DMITRY G. MELNIK AND TERRY A. MILLER The Ohio State University, Dept. of Chemistry, Laser Spectroscopy Facility, 120 W. 18th Avenue, Columbus, Ohio JINJUN LIU, Department of Chemistry, University of Louisville, 2320 South Brook Street, Louisville, Kentucky ANALYSIS OF THE ROTATIONALLY-RESOLVED SPECTRA OF ISOPROPOXY RADICAL USING MULTIMODE VIBRONIC CALCULATIONS

Motivation 1. Isopropoxy is “chemically-substituted” methoxy radical. Unlike methoxy, both electronic and vibrational wavefunctions have Cs symmetry. The effect of lowered symmetry on the electronic structure and interplay of vibronic and spin-orbit interaction is of theoretical interest 2.High resolution rotational spectroscopy to study these effects. It can provide information on: a. vibronic state symmetries b. details of the vibronic, spin-orbit interaction, etc. c. allows to compare predictions with the experiment

B̃-X̃ excitation spectra Experiment (High res LIF, T=2.7K ) Sim. c-type (in-plane) Sim. b-type (in-plane) Sim. a-type (out-of-plane) Experiment (Mod. Res. LIF, T=2.7K )

Vibronic Hamiltonian and energy level structure Basis set: Electronic vibrational spin Projection of the Vibronic Hamiltonian (excluding additive terms) onto 2x2 electronic space (diabatic representation) : C 3v (methoxy) w/o H SO with H SO C s (ethoxy) w/o H SO with H SO 61 a cm b cm -1 C s (isopropoxy) w/o H SO with H SO 60.7 cm -1 ? b T.M. Ramond et al,. J. Chem. Phys., 112, 1158 (2000) a J.Liu al,. J. Chem. Phys., 130, (2009)

Branching plane cut through APES J.J. Dillon and D. R. Yarkony, J. Chem. Phys., 130, (2009) PointCalcFit Q min Q min Q ts Q ts Q min1 Q min2 Q ts2 Q min1

H=H harm + H 1 ev +H 2 ev Vibrational basis set size N vib = 10 Solutions (excluding spin): cm -1 Vibronic eigenvalues and eigenfunctions

Intensities of transitions between purely vibronic states In the absence of the spin-orbit coupling, only in-plane transitions are allowed between two states of the same vibronic symmetry regardless of the magnitude of the vibronic coupling.

Effects of the spin-orbit interaction The spin-vibronic Hamiltonian in basis z(c) y(a) x(b)

B̃-X̃ transition intensities Transition intensities: Introducing a new parameter x, assuming x I out /I in in-plane out-of-plane

The effective rotational Hamiltonian (ERH) for the X state The ERH: the nonrigid asymmetric rotor with spin-rotation: First order ERH: Second order ERH: Defining a shorthand notation for the integrals in : Term1 st order2 nd order Contributions to the parameters of the ERH

Experimental spectra and simulations Experiment Fit, c-type (in-plane) transitions only Prediction, using fit constants adding a-type (out of plane) transitions. Experimental: For we obtain

Parameters of the effective rotational Hamiltonian ParameterExperimental“Isotopic” predict. ab initio 1 ab initio 2 vibronic calc. 3, (3) (3) (3) (2) (2) (1) (3) X̃ state parameters (GHz): [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]

Summary 1. We used simple model vibronic analysis to predict the structure and symmetries of the lowest vibronic levels of isopropoxy. The observed selection rules in rotationally resolved B-X spectrum indicate that the lowest vibronic state has A’ symmetry which is consistent with the prediction. 2. We used spin-vibronic analysis to evaluate the effect of the spin-orbit interaction on the vibronic level structure and transition intensities in B-X origin band. The apparent lack of intensity of the perpendicular transitions indicates that the spin-orbit interaction is substantially quenched, and A-X splitting is mostly due to the effects of vibronic coupling. 3. The wavefunctions of the lowest vibronic states have been used to predict the values of the parameters of the ERH, specifically, the components of the effective spin-rotational tensor. While the simulations predict large values of  , further analysis is needed to fully understand the experimental results.

Acknowledgements Colleagues: Dr. Mourad Roudjane Dr. Takashige Fujiwara Dr. Dianping Sun Terrance Codd, Neal Kline Rabi Chhantyal Pun OSU NSF

Supplementary slides

Probability distribution of the lowest 6 vibronic eigenstates

Parameters of the spin-rotational tensor for the ERH Leading contribution terms for the components of the spin-rotational tensor

Microscopic rotational Hamiltonian for the isolated X state. To simplify treatment, we use vibronic basis set to calculate wavefunction of the ground level and treat spin-orbit interaction as part of rotational Hamiltonian. The microscopic rotational Hamiltonian then writes: End-over end rotational part expands as:

Effects of the spin-orbit interaction Diagonal in spin Off-diagonal in spin