Abstract
Several concepts of information theory (IT) are extended to cover the complex probability amplitudes (wave functions) of molecular quantum mechanics. The classical and non-classical aspects of the electronic structure are revealed by the electronic probability and phase distributions, respectively. The information terms due to the probability and current distributions are accounted for in the complementary Shannon and Fisher measures of the resultant information content of quantum states. Similar generalization of the information-distance descriptors is also established. The superposition principle (SP) of quantum mechanics, which introduces the conditional probabilities between quantum states, is used to generate a network of quantum communications in molecules, and to identify the non-additive contributions to physical and information quantities. The phase-relations in two-orbital model are explored. The orbital communication theory of the chemical bond introduces the entropic bond multiplicities and their partition into IT covalent/ionic components. The conditional probabilities between atomic orbitals, propagated via the network of the occupied molecular orbitals, which define the bond system and orbital communications in molecules, are generated from the bond-projected SP. In the one-determinantal representation of the molecular ground state the communication amplitudes are then related to elements of the charge and bond-order matrix. Molecular equilibria are reexamined and parallelism between the vertical (density-constrained) energy or entropy/information principles of IT and the corresponding thermodynamic criteria is emphasized.
Highlights
Concepts and techniques of information theory (IT) [1,2,3,4,5,6,7,8] have been 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]
In order to examine the phase aspect of orbital superposition and orbital communications in a more detail we examine the 2-atomic orbitals (AO) model of the preceding section, with each of the complex basis functions ψ(r) = [ψ1(r), ψ2(r)] of the promolecular reference again contributing a single electron to this model two-electron system
For simplicity we focus on the probability and amplitude channels in a single electron configuration; for the multi-configuration extension the reader is referred to refs. [33,43]
Summary
Concepts and techniques of information theory (IT) [1,2,3,4,5,6,7,8] have been 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]. In Schrödinger’s quantum mechanics the electronic state is determined by the system wave function, the (complex) amplitude of the particle probability-distribution, which carries the resultant information content Both the electron density or its shape factor, the probability distribution determined by the wave-function modulus, and the system current-distribution, related to the gradient of the wave-function phase, contribute to the quantum information descriptors of molecular states. In the present analysis we shall emphasize the non-classical, (phase/current)-related contributions to quantum information measures of electronic states in molecules It is the main purpose of this work to identify the non-classical supplements of the classical cross (relative) entropy (information-distance) descriptors within both the Fisher and Shannon measures of the information content, and to explore the the role of the phase dependence of scattering amplitudes in the orbital communication theory (OCT) [12,13,18,24,25,26,27].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
