DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Energy cost to make a hole in the Fermi sea.

The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation.

The electronic ground-state energy problem: a new reduced density matrix approach.

We present here a formulation of the electronic ground-state energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the ground-state energy reduces to the search of the projection of some two-electron reduced Hamiltonian on the dual cone of N-representability conditions. Some numerical results validate the approach, both for equilibrium geometries and for the dissociation curve of N(2).