This conference will provide an overview of the challenges remaining in the field of both density functional and density matrix theories.

Density Functional Theory (DFT) has constituted a very important breakthrough in quantum mechanics, proposing the electron density function and not the much more complicated many-electron wave function as basic carrier of information. The theorems by Hohenberg and Kohn and the Kohn-Sham ansatz brought DFT from an essentially solid state physics tool to the chemist’s desktop. In addition, there is also a growing interest in using density matrices as basic descriptors of quantum chemical systems. In Density Matrix Functional Theory (DMFT), a functional is used to relate the one particle or first order density matrix to the energy and the search of this functional is a central topic in this research area. On the other hand, the second order density matrix can also be directly variationally optimized (so-called v2DM theory). Indeed, the energy of the system as a functional of this matrix is exactly known but now the need emerges to implement non-trivial N-representability constraints in computationally rather demanding algorithms such that behind the v2DM there lies a proper wave function.

Both DFT and DMFT still face a number of challenges; for DFT, this involves, among others, the design of functionals able to accurately describe dispersion, the accurate computation of reaction energies and activation barriers of chemical reactions, the extension to include molecular dynamics and the treatment of excited states. In the case of v2DM, the main challenges lie in identifying N-representability conditions that are important for describing chemical systems, but are still computationally attractive. In DMFT, the search for functionals of ever increasing accuracy is a central topic.
This conference aims at providing a recent summary of these challenges and their possible solutions as presented by international leading authorities in the field. The relatively small size of the conference is ideal for stimulating scientific discussions on these topics and for the setup of new collaborations.