Density Functional Theory and Application

Work with Stefan Grimme, Eike Caldeweyher, Georg Kresse, and Peter Schwerdtfeger

PAW Pseudopotetials and DFT-D3 Parameters for Superheavies - My first contact with DFT development was application-driven: The aim was to establish a consistent methodology for first-principles simulations of the Main Group superheavy elements Cn-Og (Z=112-118) to explore their bulk properties (see also Periodic Trends) together with Peter Schwerdtfeger. The first part of this methodology are Projector-Augmented Wave (PAW) pseudopotentials, the first of which I generated in cooperation with G. Kresse. These enable efficient plane-wave DFT simulations of the liquid and solid phases of the respective elements by taking care of the numerous (100) core electrons via an effective one-electron potential, which includes a large part of the relativistic effects (I also made non-relativistic PPs). The second part is an extension of the set of atomic parameters for DFT-D3 dispersion correction, which was done in cooperation with S. Grimme and S. Ehlert. These are particularly desirable for non-metallic elements, like relativistic Cn, Fl, and Og, where pure functionals like DFT/PBEsol provide the wrong asymptotic behavior (illustrated in Fig. 2 of this article on Og). The final methodology and some exemplary applications to cohesive energies and the adsorption on Au-surfaces can be found in this PCCP article “Exploring the chemical nature of super-heavy main-group elements through efficient plane-wave density-functional theory”, which made the cover page (left) and was designated as a “Hot Article”.

Refinement of DFT-D4 for Periodic Systems - Having moved to Stefan Grimme’s Group in Bonn, I joined E. Caldeweyher, who was working on an extension of DFT-D4 for periodic systems. Here, my extensive expertise with VASP for periodic systems, surfaces, and plane-wave DFT came in handy in this framework. For this work, we benchmarked a comprehensive set of dispersion-corrected DFT methods for a variety of applications, ranging from the prediction of salt polarizabilities, over the absorption of polar and polar molecules on different substrates, to the prediction of the lattice/cohesive energy of molecular crystals and metals. As expected, the extended D4 model was superior to D3, particularly in highly coordinated Group 1-5 elements, for which highly coordinated reference systems were lacking (D3/D4 derive the polarizability and C6 coefficients via interpolation based on a fractional coordination number CN).

r²SCAN-3c composite DFT Method - A recent project in cooperation with Stefan Grimme was designing, implementing, and testing the r²SCAN-3c composite DFT method. This project was kicked-off with the publication of the re-regularized r²SCAN functional of Furness and coworkers, specifically when Stefan realized the potential of this new meta-GGA functional for conformational energies. While we were tailoring the ingredients for this composite methods, like the purpose-made mTZVPP basis set, specific parameters for the DFT-D4, and a generalized gCP correction for basis-set superposition error, my main task was to make sure that the new method performs as well for periodic solids and molecular crystals as for molecules. To this end, I considered the X23, DMC8, and ICE10 benchmark sets, benzene adsorption on Cu, Ag, and Au, CO on MgO, and Ethyne on NaCl, which are all showcased in the final article. Most notably, these tests revealed that it is beneficial to scale up the three-body terms in the D4 model significantly and fine-tune the charge-scaling of the D4 polarizabilities. Apart from these tales about its development, the resulting r²SCAN-3c shows an impressive cost/accuracy ratio, and I have started using it heavily in my normal workflows. The perhaps most striking use-case is that r²SCAN-3c can provide “quick-but-not-dirty” results for conformational and reaction energies with an accuracy rivaling that of hybrid-DFT/QZ calculations at two to three orders of magnitude lower cost. Another key feature of this functional which clearly surpasses its predecessor SCAN is the performance in the short- and mid-range (mGGA) correlation. This makes for a particularly good fit with the long-ranged (semiclassical DFT-D4) dispersion correction. I believe this feature is responsible for the excellent performance of r²SCAN-3c for adsorption energies (see Figure below) and presumably also for intramolecular non-covalent interactions (conformational energies).

ω-dependency of the DFT-D damping function in RSHs - This project is the merger of my endeavors into the fields of DFT-D development and excited-state methods: We explore how a variation of the range-separation parameter in range-separated hybrid functionals affects the parameters of the dispersion correction. This is an important topic since these functionals are often combined with optimal tuning, which theoretically means the DFT-D parameters obtained for the default ω are no longer suitable. First results show that for PBE-derived RSHs (ωPBE, ωPBEh) and ωB97M-V, the performance is robust over a large ω-range, whereas BLYP/B88 derived RSHs (in particular LC-BLYP but also CAM-QTP01) show some odd behavior even at moderate ω-values, indicating there might be a problem with the B88 exchange functional or the µB88 range-separated GGA exchange. The results are written up, and the paper is currently under review.