Related papers: Optimized auxiliary functions for robust mitigatio…
Semilocal exchange-correlation functionals are the most accurate, realistic and widely used ones to describe the complex many-electron effects of two-dimensional quantum systems. Beyond local density approximation, the generalized gradient…
Further developments are introduced in the theory of finite size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced Model Periodic Coulomb interaction [A. J.…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
A new algorithm for eigenvalue problems for the fractional Jacobi type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some…
The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves…
In approximate density functional theory (DFT), the self-interaction error is an electron delocalization anomaly associated with underestimated insulating gaps. It exhibits a predominantly quadratic energy-density curve that is amenable to…
The symmetric simple exclusion process is one of the simplest out-of-equilibrium systems for which the steady state is known. Its large deviation functional of the density has been computed in the past both by microscopic and macroscopic…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…
The selective frequency damping (SFD) method is an alternative to classical Newton's method to obtain unstable steady-state solutions of dynamical systems. However this method has two main limitations: it does not converge for arbitrary…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…
We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional…
Coupled cluster theory is one of the most popular post-Hartree-Fock methods for ab initio molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating…
We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching $\sim 100,000$ electrons) using Kohn-Sham density functional theory (DFT). DFT-FE is based on a local…
A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…
Despite the success of density functional approximations (DFAs) in describing the electronic properties of many-electron systems, the most widely used approximations suffer from self-interaction errors (SIE) that limit their predictive…
The evaluation of exact (Hartree--Fock, HF) exchange operator is a crucial ingredient for the accurate description of electronic structure in periodic systems through ab initio and hybrid density functional approaches. An efficient…
The expensive cost of computing exact exchange in periodic systems limits the application range of density functional theory with hybrid functionals. To reduce the computational cost of exact change, we present a range-separated algorithm…
We present an \emph{Effective Static Approximation} (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor $S(q,\omega)$, the static…