An effective representation of the electronic structure of molecules must be properly based on quantum mechanics. Thus, we have developed the structure representation using quantum topology (StruQT) method where the electronic structure of molecuLes is re presented as critical points on the electron density distribution. StruQT is based on the Atoms in Molecules (MM) theory by Richard Bader. Comparing molecules in this representation means comparing sets of critical points and their properties for the diff erent molecules involved. However, the StruQT method needs automatic routines for finding comparable critical points between molecules. Two approaches are suggested: - The use of inductive logic programming (ILP) which is a non-attribute based method from machine learning. ILP has been used successfully in drug design and is much lesssensitive to the problem of finding comparable molecular features. - The use of scale space trees of the critical points on the electron densities. Sca le space analysis from the field of image analysis performs multiple smoothings of the electron densities to create a 4-D space where critical points merge into a hierarchy of simpler structures. These bifurcating critical point trees can be used to find comparable critical points between molecules. The project has changed direction from creating its own software for finding critical points in scalar fields to using a commercial program and focusing on the modeling aspect of using AIM descriptors in QSAR/QSPR. In particular we are investigating the u se of inductive logic programming (ILP) which is very suitable for representing and comparing graph-like structure without having to perform 3D alignments. We will also investigate other non-alignment method approaches based on nearest neighbour geometrie s in combination with bond critical point (BCP) descriptors.A discretisation of the BCP for use with ILP will also be investigated.