THE ANALYSIS OF HIGH RESOLUTION SPECTRA OF ASYMMETRICALLY DEUTERATED METHOXY RADICALS CH 2 DO AND CHD 2 O (RI09) MING-WEI CHEN 1, JINJUN LIU 2, DMITRY G. MELNIK 1 and TERRY A. MILLER 1, and ROBERT F. CURL 3 and C. BRADLEY MOORE 4 1 Laser Spectroscopy Facility Department of Chemistry The Ohio State University, 2 Laboratory of Physical Chemistry ETH, Zurich, Switzerland 3 Department of Chemistry and Rice Quantum Institute, Rice University, 4 Department of Chemistry, University of California, Berkeley.

Outline The goal: Understand the molecular properties of methoxy radicals “beyond numbers” Built the relationship between the molecular properties of different isotopomers Study the effect of symmetry reduction on the molecular parameters Methods: Comparison of the molecular parameters of the symmetric methoxy species, CH 3 O and CD 3 O. High resolution spectroscopic study of asymmetrically deuterated methoxy species, CHD 2 O and CH 2 DO. Extension of global analysis to experimentally determined molecular parameters of substituted species.

The Benefits of the Isotopic Studies The potential hypothetical molecule along normal mode q q Levels of Isotopomer 2 Isotopic scaling of rotationally resolved spectra: Molecular properties manifest themselves through the effective parameters of the rotational Hamiltonian: The X i are the effective parameters that are co-factors to the terms with the unique functional dependence on quantum numbers f i (J, P, , etc...). Parameters X i have different contributions: If F 1, F e and F v have different functional dependence, they can be separated, e.g. through studying the isotopic dependencies. Interactions with excited vibrational states Interactions with excited electronic states Levels of Isotopomer 1

Hamiltonian parameters and corrections H EFF = H ROT + H COR + H SO + H SR + H JT + H CD [1] J.Mol.Spectrosc., 81, 73 (1980) [2] J.Mol.Spectrosc., 140,112 (1990) [3] J. Chem. Phys, 42, 2283 (1965) [4] Can.J.Phys, 59, 428 (1981) [5] This work Note: we assume that the ratio  of the vibrational frequency wi of the normal and substituted species is approximately the same for all modes. A,B – rotational constants, m H – mass of the hydrogen isotope a – spin-orbit coupling constant  – the ratio of the average vibational frequency of the protonated isotopomer ( ) to that of the species in question ( ). Dominating terms are highlighted

Isotopic Dependence and Structural Parameters Experimentally obtained values and their ratios: Experiment vs. estimation Experimentally obtained structural parameters of methoxy radical*: [a] parameters obtained from re-fitting the 13 CH 3 O data by Momose et al, J.Chem. Phys. 88, 5338 (1988)

What Happens When the Symmetry is Reduced (CHD 2 O)? C 3v CsCs Basis set: Vibronic eigenfunctions: a a J. Mol.Struct. 780, 163 (2006) Vibronic problem: “asymmetry” Hamiltonian The effective rotational Hamiltonian: Treat asymmetry effects as perturbation. Use C 3v vibronic functions. Use the obtained isotopic dependence to predict the properties of the asymmetrically substituted species. H EFF = H ROT + H COR + H SO + H SR + H JT + H CD + H ASYM

1.Traditional treatment, principal 2. Axis system with z axis placed axis system (PAS): along C-O bond, or “internal axis system” (IAS) a c D D H  D D H z x Coordinate System for Rotational Hamiltonian (CHD 2 O) Mol.Physics, 105, 529 (2007)

LIF – Rotational structure of E 3/2 state (  =50MHz) LIF – Rotational structure of E 3/2 state (  =50MHz) Direct microwave absorption – rotational structure of E 3/2 state across parity stacks (  =2 MHz) Direct microwave absorption – rotational structure of E 3/2 state across parity stacks (  =2 MHz) SEP – rotational structure of E 1/2 state (  =70 MHz) SEP – rotational structure of E 1/2 state (  =70 MHz) Rotational level parity: even odd Diagram of the Levels Accessed by the Measurements.

MHz MHz 1.8 MHz MHz 2.7 MHz 3.2 MHz 1.2 MHz MHz CHD 2 O CH 2 DO Microwave Spectra.

LIF SEP LIF and SEP Spectra (CHD 2 O)

Parameters of the Effective Hamiltonian (CHD 2 O) Number of assigned transitions: microwave 14 LIF 165 SEP 6 Exp. accuracy [std deviation], MHz microwave* 2.0 [ 1.52 ] LIF 50 [ 36 ] SEP 70 [ 76 ] Number of parameters used: 16 5 * due to partially unresolved hyperfine structure, centers-of-mass of transitions were used

Molecular Parameters, Isotopic Trends Isotopic trends of some of the effective Hamiltonian parameters Parameters used to predict values of CHD 2 O

Asymmetry effects in Rotational Jahn-Teller Hamiltonian C 3v case, effective Jahn-Teller Hamiltonian Cs case, effective Hamiltonian: The values of h 1 and h 2 are modified: where are functions of derivatives of the Components of tensor of inertia with respect to normal Coordinates and energy difference  E. These functions vanish in the C 3v limit. The potential sources of discrepancies between the prediction and experiment: Neglect of the coupling between the q ua components of the Jahn-Teller active modes with totally symmetric modes when the symmetry is reduced: Vibronic coupling in the system with reduced symmetry (new type of X 2v contributions). terms?

Summary Accomplished: The isotopic dependencies of various parameters of the effective rotational Hamiltonian are summarized end extended, including the h 1 and h 2 Jahn-Teller terms. The global analysis of the symmetric species is performed. Its results allowed to approach the problem of the analysis of the asymmetrically substituted molecules. The analysis of the CHD 2 O is reasonably successful within the approximation of the model used. The higher order treatment is needed to achieve the agreement of the theory with observed data within the experimental error. Future development: Refine the analysis of the Jahn-Teller terms in the asymmetrically substituted species. Global analysis of both asymmetric species with symmetric ones.

Funding: NSF Acknowledgements Colleagues: Gabriel Just Phillip Thomas Linsen Pei Rabi Chhantyal-Pun Shenghai Wu (alumni) Patrick Rupper (alumni) John T. Yi (alumni) Jinjun Liu (alumni) Erin Sharp (alumni)