A chemical property space defines the adaptability of a molecule to changing conditions and its interaction with other molecular systems determining a pharmacological response. Within a congeneric molecular series (compounds with the same derivatization algorithm and thus the same brute formula) the chemical properties vary in a monotonic manner, i.e., congeneric compounds share the same chemical property space. The chemical property space is a key component in molecular design, where some building blocks are functionalized, i.e., derivatized, and eventually self-assembled in more complex systems, such as enzyme-ligand systems, of which (physico-chemical) properties/bioactivity may be predicted by QSPR/QSAR (quantitative structure-property/activity relationship) studies. The system structure is determined by the binding type (temporal/permanent; electrostatic/covalent) and is reflected in its local electronic (and/or magnetic) properties. Such nano-systems play the role of molecular devices, important in nano-medicine. In the present article, the behavior of polyethylenimine (PEI) macromolecules (linear LPEI and branched BPEI, respectively) with respect to the glucose oxidase enzyme GOx is described in terms of their (interacting) energy, geometry and topology, in an attempt to find the best shape and size of PEIs to be useful for a chosen (nanochemistry) purpose.

In this review we describe various applications of Szeged (Sz) index for modeling physicochemical properties as well as physiological activities of organic compounds acting as drugs or possess pharmacological activity.

Square tori are transformed into hexagonal and other tiling tori by several cutting procedures. The toroidal objects thus generated are optimized by a molecular mechanics procedure. The strain energy, defined as the difference between the energy of toroidal structure and the energy of its corresponding straight, open tube, is shown to decrease as the torus diameter increases, in the series 10,n of polyhex tori, up to 5000 atoms. Graph-theoretical characterization of toroidal structures including the Hosoya polynomial, Distance Degree Sequence, and Wiener index is also given.