Structural and Vibrational Properties of Small Vanadium Clusters

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Structural and Vibrational Properties of Small
Vanadium Clusters
C. Ratsch UCLA, Department of Mathematics Visitor
at the Fritz-Haber-Institut in Berlin, Germany

• Why do we care about small metal clusters?
• Many catalytic converters are based on clusters
• Clusters will play a role in nano-electronics
  (quantum dots)
• Importance in Bio-Chemistry

Collaborators Theory Jörg Behler, Matthias
Scheffler (Fritz-Haber-Institut,
Berlin) Experiment Andre Fielicke, Gert von
Helden, Andrei Kirilyuk, Gerard
Meijer (Fritz-Haber-Institut, Berlin, and FOM
Institute for Plasma Physics Rijnhuizen,
Netherlands)
Small clusters (consisting of a few atoms) are
the smallest nano-particles!
In this talk we will describe a method that
combines experiment and theory to obtain the
atomic structure of small clusters!
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Experimental Setup Using a Tunable Free Electron
Laser
Laser Beam clusters are formed, Ar attaches
Mass-Spectrometer
Gas flow (1 Ar in He)
metal-rod
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Spectra for VxAry

• Each cluster has an individual signature

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What Can Theory Contribute?

• Confirm the observed spectra
• Determine the structure of the clusters
• Is the spectrum the result of one or several
  isomers?
• What is the effect of the Ar atoms?

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Density-Functional Theory (DFT)
Hohenberg, Kohn, Sham (1964/65 Noble Prize in
Chemistry 1998 for W. Kohn)
The ground-state energy of a system can be
obtained without explicit knowledge of the
many-electron wave function, but by minimizing an
energy functional En.

• Kohn-Sham orbitals need to be expanded! Choices
  for basis sets
• Plane-waves (FHI98md)
• Localized basis sets DMol3 uses atomic orbitals

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Density Functional Theory (DFT) Calculations

• Computer Code used DMol3
• GGA for Exchange-Correlation (PBE)
• Determine the energetically most preferred
  structures
• Calculate the vibrational spectra of a large
  number of vanadium clusters with DFT (by
  diagonalizing force constant matrix, which is
  obtained by displacing each atom in all
  directions)
• Calculate the IR intensities from derivative of
  the dipol moment

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Small Clusters V3 - V6
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V7 and V8
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V9 and V10
10
V11 and V12
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V13 and V14
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V15
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Summary of stable structures

• All stable structures consist of a few
  well-defined building blocks
• Pyramids and bi-pyramids
• Trigons, tetragons, pentagons, hexagons, and
  corresponding pyramid structures.
• They are typically stacked and/or rotated
• Up to size 12, all atoms are surface atoms
• Beginning at size 13, there is (at least) one
  central atom

The big question How does one test efficiently a
large number of structures to scan the largest
possible parameter space?
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Possible Approaches to Scan Parameter Space

• By hand This is what I have done so far. It
  is certainly fine (and probably most efficient
  for clusters up to sizes 6, maybe 8. It is not so
  good anymore for clusters of size around 10. It
  is questionable once they reach size 15. It is
  hopeless (I think) for clusters of size 20 and
  larger.
• Molecular Dynamics In principle a good
  approach. In practise, much too slow.
• Simulated Annealing I think this is better. But
  I think one needs to put some physics (knowledge
  of the plausible structures) into it, to not test
  unrealistic configurations.
• Smart Simulated Annealing Test only
  structures that are plausible, I.e., that consist
  of trigonal, tetragonal, pentagonal, and
  hexagonal pyramids, bi-pyramids. Maybe with
  bulk-like features in the middle for the bigger
  clusters.
• Something else??

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Whats next?

• Better scheme to span parameter-space of large
  number of structures
• Move on to next element Niobium

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• Open issues
• Sometimes neutral and cationic niobium have
  similar spectrum, sometimes they are very
  different
• Cationic Nb is sometimes like cationic V,
  sometimes different.

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Niobium 5
neutral
cationic
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Niobium 6
neutral
cationic
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Different Isomers for Nb9
Experimentally, one can distinguish between 2
isomers for Nb9 (basically, different numbers of
Ar atoms attach to the different isomers)