Distribution-Based Descriptors of the Molecular Shape

A rational design of economically cost-effective chemical libraries as well as successful data mining during
a process of drug discovery employs a vast array of the molecular descriptors. Despite the huge importance
of this area of the research there is still a need for the further development of the simple, intuitive, easily
calculable, specific and size-invariant parameters of the molecular shape. Here we present ab initio calculation
of the molecular volumes and expectations for the molecular areas of projection. These molecular size
parameters were used as a basis to define a group of novel descriptors of the molecular shape. A set of
molecular descriptors was developed:  ovality, roughness, size-corrected parameters, and the parameters
derived from the higher central momenta of the distributions of the size descriptorsskewness and kurtosis.
The rationale for the construction of the descriptors was first to calculate the descriptors of the molecular
size along many directions in the space and second to use the statistical parameters of the distribution of
those descriptors as the shape descriptors. The size descriptors well suited for the above purpose and discussed
in this paper are generalized molecular radii and the molecular areas of projection. Molecular volume and
projection area-derived descriptors were calculated and their applicability as shape descriptors was illustrated
using exploratory methods (factor analysis and hierarchical cluster analysis). The shape descriptors appear
to be promising in their ability to discriminate and classify the molecular shapes e.g. spheroids, disklike,
rodlike, starlike, crosslike, anglelike, etc.