Related papers: Relating the pure and ensemble density matrix func…
We characterise purely $n$-unrectifiable subsets $S$ of a complete metric space $X$ with finite Hausdorff $n$-measure by studying arbitrarily small perturbations of elements of the set of all bounded 1-Lipschitz functions $f\colon X \to…
In practical implementations of density-functional theory, the only term where an orbital description is needed is the kinetic one. Even this term in principle depends on the density only, but its explicit form is unknown. We provide a…
Density functional theory (DFT) serves as the basis for computational discovery in materials science and chemistry, yet each calculation demands extensive human effort: adjusting algorithms when convergence stalls, revising plans when…
This paper studies DFT models for homogeneous 2D materials in 3D space, under a constant perpendicular magnetic field. We show how to reduce the three--dimensional energy functional to a one--dimensional one, similarly as in our previous…
Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are…
Classical density functional theory (DFT) is the primary method for investigations of inhomogeneous fluids in external fields. It requires the excess Helmholtz free energy functional as input to an Euler-Lagrange equation for the one-body…
Density functional theory (DFT) is one of the most widely used tools to solve the many-body Schrodinger equation. The core uncertainty inside DFT theory is the exchange-correlation (XC) functional, the exact form of which is still unknown.…
In this paper we establish a connection between density functional theory (DFT) for lattice models and common real-space DFT. We consider the lattice DFT description of a two-level model subject to generic interactions in Mermin's DFT…
A classical result in approximation theory states that for any continuous function \( \varphi: \mathbb{R} \to \mathbb{R} \), the set \( \operatorname{span}\{\varphi \circ g : g \in \operatorname{Aff}(\mathbb{R})\} \) is dense in \(…
Recently it has been shown that the heuristic Rosenfeld functional derives from the virial expansion for particles which overlap in one center. Here, we generalize this approach to any number of intersections. Starting from the virial…
Density-functional theory (DFT) has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate…
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated…
In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most…
An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density…
Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and $N$-centered ensemble formalisms, which are mathematically very similar and…
One-parameter natural exponential family (NEF) plays fundamental roles in probability and statistics. This article contains two independent results: (a) A conjecture of Bar-Lev, Bshouty and Enis states that a polynomial with a simple root…
This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a…
Kohn-Sham density functional theory is the base of modern computational approaches to electronic structures. Their accuracy vitally relies on the exchange-correlation energy functional, which encapsulates electron-electron interaction…