Toward <i>GW</i> Calculations on Thousands of Atoms

The <i>GW</i> approximation of many-body perturbation theory is an accurate method for computing electron addition and removal energies of molecules and solids. In a canonical implementation, however, its computational cost is O(N4) in the system size <i>N</i>, which prohibits its application to many systems of interest. We present a full-frequency <i>GW</i> algorithm in a Gaussian-type basis, whose computational cost scales with <i>N</i>² to <i>N</i>³. The implementation is optimized for massively parallel execution on state-of-the-art supercomputers and is suitable for nanostructures and molecules in the gas, liquid or condensed phase, using either pseudopotentials or all electrons. We validate the accuracy of the algorithm on the <i>GW</i>100 molecular test set, finding mean absolute deviations of 35 meV for ionization potentials and 27 meV for electron affinities. Furthermore, we study the length-dependence of quasiparticle energies in armchair graphene nanoribbons of up to 1734 atoms in size, and compute the local density of states across a nanoscale heterojunction

Termini of Bottom-Up Fabricated Graphene Nanoribbons

Atomically precise graphene nanoribbons (GNRs) can be obtained via thermally induced polymerization of suitable precursor molecules on a metal surface. This communication discusses the atomic structure found at the termini of armchair GNRs obtained via this bottom-up approach. The short zigzag edge at the termini of the GNRs under study gives rise to a localized midgap state with a characteristic signature in scanning tunneling microscopy (STM). By combining STM experiments with large-scale density functional theory calculations, we demonstrate that the termini are passivated by hydrogen. Our results suggest that the length of nanoribbons grown by this protocol may be limited by hydrogen passivation during the polymerization step

On-Surface Synthesis and Characterization of 9‑Atom Wide Armchair Graphene Nanoribbons

The bottom-up approach to synthesize graphene nanoribbons strives not only to introduce a band gap into the electronic structure of graphene but also to accurately tune its value by designing both the width and edge structure of the ribbons with atomic precision. We report the synthesis of an armchair graphene nanoribbon with a width of nine carbon atoms on Au(111) through surface-assisted aryl–aryl coupling and subsequent cyclodehydrogenation of a properly chosen molecular precursor. By combining high-resolution atomic force microscopy, scanning tunneling microscopy, and Raman spectroscopy, we demonstrate that the atomic structure of the fabricated ribbons is exactly as designed. Angle-resolved photoemission spectroscopy and Fourier-transformed scanning tunneling spectroscopy reveal an electronic band gap of 1.4 eV and effective masses of ≈0.1 <i>m</i>_e for both electrons and holes, constituting a substantial improvement over previous efforts toward the development of transistor applications. We use <i>ab initio</i> calculations to gain insight into the dependence of the Raman spectra on excitation wavelength as well as to rationalize the symmetry-dependent contribution of the ribbons’ electronic states to the tunneling current. We propose a simple rule for the visibility of frontier electronic bands of armchair graphene nanoribbons in scanning tunneling spectroscopy