A. Grüneis

Nitrogen-Doped Graphene: Efficient Growth, Structure, and Electronic Properties

A novel strategy for efficient growth of nitrogen-doped graphene (N-graphene) on a large scale from s-triazine molecules is presented. The growth process has been unveiled in situ using time-dependent photoemission. It has been established that a postannealing of N-graphene after gold intercalation causes a conversion of the N environment from pyridinic to graphitic, allowing to obtain more than 80% of all embedded nitrogen in graphitic form, which is essential for the electron doping in graphene. A band gap, a doping level of 300 meV, and a charge-carrier concentration of ∼8×10(12) electrons per cm2, induced by 0.4 atom % of graphitic nitrogen, have been detected by angle-resolved photoemission spectroscopy, which offers great promise for implementation of this system in next generation electronic devices.

Accurate surface and adsorption energies from many-body perturbation theory

Kohn-Sham density functional theory is the workhorse computational method in materials and surface science. Unfortunately, most semilocal density functionals predict surfaces to be more stable than they are experimentally. Naively, we would expect that consequently adsorption energies on surfaces are too small as well, but the contrary is often found: chemisorption energies are usually overestimated. Modifying the functional improves either the adsorption energy or the surface energy but always worsens the other aspect. This suggests that semilocal density functionals possess a fundamental flaw that is difficult to cure, and alternative methods are urgently needed. Here we show that a computationally fairly efficient many-electron approach, the random phase approximation to the correlation energy, resolves this dilemma and yields at the same time excellent lattice constants, surface energies and adsorption energies for carbon monoxide and benzene on transition-metal surfaces.

Towards an exact description of electronic wavefunctions in real solids

The properties of all materials arise largely from the quantum mechanics of their constituent electrons under the influence of the electric field of the nuclei. The solution of the underlying many-electron Schrödinger equation is a ‘non-polynomial hard’ problem, owing to the complex interplay of kinetic energy, electron–electron repulsion and the Pauli exclusion principle. The dominant computational method for describing such systems has been density functional theory. Quantum-chemical methods—based on an explicit ansatz for the many-electron wavefunctions and, hence, potentially more accurate—have not been fully explored in the solid state owing to their computational complexity, which ranges from strongly exponential to high-order polynomial in system size. Here we report the application of an exact technique, full configuration interaction quantum Monte Carlo to a variety of real solids, providing reference many-electron energies that are used to rigorously benchmark the standard hierarchy of quantum-chemical techniques, up to the ‘gold standard’ coupled-cluster ansatz, including single, double and perturbative triple particle–hole excitation operators. We show the errors in cohesive energies predicted by this method to be small, indicating the potential of this computationally polynomial scaling technique to tackle current solid-state problems.

Graphene Epitaxy by Chemical Vapor Deposition on SiC

We demonstrate the growth of high quality graphene layers by chemical vapor deposition (CVD) on insulating and conductive SiC substrates. This method provides key advantages over the well-developed epitaxial graphene growth by Si sublimation that has been known for decades. (1) CVD growth is much less sensitive to SiC surface defects resulting in high electron mobilities of ∼1800 cm(2)/(V s) and enables the controlled synthesis of a determined number of graphene layers with a defined doping level. The high quality of graphene is evidenced by a unique combination of angle-resolved photoemission spectroscopy, Raman spectroscopy, transport measurements, scanning tunneling microscopy and ellipsometry. Our measurements indicate that CVD grown graphene is under less compressive strain than its epitaxial counterpart and confirms the existence of an electronic energy band gap. These features are essential for future applications of graphene electronics based on wafer scale graphene growth.

Tunable Band Gap in Hydrogenated Quasi-Free-Standing Graphene

We show by angle-resolved photoemission spectroscopy that a tunable gap in quasi-free-standing monolayer graphene on Au can be induced by hydrogenation. The size of the gap can be controlled via hydrogen loading and reaches approximately 1.0 eV for a hydrogen coverage of 8%. The local rehybridization from sp(2) to sp(3) in the chemical bonding is observed by X-ray photoelectron spectroscopy and X-ray absorption and allows for a determination of the amount of chemisorbed hydrogen. The hydrogen induced gap formation is completely reversible by annealing without damaging the graphene. Calculations of the hydrogen loading dependent core level binding energies and the spectral function of graphene are in excellent agreement with photoemission experiments. Hydrogenation of graphene gives access to tunable electronic and optical properties and thereby provides a model system to study hydrogen storage in carbon materials.

Making the random phase approximation to electronic correlation accurate

We show that the inclusion of second-order screened exchange to the random phase approximation allows for an accurate description of electronic correlation in atoms and solids clearly surpassing the random phase approximation, but not yet approaching chemical accuracy. From a fundamental point of view, the method is self-correlation free for one-electron systems. From a practical point of view, the approach yields correlation energies for atoms, as well as for the jellium electron gas within a few kcal/mol of exact values, atomization energies within typically 2-3 kcal/mol of experiment, and excellent lattice constants for ionic and covalently bonded solids (0.2% error). The computational complexity is only O(N(5)), comparable to canonical second-order Møller-Plesset perturbation theory, which should allow for routine calculations on many systems.

Second-order Møller–Plesset perturbation theory applied to extended systems. I. Within the projector-augmented-wave formalism using a plane wave basis set

We present an implementation of the canonical formulation of second-order Møller-Plesset (MP2) perturbation theory within the projector-augmented-wave method under periodic boundary conditions using a plane wave basis set. To demonstrate the accuracy of our approach we show that our result for the atomization energy of a LiH molecule at the Hartree-Fock+MP2 level is in excellent agreement with well converged Gaussian-type-orbital calculations. To establish the feasibility of employing MP2 perturbation theory in its canonical form to systems that are periodic in three dimensions we calculated the cohesive energy of bulk LiH.

Second-order Møller–Plesset perturbation theory applied to extended systems. II. Structural and energetic properties

Results for the lattice constants, atomization energies, and band gaps of typical semiconductors and insulators are presented for Hartree-Fock and second-order Moller-Plesset perturbation theory (MP2). We find that MP2 tends to undercorrelate weakly polarizable systems and overcorrelates strongly polarizable systems. As a result, lattice constants are overestimated for large gap systems and underestimated for small gap systems. The volume dependence of the MP2 correlation energy and the dependence of the MP2 band gaps on the static dielectric screening properties are discussed in detail. Moreover, the relationship between MP2 and the G(0)W(0) quasiparticle energies is elucidated and discussed. Finally, we demonstrate explicitly that the correlation energy diverges with decreasing k-point spacing for metals.

Hybrid functionals including random phase approximation correlation and second-order screened exchange.

There has been considerable recent interest in density functionals incorporating random phase approximation (RPA) ground-state correlation. By virtue of its full nonlocality, RPA correlation is compatible with exact Hartree-Fock-type exchange and describes van der Waals interactions exceptionally well [B. G. Janesko et al., J. Chem. Phys. 130, 081105 (2009); J. Chem. Phys. 131, 034110 (2009)]. One caveat is that RPA correlation contains one-electron self-interaction error, which leads to disturbingly large correlation energies in the stretched bond situation of, e.g., H(2)(+), He(2)(+), or Ne(2)(+). In the present work, we show that inclusion of second-order screened exchange rectifies the aforementioned failure of RPA correlation. We present a large number of molecular benchmark results obtained using full-range as well as long-range corrected hybrids incorporating second-order screened exchange correlation. This correction has a generally small, and sometimes undesirable, effect on RPA predictions for chemical properties, but appears to be very beneficial for the dissociation of H(2)(+), He(2)(+), and Ne(2)(+).

Natural Orbitals for Wave Function Based Correlated Calculations Using a Plane Wave Basis Set

We demonstrate that natural orbitals allow for reducing the computational cost of wave function based correlated calculations, especially for atoms and molecules in a large box, when a plane wave basis set under periodic boundary conditions is used. The employed natural orbitals are evaluated on the level of second-order Møller-Plesset perturbation theory (MP2), which requires a computational effort that scales as [Formula: see text](N(5)), where N is a measure of the system size. Moreover, we find that a simple approximation reducing the scaling to [Formula: see text](N(4)) yields orbitals that allow for a similar reduction of the number of virtual orbitals. The MP2 natural orbitals are applied to coupled-cluster singles and doubles (CCSD) as well as full configuration interaction Quantum Monte Carlo calculations of the H2 molecule to test our implementation. Finally, the atomization energies of the LiH molecule and solid are calculated on the level of MP2 and CCSD.