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Perturbation Theory Of The Hooke's Law Model For The Two‐Electron Atom, Ronald White, W. Byers Brown
Perturbation Theory Of The Hooke's Law Model For The Two‐Electron Atom, Ronald White, W. Byers Brown
Center for Advanced Mineral and Metallurgical Processing (CAMP)
The Hooke model for the two‐electron atom replaces the electron–nuclear interaction by a harmonic oscillator potential, but retains the Coulomb repulsion of the electrons. The first‐order perturbation equation for the electron repulsion is solved analytically, and the exact first‐, second‐, and third‐order perturbation energies are obtained. A similar Z-1 perturbation treatment is carried out for the Hartree–Fock equation and other variational approximations. The Z-1 of the correlation energy is compared with that for helium-like atoms and found to be similar.
Analytic Approach To Electron Correlation In Atoms, Ronald White, Frank Stillinger
Analytic Approach To Electron Correlation In Atoms, Ronald White, Frank Stillinger
Center for Advanced Mineral and Metallurgical Processing (CAMP)
A novel perturbative treatment of electron correlation in N‐electron atoms is devised. The unperturbed starting point is a central‐force “hydrogenic” problem in the full dN‐dimensional configuration space (d = dimensionality). The central potential in this solvable “hydrogenic” problem is obtained by averaging the actual electron–electron and electron–nucleus potentials over all dN − 1dN − 1 hyperspherical polar angles in the configuration space. The relevant projected Green's functions are computed for the ground states of the model one‐dimensional two‐electron atom (with delta function interactions), as well as for the real three‐dimensional helium isoelectronic sequence. The corresponding first‐order wavefunctions exhibit weakly singular …