An iterative scheme to derive pair potentials from structure factors and its application to liquid mercury

Transferable Force Fields from Experimental Scattering Data with Machine Learning Assisted Structure Refinement

Deriving transferable pair potentials from experimental neutron and X-ray scattering measurements has been a longstanding challenge in condensed matter physics. State-of-the-art scattering analysis techniques estimate real-space microstructure from reciprocal-space total scattering data by refining pair potentials to obtain agreement between simulated and experimental results. Prior attempts to apply these potentials with molecular simulations have revealed inaccurate predictions of thermodynamic fluid properties. In this Letter, a machine learning assisted structure-inversion method applied to neutron scattering patterns of the noble gases (Ne, Ar, Kr, and Xe) is shown to recover transferable pair potentials that accurately reproduce both microstructure and vapor-liquid equilibria from the triple to critical point. Therefore, it is concluded that a single neutron scattering measurement is sufficient to predict macroscopic thermodynamic properties over a wide range of states and provide novel insight into local atomic forces in dense monatomic systems.

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.

Interactions from diffraction data: historical and comprehensive overview of simulation assisted methods

A large part of statistical mechanics is concerned with the determination of condensed matter structure on the basis of known microscopic interactions. An increasing emphasis has been put on the opposite situation in the last decades as well, where structural data, e.g. pair-distance statistics, are known from diffraction experiments, and one looks for the corresponding interaction functions. The solution of this inverse problem was searched for within the integral equation theories of condensed matter in the early investigations, but before long computer simulation assisted methods were suggested. The interest in this field showed an increasing trend after some attempts appeared in the late 1980s. Several methods were published in the 1990s, and one-two methods appear annually nowadays. In this paper a comprehensive and historical overview is given on the solution of the inverse problem with simulation assisted methods. Emphasis is put on the theoretical grounds of the methods, on the choice of possible input structural functions, on the numerically local or global schemes of the potential modifications, on some advantages and limits of the different methods and on the scientific impact of the methods.

An effective pair potential for thermodynamics and structural properties of liquid mercury

The properties of liquid mercury are investigated by using an empirical effective pair potential. Its parameters are determined with the aid of Monte Carlo simulation along the liquid branch of the liquid-vapor coexistence curve. The complexity of the electronic structure of dense metal mercury supposes a state dependence of the interatomic interactions, while no more state dependence is found in the metal-nonmetal transition region. It is shown that the use of this effective potential leads to an accurate description of the structural and thermodynamic properties of the expanded liquid mercury. Then, the melting and freezing phenomena are investigated with that potential. Sharp melting and freezing temperatures are observed at 234 and 169 K, respectively. This large hysteresis loop between freezing and melting is consistent with the experiments for the bulk mercury.

Pair potentials from diffraction data on liquids: A neural network solution

The inverse theorem of liquids states a one to one correspondence between classical mechanical pair potentials and structural functions. Molecular-dynamics and Monte Carlo simulations provide exact structural functions for known pair interactions. There is no exact or widespread method in the opposite direction, where the pair interactions are to be determined from a priori known pair-correlation functions or structure factors. The methods based on the integral equation theories of liquids are approximate and the iterative refinements of pair potentials with simulations take a long time. We applied artificial neural networks to get pair interactions from known structure factors in this study. We performed molecular-dynamics simulations on one-component systems with different pair potentials and the structure factors were calculated. To optimize (train) the weights of neural networks 2000 pair interaction-structure factor pairs were used. The performance of the method was tested on further 200 data pairs. The method provided reasonable potentials for the majority of the systems opening a "quick and dirty" method to determine pair interactions.

Determination of effective pair interactions from the structure factor

In this work we present an efficient procedure to evaluate effective pair potentials, compatible with "experimental" structure factors, using a Monte Carlo simulation scheme. The procedure does not require the use of inverse Fourier transforms and is robust and rapidly convergent. As a test case the structure factor of liquid Selenium obtained from a Tight-Binding Molecular Dynamics simulation is inverted to obtain an effective pair potential and, as a by-product, the pair distribution function. The inversion procedure yields a pair structure in perfect agreement with the original molecular dynamics calculations and the analysis of the triplet structure and the dynamics also illustrates the limitations of the use of pair potentials in the description of liquids with strongly directional bonding, such as the covalent liquid Selenium.