Related papers: Communication: Curing basis set overcompleteness w…
It is well known that matrices with low Hessenberg-structured displacement rank enjoy fast algorithms for certain matrix factorizations. We show how $n\times n$ principal finite sections of the Gram matrix for the orthogonal polynomial…
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…
The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional…
The $GW$ approximation has been recently gaining popularity among the method for simulating molecular core-level X-ray photoemission spectra. Traditionally, $GW$ core-level binding energies have been computed using either the cc-pV$n$Z or…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
We present a protocol for computing core-ionisation energies for molecules, which is essential for reproducing X-Ray photoelectron spectroscopy experiments. The electronic structure of both the ground state and the core-ionised states are…
A common way to evaluate electronic integrals for polyatomic molecules is to use Becke's partitioning scheme [J. Chem. Phys.88, 2547 (1988)] in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed…
The partial pivoted Cholesky approximation accurately represents matrices that are close to being low-rank. Meanwhile, the Vecchia approximation accurately represents matrices with inverse Cholesky factors that are close to being sparse.…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…
We present a novel and efficient implementation of coupled-cluster with singles and doubles (CCSD) analytic gradients that combines the Cholesky decomposition (CD) of electron-repulsion integrals with the exploitation of Abelian point-group…
The implementation of the orbital minimization method (OMM) for solving the self-consistent Kohn-Sham (KS) problem for electronic structure calculations in a basis of non-orthogonal numerical atomic orbitals of finite-range is reported. We…
Atom loss is a major error source in neutral-atom quantum computers, accounting for over 40% of the total physical errors in recent experiments. Its nonlinear and correlated nature poses significant challenges: current syndrome extraction…
Atomic-resolution imaging with scanning transmission electron microscopy is a powerful tool for characterizing the nanoscale structure of materials, in particular features such as defects, local strains, and symmetry-breaking distortions.…
It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. The goal is to recover the…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…
An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…