1. DMITRY G. MELNIK AND TERRY A. MILLER The Ohio State University, Dept. of Chemistry, Laser Spectroscopy Facility, 120 W. 18th Avenue, Columbus, Ohio 43210 JINJUN LIU, Department of Chemistry, University of Louisville, 2320 South Brook Street, Louisville, Kentucky 40292. ANALYSIS OF THE ROTATIONAL STRUCTURE OF THE TRANSITION OF ISOPROPOXY RADICAL: ISOLATED vs. COUPLED STATE MODEL

2. Jahn Teller Effect Pseudo Jahn Teller Effect Pseudo Jahn Teller Effect 355(10) cm -1 60.7(7) cm -1 b Ramond et. al. J. Chem. Phys. 112, 1158 (2000) c Rabi Chhantyal-Pun, Jinjun Liu and Terry A. Miller, TI14, MSS 2012 Columbus d Jin et. al. J. Chem. Phys. 121, 11781 (2004) CH 3 O C2H5OC2H5O i-C 3 H 7 O a Foster et. al. J. Phys. Chem. 90 6766 (1986) Background (a) (b) (c,d)

3. Background 1.Rotationally resolved spectrum of isopropoxy radical has been has been quantitatively fit to a simple isolated asymmetric rotor model with spin rotation a 2.Experimentally observed rotational constants are consistent with the quantum chemistry calculations. 3.Experimentally observed spin-rotational parameters are inconsistent with (i) quantum chemistry calculations (ii) predictions based on the previously obtained values for other alkoxy radicals. (iii) multimode vibronic calculations 4.Despite the expected strong Coriolis and spin-orbit mixing with the closely lying electronic state, which would expect to produce characteristic a-type transitions, none are observed. The physics behind pp. 3 and 4 needs to be understood. a D. G. Melnik, T. A. Miller and J. Liu, TI15, 67 th MSS, Columbus OH 2012

4. Experimental and predicted spectra: simple asymmetric rotor Exp c-type b-type c b c b

5. Parameters of the effective rotational Hamiltonian ParameterExperimental“Isotopic” predict. ab initio 1 ab initio 2 vibronic calc. 3,4,5 9.338(3)9.1879.23 8.064(3)8.0088.15 4.893(3)4.8254.90 +4.26(2)-0.11 -0.13 -4.59(2)-13.94-0.76-2.85 +1.72(1)-0.47-0.03-0.15 1.96(3)+2.55+0.17-0.48 X̃ state parameters (GHz) a : [1] B3LYP/6-31G(d) [2] CCSD/cc-pVTZ – Gyorgy Tarczay, private communication. [3] We assumed the value for an unquenched spin-orbit coupling constant -145 cm -1, and the angle between the CO bond and z-axis 72 degrees. [4] [5] a D. G. Melnik, T. A. Miller and J. Liu, TI15, 67 th MSS, Columbus OH 2012

6. Traditional treatment of spin-rotation Second order PT treatment For the lowest vibronic state the expected sign for  ab is that of the spin orbit coupling constant (i.e., negative). all other vibronic states Second order PT: Vibronic calculations a + experiment: a D. G. Melnik, T. A. Miller and J. Liu, TI15, 67 th MSS, Columbus OH 2012

7. Isolated and twofold coupled Hamiltonian Isolated state modelTwofold (coupled state) model 1. Van-Vleck transformation (usually 2 nd order PT) Van-Vleck transformation within the twofold X state rotation levels are treated as parts of “compound” twofold state  constraints on X and A state parameters need to be imposed

8. Hamiltonian and the basis set. Vibronic basis set (basis functions are real): -- eigenfunctions of the vibronic Hamiltonian. Rotational Hund’s case “b” basis Effective rotational Hamiltonian:

9. Transition intensities. Spin-rovibronic eigenvectors for the twofold and the B state: Rotational transition intensity: Isolated state model: No explicit summation over components with different rovibronic symmetry  only in-plane transitions are allowed Twofold model: Explicit summation is performed over components with different rovibronic symmetry  both in-plane and out-of-plane transitions are allowed.

10. Molecular constants for the coupled twofold. Parameter GHzvalue (twofold)value (isolated) A9.350 (5)9.338 (3) B8.070 (4)8.064 (4) C4.903 (4)4.893 (3) a  e d (cm -1 ) -38.84 (10) --- tt 0.264(6)---  E 0 (cm -1 ) 46.6 (15)---  19.2(7)---  aa 0+4.26 (2)  bb 0-4.59 (1)  cc 01.72 (1)  bc 01.96 (3) Constraints for the twofold Hamiltonian: Spin-rotation parameters for the X state are restricted to 0 due to 100% correlation to spin-orbit and Coriolis parameters.

11. Experimental spectra and simulation. Experimental. Twofold model, all transition types. Isolated model, c-type + b-type.

12. Component contribution to transition intensities. Full simulation, a,b, and c-type c-type b-type a-type

13. Correlation of isolated state and twofold models. Twofold HamiltonianIsolated state Hamiltonian 1.Van-Vleck transformation within the twofold (i.e. transition from twofold to isolated model) does not introduce new rotational operators, but affects the parameters of the existing ones (spin-rotation). 2.On the other hand, second order PT fails to predict parameters of SR tensor even qualitatively (specifically, second order contribution to ). 3.Two types contribution to the spin-rotation parameters in the isolated state model: -- even order VVT (the second order, n=0 is already discussed) -- odd order VVT, independent of Coriolis coupling (dominated by spin-orbit terms)

14. Third order contribution to spin-rotation parameters. “Geometric” approximation for the components of the spin-orbit coupling: ; A rot. constant is usually well-determined and unaffected by the third order spin-orbit effects. Therefore it provides the direct measure of

15. Summary. 1.Rotationally resolved spectra of the is analyzed using two models, isolated state and twofold (coupled states). Both analyses adequately predict spectra to the experimental error. 2.Parameters of the two models are related to each other, but have more transparent physical meaning. 3.Application of the twofold model for the analysis of the rotational structure of isopropoxy radical provides a good opportunity to test multifold approach for the analysis of the spectra involving strongly coupled vibronic states.

16. Acknowledgements Colleagues: Dr. Mourad Roudjane Dr. Rabi Chhantyal Pun Terrance Codd, Neal Kline OSU NSF UoL

17. Spin-Rotation: third order and beyond.  yy, GHz Simulations A = 9.338 GHz.  E 0 = 47.4 cm -1 Third order VVT is clearly insufficient for qualitative prediction of spin-rotational parameters in the isolated model. Application of the twofold model eliminates the need of cumbersome calculations. Isopropoxy