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

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 Erot < Ephonon (~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

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

3284.7 3285.0 3285.3

5 kV/cm

Field Free

?New Systems

• Large effective centrifugal distortion constants observed in the early experiments

Centrifugal distortion in helium: Early experiments

SF6 - 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).

SF6 OCS

SF6 He Gas OCS He Gas

B 1019 MHz 2730 MHz B 2212 MHz 6063 MHz

D 1.12 MHz 1.66×10-4 MHz D 11.4 MHz 1.31× 10-3 MHz

÷ 2.7 ÷ 2.7× 8700× 6700

• Dozens of systems have been studied: ×102-106 times larger than in the gas phase.

• Anomalously large values (~.02 cm-1) for HCCH and C2H4

• Deff 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)

*

I1

He

He

He

He

HeHeHe

He

He

He

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 rotorB =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)

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 lawdependence!

Fit and comparison to gas phase centrifugal distortion

• Good power lawcorrelation, spanningover four ordersof magnitude

• All He data present included in fit exceptCH4, *

• Nearly quadraticdependence on Beff

*

Fit and comparison to gas phase centrifugal distortion

• Good power lawcorrelation, spanningover four ordersof magnitude

• All He data present included in fit exceptCH4, *

• Nearly quadraticdependence on Beff

• No correlation toexists in gas phase

Gas phase data taken from Herzberg, Townes & Schalow, NIST spectral database, and helium droplet papers

*

Simulations of Deff

• Monte Carlo simulations predict correct magnitude of Deff

• Two very different approaches for light and heavy rotors

References for Calculations:HCN, DCN Phys. Rev. B, 69 1014517 (2004) N2O J. Chem. Phys. 121 5293 (2004)HCCH Phys. Rev. Lett., 93 250401 (2004) OCS J. Chem. Phys. 121 4180 (2004)CO Phys. Rev. B, 73 1 (2006) CO2 Phys. Rev. Lett. 94 1 (2005)

POITSE-DMC calc. ofPaesani and Whaley

CBF-DMC calc. ofZillich and Whaley

Simulations of Deff

• Monte Carlo simulations predict correct magnitude of Deff

• 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

Discussion

• What does it all mean?!?!

• Is this a general phenomenon? CO and HCN in solid p-H2…

CO in p-H2

HCN in p-H2

Deff=0.029(5)×Beff1.78(5)

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…

Deff=0.029(5)×Beff1.78(5)