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

Abstract

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.electron deformation orbitals, molecular conductance, molecular electronics, transmission channel 1 | I N TR ODU C TI ON The field of molecular electronics aims to revolutionize the current electronic components by introducing materials constructed at atomic scale. [1][2][3][4][5] Fabrication of electronic circuits using single molecular structures is fascinating and situates miniaturization of electronic devices in the limits of current nanotechnology. Nowadays, it is possible to form molecular junctions where a single molecular structure is linked, even covalently, to metallic electrodes. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] Therefore, an electronic current induced across the junction by an external voltage can be measured. However, from the current stage to the development of efficient molecular circuits integrated in complex electronic devices there is still a long way to go. During this transition, theoretical methods, which go several steps ahead with respect to experimental developments, will play a crucial role. These methods will be all-important in an efficient design of molecular electronic devices that may execute specific functions. It is in this aspect that there is plenty of room for new theoretical approaches to emerge.In designing molecular electronic devices, the effects of structural changes on the electric conduction, including conformational modifications, isomerization processes, or chemical substitutions, must be perfectly controlled and understood. [44][45][46] Then, the study of the electron transport in molecular junction...

Anti-ohmic single molecule electron transport: is it feasible?

“…Batra 35,36 derived the expression of G 0 by applying the uncertainty relation to the case of a free electron crossing a monodimensional conductor under the action of a nite bias voltage, DV. Recently, a generalization to interacting electrons subjected to the external potential created by the nuclei in a molecule was proposed, 34 giving rise to the following expression,…”

“…For instance, the amount of electrons promoted from valence to conduction bands upon the electric perturbation can be obtained, 14 and simple orbital symmetry rules for the formation of transmission channels can be inferred. 34 Another appealing feature of using EDOs is that electron and hole densities associated to a given transmission channel can be represented in real space. This provides, as will be shown in the next section, a visual tool to understand the conducting/ insulating character of molecular wires by means of the electron and hole density distributions along the transport region.…”

“…The main channel is formed by the pair of EDOs with the largest absolute eigenvalues, which in turn are constructed as linear combinations of close in energy occupied and virtual molecular orbitals. 34,37 In Fig. 3(A), the channel is represented for the pX2 structure with n ¼ 5, where the mixed occupied and virtual orbitals correspond mainly to the HOMO and LUMO.…”

Theoretical Prediction of Capacitance of Bilayer Graphene Flakes

“…These channels provide both qualitative and quantitative mechanism of charge flow through the molecular conductor. [50] It is found that EDOs pair off, displaying the same eigenvalue but opposite sign, where each pair represents the magnitude of accumulation/depletion of charge at different molecular regions. n def , as total charge displacement can be found as summation over positive eigenvalues of deformation density matrix, equation 3.…”

“…EDO concept has been also used in the construction and molecular expression of transmission channels which plays a crucial role in molecular‐level conduction and can be found by diagonalization of transmission matrix as eigenchannels. These channels provide both qualitative and quantitative mechanism of charge flow through the molecular conductor …”