# Revised autocorrelation functions (RACs)#

Revised autocorrelation functions have originally been proposed for metal-complexes [Janet2017]. Autocorrelation functions have been widely used as compact, fixed-length descriptors and are defined as

$P_{d}=\sum_{i} \sum_{j} P_{i} P_{j} \delta\left(d_{i j}, d\right)$

where $$P_d$$ is the autocorrelation for property $$P$$ at depth $$d$$, δ is the Dirac delta function, and $$d_{ij}$$ is the bond wise path distance between atoms $$i$$ and $$j$$. Janet and Kulik proposed to constrain both the starting indices and the scopes of the autorcorrelation functions to account for the (potentially) greater importance of certain atoms such as the metal and its coordination sphere.

$\underset{\text{ax / eq / all}}{\text{lc / mc}} P_{d}^{\prime}=\sum_{i}^{l c \text {or mc scope }} \sum_{j}\left(P_{i}-P_{j}\right) \delta\left(d_{i j}, d\right)$

[Moosavi2021] adapted this concept for MOFs and proposed to compute metal-, ligand-, and functional-groups centered RACs.

In mofdscribe, you can customize the encodings $$P$$ (using all properties that are available in our element-coder package) as well as the aggregation functions.

 Featurizers: RACS style: only-light considers_geometry: False considers_structure_graph: True encodes_chemistry: optionally scalar: False scope: local Initially described in [Janet2017] for metal complexes, extended to MOFs in [Moosavi2021].