PhD Conferral Sara Giarrusso
Aula, Vrije Universiteit Amsterdam
Approximations and exact properties of density functionals from the strong-interaction limit of DFT
Prof.dr. P. Gori Giorgi, copromotor dr. K.J.H. Giesbertz
Amsterdam Institute of Molecular and Life Sciences
In the last decades, Density Functional Theory, in its Kohn-Sham formulation (KS-DFT), has emerged as an essential method for predicting and understanding a wide range of chemical and physical properties, due to its excellent accuracy compared to its computational cost.
In practice, it accounts for over 90% of all quantum mechanical simulations.
The use of KS-DFT relies, however, on models for the so-called exchange-correlation (XC) functional, which is the term that collects all effects which we are not able to treat explicitly. Despite its numerous successes, there is still a lot of cases (dissociation processes, reactions involving transition metals, non-covalent interactions) where its accuracy and, therefore, its applicability have to be improved. The overall goal of my research is to extend the applicability of KS-DFT by developing new models anchored on solid theoretical ground, from the standpoint of a mathematically exact limit of the theory, known as its “strong-interaction limit”.
In particular, the work presented in my Ph.D. thesis
• highlights the broad potential of models, containing the strong-interaction limit ingredient, for future applications on challenging compounds such as those containing noble metal clusters and complexes;
• proposes a novel approach towards an efficient resummation of the perturbation series expansion around the Hartree-Fock reference state which possesses many promising qualities at the theoretical level;
• reports for the first time several exact properties useful to guide density functionals development, such as an analytical relation between the two most commonly used definitions of the XC functional, a qualitative feature of the effective potential in the case of a stretched hetero-nuclear bond and a new sum rule (among others).
In summary, this work contributes to show that explicit functionals of the density which are distinctive of the strong-interaction limit can be used to build novel methodologies, in contrast with a famous classification of the possible methods in the field - known as the Jacob’s ladder towards the “heaven of chemical accuracy” – according to which implicit and computationally expensive functionals are required for improved quality.