Simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling. Academic Article uri icon


  • We present a new dimensional scaling transformation of the Schrdinger equation for the two electron bond. This yields, for the first time, a good description of the bond via D scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential curves for the lowest singlet, triplet, and excited states of H2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.

published proceedings

  • Phys Rev Lett

altmetric score

  • 1

author list (cited authors)

  • Svidzinsky, A. A., Scully, M. O., & Herschbach, D. R.

citation count

  • 27

complete list of authors

  • Svidzinsky, Anatoly A||Scully, Marlan O||Herschbach, Dudley R

publication date

  • August 2005