1. Silver Nyambo Department of Chemistry, Marquette University, Wisconsin Towards a global picture of spin-orbit coupling in the halocarbenes June 22 2012

2. Electronic structure of carbenes Carbenes contain a divalent carbon and feature low-lying singlet and triplet states that differ greatly in reactivity A central goal in carbene chemistry has been to experimentally determine and theoretically predict the magnitude of the singlet-triplet gap, and probe spin orbit coupling between the singlet and triplet states

3. Studied by Merer and Travis, Lineberger, Harmony, Hirota, Sears, Chang, Kable, Reid, … Mono- halocarbenes (:CHX) :CHF :CHCl :CHBr :CHI S0S0 T1T1 S1S1 0 4000 8000 12000 16000 20000 Energy in cm -1 24000 28000 S2S2 3

4. SVL Emission Spectroscopy Energy S0S0 S1S1 T1T1 Bond angle supplement Camera Diffraction grating time Intensity Gate 4

5. Triplet levels as observed in SVL emission spectra CHClCDBr 5

6. CHI and CDI Here we were originally unable to assign many of the observed levels in our SVL emission spectra Bending states are severely perturbed, with shift of 100 cm -1 for fundamental Putative triplet origin is observed at 1407 cm -1 In CDI, triplet origin is observed near 1285 cm -1 6

7. Developing a global picture of spin-orbit coupling Set up H matrix  diagonalize  least squares fit to observed levels H SO Singlet levels (Dunham Expansion) Triplet levels (Dunham Expansion) 7

8. What about H SO ? Even for the smallest data set, we need > 250 spin-orbit matrix elements. How can we determine these? Assume: The vibrational overlaps are calculated from theoretical data (vibrational frequencies and l-matrix elements) at a benchmarked level of theory, using PGOPHER Fit parameters: harmonic frequencies of S 0 and T 1, limited set of anharmonic parameters, H SO, and T 00 (S 0 -T 1 ) 8

9. Isn’t this a severe assumption? We assume that the spin-orbit coupling is independent of nuclear coordinates: Support for this comes in previous studies of CH 2 by McKellar et al. where spin-orbit coupling varied by less than 20% over a broad range of bond angles (CALCS – Richard Dawes) As we expect, the largest vibrational overlaps are for levels containing bending excitation 9

10. Results: CHI and CDI Data for the two isotopomers were fit with a common H SO : (cm -1 ) 10

11. Results: Vibrational Frequencies (cm - ¹) a Unscaled, B3LYP/Sadlej-pVTZ level. b Anharmonic value. 11

12. Energy Levels: CHI Eigenvectors quantify the presence of strong mixing: S 0 (0,0,3) S 0 (0,1,1) Ψ=0.82Ψ So(0,1,1) +0.33Ψ T1(0,0,0) +… Ψ=0.98Ψ So(0,0,3) +.. Calc singlet levels Obs Calc triplet levels 12

13. Results for CHBr/CDBr CHBr: a fit to 36 levels yielded a Mean Absolute Difference (MAD) of 3.8 cm -1, improved from 16 cm -1 for a Dunham fit without spin-orbit coupling. CDBr: 40 levels were fit to MAD of 3.2 cm -1 CH 35 Cl: a combination of SVL emission and SEP data including 53 levels were fit, with an MAD of 3.0 cm -1, representing a factor of two improvement from a simple Dunham fit 13

14. Comparison of derived spin-orbit coupling constants with those of the bare halogen atoms: Spin-orbit coupling constants CHI CHBr CHCl (cm-1) Slope = 0.142(1) Halogen atom X a Spin Orbit Coupling Constant, X so cm -1 Spin Orbit Coupling Constant, CHX so cm -1 I5069731 Br2460355 Cl58781 F269- a Handbook of photochemistry, 3 rd edition 14

15. Summary Carbenes are important reactive intermediates that display complicated spectroscopy and dynamics Using SVL emission and SEP spectroscopy, we have probed the singlet-triplet gap and spin-orbit coupling between S 0 and T 1 In this talk, we used a global analysis to fit the observed data – in all cases to within experimental error The derived spin-orbit coupling constants show a good correlation with those of the halogen atom New values for the singlet-triplet gaps are obtained (not discussed here) 15

16. Acknowledgements Advisor: Scott A. Reid People: Chong Tao Calvin Mukarakate Scott Kable Tim Schmidt Richard Dawes George Bacskay Richard Judge Will Polik Trevor Sears Eric Brown Funding: National Science Foundation