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7f83a351a8 Updates to publications and links 2018-04-23 15:10:05 +02:00
4551e8cc05 Small corrections 2018-03-22 14:08:37 +01:00
c5670f0bfc Updates to website 2018-03-20 14:44:50 +01:00
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e92a6bd03f Small correction 2016-06-16 15:26:04 +02:00
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<title>Theory of Cluster Dynamics</title>
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<p><font color="white" size="6"><b>Theory of Cluster Dynamics</b></font><font size="5"><br>
</font><font size="6">
</font><font size="5">The Toulouse - Erlangen Collaboration</font></p>
</div>
<a name="oben">
<div id="content">
<div style="margin:15px;width:770px;border:1px solid gray;float:left;font-size:10px;">
<div style="width:220px;float:left;text-align:center;font-weight:900;font-size:12px;">
<a href="detail1.html">1. Analysis of cluster dynamics</a>
</div>
<div style="width:220px;float:left;text-align:center;">
<a href="detail2.html"> 2. Clusters in external fields</a>
</div>
<div style="width:220px;float:left;text-align:center;">
<a href="../tddft-md/formal.html"> 3. Theoretical developments </a>
</div>
</div>
</a>
<div id="WideContent">
<div id="contentBoxWide">
<div id="contentBoxHeader">
<p> Analysis of cluster dynamics</p>
</div>
<div id="contentBoxContent">
<!-- START CONTENT HERE -->
<p>
<img src="figs/na8p_mie.gif" width="250" align="right">
<br><br>
The basic dynamical property of a metal cluster is the optical
absorption spectrum which has a pronounced collection of strength in
the region of the Mie plasmon. TDLDA driven with small amplitude
excitations allows to explore the optical response [<a href="../literatur.html#own1155">9</a>].
The figure beneath shows results for Na<sub>8</sub><sup>+</sup> as
example (taken from [<a href="../literatur.html#own1315"><font color="red">???</font></a>]) in comparison
to experiment (upper panel) and CI calculations (<font color="red"><b>???</b></font>)(second from above).
The overall position of the peak strength is nicely reproduced by all
methods, even by the semiclassical approach. CI produces the most
detailed spectrum. The green bars show the discrete spectrum as it
emerges from the CI calculation, and the red curve results from Lorentzian
smoothing which simulates to some extend the finite experimental
resolution and thermal fluctuations. The enormous number of spectral
lines (green) is due to electronic correlations which are absent in
TDLDA. Nonetheless, the unavoidable smoothing overrules these details
and makes TDLDA spectra competitive. It is noteworthy that also the
semiclassical approximation (Vlasov-LDA) performs surprisingly well.
This provides a good starting point for the subsequent applications
in more energetic situations.
<br>
</p>
<p>
<br><br><br><br><br>
<img src="figs/na_vgl_small.gif" width="400" align="left">
<br><br>
Laser induced direct photo-emission of electrons allows to conclude on
the clusters single-electron states by measuring the photo-electron
spectra (PES). TDLDA with appropriate self-interaction correction
(SIC) [<a href="../literatur.html#own1252">277</a>] allows to simulate that
process in detail [<a href="../literatur.html#own1227">251</a>] . The figure to
the left shows two examples for two clusters which are nearly
spherical (taken from [<a href="../literatur.html#own1285">304</a>]). The arrows
indicate the level classification according to principal quantum
number and angular momentum. The PES depend, of course, on the
direction of emission (checked here are the case where the cluster
axis is ``perpendicular'' or ``parallel'' to the laser
polarization). Experiments take an average over all direction.
The summed theoretical PES agree fairly well with the data.
</p>
<p>
<br><br><br><br>
<img src="figs/na41p+3_comb.gif" width="350" align="right">
<br><br><br><br><br>
Pump and probe (P&P) techniques are an extremely powerful tool for
time-resolved analysis. The complexity of clusters allows an
enormous manifold of P&P scenarios. The figure to the right sketches
a simple and robust scenario for a nearly spherical cluster, actually
Na<sub>41</sub><sup>+</sup> [<a href="../literatur.html#own1246">290</a>]. The idea is to map the
radius vibrations of the cluster by an off-resonant laser pulse. The
pump pulse ionizes the Na<sub>41</sub><sup>+</sup> within 50 fs by three more charge
units, see second panel from top for dipole response (black line) and first
panel for ionization. The generated Coulomb pressure drives
oscillations of the radius <i>R<sub>ion</sub></i>, shown in the lowest panel.
</br></br>
The Mie plasmon
frequency depends on the cluster extension as w<sub>Mie</sub>~
R<sup>-3/2</sup> and oscillates with opposite phase, see third panel. Thus
the changing distance to the off-resonant laser frequency (green
horizontal line) modulates the dipole response to probe pulses
accordingly (second panel) which, in turn, yields changing ionization
through the probe pulse as function of delay time. The final
ionization (upper panel) becomes then a direct map of the underlying
breathing oscillations of the cluster.
</p>
<center>
<table width="70%">
<tr>
<td align="right">
<a href="#top">Back to top </a>
</td>
</tr>
</table>
</center>
</div>
</div>
<head>
<meta http-equiv="content-type" content="application/xhtml+xml; charset=iso-8859-1" />
<title>Theory of Cluster Dynamics</title>
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<div id="image">
<p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font
size="5"><br />
</font><font size="6"> </font><font size="5">The Toulouse -
Erlangen Collaboration</font></p>
</div>
<a name="oben"> </a>
<div id="content"><a name="oben"> </a>
<div style="margin:15px;width:770px;border:1px solid gray;float:left;font-size:10px;"><a
name="oben">
</a>
<div style="width:180px;float:left;text-align:center;font-size:10px"><a
name="oben">
</a><a href="../tddft-md/formal.html">1. Theoretical developments </a> </div>
<div style="width:200px;float:left;text-align:center;font-size:12px;">
<a href="detail1.html"> 2. Analysis of cluster
dynamics </a> </div>
<div style="width:200px;float:left;text-align:center;font-weight:900;font-size:10px;">
<a href="detail2.html"> 3. Clusters in strong external
fields </a> </div>
<div style="width:180px;float:left;text-align:center;font-weight:900;font-size:10px;">
<a href="../tddft-md/detailQMMM.html"> 4. Embedded clusters </a> </div>
</div>
<div id="WideContent">
<div id="contentBoxWide">
<div id="contentBoxHeader">
<p> Analysis of cluster dynamics</p>
</div>
<div id="contentBoxContent">
<!-- START CONTENT HERE -->
<p> <img src="figs/na8p_mie.gif" width="250" align="right" /> <br />
<br />
The basic dynamical property of a metal cluster is the optical
absorption spectrum which has a pronounced collection of
strength in the region of the Mie plasmon. TDLDA driven with
small amplitude excitations allows to explore the optical
response [<a href="../publications.html#Cal97">Cal97</a>]. The
figure beneath shows results for Na<sub>8</sub><sup>+</sup> as
example (taken from [<a href="../publications.html#Leg06">Leg06</a>])
in comparison to experiment (upper panel) and CI calculations
(second from above). The
overall position of the peak strength is nicely reproduced by
all methods, even by the semiclassical approach. CI produces
the most detailed spectrum. The green bars show the discrete
spectrum as it emerges from the CI calculation, and the red
curve results from Lorentzian smoothing which simulates to
some extend the finite experimental resolution and thermal
fluctuations. The enormous number of spectral lines (green) is
due to electronic correlations which are absent in TDLDA.
Nonetheless, the unavoidable smoothing overrules these details
and makes TDLDA spectra competitive. It is noteworthy that
also the semiclassical approximation (Vlasov-LDA) performs
surprisingly well. This provides a good starting point for the
subsequent applications in more energetic situations. <br />
</p>
<p> <br />
<br />
<br />
<br />
<br />
<img src="figs/na_vgl_small.gif" width="400" align="left" /> <br />
<br />
Laser induced direct photo-emission of electrons allows to
conclude on the clusters single-electron states by measuring
the photo-electron spectra (PES). TDLDA with appropriate
self-interaction correction (SIC) [<a href="../publications.html#Leg02">Leg02</a>]
allows to simulate that process in detail [<a href="../publications.html#Poh00">Poh00</a>]
. The figure to the left shows two examples for two clusters
which are nearly spherical (taken from [<a href="../publications.html#Poh03">Poh03</a>]).
The arrows indicate the level classification according to
principal quantum number and angular momentum. The PES depend,
of course, on the direction of emission (checked here are the
case where the cluster axis is ``perpendicular'' or
``parallel'' to the laser polarization). Experiments take an
average over all direction. The summed theoretical PES agree
fairly well with the data. </p>
<p> <br />
<br />
<br />
<br />
<img src="figs/na41p+3_comb.gif" width="350" align="right" />
<br />
<br />
<br />
<br />
<br />
Pump and probe (P&amp;P) techniques are an extremely powerful
tool for time-resolved analysis. The complexity of clusters
allows an enormous manifold of P&amp;P scenarios. The figure
to the right sketches a simple and robust scenario for a
nearly spherical cluster, actually Na<sub>41</sub><sup>+</sup>
[<a href="../publications.html#And02">And02</a>]. The idea is to
map the radius vibrations of the cluster by an off-resonant
laser pulse. The pump pulse ionizes the Na<sub>41</sub><sup>+</sup>
within 50 fs by three more charge units, see second panel from
top for dipole response (black line) and first panel for
ionization. The generated Coulomb pressure drives oscillations
of the radius <i>R<sub>ion</sub></i>, shown in the lowest
panel. <br />
<br />
The Mie plasmon frequency depends on the cluster extension as
w<sub>Mie</sub>~ R<sup>-3/2</sup> and oscillates with opposite
phase, see third panel. Thus the changing distance to the
off-resonant laser frequency (green horizontal line) modulates
the dipole response to probe pulses accordingly (second panel)
which, in turn, yields changing ionization through the probe
pulse as function of delay time. The final ionization (upper
panel) becomes then a direct map of the underlying breathing
oscillations of the cluster. </p>
<center>
<table width="70%">
<tbody>
<tr>
<td align="right"> <a href="#top">Back to top </a> </td>
</tr>
</tbody>
</table>
</center>
</div>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
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<meta http-equiv="content-type" content="application/xhtml+xml; charset=iso-8859-1" />
<title>Theory of Cluster Dynamics</title>
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<div id="container">
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<li><a href="../publications.html">Publications/Talks</a></li>
<li><a href="../contact.html">Contact</a></li>
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</div>
<div id="image">
<p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font
size="5"><br />
</font><font size="6"> </font><font size="5">The Toulouse -
Erlangen Collaboration</font></p>
</div>
<a name="oben"> </a>
<div id="content"><a name="oben"> </a>
<div style="margin:15px;width:770px;border:1px solid gray;float:left;font-size:10px;"><a
name="oben">
</a>
<div style="width:180px;float:left;text-align:center;font-size:10px"><a
name="oben">
</a><a href="../tddft-md/formal.html">1. Theoretical developments </a> </div>
<div style="width:200px;float:left;text-align:center;font-size:12px;">
<a href="detail1.html"> 2. Analysis of cluster
dynamics </a> </div>
<div style="width:200px;float:left;text-align:center;font-weight:900;font-size:10px;">
<a href="detail2.html"> 3. Clusters in strong external
fields </a> </div>
<div style="width:180px;float:left;text-align:center;font-weight:900;font-size:10px;">
<a href="../tddft-md/detailQMMM.html"> 4. Embedded clusters </a> </div>
</div>
<div id="WideContent">
<div id="contentBoxWide">
<div id="contentBoxHeader">
<p> Analysis of cluster dynamics</p>
</div>
<div id="contentBoxContent">
<!-- START CONTENT HERE -->
<p> <img src="figs/na8p_mie.gif" width="250" align="right" /> <br />
<br />
The basic dynamical property of a metal cluster is the optical
absorption spectrum which has a pronounced collection of
strength in the region of the Mie plasmon. TDLDA driven with
small amplitude excitations allows to explore the optical
response [<a href="../literatur.html#own1155">9</a>]. The
figure beneath shows results for Na<sub>8</sub><sup>+</sup> as
example (taken from [<a href="../literatur.html#own1315"><font
color="red">???</font></a>])
in comparison to experiment (upper panel) and CI calculations
(<font color="red"><b>???</b></font>)(second from above). The
overall position of the peak strength is nicely reproduced by
all methods, even by the semiclassical approach. CI produces
the most detailed spectrum. The green bars show the discrete
spectrum as it emerges from the CI calculation, and the red
curve results from Lorentzian smoothing which simulates to
some extend the finite experimental resolution and thermal
fluctuations. The enormous number of spectral lines (green) is
due to electronic correlations which are absent in TDLDA.
Nonetheless, the unavoidable smoothing overrules these details
and makes TDLDA spectra competitive. It is noteworthy that
also the semiclassical approximation (Vlasov-LDA) performs
surprisingly well. This provides a good starting point for the
subsequent applications in more energetic situations. <br />
</p>
<p> <br />
<br />
<br />
<br />
<br />
<img src="figs/na_vgl_small.gif" width="400" align="left" /> <br />
<br />
Laser induced direct photo-emission of electrons allows to
conclude on the clusters single-electron states by measuring
the photo-electron spectra (PES). TDLDA with appropriate
self-interaction correction (SIC) [<a href="../literatur.html#own1252">277</a>]
allows to simulate that process in detail [<a href="../literatur.html#own1227">251</a>]
. The figure to the left shows two examples for two clusters
which are nearly spherical (taken from [<a href="../literatur.html#own1285">304</a>]).
The arrows indicate the level classification according to
principal quantum number and angular momentum. The PES depend,
of course, on the direction of emission (checked here are the
case where the cluster axis is ``perpendicular'' or
``parallel'' to the laser polarization). Experiments take an
average over all direction. The summed theoretical PES agree
fairly well with the data. </p>
<p> <br />
<br />
<br />
<br />
<img src="figs/na41p+3_comb.gif" width="350" align="right" />
<br />
<br />
<br />
<br />
<br />
Pump and probe (P&amp;P) techniques are an extremely powerful
tool for time-resolved analysis. The complexity of clusters
allows an enormous manifold of P&amp;P scenarios. The figure
to the right sketches a simple and robust scenario for a
nearly spherical cluster, actually Na<sub>41</sub><sup>+</sup>
[<a href="../literatur.html#own1246">290</a>]. The idea is to
map the radius vibrations of the cluster by an off-resonant
laser pulse. The pump pulse ionizes the Na<sub>41</sub><sup>+</sup>
within 50 fs by three more charge units, see second panel from
top for dipole response (black line) and first panel for
ionization. The generated Coulomb pressure drives oscillations
of the radius <i>R<sub>ion</sub></i>, shown in the lowest
panel. <br />
<br />
The Mie plasmon frequency depends on the cluster extension as
w<sub>Mie</sub>~ R<sup>-3/2</sup> and oscillates with opposite
phase, see third panel. Thus the changing distance to the
off-resonant laser frequency (green horizontal line) modulates
the dipole response to probe pulses accordingly (second panel)
which, in turn, yields changing ionization through the probe
pulse as function of delay time. The final ionization (upper
panel) becomes then a direct map of the underlying breathing
oscillations of the cluster. </p>
<center>
<table width="70%">
<tbody>
<tr>
<td align="right"> <a href="#top">Back to top </a> </td>
</tr>
</tbody>
</table>
</center>
</div>
</div>
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</div>
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<p></p>
</div>
</div>
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<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" />
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<li><a href="../contact.html">Contact</a></li>
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<div id="image">
<p><font color="white" size="6"><b>Theory of Cluster Dynamics</b></font><font size="5"><br>
</font><font size="6">
</font><font size="5">The Toulouse - Erlangen Collaboration</font></p>
</div>
<a name="oben">
<div id="content">
<div style="margin:15px;width:770px;border:1px solid gray;float:left;font-size:10px;">
<div style="width:220px;float:left;text-align:center;">
<a href="../analysis/detail1.html">1. Analysis of cluster dynamics</a>
</div>
<div style="width:220px;float:left;text-align:center;font-weight:900;font-size:12px;">
<a href="../analysis/detail2.html"> 2. Clusters in external fields</a>
</div>
<div style="width:220px;float:left;text-align:center;">
<a href="../tddft-md/formal.html"> 3. Theoretical developments </a>
</div>
</div>
</a>
<div id="WideContent">
<div id="contentBoxWide">
<div id="contentBoxHeader">
<p> Clusters in strong external perturbations</p>
</div>
<div id="contentBoxContent">
<!-- START CONTENT HERE -->
<br>
<p><img src="figs/na8_nacl_SHG.gif" align="right" width="300">
Many experiments are done for clusters in contact with a
substrate. The strong interface interaction modifies the cluster and
theoretical simulations become more involved. However, some features
can only be explored in connection with a substrate. E.g., the
symmetry breaking through a surface gives access to second-harmonic
generation (SHG). </br></br>
The figure beneath shows the results from a TDLDA
simulation of SHG for Na<sub>8</sub> attached to a NaCl surface
[<a href="../literatur.html#own1224">248</a>]. The spectra resulting
from
irradiation with a 1.4 eV pulse shows nicely the peaks at multiple
frequencies. The SHG signal can be enhanced by increasing the laser
intensity. This, however, breaks down at some point where the signals
are substantially broadened. This is caused by a large ionization
which spoils the otherwise clean dipole response of metal clusters.
</p>
<br>
<br>
<p>
<img src="figs/na6_ar384d_deposit.gif" align="left" width="300">TDLDA
coupled with molecular dynamics (MD) for ionic motion is a very
powerfull tool to describe cluster dynamics. One application is
cluster deposition which is illustrated in the figure on the left. It shows
Na<sub>6</sub> impinging on an Ar surface (see [<a
href="../literatur.html#own1303">328</a>] for further details). The substrate consists of
six layers of Ar
taken from an appropriate cut of the Ar fcc structure. The Na<sub>6</sub>
cluster consist in a ring of 5 ions topped by one ion on the symmetry
axix. The Na<sub>6</sub> approaches the surface with the symmetry axis
in <i>z</i>
direction (=perpendicular) and the top ion facing away from the
surface. </br></br>
The upper panel shows the evolution of the <i>z</i>
coordinates,
Na ions in red and Ar atoms in green. The cluster is immediately
stopped by the surface. A large fraction of impact momentum is
transferred at once to the substrate and propagates with velocity of
light through the layers. The large dissipation through energy
transfer and intrinsic cluster excitation leads to catching of the
cluster by the subtrate. The kinetic energies in the lower panel
confirm the dramatic and very fast energy exchange at the moment of
first impact. Another fraction of energy, not shown in the figure, is
turned into the large shape changes.
</p>
<br><br>
<p>
Clusters in the strong fields of extremely intense lasers show a much
different dynamics. Core electrons can be released and contribute
strongly to the process. The detailed description at the fully quantum
mechanical level of TDLDA becomes untractable. However, the
excitations involved validate classical approaches. </br></br>
<img src="figs/MD_fig5.gif" align="right" width="300">
The figure to the
right shows the result of a molecular dynamics simulation of
electronic and ionic dynamics of Na<sub>41</sub><sup>+</sup> under the
influence of
strong laser fields [<a href="../literatur.html#own1308">332</a>].
Ionization is
drawn as function of laser intensity. One sees a sharp kink at a
critical intensity of I = 10<sup>16</sup> W/cm<sup>2</sup>. This
threshold value is
explained by the fact that the Coulomb force from the laser field
at the threshold just equals the binding forces of the core electrons. The increase is
due to the core electrons which now start to participate in the
dynamics. This view is illustrated by separating the contributions from
valence (green line) and core electrons (red line). There is indeed zero
emission from core electrons up to I = 10<sup>16</sup> W/cm<sup>2</sup>
and the
strong increase above that critical intensity is exclusively due to
the contribution from core electrons.
<br>
<br>
<br>
</p>
<center>
<table width="70%">
<tr>
<td align="right">
<a href="#top">Back to top </a>
</td>
</tr>
</table>
</center>
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<p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font
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Erlangen Collaboration</font></p>
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<a name="oben"> </a>
<div id="content"><a name="oben"> </a>
<div style="margin:15px;width:770px;border:1px solid gray;float:left;font-size:10px;"><a
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fields </a> </div>
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<p> Clusters in strong external perturbations</p>
</div>
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<!-- START CONTENT HERE --> <br />
<p> Clusters in the strong fields of extremely intense lasers
show a much different dynamics. Core electrons can be released
and contribute strongly to the process. The detailed
description at the fully quantum mechanical level of TDLDA
becomes untractable. However, the excitations involved
validate classical approaches. <br />
<br />
<img src="figs/MD_fig5.gif" width="300" align="right" /> The
figure to the right shows the result of a molecular dynamics
simulation of electronic and ionic dynamics of Na<sub>41</sub><sup>+</sup>
under the influence of strong laser fields [<a href="../publications.html#Bel06">Bel06</a>].
Ionization
is drawn as function of laser intensity. One sees a sharp kink
at a critical intensity of I = 10<sup>16</sup> W/cm<sup>2</sup>.
This threshold value is explained by the fact that the Coulomb
force from the laser field at the threshold just
equals the binding forces of the core electrons.
The increase is due to the core electrons which now start to
participate in the dynamics. This view is illustrated by
separating the contributions from valence (green line) and
core electrons (red line). There is indeed zero emission from
core electrons up to I = 10<sup>16</sup> W/cm<sup>2</sup> and
the strong increase above that critical intensity is
exclusively due to the contribution from core electrons. <br />
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<p> Clusters in strong external perturbations</p>
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<p> Clusters in the strong fields of extremely intense lasers
show a much different dynamics. Core electrons can be released
and contribute strongly to the process. The detailed
description at the fully quantum mechanical level of TDLDA
becomes untractable. However, the excitations involved
validate classical approaches. <br />
<br />
<img src="figs/MD_fig5.gif" width="300" align="right" /> The
figure to the right shows the result of a molecular dynamics
simulation of electronic and ionic dynamics of Na<sub>41</sub><sup>+</sup>
under the influence of strong laser fields [<a href="../literatur.html#own1308">332</a>].
Ionization
is drawn as function of laser intensity. One sees a sharp kink
at a critical intensity of I = 10<sup>16</sup> W/cm<sup>2</sup>.
This threshold value is explained by the fact that the Coulomb
force from the laser field at the threshold just
equals the binding forces of the core electrons.
The increase is due to the core electrons which now start to
participate in the dynamics. This view is illustrated by
separating the contributions from valence (green line) and
core electrons (red line). There is indeed zero emission from
core electrons up to I = 10<sup>16</sup> W/cm<sup>2</sup> and
the strong increase above that critical intensity is
exclusively due to the contribution from core electrons. <br />
<br />
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P.-G. Reinhard, E. Suraud<br>
"Introduction to Cluster Dynamics"<br>
Wiley-VCH (2003)<br>
ISBN: 3527403450
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="content-type" content="application/xhtml+xml; charset=windows-1252" /> <title>Theory of Cluster Dynamics</title> <link href="style.css" rel="stylesheet" type="text/css" /> </head> <!-- --> <body> <div id="container"> <div id="header"> <div id="menu"> <div id="navMenu"> <ul> <li style="margin-top:1px;border-top:1px solid #B0C4DE; "><a href="index.html">Home</a></li> <li><a href="intro.html">Introductory Overview</a></li> <li><a href="research.html">Scientific Information</a></li> <li><a href="staff.html">Staff</a></li> <li><a href="publications.html">Publications/Talks</a></li> <li><a href="contact.html">Contact</a></li> <li><br /> </li> </ul> </div> </div> <div id="image"> <p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font size="5"><br /> </font><font size="6"> </font><font size="5">The Toulouse - Erlangen Collaboration</font></p> </div> </div> <div id="content"> <div id="leftContent"> <div id="contentBox"> <div id="contentBoxHeader"> <p>Welcome</p> </div> <div id="contentBoxContent"> <p> Welcome to our website about the Theory of Cluster Dynamics. We are a collaboration between theoretical physics groups of the <a href="http://www.theorie2.physik.uni-erlangen.de" target="_blank"> University of Erlangen</a> (Germany) and the <a href="http://www.lpt.ups-tlse.fr/" target="_blank"> University Paul Sabatier of Toulouse</a> (France). </p> <p> Here you can find </p> <ul> <li> <a href="intro.html">popular</a> as well as <a href="research.html">scientific
information </a>about our research projects, </li> <br /> <li> information about our <a href="staff.html">members </a>and
how to <a href="contact.html">contact </a>us, </li> <br /> <li> and of course references and material to our <a href="publications.html">publications
and recent talks</a>.</li> </ul> <p></p> <p><br /> <br /> </p> </div> </div> </div> <div id="rightContent"> <div id="infoBox"> <div id="infoBoxHeader"> <p>Further Reading:</p> </div> <div id="infoBoxContent"> <p></p> <div id="HalfRContent"> <center> <a href="https://www.wiley.com/en-gb/Introduction+to+Cluster+Dynamics-p-9783527621019"><img src="images/buch.jpg" style="width: 116px; height: 166px; margin-top: 30px" /></a> </center> <p></p> <center style="font-size: 9px"> P.-G. Reinhard, E. Suraud<br /> "Introduction to Cluster Dynamics"<br /> Wiley-VCH (2003)<br /> ISBN: 3527403450 </center> </div> <p></p> <div id="HalfLContent"> <center> <a href="https://www.wiley.com/en-gb/An+Introduction+to+Cluster+Science-p-9783527411184"><img src="images/buch2.png" style="width: 116px; height: 166px; margin-top: 30px; margin-left: -15px" /></a> </center> <p></p> <center style="font-size: 9px; margin-left: -15px"> Ph. M. Dinh, P.-G. Reinhard, E. Suraud<br /> "An Introduction to Cluster Science"<br /> Wiley-VCH (2013)<br /> ISBN: 3527411186 </center> </div> </div> </div> </div> </div> <div id="footer"> <p>Latest update: March 19, 2018</p> </div> </div> </body> </html>

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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="content-type" content="application/xhtml+xml; charset=windows-1252" /> <title>Theory of Cluster Dynamics</title> <link href="style.css" rel="stylesheet" type="text/css" /> </head> <!-- --> <body> <div id="container"> <div id="header"> <div id="menu"> <div id="navMenu"> <ul> <li style="margin-top:1px;border-top:1px solid #B0C4DE; "><a href="index.html">Home</a></li> <li><a href="intro.html">Introductory Overview</a></li> <li><a href="research.html">Scientific Information</a></li> <li><a href="staff.html">Staff</a></li> <li><a href="publications.html">Publications/Talks</a></li> <li><a href="contact.html">Contact</a></li> <li><br /> </li> </ul> </div> </div> <div id="image"> <p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font size="5"><br /> </font><font size="6"> </font><font size="5">The Toulouse - Erlangen Collaboration</font></p> </div> </div> <div id="content"> <div id="leftContent"> <div id="contentBox"> <div id="contentBoxHeader"> <p>Welcome</p> </div> <div id="contentBoxContent"> <p> Welcome to our website about the Theory of Cluster Dynamics. We are a collaboration between theoretical physics groups of the <a href="http://www.theorie2.physik.uni-erlangen.de" target="_blank"> University of Erlangen</a> (Germany) and the <a href="http://www.lpt.ups-tlse.fr/" target="_blank"> University Paul Sabatier of Toulouse</a> (France). </p> <p> Here you can find </p> <ul> <li> <a href="intro.html">popular</a> as well as <a href="research.html">scientific
information </a>about our research projects, </li> <br /> <li> information about our <a href="staff.html">members </a>and
how to <a href="contact.html">contact </a>us, </li> <br /> <li> and of course references and material to our <a href="publications.html">publications
and recent talks</a>.</li> </ul> <p></p> <p><br /> <br /> </p> </div> </div> </div> <div id="rightContent"> <div id="infoBox"> <div id="infoBoxHeader"> <p>Further Reading:</p> </div> <div id="infoBoxContent"> <p></p> <div id="HalfRContent"> <center> <a href="https://www.wiley.com/en-gb/Introduction+to+Cluster+Dynamics-p-9783527621019"><img src="images/buch.jpg" style="width: 116px; height: 166px; margin-top: 30px" /></a> </center> <p></p> <center style="font-size: 9px"> P.-G. Reinhard, E. Suraud<br /> "Introduction to Cluster Dynamics"<br /> Wiley-VCH (2003)<br /> ISBN: 3527403450 </center> </div> <p></p> <div id="HalfLContent"> <center> <a href="https://www.wiley.com/en-gb/An+Introduction+to+Cluster+Science-p-9783527411184"><img src="images/buch2.png" style="width: 116px; height: 166px; margin-top: 30px; margin-left: -15px" /></a> </center> <p></p> <center style="font-size: 9px; margin-left: -15px"> Ph. M. Dinh, P.-G. Reinhard, E. Suraud<br /> "An Introduction to Cluster Science"<br /> Wiley-VCH (2013)<br /> ISBN: 3527411186 </center> </div> </div> </div> </div> </div> <div id="footer"> <p>Latest update: March 19, 2018</p> </div> </div> </body> </html>

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<b>Permanent staff:</b>
<ul>
<li><a href="PG.html"> Prof. Dr. P.-G. Reinhard</a></li>
</ul>
</p>
<p>
<b>PhD Students:</b>
<ul>
<li>Philipp Wopperer</li>
<li>Bernhard Faber</li>
<li>
<a href="http://www.theorie2.physik.uni-erlangen.de/~baer">
Matthias B<>r*</a></li>
<li>Frank Fehrer*</li>
<li>Andreas Pohl*</li>
<li>Karsten Andrae*</li>
<li>Michael Mundt*</li>
<li>Christian Kohl*</li>
<li>M. Montag*</li>
</ul>
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<b>Diploma Students:</b>
<ul>
<li>Daniel Berger</li>
</ul>
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<p><b>Permanent staff:</b>
<ul>
<li><a href="ES.html">Prof. Dr. E. Suraud</a></li>
<li><a href="MD.html">Dr. P. M. Dinh</a></li>
</ul>
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<p>
<b>PhD Students:</b>
<ul>
<li>Gaspard Bousquet</li>
<li>F. M<>gi*</li>
<li>L. M. Ma*</li>
<li>E. Giglio*</li>
<li>A. Domps*</li>
<li>F. Calvayrac*</li>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="content-type" content="application/xhtml+xml; charset=iso-8859-1" /> <title>Theory of Cluster Dynamics</title> <link href="style.css" rel="stylesheet" type="text/css" /> </head> <body> <div id="container"> <div id="header"> <div id="menu"> <div id="navMenu"> <ul> <li style="margin-top:1px;border-top:1px solid #B0C4DE; "><a href="index.html">Home</a></li> <li><a href="intro.html">Introductory Overview</a></li> <li><a href="research.html">Scientific Information</a></li> <li><a href="staff.html">Staff</a></li> <li><a href="publications.html">Publications/Talks</a></li> <li><a href="contact.html">Contact</a></li> </ul> </div> </div> <div id="image"> <p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font size="5"><br /> </font><font size="6"> </font><font size="5">The Toulouse - Erlangen Collaboration</font></p> </div> </div> <div id="content"> <div id="HalfContent"> <div id="contentBoxHalf"> <div id="contentBoxHeader"> <p>Permanent Staff</p> </div> <div id="contentBoxContent"> <ul> <li>Prof. Dr. P.-G. Reinhard</li> <br /> <li><a href="http://www.lpt.ups-tlse.fr/spip.php?article35&amp;lang=en">Prof.
E. Suraud</a></li> <br /> <li><a href="http://www.lpt.ups-tlse.fr/spip.php?article25&amp;lang=en">Prof.
Ph. M. Dinh</a></li> <br /> <li><a href="http://www.lpt.ups-tlse.fr/spip.php?article1183&amp;lang=en">Dr.
M. Belkacem</a></li> </ul> <p></p> <br /> </div> </div> </div> <div id="HalfContent"> <div id="contentBoxHalf"> <div id="contentBoxHeader"> <p>Recent non-permanent Staff</p> </div> <div id="contentBoxContent"> <p><b>Post-docs:</b> </p> <ul> <li>Jose-Maria Escartin*</li> <li>Thomas Raitza*</li> </ul> <p></p> <p> <b>PhD Students:</b> </p> <ul> <li>Philipp Wopperer*</li> <li>Bernhard Faber*</li> <li> <a href="http://www.theorie2.physik.uni-erlangen.de/%7Ebaer"> </a>Matthias Baer*</li> <li>Frank Fehrer*</li> <li>Nader Slama*</li> <li>Cong-Zhang Gao*<br /> </li> <li>Lionel Lacombe*</li> <li>Charline Lemma</li> <li>Marc Vincendon</li> <li>Jordan Heraud</li> </ul> <p></p> </div> </div> </div> </div> <div id="footer"> <p>* former members</p> </div> </div> </body> </html>

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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="content-type" content="application/xhtml+xml; charset=iso-8859-1" /> <title>Theory of Cluster Dynamics</title> <link href="style.css" rel="stylesheet" type="text/css" /> </head> <body> <div id="container"> <div id="header"> <div id="menu"> <div id="navMenu"> <ul> <li style="margin-top:1px;border-top:1px solid #B0C4DE; "><a href="index.html">Home</a></li> <li><a href="intro.html">Introductory Overview</a></li> <li><a href="research.html">Scientific Information</a></li> <li><a href="staff.html">Staff</a></li> <li><a href="publications.html">Publications/Talks</a></li> <li><a href="contact.html">Contact</a></li> </ul> </div> </div> <div id="image"> <p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font size="5"><br /> </font><font size="6"> </font><font size="5">The Toulouse - Erlangen Collaboration</font></p> </div> </div> <div id="content"> <div id="HalfContent"> <div id="contentBoxHalf"> <div id="contentBoxHeader"> <p>Permanent Staff</p> </div> <div id="contentBoxContent"> <ul> <li>Prof. Dr. P.-G. Reinhard</li> <br /> <li><a href="http://www.lpt.ups-tlse.fr/spip.php?article35&amp;lang=en">Prof. 
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Ph. M. Dinh</a></li> <br /> <li><a href="http://www.lpt.ups-tlse.fr/spip.php?article1183&amp;lang=en">Dr.
M. Belkacem</a></li> </ul> <p></p> <br /> </div> </div> </div> <div id="HalfContent"> <div id="contentBoxHalf"> <div id="contentBoxHeader"> <p>Non-permanent Staff</p> </div> <div id="contentBoxContent"> <p><b>Post-docs:</b> </p> <ul> <li>Escartin*</li> <li>Thomas Raitza*</li> </ul> <p></p> <p> <b>PhD Students:</b> </p> <ul> <li>Philipp Wopperer*</li> <li>Bernhard Faber*</li> <li> <a href="http://www.theorie2.physik.uni-erlangen.de/%7Ebaer"> </a>Matthias Bär*</li> <li>Frank Fehrer*</li> <li>Nader Slama*</li> <li>Cong-Zhang*<br /> </li> <li>Lionel*</li> <li>Charline Lemma</li> <li>Marc Vincendon</li> <li>Jordan</li> </ul> <p></p> </div> </div> </div> </div> <div id="footer"> <p>* former members</p> </div> </div> </body> </html>

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<p><a name="top"<font size="5" color="white">Theory of Cluster&nbsp;Dynamics</font><font size="5"></a><br/>
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</font><font size="4">The Toulouse - Erlangen Collaboration</font></p>
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<a href="../analysis/detail1.html">1. Analysis of cluster dynamics</a>
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<div style="width:220px;float:left;text-align:center;font-weight:900;font-size:12px;">
<a href="../analysis/detail2.html"> 2. Clusters in external fields</a>
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<a href="../tddft-md/formal.html"> 3. Theoretical developments </a>
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<p> Clusters in strong external perturbations</p>
</div>
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<!-- START CONTENT HERE -->
<p><img src="na8_nacl_SHG.gif" align="right" width="300">
Many experiments are done for clusters in contact with a
substrate. The strong interface interaction modifies the cluster and
theoretical simulations become more involved. However, some feature
can only be explored in connection with a substrate. E.g., the
symmetry breaking through a surface gives access to second-harmonic
generation (SHG). The figure benaeth shows the results from a TDLDA
simulation of SHG for Na<sub>8</sub> attached to a NaCl surface
[<a href="../literatur.html#own1224">248</a>]. The spectra resulting
from
irradiation with a 1.4 eV pulse shows nicely the peaks at multiple
frequencies. The SHG signal can be enhanced by increasing the laser
intensity. This, however, breaks down at some point where the signals
are substantially broadened. This is caused by a large ionization
which spoils the elsewise clean dipole response of metal clusters.
</p>
<br>
<br>
<p>
<img src="na6_ar384d_deposit.gif" align="left" width="300">TDLDA
coupled with molecular dynamics (MD) for ionic motion is a very
powerfull tool to describe cluster dynamics. One application is
cluster deposition which is illustrated in the left figure. It shows
Na<sub>6</sub> impinging on an Ar surface (for the modeling [<a
href="../literatur.html#own1303">328</a>]). The substrate consists of
six layers of Ar
taken from an appropriate cut of the Ar fcc structure. The Na<sub>6</sub>
cluster consist in a ring of 5 ions topped by one ion on the symmetry
axix. The Na<sub>6</sub> approaches the surface with the symmetry axis
in <i>z</i>
direction (=perpendicular) and the top ion facing away from the
surface. The upper panel shows the evolution of the <i>z</i>
coordinates,
Na ions in red and Ar atoms in green. The cluster is immediately
stopped by the surface. A large fraction of impact momentum is
transferred at once to the substrate and propagates with velocity of
light through the layers. The large dissipation through energy
transfer and intrinsic cluster excitation leads to catching of the
cluster by the subtrate. The kinetic energies in the lower panel
confirm the dramatic and very fast energy exchange at the moment of
first impact. Another fraction of energy, missing in that figure, is
turned into the large shape changes.
</p>
<p>
Clusters in the strong fields of extremely intense lasers show a much
different dynamics. The core electrons can be released and contribute
strongly to the process. The detailed description at the fully quantum
mechanical level of TDLDA becomes untractable. However, the
excitations involved validate classical approaches. <img
src="MD_fig5.gif" align="right" width="300">
The figure to the
right shows the result of a molecular dynamics simulation of
electronic and ionic dynamics of Na<sub>41</sub><sup>+</sup> under the
influence of
strong laser fields [<a href="../literatur.html#own1308">332</a>].
Ionization is
drawn as function of laser intensity. One sees a sharp kink at a
critical intensity of <i>I</i>=10<sup>16</sup> W/cm<sup>2</sup>. The
critical value is
diistinguished by the fact that the Coulomb force from the laser field
just equals the binding forces of the core electrons. The increase is
due to the core electrons which now start to participate in the
process. This view is checked by sepparating the contributions from
valence (green) and core electrons (red line). There is indeed zero
emission from core electrons up to <i>I</i>=10<sup>16</sup> W/cm<sup>2</sup>
and the
strong increase above that critical intensity is exclusively due to
the core contribution.
<br>
<br>
<br>
<br>
</p>
<table>
<tbody>
<tr>
<td>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="content-type" content="application/xhtml+xml; charset=iso-8859-1" /> <title>Theory of Cluster Dynamics</title> <link href="../style.css" rel="stylesheet" type="text/css" /> </head> <body> <div id="container"> <div id="header"> <div id="menu"> <div id="navMenu"> <ul> <li style="margin-top:1px;border-top:1px solid #B0C4DE; "><a href="../index.html">Home</a></li> <li><a href="../intro.html">Introductory Overview</a></li> <li><a href="../research.html">Scientific Information</a></li> <li><a href="../staff.html">Staff</a></li> <li><a href="../publications.html">Publications/Talks</a></li> <li><a href="../contact.html">Contact</a></li> </ul> </div> </div> <div id="image"> <p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font size="5"><br /> </font><font size="6"> </font><font size="5">The Toulouse - Erlangen Collaboration</font></p> </div> <a name="oben"> </a> <div id="content"><a name="oben"> </a> <div style="margin:15px;width:770px;border:1px solid gray;float:left;font-size:10px;"><a name="oben"> </a> <div style="width:180px;float:left;text-align:center;font-size:10px"><a name="oben"> </a><a href="formal.html">1. Theoretical developments </a> </div> <div style="width:200px;float:left;text-align:center;font-size:10px;"> <a href="../analysis/detail1.html"> 2. Analysis of cluster dynamics </a> </div> <div style="width:200px;float:left;text-align:center;font-weight:900;font-size:10px;"> <a href="../analysis/detail2.html"> 3. Clusters in strong external fields </a> </div> <div style="width:180px;float:left;text-align:center;font-weight:900;font-size:12px;"> <a href="detailQMMM.html"> 4. Embedded clusters </a> </div> </div> <div id="WideContent"> <div id="contentBoxWide"> <div id="contentBoxHeader"> <p> Clusters in contact with a polarizable environment</p> </div> <div id="contentBoxContent"> <!-- START CONTENT HERE --> <br /> <p><img src="figs/na8_nacl_SHG.gif" width="300" align="right" /> Many experiments are done for clusters in contact with a substrate. The strong interface interaction modifies the cluster and theoretical simulations become more involved. However, some features can only be explored in connection with a substrate. E.g., the symmetry breaking through a surface gives access to second-harmonic generation (SHG). <br /> <br /> The figure beneath shows the results from a TDLDA simulation of SHG for Na<sub>8</sub> attached to a NaCl surface [<a href="../publications.html#Koh00">Koh00</a>].
The spectra resulting from irradiation with a 1.4 eV pulse shows nicely the peaks at multiple frequencies. The SHG signal can be enhanced by increasing the laser intensity. This, however, breaks down at some point where the signals are substantially broadened. This is caused by a large ionization which spoils the otherwise clean dipole response of metal clusters. </p> <br /> <br /> <p> <img src="figs/na6_ar384d_deposit.gif" width="300" align="left" />TDLDA
coupled
with molecular dynamics (MD) for ionic motion is a very powerfull tool to describe cluster dynamics. One application is cluster deposition which is illustrated in the figure on the left. It shows Na<sub>6</sub> impinging on an Ar surface (see [<a href="../publications.html#Feh06">Feh06</a>] for further details). The substrate consists of six layers of Ar taken from an appropriate cut of the Ar fcc structure. The Na<sub>6</sub> cluster consist in a ring of 5 ions topped by one ion on the symmetry axix. The Na<sub>6</sub> approaches the surface with the symmetry axis in <i>z</i> direction (=perpendicular) and the top ion facing away from the surface. <br /> <br /> The upper panel shows the evolution of the <i>z</i> coordinates, Na ions in red and Ar atoms in green. The cluster is immediately stopped by the surface. A large fraction of impact momentum is transferred at once to the substrate and propagates with velocity of light through the layers. The large dissipation through energy transfer and intrinsic cluster excitation leads to catching of the cluster by the subtrate. The kinetic energies in the lower panel confirm the dramatic and very fast energy exchange at the moment of first impact. Another fraction of energy, not shown in the figure, is turned into the large shape changes. </p> <br /> <br /> <center> <table width="70%"> <tbody> <tr> <td align="right"> <a href="#top">Back to top </a> </td> </tr> </tbody> </table> </center> </div> </div> </div> </div> <div id="footer"> <p></p> </div> </div> </div> </body> </html>

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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="content-type" content="application/xhtml+xml; charset=iso-8859-1" /> <title>Theory of Cluster Dynamics</title> <link href="../style.css" rel="stylesheet" type="text/css" /> </head> <body> <div id="container"> <div id="header"> <div id="menu"> <div id="navMenu"> <ul> <li style="margin-top:1px;border-top:1px solid #B0C4DE; "><a href="../index.html">Home</a></li> <li><a href="../intro.html">Introductory Overview</a></li> <li><a href="../research.html">Scientific Information</a></li> <li><a href="../staff.html">Staff</a></li> <li><a href="../publications.html">Publications/Talks</a></li> <li><a href="../contact.html">Contact</a></li> </ul> </div> </div> <div id="image"> <p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font size="5"><br /> </font><font size="6"> </font><font size="5">The Toulouse - Erlangen Collaboration</font></p> </div> <a name="oben"> </a> <div id="content"><a name="oben"> </a> <div style="margin:15px;width:770px;border:1px solid gray;float:left;font-size:10px;"><a name="oben"> </a> <div style="width:180px;float:left;text-align:center;font-size:10px"><a name="oben"> </a><a href="formal.html">1. Theoretical developments </a> </div> <div style="width:200px;float:left;text-align:center;font-size:10px;"> <a href="../analysis/detail1.html"> 2. Analysis of cluster dynamics </a> </div> <div style="width:200px;float:left;text-align:center;font-weight:900;font-size:10px;"> <a href="../analysis/detail2.html"> 3. Clusters in strong external fields </a> </div> <div style="width:180px;float:left;text-align:center;font-weight:900;font-size:12px;"> <a href="detailQMMM.html"> 4. Embedded clusters </a> </div> </div> <div id="WideContent"> <div id="contentBoxWide"> <div id="contentBoxHeader"> <p> Clusters in strong external perturbations</p> </div> <div id="contentBoxContent"> <!-- START CONTENT HERE --> <br /> <p><img src="figs/na8_nacl_SHG.gif" width="300" align="right" /> Many experiments are done for clusters in contact with a substrate. The strong interface interaction modifies the cluster and theoretical simulations become more involved. However, some features can only be explored in connection with a substrate. E.g., the symmetry breaking through a surface gives access to second-harmonic generation (SHG). <br /> <br /> The figure beneath shows the results from a TDLDA simulation of SHG for Na<sub>8</sub> attached to a NaCl surface [<a href="../literatur.html#own1224">248</a>].
The spectra resulting from irradiation with a 1.4 eV pulse shows nicely the peaks at multiple frequencies. The SHG signal can be enhanced by increasing the laser intensity. This, however, breaks down at some point where the signals are substantially broadened. This is caused by a large ionization which spoils the otherwise clean dipole response of metal clusters. </p> <br /> <br /> <p> <img src="figs/na6_ar384d_deposit.gif" width="300" align="left" />TDLDA
coupled
with molecular dynamics (MD) for ionic motion is a very powerfull tool to describe cluster dynamics. One application is cluster deposition which is illustrated in the figure on the left. It shows Na<sub>6</sub> impinging on an Ar surface (see [<a href="../literatur.html#own1303">328</a>] for further details). The substrate consists of six layers of Ar taken from an appropriate cut of the Ar fcc structure. The Na<sub>6</sub> cluster consist in a ring of 5 ions topped by one ion on the symmetry axix. The Na<sub>6</sub> approaches the surface with the symmetry axis in <i>z</i> direction (=perpendicular) and the top ion facing away from the surface. <br /> <br /> The upper panel shows the evolution of the <i>z</i> coordinates, Na ions in red and Ar atoms in green. The cluster is immediately stopped by the surface. A large fraction of impact momentum is transferred at once to the substrate and propagates with velocity of light through the layers. The large dissipation through energy transfer and intrinsic cluster excitation leads to catching of the cluster by the subtrate. The kinetic energies in the lower panel confirm the dramatic and very fast energy exchange at the moment of first impact. Another fraction of energy, not shown in the figure, is turned into the large shape changes. </p> <br /> <br /> <center> <table width="70%"> <tbody> <tr> <td align="right"> <a href="#top">Back to top </a> </td> </tr> </tbody> </table> </center> </div> </div> </div> </div> <div id="footer"> <p></p> </div> </div> </div> </body> </html>

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</font><font size="4">The Toulouse - Erlangen Collaboration</font></p>
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<div style="width:220px;float:left;text-align:center;">
<a href="../analysis/detail1.html">1. Analysis of cluster dynamics</a>
</div>
<div style="width:220px;float:left;text-align:center;font-weight:900;font-size:12px;">
<a href="../analysis/detail2.html"> 2. Clusters in external fields</a>
</div>
<div style="width:220px;float:left;text-align:center;">
<a href="../tddft-md/formal.html"> 3. Theoretical developments </a>
</div>
</div>
</a>
<div id="WideContent">
<div id="contentBoxWide">
<div id="contentBoxHeader">
<p> Clusters in strong external perturbations</p>
</div>
<div id="contentBoxContent">
<!-- START CONTENT HERE -->
<p><img src="na8_nacl_SHG.gif" align="right" width="300">
Many experiments are done for clusters in contact with a
substrate. The strong interface interaction modifies the cluster and
theoretical simulations become more involved. However, some feature
can only be explored in connection with a substrate. E.g., the
symmetry breaking through a surface gives access to second-harmonic
generation (SHG). The figure benaeth shows the results from a TDLDA
simulation of SHG for Na<sub>8</sub> attached to a NaCl surface
[<a href="../literatur.html#own1224">248</a>]. The spectra resulting
from
irradiation with a 1.4 eV pulse shows nicely the peaks at multiple
frequencies. The SHG signal can be enhanced by increasing the laser
intensity. This, however, breaks down at some point where the signals
are substantially broadened. This is caused by a large ionization
which spoils the elsewise clean dipole response of metal clusters.
</p>
<br>
<br>
<p>
<img src="na6_ar384d_deposit.gif" align="left" width="300">TDLDA
coupled with molecular dynamics (MD) for ionic motion is a very
powerfull tool to describe cluster dynamics. One application is
cluster deposition which is illustrated in the left figure. It shows
Na<sub>6</sub> impinging on an Ar surface (for the modeling [<a
href="../literatur.html#own1303">328</a>]). The substrate consists of
six layers of Ar
taken from an appropriate cut of the Ar fcc structure. The Na<sub>6</sub>
cluster consist in a ring of 5 ions topped by one ion on the symmetry
axix. The Na<sub>6</sub> approaches the surface with the symmetry axis
in <i>z</i>
direction (=perpendicular) and the top ion facing away from the
surface. The upper panel shows the evolution of the <i>z</i>
coordinates,
Na ions in red and Ar atoms in green. The cluster is immediately
stopped by the surface. A large fraction of impact momentum is
transferred at once to the substrate and propagates with velocity of
light through the layers. The large dissipation through energy
transfer and intrinsic cluster excitation leads to catching of the
cluster by the subtrate. The kinetic energies in the lower panel
confirm the dramatic and very fast energy exchange at the moment of
first impact. Another fraction of energy, missing in that figure, is
turned into the large shape changes.
</p>
<p>
Clusters in the strong fields of extremely intense lasers show a much
different dynamics. The core electrons can be released and contribute
strongly to the process. The detailed description at the fully quantum
mechanical level of TDLDA becomes untractable. However, the
excitations involved validate classical approaches. <img
src="MD_fig5.gif" align="right" width="300">
The figure to the
right shows the result of a molecular dynamics simulation of
electronic and ionic dynamics of Na<sub>41</sub><sup>+</sup> under the
influence of
strong laser fields [<a href="../literatur.html#own1308">332</a>].
Ionization is
drawn as function of laser intensity. One sees a sharp kink at a
critical intensity of <i>I</i>=10<sup>16</sup> W/cm<sup>2</sup>. The
critical value is
diistinguished by the fact that the Coulomb force from the laser field
just equals the binding forces of the core electrons. The increase is
due to the core electrons which now start to participate in the
process. This view is checked by sepparating the contributions from
valence (green) and core electrons (red line). There is indeed zero
emission from core electrons up to <i>I</i>=10<sup>16</sup> W/cm<sup>2</sup>
and the
strong increase above that critical intensity is exclusively due to
the core contribution.
<br>
<br>
<br>
<br>
</p>
<table>
<tbody>
<tr>
<td>
<a href="#oben">back to top</a>
</td>
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