Transmission channels in the time‐energy uncertainty relation approach to molecular conductance: Symmetry rules for the electron transport in molecules

The concept of transmission channel plays a key role in the theory of molecular conductors. They are usually constructed from one‐electron functions (molecular spin orbitals) in the extensively employed LCAO‐MO method. Thus, the electric conductance can be obtained from the transmission matrix, whose diagonalization leads to a set of transmission eigenchannels. In this work, it is shown how using the time‐energy uncertainty relation approach, the electron transport can be also analysed in terms of coupled transmission channels. Here, the transmission channels are constructed in terms of electron deformation orbitals (EDOs), which in turn arise from linear combinations of occupied and unoccupied one‐electron functions. These transmission channels allow linking the electric conduction in molecular junctions with the traditional interpretation in mesoscopic systems, where the electron transport occurs by promotion of electrons from the valence to the conduction bands. Moreover, they lead to an expression of the electric conductance within the Landauer formalism, with the conductance given by the product of the quantum conductance and a transmission function. Transmission channels of junctions formed by polycyclic aromatic chains attached to gold atoms are analysed in detail. Symmetry rules for the MOs involved in these channels are established, giving rise to a straightforward method for the analysis of the transport ability in molecular systems.