General type of a uniform and reversible representation of chemical structures

In any type of modelling (be classical or by artificial neural networks) involving chemical structures and their corresponding properties, the first problem encountered is the representation of chemical structures. A good structure representation should have different code for each 3-D structure (uniqueness), it should have the same number of variables for all structures, it should be reversible, and should be translation and rotational invariant. In the present contribution we are discussing a new method for representing chemical structures which, at least in principle and within limitations bound to the precision and resolution of the projection, fulfils all mentioned requirements with the exception (in some cases) of the rotational invariance. The discussed representation is based on the projections of atoms on the sphere with an arbitrary radius. The new structure representation of a molecule with N atoms is defined as n-dimensional vector S = (s1, s2,…, Si,…, sn) with each component defined as a cumulative intensity si at a given point i on the circle with an arbitrary radius. The cumulative intensity si (the ith point on the circle at angle ϑi) is a sum of N contributions I(i, rj, ϑj) from each atom j in the molecule: Si= σj=iN I(i,rj, ϑj)= σj=iN rj(ϑi − ϑj) 2 + ϑ2j, i = 1,…, n. The intensity function I(i, rj, ϑj) can be any bell-shaped function. In our case we have chosen the Lorentzian shape with maximum at the angle ϑj, maximal intensity proportional to the ρj, and having the width, σj, related to the type of the atom. The new proposed ‘spectrum-like’ representation is additive with respect to the constituent atoms of a given structure and can be easily decoded. Because the representation is additive it allows to subtract a part of the ‘spectrum-like’ representation which belongs to the structurally identical skeletons of all molecules in the study.