Transmission of renormalized benzene circuits

The renormalization equations emerge from a Greenian-matrix solution of the discretized Schr¨odinger 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 transmissionenergy 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.