Figure 7.

Descriptors for atomistic structure. (a) Conventional 2-body and 3-body terms, viz. distances and angles between atoms, as typically used in empirical force fields. Adapted from ref (29) with permission. Copyright 2019 Wiley-VCH. (b) General descriptor for 3-body terms: the three distances, d, between the atoms, specify the relative geometry of the three atoms completely. (c) Schematic of the smooth overlap of atomic positions (SOAP) descriptor.⁵² The neighbor density ρ is permutationally invariant; expanding it in a local basis of radial functions and spherical harmonics, Y_l^m, and then summing up the square modulus of the expansion coefficients c_nlm over the index m ensures rotational invariance of the power spectrum p (eq 56). Adapted from ref (53). Original figure published under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/). (d) Illustration why the power-spectrum vector, p, is a 3-body descriptor (here shown without element indices for clarity); the consequences of this are discussed in the text.