^{1}, H. J. Wörner

^{2}and F. Merkt

^{1,a)}

### Abstract

The Jahn–Teller effect in the ground state of has been studied by pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy. The lowest three bands have been assigned to the three isomers , , and , in which the deuterium atoms are attached to the central carbon atom by two short bonds, one short and one long bond, and two long bonds, respectively, and which have different zero-point vibrational energies. Whereas and can each be described by a single structure with symmetry, corresponds to four equivalent structures that interconvert by tunneling. The rotational structure of these three bands is compared with predictions made on the basis of a tunneling Hamiltonian combined with a rotational Hamiltonian that incorporates the effects of the large-amplitude tunneling motion. The zero-point energies of and relative to that of are and , respectively, and the tunneling matrix element coupling the four equilibrium structures of is .

We thank Professor R. Signorell and Dr. M. Sommavilla for their early contributions to these studies. This work was supported financially by the Swiss National Science Foundation under Project No. 200020-125030.

I. INTRODUCTION

II. EXPERIMENT

III. THEORETICAL TREATMENT OF THE JAHN–TELLER EFFECT IN

A. Vibronic tunneling Hamiltonian

B. Rovibronic problem

IV. RESULTS AND DISCUSSION

V. CONCLUSIONS

### Key Topics

- Tunneling
- 38.0
- Photoelectron spectra
- 17.0
- Chemical bonds
- 15.0
- Zero point energy
- 11.0
- Ground states
- 10.0

## Figures

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.

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.

(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).

(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).

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 .

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 .

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.

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.

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.

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

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

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

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

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

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

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

Article metrics loading...

Full text loading...

Commenting has been disabled for this content