{CONSPECTUS}: The emerging field of flexible electronics based on organics and two-dimensional (2D) materials relies on a fundamental understanding of charge and spin transport at the molecular and nanoscale. It is desirable to make predictions and shine light on unexplained experimental phenomena independently of experimentally derived parameters. Indeed, density functional theory ({DFT}), the workhorse of first-principles approaches, has been used extensively to model charge/spin transport at the nanoscale. However, {DFT} is essentially a ground state theory that simply guarantees correct total energies given the correct charge density, while charge/spin transport is a nonequilibrium phenomenon involving the scattering of quasiparticles. In this Account, we critically assess the validity and applicability of {DFT} to predict charge/spin transport at the nanoscale. We also describe a {DFT}-based approach, {DFT}+Sigma, which incorporates corrections to Kohn-Sham energy levels based on many-electron calculations. We focus on single-molecule junctions and then discuss how the important considerations for {DFT} descriptions of transport can differ in 2D materials. We conclude that when used appropriately, {DFT} and {DFT}-based approaches can play an important role in making predictions and gaining insight into transport in these materials. Specifically, we shall focus on the low-bias quasi-equilibrium regime, which is also experimentally most relevant for single-molecule junctions. The next question is how well can the scattering of {DFT} Kohn-Sham particles approximate the scattering of true quasiparticles in the junction? Quasiparticles are electrons (holes) that are surrounded by a constantly changing cloud of holes (electrons), but Kohn-Sham particles have no physical significance. However, Kohn-Sham particles can often be used as a qualitative approximation to quasiparticles. The errors in standard {DFT} descriptions of transport arise primarily from errors in the Kohn-Sham energy levels (self-energy errors). These errors are small in the strong-coupling regime where the molecular levels are significantly broadened at the Fermi level but are large in the coherent off-resonant tunneling regime where {DFT} overestimates conductance by orders of magnitude. The {DFT}+Sigma approach uses a physically motivated, parameter free estimate of the self-energy corrections to correct the energy levels in {DFT}, giving conductance in quantitative agreement with experiment for a large but nonexhaustive class of single-molecule junctions. In 2D materials, the self-energy error is relatively small, and critical issues stem instead from the large length scales in experiments, which make it necessary to consider band-bending within the 2D material, as well as scattering due to electron-phonon interactions, spin-flip interactions, defects, etc.

}, keywords = {alignment, conductance, electronic devices, formalism, interface, magnetoresistance, organic semiconductors, resistance, Spintronics, wires}, issn = {0001-4842}, doi = {10.1021/ar4002526}, author = {Quek, Su Ying and Khoo, Khoong Hong} }