1. Mike Lindsay * and Roger Miller University of North Carolina at Chapel Hill OSU International Symposium on Molecular Spectroscopy, TI02, 6/22/2006 * Current address: AFRL/MNME, Energetic Materials Branch, Ordnance Division, U.S. Air Force Research Lab, 2306 Perimeter Rd., Eglin AFB, FL 32542-5910 An Empirical Relationship Between the Centrifugal Distortion and Rotational Constants of Rotors Solvated in Superfluid Helium Droplets

2. Dynamics of rotors in liquid helium Helium provides a weakly interacting, homogeneous environment for impurities Rotationally resolved spectra –Observed, even for fairly large molecules, –Relatively slow rotational relaxation rates for E rot < E phonon (~5 cm -1 ) Rotational structure –Exhibits the same symmetry as that in the gas phase system. –Provides structural information about the rotor Moment of inertia is modified by the helium: –B reduced by factor of 2-6 (for large rotors) –Some of the helium density rotates with rotor Adiabatic following

3. Dynamics of rotors in liquid helium “Rules of thumb” on the solvent interactions are becoming increasingly necessary to extract information about novel systems. Experiments *POITSE-DMC Calculations of F. Paesani and B Whaley, private communication. * Simulations 3284.73285.03285.3 5 kV/cm Field Free ? New Systems

4. Large effective centrifugal distortion constants observed in the early experiments Centrifugal distortion in helium: Early experiments SF 6 - M. Hartmann, R. E. Miller, J. P. Toennies, and A. Vilesov, Phys. Rev. Lett. 75 1566 (1995). OCS - Grebenev, Hartmann, Havenith, Sartakov, Toennies, and Vilesov, J. Chem. Phys. 112, 4485 (2000). SF 6 OCS ÷ 2.7 × 8700 × 6700

5. Dozens of systems have been studied: ×10 2 -10 6 times larger than in the gas phase. Anomalously large values (~.02 cm -1 ) for HCCH and C 2 H 4 D eff in all systems is positive, not negative! Classically,  = 2BJ –Coupling decreases with increased B –Coupling increases with increased J Lehmann’s toy model –Increased anisotropy with higher J reduces the superfluid fraction Centrifugal distortion in He: Anisotropy dependence on J * M. Hartmann, R. E. Miller, J. P. Toennies, and A. Vilesov, Phys. Rev. Lett. 75 1566 (1995). K. K. Lehmann, J. Chem. Phys, 114 4643 (2001) * I1I1 He

6. Centrifugal distortion in He: Another contribution In addition to the anisotropy, Zillich & Whaley* showed that when B is sufficiently large, higher levels interact with the phonon- roton modes. Effect should be present in spectra of small molecules with B > 1 cm -1 Bulk Helium density of states B =1 cm -1 Free rotor B =1 cm -1 Rotor (in He) J = 1 J = 0 J = 2 * R. E. Zillich and K. B. Whaley, Phys. Rev. B 69 1014517 (2004)

7. Compilation of He data Compilation of reported and unreported spectroscopic constants in helium were performed as part of a recent review* Data includes ~50 systems (molecules, weakly bound clusters, strongly- bound clusters, open shell systems, many body clusters, etc…) * Miller group, Int. Rev. Phys. Chem. 25, 15-75 (2006) Linear Plot Logarithmic Plot Power law dependence!

8. Fit and comparison to gas phase centrifugal distortion Good power law correlation, spanning over four orders of magnitude All He data present included in fit except CH 4, * Nearly quadratic dependence on B eff *

9. Fit and comparison to gas phase centrifugal distortion Good power law correlation, spanning over four orders of magnitude All He data present included in fit except CH 4, * Nearly quadratic dependence on B eff No correlation to exists in gas phase Gas phase data taken from Herzberg, Townes & Schalow, NIST spectral database, and helium droplet papers *

10. Simulations of D eff Monte Carlo simulations predict correct magnitude of D eff Two very different approaches for light and heavy rotors References for Calculations: HCN, DCN Phys. Rev. B, 69 1014517 (2004)N 2 OJ. Chem. Phys. 121 5293 (2004) HCCHPhys. Rev. Lett., 93 250401 (2004)OCSJ. Chem. Phys. 121 4180 (2004) COPhys. Rev. B, 73 1 (2006)CO 2 Phys. Rev. Lett. 94 1 (2005) POITSE-DMC calc. of Paesani and Whaley CBF-DMC calc. of Zillich and Whaley

11. Simulations of D eff Monte Carlo simulations predict correct magnitude of D eff Two very different approaches for light and heavy rotors Varying only the energy level spacings (i.e. phono-roton coupling) does not capture the trend… HCCH Potential, vary rotor energy level spacings

12. Discussion What does it all mean?!?! Is this a general phenomenon? CO and HCN in solid p-H 2 … CO in p-H 2 HCN in p-H 2 D eff =0.029(5)×B eff 1.78(5)

13. Summary Effective centrifugal distortion constants appear to vary approximately quadratically with effective rotational constant. Qualitative picture is unclear, but Monte Carlo simulations contain the underlying mechanism Similar effect may also be occurring in rotors in solid-parahydrogen… (see next talk!) Acknowledgements: N$F Robert Zillich and Francesco Paesani (Whaley Group) Miller Group The students who slaved over the spectra of all these systems… D eff =0.029(5)×B eff 1.78(5)