A method of extracting useful information from the free-energy profiles

A free-energy profile helps in comparing the stability of different states that are distinguished by an order parameter. The selection of order parameter generally depends upon the molecular insight that one desires,... [ view full abstract ]

A free-energy profile helps in comparing the stability of different states that are distinguished by an order parameter. The selection of order parameter generally depends upon the molecular insight that one desires, and the ease of computation. We discuss a generic method to relate the shape of a free-energy profile to the molecular processes that accompany the change in the order parameter. We use the observation that an order parameter can be expressed as a linear combination of multiple parameters of the system. If we select one of these parameters and plot the free-energy as its function by keeping others constant, then the resulting profile will have the same shape as the original. Depending on the selected parameter, generalized ensembles (Jaynes, E. T., Physical review 106, 620) and Legendre transformations enable us to relate the geometric features of this new profile to the ensemble-averages and fluctuations of certain molecular-scale properties. We demonstrate the application of our method to the profile of free-energy vs distance between two Lennard-Jones solutes in Lennard-Jones solvent.