# Research areas

In present days there is a clear shift towards a new way of doing physics, which relies strongly on the use of computational means. Computational Physics, which is expanding with the availability of modern and more powerful computers, has been offering new insights on various natural phenomena, complementing and going beyond more traditional visions based on analytical approaches.

Our research can be broadly defined as Computational Condensed Matter, sometimes touching the fields of Material Science, Quantum Chemistry, or even Biophysics. This is a small summary of the current interests of the group.

## Ab-initio structural prediction

We have recently started to work in the rapidly expanding field of structural predictions for material design. Our method of choice is the Minima Hopping Method (MHM) developed by the group of Prof. Stefan Goedecker at the University of Basel. We have been applying the MHM to many systems of technological relevance, where there were contradictory results concerning the identification of the lowest-enthalpy structures, in particular under pressure. Given only the chemical composition of a system, the MHM aims at finding the global minimum on the enthalpy surface while gradually exploring low-lying structures. Moves on the enthalpy surface are performed by using variable cell shape molecular dynamics with initial velocities approximately chosen along soft mode directions. This method is particularly efficient to explore the potential energy surfaces, and we succeeded in discovering several low-enthalpy structures that had been missed by previous studies of structural search done with other methods available on the market. After finding a previously unknown structure, we proceed to the characterization of the physical properties of the new crystal, by calculating structural constants, electronic band structures, optical response, etc., using state-of-the-art methods based on and going beyond density functional theory. At present we are developing our activities related to structural search and we have started to explore the phase diagram of many materials that are still poorly characterized (including materials for hydrogen storage, topological insulators, superconductors, etc.).

## New materials for photovoltaic applications

Many different technological applications - like flat-panel displays - require the use of materials that are transparent in the visible range, but that have fairly high electric conductivity. These normally incompatible properties can be found together in three different classes of materials: very thin pure metals, highly doped conjugated organic polymers, and doped wide band gap oxide or nitrite semiconductors. During the past years, the latter, commonly referred to as transparent conductive oxide (TCO) materials, have attracted a considerable amount of interest, especially due to their applications in displays and in solar cells. In fact, many new solar cells technologies, like the CIS and CIGS thin film solar cells, use TCOs as contacts. Our group works to provide a reliable theoretical understanding of the electronic properties, both quasiparticle band structures and absorption spectra of these materials. This is achieved by using state-of-the-art self-consistent GW methods (for the band structures) combined with the solution of the Bethe-Salpeter equation for the evaluation of the absorption.

## Spectroscopy of clusters and molecules within time-dependent DFT

Time-dependent density-functional theory (TDDFT) has repeatedly shown in the last decade its usefulness when attempting the challenge of predicting spectra of clusters and of molecules of biological interest. The reason is the unparalleled balance between the computational load that it requires and the accuracy that it provides. In the past few years, we have performed a number of theoretical studies on the photo-response of inorganic and organic molecules by making use of TDDFT.

## van der Waals interactions

Van der Waals interactions have been studied for more than a century in fields ranging from Physics to Biology. Although very weak at short ranges, they can become the dominant force at larger distances. It is therefore not surprising to see van der Waals terms appearing in the simulation of protein folding, or in the study of the interaction between nanostructures.

We use TDDFT to calculate the Casimir-Polder coefficients that appear in the asymptotic expansion of the van der Waals interaction. We study both the case of molecule-molecule and molecule-surface interactions. Currently we are using this framework to derive classical force-fields to be used in the simulation of proteins on semiconducting surfaces.

## Functionals for (TD)DFT and RDMFT

For many cases, excellent approximations for the xc functional - the key quantity in (TD)DFT exist. In fact, the so-called adiabatic local density approximation (or the adiabatic generalized density approximation) already yields equilibrium geometries, vibrational frequencies, optical spectra, etc. in very good agreement with experiment. However, these approximations fail spectacularly in several systems, namely for extended solids (where the gap is strongly underestimated), charge transfer excitations (whose frequencies are strongly underestimated), and the interaction of finite systems with strong lasers (ionization is overestimated sometimes by several orders of magnitude, for example). In general, these deficiencies can be traced back to the lack of a non-local (either in time and/or in space) dependence on the density, or to a self-interaction problem that leads to the wrong asymptotic behaviour of the exchange-correlation potential. A possible solution for this problem has been proposed by Becke and Johnson in 2006. They devised a semi-local functional, a meta-generalized gradient approximation (meta-GGA), that is able to reproduce to a very large extent the exchange potential. Since then other functionals appeared that not only have the correct asymptotic behavior, but also yield excellent bang-gaps for solids.

A very promising approach in the field of electronic correlation to go beyond DFT through the use of Reduced Density Matrix Functional Theory (RDMFT). RDMFT has been emerging as an excellent tool for the study of correlation in molecular systems. It is based on Gilbert's theorem, that asserts a one-to-one correspondence between the ground-state many-body wave function and the one-particle reduced density matrix (1-RDM). Several theoretical advantages are immediately evident from using the 1-RDM instead of, e.g., the electronic density as in standard DFT and, therefore, one could expect that it is much easier to find good correlation functionals for RDMFT than to standard DFT.

## Development of scientific software

We are active developers of the computer code octopus. This program, which is open source software under the GNU general public license (GPL), simulates the dynamics of electrons and nuclei under the influence of time-dependent fields. The electronic degrees of freedom are treated quantum-mechanically within TDDFT, while the nuclei are considered to behave as classical point particles. In this code, all quantities are discretised in real space using a uniform grid, and the simulations are performed in real time. Over the past years, octopus has evolved into a fairly complex and complete tool, and is now used by several research groups around the world. Due to the open nature of the project, it is hard to estimate the total number of users. However, an estimate can be made from the number of downloads (an average of 164 downloads per month in 2009), and from the number of participants in the users mailing list (230 participants as of October 2009). Even in this short time-scale, there were several papers published or submitted by independent groups presenting calculations performed with octopus.

We also develop libxc, a library of exchange-correlation functionals for density-functional theory. The aim is to provide a portable, well tested and reliable set of exchange and correlation functionals that can be used by all codes. In Libxc you can find different types of functionals: LDA, GGA, hybrids, and mGGA. It can calculate the functional itself and its derivative; for most functionals, higher-order derivatives are available.