Quantum Monte Carlo simulations of helium clusters doped with molecular and ionic impurities Stefano Paolini CNR-INFM-Democritos National Simulation Center and Physics Department “G. Galilei” University of Padova The Towler Institute, Vallico Sotto, July 27 th , 2 uantum Monte Carlo in the Apuan Alps III
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Quantum Monte Carlo simulations of helium clusters doped with molecular and ionic impurities Stefano Paolini CNR-INFM-Democritos National Simulation Center.
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Quantum Monte Carlo simulations
of helium clusters doped with
molecular and ionic impurities Stefano Paolini
CNR-INFM-Democritos National Simulation Center and
Physics Department “G. Galilei” University of Padova
The Towler Institute, Vallico Sotto, July 27th, 2007Quantum Monte Carlo in the Apuan Alps III
from G. Scoles and K. K. Lehmann Science 287, 5462 (2000)
4He nanodroplets are superfluidR
ela
tiv
e D
ep
leti
on
[%
]
• Pure 3He droplets
•T=0.15K •Broad peak
Experiment: (Toennies et al. Science, 1998)
Wave Number Change [ cm -1]
Re
lati
ve
De
ple
tio
n
[%]
• Pure 4He droplets
• T=0.38K
• free rotor spectrum with increased inertia
•Superfluidity: response to an imposed rotation
How small can a superfluid droplet be?
How does superfluidity How does superfluidity start to show up? start to show up?
• N = 1 - 8
J. Tang , Y. Xu, A.R.W. McKellar, and W. Jäger, Science, 297 2030 (2002)
• N-selective experiments: OCS@OCS@44HeHeNN
Understanding the rotational dynamics
• What is the relation between structure and dynamics?
• What determines the increase of inertia?
Can we predict the increase of the inertia? How does B saturate to the nanodroplet value, Beff?
Can we extrapolate Beff from the small size behavior?
Theory - previous scenario
• Models Suited for large droplets
dynamical properties are indirectly derived from structural information (calculated by simulations)
• QMC results spurred the view that: B attains its asimptotic value fast for heavy rotors (e.g. OCS): before the 1st solvation shell is completed slowly for light rotors (e.g. HCN): well beyond the 1st solvation shell
The reduction of B upon solvation is due to the molecular mass large reduction for heavy rotors
small reduction for light rotors
Experiments do not validate this picture
CO2@4HeN N2O@4HeN
J. Tang et al. PRL (2004) W. Jager et al. JCP (2006)
For some heavy molecules the convergence is slow
For N2O (lighter than OCS) B reduction is larger than for OCS
Ground-state path integral Monte Carlo
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•
•
•
Reptation quantum Monte Carlo
•Path probability :
• Random walk:
• Weight of the path:
(S.Baroni and S. Moroni, Phys. Rev. Lett. 82, 4745 (1999))
Reptation quantum Monte Carlo
• Sampling the paths
• Metropolis test
• For large systems ( N > 50), bisection-multilevel algorithm is more efficient