Abstract:
The dynamical transverse magnetic Kohn-Sham susceptibility calculated within time-dependent density functional theory shows a fairly linear behavior for a finite energy window. This observation is used to propose a scheme where the computation of this quantity is greatly simplified. Regular simulations based on static density functional theory can be used to extract the dynamical behavior of the magnetic response function. Besides the ability to calculate elegantly damping of magnetic excitations, we derive along the way useful equations giving the main characteristics of these excitations: effective $g$-factors and the resonance frequencies that can be accessed experimentally using inelastic scanning tunneling spectroscopy or spin-polarized electron energy loss spectroscopy.

Abstract:
Given a vector space of microscopic quantum observables, density functional theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem and the existence of the universal energy functional in the dual space are proven. In this context ordinary density functional theory corresponds to the space of one-body multiplication operators. When the operators close under commutation to form a Lie algebra, the energy functional defines a Hamiltonian dynamical system on the coadjoint orbits in the algebra's dual space. The enhanced density functional theory provides a new method for deriving the group theoretic Hamiltonian on the coadjoint orbits from the exact microscopic Hamiltonian.

Abstract:
Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment densities. An example is given and consequences discussed.

Abstract:
In this tutorial presentation, we give a comprehensive introduction into the Gutzwiller variational approach and its merger with the density functional theory. The merits of this method are illustrated by a discussion of results for two-band Hubbard models and realistic multi-band Hamiltonians for iron-pnictide systems.

Abstract:
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often considered too lengthy to be included in various curricula. An alternative introduction to DFT is presented here, drawing on ideas which are well-known from thermodynamics, especially the idea of switching between different independent variables. The central theme of DFT, i.e. the notion that it is possible and beneficial to replace the dependence on the external potential v(r) by a dependence on the density distribution n(r), is presented as a straightforward generalization of the familiar Legendre transform from the chemical potential (\mu) to the number of particles (N). This approach is used here to introduce the Hohenberg-Kohn energy functional and to obtain the corresponding theorems, using classical nonuniform fluids as simple examples. The energy functional for electronic systems is considered next, and the Kohn-Sham equations are derived. The exchange-correlation part of this functional is discussed, including both the local density approximation to it, and its formally exact expression in terms of the exchange-correlation hole. A very brief survey of various applications and extensions is included.

Abstract:
Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science. Electronic structure problems in a dazzling variety of fields are currently being tackled. However, DFT has many limitations in its present form: Too many approximations, failures for strongly correlated systems, too slow for liquids, etc. This perspective reviews some recent progress and ongoing challenges.

Abstract:
The application of density functional theory to nuclear structure is discussed, highlighting the current status of the effective action approach using effective field theory, and outlining future challenges.

Abstract:
We combine density-functional theory with density-matrix functional theory to get the best of both worlds. This is achieved by range separation of the electronic interaction which permits to rigorously combine a short-range density functional with a long-range density-matrix functional. The short-range density functional is approximated by the short-range version of the Perdew-Burke-Ernzerhof functional (srPBE). The long-range density-matrix functional is approximated by the long-range version of the Buijse-Baerends functional (lrBB). The obtained srPBE+lrBB method accurately describes both static and dynamic electron correlation at a computational cost similar to that of standard density-functional approximations. This is shown for the dissociation curves of the H$_{2}$, LiH, BH and HF molecules.

Abstract:
The phenomenon of electrowetting, i.e., the dependence of the macroscopic contact angle of a fluid on the electrostatic potential of the substrate, is analyzed in terms of the density functional theory of wetting. It is shown that electrowetting is not an electrocapillarity effect, i.e., it cannot be consistently understood in terms of the variation of the substrate-fluid interfacial tension with the electrostatic substrate potential, but it is related to the depth of the effective interface potential. The key feature, which has been overlooked so far and which occurs naturally in the density functional approach is the structural change of a fluid if it is brought into contact with another fluid. These structural changes occur in the present context as the formation of finite films of one fluid phase in between the substrate and the bulk of the other fluid phase. The non-vanishing Donnan potentials (Galvani potential differences) across such film-bulk fluid interfaces, which generically occur due to an unequal partitioning of ions as a result of differences of solubility contrasts, lead to correction terms in the electrowetting equation, which become relevant for sufficiently small substrate potentials. Whereas the present density functional approach confirms the commonly used electrocapillarity-based electrowetting equation as a good approximation for the cases of metallic electrodes or electrodes coated with a hydrophobic dielectric in contact with an electrolyte solution and an ion-free oil, a significantly reduced tendency for electrowetting is predicted for electrodes coated with a dielectric which is hydrophilic or which is in contact with two immiscible electrolyte solutions.

Abstract:
This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by illustrating some of its key reformulations. The basics of DFT for thermal ensembles are explained in this context, as are tools useful for analysis and development of approximations. We close by discussing some key ideas relating thermal DFT and the ground state. This review emphasizes thermal DFT's strengths as a consistent and general framework.