Van der Waals effects with Density Functional Theory: exact approach for small isolated systems and improved description of interlayer bonding in TiS2.

In this Thesis we propose to improve the description of vdW effects with DFT considering two approaches. In the first one we derive a novel sum-rule approach, applied to simple, but emblematic, systems such as the Hydrogen atom, a system of quantum harmonic oscillators and a particle confined in a spherical well potential. In this context, firstly, we derive exact expressions concerning both polarizability and vdW density functionals, giving anlytical results when it is possible and then we make a comparison between our results and those obtained within popular, well established theoretical vdW approaches. In the second part of the Thesis instead we mainly focus on a the description of vdW interactions with DFT considering the specific class of layered materials, analyzing one of them, TiS2, in detail. We characterize the way vdW interactions are modeled by state of the art Density Functional Theory (DFT) methods, particularly focusing on the electron density distribution, being this latter the physical quantity lying at the core of DFT. We provide extensive benchmarking for the electron density distribution, first by reproducing reported hortcomings of standard approaches, and, then, on the basis of physical considerations, by generating a novel pseudopotential whose integration in a DFT scheme almost totally overcome the issues mentioned above.