The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term "Anderson transition" is understood in a broad sense, including both metalinsulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations.1 A remarkable exception is the behavior of ξ in disordered wires of the chiral symmetry, see Eqs. (5.21), (5.22).

Recent STM molecular break-junction experiments have revealed multiple series of peaks in the conductance histograms of alkanedithiols. To resolve a current controversy, we present here an in-depth study of charge transport properties of Au|alkanedithiol|Au junctions. Conductance histograms extracted from our STM measurements unambiguously confirm features showing more than one set of junction configurations. On the basis of quantum chemistry calculations, we propose that certain combinations of different sulfur-gold couplings and trans/gauche conformations act as the driving agents. The present study may have implications for experimental methodology: whenever conductances of different junction conformations are not statistically independent, the conductance histogram technique can exhibit a single series only, even though a much larger abundance of microscopic realizations exists.

The GW-technology corrects the Kohn-Sham (KS) single particle energies and single particle states for artifacts of the exchange-correlation (XC) functional of the underlying density functional theory (DFT) calculation. We present the formalism and implementation of GW adapted for standard quantum chemistry packages. Our implementation is tested using a typical set of molecules. We find that already after the first iteration of the self-consistency cycle, G0W0, the deviations of quasi-particle energies from experimental ionization potentials and electron affinities can be reduced by an order of magnitude against those of KS-DFT using GGA or hybrid functionals. Also, we confirm that even on this level of approximation there is a considerably diminished dependency of the G0W0-results on the XC-functional of the underlying DFT.

We have designed and synthesized a molecular rod that consists of two weakly coupled electronic -systems with mutually shifted energy levels. The asymmetry thus implied manifests itself in a current-voltage characteristic with pronounced dependence on the sign of the bias voltage, which makes the molecule a prototype for a molecular diode. The individual molecules were immobilized by sulfur-gold bonds between both electrodes of a mechanically controlled break junction, and their electronic transport properties have been investigated. The results indeed show diode-like current-voltage characteristics. In contrast to that, control experiments with symmetric molecular rods consisting of two identical -systems did not show significant asymmetries in the transport properties. To investigate the underlying transport mechanism, phenomenological arguments are combined with calculations based on density functional theory. The theoretical analysis suggests that the bias dependence of the polarizability of the molecule feeds back into the current leading to an asymmetric shape of the current-voltage characteristics, similar to the phenomena in a semiconductor diode. molecular electronics ͉ rectification ͉ single-molecule studies

We present the GW100 set. GW100 is a benchmark set of the ionization potentials and electron affinities of 100 molecules computed with the GW method using three independent GW codes and different GW methodologies. The quasi-particle energies of the highest-occupied molecular orbitals (HOMO) and lowest-unoccupied molecular orbitals (LUMO) are calculated for the GW100 set at the G0W0@PBE level using the software packages TURBOMOLE, FHI-aims, and BerkeleyGW. The use of these three codes allows for a quantitative comparison of the type of basis set (plane wave or local orbital) and handling of unoccupied states, the treatment of core and valence electrons (all electron or pseudopotentials), the treatment of the frequency dependence of the self-energy (full frequency or more approximate plasmon-pole models), and the algorithm for solving the quasi-particle equation. Primary results include reference values for future benchmarks, best practices for convergence within a particular approach, and average error bars for the most common approximations.