Permutation invariant potential energy surfaces for polyatomic reactions using atomistic neural networks

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Abstract

The applicability and accuracy of the Behler-Parrinello atomistic neural network method for fitting reactive potential energy surfaces is critically examined in three systems, H + H2 → H2 + H, H + H2O → H2 + OH, and H + CH4 → H2 + CH3. A pragmatic Monte Carlo method is proposed to make efficient choice of the atom-centered mapping functions. The accuracy of the potential energy surfaces is not only tested by fitting errors but also validated by direct comparison in dynamically important regions and by quantum scattering calculations. Our results suggest this method is both accurate and efficient in representing multidimensional potential energy surfaces even when dissociation continua are involved.

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Atom-centered symmetry functions for constructing high-dimensional neural network potentials.

Jörg Behler (2011)

Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calculations, and thus enable molecular dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the atomic positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as molecules, crystalline and amorphous solids, and liquids.