Structural analysis and potential extraction from diffraction data of disordered systems by least-biased feature matching.

Determining the structure and underlying potential from the experiment data is an important task in the study of disordered systems such as liquids and glasses. In this article, a new approach to tackle this problem is proposed. This method can iteratively refine any interaction potential u with the form of a fixed potential ψ added by a dot product between adjustable parameter θ and some functions of atomic coordinates called features f (i.e., potential u = ψ + θ · f). The updating rule for parameters is very simple as it only uses the difference of the ensemble mean of f between the simulation box and experiment. The solution found by this method minimizes the Kullback-Leibler divergence of the atomic distribution under the parameterized potential u and the prior potential ψ, subject to the condition that the ensemble mean of f of the simulation box is equal to its experimental value, ensuring that the potential given will be the least biased one from the prior potential but still consistent with the experiment. It is also shown that this method approximately minimizes the squared difference between the parameterized potential and the unknown true potential. Furthermore, the flexibility of the potential functional form allows the potential to be automatically fitted to some convenient forms or to encode additional known properties of the system under study. The method is tested on Lennard-Jones liquid as well as SiO2 liquid and glass for potential extraction or structure refinement using simulated data and real experiment data. Good results are obtained for both systems.