Abstract
The classical Information Theory (IT) deals with entropic descriptors of the probability distributions and probability-propagation (communication) systems, e.g., the electronic channels in molecules reflecting the information scattering via the system chemical bonds. The quantum IT additionally accounts for the non-classical (current/phase)-related contributions in the resultant information content of electronic states. The classical and non-classical terms in the quantum Shannon entropy and Fisher information are reexamined. The associated probability-propagation and current-scattering networks are introduced and their Fisher- and Shannon-type descriptors are identified. The non-additive and additive information descriptors of the probability channels in both the Atomic Orbital and local resolution levels are related to the network conditional-entropy and mutual-information, which represent the IT covalency and ionicity components in the classical communication theory of the chemical bond. A similar partition identifies the associated bond indices in the molecular current/phase channels. The resultant bond descriptors combining the classical and non-classical terms, due to the probability and current distributions, respectively, are proposed as generalized communication-noise (covalency) and information-flow (iconicity) concepts in the quantum IT.
Highlights
These molecular channels constitute the basis of the Communication Theory of the Chemical Bond (CTCB) [11] and its newest version—the Orbital Communication Theory (OCT) [12,13], in which the input probability “signal” is propagated via the system chemical bonds
In the present analysis we address the natural question about the non-classical complements of such classical molecular channels, which reflect the current/phase-scattering in electronic states
The quantum-generalized information measures have been summarized and the associated information-scattering networks have been introduced. This analysis has stressed the need for using the resultant information measures, which take into account both the classical and non-classical contributions due to the electronic probability and current distributions, respectively
Summary
Concepts and techniques of Information Theory (IT) [1,2,3,4,5,6,7,8] have been widely and successfully applied to explore the molecular electron probabilities and the associated patterns of chemical bonds, e.g., [9,10,11,12,13,14,15,16,17,18]. The system electron distribution, related to the wave-function modulus, reveals only the classical, probability aspect of the molecular information content, while the phase/current component gives rise to the associated non-classical entropy/information terms [9,10,16,17,24,25] in the corresponding overall quantum measure. The vanishing spatial phase in the ground (stationary) state signifies the complete absence of the current aspect in the molecular electronic structure Any displacement from this extreme situation is manifested in the non-classical entropy/information quantities either by the average magnitude of phase (in Shannon’s measure) or its gradient (in Fisher’s descriptor).
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