Related papers: KSSOLV 2.0: An efficient MATLAB toolbox for solvin…

Dictionary learning has recently emerged as a promising approach for mechanistic interpretability of large transformer models. Disentangling high-dimensional transformer embeddings requires algorithms that scale to high-dimensional data…

We describe a rapidly converging algorithm for solving the Kohn--Sham equations and equations of similar structure that appear frequently in calculations of the structure of inhomogeneous electronic many--body systems. The algorithm has its…

We formulate a set of equations that facilitate an exact numerical solution of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour hopping and arbitrary site potentials. The approach relies on a mapping of the…

The knowledge of the local electronic structure of heterogeneous solid materials is crucial for understanding their electronic, magnetic, transport, optical, and other properties. VASP, one of the mostly used packages for density-functional…

By introducing a set of auxiliary equations representing a many-body system, we have derived an extension of the Kohn-Sham scheme for the density functional theory. These equations consist of a Kohn-Sham-type equation determining…

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current…

DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation…

A system of electrons in a local or nonlocal external potential can be studied with 1-matrix functional theory (1MFT), which is similar to density functional theory (DFT) but takes the one-particle reduced density matrix (1-matrix) instead…

An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…

The `equation-free toolbox' empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because…

Kohn-Sham density functional theory (DFT) is the workhorse of quantum chemistry, offering an attractive balance between accuracy and computational cost. Although exact in principle, DFT in practice relies on an approximation to the unknown…

We present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham DFT calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by…

Coupled cluster theory with a Kohn-Sham reference (KS-CC) can dramatically outperform its Hartree-Fock counterpart for strongly correlated systems, but the origin of these improvements has remained unclear. Here we demonstrate that these…

This paper presents the development of a density-based solver suitable for cavitating flows in the OpenFOAM framework. In this solver, the thermodynamic equilibrium mixture approach is adopted to model the presence of and the phase…

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By inclusion of the kinetic…

We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive…

Time-dependent density functional theory (TDDFT) simulations of transient core-level spectroscopies require a balanced treatment of both valence- and core-electron excitations. To this end, tuned range-separated hybrid exchange-correlation…

A systematic strategy for the calculation of density functionals (DFs) consists in coding informations about the density and the energy into polynomials of the degrees of freedom of wave functions. DFs and Kohn-Sham potentials (KSPs) are…

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…

This paper presents a new Matlab toolbox, aimed at facilitating the use of polynomial optimization for stability analysis of nonlinear systems. In the past decade several decisive contributions made it possible to recast this type of…