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Academic Journal of Chemistry

Continuity Relations, Probability Acceleration Current Sources and Internal Communications in Interacting Fragments

Roman F. Nalewajski

Published Jun 20, 2020• 8 citations
Publisher

Abstract

Classical issues of local continuities and density partition in molecular quantum mechanics are reexamined. An effective velocity of the probability current is identified as the current-per-particle and its properties are explored. The local probability acceleration and the associated force concept are introduced. They are shown to identically vanish in the stationary electronic states. This acceleration measure also determines the associated productions of physical currents, e.g., the local source of the resultant content of electronic gradient information. The probability partitioning between reactants is revisited and illustrated using the stockholder division rule of Hirshfeld. A simple orbital model is used to describe the polarized (disentangled) and equilibrium (entangled) molecular fragments containing the distinguishable and indistinguishable groups of electrons, respectively, and their mixed quantum character is emphasized. The fragment density matrix is shown to determine the subsystem internal electron communications.

DOI
10.32861/ajc.56.58.68

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Abstract: The quantum entanglement of molecular fragments in reactive systems is approached. The "external" (inter-fragment) and “internal” (intra-fragment) correlation energies are expressed in terms of the DFT average correlation holes resulting from the coupling constant integration of the scaled electron repulsion terms in the electronic Hamiltonian. Information networks in the local and configuration resolutions are examined, and their conditional entropy (covalency) and mutual information (iconicity) descriptors are summarized. The local channels in the single Slater determinant approximation of HF theory are explored in some detail. The multisite events in the bond system for the specified molecular state are tackled, cascade (bridge) propagations are examined, and the Fermi (exchange) correlation of HF theory is discussed. The partial density matrices of interacting fragments are introduced, and their role in shaping the ensemble averages of physical observables and effective communications within reactants is examined.