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

Chen, Goong; Chin, Siu A.; Dou, Yusheng; Kapale, Kishore T.; Kim, Moochan; Svidzinsky, Anatoly A.; Urtekin, Kerim; Xiong, Han; Scully, Marlan O.

doi:10.1016/s1049-250x(05)51015-2

Cited by 13 publications

(14 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, we would like to state that the two-center orbitals obtained by solving the Schrödinger equation for two-center problem in prolate-spheroidal coordinates can be used to describe systems numerically with more than two electrons if electron correlations can be included directly, for example, in Monte Carlo simulations [13] . In this case, excellent results can be obtained with very compact wave function, as in the two-electron cases.…”

Section: Resultsmentioning

confidence: 99%

Molecular calculations for HeH+ with two-center correlated orbitals

Dou

Tang

Bai

2009

Sci. China Ser. B-Chem.

Self Cite

View full text Add to dashboard Cite

A two-center correlated orbital approach was used to calculate the electronic ground state energy for the HeH + molecular ion. The wavefunctions were constructed from the exact solution of the Schrödinger equation for the HeH ++ problem in prolate-spheroidal coordinates taken together with a Hylleraas type correlation factor. With a simple single term wavefunction, we obtained ground state energy of −2.95308691 hartree without any variational parameters in the calculation. When a two-configuration-state wavefunction was used and effective charges were allowed to be adjusted, we found an energy of −2.97384868 hartree, which is to be compared with −2.97869074 hartree obtained by an 83 term configuration interaction wavefunction or −2.97364338 hartree by an ab initio calculation (at the MP4(SDQ)/6-311++G(3df, 3dp) level) using the well-known "canned" code.HeH + , two-center orbitals, prolate-spheroidal coordinates, correlation function

show abstract

Section: Resultsmentioning

confidence: 99%

Molecular calculations for HeH+ with two-center correlated orbitals

Dou

Tang

Bai

2009

Sci. China Ser. B-Chem.

Self Cite

View full text Add to dashboard Cite

show abstract

“…At the end of summer 2004, I felt that I had learned a lot about ChemPhysChem (as a mathematician). A major outcome of the two summers of work was a long (145-page) article in [15], for which I was the lead author, although my role was somewhat like that of scribe and editor in putting that work together.…”

Section: Dr Philip J Morris Aerospace Engineermentioning

confidence: 99%

Interdisciplinary Research—Mathematical Interactions Viewed from Four Portrayals

Chen¹

2012

Notices Amer. Math. Soc.

View full text Add to dashboard Cite

“…This Laplacian was obtained more than a century ago [87]; detailed derivations are readily available [14,[88][89][90][91].…”

Section: Interplay Of Laplacians and Jacobiansmentioning

confidence: 99%

Bohr model and dimensional scaling analysis of atoms and molecules

Svidzinsky

Chen

Chin

et al. 2008

International Reviews in Physical Chemistry

Self Cite

View full text Add to dashboard Cite

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 H 2 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 Schro¨dinger 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 H 2 , HeH, He 2 , LiH, BeH and Li 2 . 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 H 2 and H 3 . 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.

show abstract

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

Cited by 13 publications

References 76 publications

Molecular calculations for HeH+ with two-center correlated orbitals

Molecular calculations for HeH+ with two-center correlated orbitals

Interdisciplinary Research—Mathematical Interactions Viewed from Four Portrayals

Bohr model and dimensional scaling analysis of atoms and molecules

Contact Info

Product

Resources

About