Exact density matrix for a two-electron model atom and approximate proposals for realistic two-electron systems
- Dipartimento di Chimica e Chimica Industriale, Universita di Pisa, Via Risorgimento 35, 56126 Pisa (Italy)
- Department of Physics, University of Antwerp (RUCA), Groenenborgerlaan 171, B-2020 Antwerp (Belgium)
Moshinsky introduced an exactly soluble model of a two-electron atom consisting of two spin-(1/2) particles interacting via harmonic forces and moving in a harmonic-oscillator potential. Here, the exact ground-state density {rho}(r) is related to the (also analytically known) Hartree-Fock density {rho}{sub HF}(r). The generalization to the off-diagonal matrix {gamma}(r,r{sup '}) is then effected, this being related to the idempotent {gamma}{sub HF}(r,r{sup '})/2. This exact information on this 'model atom' prompts us to propose an approximate form of {gamma}(r,r{sup '}) for the He-like ions, the H{sub 2} molecule and, in general, all two-electron systems. {gamma}(r,r{sup '}) is constructed solely from the exact {rho}(r) and its Hartree-Fock counterpart. Some detailed treatment of the two-electron Hookean atom with spring constant k=1/4 (atomic units) is also presented.
- OSTI ID:
- 20633709
- Journal Information:
- Physical Review. A, Vol. 67, Issue 2; Other Information: DOI: 10.1103/PhysRevA.67.022509; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Momentum density and spatial form of correlated density matrix in model two-electron atoms with harmonic confinement
Force-balance and differential equation for the ground-state electron density in atoms and molecules