Related papers: Scaling Invariance of Density Functionals
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of…
Density scaling has a rich history in density functional theory, providing exact conditions for use in the construction of ever more accurate approximations to the unknown exchange-correlation functional. We define a conjugate potential…
We address the problem of interacting electrons in an external potential by introducing the occupied spectral density $\rho(\mathbf{r},\omega)$ as fundamental variable. First, we formulate the problem using an embedding framework, and prove…
We construct a stationary density functional for the partition function from a chosen set of one (boson) line irreducible Feynman diagrams. The construction does not proceed by the inversion of a Legendre transform. It is formulated for…
A recent discovery about the inertial range of homogeneous and isotropic turbulence is the saturation of the scaling exponents $\zeta_n$ for large $n$, defined via structure functions of order $n$ as $S_{n}(r)=\overline{(\delta_r…
The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional…
A large number of observations have shown that the dark matter halo surface density, given by the product of halo core radius and core density is nearly constant for a diverse suite of galaxies. Although this invariance of the halo surface…
Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spin polarization, an accurate estimate for the energy of a modified homogeneous electron gas where electrons repel each other only with a long-range…
The scaling function $f(\psi')$ for medium and heavy nuclei with $Z\neq N$ for which the proton and neutron densities are not similar is constructed within the coherent density fluctuation model (CDFM) as a sum of the proton and neutron…
An atom placed inside a cavity of finite dimension offers many interesting features, and thus has been a topic of great current activity. This work proposes a density functional approach to pursue both ground and excited states of a…
We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key examples are versions of the weight-dependent random connection…
We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is deter-mined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient…
We consider inference problems for high-dimensional (HD) functional data with a dense number (T) of repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal…
Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between thermal fluctuations between virial and potential-energy in the isochoric ensemble. This…
We describe how density-functional theory, well-known for its many uses in ab initio calculations of electronic structure, can be used to study the ground state of inhomogeneous model Hamiltonians. The basic ideas and concepts are discussed…
We investigate the dependence of cluster abundance $n(>M,r_{cl})$, i.e., the number density of clusters with mass larger than $M$ within radius $r_{cl}$, on scale parameter $r_{cl}$. Using numerical simulations of clusters in the CDM…
We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…
The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We…
A simple model is proposed for the direct correlation function (DCF) for simple fluids consisting of a hard-core contribution, a simple parametrized core correction, and a mean-field tail. The model requires as input only the free energy of…
We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the {\Gamma}-limit for constant target functions, revealing how the…