Density-functional theory and beyond for organic electronic materials

Organic electronics is a vibrant research field in both industry and academia as it promises easy-to-process, low-cost and flexible (opto)electronic devices. However, from a theoretical point of view the relevant materials open the Pandora’s box of ‘standard’ density-functional theory (DFT) with semi-local or hybrid approximations to the exchange correlation (XC) functional. These functionals lack the long-range tail of van der Waals (vdW) interactions and suffer from severe self-interaction errors. Both aspects need to be corrected when molecules weakly interact with each other. Otherwise, electron transfer and binding-curve artefacts may occur, which is demonstrated in this thesis for the tetrathiafulvalene (TTF) – tetracyanoquinodimethane (TCNQ) complex. To overcome this limitation, I construct an XC functional that obtains the exchange energy by exploiting a formally exact condition of DFT and the singleparticle Green’s function. With this procedure, the fraction of exact exchange is obtained in a non-empirical, material-specific way. The functional reduces the selfinteraction error and exhibits significantly improved spectral properties compared to standard DFT functionals. It is able to satisfactorily describe the ground-state electron density of the TTF-TCNQ complex. Furthermore, it is compatible with the vdW correction scheme of Tkatchenko and Scheffler, which adds the long-range 1/R vdW tail to a given DFT functional with density-dependent C6 coefficients. Alternatively, vdW interactions can be described by methods based on the random-phase approximation to the correlation energy, most notably second-order renormalized perturbation theory (rPT2). As rPT2 resides in the framework of many-body perturbation theory, this thesis assesses its starting point dependence, i.e., the dependence on the unperturbed Hamiltonian. Extensive benchmark calculations show that rPT2 is sensitive to the starting point with a clear trend of performance loss upon increasing the fraction of exact exchange in the underlying DFT Hamiltonian. Both, TTF and TCNQ form molecular crystals. Based on the implementation of the stress tensor and unit cell relaxation in the FHI-aims code, their basic geometric, energetic and electronic properties are investigated. It is shown that the inclusion of vdW interactions is crucial, in particular for the description of lattice parameters. The thermal crystalline expansion is estimated and shown to be anisotropic along the individual lattice vectors. Furthermore, the low-index surfaces of both crystals exhibit a strong orientation dependence in the ionization potential.

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