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Density-functional theory simplifies many-electron calculations by approximating the exchange and correlation interactions with a one-electron operator that is a functional of the density. Hybrid functionals incorporate some amount of exact…
In the recent work of S. Sharma \emph{et al.}, (arxiv.org: arxiv:0912.1118), a single-electron spectrum associated with the natural orbitals was defined as the derivative of the total energy with respect to the occupation numbers at half…
Based on the time-dependent density-functional theory, we have derived a rigorous formula for the stopping power of an {\it interacting} electron gas for ions in the limit of low projectile velocities. If dynamical correlation between…
We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…
The frequency-dependent exchange-correlation potential, which appears in the usual Kohn-Sham formulation of a time-dependent linear response problem, is a strongly nonlocal functional of the density, so that a consistent local density…
An exchange correlation energy functional involving fractional power of the one-body reduced density matrix [Phys. Rev. B {\bf 78}, 201103 (2008)] is applied to finite systems and to the homogeneous electron gas. The performance of the…
It is shown that the equation of motion of the one-particle Green function of an interacting many-electron system is governed by a multiplicative time-dependent exchange-correlation potential, which is the Coulomb potential of a…
Reduced-density-matrix-functional theory is applied to open-shell systems. We introduce a spin-restricted formulation by appropriately expressing approximate correlation-energy functionals in terms of spin-dependent occupation numbers and…
The Coulomb exchange and correlation energy density functionals for electron systems are applied to nuclear systems. It is found that the exchange functionals in the generalized gradient approximation provide agreements with the exact-Fock…
We propose exchanging the energy functionals in ground-state DFT with physically equivalent exact force expressions as a new promising route towards approximations to the exchange-correlation potential and energy. In analogy to the usual…
Using non-equilibrium Green's functions combined with many-body perturbation theory, we have calculated steady-state densities and currents through short interacting chains subject to a finite electric bias. By using a steady-state…
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional…
First-principles calculations based on density functional theory have been widely used in studies of the structural, thermoelastic, rheological, and electronic properties of earth-forming materials. The exchange-correlation term, however,…
A review of the approximations in any time-dependent density functional calculation of excitation energies is given. The single-pole approximation for the susceptibility is used to understand errors in popular approximations for the…
Quantum mechanical methods based on the density functional theory (DFT) offer a realistic possibility of first-principles design of organic donor-acceptor systems and engineered band-gap materials. This promise is contingent upon the…
Fractional occupation numbers can produce open-shell degeneracy in density functional theory. We develop the corresponding perturbation theory by requiring that a differentiable map connects the initial and perturbed states. The degenerate…
Using an accurate semi-analytic wavefunction for two electron atoms, we construct the external potential for varying strength of electron-electron (e-e) interaction. Using this potential we explicitly calculate the energy of their positive…
The current-current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson's localization length can be computed entirely from this…
We analytically construct the wave function that, for a given initial state, produces a prescribed density for a quantum ring with two non-interacting particles in a singlet state. In this case the initial state is completely determined by…
In this chapter, we provide a review of ground-state Kohn-Sham density-functional theory of electronic systems and some of its extensions, we present exact expressions and constraints for the exchange and correlation density functionals,…