Related papers: Numerical Analysis of Finite Dimensional Approxima…

The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element…

In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional…

In this chapter, we provide a review of ground-state Kohn-Sham density-functional theory of electronic systems and some of its extensions, we present exact expressions and constraints for the exchange and correlation density functionals,…

A sufficiently damped iteration of the Kohn-Sham equations with the exact functional is proven to always converge to the true ground-state density, regardless of the initial density or the strength of electron correlation, for finite…

To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose and analyze a class of iteration schemes for the discretized…

A model is developed, based on the density functional perturbation theory and the inverse Kohn-Sham method, that can be used to improve relativistic nuclear energy density functionals towards an exact but unknown Kohn-Sham…

The Kohn-Sham method uses a single model system, and corrects it by a density functional the exact user friendly expression of which is not known and is replaced by an approximated, usable, model. We propose to use instead more than one…

In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance…

To leverage the redundancy between the electronic structure computed at each step of first-principles molecular dynamics, we present a data-driven modeling framework for Kohn-Sham Density Functional Theory that bypasses the explicit…

In [Dai et al, Multi. Model. Simul., 2020], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory, based on which a linearized method was developed in [Hu, et al,…

We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…

Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…

The Kohn-Sham scheme of density functional theory is one of the most widely used methods to solve electronic structure problems for a vast variety of atomistic systems across different scientific fields. While the method is fast relative to…

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to…

We review thermodynamic limits and scaling limits of electronic structure models for condensed matter. We discuss several mathematical ways to implement these limits in three models of increasing chemical complexity and mathematical…

A recently developed formalism in which Kohn-Sham calculations are combined with an ``average pair density functional theory'' is reviewed, and some new properties of the effective electron-electron interaction entering in this formalism…

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…

Density functional theory is the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, and machine learning. At its heart lies the exchange-correlation functional, a…

One of the goals in the development of large scale electronic structure methods is to perform calculations explicitly for a localised region of a system, while still taking into account the rest of the system outside of this region. An…

As a proof of principle, self-consistent Kohn--Sham calculations are performed with the exact exchange-correlation functional. Finding the exact functional for even one trial density requires solving the interacting Schr\"odinger equation…