Quantum Information Theory of Molecular States

This book aims at the full information-theoretic (IT) description of the quantum electronic structure of molecular systems.

The Classical Information Theory (CIT) treatment of molecular systems deals with entropic descriptors of the electron probability distributions and the associated communication (probability-propagation) systems, e.g., the electronic channels in molecules reflecting the probability-information scattering via the system chemical bonds. This book emphasizes the need for a nonclassical (quantum) extension of this familiar CIT approach, within the Quantum IT (QIT) which additionally accounts for the (current/phase)-related contributions in appropriate measures of the resultant information content of electronic states. Several concepts and techniques of the ordinary CIT will be extended to cover such complex probability amplitudes (wave functions) of molecular QM. The classical and non-classical aspects of the system electronic structure will be revealed by the electronic probability and phase/current densities, respectively. Propagation of these fundamental distributions among the elementary events determining the structural resolution level in question will then define the associated "communications" in the molecular quantum information system.

This monograph emphasizes the entropic concepts due to the phase component of electronic states. The information terms generated by the particle probability and current distributions are accounted in the complementary Shannon and Fisher measures of the resultant entropy/information content of quantum states. Such generalized measures are required to distinguish the information content of wavefunctions exhibiting the same probability density but differing in their current composition. Similar generalization of the classical information-distance (entropy-deficiency) concept and of the molecular information channel itself, the basic concept of the Communication Theory of the Chemical Bond (CTCB), will also be established. In this combined "density-and-current" description the principle of the extreme overall information content can be used to determine the phase-equilibria of molecular systems, "vertical" and "horizontal", marking the extrema of the state nonclassical and resultant information content, respectively. These entropic rules give rise to the unitary phase-transformation of molecular wave functions. Thermodynamic analogies of these entropic equilibrium criteria are commented upon and the local phenomenological description of molecular states, in spirit of the ordinary irreversible thermodynamics, will be presented. The continuity equations for the state phase and resultant entropy are briefly explored and the corresponding flow concepts and the associated sources are established.