Related papers: Machine learning optimization of the collocation p…

Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…

To solve the Kohn-Sham equation within the framework of density functional theory, we develop a scheme to construct numerical atomic orbital (NAO) basis sets by contracting truncated spherical waves (TSWs). The contraction minimizes the…

We present a method to invert a given density and find the Kohn-Sham (KS) potential in Density Functional Theory (DFT) which shares that density. Our method employs the concept of screening density, which is naturally constrained by the…

The standard way to calculate the Kohn-Sham orbitals utilizes an approximation of the potential. The approximation consists in a projection of the potential into a finite subspace of basis functions. The orbitals, calculated with the…

In this paper, we introduce a highly accurate and efficient numerical solver for the radial Kohn--Sham equation. The equation is discretized using a high-order finite element method, with its performance further improved by incorporating a…

In this paper, we propose and analyze a gradient flow based Kohn-Sham density functional theory. First, we prove that the critical point of the gradient flow based model can be a local minimizer of the Kohn-Sham total energy. Then we apply…

We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory (DFT), with a focus on functionals based on the strictly-correlated electrons (SCE) regime,…

Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…

In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…

Separating the Coulomb potential into short-range and long-range components enables the use of different electron repulsion integral algorithms for each component. The short-range part can be efficiently computed using the analytical…

We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…

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…

A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale…

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…

This paper constructs a predictor-corrector technique with orthogonal spline collocation finite element method for simulating a FitzHugh-Nagumo system subject to suitable initial and boundary conditions. The developed computational…

Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of…

We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of…

Accurate numerical solutions for the Schr\"odinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining…

Reinforcement learning (RL) has made significant advancements, achieving superhuman performance in various tasks. However, RL agents often operate under the assumption of environmental stationarity, which poses a great challenge to learning…

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to…