Related papers: A step toward density benchmarking -- the energy-r…
The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to…
Background: Mean-field methods based on an energy density functional (EDF) are powerful tools used to describe many properties of nuclei in the entirety of the nuclear chart. The accuracy required on energies for nuclear physics and…
We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
Machine learning has now become an integral part of research and innovation. The field of machine learning density functional theory has continuously expanded over the years while making several noticeable advances. We briefly discuss the…
Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for…
Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the…
The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation…
We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density…
Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…
The calculation of the band-gap by density-functional theory (DFT) methods is examined by considering the behavior of the energy as a function of number of electrons. It is found that the incorrect band-gap prediction with most approximate…
We review the role of self-consistency in density functional theory. We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to Partition-DFT, which generalizes all aspects of standard DFT. In each case, the analysis…
It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…
We present a detailed analysis of the broken-symmetry mean-field solutions using a four-electron rectangular quantum dot as a model system. Comparisons of the density-functional theory predictions with the exact ones show that the symmetry…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
Density functional theory (DFT) is an essential building block for modern theoretical physics, chemistry, and engineering, especially those concerning electronic properties. Through decades of development, various program packages for…
We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher…
HF-DFT, the practice of evaluating approximate density functionals on Hartree-Fock densities, has long been used in testing density functional approximations. Density-corrected DFT (DC-DFT) is a general theoretical framework for identifying…
Empirical fitting of parameters in approximate density functionals is common. Such fits conflate errors in the self-consistent density with errors in the energy functional, but density-corrected DFT (DC-DFT) separates these two. We…
Variable selection for a multiple regression model (Noisy Linear Perceptron) is studied with a mean field approximation. In our Bayesian framework, variable selection is formulated as estimation of discrete parameters that indicate a subset…