22364 |Phys. Chem. Chem. Phys., 2014, 16, 22364--22372 This journal is ©the Owner Societies 2014
Cite this: Phys.Chem.Chem.Phys.,
2014, 16, 22364
Vibrational spectra and structures of neutral Si
6
X
clusters (X = Be, B, C, N, O)†
Nguyen Xuan Truong,
a
Marco Savoca,
a
Dan J. Harding,
bc
Andre
´Fielicke
a
and
Otto Dopfer*
a
Neutral silicon clusters doped with first row elements (Si
6
X) have been generated (X = B, C, N, O) and
characterized by infrared–ultraviolet (IR–UV) two-photon resonance-enhanced ionization spectroscopy
(X = C, O) and quantum chemical calculations (X = Be, B, C, N, O, Si). In the near threshold UV photoionization,
the ion signal of specific cluster sizes can be significantly enhanced by resonant excitation with tunable IR
light prior to UV irradiation, allowing for the measurement of the IR spectra of Si
7
,Si
6
C, and Si
6
O clusters.
Structural assignments are achieved with the help of a global optimization procedure using density functional
theory (DFT). The most stable calculated structures show the best agreement between predicted and
measured spectra. The dopant atoms in the Si
6
XclustershaveanegativenetchargeandtheSiatomsactas
electron donors within the clusters. Moreover, the overall structures of the Si
6
X clusters depend strongly on
the nature of the dopant atom, i.e., its size and valency. While in some of the Si
6
X clusters one Si atom
in Si
7
is simply substituted by the dopant atom (X = Be, B, C), other cases exhibit a completely different
geometry (X = N, O). As a general trend, doping of the Si
7
cluster with first-row dopants is predicted to
shift the optically allowed electronic transitions into the visible or even near-IR spectral range due to
symmetry reduction or the radical character of the doped cluster.
I. Introduction
Small silicon clusters have attracted great interest in the current
move towards nanoelectronics.
1
At the nanometer scale, where
every atom counts, structure determination plays a crucial role.
It has been shown that by changingtheclustersizeordopant
species, new stable nanostructures with tailored chemical, optical,
or magnetic properties can be obtained.
2–8
While pure silicon
clusters have been often studied as a test model system for
quantum theories, doped silicon clusters have even more potential
for applications in numerous fields of materials science.
9
Charged
Si-containing clusters have been widely investigated, in part
because they can be easily manipulated and detected using
mass spectrometric methods. Gas-phase neutral clusters are
more difficult to detect and thus less is known about them.
Infrared photodissociation has been used for neutral clusters,
in combination with ionization, to allow for mass spectrometric
analysis of the cluster sizes.
10–12
Besides this, there have been
two major spectroscopic methods used that directly influence the
ionization process of the neutral clusters by absorption of IR
photons, namely, infrared resonance-enhanced multiple photon
ionization (IR–REMPI)
13
and infrared–ultraviolet two-color ioni-
zation (IR–UV2CI).
14
Generally, they are applied to cluster distri-
butions and take advantage of the change in charge state
resulting from photoionization of the cluster. In IR–REMPI,
several hundred IR photons usually need to be absorbed in order
to induce ionization. The method therefore works only for a
limited range of very strongly bound systems like fullerenes and
clusters of certain (refractory) metals and metal compounds.
13,15
The multiple photonic character can also make the interpreta-
tion of IR–REMPI spectra more difficult. Consequently, elaborate
models have been applied to gain more insight into the multiple
photon excitation mechanism.
16,17
IR–UV2CI, on the other hand,
is more widely applicable. In IR–UV2CI experiments, a cluster
first resonantly absorbs one or more IR photons to make a
vibrational transition. It is then post-ionized by absorbing a
single UV photon and finally detected in a mass spectrometer.
The energy of the UV photon is chosen to be close to the
ionization threshold, such that without the IR photons almost
no ion signal is observed. Because only a few IR photons are
involved in an IR–UV2CI measurement, the resulting vibra-
tional spectra are closely related to the linear absorption
spectra and hence much better resolved than typical IR–REMPI
spectra. However, as the ionization energy (IE) of clusters is
a
Institut fu
¨r Optik und Atomare Physik, Technische Universita
¨t Berlin,
Hardenbergstraße 36, D-10623 Berlin, Germany. E-mail: dopfer@physik.tu-berlin.de
b
Institut fu
¨r Physikalische Chemie, Georg-August-Universita
¨tGo
¨ttingen,
Tammannstraße 6, D-37077 Go
¨ttingen, Germany
c
Department of Dynamics at Surfaces, Max-Planck-Institut fu
¨r Biophysikalische Chemie,
Am Faßberg 11, D-37077 Go
¨ttingen, Germany
†Electronic supplementary information (ESI) available. See DOI: 10.1039/
c4cp03414g
Received 31st July 2014,
Accepted 27th August 2014
DOI: 10.1039/c4cp03414g
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usually size-dependent, only selected cluster sizes may be
probed with a given UV photon energy.
Whereas an enormous amount of theoretical work on small
doped silicon clusters is available (e.g., ref. 12, 18–34), only a
few experiments have been reported in the gas phase.
8,14,35–38
By sequential doping of silicon clusters with carbon atoms, i.e.,
for Si
m
C
n
with m+n= 6, we recently observed a systematic
transition from one-dimensional geometries for pure C
6
to
three-dimensional structures for pure Si
6
.
38
In this study, we
present complementary experimental and theoretical results on
silicon clusters doped with first row elements (Si
6
X, with X = Be,
B, C, N, O). Structures of these clusters have been predicted
using DFT-based basin hopping (BH) global optimization.
39,40
Refined DFT calculations have been performed for the most
stable isomers, yielding detailed information such as vibrational
spectra, excitation and ionization energies, HOMO–LUMO gaps,
and natural charge populations. By comparing the IR–UV2CI
spectra of Si
6
C and Si
6
O clusters to the calculations, the corre-
sponding structures are assigned.
II. Experimental and
computational methods
The experimental setup used for IR–UV2CI spectroscopy has
been described in detail elsewhere.
14,38,41
Briefly, Si-rich Si
m
X
n
clusters are produced by laser ablation of a pure silicon rod
within a pulsed flow of He gas (containing 1% CH
4
, 0.7% N
2
,or
0.07% O
2
, depending on the desired dopant) and thermalized
to B100 K in a liquid-nitrogen cooled expansion channel. For
the case of boron, a dual target source with pure He carrier gas
is used.
42
After passing through a skimmer, the neutral Si
m
X
n
clusters are overlapped with counter-propagating IR radiation
from the ‘Free Electron Laser for Infrared eXperiments’ FELIX
and then post-ionized by an unfocused F
2
laser (7.87 eV) in the
extraction zone of a reflectron time-of-flight mass spectrometer.
Fig. 1 shows typical mass spectra of the doped silicon clusters
exposed to either UV only or the IR and UV lasers. The ion signal
intensities depend strongly on the cluster size and the corre-
sponding ionization energies. For clusters of specific sizes, with
an IE close to the photon energy of the ionizing laser, prior
resonant excitation with IR photons from a pulse of FELIX may
enhance the ionization efficiency (Fig. 1d). Therefore, the
enhancement of the ion yield as a function of the IR wavelength
largely reflects the vibrational absorption spectrum of the
original neutral cluster. Further details of the IR–UV ionization
mechanism are provided in ref. 14 and 41.
The reported IR spectra are obtained from the relative
ionization enhancement determined by the difference of the ion
IR
on
and IR
off
signals normalized with the IR
off
signal and the IR
photon flux. The observed widths of the bands of 15–45 cm
1
arise from a combination of unresolved rotational structure,
sequence hot band transitions involving low-frequency modes,
the FELIX bandwidth (ca. 0.5–1% full width at half maximum
(FWHM) of the central wavelength), and possibly the multiple
photon absorption process.
Quantum chemical calculations have been performed to aid
in the assignment of the cluster structures, to give more insight
into their physical and chemical properties, and to serve as a
guide for future experiments. By comparing the measured IR
spectrum with the calculated spectra of the low lying isomers,
the geometric structure of the observed cluster can be deter-
mined. Furthermore, an estimate of the IE of the clusters of
interest is crucial for choosing the appropriate UV photon
energy in the IR–UV2CI experiments.
For each cluster size, many geometric configurations are
possible. In an effort to thoroughly explore these possibilities,
we have employed the basin hopping technique,
40,43–46
which has proven to be an effective stochastic global search
algorithm. Details of our implementation have been described
elsewhere.
39
Basically, there are two main steps. First, for each
cluster thousands of structures are evaluated in terms of the
total energy by a BH algorithm coupled with DFT calculations at
the RI-BP86/def-SVP level using Turbomole V6.3.1.
47–49
The BH
uses a Monte Carlo (MC) simulation at a constant temperature
Fig. 1 Mass spectra (black lines) of doped silicon clusters Si
n
X
m
(n= 5–8,
m= 1–2, and X = B, C, N, O) obtained by ionization with an F
2
laser.
The Si
6
X clusters are marked by arrows. For the case of oxygen (d), an
additional mass spectrum (red line) is included to highlight the enhance-
ment of the Si
6
O ion yield with the presence of IR radiation at 865 cm
1
.
For each group of signals, the leading mass peak corresponds to the all-
28
Si
isotopologue, while most of the adjacent peaks are assigned to other
Si isotopologues.
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of 1200 K and consists of 1500 MC steps. New structures are
generated with the significant structure variant using single-
atom moves, followed by all-atom displacements at every five
steps.
39
The self-consistent field (SCF) convergence criterium of
10
5
hartree on the total energy was chosen. The relatively low
computational cost enables the BH approach to explore a large
number of test structures. Second, the structures of interest,
e.g., the first 10–15 different low-energy isomers, are refined with
different functionals, i.e., the B3LYP/cc-pVTZ, TPSS/def2TZVP,
and BP86/SVP levels, with SCF convergence conditions of better
than 10
8
hartree and the resolution-of-the-identity approxi-
mation as implemented in the Gaussian 09 package.
50
We note
that these methods have proven reliable for silicon-containing
clusters reported previously.
14,38
At such levels, detailed infor-
mation about the linear IR absorption spectra, ionization
energies, and natural bond orbital populations is obtained.
If not stated otherwise, all relative energies include zero-
point vibrational energy corrections except for the vertical
ionization energy (VIE) values. The electronic ground state of
the considered clusters has the lowest possible spin multi-
plicity. The electronic transitions of the ground state structures
are calculated at the CAM-B3LYP/cc-pVTZ level
50
to explore
their electronic structure. To facilitate convenient comparison
with the experimental spectra, the theoretical IR stick absorp-
tion spectra are convoluted with a Gaussian line profile using
a FWHM of 15 cm
1
. The reported vibrational frequencies are
unscaled.
III. Results and discussion
A. Predicted structures
The five lowest-energy isomers of the Si
6
X clusters identified
using the global optimization procedure described in Section II
are shown in Fig. 2. The energetic, vibrational, and electronic
parameters of the most stable isomers are listed in Tables 1–3,
respectively. We note that the three functionals predict the
same ground state structures while for higher-energy isomers
the energetic ordering is only slightly changed. Therefore, the
optimized geometric and vibrational parameters obtained
with the B3LYP/cc-pVTZ level will be used in the following
discussion.
Interestingly, for the most stable configurations of Si
6
Be
(
1
A
1
), Si
6
B(
2
A0), and Si
6
C(
1
A
1
), the dopant atom simply replaces
one Si atom of pure Si
7
(D
5h
), leading to a reduction of the
molecular symmetry. On the contrary, completely new struc-
tures are formed for Si
6
N(
2
A
2
) and Si
6
O(
1
A). In most cases, the
dopant atom prefers a location surrounded by as many Si atoms
as possible. The Si
6
O isomers are, however, most stable with an
O atom on the edge of a low-energy isomer of the Si
6
cluster.
Our numerical results are in good agreement with earlier
calculations of Si
6
O
24
and Si
6
B.
51
Furthermore, to the best of
our knowledge, we have found a new lowest-energy structure
for the Si
6
N cluster (d0, Fig. 2), which is significantly lower
in energy (0.49 eV at the B3LYP/cc-pVTZ level) than the
best structure reported previously (d2, Fig. 2 and, e.g., ref. 52).
While the d2 structure is formed by the substitution of a
Si atom, our new d0 structure has a completely different
geometry with only one Si atom attached to the divalent
N atom, leading to an isocyanide-type linear configuration.
Calculations with different methods, e.g., genetic algorithms,
53
functionals, and basis sets (not shown here) support our finding.
If one only considers the substitutional isomers of Si
7
, there
are two possible places to exchange a Si atom for a dopant
atom, namely, in the ring and at the apexes of the bipyramid.
When located in the ring, Si
6
Be, Si
6
B, and Si
6
N form C
2v
symmetry isomers (a0,b4, and d2, Fig. 2), while Si
6
C has C
s
symmetry (c3, Fig. 2). When the dopant atom is placed at an
apex of the bipyramid, Si
6
C(c0, Fig. 2) and Si
6
N(E
rel
= 1.69 eV,
not shown) form highly symmetrical configurations (C
5v
), whereas
the other clusters form lower symmetry C
s
structures. The shortest
Si–X bond lengths (in Å) in the most stable Si
6
X structures are
2.16 (Be), 2.08 (B), 2.05 (C), 1.58 (N), and 1.66 (O).
B. Ionization energetics
The value of the ionization energy of a cluster compared to the
UV photon energy used to finally ionize the cluster determines the
success of an IR–UV2CI measurement. Experiments on neutral Si
clusters suggest that the IE has to be within 0.1–0.2 eV of the UV
photon energy to obtain sufficient enhancement in the ionization
efficiency by resonant absorption of IR photons.
14,41
This also
explains that in case of the Si
m
C
n
(m+n= 6) clusters no effect on
the ionization efficiency of Si
3
C
3
could be observed due to its high
IE (9.12 eV) compared to the photon energy of 7.87 eV used for
ionization.
38
The calculated adiabatic and vertical ionization
energies and binding energies of the most stable Si
6
Xclusters
with different functionals and basis sets are shown in Table 1.
Note that our calculated values for Si
7
are in excellent agreement
with experiments.
54,55
Except for the case of Si
6
N with a calculated VIE of B7.5 eV,
the IEs of other clusters are close to the F
2
laser photon energy
of 7.87 eV, making them promising candidates for IR–UV2CI
spectroscopy using such a UV laser. Indeed, experimental
IR–UV2CI spectra have been successfully recorded for Si
6
C
and Si
6
O and are shown in Fig. 3. Si
6
N may need a different
experimental approach, as its predicted IE is too high for using
an ArF laser (6.4 eV) and no other simple laser source exists in
this UV range.
Finally, the binding energy (BE) of the dopant atom to the Si
6
cluster varies drastically between 2.2 and 8.7 eV depending on
the nature of the dopant. While the BEs for the electropositive
Be and B dopant atoms are similar or lower than that of Si,
those of the more electronegative C, N, and O atoms are strikingly
high (B8 eV).
C. Electronic properties
Mulliken populations are not very suitable for an analysis of the
charge transfer in silicon clusters.
56
We have therefore used
natural bond orbital concepts
57
to analyze the most stable Si
6
X
structures. The natural electronic configurations and natural
populations are detailed in Table S1 in ESI.†For all of the
dopants, the net atomic population is negative (0.166 e (Be),
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1.449 e (B), 1.884 e (C), 1.673 e (N), and 1.241 e (O)),
hinting at the role as electron donors of Si atoms and the ionic
characteristics of the Si–X bonding. This has also been
observed for a number of silicon-containing clusters in earlier
reports
56,58–60
and is attributed to the low electronegativity of Si.
In terms of the natural electronic configurations, most of the
dopants considered show an idealized promoted configuration
for sp
3
hybridization, which is most preferable for Si atoms,
except for the Be atom which has the valence configuration
2s
0.66
2p
1.45
.
Excited states of the most stable Si
6
X structures are calcu-
lated with the TD-DFT method (CAM-B3LYP/cc-pVTZ) as listed
in Table 3 for the first three vertical electronic transitions along
with the HOMO–LUMO gaps. The corresponding HOMO and
LUMO orbitals are shown in Fig. 4. While the HOMO–LUMO
gaps are comparable for all Si
6
X, their first electronic transitions
show a clear trend oscillating between closed- and open-shell
clusters, i.e., low excitation energies (0.5–1.2 eV) for open-shell
vs. high values (42.0 eV) for closed-shell systems. Interestingly,
Table 1 Vertical ionization energy (VIE), adiabatic ionization energy (AIE),
and binding energy (BE) of the lowest-energy Si
6
X isomers (a0–f0)
calculated at the B3LYP/cc-pVTZ, TPSS/def2TZVP, and BP86/SVP levels
(separated by semicolons, left to right, respectively)
Cluster VIE [eV] AIE [eV] BE
a
[eV]
Si
6
Be 7.96; 7.54; 7.80 7.41; 7.37; 7.61 2.25; 2.59; 2.50
Si
6
B 7.96; 8.22; 8.36 7.59; 7.75; 7.84 4.41; 4.76; 4.98
Si
6
C 7.85; 7.82; 8.07 7.55; 7.66; 7.85 7.53; 7.94; 8.26
Si
6
N 7.46; 7.57; 7.72 6.75; 6.93; 7.02 7.40; 5.31; 7.66
Si
6
O 7.99; 8.02; 8.19 7.71; 7.74; 7.93 8.33; 8.69; 8.69
Si
7
7.98; 7.97; 8.23
b
7.68; 7.71; 7.93
b
4.84; 5.58; 5.40
a
The binding energy of the Si
6
X cluster is given as BE = E(Si
6
)+E(X)
E(Si
6
X).
b
Experimental value is B7.9 eV.
54,55
Fig. 2 Optimized geometries of the first five low-energy Si
6
X isomers (with X = Be, B, C, N, O, Si) found with the global optimization algorithm.
Point group symmetries and electronic states are given in parentheses. The relative energies E
rel
(in eV) obtained at the B3LYP/cc-pVTZ, TPSS/def2TZVP,
and BP86/SVP levels (separated by semicolons, left to right, respectively) are also provided for comparison. Atomic coordinates are available in the ESI.†
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the HOMO–LUMO gaps drastically overestimate the energy of the
lowest electronic transitions. High-symmetry structures exhibit
several forbidden transitions. For instance, the first optically
active state for Si
7
is the seventeenth excited state at 3.35 eV
with an oscillator strength f= 0.0082.
At the first glance, the spatial distributions of the HOMO
and LUMO are very different for each cluster. Furthermore, the
HOMOs are localized at the Si atoms and not on the dopant.
Clusters with similar topological geometries show similar
HOMOs, i.e.,Si
6
Be, Si
6
B, Si
6
C, and Si
7
. For Si
6
Be, Si
6
C, and
Si
7
, the LUMOs are very similar, although the localization of the
dopant atom within the cluster is different.
D. Vibrational spectra
Fig. 3 shows the calculated vibrational spectra of the most
stable isomers of Si
6
X (X = Si, C, O, Be, B, N), which are detailed
in Table 2. Experimental spectra are available for Si
7
,Si
6
C, and
Si
6
O, allowing for a comparison with the spectra of the pre-
dicted isomers (Fig. 3a–c). In all three cases, the spectrum of the
lowest-energy isomer shows the best agreement to the experi-
mental one (see Fig. S1–S5 in ESI†for further IR spectra of
higher-energy isomers). The result for Si
7
published earlier
14
is
recalled here for completeness. The Si
7
spectrum shows a single
band at 417 cm
1
that has been assigned to the intense doubly
degenerate e
1
0mode of the highly symmetric D
5h
pentagonal
bipyramidal structure.
Replacing one Si by a C atom in pure Si
7
significantly
changes the IR–UV2CI spectrum (Fig. 3b). While the C-rich
clusters prefer chain-like geometries, e.g., SiC
6
,
61
stable Si-rich
clusters have 3D structures. The predicted c0 structure of Si
6
C
has C
5v
symmetry, which is deformed from the D
5h
structure of
Si
7
due to the greater strength of the C–Si bond cf. to Si–Si. The
e
1
0mode that dominates the spectrum of Si
7
has its counterpart in
the e
1
mode for Si
6
C. However, in Si
6
C this mode is shifted to higher
frequency, as it involves the lighter, but stronger bound C atom, and
coincides with an intense a
1
mode that is not IR active in Si
7
(cf.
Table 2). Together they can be assigned to the experimental band B.
Similarly, the experimentally observedbandAalsocorrespondsto
an a
1
mode that is not IR active in the pure Si
7
cluster. The band C
at 664 cm
1
cannot be explained by the fundamental modes of the
c0 isomer, nor by any of the ten Si
6
C isomers found within 1 eV in
energy, suggesting that the band may be due to a combination band
of the a
1
mode at 438 cm
1
with the low frequency modes at
231 cm
1
(e
1
) or 261 cm
1
(a
1
). The 3D structure of the most stable
Si
6
C isomer is in good agreement with our earlier findings for Si
m
C
n
(m+n= 6), where the first C atom does not change the topology of
the geometry of the pure Si
6
cluster.
38
The spectrum of Si
6
O is dominated by an intense absorption
band (G) centered at about 853 cm
1
. Comparison with the
calculated spectrum of the e0 isomer shows that the band is
due to the symmetric stretch mode of the Si–O–Si bridge
Table 2 Vibrational frequencies (in cm
1
) of the most stable Si
6
X isomers shown in Fig. 2 calculated at the B3LYP/cc-pVTZ level
Si
6
Be (C
2v
)Si
6
B(C
s
)Si
6
C(C
5v
)Si
6
N(C
2v
)Si
6
O(C
1
)Si
7
(D
5h
)
129 (0.6, a
1
) 32 (0.6, a00 ) 105 (0, e
2
) 71 (0.6, b
1
) 75 (0.3, a) 159 (0, e
2
00 )
139 (0, a
2
) 109 (0.1, a0) 231 (4, e
1
) 74 (1.0, b
2
) 120 (1, a) 216 (0.04, e
1
0)
191 (0.3, b
1
) 186 (1.0, a00 ) 261 (2, a
1
) 157 (0.1, a
1
) 192 (0.4, a) 217 (1, a
2
00 )
230 (6, b
2
) 212 (9, a00 ) 274 (0, e
2
) 204 (11, b
1
) 234 (0.5, a) 271 (0, e
2
0)
286 (0.2, b
2
) 220 (3, a00 ) 355 (0.6, e
1
) 234 (6, b
2
) 240 (0.7, a) 320 (0, e
1
00 )
289 (2, b
1
) 256 (0.1, a00 ) 421 (0, e
2
) 236 (3, b
1
) 272 (0.2, a) 333 (0, e
2
0)
310 (2, a
1
) 282 (0.5, a0) 432
A
(10, a
1
) 264 (0, a
1
) 285 (3, a) 350 (0, a
1
0)
331 (3, a
1
) 286 (2, a0) 552
B
(50, e
1
) 291 (5, b
2
) 316 (8, a) 404 (31, e
1
0)
336 (0, a
2
) 347 (0.1, a00 ) 553
B
(69, a
1
) 304 (0.01, a
1
) 363 (3, a) 421 (0, a
1
0)
356 (1, a
1
) 386 (0.1, a0) 319 (0, a
2
) 376 (11, a)
408 (3, b
1
) 416 (13, a0) 403 (1, b
1
) 403 (2, a)
419 (13, b
2
) 451 (0.2, a00 ) 415 (4, a
1
) 422
D
(8, a)
424 (15, a
1
) 519 (33, a0) 471 (0.2, b
2
) 466
E
(27, a)
598 (8, a
1
) 646 (29, a0) 665 (26, a
1
) 572
F
(15, a)
617 (0.04, b
2
) 652 (28, a00 ) 1350 (330, a
1
) 855
G
(80, a)
IR intensities (in km mol
1
) and the symmetries of the modes are listed in parentheses. A–G: assigned bands determined by our experiments as
shown in Fig. 3.
Table 3 The first three electronic transitions and HOMO–LUMO gaps for
the ground state structures of Si
6
X calculated with the CAM-B3LYP/cc-
pVTZ method. The respective oscillator strengths f(10
3
) are given in
parentheses. For the open-shell Si
6
BandSi
6
N, the HOMO–LUMO gaps for
a/bspin components are indicated by up/down arrows
Cluster Transition
energy [eV] HOMO–LUMO
gap [eV]
Si
6
Be (a0,C
2v
,
1
A
1
) 2.27 (0.0) 5.24
2.40 (5.7)
2.60 (0.4)
Si
6
B(b0,C
s
,
2
A0) 0.52 (0.1) 6.45m
1.10 (0.1) 3.83k
1.25 (1.5)
Si
6
C(c0,C
5v
,
1
A
1
) 2.62 (0.0) 5.64
3.37 (30.6)
3.48 (0.0)
Si
6
N(d0,C
2v
,
2
A
2
) 1.15 (0.0) 5.59m
1.17 (0.7) 4.33k
1.79 (9.7)
Si
6
O(e0,C
1
,
1
A) 2.40 (0.9) 5.43
2.49 (3.6)
2.66 (11.8)
Si
7
(f0,D
5h
,
1
A
1
0) 2.13 (0.0) 5.37
2.19 (0.0)
2.31 (0.0)
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predicted at 855 cm
1
. The asymmetric stretch vibration of the
Si–O–Si unit is calculated at 572 cm
1
and can be assigned to
the band F observed at 554 cm
1
.
For Si
6
Be, Si
6
B, and Si
6
N, no experimental IR spectra have
been obtained so far, but the calculated spectra are included for
completeness. We refrain from a more detailed discussion
here, but only point to the intense high-frequency band pre-
dicted for Si
6
N (1350 cm
1
). This vibration is characteristic of
the isolated silaisonitrile (–NQSi) group and can be compared
to the Si–N stretch in H–NQSi found at B1200 cm
1
.
62
IV. Conclusions
In this study, neutral silicon clusters doped with the first row
elements (B, C, N, O) have been generated in a laser vaporiza-
tion source and characterized using time-of-flight mass spectro-
metry. The vibrational spectra of the C- and O-doped clusters
have been measured using IR–UV2CI spectroscopy. The low
energy structures of the Si
6
X clusters doped with the first row
elements Be–O have been investigated using DFT calculations.
Candidate structures have been found using a DFT-based basin
hopping global optimization scheme. In general, the most
stable Si
6
X structures and their IR spectra strongly depend on
the dopant atom due to the effects arising from different size,
mass, valency, and force fields. The calculations show that
clusters doped with Be, B, or C favor structures based on the
Si
7
pentagonal bipyramid, with substitution of a single Si atom
in either the ring (Be) or at an apex (B, C). Si
6
N and Si
6
O,
however, exhibit completely different structures. By comparison
between the measured IR spectra and the predicted ones,
Fig. 3 IR spectra of the most stable isomers of Si
6
X clusters (X = Si, C, O,
Be, B, N) calculated at the B3LYP/cc-pVTZ level. The experimental IR
spectra available for Si
7
(from ref. 14), Si
6
C, and Si
6
O are obtained by the
IR–UV2CI technique (blue dots: original data; red lines: three-point
adjacent average). The measured IR intensities are given on a linear scale
in arbitrary units. The experimental line positions (in cm
1
) are 438 (A), 566 (B),
664 (C), 446 (D), 474 (E), 554 (F), and 853 (G).
Fig. 4 HOMO and LUMO orbitals of the ground state structures of Si
6
X
shown in Fig. 2 (a0–f0). The structural orientations are adjusted for a clear
illustration of the orbitals.
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the structures of Si
6
C and Si
6
O have been determined. We find
good agreement between the experimental and the calculated
spectra of the lowest-energy isomers. The calculated ionization
energies also appear to be reliable, providing useful information
for future experiments on, e.g.,BandNdopedclusters.Charge
analysis with the natural bond orbital method shows that in all
casesSiatomsactaselectrondonorswithintheclusters.Asa
general trend, doping of the Si
7
cluster with first-row dopants is
predicted to shift the optically allowed electronic transitions into
the visible range, which is partly ascribed to symmetry reduction or
the radical character of the doped cluster. In particular, the open-
shell Si
6
B and Si
6
N clusters have predicted absorptions in the
near-IR spectral range. These theoretical predictions will guide
our efforts in recording optical spectra of these doped silicon
clusters. In addition, experiments with the dual-target laser ablation
source are envisaged to record vibrational spectra of Si
n
B.
Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft
within the research unit FOR 1282 (DO 729/5, FI 893/4). We
gratefully acknowledge the support of the Stichting voor Funda-
menteel Onderzoek der Materie (FOM) in providing beam time of
FELIX and the FELIX staff for their skillful assistance, in particular,
B. Redlich and A. F. G. van der Meer. The research leading to these
results has received funding from the European Community’s
Seventh Framework Programme (FP7/2007–2013) under Grant
Agreement No. 226716. We would like to acknowledge the colla-
boration with E. Janssens and P. Lievens using the dual target laser
ablation cluster source. We thank C. Kerpal for fruitful discussion
of the basin hopping technique.
References
1 V. Kumar, Nanosilicon, Elsevier Ltd, Oxford, 2007.
2 H. F. Li, X. Y. Kuang and H. Q. Wang, Probing the structural
and electronic properties of lanthanide-metal-doped silicon
clusters: M@Si
6
(M = Pr, Gd, Ho), Phys. Lett. A, 2011, 375,
2836–2844.
3 S. Zhan, B. Li and J. Yang, Study of aluminum-doped silicon
clusters, Phys. B, 2007, 387, 421–429.
4 A. Titov, F. Michelini, L. Raymond, E. Kulatov and Y. A.
Uspenskii, Gap narrowing in charged and doped silicon
nanoclusters, Phys. Rev. B: Condens. Matter Mater. Phys.,
2010, 82, 235419.
5 P. Karamanis, R. Marchal, P. Carbonniere and C. Pouchan,
Doping-enhanced hyperpolarizabilities of silicon clusters:
A global ab initio and density functional theory study of
Si
10
(Li, Na, K)
n
(n= 1, 2) clusters, J. Chem. Phys., 2011,
135, 044511.
6 L. Ma, J. Wang and G. Wang, Site-specific analysis of dipole
polarizabilities of heterogeneous systems: Iron-doped Si
n
(n= 1–14) clusters, J. Chem. Phys., 2013, 138, 094304.
7 V. T. Ngan, E. Janssens, P. Claes, J. T. Lyon, A. Fielicke,
M. T. Nguyen and P. Lievens, High Magnetic Moments in
Manganese-Doped Silicon Clusters, Chem. – Eur. J., 2012, 18,
15788–15793.
8 J. De Haeck, S. Bhattacharyya, H. T. Le, D. Debruyne, N. M.
Tam, V. T. Ngan, E. Janssens, M. T. Nguyen and P. Lievens,
Ionization energies and structures of lithium doped silicon
clusters, Phys. Chem. Chem. Phys., 2012, 14, 8542–8550.
9 M. Jarrold, Nanosurface Chemistry on Size-Selected Silicon
Clusters, Science, 1991, 252, 1085–1092.
10 M. B. Knickelbein, The infrared photodissociation spectra
of Fe
n
(CH
3
OH)
m
complexes and their deuterated analogs
near 10m,J. Chem. Phys., 1996, 104, 3517–3525.
11 P. Gruene, D. M. Rayner, B. Redlich, A. F. G. van der Meer,
J. T. Lyon, G. Meijer and A. Fielicke, Structures of neutral
Au
7
,Au
19
, and Au
20
clusters in the gas phase, Science, 2008,
321, 674–676.
12 M. Haertelt, J. T. Lyon, P. Claes, J. de Haeck, P. Lievens and
A. Fielicke, Gas-phase structures of neutral silicon clusters,
J. Chem. Phys., 2012, 136, 064301.
13 G. von Helden, D. van Heijnsbergen and G. Meijer, Reso-
nant ionization using IR light: A new tool to study the
spectroscopy and dynamics of gas-phase molecules and
clusters, J. Phys. Chem. A, 2003, 107, 1671–1688.
14 A. Fielicke, J. T. Lyon, M. Haertelt, G. Meijer, P. Claes,
J. de Haeck and P. Lievens, Vibrational spectroscopy of
neutral silicon clusters via far-IR-VUV two color ionization,
J. Chem. Phys., 2009, 131, 171105.
15 V. J. F. Lapoutre, M. Haertelt, G. Meijer, A. Fielicke and
J. M. Bakker, Communication: IR spectroscopy of neutral
transition metal clusters through thermionic emission,
J. Chem. Phys., 2013, 139, 121101.
16 A. Bekkerman, E. Kolodney, G. von Helden, B. Sartakov,
D. van Heijnsbergen and G. Meijer, Infrared multiphoton
ionization of superhot C
60
: Experiment and model calcula-
tions, J. Chem. Phys., 2006, 124, 184312.
17 F. Calvo and P. Parneix, Amplification of anharmonicities in
multiphoton vibrational action spectra, ChemPhysChem,
2012, 13, 212–220.
18 G. Forte, G. G. N. Angilella, V. Pittala, N. H. March and
R. Pucci, Neutral and cationic free-space oxygen-silicon
clusters SiO
n
(1 onr6), and possible relevance to crystals
of SiO
2
under pressure, Phys. Lett. A, 2012, 376, 476–479.
19 H. Ning, H. Fan and J. Yang, Probing the electronic
structures and properties of neutral and charged CaSi
n
(n= 2–10) clusters using Gaussian-3 theory, Comput. Theor.
Chem., 2011, 976, 141–147.
20 M. Jadraque and M. Martin, Charge-Transfer Processes in
the Assembly of Si
n
O
m
Neutral Clusters, J. Comput. Chem.,
2011, 32, 3497–3504.
21 Y. S. Wang and S. D. Chao, Structures and Energetics of
Neutral and Ionic Silicon-Germanium Clusters: Density
Functional Theory and Coupled Cluster Studies, J. Phys.
Chem. A, 2011, 115, 1472–1485.
22 H. Fan, Z. Ren, J. Yang, D. Hao and Q. Zhang, Study on
structures and electronic properties of neutral and charged
MgSi
n
(n= 2–10) clusters with a Gaussian-3 theory,
THEOCHEM, 2010, 958, 26–32.
PCCP Paper
Published on 16 September 2014. Downloaded by TU Berlin - Universitaetsbibl on 24/02/2016 15:55:14.
View Article Online
This journal is ©the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16, 22364--22372 | 22371
23 Y. H. Zhu, B. X. Li, F. S. Liang and J. Xu, Theoretical Study of
Neutral and Ionic Si
n
O(n= 1–13) Clusters, Int. J. Mod. Phys.
B, 2009, 23, 3527–3536.
24 M. C. Caputo, O. Ona and M. B. Ferraro, Theoretical
prediction of atomic and electronic structure of neutral
Si
6
O
m
(m= 1–11) clusters, J. Chem. Phys., 2009, 130, 134115.
25 Y. Z. Lan and Y. L. Feng, Comparative study on the geometric
and energetic properties, absorption spectra, and polarizabilities
of charged and neutral Cu@Si
n
clusters (n= 9–14), Phys. Rev. A:
At., Mol., Opt. Phys., 2009, 79, 033201.
26 D. Hossain, F. Hagelberg, C. U. Pittman, Jr. and S. Saebo,
Structures and stabilities of clusters of Si
12
,Si
18
, and Si
20
containing endohedral charged and neutral atomic species,
J. Phys. Chem. C, 2007, 111, 13864–13871.
27 R.Zhao,Z.Ren,P.Guo,J.Bai,C.ZhangandJ.Han,Geometries
and electronic properties of the neutral and charged rare earth
Yb-doped Si
n
(n= 1–6) clusters: A relativistic density functional
investigation, J. Phys. Chem. A, 2006, 110, 4071–4079.
28 C. Sporea, F. Rabilloud, A. R. Allouche and M. Frecon, Ab
initio study of neutral and charged Si
n
Na
p+
(nr6, pr2)
clusters, J. Phys. Chem. A, 2006, 110, 1046–1051.
29 B. X. Li, Stability of medium-sized neutral and charged
silicon clusters, Phys. Rev. B: Condens. Matter Mater. Phys.,
2005, 71, 235311.
30 A. Sieck, T. Frauenheim and K. Jackson, Shape transition of
medium-sized neutral silicon clusters, Phys. Status
Solidi B, 2003, 240, 537–548.
31 C. Xiao, F. Hagelberg and W. Lester, Geometric, energetic,
and bonding properties of neutral and charged copper-
doped silicon clusters, Phys. Rev. B: Condens. Matter Mater.
Phys., 2002, 66, 075425.
32 S. Nayak, B. Rao, S. Khanna and P. Jena, Atomic and
electronic structure of neutral and charged Si
n
O
m
clusters,
J. Chem. Phys., 1998, 109, 1245–1250.
33 M. Gomei, R. Kishi, A. Nakajima, S. Iwata and K. Kaya,
Ab initio MO studies of neutral and anionic SiC
n
clusters
(n= 2–5), J. Chem. Phys., 1997, 107, 10051–10061.
34 S. Wei, R. Barnett and U. Landman, Energetics and struc-
tures of neutral and charged Si
n
(nr10) and sodium-doped
Si
n
Na clusters, Phys. Rev. B: Condens. Matter Mater. Phys.,
1997, 55, 7935–7944.
35 K. Koyasu, M. Akutsu, M. Mitsui and A. Nakajima, Selective
formation of MSi
16
(M = Sc, Ti, and V), J. Am. Chem. Soc.,
2005, 127, 4998–4999.
36 K. Koyasu, J. Atobe, M. Akutsu, M. Mitsui and A. Nakajima,
Electronic and geometric stabilities of clusters with transition
metal encapsulated by silicon, J. Phys. Chem. A, 2007, 111, 42–49.
37 P. Claes, V. T. Ngan, M. Haertelt, J. T. Lyon, A. Fielicke,
M. T. Nguyen, P. Lievens and E. Janssens, The structures of
neutral transition metal doped silicon clusters, Si
n
X(n=6–9;
X=V,Mn),J. Chem. Phys., 2013, 138, 194301.
38 M. Savoca, A. Lagutschenkov, J. Langer, D. J. Harding,
A. Fielicke and O. Dopfer, Vibrational Spectra and Struc-
tures of Neutral Si
m
C
n
Clusters (m+n= 6): Sequential
Doping of Silicon Clusters with Carbon Atoms, J. Phys.
Chem. A, 2013, 117, 1158–1163.
39 D. J. Harding, C. Kerpal, G. Meijer and A. Fielicke, Unusual
Bonding in Platinum Carbido Clusters, J. Phys. Chem. Lett.,
2013, 4, 892–896.
40 R. Gehrke and K. Reuter, Assessing the efficiency of first-
principles basin-hopping sampling, Phys. Rev. B: Condens.
Matter Mater. Phys., 2009, 79, 085412.
41 M. Haertelt, A. Fielicke, G. Meijer, K. Kwapien, M. Sierka
and J. Sauer, Structure determination of neutral MgO
clusters-hexagonal nanotubes and cages, Phys. Chem. Chem.
Phys., 2012, 14, 2849–2856.
42 W. Bouwen, P. Thoen, F. Vanhoutte, S. Bouckaert, F. Despa,
H. Weidele, R. Silverans and P. Lievens, Production of
bimetallic clusters by a dual-target dual-laser vaporization
source, Rev. Sci. Instrum., 2000, 71, 54–58.
43 D. Wales and J. Doye, Global optimization by basin-hopping
and the lowest energy structures of Lennard-Jones clusters
containing up to 110 atoms, J. Phys. Chem. A, 1997, 101,
5111–5116.
44 M. Iwamatsu and Y. Okabe, Basin hopping with occasional
jumping, Chem. Phys. Lett., 2004, 399, 396–400.
45 L. Zhan, J. Z. Y. Chen and W. K. Liu, Monte Carlo basin
paving: An improved global optimization method, Phys. Rev.
E: Stat., Nonlinear, Soft Matter Phys., 2006, 73, 015701.
46 M. T. Oakley, R. L. Johnston and D. J. Wales, Symmetrisa-
tion schemes for global optimisation of atomic clusters,
Phys. Chem. Chem. Phys., 2013, 15, 3965–3976.
47 A. D. Becke, Density-functional exchange-energy approxi-
mation with correct asymptotic behavior, Phys. Rev. A: At.,
Mol., Opt. Phys., 1988, 38, 3098–3100.
48 J. P. Perdew, Density-functional approximation for the
correlation energy of the inhomogeneous electron gas,
Phys. Rev. B: Condens. Matter Mater. Phys., 1986, 33,
8822–8824.
49 F. Weigend, M. Haser, H. Patzelt and R. Ahlrichs, RI-MP2:
optimized auxiliary basis sets and demonstration of effi-
ciency, Chem. Phys. Lett., 1998, 294, 143–152.
50 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria,
M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone,
B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato,
X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng,
J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda,
J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao,
H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta,
F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin,
V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari,
A.Rendell,J.C.Burant,S.S.Iyengar,J.Tomasi,M.Cossi,
N.Rega,J.M.Millam,M.Klene,J.E.Knox,J.B.Cross,
V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E.
Stratmann,O.Yazyev,A.J.Austin,R.Cammi,C.Pomelli,
J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski,
G.A.Voth,P.Salvador,J.J.Dannenberg,S.Dapprich,A.D.
Daniels, O
¨. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski
and D. J. Fox, Gaussian 09 revision a.1, Gaussian Inc.,
Wallingford, CT, 2009.
51 N. M. Tam, T. B. Tai and M. T. Nguyen, Thermochemical
Parameters and Growth Mechanism of the Boron-Doped
Paper PCCP
Published on 16 September 2014. Downloaded by TU Berlin - Universitaetsbibl on 24/02/2016 15:55:14.
View Article Online
22372 |Phys. Chem. Chem. Phys., 2014, 16, 22364--22372 This journal is ©the Owner Societies 2014
Silicon Clusters, Si
n
B
q
with n= 1–10 and q=1, 0, +1,
J. Phys. Chem. C, 2012, 116, 20086–20098.
52 J. Zh. Ye and B. X. Li, First-principles study on mixed Si
m
N
n
(m+n= 2–9) clusters, Comput. Theor. Chem., 2012, 992,
84–91.
53 D. E. Goldberg, Genetic algorithms in search, optimization, and
machine learning, Addison-Wesley Professional, New York,
1989.
54 O. Kostko, S. R. Leone, M. A. Duncan and M. Ahmed,
Determination of ionization energies of small silicon clus-
ters with vacuum ultraviolet radiation, J. Phys. Chem. A,
2010, 114, 3176–3181.
55 K. Fuke, K. Tsukamoto, F. Misaizu and M. Sanekata,
Near threshold photoionization of silicon clusters in the
248–146 nm region: Ionization potentials for Si
n
,J. Chem.
Phys., 1993, 99, 7807–7812.
56 J. Han and F. Hagelberg, A density functional theory investiga-
tion of CrSi
n
(n= 1–6) clusters, Chem. Phys., 2001, 263, 255–262.
57 A. E. Reed, R. B. Weinstock and F. Weinhold, Natural
population analysis, J. Chem. Phys., 1985, 83, 735–746.
58 C. Xiao and F. Hagelberg, Charge transfer mechanism
in Cu-doped silicon clusters: a density functional study,
THEOCHEM, 2000, 529, 241–257.
59 J. Han and F. Hagelberg, A density functional investigation
of MoSi
n
(n= 1–6) clusters, THEOCHEM, 2001, 549, 165–180.
60 J. Han, C. Xiao and F. Hagelberg, Geometric and electronic
structure of WSi
N
(N= 1–6, 12) clusters, Struct. Chem., 2002,
13, 173–191.
61 V. Gordon, E. Nathan, A. Apponi, M. McCarthy, P. Thaddeus
and P. Botschwina, Structures of the linear silicon carbides
SiC
4
and SiC
6
: Isotopic substitution and Ab Initio theory,
J. Chem. Phys., 2000, 113, 5311–5320.
62 M. Chen, A. Zheng, H. Lu and M. Zhou, Reactions of atomic
silicon and germanium with ammonia: A matrix-isolation
FTIR and theoretical study, J. Phys. Chem. A, 2002, 106,
3077–3083.
PCCP Paper
Published on 16 September 2014. Downloaded by TU Berlin - Universitaetsbibl on 24/02/2016 15:55:14.
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