The electronic structure of a molecule plays a crucial role in determining its conductivity at the nanoscale level. The quantum transport properties of molecular systems can be investigated through various theoretical and experimental approaches. Here, we will discuss some key factors that influence the conductivity of molecules and compare the results with theoretical predictions.1. Molecular orbitals and energy levels: The electronic structure of a molecule is described by its molecular orbitals, which are formed by the linear combination of atomic orbitals. The energy levels of these molecular orbitals determine the ease with which electrons can move through the molecule. A molecule with closely spaced energy levels will have a higher conductivity, as electrons can easily move between these levels.2. Conjugation and delocalization: Conjugated systems, where alternating single and double bonds are present, allow for the delocalization of electrons across the molecule. This delocalization leads to the formation of extended molecular orbitals, which facilitate electron transport and increase the conductivity of the molecule.3. Molecular length and contact geometry: The length of the molecule and the way it is connected to the electrodes in a molecular junction can significantly affect its conductivity. Generally, as the length of the molecule increases, the conductivity decreases due to increased electron scattering and a higher probability of defects. Additionally, the contact geometry between the molecule and the electrodes can influence the coupling between the molecular orbitals and the electrode states, affecting the overall conductivity.4. Quantum interference: Quantum interference can occur when electrons travel through different pathways within the molecule, leading to constructive or destructive interference. This phenomenon can significantly impact the conductivity of the molecule, depending on the specific molecular structure and the energy of the electrons.To investigate the quantum transport properties of specific molecular systems, one can use computational methods such as density functional theory DFT combined with non-equilibrium Green's function NEGF formalism. This approach allows for the calculation of the electronic structure and the transmission coefficients of the molecular systems, which can be used to predict their conductance.Experimental techniques, such as scanning tunneling microscopy STM and mechanically controllable break junctions MCBJ , can be employed to measure the conductance of single molecules. By comparing the experimental results with the theoretical predictions, one can gain insights into the factors that govern the conductivity of molecular systems at the nanoscale level.In conclusion, the electronic structure of a molecule, including factors such as molecular orbitals, energy levels, conjugation, and quantum interference, plays a significant role in determining its conductivity at the nanoscale level. By studying the quantum transport properties of specific molecular systems and comparing their results to theoretical predictions, we can gain a deeper understanding of the relationship between electronic structure and conductivity in these systems.