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We investigate the construction of approximated exchange-correlation functionals by interpolating locally along the adiabatic connection between the weak- and the strong-coupling regimes, focussing on the effect of using approximate…
In the framework of density-functional theory, several popular density functionals for exchange and correlation have been constructed to satisfy a local form of the Lieb-Oxford bound. In its original global expression, the bound represents…
We describe a method for calculating the exchange and correlation (XC) contributions to the total energy, effective potential, and stress tensor in the generalized gradient approximation. We avoid using the analytical expressions for the…
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…
We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small…
Motivated by recent suggestions --to split the electron-electron interaction into a short-range part, to be treated within the density functional theory, and a long-range part, to be handled by other techniques-- we compute, with a…
A non-empirical exchange functional based on an interpolation between two limits of electron density: slowly varying limit and asymptotic limit, is proposed. In the slowly varying limit, we follow the study by Kleinman in 1984 which…
We propose a simple gradient-dependent bound for the exchange-correlation energy (sLL), based on the recent non-local bound derived by Lewin and Lieb. We show that sLL is equivalent to the original Lieb-Oxford bound in rapidly-varying…
Density functionals with a range-separated treatment of the exchange energy are known to improve upon their semilocal forerunners and fixed-fraction hybrids. The conversion of a given semilocal functional into its short-range analog is not…
We derive an approximate local density functional for the exchange-correlation energy to be used in density-functional calculations of two-dimensional systems. In the derivation we employ the Colle-Salvetti wave function within the scheme…
The increasing interest in the Mueller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock functional, but with a modified exchange term in…
We present a practical and accurate density functional for the exchange-correlation energy of electrons in two dimensions. The exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the…
Exact-exchange energy density and energy density of a semilocal density functional approximation are two key ingredients for modeling the static correlation, a strongly nonlocal functional of the density, through a local hybrid functional.…
According to time-dependent density functional theory, the exact exchange-correlation kernel f$_{xc}$(n, q, $\omega$) determines not only the ground-state energy but also the excited-state energies/lifetimes and time-dependent linear…
The State--Specific Kohn--Sham Density Functional Theory [arXiv:physics/0506037] is used to derive the Kohn-Sham exchange-correlation potential $\vxc$ and exchange-correlation energy $\Eco$ as explicit functionals of $v_s$ and $\phi_1$,…
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one…
Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…
The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals is available, but nearly all are based on the hierarchy of inputs commonly…
A method for calculating the Kohn--Sham exchange-correlation potential, $v_\text{XC}(\mathbf{r})$, from a given electronic wavefunction is devised and implemented. It requires on input one- and two-electron density matrices and involves…
Is the plasmon description within the non-local correlation of the van der Waals density functional by Dion and coworkers (vdW-DF1) robust enough to describe all exchange-correlation components? To address this question, we design an…