Information-Theoretic Representation of the Chemical Space of Many Electron Systems

In this chapter we review the utility of an information-theoretic threedimensional (IT-3D) space to unveil the unique physical, chemical and biological aspects of a great diversity of many electron systems, ranging from neutral and ionized atomic systems and simple molecules to much more complex ones such as amino-acids and pharmacological molecular ensembles. This space is generated from the Shannon entropy, the Fisher information and the disequilibrium measures along with their corresponding Fisher-Shannon and López-Ruíz-Mancini-Calvet (LMC) complexity measures. To achieve it we start from the theoretical ground that atoms and molecules can be described by means of the basic information-theoretical notions of delocalization, order, uniformity and complexity; thus, revealing the possible existence of an universal three-dimensional information-theoretic space for all systems in Nature. On the other hand, we discuss the abilities of the Shannon entropy, Fisher information and disequilibrium to capture the spatial spreading features of delocalizability, order and uniformity of biological molecules. Indeed, these three entropic measures are found to uniquely characterize all amino acids, and some selected pharmacological systems, through a predominant information-theoretic quality scheme (PIQS) which gathers all chemical families by means of three major spreading features: delocalization, narrowness and uniformity. This scheme is shown to recognize 4 chemical groups characterized by this entropic scheme: delocalized (aliphatic and aromatic), narrowed (electro-attractive) and uniform (tiny). Chemical groups are differentiated according to their energy classifications. Also, it is shown that information planes produce interesting patterns associated to the PIQS scheme.