Related papers: Issues and Challenges in Orbital-free Density Func…
The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation…
Orbital-free density functional theory (OF-DFT) constitutes a computationally highly effective tool for modeling electronic structures of systems ranging from room-temperature materials to warm dense matter. Its accuracy critically depends…
Consider two manifolds~$M^m$ and $N^n$ and a first-order Lagrangian $L(u)$ for mappings $u:M\to N$, i.e., $L$ is an expression involving $u$ and its first derivatives whose value is an $m$-form (or more generally, an $m$-density) on~$M$.…
We present a kinetic energy tensor that unifies a scalar kinetic energy density commonly used in meta-Generalized Gradient Approximation functionals and the vorticity density that appears in paramagnetic current-density-functional theory.…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
The modified local spin density functional and the related local potential for excited states is tested by employing the ionization potential theorem. The functional is constructed by splitting $k$-space. Since its functional derivative…
One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory…
We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density…
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled…
Response calculations in density functional theory aim at computing the change in ground-state density induced by an external perturbation. At finite temperature these are usually performed by computing variations of orbitals, which involve…
Orbital-free density functional theory (OFDFT) offers a challenging way of electronic-structure calculations scaled as $\mathcal{O}(N)$ computation for system size $N$. We here develop a scheme of the OFDFT calculations based on the…
Nonlocal kinetic energy density functionals (KEDFs) with density-dependent kernels are currently the most accurate functionals available for orbital-free density functional theory (OF-DFT) calculations. However, despite advances in…
An accurate expression of the kinetic energy density of an electronic distribution in terms of the single particle reduced density matrix for atomic and molecular systems is a long-standing problem in electron structure theory. Existing…
The pseudospectral method is a powerful tool for finding highly precise solutions of Schr\"{o}dinger's equation for few-electron problems. We extend the method's scope to wave functions with non-zero angular momentum and test it on several…
Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is…
Two electrons at the threshold of ionization represent a severe test case for electronic structure theory. A pseudospectral method yields a very accurate density of the two-electron ion with nuclear charge close to the critical value.…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (XC) free energy functional accurate over a wide range of state conditions.…
We consider optimization problems that arise when estimating a set of unknown parameters from experimental data, particularly in the context of nuclear density functional theory. We examine the cost of not having derivatives of these…
Density Functional Theory has long struggled to obtain the exact exchange-correlational (XC) functional. Numerous approximations have been designed with the hope of achieving chemical accuracy. However, designing a functional involves…