Electronically excited states in size selected solvated alkali metal atoms III:
Depletion Spectroscopy of Na(NH3 )n -Clusters
Peter Brockhaus ∗ , Ingolf V. Hertel † , and Claus Peter Schulz
Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie
Rudower Chaussee 6, D-12474 Berlin, Germany
(Received 30 June 1998; accepted 25 September 1998)
Mg+ (H2 O)n complexes8,9 and Ca+ (H2 O)n .10 The metal
ions in these complexes are isoelectronic to neutral alkali atoms. As an example of a neutral cluster system
Hg(NH3 )n has been studied by resonantly enhanced multiphoton ionization.11
Our own efforts over the past years have concentrated on neutral sodium atom-water and -ammonia
complexes.12–15 Ionization potentials (IP) for Na(H2 O)n
and Na(NH3 )n clusters up to n ≈ 20 have been determined by one-photon ionization. It was found that the IP
decreases with an increasing number of solvent molecules.
For Na(H2 O)n clusters the ionization potential reaches
the bulk value16 of 3.2 eV already for only four water
molecules. For Na(NH3 )n clusters with n ≥ 4 a nearly
linear decrease of the IP towards the bulk value (1.5 eV)
with increasing cluster radius is observed. Fuke et al.
have found the same behavior in water and ammonia
clusters containing cesium.17
The first two publications of this series18,19 we have reported experimental result on the electronically excited
NaNH3 complex using two color resonant two photon ionization (2C-R2PI). The Na (3s → 3p) transition at 16950
cm−1 (590 nm) is shifted massively to lower photon energies (12200 cm−1 ∼
= 820 nm) even with only one ammonia molecule attached to the alkali atom. This trend
is expected to continue for larger clusters. However, we
were not able to verify this with the 2C-R2PI method,
presumably because for n ≥ 2 the clusters Na(NH3 )n
fragment or rearrange rapidly after photoexcitation. In
a pump-probe experiment with femtosecond laser pulses
performed recently in our lab20 , we were able to determine the lifetime of the electronically excited state of
Na(NH3 )2 at 12200 cm−1 (820 nm) to be 32 ps. However, no information on the width and the shape of the
absorption band of Na(NH3 )2 could be extracted from
the pump-probe experiment.
Although numerous theoretical studies on Na(NH3 )n
clusters exist in the literature (e.g. 21 and references
therein) these calculations are mostly concerned with ionization potentials and structures of very small clusters.
Greer et al.22 have calculated one dimensional potential surfaces for excited electronic states of Na(NH3 )n
for n = 1, 2. Unfortunately, they do not provide a direct
insight into the mechanisms of the experimentally observed photodissociation. Neither theoretical nor experimental studies on the excited electronic levels of larger
Na(NH3 )n clusters are available up to now.
The present paper presents the results of a system-
The first electronically excited state of small Na(NH3 )n
clusters up to n = 22 is studied by means of depletion spectroscopy. A drastic decrease of the excitation energy from
the 3s → 3p transition of the Na-atom (16950 cm−1 ) down
to 6000 cm−1 for the Na(NH3 )4 cluster, the closing of the
first solvation shell, is observed. For larger clusters the excitation energy increases slightly towards the bulk value (6300
cm−1 ) which represents the absorption of the “solvated” electron. For all Na(NH3 )n clusters with n ≥ 3 a strong absorption peak is observed near 6600 cm−1 . By comparison with
deuterated sodium-ammonia clusters this absorption can be
assigned to an intramolecular vibrational overtone of the ammonia molecule. This indicates a strong coupling between
electronical and vibrational excitation in the Na(NH3 )n clusters.
I. INTRODUCTION
A detailed understanding of the interaction between
metal atoms and polar molecules is crucial for our concepts of solvation processes. In the liquid phase solvated
electrons are formed when alkali metal atoms are dissolved in certain polar solvents. These solutions exhibit
unique spectroscopic fingerprints, e.g. in ammonia a deep
blue solution is formed1 . The spectroscopy of metalatom solvent-molecule complexes as a function of size is
a prerequisite for modeling the formation of the solvated
electron. We expect that in small complexes the spectroscopic patterns will still bear the fingerprints of the
electronic states of the metal atom while for larger complexes absorption of the solvated electron will dominate
the spectra.
Many research groups have studied different combinations of metal atoms or ions and solvent molecules,
of which water and ammonia are the most important
species (see e.g. 2–4). However, only a few experiments
on electronically excited states have been reported so far.
Farrar and coworkers5–7 have investigated the photodissociation of Sr+ (H2 O)n and Sr+ (NH3 )n clusters in the
visible spectral range. Similar experiments were done on
∗
present address: University of Southern California, Department of Physics SSC 300, Los Angeles, CA 90089, USA
†
also: Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
1
The photoabsorption of the Na(NH3 )n clusters is determined with the depletion method since all clusters for
n > 1 undergo fragmentation after photoexcitation. The
method was introduced to cluster physics by Broyer et
al.24 for studying Na3 . Two light sources are required.
The first is a tunable laser, which excites the clusters to
a dissociative state from which in our case mainly a loss
of one ammonia molecule occurs. The photoabsorption
is detected by the decrease of the cluster ion signal in the
corresponding mass channel. We use the idler beam of an
OPO system to excite the clusters in the infrared spectral region. The OPO (Spectra Physics MOPO 730-10) is
pumped by the third harmonic of a Nd:YAG-laser (Spectra Physics Model 270-10) and delivers an idler output
between 4500 cm−1 (2200 nm) and 12000 cm−1 (835 nm)
with up to 15 mJ pulse energy. A typical pulse length is
4-6 ns. The beam passes a variable attenuator since only
some hundred µJ are needed for the experiment as will
be shown below. Finally, the laser beam is collimated by
a telescope and passes two apertures before entering the
cluster apparatus. The power density variation across the
beam profile have been measured with an infrared camera and is below 20 %. To monitor the laser wavelength
and bandwidth accurately a wavemeter (Burleigh) is positioned in the signal output of the OPO. The relative
laser power is measured by directing a residual reflection
from a quartz plate into a power meter. Laser intensities
measured with the reference powermeter are calibrated
by taking the laser energy at a position with the same
distance from the laser as the interaction zone with the
cluster beam. These measurements ensure that the laser
fluence can be determined with a sufficient accuracy to
determine absolute absorption cross sections. A chopper
is placed in the idler beam for recording depleted and
undepleted cluster ion signal.
The second laser ionizes the clusters in a single excitation step with photon energies close to the ionization
threshold to avoid fragmentation of the ionic clusters.
The third (355 nm ∼
= 4.66
= 3.49 eV) or fourth (266 nm ∼
eV) harmonics of a Nd:YAG laser (Continuum Surelight)
are used. The ionizing laser beam crosses the cluster
beam perpendicularly in the extraction field of the TOF
mass spectrometer. Typically pulse energies of 0.5 mJ
are used with a pulse duration of ca. 5-6 ns. A comparison between the photon energy of the ionizing laser
and the ionization potential (IP) of the cluster is given in
Table I. The excess energy Eex ranges from 0.35 eV to
1.1 eV which is comparable to the binding energy of an
ammonia molecule to the cluster. However, it has been
shown previously15,25 that the photoelectron carries most
of the excess energy and fragmentation does not play a
significant role in one-photon ionization process.
The dissociation of the Na(NH3 )n clusters after photoexcitation leads to the formation of smaller clusters,
which can also be ionized with the ionizing laser and may
eventually lead to an increase of the ion signal on this particular mass and distort the photo-absorption pattern of
Na(NH3 )n−1 . To avoid this problem we have directed the
atic spectroscopy study on the first excited states of
Na(NH3 )n and Na(ND3 )n clusters for n ≤ 20 by two photon depletion spectroscopy using ns laser systems over a
spectral range from the visible into the near infrared. The
outline of this paper is as follows. After a short description of the experimental setup and the photodepletion
method used, we will present the experimental results.
The discussion is structured in four aspects. First we will
focus on Na(NH3 )2 where theoretical22 and dynamical20
information is available. Secondly we discuss the spectral shift of the absorption bands as a function of size for
clusters containing three and more ammonia molecules.
A comparison with deuterated clusters illuminates the
nature of the observed spectral patterns. A third aspect
are the measured oscillator strengths of the transitions.
Finally a comparison of our results to photodetachment
spectra measured by Fuke and coworkers23 is given.
II. EXPERIMENTAL
A. Setup
Fig. 1 shows the experimental setup which is based
on a design described in detail previously13,15 . Sodium
is evaporated from an oven and seeded into the expansion zone of a pulsed ammonia beam. The cluster beam
propagates through a skimmer into the interaction zone
with the laser beams, where the clusters are excited and
ionized by nanosecond laser pulses as described further
below.
time-of-flight
aperture
pulsed
gas
valve
excitation
laser
skimmer
sodium
oven
ionization
laser
FIG. 1. Scheme of the experimental setup. The excitation
laser enters the apparatus counterpropagating to the cluster
beam, while the ionization laser is perpendicular to the cluster
beam.
2
excitation laser beam collinear and counterpropagating
to the cluster beam in an arrangement similar to experiments investigating sodium clusters26,27 . The infrared
laser pulse excites the clusters 100 µs before the ionizing laser pulse. The diameter of the infrared laser beam
(3 mm) is chosen in such a way that it completely illuminates the 2 mm wide cluster beam. Since the fragments
have a velocity component perpendicular to the cluster
beam, they can be effectively skimmed by an additional
3 mm aperture in front of the mass spectrometer. This
geometry ensures that for small clusters up to n ≈ 10
more than 90 percent of these fragments are suppressed.
This have been verified by varying the delay between the
depletion and ionization lasers. A somewhat smaller suppression is expected for larger clusters.
The cluster ions are mass selected in a linear time-offlight (TOF) spectrometer, which is oriented perpendicular to the cluster beam axis. The cluster ions are detected
by micro-sphere plates and the ion signal is recorded by a
transient digitizer. The resulting mass spectra are averaged for 150 laser pulses at each laser wavelength. First
the ion signal is measured without depletion laser, then
the measurement is repeated with depletion laser. The
data are transferred to a PC and stored. All wavelength
scans are recorded at least six times and averaged afterwards.
B. Spectroscopic method
Depletion spectroscopy is based on recording mass
spectra after one-photon ionization with and without a
depletion laser which can be tuned through the excitation region of interest. Fig. 2 shows typical mass spectra
and illustrates the ionization and excitation scheme: in
the upper panel only the ionization laser (hν2 = 4.03
eV) is used, while in the middle panel the depletion laser
(hν1 = 1.21 eV ∼
= 9775 cm−1 ) is added. A comparison
between the two mass spectra reveals that the ion signal of Na(NH3 )2 is depleted by 75%. The lower panel of
Fig. 2 shows the difference between the two mass spectra,
documenting that mostly Na(NH3 )2 is excited with the
depletion laser wavelength chosen while larger clusters
are almost transparent at this photon energy.
n=2
250
photon energy / eV
4.67
3.49
3.49
3.49
3.49
3.49
3.49
3.49
3.49
3.49
3.49
3.49
3.49
3.49
3.49
10
Na(NH3)n
20
30
+
150
100
50
0
ion signal / arb.un.
IP / eV
3.58
3.14
2.928
2.821
2.75
2.61
2.58
2.50
2.48
2.47
2.46
2.47
2.46
2.44
< 2.33
6
200
TABLE I. Excess energy of cluster ionization process. Ionizationspotentials are taken from Ref. 15.
Na(NH3 )n
2
3
4
5
6
7
8
9
10
11
12,13
14-16
17
18
19-22
4
Eex / eV
1.09
0.35
0.56
0.67
0.74
0.88
0.91
0.99
1.01
1.02
1.03
1.02
1.03
1.05
1.16
250
200
150
100
50
0
250
difference
200
150
100
50
0
10
20
30
40
50
60
time of flight / µs
FIG. 2. For depletion spectroscopy different mass spectra
are taken: in the upper part the ionization laser (hν2 = 4.03
eV) is used only; in the middle part the depletion laser
(hν1 = 1.21 eV ∼
= 9775) cm−1 ) is added. With the laser
parameters chosen for these mass spectra the Na(NH3 )+
2 ion
signal is depleted selectively as shown in difference mass spectrum (lower part). The insert shows the excitation processes
schematically.
An important aspect of depletion spectroscopy is the
3
dependence of the depletion signal on the laser fluence. If the absorption of the laser beam passing
through the cluster beam is negligible the depletion signal can be described by an inverse Beer-Lambert law27 :
− ln (Son /Soff ) = σφ where σ is the photoabsorption
cross section and φ the photon fluence. Son and Soff
denote the signals with depletion laser on and off, respectively. As a typical example Fig. 3 gives the dependence on the laser fluence observed for Na(NH3 )4 .
The depletion signal increases linearly with the laser fluence as predicted by the Lambert-Beer law up to 350
µJ/cm2 . Beyond this laser fluence the signal saturates
for Na(NH3 )4 . The line in Fig. 3 presents a fit to the
linear part of the data points from which a cross section
of 3.5±0.4 Å2 can be extracted. For all other cluster
sizes the onset of saturation measured at the maximum
absorption wavelength is found at even higher laser fluences. In the absorption spectra shown throughout this
paper the laser fluence was kept below 300 µJ/cm2 to
ensure linearity. The photoabsorption cross section σ is
displayed in all figures below but we refrain here from
giving absolute absorption cross sections for Na(NH3 )n ,
n > 6 because of uncertainties arising from fragmentation of larger clusters during the ionization process.
ion yield /
arb.un.
the NaNH3 complex and the larger clusters. While the
NaNH3 complex shows sharp lines with distinct vibrational progressions which have been assigned recently19
the absorption spectra of the larger clusters are broad
and more or less unstructured. The origin of this observation is twofold. The NaNH3 complex is a five atomic
molecule with a well defined C2v geometry in the ground
and excited state. This limits the accessible rovibronic
states. With increasing cluster size the geometry of the
ground and excited state is less well defined leading to
an increasing density of accessible states. Second, the
spectra of the NaNH3 complex were recorded with the
2C-R2PI technique since the lifetime of the excited state
is in the ns time regime. The spectra of larger clusters
were recorded with the depletion technique which implies
a much shorter lifetime and, thus, an increasing intrinsic
linewidth of the individual rovibronic transition.
4
Na(NH3)n
n=1
n=2
1,25
2
0
absorption cross section / Å
-ln(Son/Soff)
2
1,00
0,75
0,50
0,25
0,00
0
100
200
300
400
500
600
laser fluence / µJ/cm
700
800
2
FIG. 3. Laser fluence dependence of the Na(NH3 )4 depletion signal. Photon energy of the depletion laser is 6640 cm−1 .
The depletion signal saturates for laser fluences greater than
350 µJ/cm−1 . The solid line presents a fit to linear increase
of the depletion signal. From the slope the photo absorption
cross section can be deduced.
4
n=3
2
0
3
2
1
0
3
n=4
2
n=5
1
0
1
n=6
0
6000
8000
10000
energy / cm
12000
14000
-1
III. RESULTS AND DISCUSSION
FIG. 4. Absorption spectra of Na(NH3 )n , n = 1 . . . 6. The
NaNH3 spectra are 2C-R2PI data taken from Ref. 18. For
the depletion spectra (n ≥ 2) the laser intensities are 600
µJ/cm2 for the ionization laser and 100-300 µJ/cm2 for the
depletion laser. The solid lines are fits to the data. The strong
intensity corresponds to a vibrational excitation of the 2ν1 ,
2ν3 and ν1 + ν3 modes. The energy of these mode in the free
ammonia molecule is indicated by the dashed line.
A. Overview
We have successfully recorded depletion spectra for
Na(NH3 )n clusters up n = 20. Fig. 4 shows the absorption spectra for the smallest clusters up to n = 6.
For comparison, the figure also incudes the spectrum of
NaNH3 , which was recorded earlier by 2C-R2PI.18 One
immediately notices the difference between the spectra of
4
The second important observation shown in Fig. 4
is the shift of the spectra to lower excitation energies.
With only four ammonia molecules bound to the sodium
atom the absorption is already shifted from the visible
(589 nm, yellow) sodium line to the near infrared (1670
nm, NIR) spectral region. For larger clusters (n > 4)
only small additional shifts of the absorption bands are
found. In the next subsections a closer look at the absorption spectra of the individual clusters will be given.
We will also focus on the nature of the strong absorption
peak at 6600 cm−1 observed for Na(NH3 )3 and larger
clusters which we attribute to vibrational excitation of
the ammonia molecules.
4
Na(NH3)2
3
absorption cross section / Å
2
2
B. Properties of Na(NH3 )2
The absorption spectrum of Na(NH3 )2 is again shown
in the upper part of Fig. 5. The observed spectrum is
relatively unstructured and extends from 8500 cm−1 to
12000 cm−1 . The oscillation of the signal must essentially be attributed to fluctuations of the laser and the
cluster source. The steep rise of the absorption on the
low energy edge of the spectrum indicates an only small
amount of hot band excitation of the clusters and a sharp
onset of the absorption at the 0-0 transition. According
to the calculations of Greer et al.22 the ground state of
Na(NH3 )2 is bent with an N − Na − N angle θN−Na−N of
103◦ (C2v -geometry). The sodium diammonia cation has
a D3h symmetry (θN−Na−N = 180◦ ). One expects the
first excited state to have C2v geometry with θN−Na−N
being in between 103◦ and 180◦ , probably closer to the
latter value. This geometry gives rise to three excited
states which asymptotically correlate to the Na(3p) state.
The three states are given by the three possible orientations of the p-orbital with respect to C2 -axis: Ã 2 A1 (pz
orbital), B̃ 2 B1 (px orbital), and C̃ 2 B2 -state (py orbital).
The arrows in Fig. 5 give the respective energies as calculated by Greer et al. and the fit in Fig. 4 for n = 2
reflects this explicitly. If the onset of the absorption is
identified with the position of the Ã2 A1 -state, the agreement between experiment and calculation is excellent,
especially so when keeping in mind that the excited state
energy was calculated with the geometry of the ground
state of Na(NH3 )2 . Relaxation of the excited state geometry would shift the energy to somewhat lower energies
in even better agreement with the experiment. The more
or less smooth absorption band towards higher energies
can be understood by an overlap of dense rotational and
vibrational states decreasing in intensity as the FranckCondon overlap degrades.
1
~
A
~
B
~
C
0
7000
4
8000
9000
10000
11000
12000
13000
Na(ND3)2
3
2
1
0
7000
8000
9000
10000
11000
energy / cm
12000
13000
-1
FIG. 5. Depletion spectra of Na(NH3 )2 and Na(ND3 )2 .
Laser fluences are 600 µJ/cm2 for the ionization laser and
100-300 µJ/cm2 for the depletion laser. The arrows indicate
the energy minima of the excited states as calculated by Greer
et al. (Ref. 22).
The lower part of Fig. 5 shows the corresponding spectrum for the deuterated species Na(ND3 )2 which extends
over the same spectral range as the undeuterated species.
The onset of the spectrum at the low energy end is at
the same photon energy and shows again a steep rise
of the absorption. The overall strength of the signal is
smaller and towards higher energies the absorption decreases faster than for Na(NH3 )2 . On the basis of our
data we can only speculate about the origin of the differences. Recent pump probe experiments with femtosecond laser pulses20 have shown that the excited state of
Na(NH3 )2 decays in about 30 ps at 12000 cm−1 which
is the high energy end of the observed absorption band.
New results on the deuterated complex, Na(ND3 )2 , indicate a much longer lifetime larger than 1 ns.28 Since the
depletion technique used here to determine the absorption is only sensitive to fast decaying excited states with
subsequent dissociation of the cluster the long lifetime of
Na(ND3 )2 may lead to a reduction of the measured absorption signal compared to Na(NH3 )2 . The present set
of data is not sufficient for a closer understanding of the
5
differences observed.
C. Spectra of larger Na(NH3 )n clusters
n=1000 100
The spectra of the Na(NH3 )n clusters (n > 2) shown
in Fig. 4 are qualitatively similar to that of Na(NH3 )2 .
The spectra are broad and no sharp lines associated with
a specific vibrational progression are observed. However,
two well separated features can be distinguished for all
n > 2: a less intense and broad absorption which is centered around 8000 cm−1 for Na(NH3 )3 . It shifts towards
lower energies for larger clusters and will be discussed
in the next paragraph. The second feature is a strong
absorption line near 6600 cm−1 for all cluster sizes with
n ≥ 3 which we attribute to a vibrational excitation of
ammonia molecules. This feature will be discussed further below together with the spectra of Na(ND3 )n which
have been recorded for comparison.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
∞(fluid)
maximum
12217
8721(44)
9113(88)
10121(140)
7668(80)
8310(112)
5987(188)
6119(84)
5659(216)
5851(168)
6035(232)
6041(188)
6163(244)
6024(452)
6000(628)
5887(316)
5899(392)
5841(240)
6065(548)
6091(492)
6332(296)
6195(660)
6386(304)
6140(308)
6367(224)
6311(296)
6330
2
1
Na-Atom
0
5
energy / eV
R1
-2
R2
Rc
-4
-6
4
0
5
10
15
20
energy / eV
r / a0
TABLE II. Experimentally determined absorption energies
and width of the absorption bands. All values in cm−1 .
n
1
2
16 10 6 4
3
+
Na(NH3)n
2
1
*
Na(NH3)
width
240(39)
793(56)
1485(59)
452(57)
711(58)
563(143)
508(25)
583(112)
936(97)
1213(110)
1180(92)
1329(95)
1050(208)
1092(306)
824(181)
847(207)
648(149)
513(325)
604(200)
1053(103)
1175(212)
1202(129)
1152(163)
811(130)
811(174)
3200
0
0,0
0,2
0,4
(n+1)
0,6
0,8
1,0
-1/3
FIG. 6. Summary of the spectroscopic properties of
Na(NH3 )n clusters. The open squares presents the experimental ionization potentials from Ref. 15. The full squares
are the maxima of the absorption band from this work. The
dashed line presents calculated IP’s using a one dimensional
model potential as indicated in the inset (taken from Ref. 14).
The same model was user to calculate the excitation energies.
For details see text.
For Na(NH3 )3 the broad absorption centered around
8000 cm−1 is approximately a factor of 2 weaker than
that of the vibrational peak at 6600 cm−1 . This absorption arises from the electronic excitation of the sodium
valence electron which acts as a chromophore. Due to
the change of the electronic wavefunction the maximum
and the width of this absorption band changes with cluster size. We have extracted the peak positions and the
width of the absorption band from our measured curves
(Fig. 4) by fitting multiple Gaussian functions to it.
Peak values were optimized by a nonlinear least square
fit procedure. For the Na(NH3 )n clusters with n = 3
and 5, which have more than one maximum, we assigned
more than one value to the corresponding cluster size.
Table II report the observed absorption energies and
band widths for all cluster sizes. They are plotted in
Fig. 6 as a function of (n + 1)−1/3 , a quantity which
is essentially proportional to the inverse cluster radius.
6
potential originating from the Na+ core screened by the
dielectric environment. The model potential is depicted
in the insert of Fig. 6. It contains four different regions: From the origin up to the radius R1 the Na+
core potential Vc (r) from Aymar29 is used which reproduces the Na (3s) ground state and a number of excited states perfectly well. For the radius R1 the sum
of the ionic Na+ core radius and the van der Waals
radius of N was chosen (R1 = 4.66a0 ). The next region, R1 ≤ r ≤ R2 , corresponds to the first solvation
shell. We have assumed that the Na+ is surrounded by
four ammonia molecules and the potential is screened as
Vc (r) + qeff neff /r, with neff = n for n ≤ 4 and neff = 4
for n > 4. The effective screening charge qeff was treated
as a fit parameter and adjusted to reproduce the experimental IP for Na(NH3 )4 . The radius R2 is given by
R1 + Rd + RH = 7.27a0 with Rd the distance between
the nitrogen atom and the plane of the hydrogen atoms in
the ammonia molecule and RH the van der Waals radius
of the H atom. Between the first
and
¤1/3the
£ solvation shell
3
cluster radius, R2 ≤ r ≤ Rc = R23 + (n − 4) RW
,a
S
screened Coulomb potential −1/²opt r was used. Outside
the cluster Rc ≤ r we have used −1/r. The different
parts are adjusted at R1 , R2 and Rc by adding constants
so that the overall potential is continuous. When the one
dimensional Schrödinger equation is solved, the binding
energy of the electron which corresponds to the ionization potential can be calculated. The result shown as the
dashed line in Fig. 6 gives a reasonable agreement with
the experimental ionization potentials. Details have been
discussed in Ref. 14.
We have now repeated this calculation for the excited
3p electron by adding the centrifugal term 1/r2 to the
potential described above. The solid line in Fig. 6 represents the resulting energies for the 3s → 3p transition.
Although this radially symmetric model ignores details
of the molecular structure, especially so for small clusters, it reproduces the experimentally observed drop of
the excitation energy up to n = 4 and the much slower
change for larger clusters quite well. One may argue here
that sharp change at n = 4 is a result of our choice of
the number of ammonia molecules in the first solvation
shell and can be shifted at will by changing the number of molecules. The fact that this agrees well with the
experimental observation for behavior of the excitation
energy justifies this assumption ex post even though the
ionization potentials were not conclusive in this respect.
The choice of four ammonia molecules to be in the
first solvation shell is also justified by quantum chemical
calculation of Hashimoto et al.21 who have investigated
structures and stabilities of Na(NH3 )n clusters for n = 16 by ab initio methods. They have found for the neutral
ground state, that the NH3 molecules interact directly
with the central Na up to n = 5 avoiding the steric hindrance. For n ≥ 6 direct interaction of additional NH3
molecules becomes unfavorable due to steric repulsion
among NH3 molecules, and a second solvation shell is
formed. At first glance this seems to be a contradiction
For comparison, the ionization potentials for Na(NH3 )n
clusters from our earlier measurements14,15 are also included in Fig. 6. From the 3s → 3p transition of the
free sodium atom at 16950 cm−1 the absorption energy
decreases more or less linearly down to a value of 6000
cm−1 for the Na(NH3 )4 cluster. Towards larger clusters
the absorption energy increases slightly and will eventually reach the bulk value at 6300 cm−1 which corresponds
to the absorption of the “solvated” electron.1 The sharp
change of the size dependence in the absorption energy at
n = 4 indicates a change in the structure of the cluster at
this size. From thermochemical measurements of binding
energies of Na+ (NH3 )n clusters2 it has been suggested
that the first solvation shell is closed when four ammonia
molecules surround the sodium ion. Our earlier study of
the ionization potential of Na(NH3 )n clusters does not
give a clear picture: The ionization potentials decrease
with increasing clusters size. Only a small change in the
slope is observed at n = 4 while the IP is more or less
constant between n = 10 and 16. A very useful alternative representation of these data is given in Fig. 7 in
an energy scheme of the whole series of clusters. The
scheme is based on the measured ionization potentials15
and on the binding energies of the ions2 (from which the
neutral binding energies follow). The measured excited
state energies indicated as shaded areas indicate the position and width of the excited states - except for the
higher levels in the NaNH3 electronically excited state
system which represent the energies which Greer et al.22
have calculated. As schematically indicated for n up to
4, the diagram may also be viewed as a graphic representation of the energetically open dissociation and decay
channels after photo-excitation of the first electronically
excited states.
Na
+
5
5s
4p
4
Na(NH3)
+
3d
4s
Na(NH3)2
energy / eV
3
2
E (4p)
+
Na(NH3)3
2
2
3p
2
2
+
E (3d)
A1 (4s)
+
2
Na(NH3)4
A1 (5s)
A1 (3p)
Na(NH3)5
2
A1 (4s)
2
E (3p)
+
Na(NH3)6
1
+
2
0
2
Na
-1
-2
B1 (3p)
3s
A1 (3s)
2
Na(NH3)
A1 (3s)
Na(NH3)2
Na(NH3)3
Na(NH3)4
Na(NH3)5
Na(NH3)6
FIG. 7. Schematic of the energy diagram for Na(NH3 )n
clusters. The ionization potentials are taken from Ref. 15, the
binding energies of the ions from Ref. 2 and the shaded areas
give the present positions and widths of the first electronically
excited states. For details see text.
In our earlier publication14 a simple model was used
to calculate the ionization potentials. We have solved
a one dimensional Schrödinger equation for a spherical
7
to the shell closing at n = 4 as suggested by the spectroscopic data. A closer inspection of the optimized structures calculated by Hashimoto et al. shows, that in the
Na(NH3 )3 cluster which has C3v geometry the Na atom
is still on the surface of the cluster. This changes at n = 4
where the most stable structure has C3 geometry with the
four N atoms located nearly tetrahedrally. A “surface”
complex of Na(NH3 )4 is unstable according to the calculations. In the Na(NH3 )5 cluster one additional NH3
molecule is bound directly to the Na atom. Thus, starting from the Na(NH3 )4 cluster the sodium atom is completely surrounded by ammonia molecules. Obviously,
the absorption spectrum has the lowest energy when the
Na atom is completely caged by NH3 molecules for the
first time at n = 4. Towards larger clusters where the Na
atom is always caged only a small shift of the absorption
energy occurs. Unfortunately, no ab initio calculations
of the structure and energy of excited states are available except for n = 1, 2. The nature of the double peaks
in the absorption spectrum of Na(NH3 )3 and Na(NH3 )5
remains unexplained presently. Either different isomers
which exist with low barriers as calculated by Hashimoto
et al.21 play a role or the splitting of the 3p state of the
Na atom in the presence of the ammonia molecules may
lead to the observed double peaked spectrum.
The total width of the absorption bands may be another indicator for the filling of solvation shells, even
though the experimental uncertainties are large due to
the fact that we have to subtract the vibrational structure centered around 6600 cm−1 (see next paragraph).
We have observed narrow absorption bands for n = 4
(note that n = 5 is significantly double peaked) and also
for n = 16. Again, this may be attributed to the closing
of solvation shells with distinct geometrical structures as
already suggested in earlier publications.15
Na(NH3 )n clusters with n ≥ 3 show the strongest absorption near 6600 cm−1 . Since the fundamental symmetric and asymmetric N—H3 stretching vibrations (ν1
and ν3 ) of neat ammonia have energies of 3336 cm−1 and
3414 cm−1 , respectively, it is plausible to assume that the
strong absorption originates from an overtone or combination band of these modes. For the ammonia molecule
two absorption lines at 6595 cm−1 and 6624 cm−1 are
mentioned in the book of Herzberg30 which are assigned
to 2ν1 , 2ν3 , or ν1 +ν3 . In Fig. 4 the dashed line marks the
energy of the overtones. The observed strong absorption
in the Na(NH3 )n clusters agrees remarkably well with
this absorption in neat ammonia. There is an indication
of a small blue shift for some cluster sizes for n > 6 (the
one seen for n = 3 may be an artifact caused by the onset
of a reversed depletion signal, i.e. amplification due to
a small amount of indiscriminated fragmentation products from larger clusters). Barth and Huisken31 studied
ammonia clusters using CARS spectroscopy in the energy range between 3000 cm−1 and 4000 cm−1 . They
found a relatively large red shift of about 100 cm−1 for
the stretching modes in the clusters compared to the free
ammonia molecule which is, however, small compared to
the widths and uncertainties of the measured bands in
the present work.
15
Na(NH3)8
absorption cross / arb. un.
10
5
0
25
4000
5000
6000
7000
8000
20
Na(ND3)8
15
10
5
0
-5
4000
5000
6000
energy / cm
7000
8000
-1
FIG. 8. Depletion spectra of Na(ND3 )8 in comparison with
Na(NH3 )8 . The dashed lines presents the energy of the corresponding vibrational modes.
Thus, we tentatively attribute the strong absorption
band close to 6600 cm−1 observed for all Na(NH3 )n clusters with n ≥ 3 to a overtone or combination band of the
ν1 or ν3 ammonia vibrations which is in the free molecule
two orders of magnitude smaller than the electronic transition in the clusters and “borrows” oscillator strength
from this electronic transition. To glean additional support for this hypothesis we study deuterated clusters as
well. The vibrational frequencies should be drastically
different if all NH3 are replaced by deuterated ammonia
ND3 while the electronic part of the absorption should
remain essentially unchanged. Fig. 8 shows as a typical
example the absorption spectrum of Na(ND3 )8 (bottom)
in comparison with the previously shown spectrum of
Na(NH3 )8 (top). It is evident that for the deuterated
cluster a new absorption band shows up around 4800
cm−1 . The narrow vibrational peak at 6600 cm−1 has apparently been replaced by a much broader feature which
we attribute to the somewhat less red shifted electronic
absorption band. According to Herzberg30 the ν1 and ν3
modes of ND3 have energies of about 2400 cm−1 . This
leads to overtones near 4800 cm−1 as indeed observed in
the spectrum. It should be noted, that the strong noise
of the signal at these wave numbers is caused by the OPO
which is running at the limit of its spectral range. Nevertheless, this measurement confirms our assumption of a
strong interaction between electronic and vibrational excitation in the sodium-ammonia clusters. We may even
understand the slight blue shift of the vibrational overtone in Na(NH3 )n compared to the free NH3 and the
stronger red shift of the electronic states in Na(NH3 )n in
comparison to the Na(ND3 )n system in terms of states
repelling each other which are nearly in Fermi resonance.
A rough estimate of all cluster sizes studied, except
for the n = 2 case where Na(NH3 )2 absorbs stronger,
leads to an electronic absorption cross section for the
8
Na(ND3 )n system which is to a factor of two larger
than for Na(NH3 )n while the vibrational part is generally smaller in the former case. One might argue that
this support the hypothesis of the vibrational transition
obtaining transition moment at the cost of the allowed
electronic transition: for a larger energy gap between
electronic and vibronic states (i.e. for the deuterated
system) this sharing of oscillator strength would be less
efficient. The experimental uncertainties for the deuterated system are, however, relatively large and do not
allow a rigorous conclusion.
The above discussion can be summarized as follows: In
the Na(NH3 )n clusters a broad absorption band originating from the excitation of the delocalized metal electron
coexists with a sharp peak assigned as intramolecular
vibrational overtone. In the case of n = 2 where the
overtone peak does not overlap with electron band only
the latter one is observed because the overtone peak itself
does not possess a sizeable oscillator strength. With increasing cluster size the electron band shifts toward lower
energies and the overtone peak starts to grow by borrowing oscillator strength from the overlapping electron
band. This observation indicates a strong electron vibrational interaction. The red shift of the electron band
stops at n = 4 due to the closing of the first solvation
shell around the sodium atom. By deuteration of the
sodium-ammonia clusters the overtone peak shifts in a
proper way to the red as shown in Fig. 8. The small
blue shift of the electron band in Na(ND3 )8 can be understood as a reduction of state repelling because of the
larger energy difference between the electron band and
the overtone peak.
n=6
4
3
2
1
Na(NH3 )n up to n = 6. The result is shown in Fig. 9 and
Table III. The oscillator strength decreases monotonically from the 3s → 3p transition in free atomic sodium
where it is nearly 1 (the maximum value for a effective
one electron system) when ammonia molecules are added.
For the NaNH3 complex where no photoabsorption cross
sections are available a value of 0.36 has been estimated
by observation of saturation intensity with femtosecond
pulses.32 This value is also in good agreement with recent
theoretical calculations.33 For larger Na(NH3 )n clusters
the oscillator strength decreases until it reaches the value
of 0.024 for Na(NH3 )6 . No theoretical calculation for
these larger clusters are available. We have tried to estimate the oscillator strength by using the wavefunctions
derived for the model potential described above. However, except for a general trend no agreement in detail
was found. This reflects the well known fact that the
oscillator strength is a much more sensitive overall probe
for the electronic and molecular structure than energetic
observables. Clearly, this aspect has been highly oversimplified in our one dimensional, spherically symmetric
model for the clusters.
One interesting aspect deserves to be noted when considering the transition to the bulk, where the oscillator
strength for the solvated electron is known to be 1 again:
Since in the larger clusters the sodium atom with its one
active electron still acts as the chromophore, the oscillator strengths must remain unity when summing over
all allowed transitions. Thus the observed decreasing oscillator strength for the transition correlated with the
3s → 3p excitation in the cluster implies an increase of
oscillator strength in other spectral regions. Due to the
decreasing energetic separation of higher lying electronic
states and an increased number of vibrational modes with
increasing cluster size we expect also an enhancement of
the absorption in the IR beyond the region studied. One
aspect of this trend has already been seen in terms of the
overtone or combination bands in Na(NH3 )n for n > 3 as
discussed above. With further increasing cluster size the
levels with gradually overlap more and more until finally
the well known very broad absorption band with oscillator strength 1 is observed for the solvated electron in the
liquid phase.
Na-atom
oscillator strength
1,0
0,8
0,6
0,4
0,2
TABLE III. Oscillator strength f of the Na(NH3 )n clusters
(n = 0 . . . 6) for the 3s → 3p transition compared to the value
of the sodium 3s → 3p transition.
0,0
0,5
0,6
0,7
(n+1)
0,8
0,9
1,0
-1/3
n
0
1
2
3
4
5
6
FIG. 9. Oscillator strength for Na(NH3 )n as determined
from the absorption spectra.
D. Oscillator strength
From the absolute cross sections which we have determined by the power dependence of the depletion signal
the oscillator strength can be calculated by simply integrating over the absorption band. This has been done for
9
f
0.982
0.36 ± 0.18
0.19 ± 0.10
0.11 ± 0.05
0.056 ± 0.030
0.050 ± 0.030
0.024 ± 0.015
Ref. 35
see text
this work
this work
this work
this work
this work
depletion technique. Whether only one or more ammonia
molecules leave the sodium-ammonia cluster after photoexcitation cannot be decided with the present experiment, a question which deserves further studies. Time
resolved experiments using femtosecond laser pulses will
enable us follow the ionization and fragmentation dynamics in real time. Additional tools such as the recently developed femtosecond time resolved photoelectron spectroscopy36 will lead us to details of the electron
solvation dynamics and help elucidating the nature of the
observed strong coupling between electronic and vibronic
excitation in sodium-ammonia clusters. Much more theoretical work is needed on a variety of aspects of structure
and dynamics for these model systems on the way to a
fundamental understanding of solvation processes on a
molecular level.
E. Comparison to photodetachment spectra
Recently, Fuke and coworkers23 have investigated
the photoelectron spectra of mass selected, negatively
−
charged Na(NH3 )n clusters. Generally, the photoelectron spectra show two peaks, where the peak with the
lowest electron binding energy comes from the ground
state of the neutral cluster and corresponds to the electron affinity (EA). The authors have assigned the second peak which was observable up to n = 12 to the
Na− (3s2 ) → Na(3p) + e− transition. Thus, the difference energy between the two peaks can be directly compared to our absorption spectra although this comparison
can only be of qualitative significance due to the different
structure of the initially prepared system and the limited
resolution of the electron spectrometer (120 meV = 970
cm−1 ). For the Na(NH3 )2 the electron spectrum gives
an energy for the first excited state of ca. 8500 cm−1
in good agreement with our experimental findings. Also
for larger clusters the agreement between the electron
spectra and our absorption spectra is satisfactory. At
first glance this agreement is astonishing since one can
assume, that the extra electron in the negatively charged
clusters is located at the sodium atom and consequently
the ammonia molecules are bound in the cluster with the
hydrogen atoms pointing towards the Na atom due to
the permanent dipole moment. Recent calculations by
Hashimoto and Kamimoto34 show that for the smallest
−
Na(NH3 )n clusters (n ≤ 3) two different stable structure
exists: one with the hydrogen atoms pointing towards
the Na atom as intuitively assumed and one with the hydrogen atom pointing away from the Na atom resembling
nearly the same structure as the neutral clusters.
ACKNOWLEDGMENTS
The authors wish to thank Dr. Maxim Tschaplyguine
for his help with the cluster machine. Financial support
by the Deutsche Forschungsgemeinschaft through SFB
337, Project A11, is gratefully acknowledged.
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IV. CONCLUSION
We have determined for the first time the energy of the
first electronically excited state of Na(NH3 )n clusters up
to n = 22. The sharp drop of the excitation energy from
the atomic value of Na (16950 cm−1 ) down to 6000 cm−1
for the Na(NH3 )4 cluster and the subsequent slight increase for larger clusters towards the bulk value at 6300
cm−1 supports the general belief that the first solvation
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a fragmentation process since they are measured by the
10
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17
11