^{1,2}, Scott W. Wren

^{1}, Kristen M. Vogelhuber

^{1}, Adam J. Gianola

^{1}, W. Carl Lineberger

^{1,a),b)}and John F. Stanton

^{3,a),c)}

### Abstract

The 351.1 nm photoelectron spectrum of the cyclopentadienide ion has been measured, which reveals the vibronic structure of the state of the cyclopentadienyl radical. Equation-of-motion ionization potential coupled-cluster (EOMIP-CCSD) calculations have been performed to construct a diabatic model potential of the state, which takes into account linear Jahn–Teller effects along the normal coordinates as well as bilinear Jahn–Teller effects along the and ring-breathing coordinates. A simulation based on this *ab initio* model potential reproduces the spectrum very well, identifying the vibronic levels with linear Jahn–Teller angular momentum quantum numbers of . The angular distributions of the photoelectrons for these vibronic levels are highly anisotropic with the photon energies used in the measurements. A few additional weak photoelectron peaks are observed when photoelectrons ejected parallel to the laser polarization are examined. These peaks correspond to the vibronic levels for out-of-plane modes in the ground state, which arise due to several pseudo-Jahn–Teller interactions with excited states of the radical and quadratic Jahn–Teller interaction in the state. A variant of the first derivative of the energy for the EOMIP-CCSD method has been utilized to evaluate the strength of these nonadiabatic couplings, which have subsequently been employed to construct the model potential of the state with respect to the out-of-plane normal coordinates. Simulations based on the model potential successfully reproduce the weak features that become conspicuous in the spectrum. The present study of the photoelectron spectrum complements a previous dispersed fluorescencespectroscopic study Miller and co-workers [J. Chem. Phys.114, 4855 (2001); 4869 (2001)Miller and co-workers [J. Chem. Phys.114, 4869 (2001)] to provide a detailed account of the vibronic structure of cyclopentadienyl. The electron affinity of the cyclopentadienyl radical is determined to be . This electron affinity and the gas-phase acidity of cyclopentadiene have been combined in a negative ion thermochemical cycle to determine the C–H bond dissociation energy of cyclopentadiene; . The standard enthalpy of formation of the cyclopentadienyl radical has been determined to be .

We would like to thank Dr. Jeffery Rathbone for his help in understanding the vibronic structure of the cyclopentadienyl radical. Portions of electronic structure calculations and model potential calculations were performed with the JILA Keck Cluster supported by the W. M. Keck Foundation. This research was funded by the Air Force Office of Scientific Research, the National Science Foundation, the Department of Energy, and the Welch Foundation.

I. INTRODUCTION

II. PHOTOELECTRON SPECTROSCOPY

A. Experimental procedure

B. Results

III. SPECTRALANALYSIS

A. LJT effects

B. Bilinear JT effects

C. PJT and QJT effects

1. mode coupling

2. mode coupling

3. mode coupling

4. mode coupling

5. Assignments of the spectrum

IV. DISCUSSION

A. Nonadiabatic effects in the cyclopentadienyl radical

B. LJT vibronic levels

C. Comparison with fluorescencespectrum

D. Thermochemistry

V. CONCLUSION

### Key Topics

- Photoelectron spectra
- 50.0
- Fluorescence spectra
- 42.0
- Wave functions
- 24.0
- Spectrum analysis
- 19.0
- Ab initio calculations
- 10.0

## Figures

The 351.1 nm photoelectron spectra of the cyclopentadienide ion. (a) A spectrum taken at the magic angle. (b) Spectra taken at (black), (red), and (blue).

The 351.1 nm photoelectron spectra of the cyclopentadienide ion. (a) A spectrum taken at the magic angle. (b) Spectra taken at (black), (red), and (blue).

The 351.1 nm photoelectron spectra of the cyclopentadienide ion taken at (a) and (b) . Note the different scales of photoelectron counts.

The 351.1 nm photoelectron spectra of the cyclopentadienide ion taken at (a) and (b) . Note the different scales of photoelectron counts.

Relative atomic displacements for the normal modes of the state of the cyclopentadienide ion evaluated with CCSD/DZP calculations. For the out-of-plane modes, the diameters of the circles represent the relative magnitudes of displacements, while open and filled circles represent the opposite phases of displacements.

Relative atomic displacements for the normal modes of the state of the cyclopentadienide ion evaluated with CCSD/DZP calculations. For the out-of-plane modes, the diameters of the circles represent the relative magnitudes of displacements, while open and filled circles represent the opposite phases of displacements.

A simulation for the state of the cyclopentadienyl radical based on the model potential of Eq. (2) accounting for LJT effects. The sticks (red) represent the positions and relative intensities of individual transitions to vibronic levels of symmetry. The solid line is the simulated spectrum with a Gaussian convolution of a 10 meV full width at half maximum, superimposed on the experimental spectrum (dots).

A simulation for the state of the cyclopentadienyl radical based on the model potential of Eq. (2) accounting for LJT effects. The sticks (red) represent the positions and relative intensities of individual transitions to vibronic levels of symmetry. The solid line is the simulated spectrum with a Gaussian convolution of a 10 meV full width at half maximum, superimposed on the experimental spectrum (dots).

A simulation for the state of the cyclopentadienyl radical, based on the model potential of Eqs. (2) and (3) accounting for LJT and BLJT effects. The sticks (red) represent the positions and relative intensities of individual transitions to vibronic levels of symmetry. The solid line is the simulated spectrum with a Gaussian convolution of a 10 meV full width at half maximum, superimposed on the experimental spectrum (dots).

A simulation for the state of the cyclopentadienyl radical, based on the model potential of Eqs. (2) and (3) accounting for LJT and BLJT effects. The sticks (red) represent the positions and relative intensities of individual transitions to vibronic levels of symmetry. The solid line is the simulated spectrum with a Gaussian convolution of a 10 meV full width at half maximum, superimposed on the experimental spectrum (dots).

Schematic representations of the highest occupied molecular orbitals of the state of the cyclopentadienide ion and their energy diagram obtained from SCF calculations.

Schematic representations of the highest occupied molecular orbitals of the state of the cyclopentadienide ion and their energy diagram obtained from SCF calculations.

Relative vertical energies of the electronic states of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Relative vertical energies of the electronic states of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Simulations for the state of the cyclopentadienyl radical based on the model potential in terms of (a) mode accounting for PJT interaction with the state, (b) mode accounting for QJT effects and PJT interaction with the state, (c) mode accounting for QJT effects and PJT interactions with the , , and states, and (d) mode accounting for PJT interactions with the , , and states. The sticks represent the positions and relative intensities of individual transitions to vibronic levels of symmetry (red), (a) symmetry (blue), (b) symmetry (blue), (c) symmetry (green), symmetry (blue), (d) symmetry (green), and symmetry (blue). The solid lines are the simulated spectra with a Gaussian convolution of a 10 meV full width at half maximum. The intensity scale has been chosen to emphasize weak peaks. The intensity of the origin peak has been set to unity in each simulated spectrum.

Simulations for the state of the cyclopentadienyl radical based on the model potential in terms of (a) mode accounting for PJT interaction with the state, (b) mode accounting for QJT effects and PJT interaction with the state, (c) mode accounting for QJT effects and PJT interactions with the , , and states, and (d) mode accounting for PJT interactions with the , , and states. The sticks represent the positions and relative intensities of individual transitions to vibronic levels of symmetry (red), (a) symmetry (blue), (b) symmetry (blue), (c) symmetry (green), symmetry (blue), (d) symmetry (green), and symmetry (blue). The solid lines are the simulated spectra with a Gaussian convolution of a 10 meV full width at half maximum. The intensity scale has been chosen to emphasize weak peaks. The intensity of the origin peak has been set to unity in each simulated spectrum.

Single-mode simulations for the state of the cyclopentadienyl radical. The model potential of Eq. (2) has been simplified to take into account (a) only mode , (b) only mode , (c) only mode , and (d) only mode . The sticks (red) represent the positions and relative intensities of individual transitions to vibronic levels of symmetry. The black solid line is the simulated spectrum with a Gaussian convolution of a 10 meV full width at half maximum. The simulated spectrum shown in Fig. 5 is reproduced here with the blue solid line for comparison.

Single-mode simulations for the state of the cyclopentadienyl radical. The model potential of Eq. (2) has been simplified to take into account (a) only mode , (b) only mode , (c) only mode , and (d) only mode . The sticks (red) represent the positions and relative intensities of individual transitions to vibronic levels of symmetry. The black solid line is the simulated spectrum with a Gaussian convolution of a 10 meV full width at half maximum. The simulated spectrum shown in Fig. 5 is reproduced here with the blue solid line for comparison.

Plots of vibronic wave functions with respect to the coordinates for the three lowest vibronic levels of single-mode LJT systems. The wave functions have been calculated with the model potentials used for the single-mode simulations shown in Fig. 9. The three main columns correspond to the three modes: , , and . In each main column, there are three main rows corresponding to the three vibronic levels. For each main row in each main column, a collection of six plots are displayed. In this subset, the upper and lower rows represent the two degenerate vibronic levels. Each of these rows contains three plots. The leftmost and center plots depict the vibrational wave functions for the two degenerate electronic states. The summation of the squares of these two wave functions is shown in the rightmost plot, which corresponds to the square of the vibronic wave function for one of the degenerate vibronic levels. The summation of the squares of the vibronic wave functions for the two degenerate vibronic levels results in the square of the total vibronic wave function for the degenerate vibronic level. These squared total vibronic wave functions are displayed at the bottom of the figure for the three vibronic levels, with the lowest at the leftmost and the highest at the rightmost. In each plot, the horizontal and vertical axes represent the symmetric (with respect to the subgroup) and asymmetric components of the coordinates, ranging from to 5 in dimensionless units.

Plots of vibronic wave functions with respect to the coordinates for the three lowest vibronic levels of single-mode LJT systems. The wave functions have been calculated with the model potentials used for the single-mode simulations shown in Fig. 9. The three main columns correspond to the three modes: , , and . In each main column, there are three main rows corresponding to the three vibronic levels. For each main row in each main column, a collection of six plots are displayed. In this subset, the upper and lower rows represent the two degenerate vibronic levels. Each of these rows contains three plots. The leftmost and center plots depict the vibrational wave functions for the two degenerate electronic states. The summation of the squares of these two wave functions is shown in the rightmost plot, which corresponds to the square of the vibronic wave function for one of the degenerate vibronic levels. The summation of the squares of the vibronic wave functions for the two degenerate vibronic levels results in the square of the total vibronic wave function for the degenerate vibronic level. These squared total vibronic wave functions are displayed at the bottom of the figure for the three vibronic levels, with the lowest at the leftmost and the highest at the rightmost. In each plot, the horizontal and vertical axes represent the symmetric (with respect to the subgroup) and asymmetric components of the coordinates, ranging from to 5 in dimensionless units.

Plots of vibronic wave functions with respect to the coordinates for vibronic levels calculated with the model potentials of Eqs. (2) and (3). The corresponding simulation is shown in Fig. 5. See Fig. 10 caption for explanation of the plots. For all the plots, the wave functions have been calculated at the minimum of the adiabatic potential energy surface (i.e., integrated along the bottom of the pseudorotation path).

Plots of vibronic wave functions with respect to the coordinates for vibronic levels calculated with the model potentials of Eqs. (2) and (3). The corresponding simulation is shown in Fig. 5. See Fig. 10 caption for explanation of the plots. For all the plots, the wave functions have been calculated at the minimum of the adiabatic potential energy surface (i.e., integrated along the bottom of the pseudorotation path).

Plots of vibronic wave functions with respect to the coordinates for a vibronic level calculated with the model potentials of Eqs. (2) and (3). The corresponding simulation is shown in Fig. 5. This vibronic level corresponds to peak . See Fig. 10 caption for explanation of the plots. For the top main row, the wave functions have been calculated at the minimum of the adiabatic potential energy surface (i.e., integrated along the bottom of the pseudorotation path). For the remaining three main rows, integration over one of the three coordinates has been performed with a radial shift of one dimensionless unit off the minimum. These particular modes are (the second main row), (the third), and (the bottom row).

Plots of vibronic wave functions with respect to the coordinates for a vibronic level calculated with the model potentials of Eqs. (2) and (3). The corresponding simulation is shown in Fig. 5. This vibronic level corresponds to peak . See Fig. 10 caption for explanation of the plots. For the top main row, the wave functions have been calculated at the minimum of the adiabatic potential energy surface (i.e., integrated along the bottom of the pseudorotation path). For the remaining three main rows, integration over one of the three coordinates has been performed with a radial shift of one dimensionless unit off the minimum. These particular modes are (the second main row), (the third), and (the bottom row).

Plots of vibrational wave functions with respect to the coordinate for vibronic levels calculated with the model potentials of Eqs. (2) and (3). The corresponding simulation is shown in Fig. 5. The plots correspond to the wave functions for one of the degenerate states, but the identical wave functions have been obtained for the other state (with possible phase reversal). The wave functions have been calculated at the minimum of the adiabatic potential energy surface (i.e., integrated along the bottom of the pseudorotation path). The vertical line indicates the position of the adiabatic potential energy minimum.

Plots of vibrational wave functions with respect to the coordinate for vibronic levels calculated with the model potentials of Eqs. (2) and (3). The corresponding simulation is shown in Fig. 5. The plots correspond to the wave functions for one of the degenerate states, but the identical wave functions have been obtained for the other state (with possible phase reversal). The wave functions have been calculated at the minimum of the adiabatic potential energy surface (i.e., integrated along the bottom of the pseudorotation path). The vertical line indicates the position of the adiabatic potential energy minimum.

A simulation for the state of the cyclopentadienyl radical based on the model potential of Eq. (2) accounting for LJT effects, but the coupling constants of the model potential have been taken from Ref. 27. The mode is excluded from the model potential. The sticks (red) represent the positions and relative intensities of individual transitions to vibronic levels of symmetry. The solid line is the simulated spectrum with a Gaussian convolution of a 10 meV full width at half maximum, superimposed on the experimental spectrum (dots).

A simulation for the state of the cyclopentadienyl radical based on the model potential of Eq. (2) accounting for LJT effects, but the coupling constants of the model potential have been taken from Ref. 27. The mode is excluded from the model potential. The sticks (red) represent the positions and relative intensities of individual transitions to vibronic levels of symmetry. The solid line is the simulated spectrum with a Gaussian convolution of a 10 meV full width at half maximum, superimposed on the experimental spectrum (dots).

(Left) Plots of vibronic wave functions with respect to the coordinates for the overtone sublevels of vibronic symmetry calculated with the corresponding model potential. The corresponding simulation is shown in Fig. 8(c). See Fig. 10 caption for explanation of the plots. (Right) Plots of vibronic wave functions with respect to the coordinates for one of the overtone levels of vibronic symmetry calculated with the corresponding model potential. The corresponding simulation is shown in Fig. 8(d).

(Left) Plots of vibronic wave functions with respect to the coordinates for the overtone sublevels of vibronic symmetry calculated with the corresponding model potential. The corresponding simulation is shown in Fig. 8(c). See Fig. 10 caption for explanation of the plots. (Right) Plots of vibronic wave functions with respect to the coordinates for one of the overtone levels of vibronic symmetry calculated with the corresponding model potential. The corresponding simulation is shown in Fig. 8(d).

## Tables

Peak positions and assignments for the photoelectron spectrum of the cyclopentadienide ion. See Fig. 2 for peak labels.

Peak positions and assignments for the photoelectron spectrum of the cyclopentadienide ion. See Fig. 2 for peak labels.

Direct products of irreducible representations of the point group.

Direct products of irreducible representations of the point group.

Harmonic vibrational frequencies of the state of the cyclopentadienide ion evaluated with CCSD/DZP calculations.

Harmonic vibrational frequencies of the state of the cyclopentadienide ion evaluated with CCSD/DZP calculations.

Linear coupling constants (eV) for the state of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Linear coupling constants (eV) for the state of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Equilibrium geometries of the state of the cyclopentadienyl radical located with EOMIP-CCSD/DZP calculations. Geometries are expressed as displacements from the equilibrium geometry of cyclopentadienide ion in terms of the anion reduced normal coordinates.

Equilibrium geometries of the state of the cyclopentadienyl radical located with EOMIP-CCSD/DZP calculations. Geometries are expressed as displacements from the equilibrium geometry of cyclopentadienide ion in terms of the anion reduced normal coordinates.

Quadratic coupling constants (eV) for the state of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Quadratic coupling constants (eV) for the state of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Linear interstate coupling constants (eV) for the state of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Linear interstate coupling constants (eV) for the state of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Quadratic coupling constants (eV) for the state of the cyclopentadienyl radical evaluated with EOMIP-CCSD/DZP calculations.

Comparison of LJT coupling constants and the corresponding harmonic frequencies : ; dimensionless.

Comparison of LJT coupling constants and the corresponding harmonic frequencies : ; dimensionless.

Vibronic levels of the state of the cyclopentadienyl radical.

Vibronic levels of the state of the cyclopentadienyl radical.

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