Professor Colin J. LambertAMINAH NASSER SAEED ALQAHTANI2022-06-062020-02-052022-06-0680995https://drepo.sdl.edu.sa/handle/20.500.14154/67742In 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.113enThesis