Information-theoretical complexity for the hydrogenic identity S N 2 exchange reaction

Abstract

We investigate the complexity of the hydrogenic identity S N 2 exchange reaction by means of information-theoretic functionals such as disequilibrium (D), exponential entropy (L), Fisher information (I), power entropy (J) and joint information-theoretic measures, i.e., the I–D, D–L and I–J planes and the Fisher–Shannon (FS) and Lopez-Mancini-Calbet (LMC) shape complexities. The several information-theoretic measures of the one-particle density were computed in position (r) and momentum (p) spaces. The analysis revealed that the chemically significant regions of this reaction can be identified through most of the information-theoretic functionals or planes, not only the ones which are commonly revealed by the energy, such as the reactant/product (R/P) and the transition state (TS), but also those that are not present in the energy profile such as the bond cleavage energy region (BCER), the bond breaking/forming regions (B–B/F) and the charge transfer process (CT). The analysis of the complexities shows that the energy profile of the identity S N 2 exchange reaction bears no simple behavior with respect to the LMC and FS measures. Most of the chemical features of interest (BCER, B–B/F and CT) are only revealed when particular information-theoretic aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.