Related papers: Electronic Structure Calculation with the Exact Ps…
Using a novel self-consistent implementation of Hedin's GW perturbation theory we calculate space and energy dependent self-energy for a number of materials. We find it to be local in real space and rapidly convergent on second-- to third--…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
We propose accurate computable error bounds for quantities of interest in plane-wave electronic structure calculations, in particular ground-state density matrices and energies, and interatomic forces. These bounds are based on an…
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…
Electron-phonon coupling (EPC) is fundamental for understanding the behavior of molecules and crystals, influencing phenomena such as charge transport, energy transfer, phase transitions, and polaron formation. Accurate computational…
We present a mass lumping approach based on an isogeometric Petrov-Galerkin method that preserves higher-order spatial accuracy in explicit dynamics calculations irrespective of the polynomial degree of the spline approximation. To…
We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…
In this paper, which constitutes the first part of the series, we consider calculation of two-centre Coulomb and hybrid integrals over Slater-type orbitals (STOs). General formulae for these integrals are derived with no restrictions on the…
We propose an approximate reconstruction of random heterogeneous microstructures using the two-exponent power-law (TEPL). This rule originates from the entropic descriptor (ED) that is a multi-scale measure of spatial inhomogeneity for a…
An efficient method for calculating the electronic structure in large systems with a fully converged BZ sampling is presented. The method is based on a k.p-like approximation developed in the framework of the density functional perturbation…
Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly…
We review a recent proposal of a first principles approach to the electronic structure of materials with strong electronic correlations. The scheme combines the GW method with dynamical mean field theory, which enables one to treat strong…
This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physics. In a wavelet-Galerkin framework, we formulate learning…
Electronic structure calculations for compressed molecular hydrogen are performed to provide more insight into the diversity of phenomena recently observed experimentally. We perform full-potential LAPW calculations and analyze them in…
The electronic band structure of CeAgSb$_{2}$ has been calculated using the self-consistent full potential nonorthogonal local orbital minimum basis scheme based on the density functional theory. We investigated the electronic structure…
Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are…
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and…
In the present work, we examine and analyze an hp-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on computational meshes consisting of polytopic elements on the…
Simulating general relativistic hydrodynamics (GRHD) presents challenges such as handling curved spacetime, achieving high-order shock-capturing accuracy, and preserving key physical constraints (positive density, pressure, and subluminal…
We propose a neural-enhanced weak Galerkin (WG) finite element method for second-order elliptic problems with low-regularity solutions. The method augments the classical WG approximation space with neural network functions constructed via a…