Unorthodox Dimensional Interpolations for He, Li, Be Atoms and Hydrogen Molecule

Abstract

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We present a simple interpolation formula using dimensional limits D = 1 and D = ∞ to obtain the D = 3 ground-state energies of atoms and molecules. For atoms, these limits are linked by first-order perturbation terms of electron-electron interactions. This unorthodox approach is illustrated by ground-states for two, three, and four electron atoms, with modest effort to obtain fairly accurate results. Also, we treat the ground-state of H2 over a wide range of the internuclear distance R, and compares well with the standard exact results from the Full Configuration Interaction method. Similar dimensional interpolations may be useful for complex many-body systems.

Keywords

• dimensional interpolation
• dimensional scaling
• large-d limit
• one-dimension
• hydrogen molecule
• ground state energy and ground state binding energy