Related papers: Basis set convergence of Wilson basis functions fo…
We use a simple system, the electron configuration in a Hydrogen-like atom, to demonstrate the importance of using a complete basis set to provide a proper quantum mechanical description. We first start with what might be considered a…
We present a code-independent compact representation of one-electron wavefunctions and other volumetric data (electron density, electrostatic potential, etc.) produced by electronic-structure calculations. The compactness of the…
A detailed understanding of strong matter-photon interactions requires first-principle methods that can solve the fundamental Pauli-Fierz Hamiltonian of non-relativistic quantum electrodynamics efficiently. A possible way to extend…
Rotationally invariant combinations of the Brillouin zone-center Bloch functions are used as basis function to express in cylindrical coordinates the valence-band and Kane envelope-function Hamiltonians for wurtzite and zinc-blende…
We develop a numerical approach based on the sinc basis set for first-principles electronic structure calculations in one-dimensional systems. The method exploits the inherent accuracy and non-local character of the sinc functions to handle…
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from…
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…
In this article, we demonstrate the restricted Hartree-Fock electronic structure computation of the molecule $H_3^+$ through computational algebra. We approximate the Hartree-Fock total energy by a polynomial composed of LCAO coefficients…
Twisted multilayer systems, encompassing materials like twisted bilayer graphene (TBG), twisted trilayer graphene, and twisted bilayer transition metal dichalcogenides, have garnered significant attention in condensed matter physics.…
We present an implementation of the GW approximation for the electronic self-energy within the full-potential linearized augmented-plane-wave (FLAPW) method. The algorithm uses an all-electron mixed product basis for the representation of…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…
Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce…
The Wigner localization is an electron phase at low densities when the electrons are sharply localized around equilibrium positions. The simulation of the Wigner localization phenomenon requires careful treatment of the many-body…
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field…
We introduce a family of all-electron Gaussian basis sets, augmented MOLOPT, optimized for excited-state calculations on large molecules. We generate these basis sets by augmenting existing STO-3G, STO-6G, and MOLOPT basis sets optimized…
Electronic structure calculations for solids based on many-electron wavefunctions have been hampered by the argument that for large electron numbers wavefunctions are not a legitimate scientific concept, because they face an exponential…
We show that both confined atoms and electron-atom scattering can be described by a unified basis set method. The central idea behind this method is to place the atom inside a hard potential sphere, enforced by a standard Slater type basis…
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…
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…