Theory of electron transport through single molecules

Alqahtani, Aminah and Lambert, Colin (2020) Theory of electron transport through single molecules. PhD thesis, Lancaster University.

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Abstract

In recent years, efforts to understand electron transport at the molecular scale have intensified, driven by the desire to understand the quantum nature of electrical conductance at such length scales and by the need to design molecular-scale devices for switching, sensing and energy harvesting. The aim of this thesis is to investigate theoretically electrical properties of molecules placed between nanogap electrodes. Such structures can be realised using mechanically-controlled break junctions, which nowadays is a widely adopted experimental technique. The method used in this thesis is based on density functional theory (DFT), which is implemented in the SIESTA code, and involves combining DFT with quantum transport calculations using Greens functions. Chapter 2 presents a brief introduction to the theoretical concepts of DFT which has been developed to describe the electronic properties taking into account the full atomistic details of the systems. Chapter 3 presents solutions to the Green’s function used for infinite and semi-infinite chains and introduces the transmission coefficient equations which forms the theoretical basis of the GOLLUM quantum transport code. The theoretical work carried out in this thesis focusses on the electrical properties of gold|molecule|gold junctions, in which a single molecule (or perhaps a small number of molecules) is placed between gold electrodes since experimentally, this is the most common choice of electrodes. The first topic I investigated is the conductance of break-junctions containing imidazole and benzimidazole series of molecules. In chapter 4, I present a combined experimental and theoretical study of the electrical conductance of series. The conductance of these molecules is measured using a mechanically controlled break junction and compared with density functional theory calculations. The theoretical results are in broad agreement with experimental reveal the decrease in electrical conductance of the imidazole and benzimidazole series with increasing the length. This study establishes that hydrogen-bonding plays an important role in determining the conductance of these molecular-scale junctions. The calculations, therefore, focus on the effect of H-bonding formed from N and H atoms on both the electrical conductance. The second topic of this thesis is presented in chapter 5. In that chapter, I have computed the transmission coefficient for series of polycyclic aromatic hydrocarbons including naphthalene, anthracene and tetracene. The conductance has been obtained with either with thiol or pyridyl anchor groups linked to the aromatic cores, either at para-para positions or meta-meta positions. The conductance of these molecules is predicted using density functional theory calculations. The results demonstrate consistently higher conductance in the meta series, after adding a first 5-membered ring, compared to the para series. The conductances of these new polycyclic aromatic cores are not much affected by adding a second 5-membered ring for meta connectivity. It is observed that the width of the gap between the HOMO and LUMO resonances can be controlled by the stacking geometry of these structures and their conductances are determined by the difference in Fermi energies relative to the frontier orbitals of the molecules due to the two different anchor groups.