The descriptors obtained for the autocorrelation, BCUT and GTCI should be used carefully for QSAR models, because they are limited
to the smallest molecule or more exactly the smallest topological distance in the molecule. Although in these specail cases missing values
can be filled with zero values, because there is no probability for large distances in 'small' lead molecules. Nonetheless this is not a
good strategy, because you will not get really good models, if you have a lot of zero values, which is obviously if you have a closer look
at the data sets. Or in other words, you will get a potential 'degeneracy problem' for such molecules.

Moreau-Broto topological autocorrelation [bmv84].

**Equation 5-14. Moreau-Broto autocorrelation**

where

**d**_{ij} is the topological distance between the atoms

**i** and atom

**j**,

**w**_{i}
and

**w**_{j} are the atom properties of the atoms

**i** and

**j**.

It must be mentioned that the autocorrelation is only a special case of the radial distribution function (the Section called *Radial distribution function (RDF)*).

The radial distribution function (RDF) [msg99,wfz04b] can be interpreted as the probability distribution of finding an atom in a spherical volume of
radius **r**.

**Equation 5-15. Radial distribution function**

where

**r**_{ij} is the geometrical distance between the atoms

**i** and atom

**j**,

**w**_{i}
and

**w**_{j} are the atom properties of the atoms

**i** and

**j**.

**B** is the smoothing parameter
(fuzziness of the distance

**r**_{ij}) for the interatomic distance and

**f** the scaling factor.

If **B** aims to infinity the RDF code approximates to the autocorrelation function (the Section called *Moreau-Broto topological autocorrelation*) and the fuzziness
of the distance **r**_{ij} vanishes. So the RDF code can be treated as a generalized
autocorrelation function.

The RDF user parameters can be defined in the `joelib.properties`-file, otherwise the default parameters will be used:

jcompchem.joelib.desc.types.RadialDistributionFunction.minSphericalVolume = 0.2
joelib.desc.types.RadialDistributionFunction.maxSphericalVolume = 10.0
joelib.desc.types.RadialDistributionFunction.sphericalVolumeResolution = 0.2
joelib.desc.types.RadialDistributionFunction.smoothingFactor = 25

Optional the RDF can be calculated with protonated molecules, but you must be sure that all available atom
properties are calculated with hydrogens also. Because this is not the standard, this option should be only used by developers.