^{1}, X. Qian

^{1,a)}and F. Merkt

^{1}

### Abstract

The energy level structures of the ground vibronic states of , , and have been measured by pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy. The nuclear spin symmetries of the tunneling-rotational levels have been determined in double-resonance experiments via selected rotational levels of the and vibrational levels of the ground state of . The energy level structures of , , and have been analyzed with an effective tunneling-rotational Hamiltonian. The analysis together with a group theoretical treatment of the Jahn-Teller effect in the group prove that the equilibrium geometry of , , and has symmetry and characterize the pseudorotational dynamics in these fluxional cations. The tunneling behavior is discussed in terms of the relevant properties of the potential energy surface, some of which have been recalculated at the CCSD(T)/cc-pVTZ level of *ab initio*theory.

The authors thank R. van der Veen for her contributions to the theoretical analysis in the early phase of the project. This work is supported financially by the Swiss National Science Foundation and the ETH Zürich.

I. INTRODUCTION

II. EXPERIMENT

III. THEORY

A. The vibronic problem

B. The potential energy surface of the methane cation

C. The tunneling problem

D. The rovibronic problem

E. A general effective tunneling-rotation Hamiltonian

IV. RESULTS

A. Correlation diagram

B. PFI-ZEKE photoelectron spectra

1.

2.

3.

V. DISCUSSION

A. Comparison of experimental and simulated spectra

B. Thermochemical implications

VI. CONCLUSIONS

### Key Topics

- Tunneling
- 50.0
- Jahn Teller effect
- 25.0
- Photoelectron spectra
- 23.0
- Ground states
- 19.0
- Angular momentum
- 17.0

## Figures

Spectra of jet-cooled [trace (a)] and [trace (b)] in the region of the overtone transition recorded by monitoring, as a function of the IR wave number, the ionization of the excited vibrational level with VUV radiation. The transitions are labeled according to the associated changes in rotational angular momentum , , and the rotational angular momentum quantum number of the initial level. The transitions of are redshifted by compared to the transitions of .

Spectra of jet-cooled [trace (a)] and [trace (b)] in the region of the overtone transition recorded by monitoring, as a function of the IR wave number, the ionization of the excited vibrational level with VUV radiation. The transitions are labeled according to the associated changes in rotational angular momentum , , and the rotational angular momentum quantum number of the initial level. The transitions of are redshifted by compared to the transitions of .

Topological representation of the connectivity of the 12 equivalent minimum energy structures of symmetry of . The vertices correspond to the minimum energy geometries and the edges to the equivalent pseudorotation-tunneling paths connecting the minima via the low-lying transition states. The dotted line represents the barrier for stereomutation separating each minimum structure from its enantiomer. Four faces of the octahedron correspond to a geometry with a degenerate ground state (marked with a dot) and the other four to a geometry with a nondegenerate ground state (adapted from Ref. 15).

Topological representation of the connectivity of the 12 equivalent minimum energy structures of symmetry of . The vertices correspond to the minimum energy geometries and the edges to the equivalent pseudorotation-tunneling paths connecting the minima via the low-lying transition states. The dotted line represents the barrier for stereomutation separating each minimum structure from its enantiomer. Four faces of the octahedron correspond to a geometry with a degenerate ground state (marked with a dot) and the other four to a geometry with a nondegenerate ground state (adapted from Ref. 15).

Global axis system defined with respect to the tetrahedral reference geometry of . The rotational basis functions used in the tunneling-rotation treatment are defined in this axis system.

Global axis system defined with respect to the tetrahedral reference geometry of . The rotational basis functions used in the tunneling-rotation treatment are defined in this axis system.

Principal axis system used for the minimum energy structure labeled 1 on the right-hand side of Fig. 2.

Principal axis system used for the minimum energy structure labeled 1 on the right-hand side of Fig. 2.

Correlation diagram of the eigenvalues of tunneling-rotation Hamiltonian (13) as a function of the tunneling integral . In the limit , all levels are sixfold degenerate and coincide with the pattern of an asymmetric top which is depicted on the left-hand side. Rovibronic symmetries in the point group (left) and molecular symmetry group (right) are assigned to the levels. The vibronic symmetry in the group is indicated on the right-hand side.

Correlation diagram of the eigenvalues of tunneling-rotation Hamiltonian (13) as a function of the tunneling integral . In the limit , all levels are sixfold degenerate and coincide with the pattern of an asymmetric top which is depicted on the left-hand side. Rovibronic symmetries in the point group (left) and molecular symmetry group (right) are assigned to the levels. The vibronic symmetry in the group is indicated on the right-hand side.

Single-photon PFI-ZEKE photoelectron spectrum of [bottom trace, (b)] and [top trace, (a)] in the region of the adiabatic ionization threshold. Spectrum (a) was obtained with a sequence of pulsed electric fields of and and spectrum (b) with and .

Single-photon PFI-ZEKE photoelectron spectrum of [bottom trace, (b)] and [top trace, (a)] in the region of the adiabatic ionization threshold. Spectrum (a) was obtained with a sequence of pulsed electric fields of and and spectrum (b) with and .

Top trace: single-photon PFI-ZEKE photoelectron spectrum of in the region of the adiabatic ionization threshold obtained using electric field pulses of and . Lower traces: two-photon PFI-ZEKE PE spectra recorded via selected rotational levels of the fundamental using electric field pulses of and . The rotational angular momentum quantum number of the intermediate levels and their rovibronic symmetries are indicated above the spectra. The letters , , and correspond to the experimentally assigned nuclear spin symmetries (, , and ).

Top trace: single-photon PFI-ZEKE photoelectron spectrum of in the region of the adiabatic ionization threshold obtained using electric field pulses of and . Lower traces: two-photon PFI-ZEKE PE spectra recorded via selected rotational levels of the fundamental using electric field pulses of and . The rotational angular momentum quantum number of the intermediate levels and their rovibronic symmetries are indicated above the spectra. The letters , , and correspond to the experimentally assigned nuclear spin symmetries (, , and ).

Single-photon PFI-ZEKE photoelectron spectrum of in the region of the adiabatic ionization threshold (a) obtained using a pulsed electric field of and simulated spectrum using Hamiltonian (13) and the constants indicated in Table VI (b). Panel (b) shows a theoretical stick spectrum and its convolution with a Gaussian line profile of FWHM of . The full, dashed, and dotted sticks represent transitions to levels of rovibronic symmetries (or ), , and (or ), respectively.

Single-photon PFI-ZEKE photoelectron spectrum of in the region of the adiabatic ionization threshold (a) obtained using a pulsed electric field of and simulated spectrum using Hamiltonian (13) and the constants indicated in Table VI (b). Panel (b) shows a theoretical stick spectrum and its convolution with a Gaussian line profile of FWHM of . The full, dashed, and dotted sticks represent transitions to levels of rovibronic symmetries (or ), , and (or ), respectively.

Comparison of the experimentally determined level structure of (a) with the eigenvalues of Hamiltonian (13) calculated using the constants determined in a nonlinear least-squares fitting procedure (b). The wave number scale is defined with respect to the ground state of .

Comparison of the experimentally determined level structure of (a) with the eigenvalues of Hamiltonian (13) calculated using the constants determined in a nonlinear least-squares fitting procedure (b). The wave number scale is defined with respect to the ground state of .

## Tables

Correlation table of the rovibronic symmetries from the to the molecular symmetry group including nuclear spin-statistical weights for .

Correlation table of the rovibronic symmetries from the to the molecular symmetry group including nuclear spin-statistical weights for .

Same as Table I but with nuclear spin-statistical weights for .

Same as Table I but with nuclear spin-statistical weights for .

Reverse correlation table of irreducible representations of the point group to the molecular symmetry group.

Reverse correlation table of irreducible representations of the point group to the molecular symmetry group.

Localized asymmetric top Hamiltonian for each minimum defined in the global axis system of Fig. 3. The second column indicates the type of distortion as discussed in the text.

Localized asymmetric top Hamiltonian for each minimum defined in the global axis system of Fig. 3. The second column indicates the type of distortion as discussed in the text.

Rotational operators and their irreducible representation in the molecular symmetry group.

Rotational operators and their irreducible representation in the molecular symmetry group.

Adiabatic ionization energy, rotational constants , and tunneling splitting determined from a least-squares fitting procedure of the calculated to the observed line positions for , , and .

Adiabatic ionization energy, rotational constants , and tunneling splitting determined from a least-squares fitting procedure of the calculated to the observed line positions for , , and .

Measured line positions and deviations from the calculated line positions of the vibrationless photoionizing transition. , and , represent the vibronic and the rovibronic symmetries in the molecular symmetry group for the neutral and the ionic states, respectively. The distinction between and or and was not always possible.

Measured line positions and deviations from the calculated line positions of the vibrationless photoionizing transition. , and , represent the vibronic and the rovibronic symmetries in the molecular symmetry group for the neutral and the ionic states, respectively. The distinction between and or and was not always possible.

Measured line positions and deviations from the calculated line positions of the vibrationless photoionizing transition. , and , represent the vibronic and the rovibronic symmetries in the molecular symmetry group for the neutral and the ionic states, respectively. The distinction between and or and was not always possible.

Measured line positions and deviations from the calculated line positions of the vibrationless photoionizing transition. , and , represent the vibronic and the rovibronic symmetries in the molecular symmetry group for the neutral and the ionic states, respectively. The distinction between and was not always possible.

Measured line positions and deviations from the calculated line positions of the vibrationless photoionizing transition. , and , represent the vibronic and the rovibronic symmetries in the molecular symmetry group for the neutral and the ionic states, respectively. The distinction between and was not always possible.

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