Simple and Surprisingly Accurate Approach to the Chemical Bond Obtained from Dimensional Scaling

Anatoly A. Svidzinsky, Marlan O. Scully, and Dudley R. Herschbach
Phys. Rev. Lett. 95, 080401 – Published 17 August 2005

Abstract

We present a new dimensional scaling transformation of the Schrödinger 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.

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  • Received 7 July 2004

DOI:https://doi.org/10.1103/PhysRevLett.95.080401

©2005 American Physical Society

Authors & Affiliations

Anatoly A. Svidzinsky1,2, Marlan O. Scully1,2,3, and Dudley R. Herschbach4

  • 1Departments of Chemistry, and Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
  • 2Departments of Physics, Chemical and Electrical Engineering, Texas A&M University, Texas 77843-4242, USA
  • 3Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
  • 4Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 95, Iss. 8 — 19 August 2005

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