Related papers: New biorthogonal potential--density basis function…
In the article [11] of L. Kunyansky a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the…
Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived from the microscopic theory by a systematic coarse-graining procedure. Within the framework of this theory we obtain the…
In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for a new, admittedly academic, model, but to investigate the structure of…
We determine the fully resolved equilibrium density profiles for two binary hard-sphere crystal structures using classical density functional theory through the White Bear II functional from fundamental measure theory. While for the…
In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the…
The purpose of this paper is to establish L^p error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular,…
An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…
We introduce nested gausslet (NG) bases, an improvement on previous gausslet bases which can treat systems containing atoms with much larger atomic number. We also introduce pure Gaussian distorted gausslet bases, which allow the…
Complete orthonormal sets of exponential-type orbitals with non-integer principal quantum numbers are discussed as basis functions in non-relativistic Hartree-Fock-Roothaan electronic structure calculations of atoms. A method is proposed to…
Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel…
Using Bauer's expansion and properties of spherical Bessel and Legender functions, we deduce a new transform and briefly indicate its use.
In this work, a new functional is introduced to treat pairing correlations in finite many-body systems. Guided by the projected BCS framework, the energy is written as a functional of occupation numbers. It is shown to generalize the BCS…
We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…
We use the classical version of the density-functional theory in the weighted-density approximation to build up the entire phase diagram and the interface structure of a two-dimensional lattice-gas model which is known, from previous…
In this paper, we consider weighted Bergman spaces $\mathcal{B}_{\alpha,p}$ of log-subharmonic functions on the unit sphere. Using the isoperimetric inequality for the spherical metric we prove certain monotonicity property for super-level…
When two bodies get into contact, only a small portion of the apparent area is actually involved in producing contact and friction forces, because of the surface roughnesses. It is therefore crucial to accurately describe the morphology of…
We propose a new type of effective densities via the potential distribution theorem. These densities are for the sake of enabling the mapping of the free energy of a uniform fluid onto that of a nonuniform fluid. The potential distribution…
Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudo-potential…
An exchange-correlation energy functional $ E_{\mathrm xc} $ and the resultant exchange-correlation potential $ v_{\mathrm xc}({\bf r}) $ in density-functional theory are proposed using orbital-dependent coupling-constant-averaged pair…
There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274…