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A molecular dynamic simulation requires the local potential energy per atom because it provides the force applied to each atom. On the other hand, an electronic structure computation provides only the global potential energy of an atomic system. We propose a stochastic fitting for deducing a potential from a total energy which can be incorporated inside a molecular dynamic program. The objective of that fitting process is twofold. First, the total energy can be reproduced with a sufficient accuracy. In addition, we want to separate the potential energy into atomic contributions. The only inputs in the stochastic regression are the total energies of the atomic systems. As for the applications, we examine the performance of the method with the help of a mathematical model. Afterward, we use it for quantum applications in which we compare the direct method and the unobserved fitting with respect to the energy conservations. For a molecular dynamic application, we examine the atomic cluster formations during freezing when the proposed potential is used. Although the method is generally applicable, we restrict in this paper to total energies which are reproduced from two-body potentials for the molecular dynamic simulation.

Molecular Dynamics for Two-Body Potential from Unobserved Gaussian Regression