AUTHOR=Ghosh Kumar J. B. , Kais Sabre , Herschbach Dudley R. 

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

JOURNAL=Frontiers in Physics

VOLUME=8

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00331

DOI=10.3389/fphy.2020.00331

ISSN=2296-424X

ABSTRACT=<p>We present a simple interpolation formula using dimensional limits <italic>D</italic> = 1 and <italic>D</italic> = ∞ to obtain the <italic>D</italic> = 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 H<sub>2</sub> 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.</p>