^{1}and F. Merkt

^{1}

### Abstract

High-resolution pulsed-field-ionization zero-kinetic-energy photoelectron spectra of and have been recorded at rotational resolution from the adiabatic ionization energy up to of internal energy of the respective cations. The spectra are characterized by the effects of a large-amplitude pseudorotational motion exchanging the equivalent nuclei in each molecule. With increasing internal energy, a transition from the tunneling regime with splittings of the order of to the free pseudorotation regime is observed. A theoretical model that treats the simultaneous rotational and pseudorotational motions and incorporates the effects of the geometric phase has been developed. The model provides the appropriate rovibronic symmetries in the molecular symmetry group and reaches a near-quantitative agreement with the experimental data. The complete group-theoretical analysis of the rovibronic problem is also given. The analysis of the spectra has revealed the existence of two different isomers for both and , which differ in the bond length between the carbon atom and the unique ligand atom. All isomers are subject to a fast pseudorotational motion between three equivalent minima with a period of in and in . The analysis has also provided the ordering of the tunneling sublevels for each isomer, which enables the location of the twofold conical intersections on the potential energy surface that could not be determined from experiments on .

The authors thank Dr. X. Qian for her experimental help in the recording of the spectrum of and Professor M. S. Child (Oxford) and Professor G. Duxbury (Strathclyde) for useful discussions. This work is supported financially by the Swiss National Science Foundation and the ETH Zürich.

I. INTRODUCTION

II. EXPERIMENT

III. THEORY

A. The potential energy surfaces

B. The tunneling problem

C. The rovibronic problem

IV. RESULTS

A. Symmetry analysis and correlation diagrams

B.

C.

V. DISCUSSION

VI. CONCLUSIONS

### Key Topics

- Tunneling
- 77.0
- Potential energy surfaces
- 22.0
- Chemical bonds
- 16.0
- Photoelectron spectra
- 14.0
- Jahn Teller effect
- 12.0

## Figures

Schematic representation of several stationary points on the potential energy surface of and their topological relationships. The empty circles correspond to the three equivalent minima of the more stable isomer . The squares represent the three equivalent minima of the isomer . The filled circles on four faces of the octahedron represent the structures possessing a doubly degenerate ground electronic state and the center of the remaining four faces correspond to the structures with a nondegenerate ground state. The structure of the and stationary points that are of importance in the present study are depicted.

Schematic representation of several stationary points on the potential energy surface of and their topological relationships. The empty circles correspond to the three equivalent minima of the more stable isomer . The squares represent the three equivalent minima of the isomer . The filled circles on four faces of the octahedron represent the structures possessing a doubly degenerate ground electronic state and the center of the remaining four faces correspond to the structures with a nondegenerate ground state. The structure of the and stationary points that are of importance in the present study are depicted.

Tunneling levels of with zero total angular momentum and ground vibronic state of (full lines). The quantities and represent the tunneling integrals for the isomers and , respectively, ZPED stands for the zero-point energy difference between these isomers, and IE is the adiabatic ionization energy. describes the zero-point energy difference in the absence of tunneling.

Tunneling levels of with zero total angular momentum and ground vibronic state of (full lines). The quantities and represent the tunneling integrals for the isomers and , respectively, ZPED stands for the zero-point energy difference between these isomers, and IE is the adiabatic ionization energy. describes the zero-point energy difference in the absence of tunneling.

Tunneling levels of with zero total angular momentum and ground vibronic state of (full lines). The quantities and represent the tunneling integrals for the isomers and , respectively, ZPED stands for the zero-point energy difference between these isomers, and IE is the adiabatic ionization energy. describes the zero-point energy difference in the absence of tunneling.

Axis systems used in the derivation of the rotational Hamiltonian. The principal axis system of the neutral molecule is depicted on the left-hand side (a). After distortion of the molecule to the equilibrium structure of the cation (b), the axis system is translated to the new center of mass and then rotated about the axis until it coincides with the principal axis system of the distorted molecule (c).

Axis systems used in the derivation of the rotational Hamiltonian. The principal axis system of the neutral molecule is depicted on the left-hand side (a). After distortion of the molecule to the equilibrium structure of the cation (b), the axis system is translated to the new center of mass and then rotated about the axis until it coincides with the principal axis system of the distorted molecule (c).

Correlation diagram of the eigenvalues of the tunneling-rotation Hamiltonian (14) as a function of the tunneling integral for [panel (a)] and [panel (b)]. In the limit , all levels are threefold degenerate and coincide with the pattern of an asymmetric top which is depicted on the left-hand side. The full lines correspond to levels of rovibronic symmetry or in the group, whereas the dashed lines correspond to levels of symmetry . The vibronic symmetries of the tunneling sublevels are indicated on the right-hand side of the figure by large capital letters.

Correlation diagram of the eigenvalues of the tunneling-rotation Hamiltonian (14) as a function of the tunneling integral for [panel (a)] and [panel (b)]. In the limit , all levels are threefold degenerate and coincide with the pattern of an asymmetric top which is depicted on the left-hand side. The full lines correspond to levels of rovibronic symmetry or in the group, whereas the dashed lines correspond to levels of symmetry . The vibronic symmetries of the tunneling sublevels are indicated on the right-hand side of the figure by large capital letters.

PFI-ZEKE photoelectron spectrum (full line) and photoionization spectrum (dashed line) of . The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . The position of the zero-point-corrected *ab initio* barrier for isomerization is indicated by an arrow.

PFI-ZEKE photoelectron spectrum (full line) and photoionization spectrum (dashed line) of . The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . The position of the zero-point-corrected *ab initio* barrier for isomerization is indicated by an arrow.

Lowest band in the PFI-ZEKE photoelectron spectrum of corresponding to isomer [trace (a)] and simulation [trace (b)]. The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . Trace (b) shows a theoretical stick spectrum consisting of transitions to levels of rovibronic symmetry or (full sticks) and transitions to levels of rovibronic symmetry (dotted sticks). The stick spectrum has been convoluted with a Gaussian line shape of FWHM.

Lowest band in the PFI-ZEKE photoelectron spectrum of corresponding to isomer [trace (a)] and simulation [trace (b)]. The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . Trace (b) shows a theoretical stick spectrum consisting of transitions to levels of rovibronic symmetry or (full sticks) and transitions to levels of rovibronic symmetry (dotted sticks). The stick spectrum has been convoluted with a Gaussian line shape of FWHM.

Second lowest band in the PFI-ZEKE photoelectron spectrum of corresponding to isomer [trace (a)] and simulation [trace (b)]. The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . Trace (b) shows a theoretical stick spectrum consisting of transitions to levels of rovibronic symmetry or (full sticks) and transitions to levels of rovibronic symmetry (dotted sticks). The stick spectrum has been convoluted with a Gaussian line shape of FWHM.

Second lowest band in the PFI-ZEKE photoelectron spectrum of corresponding to isomer [trace (a)] and simulation [trace (b)]. The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . Trace (b) shows a theoretical stick spectrum consisting of transitions to levels of rovibronic symmetry or (full sticks) and transitions to levels of rovibronic symmetry (dotted sticks). The stick spectrum has been convoluted with a Gaussian line shape of FWHM.

PFI-ZEKE photoelectron spectrum (full line) and photoionization spectrum (dashed line) of . The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . The position of the zero-point-corrected *ab initio* barrier for isomerization is indicated by an arrow.

*ab initio* barrier for isomerization is indicated by an arrow.

Lowest band in the PFI-ZEKE photoelectron spectrum of corresponding to isomer [trace (a)] and simulation [trace (b)]. The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . Trace (b) shows a theoretical stick spectrum consisting of transitions to levels of rovibronic symmetry or (full sticks) and transitions to levels of rovibronic symmetry (dotted sticks). The stick spectrum has been convoluted with a Gaussian line shape of FWHM.

Second lowest band in the PFI-ZEKE photoelectron spectrum of corresponding to isomer [trace (a)] and simulation [trace (b)]. The PFI-ZEKE photoelectron spectrum was recorded using a sequence of pulsed electric fields of and . Trace (b) shows a theoretical stick spectrum consisting of transitions to levels of rovibronic symmetry or (full sticks) and transitions to levels of rovibronic symmetry (dotted sticks). The stick spectrum has been convoluted with a Gaussian line shape of FWHM.

## Tables

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.

Constants calculated using the experimental structure of determined in Ref. 19 and adjusted to reproduce the experimental spectra. , , are the asymmetric top rotational constants, is the angle by which the axis has been tilted away from the symmetric top principal axis in the rotation of the axis system, is the tunneling splitting, IE is the adiabatic ionization energy of the more stable isomer, and ZPED is the zero-point energy difference between the two isomers.

Constants calculated using the experimental structure of determined in Ref. 19 and adjusted to reproduce the experimental spectra. , , are the asymmetric top rotational constants, is the angle by which the axis has been tilted away from the symmetric top principal axis in the rotation of the axis system, is the tunneling splitting, IE is the adiabatic ionization energy of the more stable isomer, and ZPED is the zero-point energy difference between the two isomers.

Measured line positions and deviations from the calculated line positions of the origin band of the photoionizing transition of . , , and represent the vibronic and the rovibronic symmetries in the molecular symmetry group for the neutral and the ionic states, respectively.

Measured line positions and deviations from the calculated line positions of the origin band of the photoionizing transition of . , , and represent the vibronic and the rovibronic symmetries in the molecular symmetry group for the neutral and the ionic states, respectively.

Measured line positions and deviations from the calculated line positions of the origin band of the photoionizing transition of . , , and represent the vibronic and the rovibronic symmetries in the molecular symmetry group for the neutral and the ionic states, respectively.

Barrier heights at the CCSD(T)/cc-pVTZ level of *ab initio* theory after harmonic zero-point corrections. The barrier heights for pseudorotations exchanging identical nuclei are given with respect to the minima of the corresponding isomers, whereas the isomerization barriers are given with respect to the minimum of the more stable isomer. The purely electronic barrier height amounts to (Ref. 21).

Barrier heights at the CCSD(T)/cc-pVTZ level of *ab initio* theory after harmonic zero-point corrections. The barrier heights for pseudorotations exchanging identical nuclei are given with respect to the minima of the corresponding isomers, whereas the isomerization barriers are given with respect to the minimum of the more stable isomer. The purely electronic barrier height amounts to (Ref. 21).

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