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NABIL F. FARUK, HUI LI , J ING YANG, ROBERT J. LE ROY & PIERRE-NICHOLAS ROY
Simulation Studies of the Vibrational Dynamics of para-
Hydrogen Clusters
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Background: Superfluidity
Superfluids lack viscosity and have infinite thermal conductivity
Display quantized vortices and Rollin film flowConsequence of Bose-Einstein Condensation
Image retrieved from http://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Liquid_helium_Rollin_film.jpg/678px-Liquid_helium_Rollin_film.jpg
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Superfluid Clusters and Droplets
Helium-4 is a bosonHelium clusters have been studied for superfluity using
OCS, N2O, CO2 dopant molecules by observing their spectra
What about molecular superfluids?para-H2 is also a boson!
J. Tang, Y. Xu, A.R.W. McKellar and W. Jager, Science 297, 2030 (2002)
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Molecular Superfluid
Spectroscopic studies of para-H2 clusters doped with CO2 and CO have shown that they indeed have superfluid behaviour that varies with the cluster size
There are two spectroscopic properties used to probe clusters, the vibrational band origin shift of the dopants and their rotational constants
H. Li, R.J. Le Roy, P.-N. Roy and A.R.W. McKellar, Phys. Rev. Lett. 105, 133401 (2010)
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Spectroscopic Observables: Rotational Constants
Expect that a dopant’s moment of inertia increases when hydrogen molecules attach to it from the cluster
Turn arounds in this behaviour are observed at certain cluster sizes corresponding to large fractions of frictionless superfluid para-H2
H. Li, R.J. Le Roy, P.-N. Roy and A.R.W. McKellar, Phys. Rev. Lett. 105, 133401 (2010)
Top: Rotational Constant, Inversely to Moment of InertiaBottom: Superfluid Fraction
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Spectroscopic Observables: Vibrational Shifts
Indicate the quality of the potential energy surface
Vibrational bands of dopants are perturbed by cluster molecules
H. Li, N. Blinov, P.-N. Roy and R.J. Le Roy, J. Chem. Phys 130, 144305 (2009)H. Li, R.J. Le Roy, P.-N. Roy and A.R.W. McKellar, Phys. Rev. Lett. 105, 133401 (2010)
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Predicting the Shifts
Adiabatic-hindered-rotor approximation
to produce a reduced-dimensional
difference potential energy surface (PES)
Monte Carlo simulations to obtain the radial probability
distribution of hydrogen molecules
in clusters
Vibrational frequency shift for cluster of
size N
N (N 1) V 1D0
(R)P N (R)dR
G. Tejeda, J.M. Fernandez, S. Montero, D. Blume and J.P. Toennies, Phys. Rev. Lett. 92, 223401 (2004)H. Li, P.-N. Roy, and R.J. Le Roy, J. Chem. Phys. 133, 104305 (2010)
2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
-25
-20
-15
-10
-5
0
5 Ab Initio 1D PES
Difference
Ground State
1st Excited State
R [Å]
V [
cm
-1]
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Pure clusters can be probed with Raman spectroscopy
What if the dopant is another para-H2?It would be indistinguishable from the cluster
para-H2
Toennies and co-workers provided experimental results for the Raman shifts
Also fitted their data to a Lennard-Jones model to give an empirical difference potential curve:
G. Tejeda, J.M. Fernandez, S. Montero, D. Blume and J.P. Toennies, Phys. Rev. Lett. 92, 223401 (2004)
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Potential Energy Surface
V6D →V4D: average over r1, r2 using monomer bond length wavefunctions
V4D →V1D: average over θ2, φ, θ1 using Adiabatic Hindered Rotor approach
r1
r2
6D PES 1D PES
R.J. Hinde, J. Chem. Phys. 128, 154308 (2008)H. Li, P.-N. Roy, and R.J. Le Roy, J. Chem. Phys. 133, 104305 (2010)
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Results: Δν for H2-H2 Dimer
The shift is from having both molecules in the ground state to one in the first vibrationally excited state and the other in the ground stateMethod Δν (cm-1)
Observed -0.400
Toennies: L-J ΔV(R) -0.417
Hinde: ab initio ΔV(R) -0.405
Our Work: ab initio ΔV(R) -0.347
G. Tejeda, J.M. Fernandez, S. Montero, D. Blume and J.P. Toennies, Phys. Rev. Lett. 92, 223401 (2004)R.J. Hinde, J. Chem. Phys. 128, 154308 (2008)
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Results: Shifts for Varying Cluster Sizes
5 10 15 20 25 30 35 40 45-6
-5
-4
-3
-2
-1
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Raman Spectral Shifts
Experiment
L-J (DMC)
Ab Initio (PIGS)
L-J (PIGS)
N
Δν
[cm
-1]
G. Tejeda, J.M. Fernandez, S. Montero, D. Blume and J.P. Toennies, Phys. Rev. Lett. 92, 223401 (2004)J. E. Cuervo and P.-N. Roy, J. Chem. Phys. 125, 124314 (2006)J. E. Cuervo and P.-N. Roy, J. Chem. Phys. 128, 224509 (2008)
DMC: Diffusion Monte Carlo DensitiesPIGS: Path Integral Ground State Densities
2 3 4 5 6 7 8
-5
-4
-3
-2
-1
0
1
2
3
4
51D Difference PES
Ab Initio
Toennies L-J
R [Å]
ΔV
[cm
-1]
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Conclusions
The empirical and ab initio difference potentials are qualitatively different
Still need to improve ΔV1D(R); the error in the shifts however appears to be systematic
Once an accurate ΔV1D(R) is obtained, we can extend the prediction of the Raman shifts to para-H2 clusters not yet observed