Structural and Vibrational Properties of Small Vanadium Clusters

1
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!
2
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
3
Spectra for VxAry

• Each cluster has an individual signature

4
Density Functional Theory (DFT) Calculations

• Computer Code used DMol3
• GGA for Exchange-Correlation (PBE)
• 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)

• What can we learn?
• 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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What is the effect of the Ar atom?
V3 ion
V4 ion
Frequencies (cm-1) Without Ar 383, 183,
121 With Ar 383, 183, 121, 23, 21
Frequencies (cm-1) Without Ar 437, 292, 237,
215, 197, 116 With Ar 438, 288, 243, 211,
187, 75, 69, 24

• Binding energy approx. 100 meV in both cases
• Structure essentially unchanged
• Frequencies essentially unchanged
• We can do calculations of frequencies for
  cluster without the Ar

6
Comparison Experiment/Calculation
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Structure Determination for V8
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Experiment
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Conclusions

• Comparison of calculated spectra with
  experimental spectra allows us to determine the
  atomic structure of the cluster
• For all cases studied, the structure with the
  lowest energy is also the one with the best
  agreement in the spectrum
• For larger clusters (approx. larger than 14) the
  structure appears to be bulk-like
• There is essentially no effect of the Ar atom on
  the vibrational frequencies

Transparencies of this talk can be found
at www.math.ucla.edu/cratsch/presentations.html
10
Binding Energy per Atom
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Comparison Experiment/Calculation
V5
V8
V6
V9
V15
V7
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Experimental Setup
Example Excitation of V7Ar1 and V7Ar2 at 313
cm-1