Comparative study of unconventional 1s basis functions for the ¹Σ ground state of H₂ and He

Abstract

AbstractsWe investigated various nonstandard 1 s basis functions (generalized Slater-Gaussian, ellipsoidal Gaussian, floating spherical and ellipsoidal Gaussian, rational function, HulthSn approximation, two-Slater-type orbital, generalized Guillemin-Zener function, and various noninteger-n elliptical orbitals) for approximating the ' Z: ground state of H, and He: +.A CI trial wave-function including u,-type MO'S is adopted and. molecular integrals are evaluated numerically. The energy improvement on the 1s STO is small except for noninteger-n orbitals which closely approach the "SCF limit". Diverses fonctions de base non usuelles (forme gCnCralisie d'orbitale de Slater ouGaussienne, Gaussienne ellipsoidale, Gaussienne sphkrique ou ellipsoidale flottante, fonction rationelle, approximation de HulthCn, double orbitale de Slater, fonction de Guillemin-Zener gCnCralisCe, diverses orbitales a valeurs non entieres de n exprimks en coordonnCes elliptiques) sont appliquks en tant que orbitale atomique de type 1s a l'etat fondamental ' Z: de H, et He:+. On adopte une fonction d'onde incluant des orbitales moliculaires de type ug dans le cadre d'une interaction de configuration restreinte. Les intigrales molCculaires sont bvaluies numeriquement. Le gain en Cnergie est faible par rapport a l'orbitale 1s de Slater hormis le cas des orbitales a valeurs non entiires de n qui approchent fortement la "limite XF".Verschiedene nicht ubliche 1 s Grundfunktionen (VeraQgemeinertes Slater oder Gaussches Orbital, Ellipsoid-Gaussches Orbital, schwebendes spharisch-oder EllipsoidGaussches Orbital, rationelle Funktion, Hulthkn-Naherung, Doppelorbital von Slater, verallgemeinerte Funktion von Guillemin-Zener, verschiedene n-nicht ganzzahlige elliptische Orbitale) wurden zur Naherung des '2: Grundzustandes von H, und He:+ verwandt. Eine Wellenfunktion mit Molekulorbitalen des ug Types wurde als VersuchsKonfigurationswechselwirkung angenommen. Dabei wurden die Molekulintegrale numerisch geschatzt. Der Energie-Zuwachs ist gering dem Slater-1 s Orbital gegenuber, mit Ausnahme fur die n-nicht ganzzahligen Orbitalwerte, die an die "SCF Grenze" sehr nah herankommen.

Intermolecular diatomic energies of a hydrogen dimer with non-Born–Oppenheimer nuclear and electron wave packets

“…Since we restrict our numerical calculations to the stationary wave functions in this work, momentum parameters are all nullified. The spatial Gaussian EWP φ e is specified by the WP center r e and width ρ e as [47] φ e (q) = N e exp[A e |q − r…”

Use of an epoxidized oil‐based resin as matrix in vegetable fibers‐reinforced composites

“…From the early days of quantum chemistry, many nonstandard basis functions proposed by different authors have been used in the electronic structure calculations of atoms and molecules (see Refs. [11–14] and references therein). Recently, hyperbolic cosine (HC) functions with NISTO have been proposed for HFR calculations of atoms, their anions and cations [15] as radial basis functions.…”

Use of combined Hartree–Fock–Roothaan theory in evaluation of lowest states of K[Ar]4s 03d 1 and Cr + [Ar]4s 03d 5 isoelectronic series over noninteger n-Slater type orbitals

“…To improve the quality of basis-sets, many nonstandard basis functions proposed by different authors have been used in the electronic structure calculations (see refs [20,21] and references therein). To determine physical properties, such as diamagnetic susceptibility, nuclear magnetic shielding, nuclear quadrupole coupling constant, electric field gradient, etc., the high-quality wave functions are of crucial importance.…”