Atomic Fingerprints
Atomic fingerprints (descriptors) encode an atom’s local environment within a cutoff radius as a vector that is invariant to translation, rotation and permutation of neighbors, for use as input to machine-learned potentials and property models. Common handcrafted choices include Behler-Parrinello G2 (radial) and G4 (angular) symmetry functions, SOAP and bispectrum coefficients, while graph networks learn their own representations from atom types and distances.
Element-weighted symmetry functions (2020)
Liu and Kitchin noted that standard symmetry functions scale with the number of elements (N radial and N(N+1)/2 angular functions per parameter set), making fingerprints of different chemistries incompatible. They used weighted symmetry functions in which each neighbor or neighbor pair is multiplied by an element-dependent weight, so the fingerprint length is set only by the η, γ and ζ values. Of atomic number, covalent radius and Allen electronegativity as weights, electronegativity performed best for a six-element data set, and they found that rescaling fingerprints to [0, 1] was important for accurate training (Liu 2020). Summary: liu2020.
Pseudo-atom site fingerprints for adsorption energies (2021)
To predict acrolein adsorption energies on AgPd(111), a pseudo-atom was placed at each top, bridge or hollow site and described with the same Behler-Parrinello symmetry functions used for real atoms; a new site took the pseudo-adsorption energy of its nearest neighbor in fingerprint space among 287 unique labeled sites (Liu et al. 2021). Leave-one-out RMSE was 0.100 eV overall (0.038 eV for top sites), which the authors attribute partly to periodic-image effects in the small training cells. Summary: liu2021.