Photoelectron spectroscopy of the cyclopentadienide anion: Analysis of the Jahn- Teller effects in the cyclopentadienyl radical Takatoshi Ichino, Adam J. Gianola, and W. Carl Lineberger JILA and Department of Chemistry and Biochemistry University of Colorado, Boulder, Colorado John F. Stanton Department of Chemistry and Biochemistry and Institute for Theoretical Chemistry The University of Texas at Austin, Austin, TX Supported by

High-temperature oxidation of benzene Cyclopentadienyl radical is formed in combustion of benzene. Cyclopentadienyl radical is a resonance stabilized free radical which may play a role in growth of polycyclic aromatic hydrocarbons. cyclopentadienyl radical (C 5 H 5 )

Thermochemical property of the cyclopentadienyl radical C–H Bond Dissociation Enthalpy of Cyclopentadiene (1) gas-phase equilibrium measurements (i.e., dissociation and recombination reaction rate constants): D 0 (C–H) = 80.8 ± 1.0 kcal mol -1. Roy et al., Int. J. Chem. Kinet. 2001, 33, 821 (2) photoacoustic calorimetric measurements in benzene solution: DH 298 (C–H) = 85.6 ± 1.7 kcal mol -1. Nunes et al., J. Phys. Chem. A 2006, 110, 5130 (3) negative ion thermochemical cycle: D 0 (C–H) =  acid H 0 (C–H) + EA(C 5 H 5 ) – IE(H) photoelectron spectroscopy of the cyclopentadienide anion (C 5 H 5 ‾)

hemispherical energy analyzer Velocity Filter microwave discharge flowing afterglow ion source (~ 0.5 Torr He) ion optics (10 -6 Torr)(10 -8 Torr) MCP + position detector electron optics argon ion laser (351.1 nm) e‾e‾ AOM Photoelectron spectroscopy of C 5 H 5 ‾

Photoelectron spectrum of C 5 H 5 ‾ EA(C 5 H 5 ) = ± eV photon energy: eV, magic angle

Enthalpy of formation of the C 5 H 5 radical D 0 (C–H) =  acid H 0 (C–H) + EA(C 5 H 5 ) + IE(H) = 81.0 ± 0.6 kcal mol -1 DH 298 (C–H) = 82.9 ± 0.6 kcal mol -1  f H 298 (C 5 H 5 ) = DH 298 (C–H) +  f H 298 (C 5 H 6 ) −  f H 298 (H) = 62.9 ± 0.8 kcal mol -1  f H 0 (C 5 H 5 ) = 65.6 ± 0.8 kcal mol -1 cf.  f H 298 (C 5 H 5 ) = 62.5 ± 1.0 kcal mol -1,  f H 0 (C 5 H 5 ) = 65.4 ± 1.0 kcal mol -1, Roy et al., Int. J. Chem. Kinet. 2001, 33, 821

Nonadiabatic effects in X 2 E 1 ″ C 5 H 5 Jahn-Teller effects? X 1 A 1 ′ C 5 H 5 ‾ X 2 E 1 ″ C 5 H 5 − e ‾ a2″a2″ e1″e1″ e1″e1″ a2″a2″

Laser excited dispersed fluorescence A 2 A 2 ″ ― X 2 E 1 ″ C 5 H 5 electronic transition Applegate et al., J. Chem. Phys. 2001, 114, 4855, 4869 Emission from the vibraional ground state as well as from the vibrationally excited states of the Jahn-Teller active modes. Spectral simulations based on a model Hamiltonian in terms of JT eigenfunctions. Ab initio evaluation of JT coupling constants. Measurements of isotopomers.

Model Hamiltonian for a degenerate system with linear Jahn-Teller coupling where nuclear kinetic energy operator harmonic potential energy of the reference state linear and bilinear JT coupling Model potential has an expansion form around the reference geometry in terms of the reduced normal coordinates of the reference state (q i ). E : energy of the degenerate states at the reference geometry Köppel et al., Adv. Chem. Phys. 1984, 57, 59; Mayer et al., J. Chem. Phys. 1994, 100, 899 linear intrastate coupling

Electronic structure calculations: the initial state (closed-shell anion) cyclopentadienide anion (C 5 H 5 ‾ ) modesymmetryfrequencymodesymmetryfrequency 1a1′a1′ 32218e1″e1″ e2′e2′ a2′a2′ a2″a2″ e1′e1′ e2″e2″ CCSD/DZP calculation r(CC) = Å r(CH) = Å X 1 A 1 ′ C 5 H 5 ‾ is the reference state for the model potential. in units of cm -1

Electronic structure calculations: the final state (neutral radical) Equation-of-Motion Ionization Potential Coupled-Cluster method (EOMIP-CCSD) cyclopentadineyl radical (C 5 H 5 ) 2B12B1 2A22A2 C1–C C2–C C3–C C1–H C2–H C3–H C5–C1–C C1–C2–C C2–C3–C H–C1–C C1–C2–H C2–C3–H B 1 (minimum) 2 A 2 (TS) in units of angstroms and degrees J. F. Stanton, J. Chem. Phys. 2001, 115, 10382

Ab initio parametrization of the model potential X 2 E 1 ″ C 5 H 5 model potential parameter (eV) linear intrastate coupling 2 linear JT coupling bilinear JT coupling  2,10 −  2,  2, linear coupling constants: Geometry displacements from the initial (anion) to the final (radical) states are multiplied by the quadratic force constant matrix of the final state at its equilibrium geometry in terms of the anion reduced normal coordinates. bilinear coupling constants: The off-diagonal elements of the quadratic force constant matrix of the final state at its equilibrium geometry in terms of the anion reduced normal coordinates. No energy barrier is assumed along the pseudorotation path in the model potential.

Simulation based on the model Hamiltonian: linear intrastate coupling (a 1 ′ ) only No obeserved peak can be assigned to a 1 ′ mode. X 2 E 1 ″ C 5 H 5

Simulation based on the model Hamiltonian: linear intrastate (a 1 ′ ) + linear JT (e 2 ′ ) coupling X 2 E 1 ″ C 5 H 5 Observed peak positions are well reproduced by linear JT coupling.

Simulation based on the model Hamiltonian: add bilinear coupling X 2 E 1 ″ C 5 H 5 Relative peak intensities are well reproduced by addition of bilinear coupling. cf. photoelectron spectrum of CH 3 O ‾, Schmidt-Klügmann et al., Chem. Phys. Lett. 2003, 369, 21

The vibronic peaks for X 2 E 1 ″ C 5 H 5 X 2 E 1 ″ C 5 H 5 peak(J, n)position (eV)simulation (eV) a1/2, 000 b3/2, ± c1/2, ± d1/2, ± a 1 ′, 1― e1/2, ± f1/2, ± /2, 5― g1/2, ± /2, 7― Jahn-Teller stabilization energy = eV a b c d e f g

Conclusion The nm photoelectron spectrum of the cyclopentadienide anion has been measured. The electron affinity of the cyclopentadienyl radical has been determined to be ± eV. The C–H bond dissociation enthalpy of cyclopentadiene has been derived as D 0 (C–H) = 81.0 ± 0.6 kcal mol -1 from a negative ion thermochemical cycle. The enthalpy of formation of the cyclopentadienyl radical has been derived to be  f H 298 = 62.9 ± 0.8 kcal mol -1. Model potentials of X 2 E 1 ″ C 5 H 5 have been constructed around the equilibrium geometry of X 1 A 1 ′ C 5 H 5 ‾ in terms of the anion reduced normal coordinate, based on the EOMIP-CCSD calculations. A simulation based on the model Hamiltonian reproduces the observed vibronic structure very well, revealing strong Jahn-Teller activity for e 2 ′ modes in the spectrum. It is important to include the bilinear coupling between a 1 ′ and e 2 ′ modes in the model potential. The simulation is completely ab initio.