Theory of molecular conductance using a modular approach

This study probes the correlation between the conductance of a molecular wire (the property of a whole system) and its constituent backbone units (modules). By using a tight-binding Hamiltonian combined with single-particle Green's functions, we develop an approach that enables an estimate of a conductance decay constant in terms of the Hamiltonians of molecular backbone units and the couplings between two nearest-neighbor units in the off-resonant tunneling regime. For demonstration, we examine several representative molecular systems in a framework of the Hückel model (the simplest atomistic-level model). The Hückel model can be reduced to a single-orbital-per-site formulation [A. Nitzan, Annu. Rev. Phys. Chem. 52, 681 (2001)], and each energy level in the single-orbital-per-site picture can be expressed in an explicit form including the synergistic effect of all molecular orbitals of a molecular backbone unit. Based on the proposed approach, we show the correspondence between the complete destructive quantum interference and an infinite injection gap and derive the preconditions of the modified Simmons equation and the rule of intramolecular series circuits.