libAtoms / universalSOAP

heuristics to define SOAP parameters for the all chemical elements

universal-soap

scripts to create SOAP descriptors for arbitrary elements and combinations

Heuristics:

• Length scales
  • Atomic (inputs)
    • typical bond length (from equilibrium bond length in lowest energy 2D or 3D structure)
    • minimal bond length (from shortest bond length of any equilibrium structure, including dimer)
  • Pairs: typical and minimal length scales equal to the arithmetic mean of the two corresponding atomic length scales
• For each atomic number Z there is a set of length scales associated with it as the center, applying to all neighbor types
  • Typical Z-Z (homonuclear) bond length * 1.3
  • Add one spacing factor (currently 1.5) larger
  • Add additional shorter length scales, by factors of 1/spacing^n, as long as they are at least 1.3 times larger than shortest bond (over all Z_center-Z2 pairs)
  • If the longest bond times 1.3 is more than 1.1 times larger than the outermost length scale so far, add additional longer length scales, by factors of spacing^n, until the longest one is larger than 1.3 times longest bond (over all Z_center-Z2 pairs)
  • For each of these length scales there is an associated SOAP
    • The center of the cutoff transition, i,.e. cutoff - 0.5 transition, is equal to the length scale
    • The transition width is min(0.25 length_scale, 2 Angstrom)
    • The atom sigma is the length_scale / 8, divided by an optional sharpness factor

Files:

• length_scales.json: file with information on atomic length scales: minimum bond length, typical bond length, volume/atom. For each of these values there's also a string for information source (e.g. URL), and dict of other info/links

• universal_SOAPs.py: routines that actually compute length scales and corresponding SOAP hyper-params

  • descriptor_len_scales_for_center() - length scales for a given species as center in the presences of any number of neighbor species
  • SOAP_hypers() - returns dict of SOAP hyperparams (cutoff, cutoff_transition_width and atom_gaussian_width) with element atomic numbers as keys, and list of 3 entry dicts as values, one dict per SOAP descriptor/length scale

• write_descriptor_quantity_json: Executable that reads length_scales.json file and list of atomic numbers, and outputs json with per-descriptor cutoff, transition, and atom_gaussian_width values

Example

The command python write_descriptor_quantity_json --Zs 5 32 will return length scales needed to define the SOAP descriptors for a system with boron (5) and germanium (32). The output is

{"5": [{"cutoff": 2.6, "cutoff_transition_width": 0.64, "atom_gaussian_width": 0.32}, {"cutoff": 3.8, "cutoff_transition_width": 0.96, "atom_gaussian_width": 0.48}], "32": [{"cutoff": 3.8, "cutoff_transition_width": 0.94, "atom_gaussian_width": 0.47}, {"cutoff": 5.6, "cutoff_transition_width": 1.4, "atom_gaussian_width": 0.7}]}

So three SOAPs each the boron-centered and the germanium-centered descriptors, with cutoffs, cutoff_transition_widths and atom_gaussian_widths parameters given.