Weighted holistic invariant molecular descriptors. Part 2. Theory development and applications on modeling physicochemical properties of polyaromatic hydrocarbons

New theoretical three-dimensional molecular indices (weighted holistic invariant molecular (WHIM) descriptors) are defined. They contain information about the whole molecular structure in terms of size, shape, symmetry and atom distribution. These indices are calculated from the (x, y, z) coordinates of a molecule within different weighting schemes in a straight-forward manner and represent a very general approach to describe molecules in a unitary conceptual framework. Their meaning is quite evident and is defined by the same mathematical properties of the algorithm as used for their calculation. In this work further developments of the theory are proposed and the WHIM descriptors are used for modeling properties of poly-aromatic hydrocarbons (PAHs) such as melting point, boiling point and hydrophobicity. The obtained models are quite good and can be easily interpreted in terms of the meaning of WHIM descriptors.