Bohr model and dimensional scaling analysis of atoms and molecules

Anatoly Svidzinsky, Goong Chen, Siu Chin, Moochan Kim, Dongxia Ma, Robert Murawski, Alexei Sergeev, Marlan Scully, Dudley Herschbach

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28 Citations (Scopus)


It is generally believed that the old quantum theory, as presented by Niels Bohr in 1913, fails when applied to few electron systems, such as the H2 molecule. Here we review recent developments of the Bohr model that connect it with dimensional scaling procedures adapted from quantum chromodynamics. This approach treats electrons as point particles whose positions are determined by optimizing an algebraic energy function derived from the large-dimension limit of the Schrodinger equation. The calculations required are simple yet yield useful accuracy for molecular potential curves and bring out appealing heuristic aspects. We first examine the ground electronic states of H2, HeH, He2, LiH, BeH and Li2. Even a rudimentary Bohr model, employing interpolation between large and small internuclear distances, gives good agreement with potential curves obtained from conventional quantum mechanics. An amended Bohr version, augmented by constraints derived from Heitler-London or Hund-Mulliken results, dispenses with interpolation and gives substantial improvement for H2 and H3. The relation to D-scaling is emphasized. A key factor is the angular dependence of the Jacobian volume element, which competes with interelectron repulsion. Another version, incorporating principal quantum numbers in the D-scaling transformation, extends the Bohr model to excited S states of multielectron atoms. We also discuss kindred Bohr-style applications of D-scaling to the H atom subjected to superstrong magnetic fields or to atomic anions subjected to high frequency, superintense laser fields. In conclusion, we note correspondences to the prequantum bonding models of Lewis and Langmuir and to the later resonance theory of Pauling, and discuss prospects for joining D-scaling with other methods to extend its utility and scope.

Original languageEnglish
Pages (from-to)665-723
Number of pages59
JournalInternational Reviews in Physical Chemistry
Issue number4
Publication statusPublished - Oct 2008
Externally publishedYes



  • Bohr model
  • Chemistry bond
  • Dimensional scaling
  • Molecules
  • Potential curves

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

Svidzinsky, A., Chen, G., Chin, S., Kim, M., Ma, D., Murawski, R., Sergeev, A., Scully, M., & Herschbach, D. (2008). Bohr model and dimensional scaling analysis of atoms and molecules. International Reviews in Physical Chemistry, 27(4), 665-723.