DMITRY G. MELNIK 1 MING-WEI CHEN 1, JINJUN LIU 2, and TERRY A. MILLER 1, and ROBERT F. CURL 3 and C. BRADLEY MOORE 4 EFFECTS OF ASYMMETRIC DEUTERATION ON THE ROTATIONAL LEVEL STRUCTURE OF JAHN-TELLER ACTIVE METHOXY RADICALS 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.

Motivation Jahn-Teller active molecule with spin-orbit interaction High resolution spectroscopy: characterize the effects of lowering of the nuclear symmetry on the rotational level structure Connect the spectra of the molecule to intrinsic geometric properties and the properties of the electronic wavefunction Use isotopic relationships and the data obtained from the study of the normal species to facilitate the analysis

Methoxy spectroscopy LIF – Rotational structure of E 3/2 state (  =50MHz)  P = -1, 0, +1 LIF – Rotational structure of E 3/2 state (  =50MHz)  P = -1, 0, +1 Direct microwave absorption – rotational structure of E 3/2 state across parity stacks (  =1 MHz)  =0  P=0  p: Direct microwave absorption – rotational structure of E 3/2 state across parity stacks (  =1 MHz)  =0  P=0  p: SEP – rotational structure of E 1/2 state (  =70 MHz) Pump+Dump:  = -1  p = SEP – rotational structure of E 1/2 state (  =70 MHz) Pump+Dump:  = -1  p = Rotational level reflection parity: p = +1 p = -1

LIF SEP Experimental data: LIF and SEP (CHD 2 O)

MHz MHz 1.8 MHz MHz 2.7 MHz 3.2 MHz 1.2 MHz MHz CHD 2 O CH 2 DO Experimental data: microwave spectra

C 3v CsCs (a) a I.Kalinovsky Ph.D. Thesis, U.of California, Berkeley, (2001) Treat nuclear asymmetry effects as perturbation. Use C 3v vibronic functions. Ignore the effects of the totally symmetric modes (i.e. limit the discussion to the components of doubly-degenerate modes) Spin-Vibronic problem Basis set: -- eigenfunctions of in unsubstituted (normal) species Difference in ZPE along A” and A’ components

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 D.Melnik, J. Liu, R.F. Curl and T.A.Miller et al Mol.Physics, 105, 529 (2007) Choice of the axis system

General form: H EFF = H SO + H ROT + H CD + H COR + H SR + H JT + H CDJT + H SRJT + H ASYM Basis set: Effective Rotational Hamiltonian Two types of rotational matrix elements: Matrix element of the vibronic part of microscopic rotational Hamiltonian -diagonal in vibronic component, or “parity-independent” -off-diagonal in vibronic component, or “parity-dependent”. In the absecne of vibronic interaction all parity-dependent terms vanish.

Expressions for H ROT and H JT Nuclear asymmetry- induced terms. These terms vanish in the limit of symmetric molecule

Spin-rotation in an asymmetrically substituted molecule Spin-rotation interaction is dominated by the second order contribution: The parity-independent part: derived using relationships by J. Brown, T.J. Sears and J.K.G. Watson (a) The parity dependent part. Only two types of the interaction in C 3v group (b) : -- with nondegenerate states -- with doubly degenerate states The isotopic substitution does not alter the electronic wavefunctions, therefore we expect exactly the same number of independent spin-rotational parameters in the isotopically substituted species! (a) J.M. Brown, T.J. Sears, J. K. G. Watson, Mol. Phys. 41, 173, (1980) (b) J. T. Hougen, J. Mol. Spectroscopy, 81, 73 (1980)

Effective spin-rotational Hamiltonian Parity-independent terms, incl. asymmetry-induced Parity-dependent terms in normal species Nuclear asymmetry-induced parity-dependent terms. None of these parameters are independent. (a) J. T. Hougen, J. Mol. Spectroscopy, 81, 73 (1980)

Parameter constraints H SR : Additional constraints: H CD Parameters are derived from the corresponding values in the normal species using 2 nd order PT (a) A total of 18 ground state parameters were constrained in the actual fits. (a) R. N. Zare, Angular Momentum (Wiley Interscience, New Yourk, 1988) Where are the values of the corresponding parameters in normal species

Numerical analysis: statistics CH 2 DOCHD 2 O Number of assigned transitions: MW1314 LIF SEP86 Fit standard deviation (MHz) MW LIF3836 SEP5554 Number of independently fit parameters Experimental accuracy: MW: 1 MHz LIF: 50 MHz SEP: 70 MHz

Molecular constants of the ground state CH 2 DOCHD 2 O NOTE: for brevity, CDJT terms are not shown

Conclusions A simple mechanical model is used to construct the effective rotational Hamiltonian of the asymmetrically substituted methoxy radical. The parameters of this model are shown to have straightforward physical meaning by relation to the corresponding parameters in the symmetric species. The model is successfully used to calculate a number of parameters to break correlations in the fit procedure and reduce dimensionality of the problem. The model is used to describe all available high resolution spectra to the experimental error.

Acknowledgements Colleagues: Gabriel Just, Dr. Phillip Thomas, Rabi Chhantyal Pan Terrance Codd, Neal Kline OSU NSF

Calculation of the asymmetry-induced H JT terms Electronic PES is insensitive to isotopic substitution h 1, h 2 etc. terms characterize the geometry of the molecule in JT minimum (Watson) Structural parameters from fit of  (  ) to experimental values of A,B,h 1 and h 2 of C 3v species: Substitute to the expression of  for asymmetric species, calculate assymetry-induced terms in H JT

Rotational Hamiltonian H ROT and H JT A’ A’’ “O” QaQa “A” z x x y y z z y x “B” “O” Undistorted configuration at conical intersection