Electronic tunneling and exchange energy in the D-dimensional hydrogen-molecule ion

S. Kais, J. D. Morgan, D. R. Herschbach

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

Dimensional scaling generates an effective potential for the electronic structure of atoms and molecules, but this potential may acquire multiple minima for certain ranges of nuclear charges or geometries that produce symmetry breaking. Tunneling among such minima is akin to resonance among valence bond structures. Here we treat the D-dimensional H2 + molecule ion as a prototype test case. In spheroidal coordinates it offers a separable double-minimum potential and tunneling occurs in only one coordinate; in cylindrical coordinates the potential is nonseparable and tunneling occurs in two coordinates. We determine for both cases the ground state energy splitting ΔED as a function of the internuclear distance R. By virtue of exact interdimensional degeneracies, this yields the exchange energy for all pairs of g, u states of the D = 3 molecule that stem from separated atom states with m = l = n - 1, for n = 1 → ∞. We evaluate ΔED by two semiclassical techniques, the asymptotic and instanton methods, and obtain good agreement with exact numerical calculations over a wide range of R. We find that for cylindrical coordinates the instanton path for the tunneling trajectory differs substantially from either a straightline or adiabatic path, but is nearly parabolic. Path integral techniques provide relatively simple means to determine the exact instanton path and contributions from fluctuations around it. Generalizing this approach to treat multielectron tunneling in several degrees of freedom will be feasible if the fluctuation calculations can be made tractable.

Original languageEnglish
Pages (from-to)9028-9041
Number of pages14
JournalThe Journal of Chemical Physics
Volume95
Issue number12
Publication statusPublished - 1 Dec 1991
Externally publishedYes

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Hydrogen
energy transfer
Ions
instantons
Molecules
hydrogen
electronics
cylindrical coordinates
molecules
Atoms
ions
Ground state
Electronic structure
asymptotic methods
Trajectories
stems
Geometry
atoms
broken symmetry
degrees of freedom

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Electronic tunneling and exchange energy in the D-dimensional hydrogen-molecule ion. / Kais, S.; Morgan, J. D.; Herschbach, D. R.

In: The Journal of Chemical Physics, Vol. 95, No. 12, 01.12.1991, p. 9028-9041.

Research output: Contribution to journalArticle

Kais, S. ; Morgan, J. D. ; Herschbach, D. R. / Electronic tunneling and exchange energy in the D-dimensional hydrogen-molecule ion. In: The Journal of Chemical Physics. 1991 ; Vol. 95, No. 12. pp. 9028-9041.
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