Related papers: Accurate and efficient linear scaling DFT calculat…

Density functional theory (DFT) is one of the main methods in Quantum Chemistry that offers an attractive trade off between the cost and accuracy of quantum chemical computations. The electron density plays a key role in DFT. In this work,…

An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible…

The delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a…

Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with…

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

Band alignment between two materials is of fundamental importance for multitude of applications. However, density functional theory (DFT) either underestimates the bandgap - as is the case with local density approximation (LDA) or…

The density functional theory (DFT) is used in a study of point defects on both UN (001) surface and sub-surface layers. We compare results for slabs of different thicknesses (both perfect and containing nitrogen or uranium vacancies) with…

We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the…

Classical density-functional theory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functional theory to multi-site…

We formulate and implement Cyclic Density Functional Theory (Cyclic DFT) -- a self-consistent first principles simulation method for nanostructures with cyclic symmetries. Using arguments based on Group Representation Theory, we rigorously…

High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…

By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…

We explore and compare three approximate schemes allowing simple implementation of complex density functionals by making use of selfconsistent implementation of simpler functionals: (i) post-LDA evaluation of complex functionals at the LDA…

We present the first mathematical analysis of stochastic density functional theory (DFT) in the context of the Hartree approximation. We motivate our analysis via the notion of nearly-optimal or $\tilde{O}(n)$ scaling with respect to the…

The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…

Molecular-level understanding of the interactions between the constituents of an atomic structure is essential for designing novel materials in various applications. This need goes beyond the basic knowledge of the number and types of…

Density Functional Theory (DFT) is a powerful and accurate tool exploited in Nuclear Physics to investigate the ground-state and some collective properties of nuclei along the whole nuclear chart. Models based on DFT are, however, not…