DMITRY G. MELNIK AND ROBERT F. CURL, The Department of Chemistry and Rice Quantum Institute, Rice University, Houston, Texas 77005; JINJUN LIU, JOHN T. YI AND TERRY A. MILLER The Ohio State University, Dept. of Chemistry, Laser Spectroscopy Facility, 120 W. 18th Avenue, Columbus, Ohio 43210; THE ANALYSIS OF THE GROUND STATE OF ASYMMETRICALLY DEUTERATED METHOXY RADICALS: AN ALTERNATIVE APPROACH

Motivation and goals 1.An interesting spectroscopic problem of symmetry reduction (C 3v to C s ) in Jahn-Teller active molecule 2.Previously proposed model (I.Kalinovsky and C.B.Moore) a was introduced to describe moderate resolution cold spectra with relatively small number of the accessed levels in the ground electronic state. The goal: To develop a theoretical model which: a.is physically meaningful b.allows for reliable computational analysis (e.g. stable numerical fit) c.has the predictive power. a I.Kalinovsky, “Laser Induced Fluorescence Spectroscopy of CHD 2 O and CH 2 DO and High Resolution Spectroscopy of CH 3 O and HFCO'', Ph.D. Thesis, U. of California, Berkeley, 2001

Previously proposed model Kalinovsky and Moore: H EFF = H SO + H COR + H JT + H SR + H ROT + H ASYM or The matrix element of the new term (Hund’s case a): cm -1 Computational analysis by Kalinovsky and Moore:  E = cm -1 E 3/2 E 1/2  E is expected to correlate strongly with spin-orbit interaction term a  e d 2. The nature of experimental data allowed Kalinovsky and Moore to handle the problem successfully with the addition of a single new parameter. Ground state p – parity with respect to (12)* transformation

Available experimental data Kalinovsky and Moore(CHD 2 O): Rotationally resolved LIF data, 7 vibronic bands, over 200 transitions, Experimental accuracy 2000 MHz. These studies (CHD 2 O): 14 microwave transitions with partially resolved hyperfine structure, experimental accuracy 1.0 MHz (HF structure average). High resolution LIF spectra, 2 vibronic bands, 170 transitions, Experimental accuracy 50 MHz. Ground state (E 3/2 ) 33 6’ p=+1 p=-1 Levels accessed (ground state): J= 0.5…5.5 P=-1.5…2.5 High resolution UV LIF microwave

The choice of the system of coordinates 1.Traditional treatment, principal 2. Axis system with z axis placed axis system (PAS): along C-O bond, or “bond axis system” (BAS) a c D D H  D D H z CHD 2 O

Modification of the symmetric case Hamiltonian Starting with the Hamiltonian used by Watson a and Hirota b, adding new terms due to the asymmetry: (rotation) (spin-rotation) and the new term introduced by Kalinovsky and Moore : The corresponding matrix elements are: a J.K.G.Watson,, J.Mol.Spectroscopy, 103, 125 (1984) b Y.Endo, S.Saito, E.Hirota, J.Chem. Phys., 81, 122 (1984)

Numerical analysis: combination differences vs. global fit Ground state Excited state p=-1p=+1 1.Combination differences: not all of the available data is used. 2.Ambiguity: a large number of local minima that predict the accessed levels energies accurately but fail to predict the other energies consistently. 3. The computation problem is highly nonlinear and prone to diverge if the initial guess is too far away from the solution. 4.Data correlation: combination differences derived from a set of more than two transitions to the same upper state level are affected by a single mismeasured or misassigned transition 5. The global fit: the amount of data used more than doubles at the expense of the addition of the parameters of the two relatively simple and well- behaved excited states (184 transitions in global fit vs. 79 combination differences) Combination difference analysis scheme

Global analysis 1.Ground state: used Hund’s case (a) Hamiltonian described above 2.Excited states: used Hund’s case (b) Hamiltonian (S-reduction) by Brown and Sears a and Watson b. 3.Did not calculate intensities of transitions, rather, relied on the assignments made by J.Liu and co-workers [TJ05] 4.Used Levenberg-Marquadt fitting procedure a J.M.Brown and T.J.Sears, J. Mol.Spectroscopy, 75, 11 (1979) b J.K.G.Watson, “Aspects of Quadratic and Sextic Centrifugal Distortion Effects on Rotational Energy Levels”, in Vibrational Spectra and Structure, Vol.6., Chap. 1, ed. by J.R.Durig (Elsevier, Amsterdam, 1977).

Numerical analysis: preliminary results (47) cm (4) 95057(10) 23765(7) 307 (2) (fixed) (fixed) 3187(87) -3217(152) (490) -11.8(15) 1315(22) (35) cm (138) (29) cm (12) (8) 315.4(7) -9.3(28) 350(3) 12.9(4) (29) cm (2) (7) 213.4(5) 328(3) Standard deviation: MW: 0.8 MHz, UV LIF: 35 MHzData: 14 MW lines, 170 UV LIF lines Nonlinear fit summary: Molecular constants of CHD 2 O. All constants in MHz, except as noted ~ ~ ~

Correlation and error analysis 1.Confidence interval (“error bars”) for a varied Hamiltonian parameter a i : where C is the covariance matrix C=B -1, B being the normal matrix on the last successful iteration 2. The correlation between the two parameters could be estimated as If  a i is large and |Cor(a i, a j )| is close to 1, then a i cannot be accurately determined independently of a j. The potential solutions of such case: i.Refining the model ii.Fixing one of the correlated parameters to an a priori known value iiiObtaining discriminating experimental data 3. In this case:

Summary and the future work 1.A theoretical and computational approach to the solution of the problem of asymmetrically deuterated methoxy radical has been developed. 2.The model still requires fine adjustment, which can be achieved by error and correlation analysis of the obtained results 3.The application of the developed procedure on CH 2 DO radical is underway 4. The analysis of the spectra involving the levels of E 1/2 component of the ground state may serve as a test for the method presented.

Acknowledgements Rice University Welch Foundation NSF