Related papers: Exact density functional obtained via the Levy con…
The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of…
The recently published analytic probability density function for the mildly non-linear cosmic density field within spherical cells is used to build a simple but accurate maximum likelihood estimate for the redshift evolution of the variance…
Within density-functional theory, the local-density approximation (LDA) correlation functional is typically built by fitting the difference between the near-exact and Hartree-Fock (HF) energies of the uniform electron gas (UEG), together…
The density functional theory originally developed by Hohenberg, Kohn and Sham provides a rigorous conceptual framework for dealing with inhomogeneous interacting Fermi systems. We extend this approach to deal with inhomogeneous interacting…
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…
In this article, we study the density function of the numerical solution of the splitting averaged vector field (AVF) scheme for the stochastic Langevin equation. To deal with the non-globally monotone coefficient in the considered…
One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to…
A practical electronic structure method in which a two-body functional is the fundamental variable is constructed. The basic formalism of our method is equivalent to Hartree-Fock density matrix functional theory [M. Levy in {\it Density…
We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…
Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number N depends…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a path. Here I use the Hohenberg-Kohn theorems and the definition of…
An exchange energy functional is proposed and tested for obtaining a class of excited-state energies using density functional formalism. The functional is the excited-state counterpart of the local-density approximation functional for the…
The exact universal functional of integer charge leads to an extension to fractional charge asymptotically when it is applied to a system made of asymptotically separated densities. The extended functional is asymptotically local and is…
We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…
There are different ways to obtain an exact one-electron theory for a many-electron system, and the exact electron factorization (EEF) is one of them. In the EEF, the Schr\"odinger equation for one electron in the environment of other…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
A detailed convex analysis-based formulation of density-functional theory for periodic systems in arbitrary dimensions is presented. The electron-electron interaction is taken to be of Yukawa type, harmonising with underlying function…
We introduce 'single-particle-exact density functional theory' (1pEx-DFT), a novel density functional approach that represents all single-particle contributions to the energy with exact functionals. Here, we parameterize interaction energy…