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Rovibronic analysis of the Jahn–Teller effect in at low energies
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10.1063/1.3157210
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Affiliations:
1 Laboratorium für Physikalische Chemie, ETH Zürich, CH-8093 Zurich, Switzerland
2 NRC Steacie Institute for Molecular Sciences, Ottawa, Ontario K1A 0R6, Canada
a) Electronic mail: feme@xuv.phys.chem.ethz.ch.
J. Chem. Phys. 131, 024309 (2009)
/content/aip/journal/jcp/131/2/10.1063/1.3157210
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/2/10.1063/1.3157210

## Figures

FIG. 1.

Schematic representation of one of the two enantiomeric sets of six equivalent minimum energy structures on the ground-state potential energy hypersurface of the methane cation and of the network of tunneling paths connecting them. The dotted tunneling paths interconvert the , , and isomeric forms of , which have different zero-point vibrational energies, whereas the full double arrows indicate interconversion of equivalent structures of the isomeric form. The energy scale on the left-hand side indicates schematically the relative order of the zero-point energies of the three isomeric forms and the tunneling splittings of (see text for more detail). Each structure was drawn twice to facilitate the comparison of the different isomeric forms.

FIG. 2.

(a) Space-fixed axis system common to all four equivalent minimum energy structures of defined for a tetrahedral reference structure. (b) Bond-compression and bond-stretching operations and (c) bond rotations needed to convert the tetrahedral structure into the equilibrium structure 3 in Fig. 1. The arrows in (a) indicate the directions along which the bond compression, bond stretching, and bond rotations are needed to produce equilibrium structures 2–5 (see text for more details).

FIG. 3.

Correlation diagram illustrating the effect of the tunneling matrix element on the energy level structure of . The left-hand side corresponds to a fourfold degenerate asymmetric top of symmetry. The right-hand side corresponds to a near prolate symmetric top corresponding to a tunneling wave function delocalized over the four equilibrium structures 2–5 of in Fig. 1. The asymmetric-top rotational labels are given in the notation .

FIG. 4.

Upper trace: PFI-ZEKE photoelectron spectrum of the lowest three bands of the transition. Lower inverted trace: Simulation based on an effective tunneling-rotational Hamiltonian (see text for more details). The positions of the band centers (including tunneling splittings) of the three isomeric forms , , and are indicated at the bottom of the figure.

FIG. 5.

Detailed view of the experimental spectra of the three lowest vibronic bands of and the corresponding simulations (inverted traces). The experimental spectrum of higher resolution shown in the top panel was taken from Ref. 12. The top, middle, and bottom panels show the rotational structure of the bands assigned to transitions to the ground states of , , and , respectively. The calculated positions of the band centers (including tunneling splittings) are indicated at the bottom of each panel.

## Tables

Table I.

Numerical values of the expansion coefficients , , and of the rotational Hamiltonian corresponding to the minimum energy structure 3 of .

Table II.

Signs of the distortions along the and directions needed to obtain the appropriate geometric structures of the minima of .

Table III.

Molecular constants describing the structure and tunneling dynamics at low energies in the ground state of .

/content/aip/journal/jcp/131/2/10.1063/1.3157210
2009-07-14
2014-04-20

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