Related papers: A remark on the local density approximation with t…

Density functional theory offers accurate structure prediction at acceptable computational cost, but commonly used approximations suffer from delocalization error; this results in inaccurate predictions of quantities such as energy band…

The density functional theory (DFT) in electronic structure calculations can be formulated as either a nonlinear eigenvalue or direct minimization problem. The most widely used approach for solving the former is the so-called…

The description of the molecular solid phase of O$_2$, especially its ground-state antiferromagnetic insulating phase, is known to be quite unsatisfactory within the conventional local and semilocal density functional approximations used in…

We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod…

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…

With the increased focus on visual attention (VA) in the last decade, a large number of computational visual saliency methods have been developed over the past few years. These models are traditionally evaluated by using performance…

Radial basis function generated finite-difference (RBF-FD) methods have recently gained popularity due to their flexibility with irregular node distributions. However, the convergence theories in the literature, when applied to nonuniform…

The random phase approximation (RPA) is attracting renewed interest as a universal and accurate method for first-principles total energy calculations. The RPA naturally accounts for long-range dispersive forces without compromising accuracy…

We study the behavior of very thin liquid films wetting homogeneous planar and spherical substrates. In order to describe a simple fluid at very small scales, we employ a classical density functional theory (DFT). Here, we model a fluid…

The van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] is a promising approach for including dispersion in approximate density functional theory exchange-correlation functionals. Indeed, an…

Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study functionals depending on $X$. We prove an integral representation for local functionals with respect to $X$ and a result…

The structure of polydisperse hard sphere fluids, in the presence of a wall, is studied by the Rosenfeld density functional theory. Within this approach, the local excess free energy depends on only four combinations of the full set of…

This paper discusses an important issue about the virtual fields method when it is used to identify nonhomogeneous shear moduli of nearly incompressible solids. From simulated examples, we observed that conventional virtual fields, which…

Long-range exchange and correlation effects, responsible for the failure of currently used approximate density functionals in describing van der Waals forces, are taken into account explicitly after a separation of the electron-electron…

Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their…

We discuss a possible form for a theory akin to local density functional theory, but able to produce van der Waals energies in a natural fashion. The usual Local Density Approximation (LDA) for the exchange and correlation energy $E_{xc}$…

We develop a new method to isolate localized defects from extended vibrational modes in disordered solids. This method augments particle interactions with an artificial potential that acts as a high-pass filter: it preserves small-scale…

Density functional approximations are known to significantly overestimate the polarizabilities of long chain-like molecules. We study the static electric dipole polarizabilities and the vertical ionization potentials of polyacenes from…

By shifting the reference system for the local-density approximation (LDA) from the electron gas to other model systems one obtains a new class of density functionals, which by design account for the correlations present in the chosen…

Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}\}$ describing a localised projection…