Behler–Michele Parrinell symmetry functions
Behler & Parrinello (2007):
The cutoff function is given by
The radial term is given by
The angular term is given by
- ANI (e.g., TorchANI, Neurochem) uses a heavily modified version of the Behler and Parrinello symmetry functions (Smith et al., 2017).
- ænet use the BP’s symmetry functions + smooth overlap of atomic positions (SOAP) approach (Artrith et al., 2017).
- Artrith, N., Urban, A., & Ceder, G. (2017). Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species. Physical Review B, 96(1), 014112. https://doi.org/10.1103/PhysRevB.96.014112
- Behler, J., & Parrinello, M. (2007). Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces. Physical Review Letters, 98(14), 146401. https://doi.org/10.1103/PhysRevLett.98.146401
- Smith, J. S., Isayev, O., & Roitberg, A. E. (2017). ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost. Chemical Science, 8(4), 3192–3203. https://doi.org/10.1039/C6SC05720A