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Ab initio study of Ag5-8 cluster absorption spectra
1. Ab initio study of the absorption spectra of Ag n (n=5–8) clusters
Vlasta Bonačić-Koutecky, Vincent Veyret, and Roland Mitrić
Citation: The Journal of Chemical Physics 115, 10450 (2001); doi: 10.1063/1.1415077
View online: http://dx.doi.org/10.1063/1.1415077
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/115/22?ver=pdfcov
Published by the AIP Publishing
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3. bands for the Ag8 cluster which might serve as suitable fin-
gerprints of structural properties when compared with theo-
retical results. The He-droplet represents, in principle, an ul-
tracold weakly interacting medium, and it is an open
question to which extent the spectroscopic properties will be
influenced.
All above-mentioned aspects motivated us to study the
optical response properties of silver clusters larger than tet-
ramers presented in this contribution. For this purpose we
use a linear response approach based on accurate treatments
of electron correlation effects such as the equation-of-motion
coupled cluster ͑EOM-CC͒ method31
and related
techniques32
employing 11-electron relativistic effective core
potential ͑11e-RECP͒ designed for the adequate description
of excited states.17
Computational aspects are briefly de-
scribed in Sec. II. The absorption spectra calculated for the
most stable structures, as well as for energetically close-lying
isomeric forms of Ag5–8 clusters, are presented in Sec. III.
They are compared first with experimental data which are
not recorded in the gas phase.5,18,27–30
Second, the absorption
spectra obtained for deformed geometries which might arise
due to the interaction with an environment present in experi-
ments are also shown and discussed in Sec. III. The relax-
ation in excited states which might be responsible for strong
visible fluorescence observed in the rare gas matrices5
is
briefly addressed as a motivation for further investigations.
Conclusions with outlook are presented in Sec. IV.
II. COMPUTATION
The derivation of our 11-electron relativistic effective
core potential ͑11e-RECP͒ for excited states of the silver
atom together with the AO basis set has been presented in
Ref. 17. It has been also demonstrated in Ref. 17 that 11e-
RECP provides an accurate description of the excited states
of small silver clusters. In this paper a slightly larger
͑6s5p5d͒ AO basis set with contraction scheme ͑21111/311/
311͒ is used, since the excited states in a larger energy inter-
val are needed. Such relatively small AO basis set providing
adequate accuracy is requested, since 11 electrons per atom
have to be correlated in the framework of linear response
methods based on coupled cluster approach. This is compu-
tationally demanding for the cluster sizes considered in this
work and for calculations of many excited states which is
necessary in order to obtain the full information about ab-
sorption spectra. Due to the large number of electrons the
correlation treatment based on size consistent approaches is
mandatory. Therefore we adopt in this work the EOM-CCSD
method31
and the related similarity transformed equation of
motion coupled cluster technique ͑STEOM-CCSD͒.32
The
STEOM-CCSD theory has been derived from a similarity
transform of the second quantized Hamiltonian which re-
duces the coupling between singly excited configurations and
more highly excited configurations. On all tested systems the
STEOM yields comparable accuracy as the EOM-CCSD
method at lower computational requirements. As it is well
known, EOM-CCSD method gives reliable transition ener-
gies and oscillator strengths for states dominated by singly
excited configurations. For the excited states in which doubly
excited configurations have a leading role, less accurate re-
sults are expected. In order to determine if the latter is the
case, approximate excitation levels ͑AEL͒ can be used as a
measure of the number of electrons which are excited from
the CCSD ground state described by the single and double
excitations with respect to the single reference configuration.
Definition of AEL is one half of the trace of the difference
between reduced density matrixes of the ground and excited
states, expressed in the basis which diagonalizes the ground-
state coupled cluster density matrix. The values of AEL
which are considerably larger than 1 indicate that the states
have double-excitation character and therefore their accuracy
is not as high as for states with AEL ϳ1. However, the tran-
sitions with large oscillator strengths are dominantly deter-
mined by single excitations, because double excitations are
dipole forbidden. Therefore the EOM-CCSD method is suit-
able for determining patterns of absorption spectra. It is to
expect that the errors of transition energies due to the ap-
proximate treatment of correlation effects are not larger than
0.1 eV. For transitions to very high excited states above 6 eV
the accuracy can be strongly influenced by the AO basis set
which is in the present work of very moderate size. We car-
ried out also calculations of absorptions spectra for geomet-
ric deformations using lower level theory, e.g., random phase
approximation ͑RPA͒ which allowed us to gain the qualita-
tive insight into the possible influence of the environment
͑such as rare-gas atoms, solid Ar-matrix or He-droplet͒ on
the spectroscopic patterns.
III. STRUCTURES AND ABSORPTION SPECTRA
FOR Ag5–8 CLUSTERS
A. Structural properties
In order to provide a consistent theoretical description of
the ground and excited states, the structures have been opti-
mized in the framework of the analytical gradient CCSD
procedures correlating 11 electrons per Ag-atom. The geom-
etries of global and local minima for which the harmonic
frequency analysis has been carried out are shown in Fig. 1.
The ground-state properties are summarized in Table I in
which we also list for comparison the results obtained from
the DFT calculations employing BLYP functionals.33,34
Both
approaches yield equivalent energy ordering of the isomeric
forms for the given cluster size and comparable stabilities
͑binding energies per atom͒. An accurate determination of
the energy ordering of the isomeric forms is still a difficult
task. Therefore, we first compare the ground-state properties
presented in this contribution with those obtained in our ear-
lier works.6,7
There the Hartree–Fock geometry optimization
of neutral and charged silver clusters employing the 1e-
RECP was first carried out, and then the multireference con-
figuration interaction method ͑MRDCI͒ was used for the HF
structures to determine the influence of correlation effects on
the energy ordering of isomers.
The geometry optimization at the higher level of theory
taking into account also correlation of d-electrons presented
here yields for the planar structure of Ag5 lower energy than
for the trigonal bipyramid which is in agreement with our
earlier findings.6
Similarly according to present and
10451J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Absorption spectra of Agn clusters
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4. previous6
results for Ag7 , the pentagonal bipyramid is con-
siderably lower in energy than the bicapped trigonal bipyra-
mid with the C3v symmetry. The situation is different for
Ag6 and Ag8 . As shown in Fig. 1 the planar trapezoidal D3h
structure of Ag6 corresponds to the global minimum, while
the flat pentagonal pyramid C5v and the three-dimensional
C2v structure are higher-lying isomeric forms with well-
separated energies. These three structures are almost degen-
erate at the lower level of theory6
with the energy ordering:
C5vрD3hрC2v . The energy ordering of the isomeric forms
of the Ag8 cluster seems to be even more sensitive on the
details of the theoretical treatment. The highly symmetric Td
structure corresponds to the global minimum and the related
D2d structure to the local minimum in the framework of the
CCSD or DFT approach with 11e-RECP ͑cf. Fig. 1͒. In the
earlier work, the HF geometry optimization yielded also Td
ϽD2d but the post HF correlation treatment inversed the
energy ordering.
In order to determine whether the optimization of geom-
etries at the correlated level of theory or/and the inclusion of
d-electrons in correlation effects can change the energy or-
dering of isomers, we carried out also DFT-BLYP geometry
optimization with the 1e-RECP. The results are independent
from the inclusion of d-electrons in the correlation treatment
for Ag5 , Ag6, and Ag7 clusters. In the case of Ag8, the Td
structure is the global minimum only with the 11e-RECP in
the framework of the CCSD or DFT level of theory. The
above results indicate that d-electrons which are strongly lo-
calized at Ag atoms usually do not considerably influence
structural properties. But in the case that isomeric forms as-
sume closely related structures, like for Ag8, the accurate
determination of the energy ordering of isomers is more dif-
ficult and the inclusion of d-electrons in correlation treat-
ments might be necessary. Notice that at the higher level of
theory, the global minima are well-separated from the local
ones ͑cf. for energy differences of isomer forms Fig. 1 and
Table I͒.
We wish to emphasize that the most stable structures of
Ag5, Ag6, Ag7, and Ag8 presented in this work have the
same topologies as the ones corresponding to the global
minima of sodium Nan ͑nϭ5–8͒ clusters. This is also the
case of trimers and tetramers as it has been previously
pointed out.15
B. Absorption spectra
The absorption spectra obtained with the EOM-CCSD
and STEOM-CCSD methods for the most stable structures of
Ag5–8 are given in Fig. 2 together with previously calculated
spectra for Ag2–4
17
which allow illustration of the changes in
the leading features of the patterns as a function of the clus-
ter size. The calculated transition energies (Te) for optically
FIG. 1. CCSD optimized geometries of the Ag2–8 clusters using 11e-RECP
with associated AG basis ͑Ref. 17͒. Labels of the point group and the ground
state are given below structures together with relative energies in eV with
respect to the most stable structure. The isomeric forms for the same cluster
size are numbered I–III and corresponding energies and properties are given
in Table I.
TABLE I. Ground-state energies of the DFT- and CCSD-optimized Agn ͑nϭ5–8͒ clusters.
EDFT ⌬Eb
Eb /n ECCSD ⌬Ec
Eb /n
Clustera
Sym State ͑au͒ ͑eV͒ ͑eV͒ ͑au͒ ͑eV͒ ͑eV͒
Ag5(I) C2v
2
A1 Ϫ194.943 839 1.49 Ϫ187.409 370 1.49
Ag5(II) C2v
2
B1 Ϫ194.917 626 0.71 1.35 Ϫ187.395 445 0.38 1.41
Ag6(I) D3h
1
A1Ј Ϫ233.976 683 1.69 Ϫ224.943 828 1.72
Ag6(II) C5v
1
A1 Ϫ233.962 674 0.38 1.62 Ϫ224.929 496 0.39 1.66
Ag6(III) C2v
1
A1 Ϫ233.940 361 0.99 1.53 Ϫ224.925.687 0.49 1.64
Ag7(I) D5h
2
A2Љ Ϫ272.881 915 1.34 Ϫ261.564 692 1.65
Ag7(II) C3v
2
A1 Ϫ272.870 330 0.31 1.29 Ϫ261.551 46 0.36 1.70
Ag8(I) Td
1
A1 Ϫ312.004 988 1.81 Ϫ300.005 562 2.00
Ag8(II) D2d
1
A1 Ϫ312.001 480 0.09 1.80 Ϫ300.001 887 0.10 1.99
a
For geometries of clusters, ͑I͒, ͑II͒, ͑III͒ label isomers according to the energy ordering.
b
The DFT ͑BLYP͒ energy difference between isomers.
c
The CCSD energy difference between isomers.
10452 J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Bonacˇic´-Koutecky, Veyret, and Mitric´
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5. allowed states and the corresponding oscillator strengths
(fe), for the most stable structures as well as for the second
isomeric forms, are listed in Tables II–V. The absorption
spectra calculated for the second isomers of Ag5 and Ag6,
assuming three-dimensional ͑3D͒ structures, are given in Fig.
3, in order to compare them with those obtained for the pla-
nar structures ͑2D͒. The absorption spectra for all three iso-
meric forms of Ag6 calculated at the lower level of theory in
the framework of the random phase approximation ͑RPA͒ are
shown in Fig. 4. The purpose is to illustrate the influence of
the symmetry and correlation treatment on the spectroscopic
patterns. The calculated spectroscopic patterns at the
STEOM-CCSD level of theory for the Td and D2d structures
of Ag8 are compared with the experimental findings recorded
in the He-droplet in Fig. 5. The absorption spectra have been
also calculated for distorted Td structures as shown in Fig. 6
which serve as models to study the influence of the environ-
ment on the spectroscopic patterns.
From Fig. 2 we can follow the influence of an addition
of the single Ag atom ͑i͒ within the planar cluster growth and
͑ii͒ within the three-dimensional structural frame on the lo-
cations of transition energies with pronounced intensities and
relative magnitudes of oscillator strengths for Ag4 –6 and
Ag7,8 clusters, respectively ͑cf. also Tables II–V͒.
͑i͒ The significant change in spectroscopic patterns oc-
curs between Ag4 and Ag5 as well as between Ag5 and Ag6 .
The spectrum of Ag4 in the energy interval up to 5 eV is
characterized by three transitions with comparable intensities
(feϷ1) located at 3.2 and 4.3 eV ͑the latter two being de-
generate͒. In contrast, for the planar structure of Ag5 the
single dominantly intense transition to the 5 2
B2 state with
feϷ1.6 is located at 3.55 eV, and five transitions with oscil-
lator strengths ranging from 0.1 to 0.5 are distributed in a
relatively narrow energy interval between 3.8 eV and 4.7 eV.
In other words the addition of the single Ag atom to Ag4
cluster invokes substantial changes in the absorption spectra
between the pentamer and the tetramer. This seems to be
consequence of the increased size, since both clusters assume
related planar structures. Notice that similarly as in the case
of Ag4 , the intense transitions ͑e.g., to the 8 2
B2 state͒ in the
Ag5 (C2v) spectrum are characterized by the leading con-
figurations with excitations of the s- and not the d-electrons.
For the planar structure of Ag6 , the transition to the 2 1
EЈ
state located at 3.7 eV with feϭ2.4 gives rise to an even
more pronounced single dominant peak due to the high sym-
metry. Only two transitions with low intensities, which are
red and blue shifted with respect to the dominant one, are
present in the energy interval up to 5 eV. The three configu-
rations with excitations from doubly degenerate HOMO oc-
cupied by four s-electrons to LUMO and to LUMOϩk con-
tribute with weights up to ϳ70% to the expansion of the
wave function of the 2 1
EЈ state with a dominant intensity.
͑ii͒ In the case of the three-dimensional D5h structure of
Ag7 , the transition to the 7 2
E1Љ with dominant intensity lo-
cated at 3.9 eV is blue-shifted by 0.2 eV with respect to the
2 1
EЈ transition calculated for the planar D3h form of Ag6 .
Again the wave function of the 7 2
E1Љ state contains largest
contributions from configurations with excitations involving
singly occupied HOMO and doubly degenerate HOMO-1 or-
bitals ͑in other words, s-electrons͒. Consequently, the leading
features of spectroscopic patterns of the planar Ag6(D3h)
and the three-dimensional Ag7(D5h) have common charac-
teristics, while the locations and intensities of weak reso-
nances are different. The analog situation has been found for
the Td structure of Ag8 . The excitations of s-electrons from
the triple degenerate HOMO to LUMOϩk are mainly re-
sponsible for the transition to the 5 1
T2 state, with the domi-
nant intensity (feϭ3.8 eV͒ located at 4.16 eV. In addition, to
this dominant peak, the low-energy transition to the 3 2
T2
state exhibits considerable intensity (feϳ1 eV͒. The transi-
tion with weaker intensity at 4.58 eV and others above 5 eV
are also valuable for the characterization of different struc-
tures. They are usually easier to obtain for the closed shell
than for the open shell systems due to technical aspects. No-
tice that in Fig. 2, the results for Ag5 and Ag7 clusters are
available for transitions only until 5 eV.
We wish to emphasize that for the single dominant peak
in all three cases of Ag6(D3h), Ag7(D5h), and Ag8 (Td) ͑cf.
Fig. 2͒, only three leading configurations with single excita-
tions involving s- and not d-electrons contribute with the
weights up 70% in the expansion of the wave functions.
Moreover, in each case, we found that the same linear com-
bination of configurations with different sign and magnitudes
FIG. 2. Optically allowed transitions Te in eV and oscillator strengths fe
obtained from EOM-CCSD and STEOM-CCSD calculations using 11e-
RECP with associated AO basis ͑Ref. 17͒ for the lowest energy structures of
Ag2–8 . For details of Te and fe values compare Tables II–V.
10453J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Absorption spectra of Agn clusters
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6. of coefficients can be found in the expansion of wave func-
tions of the states to which transitions with considerably
weaker intensities have been calculated. This confirms that
the spectroscopic patterns of Agnϭ5–8 clusters are due to
interference phenomena known for molecules similarly as
previously found for Nan and Nan
ϩ
clusters.24,25
Due to the
common structural and related electronic properties the ab-
sorption spectra of Nanϭ5–8 and Ag5–8 exhibit striking simi-
TABLE II. Calculated transition energies (Te) and oscillator strengths (fe) for optically allowed states for the
C2v structures of the isomers I and II of Ag5 . ͑Bold symbols correspond to transitions with feу0.2 in order to
identify leading features of the spectroscopic patterns.͒
C2v͑I͒ Te
a
(fe) C2v(II) Te
a
(fe)
states ͑eV͒ AELc
states ͑eV͒ AELc
12
A1 12
B1
22
B2 1.50͑0.00͒ 1.10 22
B1 0.30͑0.00͒ 1.06
22
A1 1.89͑0.01͒ 1.08 12
B2 0.67͑0.00͒ 1.08
12
B1 2.12͑0.00͒ 1.07 22
B2 1.20͑0.00͒ 1.08
22
B2 2.19͑0.08͒ 1.07 32
B1 1.91͑0.00͒ 1.08
32
B2 2.33͑0.01͒ 1.09 32
B2 2.03͑0.00͒ 1.07
32
A1 2.64͑0.06͒ 1.06 42
B1 2.52„0.27… 1.05
42
A1 2.90͑0.03͒ 1.17 42
B2 2.63͑0.01͒ 1.24
51
A1 3.47͑0.01͒ 1.26 52
B2 2.82͑0.01͒ 1.76
42
B2 3.50͑0.13͒ 1.74 12
A1 2.95͑0.05͒ 1.04
52
B2 3.55„1.63… 1.08 62
B1 3.01͑0.00͒ 1.06
62
B2 3.74͑0.06͒ 1.16 62
B2 3.14͑0.00͒ 1.11
22
B1 3.78͑0.07͒ 1.05 52
B1 3.14͑0.01͒ 1.09
62
A1 3.81„0.39… 1.09 22
A1 3.18͑0.04͒ 1.08
72
B2 3.89͑0.03͒ 1.36 72
B2 3.35͑0.03͒ 1.12
73
A1 3.99͑0.19͒ 1.08 82
B2 3.47„1.22… 1.09
32
B1 4.06͑0.03͒ 1.15 92
B2 3.74͑0.00͒ 1.13
82
A1 4.20͑0.03͒ 1.10 32
A1 3.80͑0.00͒ 1.04
82
B2 4.22͑0.06͒ 1.15 72
B1 3.81͑0.13͒ 1.18
92
A1 4.25„0.54… 1.08 102
B2 3.86͑0.01͒ 1.15
102
A1 4.39͑0.00͒ 1.12 82
B1 3.86͑0.00͒ 1.06
92
B2 4.45͑0.00͒ 1.15 42
A1 3.98͑0.03͒ 1.27
112
A1 4.50͑0.01͒ 1.15 112
B2 4.02͑0.02͒ 1.87
102
B2 4.58͑0.01͒ 1.06 52
A1 4.05͑0.00͒ 1.07
122
A1 4.62͑0.01͒ 1.49 92
B1 4.17͑0.06͒ 1.09
42
B1 4.64͑0.11͒ 1.09 62
A1 4.29͑0.01͒ 1.46
52
B1 4.70͑0.19͒ 1.18 102
B1 4.32͑0.08͒ 1.34
112
B2 4.72͑0.00͒ 1.12 112
B1 4.35͑0.02͒ 1.52
132
A1 4.74͑0.00͒ 1.35 72
A1 4.39͑0.00͒ 1.14
122
B2 4.79͑0.00͒ 1.13 132
B2 4.40͑0.00͒ 1.05
142
A1 4.82͑0.00͒ 1.28 122
B1 4.42„0.28… 1.13
62
B1 4.87͑0.04͒ 1.30 82
A1 4.45͑0.01͒ 1.33
132
B2 4.94͑0.00͒ 1.14 132
B1 4.46͑0.00͒ 1.16
142
B2 4.98͑0.01͒ 1.11 92
A1 4.53͑0.00͒ 1.16
152
A1 5.06͑0.00͒ 1.24 102
A1 4.58͑0.10͒ 1.14
72
B1 5.07͑0.00͒ 1.26 122
B2 4.58͑0.00͒ 1.12
152
B2 5.10͑0.01͒ 1.12 152
B1 4.62͑0.00͒ 1.07
162
A1 5.18͑0.11͒ 1.15 12
A1 4.66͑0.06͒ 1.10
82
B1 5.24͑0.01͒ 1.45 122
A1 4.69͑0.11͒ 1.15
172
A1 5.25͑0.01͒ 1.13 142
B1 4.70͑0.05͒ 1.17
162
B2 5.33͑0.01͒ 1.12 132
A1 4.72͑0.04͒ 1.14
172
B2 5.36͑0.00͒ 1.22 142
B2 4.72͑0.00͒ 1.09
182
B2 5.41͑0.00͒ 1.15 152
B2 4.76͑0.02͒ 1.13
182
A1 5.44͑0.01͒ 1.13 162
B2 4.89͑0.00͒ 1.10
192
B2 5.46͑0.00͒ 1.37 ͑2.69͒b
202
B2 5.49͑0.05͒ 1.31
192
A1 5.51͑0.00͒ 1.38
212
B2 5.57͑0.00͒ 1.21
202
A1 5.60͑0.03͒ 1.17
222
B2 5.67͑0.00͒ 1.20
212
A1 5.76͑0.02͒ 1.18
222
A1 5.72͑0.00͒ 1.15
232
B2 5.82͑0.00͒ 1.15
232
A1 5.83͑0.00͒ 1.43
͑4.05͒b
a
For the C2v structures, 55 electrons have been correlated.
b
The sum of oscillator strengths for calculated states.
c
Approximate excitation level.
10454 J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Bonacˇic´-Koutecky, Veyret, and Mitric´
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7. larities in leading features which will be addressed later.
However, although the d-electrons of Ag atoms are not di-
rectly involved in excitations of the leading configurations
contributing to states for which intense transitions have been
calculated, their inclusion in the correlation effects is man-
datory for the accurate determination of the transition ener-
gies. The calculations correlating only s-electrons yield too
large transition energies. Consequently, any 1e-RECP is not
suitable for predicting the absorption spectra of silver clus-
ters independently from the choice of the correlation treat-
ment.
The calculated absorption spectra for the second isomers
of Ag5 and Ag6 clusters which assume three-dimensional
structures are presented in Fig. 3. From the comparison of
their patterns with those obtained for the planar structures of
Ag5 and Ag6 ͑cf. Fig. 2͒, the conclusion can be drawn that
the main difference between spectra of two isomers for the
given cluster size is reflected in the locations and intensities
of weaker resonances. This is particularly the case for Ag6 ,
since the flat pentagonal pyramid with C5v symmetry is
closely related to the planar D3h form, and therefore domi-
nant resonances for both structures are located at ϳ3.7 eV. In
contrast, the spectra obtained for both C2v isomers of Ag5
having planar ͑2D͒ and three-dimensional ͑3D͒ structures
differ from each other considerably, mainly in the locations
of transitions with moderate intensities. The above findings
show clearly that the identification of the structure which is
responsible for the recorded spectrum is possible if the mea-
surements have been carried out in a sufficiently large energy
interval so that in addition to the dominant resonances other
features of spectroscopic patterns can be also revealed. This
is particularly important in the case that the isomers assume
related structures.
In order to illustrate the influence of the structural
changes on the absorption spectra, the transition energies and
oscillator strengths obtained for the three isomeric forms of
Ag6 with D3h , C5v , and C2v symmetries are presented in
Fig. 4. The calculations have been carried out at the lower
level of theory, in the framework of the RPA method for
illustrative purpose. The RPA method yields in the case of
TABLE III. Calculated transition energies (Te) and oscillator strengths (fe)
for optically allowed states for the D3h and C5v structures of Ag6 . ͑Bold
symbols correspond to transitions with feу0.2 in order to identify leading
features of the spectroscopic patterns.͒
D3h Te
a
(fe) C5v Te
a
(fe)
states ͑eV͒ states ͑eV͒
11
A1Ј 11
A1
11
EЈ 3.06„0.26… 11
E1 2.09͑0.02͒
21
EЈ 3.69„2.40… 21
E1 3.09͑0.15͒
31
EЈ 4.73͑0.01͒ 31
E1 3.71„2.80…
11
A2Љ 4.73͑0.00͒ 11
A1 3.91͑0.00͒
41
EЈ 4.76͑0.02͒ 41
E1 3.92͑0.00͒
21
A2Љ 4.83„0.50… 51
E1 4.00͑0.00͒
51
EЈ 4.99͑0.01͒ 61
E1 4.44͑0.00͒
61
EЈ 5.08͑0.00͒ 71
E1 4.61͑0.00͒
71
EЈ 5.23͑0.07͒ 81
E1 4.65͑0.00͒
81
EЈ 5.29͑0.02͒ 91
E1 4.84͑0.00͒
91
EЈ 5.39͑0.01͒ 101
E1 4.96͑0.00͒
101
EЈ 5.43͑0.14͒ 111
E1 5.01͑0.00͒
111
EЈ 5.46͑0.01͒ 121
E1 5.03͑0.04͒
121
EЈ 5.55͑0.02͒ 21
A1 5.08͑0.00͒
131
EЈ 5.58͑0.03͒ 131
E1 5.16͑0.00͒
31
A2Љ 5.59͑0.00͒ 141
E1 5.25͑0.00͒
141
EЈ 5.65͑0.00͒ 151
E1 5.27͑0.03͒
151
EЈ 5.72͑0.00͒ 31
A1 5.32͑0.01͒
41
A2Љ 5.75͑0.00͒ ͑3.14͒b
161
EЈ 5.79͑0.00͒
51
A2Љ 5.84„0.29…
171
EЈ 5.90͑0.17͒
181
EЈ 5.98͑0.00͒
61
A2Љ 6.00͑0.00͒
191
EЈ 6.03͑0.05͒
201
EЈ 6.12͑0.00͒
71
A2Љ 6.12͑0.00͒
81
A2Љ 6.12͑0.02͒
211
EЈ 6.18͑0.01͒
91
A2Љ 6.25͑0.03͒
221
EЈ 6.26͑0.20͒
101
A2Љ 6.39͑0.00͒
111
A2Љ 6.56͑0.00͒
121
A2Љ 6.64͑0.00͒
131
A2Љ 6.86͑0.17͒
141
A2Ј 7.11͑0.00͒
͑4.45͒b
a
For the D3h and C5v structures, 66 electrons have been correlated.
b
The sum of oscillator strengths for calculated states.
TABLE IV. Calculated transition energies (Te) and oscillator strengths (fv)
for optically allowed states for the D5h structure of Ag7 . ͑Bold symbols
correspond to transitions with feу0.2 in order to identify leading features
of the spectroscopic patterns.͒
D5h states Te
a
(fe) ͑eV͒ AELc
12
A2Љ
12
A1Ј 1.52͑0.00͒ 1.08
22
A1Ј 1.62͑0.00͒ 1.07
12
E1Љ 2.23͑0.00͒ 1.07
22
E1Љ 2.43͑0.00͒ 1.07
31
E1Љ 2.55͑0.01͒ 1.08
32
A1Ј 2.58„0.27… 1.05
42
E1Љ 2.77͑0.00͒ 1.10
52
E1Љ 2.94͑0.03͒ 1.10
42
A1Ј 3.41͑0.00͒ 1.08
52
A1Ј 3.70͑0.00͒ 1.11
62
E1Љ 3.81͑0.17͒ 1.09
62
A1Ј 3.85͑0.00͒ 1.12
72
E1Љ 3.89„3.17… 1.11
82
E1Љ 3.72͑0.00͒ 1.05
72
A1Ј 4.01͑0.01͒ 1.05
82
A1Ј 4.08͑0.00͒ 1.10
92
E1Љ 4.13„0.25… 1.12
92
A1Ј 4.20͑0.00͒ 1.05
102
A1Ј 4.25͑0.10͒ 1.06
102
E1Љ 4.33͑0.00͒ 1.06
112
A1Ј 4.34͑0.15͒ 1.22
112
E1Љ 4.37͑0.15͒ 1.94
122
E1Љ 4.47͑0.00͒ 1.16
132
E1Љ 4.50͑0.00͒ 1.14
142
E1Љ 4.56͑0.00͒ 1.81
152
E1Љ 4.68͑0.00͒ 1.10
122
A1Ј 5.00͑0.00͒ 1.12
͑4.32͒b
a
For the D5h structure, 77 electrons have been correlated.
b
The sum of oscillator strengths for calculated states.
c
Approximate excitation level.
10455J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Absorption spectra of Agn clusters
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8. D3h and C5v structures satisfactory results in comparison
with the STEOM-CCSD method ͑cf. also Fig. 2͒. This is not
surprising for structures with high symmetry for which the
spectrum is usually characterized by the single dominant
peak and few transitions with weaker intensities, which are
all well-described by the single excited configurations. No-
tice, however that for quantitative predictions a higher level
of theory such as STEOM-CCSD is necessary. Figure 4 il-
lustrates in a straightforward manner the distinct features of
the spectroscopic pattern obtained for the C2v structure from
those of the absorption spectra calculated for the D3h and
C5v structures with higher symmetry. The latter ones are
characterized by the single dominant resonances and the
former one by a large number of transitions with comparable
intensities. In the case of the C2v structure a more sophisti-
cated theoretical treatment might influence details, but over-
all features are expected to remain unchanged.
The influence of the structural properties on the spectro-
scopic patterns can be clearly evidenced by comparing the
results obtained for the two related isomeric forms of Ag8
clusters are illustrated in Fig. 5. Differences in corresponding
spectroscopic patterns will be discussed below when com-
pared with experimental results.
C. Comparison of absorption spectra
with experimental findings
In summary, the spectroscopic patterns of Agnϭ5–8 ob-
tained for the most stable structures ͑cf. Fig. 2͒ exhibit a
single dominant peak with blue shifts of ϳ0.2 eV for an
increase of the cluster size by the single atom. A number of
transitions with low intensities have been found at very dif-
ferent locations for each cluster size. The trend concerning
dominant peaks is in agreement with the early experimental
findings for absorption of Ag5 , Ag7 , and Ag8 embedded in
solid argon,27,28
although the resolution of the fine structure
is not sufficiently high for the structural identification when
compared with calculated spectra. Our results of Fig. 2 show
FIG. 3. Optically allowed transitions Te in eV and oscillator strengths fe for
the second isomers of Ag5 and Ag6 using the same method as in Fig. 2 ͑cf.
Tables II and III͒.
TABLE V. Calculated transition energies (Te) and oscillator strengths (fe)
for optically allowed states for the Td and D2d structures of Ag8 . ͑Bold
symbols correspond to transitions with feу0.2 in order to identify leading
features of the spectroscopy patterns.͒
Td states Te
a
(fe) ͑eV͒ D2d states Te
a
(fe) ͑eV͒
11
A1 11
A1
11
T2 2.86͑0.07͒ 11
E 2.39͑0.06͒
21
T2 2.94͑0.00͒ 11
B2 2.76͑0.10͒
31
T2 3.27„0.96… 21
E 2.98͑0.00͒
41
T2 3.67͑0.00͒ 31
E 3.20͑0.02͒
51
T2 4.16„3.68… 41
E 3.31͑0.14͒
61
T2 4.58͑0.18͒ 21
B2 3.78„0.91…
71
T2 4.66͑0.00͒ 31
B2 4.08„0.78…
81
T2 4.77͑0.02͒ 51
E 4.09„1.54…
91
T2 5.11͑0.00͒ 41
B2 4.16͑0.00͒
101
T2 5.21͑0.06͒ 61
E 4.21„1.18…
111
T2 5.23͑0.00͒ 51
B2 4.42͑0.00͒
121
T2 5.41͑0.00͒ 61
B2 4.44͑0.07͒
131
T2 5.48͑0.00͒ 71
E 4.59͑0.02͒
141
T2 5.68„0.21… 71
B2 4.81͑0.01͒
151
T2 5.81͑0.16͒ 81
E 4.87͑0.00͒
161
T2 5.83͑0.11͒ 81
B2 4.90͑0.00͒
171
T2 5.91͑0.02͒ 91
E 4.95͑0.05͒
181
T2 5.99„0.22… 101
E 4.97͑0.03͒
191
T2 6.06„0.34… 111
E 5.15͑0.01͒
201
T2 6.12͑0.03͒ 121
E 5.21͑0.01͒
211
T2 6.56͑0.03͒ 131
E 5.24͑0.02͒
͑6.11͒b
141
E 5.29͑0.00͒
111
B2 5.35͑0.02͒
121
B2 5.42͑0.00͒
151
E 5.45͑0.01͒
131
B2 5.48͑0.02͒
161
E 5.49͑0.07͒
141
B2 5.55͑0.00͒
171
E 5.56͑0.16͒
181
E 5.60͑0.04͒
151
B2 5.63͑0.05͒
191
E 5.64͑0.10͒
201
E 5.67͑0.01͒
211
E 5.71͑0.03͒
161
B2 5.72͑0.04͒
221
E 5.76͑0.04͒
171
B2 5.78͑0.00͒
181
B2 5.79͑0.00͒
191
B2 5.80͑0.00͒
231
E 5.81͑0.00͒
201
B2 5.83͑0.03͒
241
E 5.87͑0.10͒
211
B2 5.90͑0.00͒
221
B2 5.93͑0.01͒
231
B2 5.97͑0.00͒
251
E 6.35͑0.06͒
261
E 6.36͑0.05͒
271
E 6.46͑0.00͒
241
B2 6.48͑0.00͒
281
E 6.58͑0.04͒
201
E 6.66͑0.09͒
͑5.92͒b
a
For the Td and D2d structures, 88 electrons have been correlated.
b
The sum of oscillator strengths for calculated states.
10456 J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Bonacˇic´-Koutecky, Veyret, and Mitric´
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9. that the influence of the argon matrix invokes a constant shift
to the red by 0.2 eV for the dominant peak. The depletion
spectrum of the Ag7Kr complex18
is characterized by the
broad band centered around ϳ3.7 eV, which is also red-
shifted by 0.2 eV with respect to the calculated one.
The calculated STEOM-CCSD absorption spectrum for
the Td ͑isomer I͒ and for the D2d ͑isomer II͒ structures of
Ag8 and the recently obtained experimental spectrum in a He
droplet using resonance two photon ionization technique
͑R2PI͒30
are shown in Fig. 5. In the case of the Td structure
the calculated resonance with the dominant intensity involv-
ing transition to the 3 1
T2 state located at 4.16 eV is blue-
shifted with respect to the measured peak located at 4.0 eV
͓cf. Fig. 5͑a͔͒. The low energy transition to the 2 1
T2 state
calculated at 3.27 eV with considerable intensity has not
been recorded. The lifetime of the low-energy resonance is
not expected to be shorter than the lifetime of the dominant
one because of similar nature of excitations found for both
resonances. Since the R2PI-technique uses the nanosecond
pulses to populate the excited levels both resonances should
be detected. It seems that the low-energy transitions might
not be accessible in this experiment because the He-
environment increases the ionization potential of the silver
clusters above the threshold which allows the detection.
In contrast, the calculated spectrum for the D2d structure
͓cf. Fig. 5͑b͔͒ is characterized by two almost degenerate tran-
sitions to the 3 1
B2 and 61
E states located at 4.08 and 4.09
eV with feϭ0.78 and 1.59, respectively, by the one
moderately-blue shifted transition to the 6 1
E state at 4.21 eV
with feϭ1.18 and by the red-shifted transition to the 2 1
B2
state at 3.78 eV with feϭ0.91, all of them lying in a rela-
tively narrow energy interval. In addition two weak reso-
nances at the lower energies ͑2.76 and 3.31 eV͒ have been
obtained. Consequently, the spectroscopic pattern of the D2d
structure is very different from the one calculated for the Td
structure, although both structures are closely related to each
other. The transformation from the Td to the D2d structure
involves the formation of one bond between the two atoms
FIG. 4. Optically allowed transition Te in eV and oscillator strengths fe for
three isomeric forms of Ag6 obtained from RPA calculations using 11e-
RECP with associated AO basis.
FIG. 5. Comparison of optical spectrum of Ag8 obtained in a helium droplet
using resonant two-photon ionization ͑Ref. 30͒ and calculated spectra for
both ͑a͒ Td and ͑b͒ D2d isomers obtained from STEOM-CCSD method with
11e-RECP and associated AO basis set ͑Ref. 17͒. For details of Te and fe
values compare Table V.
10457J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Absorption spectra of Agn clusters
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10. of the outer tetrahedron of the Td form and breaking of one
bond of the inner tetrahedron. Similarly, as in the case of the
Td structure, two dominant almost degenerate resonances at
ϳ4.09 eV calculated for the D2d structure are also slightly
blue-shifted with respect to the measured dominant peak ͓cf.
Fig. 5͑b͔͒. The right-hand side of the measured peak is
broader than the left one which is very steep and actually
excludes the presence of an additional red-shifted resonance.
This means that in the case that the resonance related to the
transitions to the 2 1
B2 state at 3.78 eV were present, it
should have been recorded in this energy interval. Since the
nature of excitations of the 2 1
B2 state is very similar to the
one of the 3 1
B2 state, similar lifetimes are also expected
which means that the nanosecond pulses used in the experi-
ment should have allowed to detect both resonances. The
broadening of the measured intense peak towards the higher
energies does not exclude the presence of an additional reso-
nance which might arise due to the geometric distortion
caused by the surrounding, which will be discussed below.
In order to clarify the blue shifts for calculated locations
of the intense transitions with respect to experimental find-
ings in different environment, either in a matrix or in a he-
lium droplet, as well as to interpret the shape of the dominant
peaks obtained in different experiments,5,29,30
we carried out
the several model calculations at the RPA level of theory.
The purpose was to gain a better understanding of the influ-
ence of the environment on the spectral features and not to
perform quantitative simulation of the environment. ͑i͒ The
Td structure has been distorted in order to lower the symme-
try and ͑ii͒ the geometry changes were introduced involving
formation and breaking of the bonds which transform the Td
into the D2d structure. The following results have been ob-
tained: ͑i͒ Distortion of the Td structure elongating one of the
bond distances from the outer and one from the inner tetra-
hedron by 0.2 Å gives rise to the red shift of all peaks, the
dominant one and less intense ones by 0.3 eV. This is due to
destabilization of the equilibrium Td structures which is re-
flected in the decrease of HOMO-LUMO and HOMO-
LUMOϩk energy gaps leading to the lowering of transition
energies. Moreover a distortion of the Td structure causes
also the splitting of the T-states into the transitions lying very
closely in energies within 0.01 eV. In other words any inter-
action with the environment which elongates the bond dis-
tances and destabilizes equilibrium structures can cause the
red shift of transitions. ͑ii͒ Geometric changes relating the Td
and the D2d structures illustrate the conditions under which
spectroscopic pattern for the D2d structure arises, character-
ized by the resonance at ϳ3.8 eV and by the dominant peaks
located in the energy interval of 4–4.3 eV ͓cf. Fig. 5͑b͔͒.
Deformation of the Td structure achieved by shortening the
distance between two atoms of the outside tetrahedron gives
rise to the spectroscopic pattern shown in Fig. 6͑a͒. It is
characterized by the resonances with moderate intensities lo-
cated at ϳ3.2 and ϳ3.4 eV, by the dominant peak located at
3.84 eV and by two transitions with considerable oscillator
strengths at 4.0 and 4.07 eV. Of course, additional rich fine
structure, due to the lowering of the symmetry, is also
present. In other words, the above described distortion of the
Td structure gives rise to the spectroscopic pattern which is
qualitatively similar to the one obtained for the D2d structure
͓cf. Fig. 6͑a͒ with 5͑b͔͒. Therefore, the influence of the en-
vironment has to be carefully considered in order to assign
structural properties to the measured features.
In fact the spectrum of Ag8 measured in a solid
argon27,28
characterized by a weak transition at 3.18 eV, by
the transition at 3.64 eV with moderate intensity and a domi-
nant peak at 3.92 eV under which two transitions might be
hidden, is in qualitative agreement with the calculated ab-
sorption spectrum for the D2d structure, but it might also
arise by a distortion of the Td structure by Ar-atoms.
The second type of distortion of the Td structure involv-
ing elongation of the bond between two atoms of the inner
tetrahedron gives rise to the red shift of the dominant peak.
Moreover the energy difference between the dominant peak
and the higher energy transition with lower oscillator
strength decreases in comparison with the one obtained for
the stable Td structure ͓cf. Figs. 6͑b͒ and 5͑a͔͒. In fact the
FIG. 6. Optically allowed transition Te in eV and oscillator strengths fe for
distorted Td structures obtained from RPA calculations ͑a͒ by shortening one
distance between two atoms ͑dark circles͒ of outer tetrahedron relating Td
and D2d structures ͑cf. text͒ and ͑b͒ by elongating one distance between two
atoms ͑dark circles͒ of the inner tegrahedron ͑cf. text͒.
10458 J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Bonacˇic´-Koutecky, Veyret, and Mitric´
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209.183.183.254 On: Tue, 02 Dec 2014 03:38:15
11. absorption spectrum obtained by elongating one bond of the
inner tetrahedron of the Td structure presented in Fig. 6͑b͒
indicates that related distortions might be responsible for the
double-peak features in the energy interval of 3.95–4.05
measured by the R2PI in a He-droplet29,30
and in the recent
laser-induced fluorescence experiments on Ag8 in
Ar–matrix.5
In addition our preliminary investigations indi-
cate that the 3 1
T2 state of the Td structure with large inten-
sity might be responsible for the observed fluorescence, since
the geometric relaxation in this state and the return to the
ground state lowers the energy of transition by ϳ0.2 eV cor-
responding to the experimental findings.5
IV. CONCLUSIONS
The absorption spectra of Ag5–8 clusters calculated for
the most stable structures assuming 2D- (Ag5 and Ag6) and
3D-͑Ag7 and Ag8͒ forms are suitable for comparison with
measurements in the gas phase and at low temperature, al-
lowing to assign the structures to the measured features. The
spectroscopic patterns are characterized by a dominant peak
located in the energy interval between 3.5 and 4.1 eV, depen-
dent on the cluster size. Addition of the single atom causes
blue shift of the resonance by 0.2 eV. The weaker resonances
are distributed in a larger energy interval and their location
and intensities are strongly dependent from the individual
structural features. The excitations of d-electrons are not ac-
tively contributing to the intense transitions, but their contri-
bution is of basic importance for the accurate locations of
transitions. The spectra can be interpreted in terms of inter-
ference phenomena typical for molecules. Due to common
structural properties of Ag5–8 and Na5–8 clusters as well as
due to the leading role of the s-electron excitations in both
cases, the spectroscopic patterns exhibit similar features with
exception of pentamers ͑cf. Ref. 22͒. Of course, the transi-
tion energies for silver cluster are blue-shifted by more than
1 eV with respect to those of Nan and quantitative differ-
ences are present.
The experimental findings of the optical response in the
gas phase are not yet available for the cluster sizes consid-
ered in this work. The measurements in a solid matrix5
or a
helium droplet29,30
give rise to the red shifts of resonances in
comparison with the calculated ones for the most stable clus-
ter structures. This is an important finding, in particular con-
cerning the experiments in a He-droplet which is assumed to
be an ultracold and weakly interacting medium for metallic
clusters. The environment clearly destabilizes structures due
to the interaction with the silver atoms and therefore causes a
decrease of HOMO-LUMO and HOMO-LUMOϩk gaps and
consequently a decrease of transition energies as illustrated
in this paper. Interaction with the rare-gas atoms or He-atoms
can also deform the structures with higher symmetry which
might additionally influence features of the spectroscopic
pattern. In fact it has been found that although a large part of
helium is in a superfluid state,35
the friction within a droplet
can lead to a large deformation forming chains from mol-
ecules with large dipole moments.36
The absorption spectra
calculated for the models of geometric distortions of the Td
structure of the Ag8 cluster, presented in this contribution
allow the interpretation of the available experimental find-
ings. According to our results a distorted Td structure of Ag8
is responsible for the measured intense resonance in the
He-droplet28,29
and in the Ar matrix.5
An important aspect of optical properties of silver clus-
ters is their ability to fluoresce, which indicates that the life-
time of the dominant resonance is not extremely short. Our
preliminary calculations of geometry relaxation in the ex-
cited states of Ag8 cluster confirm this finding. Moreover,
this phenomenon can be enhanced through the doping of
silver clusters by oxygen atom which can activate the exci-
tation of d-electrons in Ag atoms37
of the clusters giving rise
to blinking as recently observed.2
The work towards the un-
derstanding of the mechanism responsible for these effects is
in progress.
ACKNOWLEDGMENTS
This work was supported by the Deutsche Forschungs-
gemeinschaft SPP 1007 and SFB 450. The calculations have
been partly carried out at the Konrad-Zuse-Zentrum fu¨r In-
formationstechnik Berlin. The authors thank Professor R. J.
Bartlett for making available STEOM-CCSD code and Pro-
fessor K.-H. Meiwes Broer and his group for communicating
their results prior to publication. The authors also thank Dr. I.
Rabin for stimulating discussions on optical response of Ag8
clusters.
1
P. Fayet, F. Granzer, G. Hegenbart, E. Moisar, B. Pishel, and L. Wo¨ste,
Phys. Rev. Lett. 55, 3002 ͑1985͒; M. Mostafavi, J. L. Marignier, J. Am-
blard, and J. Belloni, Z. Phys. D: At., Mol. Clusters 12, 31 ͑1989͒.
2
L. A. Peyser, A. E. Vinson, A. P. Bartko, and R. M. Dickson, Science 291,
103 ͑2001͒.
3
L. Ko¨nig, I. Rabin, W. Schulze, and G. Ertl, Science 274, 1353 ͑1996͒.
4
C. Felix, C. Sieber, W. Harbich, J. Buttet, I. Rabin, W. Schulze, and G.
Ertl, Chem. Phys. Lett. 313, 105 ͑1999͒; I. Rabin, W. Schulze, G. Ertl, C.
Felix, C. Sieber, W. Harbich, and J. Buttet, Chem. Phys. Lett. 320, 59
͑2000͒.
5
C. Felix, C. Sieber, W. Harbich, J. Buttet, I. Rabin, W. Schulze, and G.
Ertl, Phys. Rev. Lett. 86, 2992 ͑2001͒.
6
V. Bonacˇic´-Koutecky´, L. Cˇ epiva, P. Fantucci, and J. Koutecky´, J. Chem.
Phys. 98, 7981 ͑1993͒.
7
V. Bonacˇic´-Koutecky´, L. Cˇ epiva, P. Fantucci, J. Pittner, and J. Koutecky´,
J. Chem. Phys. 100, 490 ͑1994͒, and references therein.
8
C. Jackschath, I. Rabin, and W. Schulze, Z. Phys. D: At., Mol. Clusters 22,
517 ͑1992͒.
9
G. Alameddin, J. Hunter, D. Cameron, and M. M. Kappes, Chem. Phys.
Lett. 192, 122 ͑1992͒.
10
J. Ho, K. M. Ervin, and W. C. Lineberger, J. Chem. Phys. 93, 6987 ͑1990͒.
11
K. J. Taylor, C. L. Pettiette-Hall, O. Chesnovsky, and R. E. Smalley, J.
Chem. Phys. 96, 3319 ͑1992͒.
12
H. Handschuh, C.-Y. Cha, P. S. Bechthold, G. Gantefo¨r, and W. Eberhardt,
J. Chem. Phys. 102, 6406 ͑1995͒.
13
M. Hartmann, J. Pittner, V. Bonacˇic´-Koutecky´, A. Heidenreich, and J.
Jortner, J. Chem. Phys. 108, 3096 ͑1998͒.
14
M. Hartmann, A. Heidenreich, J. Pittner, V. Bonacˇic´-Koutecky´, and J.
Jortner, J. Phys. Chem. A 102, 4069 ͑1998͒.
15
R. Mitric´, M. Hartmann, B. Stanca, V. Bonacˇic´-Koutecky´, and P. Fantucci,
J. Phys. Chem. A 105, 8892 ͑2001͒.
16
S. Wolf, G. Sommerer, S. Rutz, E. Schreiber, T. Leisner, and L. Wo¨ste,
Phys. Rev. Lett. 74, 4177 ͑1995͒; S. Wolf, Ph.D. thesis, Department of
Physics of the Freie Universita¨t Berlin, Berlin 1997; T. Leisner, S. Vajda,
S. Wolf, L. Wo¨ste, and R. S. Berry, J. Chem. Phys. 111, 1017 ͑1999͒; H.
Hess, S. Kwiat, L. Socaciu, S. Wolf, T. Leisner, and L. Wo¨ste, Appl. Phys.
B: Lasers Opt. 71, 337 ͑2000͒.
17
V. Bonacˇic´-Koutecky´, J. Pittner, M. Boiron, and P. Fantucci, J. Chem.
Phys. 110, 3870 ͑1999͒.
18
B. A. Collings, K. Athanassenas, D. M. Lacombe, D. M. Rayner, and P. A.
Hackett, Chem. Phys. Lett. 227, 490 ͑1994͒.
10459J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Absorption spectra of Agn clusters
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
209.183.183.254 On: Tue, 02 Dec 2014 03:38:15
12. 19
D. M. Rayner, K. Athanassenas, B. A. Collings, St. A. Mitchell, and P. A.
Hackett, in Theory of Atomic and Molecular Clusters ͑Springer Series in
Cluster Physics, edited by J. Jellinek ͑Springer, Berlin, 1999͒, pp. 371–
396.
20
S. Haupt, J. Kaller, D. Schooß, D. Cameron, and M. M. Kappes, Z. Phys.
D: At., Mol. Clusters 40, 331 ͑1997͒.
21
A. Terasaki, S. Minemoto, M. Iseda, and T. Kondow, Eur. Phys. J. D 9,
163 ͑1999͒.
22
C. Ellert, M. Schmitt, G. Schmidt, T. Reiner, and H. Haberland, Phys. Rev.
Lett. 75, 1731 ͑1995͒.
23
V. Bonacˇic´-Koutecky´, J. Pittner, C. Fuchs, P. Fantucci, M. F. Guest, and J.
Koutecky´, J. Chem. Phys. 104, 1427 ͑1996͒ and references therein.
24
V. Bonacˇic´-Koutecky´, P. Fantucci, and J. Koutecky´, Chem. Rev. 91, 1035
͑1991͒; V. Bonacˇic´-Koutecky´, L. Cˇ esˇpiva, P. Fantucci, C. Fuchs, J.
Koutecky´, and J. Pittner, in The Comments on Atomic and Molecular
Physics, 31, no
3–6, 233 ͑1995͒, and references therein.
25
V. Bonacˇic´-Koutecky´, M. M. Kappes, P. Fantucci, and J. Koutecky´, Chem.
Phys. Lett. 170, 26 ͑1990͒; V. Bonacˇic´-Koutecky´, J. Pittner, C. Schench,
M. F. Guest, and J. Koutecky´, J. Chem. Phys. 96, 7938 ͑1992͒; V.
Bonacˇic´-Koutecky´, C. Fuchs, C. Gatti, J. Pittner, and S. Polezzo, Chem.
Phys. Lett. 213, 522 ͑1993͒; V. Bonacˇic´-Koutecky´, J. Pittner, D. Rei-
chardt, P. Fantucci, and J. Koutecky´, in Metal Clusters, Wiley Series in
Theoretical Chemistry, edited by W. Ekart ͑Wiley, Chichester, 1999͒, pp.
29–68.
26
C. Wang, S. Pollack, D. Cammeron, and M. M. Kappes, J. Chem. Phys.
93, 3787 ͑1990͒; C. Wang, S. Pollack, T. Dahlseid, and M. M. Kappes, J.
Chem. Phys. 96, 7931 ͑1992͒.
27
W. Harbich, S. Fedrigo, and J. Buttet, Chem. Phys. Lett. 195, 613 ͑1992͒.
28
S. Fedrigo, W. Harbich, and J. Buttet, Phys. Rev. B 47, 10706 ͑1993͒.
29
C. Felix, C. Sieber, W. Harbich, J. Buttet, I. Rabin, W. Schulze, and G.
Ertl, Phys. Rev. Lett. 86, 2992 ͑2001͒.
30
F. Federmann, K. Hoffmann, N. Quaas, and J. P. Toennies, Eur. Phys. J. D
9, 11 ͑1999͒.
31
Th. Diederich, J. Tiggesba¨umker, and K.-H. Meiwes-Broer, J. Chem.
Phys. ͑to be published͒.
32
J. F. Stanton and R. J. Bartlett, J. Chem. Phys. 98, 7029 ͑1993͒.
33
M. Nooijen and R. J. Bartlett, J. Chem. Phys. 106, 6441 ͑1997͒.
34
A. D. Becke, Phys. Rev. A 98, 3098 ͑1988͒.
35
C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 ͑1988͒.
36
S. Grebenev, J. P. Toennies, and A. F. Vilesov, Science 279, 2083 ͑1998͒.
37
K. Nauta and R. E. Miller, Science 283, 1895 ͑1999͒.
38
V. Bonacˇic´-Koutecky´, M. Boiron, J. Pittner, P. Fantucci, and J. Koutecky´,
Eur. Phys. J. D 9, 183 ͑1999͒.
10460 J. Chem. Phys., Vol. 115, No. 22, 8 December 2001 Bonacˇic´-Koutecky, Veyret, and Mitric´
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
209.183.183.254 On: Tue, 02 Dec 2014 03:38:15
