Related papers: Gradient Flow Based Discretized Kohn-Sham Density …

We present a broadly-applicable, physically-motivated first-principles approach to determining the fundamental gap of finite systems. The approach is based on using a range-separated hybrid functional within the generalized Kohn-Sham…

Kohn-Sham density functional theory is one of the most widely used electronic structure theories. The recently developed adaptive local basis functions form an accurate and systematically improvable basis set for solving Kohn-Sham density…

Kohn-Sham density functional theory is the base of modern computational approaches to electronic structures. Their accuracy vitally relies on the exchange-correlation energy functional, which encapsulates electron-electron interaction…

One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…

The notion of dissipative dynamical systems provides a formal description of processes that cannot generate energy internally. For these systems, changes in energy can only occur due to an external energy supply or dissipation effects.…

We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal…

The grand canonical density functional theory for inhomogeneous systems of interacting bosons is developed in the effective action approach. The Legendre transform of the generating functional for Green's functions is used to define the…

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately…

We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn-Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving…

Orbital-Free Density Functional Theory (OFDFT) has re-emerged as a viable alternative to Kohn-Sham DFT, driven by recent advances in kinetic energy density functionals (KEDFs). Nonlocal (NL) KEDFs have significantly extended OFDFT's…

We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…

Recently, we introduced (e-print arXiv:1407.7128) {\em local reduced density matrix functional theory} (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local…

We present a convergence analysis of a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fatemi model. We devise an iterative algorithm to compute the solution of…

We study a discretization in space and time for a class of nonlinear diffusion equations with flux limitation. That class contains the so-called relativistic heat equation, as well as other gradient flows of Renyi entropies with respect 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 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…

We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…

Within the framework of linear-scaling Kohn-Sham density functional theory, a robust method for maintaining compact localized orbitals close to the ground state is coupled with nuclear dynamics. This allows to obviate the commonly employed…

We present an accurate and efficient formulation of the stress tensor for real-space Kohn-Sham Density Functional Theory (DFT) calculations. Specifically, while employing a local formulation of the electrostatics, we derive a linear-scaling…

Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence…