Theory and modelling of quantum transport in molecular-scale structures

The theoretical work carried out in this thesis presents the electrical properties of two different types of two terminal molecular junctions: one dealing with gold electrodes which form gold |molecule| gold structures and the other with a graphene sheet and gold electrodes forming gold |molecule| graphene junctions. The theoretical tools employed are firstly, density functional theory (DFT). Chapter 2 presents an introduction to the theoretical concept of DFT and the implementation used in this work, namely the SIESTA code. The second tool is the quantum transport code GOLLUM. To introduce this technique in Chapter 3, I present solutions of Green’s functions for infinite and semi-infinite chains and the transmission coefficient equation which forms the theoretical basis of this code. The main results of this thesis are as follows: The first topic I identify Fano resonances in the transport properties of carbine-metal- amides and demonstrate that their energetic location and magnitude can be controlled by varying the connectivity of the core to external electrodes and by rotating the pendant moiety connected to the current-carrying core. The Fano resonances can be suppressed by rotating the pendant group and increasing the linkages to electrodes. Secondly, I compute the transmission coefficient, electrical conductance and thermoelectric properties of structures formed from terthiophene with tetracyanoethylene and terthiophene with dinitrotoluene. A theoretical investigation into the Seebeck coefficient in stacked molecular junctions is performed using a first principles quantum transport method. I show that the quantum interference produces Fano resonance in the gap between the HOMO and LUMO and the stacking geometry can control the position of this quantum interference feature. The shifting of this resonance enhances the thermopower as expected when the junction is tuned through a node in the transmission function. I also found that supramolecular interactions between two molecules changed the sign of thermopower. Finally, I look at an experimental example of a molecular switch formed in a gold/molecule/graphene vertical junction. Here the charge state of a ferrocene molecule is controlled by the application of an electrochemical bias. I present the electrical conductance and IV characteristics for a molecule (6-(ferrocenyl) hexanethiol) attached to gold lead and graphene sheet and explain how the behaviour seen in the experiment arises from the electrostatic repulsion of the molecule with the graphene electrode