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This paper presents new quadrature rules for functions in a reproducing kernel Hilbert space using nodes drawn by a sampling algorithm known as randomly pivoted Cholesky. The resulting computational procedure compares favorably to previous…

Numerical Analysis · Mathematics 2023-12-08 Ethan N. Epperly , Elvira Moreno

Finite-range numerical atomic orbitals are the basis functions of choice for several first principles methods, due to their flexibility and scalability. Generating and testing such basis sets, however, remains a significant challenge for…

Chemical Physics · Physics 2013-11-12 Fabiano Corsetti , M. -V. Fernández-Serra , José M. Soler , Emilio Artacho

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular…

Machine Learning · Statistics 2022-01-11 Alexander Goscinski , Félix Musil , Sergey Pozdnyakov , Michele Ceriotti

The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of…

Numerical Analysis · Mathematics 2025-11-19 Maxime Dalery , Genevieve Dusson , Virginie Ehrlacher , Alexei Lozinski

In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…

Numerical Analysis · Mathematics 2017-07-20 Sambasiva Rao Chinnamsetty , Michael Griebel , Jan Hamaekers

Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these…

Methodology · Statistics 2026-04-10 Rakheon Kim , Emma Jingfei Zhang

A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator…

Nuclear Theory · Physics 2008-11-26 M. V. Stoitsov , W. Nazarewicz , S. Pittel

In large-scale quantum-chemical calculations the electron-repulsion integral (ERI) tensor rapidly becomes the bottleneck in terms of memory and disk space. When an external finite magnetic field is employed, this problem becomes even more…

Chemical Physics · Physics 2022-02-16 Simon Blaschke , Stella Stopkowicz

We investigate the continuous analogue of the Cholesky factorization, namely the pivoted Cholesky algorithm. Our analysis establishes quantitative convergence guarantees for kernels of minimal smoothness. We prove that for a symmetric…

Numerical Analysis · Mathematics 2025-09-19 Sungwoo Jeong , Alex Townsend

In order to increase the accuracy of the linearized augmented plane wave method (LAPW) we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different…

Materials Science · Physics 2015-12-10 A. V. Nikolaev , D. Lamoen , B. Partoens

We present a detailed comparison between ONETEP, our linear-scaling density functional method, and the conventional pseudopotential plane wave approach in order to demonstrate its high accuracy. Further comparison with all-electron…

Materials Science · Physics 2009-11-11 Chris-Kriton Skylaris , Peter D. Haynes , Arash A. Mostofi , Mike C. Payne

The computation of magnetizability tensors using gauge-including atomic orbitals is discussed in the context of Cholesky decomposition for the two-electron repulsion integrals with a focus on the involved doubly differentiated integrals.…

Chemical Physics · Physics 2024-11-14 Sophia Burger , Stella Stopkowicz , Jürgen Gauss

An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a "single" (i.e. common to all points in the…

Materials Science · Physics 2009-10-31 Sandro Scandolo , Jorge Kohanoff

The particular symmetry of the random-phase-approximation (RPA) matrix has been utilized in the past to reduce the RPA eigenvalue problem into a symmetric-matrix problem of half the dimension. The condition of positive definiteness of at…

Nuclear Theory · Physics 2008-11-26 P. Papakonstantinou

Recent advances in both theoretical and computational methods have enabled large-scale, precision calculations of the properties of atomic nuclei. With the growing complexity of modern nuclear theory, however, also comes the need for novel…

Nuclear Theory · Physics 2024-11-26 R. Y. Cheng , K. Godbey , Y. B. Niu , Y. G. Ma , W. B. He , S. M. Wang

We present an approach to accelerate real-space electronic structure methods several fold, without loss of accuracy, by reducing the dimension of the discrete eigenproblem that must be solved. To accomplish this, we construct an efficient,…

Computational Physics · Physics 2018-05-01 Qimen Xu , Phanish Suryanarayana , John E. Pask

In this paper, we propose a parallel optimization method for electronic structure calculations based on a single orbital-updating approximation. It is shown by our numerical experiments that the method is efficient and reliable for atomic…

Numerical Analysis · Mathematics 2015-11-20 Xiaoying Dai , Zhuang Liu , Xin Zhang , Aihui Zhou

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…

Condensed Matter · Physics 2009-10-31 J. E. Pask , B. M. Klein , C. Y. Fong , P. A. Sterne

The shell correction method is revisited. Contrary to the traditional Strutinsky method, the shell energy is evaluated by an averaging over the number of particles and not over the single-particle energies, which is more consistent with the…

Nuclear Theory · Physics 2009-11-10 K. Pomorski

We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The…

Materials Science · Physics 2021-06-14 Victor Wen-zhe Yu , Jonathan Moussa , Volker Blum