Related papers: Complexity in atoms: an approach with a new analyt…
This study investigates the interplay between relativistic effects and electron correlation effects on the first ionization energies of heavy atoms (Au through Rn, Z = 79-86). We perform two complementary analyses: (1) comparing…
We present a general multi-component density functional theory in which electrons and nuclei are treated completely quantum mechanically, without the use of a Born-Oppenheimer approximation. The two fundamental quantities in terms of which…
Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the…
The self-energy of the Dirac Brueckner-Hartree-Fock calculation in nuclear matter is parametrized by introducing density-dependent coupling constants of isoscalar mesons in the relativistic Hartree-Fock (RHF) approach where isoscalar meson…
According to density functional theory, any chemical property can be inferred from the electron density, making it the most informative attribute of an atomic structure. In this work, we demonstrate the use of established physical methods…
A relativistic version of the effective charge model for computation of observable characteristics of multi-electron atoms and ions is developed. A complete and orthogonal Dirac hydrogen basis set, depending on one parameter -- effective…
We give a new, short proof of the regularity away from the nuclei of the electronic density of a molecule obtained in [1,2]. The new argument is based on the regularity properties of the Coulomb interactions underlined in [3,4] and on…
Ongoing experimental efforts to measure with unprecedented precision electron-capture probabilities challenges the current theoretical models. The short range of the weak interaction necessitates an accurate description of the atomic…
The excess number of atoms around an ion immersed in a Bose-Einstein condensate is determined as a function of the condensate density far from the ion. We use thermodynamic arguments to demonstrate that in the limit of low densities the…
Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
The scattering of neutral particles by an atomic nucleus can lead to electronic ionisation and excitation through a process known as the Migdal effect. We revisit and improve upon previous calculations of the Migdal effect, using the…
The use of energy functionals based on density as the basic variable is advocated for ab initio molecular dynamics. It is demonstrated that the constraint of positivity of density can be incorporated easily by using square root density for…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as…
The non-relativistic large-$Z$ expansion of the exchange energy of neutral atoms provides an important input to modern non-empirical density functional approximations. Recent works report results of fitting the terms beyond the dominant…
This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…
The main goal of the present contribution is a pedagogical introduction to the fascinating world of neutron stars by relying on relativistic density functional theory. Density functional theory provides a powerful--and perhaps…