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Title: A new approach to the method of source-sink potentials for molecular conduction

We re-derive the tight-binding source-sink potential (SSP) equations for ballistic conduction through conjugated molecular structures in a form that avoids singularities. This enables derivation of new results for families of molecular devices in terms of eigenvectors and eigenvalues of the adjacency matrix of the molecular graph. In particular, we define the transmission of electrons through individual molecular orbitals (MO) and through MO shells. We make explicit the behaviour of the total current and individual MO and shell currents at molecular eigenvalues. A rich variety of behaviour is found. A SSP device has specific insulation or conduction at an eigenvalue of the molecular graph (a root of the characteristic polynomial) according to the multiplicities of that value in the spectra of four defined device polynomials. Conduction near eigenvalues is dominated by the transmission curves of nearby shells. A shell may be inert or active. An inert shell does not conduct at any energy, not even at its own eigenvalue. Conduction may occur at the eigenvalue of an inert shell, but is then carried entirely by other shells. If a shell is active, it carries all conduction at its own eigenvalue. For bipartite molecular graphs (alternant molecules), orbital conduction properties are governedmore » by a pairing theorem. Inertness of shells for families such as chains and rings is predicted by selection rules based on node counting and degeneracy.« less
Authors:
; ;  [1] ;  [2]
  1. Department of Chemistry, University of Sheffield, Sheffield S3 7HF (United Kingdom)
  2. Department of Mathematics, University of Malta, Msida (Malta)
Publication Date:
OSTI Identifier:
22493245
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 19; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DIAGRAMS; EIGENVALUES; EIGENVECTORS; ELECTRIC CONDUCTIVITY; ELECTRONS; GRAPH THEORY; MATRICES; MOLECULAR STRUCTURE; MOLECULES; MULTIPLICITY; POLYNOMIALS; POTENTIALS; SELECTION RULES; SINGULARITY