with small reverse perturbations, the OFR method is able to generate a piecewise reverse path that follows the piecewise forward path much more closely than any practical set of paths used in the FR method. We calculate the PMF for four different systems: a dragged Brownian oscillator, a pair of atoms in a Lennard-Jones liquid, a Na(+)-Cl⁻ ion pair in an aqueous solution, and a deca-alanine molecule being stretched in an implicit solvent. In all cases, the PMF results are in good agreement with those published previously using various other methods, and, to our knowledge, we give for the first time PMFs calculated by nonequilibrium methods for the Lennard-Jones and Na(+)-Cl⁻ systems.