Application of Cusp-Satisfying Orbitals to Some Two-Electron Systems

1972 ◽  
Vol 50 (17) ◽  
pp. 2887-2890
Author(s):  
J. E. Brown ◽  
D. P. Chong
Keyword(s):  
Electron Density ◽  
Hydrogen Molecule ◽  
Lithium Atom ◽  
Electron Systems ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series

The kind of cusp-satisfying orbitals used earlier for the lithium atom is tested on the helium isoelectronic series and the hydrogen molecule. Excellent values are obtained for the electron density at the nucleus, Qe(0), for the atoms. The results for various wavefunctions for the hydrogen molecule are not as systematic, but are still quite reasonable.

scholarly journals Shannon, R\’enyi, Tsallis entropies of 1s$^2$-State Atomic System

2021 ◽  
Author(s):  
Hamid Al-Jibbouri
Keyword(s):  
Electron Density ◽  
Atomic Number ◽  
Atomic System ◽  
Research Topic ◽  
Hartree Fock ◽  
The Core ◽  
Isoelectronic Series ◽  
The Difference ◽  
Helium Isoelectronic Series ◽  
Good Agreement

The Shannon, R\’enyi, and Tsallis entropies of normalized electron density in position and momentum spaces are studied for the 1s${}^{2}$ state of Helium-isoelectronic series. Within single-zeta $\beta$-type orbitals ($\beta$TOs), the Hartree-Fock-Roothaan (HFR) calculations are considered and condensed on the most features of the physical results. The information quantities with atomic number deal with the interactions between the core and valence regions of the atom and thus enhance a geometrical understanding for the difference. It is assumed that the presented result might be a significant reference for further research topic on theoretical information quantities of atomic and molecular. Indeed, Our results have a good agreement in comparison with the previous published results.

Additivity of the one‐third power of the electron density in the hydrogen molecule–ion and hydrogen molecule

1990 ◽  
Vol 92 (3) ◽  
pp. 2114-2115 ◽  
Author(s):  
Chengteh Lee ◽  
Slobodan Zdravkovic ◽  
Robert G. Parr
Keyword(s):  
Electron Density ◽  
Hydrogen Molecule ◽  
The One

scholarly journals Explicit Green operators for quantum mechanical Hamiltonians. II. Edge-type singularities of the helium atom

2019 ◽  
Vol 13 (07) ◽  
pp. 2050122
Author(s):  
Heinz-Jürgen Flad ◽  
Gohar Flad-Harutyunyan ◽  
Bert-Wolfgang Schulze
Keyword(s):  
Asymptotic Behavior ◽  
Helium Atom ◽  
Hydrogen Molecule ◽  
Second Order ◽  
Quantum Mechanical ◽  
Electron Systems ◽  
Explicit Formulas ◽  
Edge Type ◽  
Oppenheimer Approximation ◽  
Hamiltonian Operators

We extend our approach of asymptotic parametrix construction for Hamiltonian operators from conical to edge-type singularities which is applicable to coalescence points of two particles of the helium atom and related two electron systems including the hydrogen molecule. Up to second-order, we have calculated the symbols of an asymptotic parametrix of the nonrelativistic Hamiltonian of the helium atom within the Born–Oppenheimer approximation and provide explicit formulas for the corresponding Green operators which encode the asymptotic behavior of the eigenfunctions near an edge.

An Exciton Approach to the Excited States of Two Electron Atoms. II. Determination of Spectroscopic Parameters, Polarizabilities and Dispersion Coefficients of H-, He, Li+, Be2+ and Ne8+

1985 ◽  
Vol 38 (1) ◽  
pp. 11
Author(s):  
PE Schipper ◽  
B Martire
Keyword(s):  
Excited States ◽  
Ground State ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Exciton Model ◽  
Interaction Coefficients ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series ◽  
Good Agreement

The exciton model developed in an earlier paper is applied quantitatively to a description of the excited states of representative members of the helium isoelectronic series; viz. H-, He, Li+,Be2+ and Ne8+. The energies of the eight lowest excited states are in good agreement with experiment, for a relatively small (1s-4p) hydrogenic basis; the ground state is obtained with slightly less precision. Response properties including oscillator strengths, polarizabilities and dispersion interaction coefficients are also calculated. The method appears to be quantitatively sound, and, above all, leads to particularly simple interpretations of the wave functions and the energies.

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