1 Introduction
Silver clusters having 20–220 silver atoms have recently played an important role
as models for using electronic structure theory to understand the properties of
plasmonic nanoparticles [1, 2]. It has been found that bare silver clusters in this size
range have optical spectra that are related to what is found for much larger silver
particles (10–20 nm) often having strong conduction band transitions in the 2.5–
3.7 eV range that are related to the strong plasmon band seen in the extinction
spectra of the larger nanoparticles. Significant size-dependent effects have been
noted [3], such as strongly blue-shifted extinction bands in the smaller clusters, and
by studying a range of cluster sizes, a linear variation of cluster excitation energies
with inverse cluster size has been found [4]. Extrapolation of the cluster results to
the large particle limit leads to spectra that are in reasonable agreement with the
results of electrodynamics calculations for 20 nm clusters [4]. There have also been
attempts to study other optical properties for these clusters, such as the Raman
spectra of adsorbed molecules [5], and enhancement factors have been estimated
[6]. However the intrinsic size-dependence of the cluster optical properties provides
significant uncertainty in the connection of these results with surface enhanced
Raman spectroscopy (SERS) measurements that are always done on much larger
particles. There have been similar optical property studies for bare gold clusters that
have been done for silver clusters, however 20 atom gold clusters do not show
strong conduction band transitions that are as easily connected with the larger
nanoparticle results as for silver [3], so gold clusters have been less popular for
these studies. There have also been studies of bimetallic (silver-gold) clusters [7, 8].
The spectra of bare size-dependent silver clusters with about 20 atoms have
rarely been studied experimentally, and only limited information is available for
cluster sizes up to 22 atoms, in rare gas matrices where structures are unknown [9,
10]. There have also been theory studies using density functional theory [9],
including a recent study of clusters sizes up to 75 atoms [11]. These studies show
that the ground state of Ag 20 has a low symmetry, compact structure rather than
being a tetrahedron with the energy difference between the structures being 0.98 eV
at the PW91 level of theory. Tetrahedral structures have usually been used for Ag 20 ,
Ag 84 , and Ag 120 as these are closed shell structures that have especially simple
spectra (typically dominated by one strong conduction band transition which is
sometimes replaced by a clump of closely spaced lines due interaction between the
bright state and background states) [4]. For compact clusters other than the tetrahedra [9], one still obtains spectra that are dominated by conduction band transitions, although the conduction band spectra are usually multipeaked. The latter
property makes it harder to distinguish intrinsic contributions to the plasmon width
from heterogeneous broadening effects. Also, in all spectra there are transitions that
arise from D-band orbitals, the interband transitions. These are mostly important at
higher energies, but they also define a broad background to the conduction band
38
L.R. Madison et al.
Silver clusters having 20–220 silver atoms have recently played an important role
as models for using electronic structure theory to understand the properties of
plasmonic nanoparticles [1, 2]. It has been found that bare silver clusters in this size
range have optical spectra that are related to what is found for much larger silver
particles (10–20 nm) often having strong conduction band transitions in the 2.5–
3.7 eV range that are related to the strong plasmon band seen in the extinction
spectra of the larger nanoparticles. Significant size-dependent effects have been
noted [3], such as strongly blue-shifted extinction bands in the smaller clusters, and
by studying a range of cluster sizes, a linear variation of cluster excitation energies
with inverse cluster size has been found [4]. Extrapolation of the cluster results to
the large particle limit leads to spectra that are in reasonable agreement with the
results of electrodynamics calculations for 20 nm clusters [4]. There have also been
attempts to study other optical properties for these clusters, such as the Raman
spectra of adsorbed molecules [5], and enhancement factors have been estimated
[6]. However the intrinsic size-dependence of the cluster optical properties provides
significant uncertainty in the connection of these results with surface enhanced
Raman spectroscopy (SERS) measurements that are always done on much larger
particles. There have been similar optical property studies for bare gold clusters that
have been done for silver clusters, however 20 atom gold clusters do not show
strong conduction band transitions that are as easily connected with the larger
nanoparticle results as for silver [3], so gold clusters have been less popular for
these studies. There have also been studies of bimetallic (silver-gold) clusters [7, 8].
The spectra of bare size-dependent silver clusters with about 20 atoms have
rarely been studied experimentally, and only limited information is available for
cluster sizes up to 22 atoms, in rare gas matrices where structures are unknown [9,
10]. There have also been theory studies using density functional theory [9],
including a recent study of clusters sizes up to 75 atoms [11]. These studies show
that the ground state of Ag 20 has a low symmetry, compact structure rather than
being a tetrahedron with the energy difference between the structures being 0.98 eV
at the PW91 level of theory. Tetrahedral structures have usually been used for Ag 20 ,
Ag 84 , and Ag 120 as these are closed shell structures that have especially simple
spectra (typically dominated by one strong conduction band transition which is
sometimes replaced by a clump of closely spaced lines due interaction between the
bright state and background states) [4]. For compact clusters other than the tetrahedra [9], one still obtains spectra that are dominated by conduction band transitions, although the conduction band spectra are usually multipeaked. The latter
property makes it harder to distinguish intrinsic contributions to the plasmon width
from heterogeneous broadening effects. Also, in all spectra there are transitions that
arise from D-band orbitals, the interband transitions. These are mostly important at
higher energies, but they also define a broad background to the conduction band
38
L.R. Madison et al.