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The vibronic level structure of the cyclopentadienyl radical
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10.1063/1.2973631
/content/aip/journal/jcp/129/8/10.1063/1.2973631
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/8/10.1063/1.2973631

Figures

Image of FIG. 1.
FIG. 1.

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).

Image of FIG. 2.
FIG. 2.

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

Image of FIG. 3.
FIG. 3.

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.

Image of FIG. 4.
FIG. 4.

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).

Image of FIG. 5.
FIG. 5.

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).

Image of FIG. 6.
FIG. 6.

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

Image of FIG. 7.
FIG. 7.

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

Image of FIG. 8.
FIG. 8.

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.

Image of FIG. 9.
FIG. 9.

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.

Image of FIG. 10.
FIG. 10.

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.

Image of FIG. 11.
FIG. 11.

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).

Image of FIG. 12.
FIG. 12.

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).

Image of FIG. 13.
FIG. 13.

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.

Image of FIG. 14.
FIG. 14.

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).

Image of FIG. 15.
FIG. 15.

(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

Generic image for table
Table I.

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

Generic image for table
Table II.

Direct products of irreducible representations of the point group.

Generic image for table
Table III.

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

Generic image for table
Table IV.

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

Generic image for table
Table V.

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.

Generic image for table
Table VI.

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

Generic image for table
Table VII.

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

Generic image for table
Table VIII.

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

Generic image for table
Table IX.

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

Generic image for table
Table X.

Vibronic levels of the state of the cyclopentadienyl radical.

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/content/aip/journal/jcp/129/8/10.1063/1.2973631
2008-08-28
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The vibronic level structure of the cyclopentadienyl radical
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/8/10.1063/1.2973631
10.1063/1.2973631
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