Bandgaps, binding energies and charge transfer in density functional theory from a meta-generalized gradient approximation

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Density functional theory is a special branch of many particle quantum mechanics in which the particle density and not the wavefunction is the fundamental quantity. With the help of density functional theory calculations one can predict the structure and the properties of atoms, molecules and solids. The theory therefore is used in many areas of chemistry, condensed matter physics and material science in order to gain insight into the properties of materials in computer simulations that are based only on the fundamental laws quantum mechanics, i.e., without empirical input. For example, calculations can predict how atoms assemble to form molecules and crystals, and can thus help to discover and develop new materials. For practical calculations one needs approximations that describe the quantum mechanical many-body effects of exchange and correlation. The exchange-correlation functional is decisive both for the accuracy and the numerical expense of density functional theory calculations. In particular the prediction of properties that are important in energy relevant materials, e.g., the band gaps of solar cell materials or charge-transfer phenomena in catalysts, so far requires the use of computationally expensive exchange-correlation functionals. Therefore, it is difficult to simulate large systems with many electrons. The aim of this project is to develop a new approximation for exchange and correlation that comes at moderate computational cost, so that it allows for large simulations, yet at the same time is accurate for band gaps, binding energies, and charge transfer. Bringing these different properties together is made possible within a special class of exchange-correlation approximations called meta-Generalized Gradient Approximations.