The molecular structure and size have significant effects on quantum transport properties in nanoscale systems. In molecular wires and other nanoscale devices, the transport of electrons is governed by quantum mechanics. The molecular structure, including the arrangement of atoms and the nature of chemical bonds, influences the electronic properties of the system, such as the energy levels and wave functions of the electrons. The size of the molecule also plays a crucial role in determining the quantum transport properties, as it affects the spatial confinement of electrons and the coupling between the molecule and the electrodes.Some of the effects of molecular structure and size on quantum transport properties include:1. Conductance: The conductance of a molecular wire depends on the alignment of the molecular orbitals with the Fermi level of the electrodes. The molecular structure determines the energy levels of the molecular orbitals, which in turn affects the conductance.2. Quantum interference: The molecular structure can give rise to quantum interference effects, which can either enhance or suppress the electron transport through the molecule. This phenomenon is highly sensitive to the molecular structure and the arrangement of the atoms.3. Coulomb blockade: In small molecules, the charging energy required to add an extra electron can be significant, leading to the Coulomb blockade effect. This effect can suppress the electron transport at low bias voltages and is highly dependent on the size and geometry of the molecule.4. Vibronic coupling: The interaction between the electronic and vibrational degrees of freedom in a molecule can also influence the quantum transport properties. The strength of this coupling depends on the molecular structure and can lead to effects such as inelastic electron tunneling and negative differential conductance.Regarding the prediction of conductance in molecular wires using quantum mechanical calculations, it is possible to obtain accurate results using first-principles methods, such as density functional theory DFT combined with non-equilibrium Green's function NEGF formalism. These methods allow for the calculation of the electronic structure of the molecule and its coupling to the electrodes, providing a detailed understanding of the quantum transport properties. However, it is important to note that the accuracy of these predictions depends on the choice of the exchange-correlation functional and the treatment of electron-electron interactions, which are still subject to ongoing research and development.