# Dynamical Response in the GW Approximation

In nano-sciences many scientific challenges exist that can be addressed by calculating properties of clusters and molecular systems at a quantum mechanical level. Important topics are the accurate calculation of excitation energies, the alignment of the electronic levels of subsystems, and charge transfer. Currently available approaches are either not accurate enough or not applicable to systems of nano-scale size. For solids a new Green’s function based approach has been developed that can bridge this gap - the GW approach. It has proven to be a powerful tool for calculating the electronic properties of solids, but has to be adapted to quantum chemistry applications to be effective here as well.

We currently develop and implement the GW approach for calculations on clusters and molecules. This will enable the prediction of spectral functions of coupled systems, ionization potentials, and optical excitation spectra of intermediate sized, neutral and charged, systems at much higher accuracy than currently possible. By implementing this method in an efficient and widely used academic quantum chemistry package we will make it available to broad communities in quantum chemistry and computational materials sciences. We expect that the availability of this approach will have a significant impact on computational research in molecular electronics, atomic cluster physics and surface sciences.

**Contact:** Dr. Michiel van Setten

# Negative Index Materials

Metamaterials are artificial media composed of nanostructured building blocks that exhibit outstanding optical properties which may not be present in natural materials. One main focus of metamaterial research is the construction of building blocks leading to a negative index of refraction. For this purpose, the material is composed in such a way that both the electric permittivitty and the magnetic permeability become negative by exploiting plasmonic resonances. The main challenge, however, remains in the task to find building blocks leading to magnetic resonances within the visible regime. The resulting material is highly desirable as its applications range from perfect lenses to cloaking devices.

A common fabrication method of the building blocks is based on etching techniques, limiting the sizes to several hundred nanometers. A widely used artifical atom is the so-called split ring resonator, whose response behaviour can be easily understood in terms of circuit parameters. For resonances to appear in the optical regime, one has to go to smaller sizes than typically accessible via etching techniques. Hence, we take an alternative route and focus on organic π-conjugated molecules, mimicking a split ring resonator. By means of numerical and analytical calculations for a model system we identify the molecular parameters which determine the response of a single molecule to light. We also analyse the influence of bianisotropy and ultimately calculate the index of refraction for the effective medium, taking into account the interaction among the individual rings. Based on these calculations we make suggestions for the size and the electronic structure of canditate molecules exhibiting a negative index of refraction. Employing quantum chemical calculations with the TURBOMOLE program package, we then extract parameters from density functional theory calculations for real molecules, so that we can obtain quantitative results for the index of refraction.

# Structural Properties of Carbon-based Materials

The Dirac nature of the dispersion of graphene follows from the symmetries of its hexagonal lattice. The electronic properties of graphene “flakes” can be quite different from the bulk due to the presence of edges. In particular, they also give rise to lattice distortions, i.e, strain. Strain is particularly significant in experimental conditions as it might well be one of the reason behind the observed surface corrugation (“ripples”) in graphene.

In this project we mainly focus on the influence of graphene edges (zigzag) on bulk observables, i.e, elastic constants. In particular, we calculate the flake's free energy and disentangle the surface, bulk and corner contributions. We discover that the surface contribution exerts a pressure which substantially diminishes the carbon-carbon distance in the flake's interior. We have computed all the elastic constants (“Lamè parameters”) including bending rigidity using Density Functional Theories (DFT) as implemented in a quantum chemistry package, TURBOMOLE. By considering the contribution of zero point vibrations (phonons), We also determine the quantum corrections in the elastic energy. We found that the phonon contribution is most significant in the bending rigidity, κ, which decreases by ≈ 26% from its original value (κ=1.2eV).

Using this previous knowledge for flakes we also investigate the effect of edge termination of armchair graphene nano-ribbons (GNR) on its electronic properties. It is known that certain classes of armchair ribbons show evidence of bandgap formation, with gap size inversely proportional to the width of the GNR. To use graphene for future electronic devices it is important to have a better control mechanism on the electronic structure, i.e, the band gap of GNRs. In this work using DFT, as implemented in the periodic band structure code VASP, the main focus has been on controlling the band-gap of the armchair GNR by different chemical functionalization~(e.g, Mg, Ca, BH etc.) of edges. We investigate their effect on the atomic structure of the ribbon and on how geometrical changes effect the electronic structure. In particular, we observe that replacing the termination of GNR by Mg(Ca) or by BH (NH) one not only influence the strain in the edge but also the selection rule in the electronic structure.