Related papers: Deriving approximate functionals with asymptotics

In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the…

In order to construct a general density-functional theory for nonuniform fluid mixtures, we propose an extension to multicomponent systems of the weighted-density approximation (WDA) of Curtin and Ashcroft [Phys. Rev. A 32, 2909 (1985)].…

We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…

Consider the Riemann sum of a smooth compactly supported function h(x) on a polyhedron in R^d, sampled at the points of the lattice Z^d/t. We give an asymptotic expansion when t goes to infinity, writing each coefficient of this expansion…

We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D$\Gamma$A). This approach contains the important local correlations of DMFT, giving, among…

The Skyrme nuclear energy density functional theory (DFT) is used to model neutron-induced fission in actinides. This paper focuses on the numerical implementation of the theory. In particular, it reports recent advances in DFT code…

Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical…

Density Functional Theory (DFT) is a robust framework for modeling interacting many-body systems, including the equation of state (EoS) of dense matter. Many models, however, rely on energy functionals based on assumptions that have not…

A new functional form for the exchange enhancement in the generalized gradient approximation within density functional theory is given. The functional form satisfies the constraints used to construct the Perdew-Burke-Ernzerhof (PBE)…

We argue that any general mathematical measure of density error, no matter how reasonable, is too arbitrary to be of universal use. However the energy functional itself provides a universal relevant measure of density errors. For the…

We present a differentiation framework for plane-wave density-functional theory (DFT) that combines the strengths of forward-mode algorithmic differentiation (AD) and density-functional perturbation theory (DFPT). In the resulting AD-DFPT…

We consider a $\mathbb{R}$-extension of one dimensional uniformly expanding open dynamical systems and prove a new explicit estimate for the asymptotic spectral gap. To get these results, we use a new application of a "global normal form"…

A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the…

Local density approximation (LDA) to the density functional theory (DFT) has continuous derivative of total energy as a number of electrons function and continuous exchange-correlation potential, while in exact DFT both should be…

Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…

In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth, respectively for large gradients and small jump amplitudes. A distinctive…

A 2016 paper by M Wilkinson in Physical Review Letters suggests that large-deviation theory is a suitable framework for studying unexpectedly rapid rain formation in collector-drop collision processes. Wilkinson derives asymptotic…

We present a computational approach which is tailored for reducing the complexity of the description of extended systems at the density functional theory level. We define a recipe for generating a set of localized basis functions which are…

Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree $n$ and parameters $\alpha$ and $\beta$. From these new results, asymptotic expansions of the zeros are derived and methods are…

Multi-configurational wave functions are known to describe electronic structure across a Born-Oppenheimer surface qualitatively correct. However, for quantitative reaction energies, dynamical correlation originating from the many…