Topological Quantum Similarity Indices Based on Fitted Densities: Theoretical Background and QSPR Application

A novel methodology to derive adjacency matrices for 3-dimensional molecules is presented in this work. These matrices, which are derived from atomic quantum similarity calculations, allow redefining several adjacency matrix-based topological indices, such as Randić, Zagreb or Chi's. The present derivation is built upon a previous work, where a simpler class of density function was used to describe the atoms composing the molecule, and the present proposal suggests using fitted atomic densities from the Atomic Shell Approximation procedure, which has been proved to appropriately reproduce, in its application space, atomic ab initio densities. The construction of such matrices as well as the derived indices are presented, along with some QSPR, where these topological indices are used as molecular descriptors for heat of formation, inhibition, and toxicity with promising results.