JT distortion by neutralization of the tropylium ion. The geometrical parameters for ( and ) in Å and deg are C1–C2 (1.393, 1.419), C2–C3 (1.443, 1.371), C3–C4 (1.357, 1.457), C4–C5 (1.462, 1.354), C1–H8 (1.084, 1.081), C2–H9 (1.081, 1.084), C3–H10 (1.084, 1.082), C4–H11 (1.082, 1.083), C2–C1–C7 (129.8, 127.4), C3–C2–C1 (127.5, 129.7), and C4–C3–C2 (129.3, 127.9).
LUMOs and HOMOs of and configurations at the level (the Rydberg states slightly below LUMO are not considered here).
Schematics of the interchange between and configurations via , , and symmetries.
Interconversion barriers (without ZPE correction) via and symmetries between the two JT configurations and at the and levels.
Interconversions between and configurations along the pseudorotation mode , (center).
Potential energy surface profile (: the energy with ZPE correction except for ; energy without ZPE correction) along the transition path between and conformers (a), geometrical parameters (bond distances in Å) of the two conformers and the symmetry structure along the transition path at the level (b), and some HOMOs of tropyl radical during the interconversions between and configurations along the pseudorotation coordinates (c).
Vertical transition (from to ) which involves the configurational interchange between and .
IR spectra of averaged two configurations of tropyl radical from , , and calculations [experiment of Satink et al. (Ref. 1) (top), ROHF (second line), and B3LYP (third line), UQCISD (bottom)].
Spin , Jahn-Teller distortion energy , frequency, and relative energy of with respect to for the two Jahn-Teller configurations of the tropyl radical. All energies and frequencies are given in . is the energy difference between the lowest energy JT configuration and the degenerate state with symmetry. and and are ZPE-uncorrected and ZPE-corrected energies (ZPE correction of all other modes except ), respectively. The negative value indicates that the configuration is more stable.
Vertical excitation energy (eV) of the tropyl radical and benzene cation. In the CASSCF calculation, seven electrons and seven active orbitals are included. The basis set was used. The TDDFT results were obtained using the B3LYP method.
Calculated Jahn-Teller constants for the
Characterization of vibrational modes ( and states). The basis set was used for ROHF and UB3LYP, and the basis set was used for UQCISD. The frequencies in the table were scaled by a factor of 0.94. Frequencies are in , and IR intensities given as subscripts are in km/mol. Experimental data are from Ref. 1. The CH vibrations are not included because these experimental results are not available. Notations: swing (W), bend (B), breath (Br), and stretch (S). The vibrational frequencies of at the level were not obtained due to the convergence problem.
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