Density Functional Theory

P. Ziesche

Iris Theophilou, Teresa E. Reinhard, Ángel Rubio +1 more

Abstract Recently a novel approach to find approximate exchange–correlation functionals in density-functional theory was presented (Mordovina et al 2019 J. Chem. Theory Comput. 15 5209), which relies on approximations to the interacting wave function using density-matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced density matrix of an auxiliary system the same as the approximate interacting density matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn–Sham approach to density-functional theory. Yet other choices are possible and allow to connect DMET with other density-functional theories such as kinetic-energy density functional theory or reduced density-matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a density-functional perspective and show how both approaches can be used to supplement each other. We do not present a specific realization of combining density-functional methods with DMET but rather provide common grounds to facilitate future developments that encompass both approaches. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of density-functional theories can be used to identify uniquely defined auxiliary systems and projections in DMET and how to construct approximations for different density-functional theories using DMET inspired projections. Such alternative approximation strategies become especially important for density-functional theories that are based on non-linearly coupled observables such as kinetic-energy density-functional theory, where the Kohn–Sham fields are no longer obtainable by functional differentiation of an energy expression, or for reduced density-matrix functional theories, where a straightforward Kohn–Sham construction is not feasible.

Reiner M. Dreizler, Eberhard K. U. Gross

G. F. Bertsch, Kazuhiro Yabana

Mihai V. Putz

Primer Density Functional Theory Basics of Density Functional Theory (DFT) Physical Realizations of DFT Popular Density Functionals of Energy Chemical Realization of DFT Primer Density Functional Bose-Einstein Condensation Theory Basics of the Bose-Einstein Condensation (BEC) PSI-Density Functional Theory of Bose-Einstein Condensation Modern Quantum Theories of Chemical Bonding Bondonic Picture of Chemical Bond Chemical Action Picture of Chemical Bond Fermionic-Bosonic Picture of Chemical Bond

Jaime Keller

We analyze the notion of Density Functional Theory from the definition of a density of action over spacetime. We derive a theory to obtain the energy as a function of particle density, which contains the standard Density Functional Theory (DFT) and enlarges it by considering in one functional both the density of particles and the energy density per particle. The formulation presents a mathematical structure where the particle density is a factor of the energy per particle. The starting point is the definition of a global action density K(x) from which, by successive projections, the density Kj for a given type j of particles is projected. This density is then factorized into gauge dependent factors, which are shown to generate known relations and structures of quantum mechanics. Within DFT the minimization of the energy density functional, with respect to changes in the density, contains as a consequence two terms: the first corresponds to the standard density functional theory for non-interacting particles, and the second to the optimization of the kinetic and the interparticle interaction energy, terms that go beyond the standard DFT. We show explicitly the relation of the present approach to standard Wave Quantum Mechanics and show explicitly the reasons within spacetime- action of several basic postulates of Quantum Mechanics.