  The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic
potential that expresses the energy of each atom as a linear function of
selected bispectrum components of the neighbor atoms. An extension of the SNAP
form is proposed that includes quadratic terms in the bispectrum components.
The extension is shown to provide a large increase in accuracy relative to the
linear form, while incurring only a modest increase in computational cost. The
mathematical structure of the quadratic SNAP form is similar to the embedded
atom method (EAM), with the SNAP bispectrum components serving as counterparts
to the two-body density functions in EAM. The effectiveness of the new form is
demonstrated using an extensive set of training data for tantalum structures.
Similarly to artificial neural network potentials, the quadratic SNAP form
requires substantially more training data in order to prevent overfitting. The
quality of this new potential form is measured through a robust
cross-validation analysis.
