Related papers: Basis functions for electronic structure calculati…
The universal functional of Hohenberg-Kohn is given as a coupling-constant integral over the density as a functional of the potential. Conditions are derived under which potential-functional approximations are variational. Construction via…
We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the…
We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double-grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead…
We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the…
We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface. Built upon suitable…
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…
We present a method to compute the photoionization spectra of atoms and molecules in linear response time-dependent density functional theory. The electronic orbital variations corresponding to ionized electrons are expanded on a basis set…
In this article, we combine the periodic sinc basis set with a curvilinear coordinate system for electronic structure calculations. This extension allows for variable resolution across the computational domain, with higher resolution close…
Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…
A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation…
We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a…
One of the few methods for generating efficient function spaces for multi-D Schrodinger eigenproblems is given by Garashchuk and Light in J.Chem.Phys. 114 (2001) 3929. Their Gaussian basis functions are wider and sparser in high potential…
The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius $r$, and angle $\theta$ characterizes their positions on sphere, are investigated. Unlike the previous…
Within the well-established optical response function formalism, a new strategy with the central idea of employing the forward-backward stochastic Schr\"{o}dinger equations in a segmented way to accurately obtain the two-dimensional (2D)…
In this contribution, we present the implementation of a second-order CASSCF algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called Norm-Extended Optimization, guarantees…
We present a new theory for partitioning simulations of periodic and solid-state systems into physically sound atomic contributions at the level of Kohn-Sham density functional theory. Our theory is based on spatially localized linear…
We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Ros\'en. These are constructed through functional calculus…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
This work presents new Gaussian single- and double-zeta basis sets optimized for stochastic density functional theory (sDFT) using real-space auxiliary grids. Previous studies showed standard basis sets like STO-3G and 6-31G are sub-optimal…
We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact interval in $(0,\infty)$. These bounds…