Atomic-property labeled radial distribution function (APRDF)#

Radial distribution function (RDF) are widely used in crystallography and molecular simulations. They describe the probability of finding a pair of atoms separated by a certain distance. For crystalline solids, the RDF is an infinite sequence of sharp peaks. However, the RDF contains no information about the nature of the atoms. To introduce “chemistry” in this descriptor, Fernandez et al. [Fernandez2013] proposed to use the APRDF to describe the local environment of a given atom. The APRDF is defined as RDF weighted by the product of atomic properties.

\[\operatorname{RDF}^{P}(R)=f \sum_{i, j}^{\text {all atom pairs }} P_{i} P_{j} \mathrm{e}^{-B\left(r_{i j}-R\right)^{2}}\]
Featurizers: APRDF APRDF ../../_images/arrow-right-circle.svg
considers_geometry: True
considers_structure_graph: False
encodes_chemistry: optionally
scalar: False
scope: global

Initially described in [Fernandez2013].