1. LASER-INDUCED FLUORESCENCE (LIF) SPECTROSCOPY OF CYCLOHEXOXY
HIGH-RESOLUTION
LASER-INDUCED FLUORESCENCE (LIF) SPECTROSCOPY OF CYCLOHEXOXY
ROTATIONAL AND FINE STRUCTURE OF
MOLECULES IN NEARLY DEGENERATE ELECTRONIC STATES
JINJUN LIU
Department of Chemistry
University of Louisville
DMITRY G. MELNIK and TERRY A. MILLER
Laser Spectroscopy Facility
Department of Chemistry,
06/18/13
the 68th International Symposium on Molecular Spectroscopy

2. ? Alkoxy radicals (RO·) …… …… …… ethoxy methoxy iso-propoxy ethoxy
CH2DO ……
methoxy
CH3O
CD3O
iso-propoxy
2-butoxy
CHD2O ……
ethoxy
methoxy
iso-propoxy
cyclohexoxy …… ?

3. Potential Energy Surfaces (PESs)
ethoxy isopropoxy cyclohexoxy
min2
min2
TS3
TS3
min2
TS1 CI
min1
TS1 CI
min1
TS3
TS1 CI
min1
min3
TS2
min3
TS2
min3
TS2
Zero-point energy (ZPE) correction does NOT change the energy level ordering!
(Top) PES extremes calculated at the CASSCF(7,5)/6-31+G(d) level of theory. DFT gives similar results.
(Bottom) PES scans calculated at the B3LYP/6-31+G(d) level of theory. CASSCF gives similar results.

4. LIF Spectra of Cyclohexoxy
(CO stretch)
~64.4(4) cm-1
(origin)
Transition Type I
Transition Type II

5. Transition Types hot transition Transition Type I (perpendicular)
Conformers:
CHE: Chair Equatorial
CHA: Chair Axial
TBE: Twist Boat Equatorial
TBE: Twist Boat Axial
TBI: Twist Boat Inclinal
Transition Structures:
1-10
Transition Type I (perpendicular)
Transition Type II (parallel)
"Jet-cooled laser spectroscopy of the cyclohexoxy radical", L. Zu, J. Liu, G. Tarczay, P. Dupre, and T. A. Miller, J. Chem. Phys. 120, (2004).

6. Spectroscopic Models Separate-state model Coupled two-state model1,2
Hrot: rotational Hamiltonian
HSR: spin-rotation interaction
HQ: lifting of vibronic degeneracy
HSO: spin-orbit interaction
HCor: Coriolis interaction x z
y(b) a c θ θ
Hougen’s operators:3
D. Melnik, J. Liu, R.F. Curl, and T.A. Miller, Mol. Phys. 105, 529 (2007).
J. Liu, D. Melnik, and T.A. Miller, J. Chem. Phys. (submitted).
J.T. Hougen, J. Mol. Spectro. 81, 73 (1980).
Double

7. Basissets and Transformation
Symmetrized Hund’s case (a) basis set (used for methxoy)
Hund’s case (b) basis set (used for ethoxy et al.)
Transformation:
Rotational wavefunctions:1
1. E. Hirota, High-Resolution Spectroscopy of Transient Molecules (Speringer-Verlag, Berlin, 1985).
Real and diagonal.
Purely imaginary and off-diagonal.

8. Hamiltonian Elements In symmetrized Hund’s case (a) basis set:1
In Hund’s case (b) basis set:2
D. Melnik, J. Liu, R.F. Curl, and T.A. Miller, Mol. Phys. 105, 529 (2007).
J. Liu, D. Melnik, and T.A. Miller, J. Chem. Phys. (submitted).
Hrot & HSR not shown for clarity.

9. Simulation of Rotational Structures
Separate-state model used.
Calculated molecular constants: ?
In GHz unless otherwise indicated.
(s.m.=semiempirical.
At the B3LYP/6-31+G(d) level of theory.
At the CASSCF(7,5)/6-31+G(d) level of theory.
At the CIS/6-31+G(d) level of theory.
Predicted based on conservation of the mass-reduced spin-rotation tensor (ε’=I-1ε) in the “orbital-fixed coordinate system”1 and using isopropoxy as the reference molecule.
At the B3LYP/6-31+G(d) level of theory with ZPE correction.
1. G. Tarczay, S. Gopalakrishnan, and T. A. Miller, J. Mol. Spectrosc. 220, 276 (2003).

10. Global Fit using Separate-State Model

11. Global Fit using Separate-State Model
T=1 K. Fit constants are in GHz unless otherwise indicated. Numbers in parentheses are uncertainties in the unit of the last digit
At the CASSCF(7,5)/6-31+G(d) level of theory.
At the CIS/6-31+G(d) level of theory.
At the B3LYP/6-31+G(d) level of theory.
Semi-empirical prediction.
At the B3LYP/6-31+G(d) level of theory with ZPE correction.

12. Fit using Coupled Two-State Model

13. Mixing of the A’ and A” States by SO

14. Fit using Coupled Two-State Model
(Trot=1 K; Tel=30 K)
At the B3LYP/6-31+G(d) level of theory with ZPE correction.
At the CASSCF(7,5)/6-31+G(d) level of theory.
Fixed to
Fixed.
Fixed to the mean of the calculated values for the X and A states at the B3LYP/6-31+G(d) level of theory.
At the B3LYP/6-31+G(d) level of theory.
Predicted semi-empirically.
At the CIS/6-31+G(d) level of theory.

15. Summary
Experimentally obtained high-resolution LIF spectra of cyclohexoxy provides an ideal test bed for the coupled two-state model for molecules in nearly degenerate states;
By fitting the BA’XA” and BA’AA’ transitions simultaneously, the lifting of vibronic degeneracy (ΔE0) and the spin-orbit interaction (aζed), two effects that both separate the A and X states ( ), can now be determined independently;
The spin-orbit interaction couples the two states and introduces new transitions. The(quenched) spin-orbit constant aζed is strongly correlated with the spin-rotation constants εbb and εcc;
The Coriolis coefficient (ζt) is strongly correlated to the spin-rotation constant εaa and cannot be determined accurately without physical assumptions;
The coupled two-state model (in either case a or case b basis set) can be used to simulate the rotational and spin-rotation structure of molecules in nearly degenerate states and provide insightful understanding of the interaction/coupling between these states.
Thank you!