Related papers: Electronic Structure Calculation with the Exact Ps…
We discuss the $p$- and the $hp$-versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schr\"odinger…
Potential energy surfaces of electron dynamics (ePES) are constructed from a model of localized electron wave packets (eWP) with non-orthogonal valence-bond (VB) spin coupling and applied to quantum dynamics simulations of high harmonic…
The pseudospectral method, in conjunction with a new technique for obtaining scaling exponents $\zeta_n$ from the structure functions $S_n(r)$, is presented as an alternative to the extended self-similarity (ESS) method and the use of…
A new order-N method for calculating the electronic structure of general (non-tight-binding) potentials is presented. The method uses a combination of the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and Daw, and a…
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled…
The Gaussian Effective Potential (GEP) is shown to be a useful variational tool for the study of the magnetic properties of strongly correlated electronic systems. The GEP is derived for a single band Hubbard model on a two-dimensional…
The exchange-only optimized effective potential method is implemented with the use of Slater-type basis functions, seeking for an alternative to the standard methods of solution with some computational advantages. This procedure has been…
Numerical calculations of the electron self-energy without any expansion in the binding nuclear field are required in order to match the rapidly advancing precision of experimental spectroscopy. For the lightest elements, particularly…
This paper introduces a mathematical framework for explicit structural dynamics, employing approximate dual functionals and rowsum mass lumping. We demonstrate that the approach may be interpreted as a Petrov-Galerkin method that utilizes…
We formulate and implement a spectral method for solving the Schrodinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials…
The description of weakly bound electronic states is especially difficult with atomic orbital basis sets. The diffuse atomic basis functions that are necessary to describe the extended electronic state generate significant linear…
We present a novel "linear combination of atomic orbitals"-type of approximation, enabling accurate electronic structure calculations for systems of up to 20 or more electronically coupled quantum dots. Using realistic single quantum dot…
Supercell models are often used to calculate the electronic structure of local perturbations from the ideal periodicity in the bulk or on the surface of a crystal or in wires. When the defect or adsorbent is charged, a jellium counter…
We have recently described the implementation of atomic electronic structure calculations within the finite element method with numerical radial basis functions of the form $\chi_{\mu}(r)=r^{-1}B_{\mu}(r)$, where high-order Lagrange…
The generalized pseudospectral method is employed to study the bound-state spectra of some of the exponentially screened Coulomb potentials, \emph{viz.}, the exponential cosine screened Coulomb (ECSC) and general exponential screened…
In this work, we develop a novel numerical scheme to solve the classical Keller--Segel (KS) model which simultaneously preserves its intrinsic mathematical structure and achieves optimal accuracy. The model is reformulated into a gradient…
Numerical studies of the dynamics of gravitational systems, e.g., black hole-neutron star systems, require physical and constraint-satisfying initial data. In this article, we present the newly developed pseudo-spectral code Elliptica, an…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
Recently, a new approach for solving the three-body problem for (d,p) reactions in the Coulomb-distorted basis in momentum space was proposed. Important input quantities for such calculations are the scattering matrix elements for proton-…
We present and analyze a discontinuous Galerkin method for the numerical solution of a class of second-order linear mixed-type partial differential equations, i.e. equations that change their nature from elliptic to hyperbolic through the…