Transmission of Renormalized Benzene Circuits

Abstract: The renormalization equations emerge from a Greenian-matrix solution of the discretized Schrodinger equation. A by-product of these equations is the decimation process, which enables substituted-benzenes to be mapped onto corresponding dimers, that are used to construct the series and parallel circuits of single-, double- and triple-dimers. The transmittivities of these circuits are calculated by the Lippmann-Schwinger theory, which yields the transmission-energy function T(E). The average value of T(E) provides a measure of the electron transport in the circuit in question. The undulating nature of the T(E) profiles give rise to resonances (T=1) and anti-resonances (T=0) across the energy spectrum. Analysis of the structure of the T(E) graphs highlights the distinguishing features associated with the homo- and hetero-geneous series and parallel circuits. Noteworthy results include the preponderance of p-dimers in circuits with high T(E) values, and the fact that parallel circuits tend to be better transmitters than their series counterparts.