In the pursuit of future nano-scale applications within the field of molecular electronics, extensive investigations into electron transport through single molecules hold significant importance. As single or multiple molecules serve as crucial building blocks for designing and constructing molecular electronic devices, comprehending their electronic and transport properties becomes imperative. Countless theoretical and experimental studies have been conducted to create molecular junctions and explore their electrical performance. This thesis focuses on fundamental aspects of transport theory, employing theoretical and mathematical approaches to investigate electron transport through junctions, particularly involving a scattering region formed by a single
molecule connected to metal electrodes. The research methods used are based on a combination of density functional theory, implemented within the SIESTA code, and non-equilibrium Green's function, realized using the GOLLUM code, to delve into electrical conductance on a molecular scale.

The objective of this chapter is to address a puzzling paradox concerning meta
connectivity, which exhibits destructive quantum interference (DQI) in a tight binding model. However, in certain instances, DQI does not manifest in a DFT calculation on the same system. To shed light on this inconsistency, a selection of molecules is examined, focusing on the distinction between meta and para connectivity. Two different types of linkers, thiol (-SH) and methyl sulphide (-SMe), are employed to couple different molecules to Au electrodes. Through this investigation, we aim to gain insights into the underlying factors that lead to the observed quantum interferencebehaviors.

In project two, we conducted a comprehensive study, combining experimental and theoretical approaches, to explore charge transport in stacked graphene-like dimers. Our findings revealed that the interaction between room-temperature quantum interference and stacking significantly influences their highly non-classical electrical conductance. Notably, for the molecule CQI-L, the electrical conductance of the dimer exceeds that of the monomer by a remarkable factor of 25, attributed to the most energetically favorable stacking interactions. Conversely, for the molecule CQI-H, the dimer's conductance is approximately 40 times lower than that of the monomer. These results
unequivocally demonstrate that precise control of connectivity to molecular cores, coupled with stacking interactions between their systems, provides a versatile avenue for modifying and optimizing charge transfer between molecules. This discovery is expected to inspire further vigorous research at both macroscopic and microscopic levels.