Chapter 9 - Nonadditive Entropic Criteria

Abstract

The complex measure of an overall entropy (uncertainty) content in the specified electronic state combines as its real and imaginary parts, respectively, the classical (probability) contribution of Shannon and the nonclassical (current) supplement, due to the wavefunction phase generating the state convection velocity. The associated resultant concept of the entropy-deficiency in the given molecular state, relative to the specified promolecular reference, reflects the overall information-resemblance between the compared states of the molecule and separated atoms. The condition of the vanishing nonaddtitive components of these information-theoretic (IT) descriptors provides a useful criterion for determining the IT equilibria in subsystems: the classical part determines the optimum patitioning of electron density, while the noclassical contribution establishes the equilibrium phases of molecular fragments. The “absolute” entropy criterion of the mutual equilibrium between subsystems is satisfied by the Bader-type (physical space) partitioning of molecular electron density, while the vanishing “relative” entropy requirement predicts the stockholder (function space) division of Hirshfeld. The latter criterion also determines the phase relations between subsystems, which are shown to be satisfied by the local equilibrium (“thermodynamic”) phases of molecular fragments. The entropy and information displacements in illustrative molecular systems are examined and the role of nonadditive component of the classical Fisher (gradient) information in the bond formation and localization is explored. The contragradience approach, related to the familiar ELF criterion, is shown to provide an efficient tool for locating the direct chemical bonds in molecular systems.