Two-electron reduced density matrix as the basic variable in many-electron quantum chemistry and physics.

TL;DR: This perspective discusses the recent progress and current challenges in multireference wave function methods for dynamical electron correlation, focusing on systematically improvable methods that go beyond the limitations of configuration interaction and perturbation theory.

TL;DR: This work proves that estimating all k-RDM elements to additive precision ϵ requires on the order of (n/k)k^{3/2}log(n)/ϵ^{2} repeated state preparations, which is optimal up to the logarithmic factor.

TL;DR: In this paper, a broad range of issues lying at the foundations of Density Functional Theory, DFT, are reviewed, and the possibility of improving DFT functionals by applying in a systematic way the N -representability conditions on the second-order reduced density matrix (2-RDM) has been discussed.

TL;DR: New algorithms and computational approaches to predict and understand the behavior of correlated quantum matter are reviewed, presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum Matter with applications in grand-challenge problems.

TL;DR: In this paper, a review of current studies in density functional theory and density matrix functional theory is presented, with special attention to the possible applications within chemistry, including the concept of an atom in a molecule, calculation of electronegativities from the Xα method, pressure, Gibbs-Duhem equation, Maxwell relations and stability conditions.

TL;DR: In this paper, the authors bring students up to date with the advances in this field -the development of the theory of photoreactions, the utilization of photoresceptors in synthetic sequences, and the advancement of powerful laser techniques to study the mechanisms of the photoreaction.

TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.