Abstract
In this paper, we consider the problem of finding the energy minimum of the aggregate of atoms of a fragment of a planar crystal lattice. To calculate the energy, the Brennor or REBO (reactive empirical bond order) method is used. The REBO potential is calculated using the LAMMPS package (Large-scale Atomic / Molecular Massively Parallel Simulator). As optimization methods, both the gradientless methods and the methods using the first derivatives of the functional are used. To calculate the derivatives, the combined differentiation method, implemented in the LAMMPS package, is used, using sequentially forward and reverse methods of fast automatic differentiation.
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