The Two Electron Molecular Bond Revisited: From Bohr Orbits to Two-Center Orbitals

Abstract

Abstract Niels Bohr originally applied his approach to quantum mechanics to the H atom with great success. He then went on to show in 1913 how the same “planetary-orbit” model can predict binding for the H 2 molecule. However, he misidentified the correct dissociation energy of his model at large internuclear separation, forcing him to give up on a “Bohr's model for molecules”. Recently, we have found the correct dissociation limit of Bohr's model for H 2 and obtained good potential energy curves at all internuclear separations. This work is a natural extension of Bohr's original paper and corresponds to the D = ∞ limit of a dimensional scaling (D-scaling) analysis, as developed by Herschbach and coworkers. In a separate but synergetic approach to the two-electron problem, we summarize recent advances in constructing analytical models for describing the two-electron bond. The emphasis here is not maximally attainable numerical accuracy, but beyond textbook accuracy as informed by physical insights. We demonstrate how the interplay of the cusp condition, the asymptotic condition, the electron-correlation, configuration interaction, and the exact one electron two-center orbitals, can produce energy results approaching chemical accuracy. To this end, we provide a tutorial on using the Riccati form of the ground state wave function as a unified way of understanding the two-electron wave function and collect a detailed account of mathematical derivations on the exact one-electron two-center wave functions. Reviews of more traditional calculational approaches, such as Hartree–Fock, are also given. The inclusion of electron correlation via Hylleraas type functions is well known to be important, but difficult to implement for more than two electrons. The use of the D-scaled Bohr model offers the tantalizing possibility of obtaining electron correlation energy in a non-traditional way.