Chemical Physics 283 (2002) 85–110
www.elsevier.com/locate/chemphys
Microsolvation of the ammonia cation in argon: II. IR
photodissociation spectra of NHþ
3 –Arn ðn ¼ 1–6Þ
Otto Dopfer *, Nicola Solc
a, Rouslan V. Olkhov 1, John P. Maier
Institut f€ur Physikalische Chemie, Universit€at Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
Received 7 January 2002
Abstract
Mid-infrared photodissociation spectra of NHþ
3 –Arn (n ¼ 1–6) complexes in the electronic ground state have been
recorded in the vicinity of the N–H stretch vibrations of the ammonia cation. The rovibrational analysis of the transitions in the spectrum of the NHþ
3 –Ar dimer (n ¼ 1) is consistent with a planar, proton-bound equilibrium structure
with C2v symmetry. The three N–H stretching fundamentals occur at m1 ða1 Þ ¼ 3177:4 1 cm1 , m3 ða1 Þ ¼ 3336:0
1 cm1 , and m3 ðb2 Þ ¼ 3396:26 0:13 cm1 , and the combination band of m1 with the intermolecular stretching vibration
is observed at m1 þ ms ða1 Þ ¼ 3305:5 2 cm1 . The relatively long lifetime with respect to predissociation (s > 250 ps)
and modest complexation-induced frequency shifts ðjDm1;3 j < 70 cm1 Þ of the N–H stretch fundamentals imply weak
coupling between the intramolecular and intermolecular degrees of freedom. The linear intermolecular proton bond in
and a harmonic stretching
the ground vibrational state is characterized by an interatomic H–Ar separation of 2.27 A
force constant of 12 N/m. Observed tunneling splittings in the m3 ðb2 Þ band are attributed to hindered internal rotation
through potential barriers separating the three equivalent H-bound global minima. By comparison with theoretical
þ
data, the frequency of the infrared forbidden m1 fundamental of free NHþ
3 is estimated from the NH3 –Ar spectrum as
1
3234 15 cm , the currently most accurate value based upon experimental measurements. The vibrational spectra of
the larger NHþ
3 –Arn complexes (n ¼ 2–6) display distinct frequency shifts and splittings of the N–H stretching vibrations as a function of cluster size. The spectra are consistent with cluster geometries in which the first three Ar ligands
fill a primary solvation subshell by forming equivalent intermolecular proton bonds (n ¼ 1–3) leading to planar
structures with either C2v or D3h symmetry. The next two Ar ligands fill a second subshell by forming equivalent pbonds to the two lobes of the 2pz orbital of the central N atom leading to cluster structures with C3v (n ¼ 4) and D3h
symmetry (n ¼ 5). The first Ar solvation shell around the interior NHþ
3 ion is closed at n ¼ 5 and the 6th Ar ligand
occupies a position in the second solvation shell. The dissociation energies of the H-bonds and p-bonds are estimated
from photofragmentation branching ratios as D0 ðHÞ 950 150 cm1 and D0 ðpÞ 800 300 cm1 , respectively. In
general, the intermolecular H-bonds significantly weaken the intramolecular N–H bonds, whereas the p-bonds slightly
strengthen them. Properties of the intermolecular bonds and the cluster growth in NHþ
3 –Arn are compared to related
AHþ
k –Arn cluster systems. Ó 2002 Elsevier Science B.V. All rights reserved.
*
1
Corresponding author. Tel.: +41-61-2673823; fax: +41-61-2673855.
E-mail address: [email protected] (O. Dopfer).
Present address: Department of Chemistry, University of Birmingham, UK.
0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 4 9 7 - 4
86
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
1. Introduction
The solvation of ions with neutral ligands is of
importance for many fundamental phenomena in
the areas of physics, chemistry, and biology [1–3].
In the past, isolated cluster ions I –Ln have frequently been used to investigate ion–ligand interaction potentials and their dependence on further
solvation at the molecular level. In particular for
smaller clusters, the fruitful combination of highresolution spectroscopy and quantum chemical ab
initio calculations has led to the construction of
accurate intermolecular potential energy surfaces
(PESs) for ion–ligand interactions [4].
The present work reports infrared (IR) photodissociation spectra of mass-selected NHþ
3 –Arn
complexes ðn ¼ 1–6Þ to study the NHþ
–Ar
inter3
action potential and to characterize the stepwise
microsolvation process of the ammonia cation in
argon. The spectroscopic approach is complemented by ab initio and density functional calculations (for n ¼ 0–5) discussed in detail in the
preceding article [5]. A similar combined spectroscopic and theoretical approach has recently been
applied to other AHþ
k –Arn clusters, such as
OCHþ –Arn ðn ¼ 1–13Þ [6–8], N2 Hþ –Arn ðn ¼
1–13Þ [7,9], SiOHþ –Arn ðn ¼ 1–13Þ [7,10], NHþ
4–
Arn ðn ¼ 1–7Þ [11–13], H2 Oþ –Arn ðn ¼ 1–14Þ
[14,15], and CHþ
3 –Arn ðn ¼ 1–8Þ [16,17]. Rotationally resolved IR spectra have been obtained
for all aforementioned dimers (n ¼ 1), providing
detailed information about the properties of their
intermolecular ion–ligand PESs, such as structures, binding energies, force constants of intermolecular modes, barriers to internal motions, and
existence of isomers. Distinct size-dependent frequency shifts in the vibrational spectra of larger
clusters ðn P 2Þ have allowed the extraction of
fundamental characteristics of the microsolvation
process of these cations in argon, such as cluster
geometries and ligand binding energies, structures
of solvation shells and relative stability of various
isomers.
The NHþ
3 –Arn clusters differ in several aspects
from the AHþ
k –Arn systems studied previously.
The planar NHþ
3 ion is an open-shell trihydride
cation with D3h symmetry (Fig. 1). Previous
studies conclude that the cluster growth in
Fig. 1. Sketch of the most stable structures of NHþ
3 –Arn
ðn ¼ 0–5Þ. The first three Ar ligands are attached to the three
protons of NHþ
3 forming (nearly) linear equivalent H-bonds in
planar cluster structures with C2v and D3h symmetry for
n ¼ 1–3, respectively. The next two Ar atoms form p-bonds to
NHþ
3 leading to cluster structures with C3v and D3h symmetry
for n ¼ 4 and n ¼ 5, respectively. Hence, microsolvation of
NHþ
3 in Ar begins by filling solvation subshells with closure at
n ¼ 3 (first subshell) and n ¼ 5 (second subshell). The first Ar
solvation shell around an interior NHþ
3 ion is closed at n ¼ 5.
AHþ
k –Arn complexes sensitively depends on k.
Hence, NHþ
3 –Arn clusters represent a prototype
system to explore the solvation of a AHþ
3 ion in a
nonpolar solvent (Fig. 1). Indeed, ab initio calculations show that NHþ
3 offers several competing
binding sites for an Ar ligand [5]. According to the
three pronounced global H-bound minima on the
dimer PES calculated at the MP2 level
ðDe ¼ 1133 cm1 Þ, the first three ligands are attached to the three protons of NHþ
3 forming
equivalent and (nearly) linear H-bonds in cluster
structures with C2v and D3h symmetry for n ¼ 1–3,
respectively [5]. The cluster growth proceeds by
further complexation at the two local p-bound
minima on the dimer PES ðDe ¼ 866 cm1 Þ leading to cluster structures with C3v and D3h symmetry for n ¼ 4 and n ¼ 5, respectively.
Consequently, microsolvation of NHþ
3 in Ar begins by filling solvation subshells with closure at
n ¼ 3 (first subshell) and n ¼ 5 (second subshell).
The first Ar solvation shell around an interior
NHþ
3 ion is closed at n ¼ 5. This predicted cluster
growth [5] is rather different from that in AHk –Arn
systems with k 6¼ 3. For example, in AHþ –Arn
(k ¼ 1; e.g., HCOþ –Arn [6] and N2 Hþ –Arn [7]) the
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
first icosahedron-like solvation shell is closed at
n ¼ 12. In the 2 A002 electronic ground state, the
NHþ
3 ion has an unpaired electron in the 2pz orbital of the central N atom. This electron greatly
reduces the electrophilic character of the vacant
2pz orbital [5] and produces thus large differences
in the cluster growth between CHþ
3 –Arn [16] and
þ
NHþ
–Ar
.
In
CH
–Ar
,
charge
transfer
from the
n
n
3
3
Ar solvent into the 2pz orbital causes the p-bonds
to be much stronger than the H-bonds [16], in
contrast to NHþ
3 –Arn (Fig. 1 [5]). In the H-bound
H2 Oþ –Ar dimer, which is isoelectronic to
NHþ
3 –Ar, large spin–rotation splittings are observed and provided useful information about the
intermolecular potential [15]. As the spin–rotation
interaction in the 2 A002 ground state of NHþ
3 is
much smaller than in the 2 B1 state of H2 Oþ , the
open-shell effects in NHþ
3 –Ar are expected to be
smaller than in H2 Oþ –Ar. Moreover, although
certain similarities are expected between the cluster
þ
growth in isoelectronic NHþ
3 –Arn and H2 O –Arn ,
the different number of protons in the core ions
will cause important differences in the topology of
the dimer potential and thus the microsolvation
process. As the proton affinity (PA) of NH2 significantly exceeds that of OH [18,19], the intermolecular H-bond in H2 Oþ –Ar is calculated to be
much stronger than in NHþ
3 –Ar. The PES of
NHþ
–Ar
[5]
is
less
anisotropic
than for H2 Oþ –Ar
3
[14] with smaller barriers to internal rotation.
Hence, in contrast to H2 Oþ –Ar, tunneling splittings are expected to be resolved for NHþ
3 –Ar for
the barriers calculated at the MP2 level [5]. Comparison within the NHþ
k –Arn series with k ¼ 2 [20],
3, and 4 [11–13] will show the effects of the number
of equivalent protons on the interaction with Ar
ligands. Of particular interest are radial strength
and angular anisotropy of the intermolecular interaction as well as structures of the first solvation
shells. Comparison between neutral NH3 –Ar and
the NHþ
3 –Ar cation will show the profound effect
of ionization on the origin and properties of the
intermolecular interaction.
The planar ammonia cation, NHþ
3 (ammoniumyl), with D3h symmetry acts as the chromophore in the present IR studies of NHþ
3 –Arn . The
structure and all four vibrational frequencies in the
2 00
A2 electronic ground state of NHþ
3 and several
87
isotopic species have been characterized by IR [21–
23] and photoelectron spectra [24–30] in the gas
phase as well as an IR spectrum in solid neon [31].
Additional theoretical information is provided by
rovibrational calculations on (scaled) ab initio
PESs [32–35]. The available structural and vibrational parameters are compiled in Tables 1 and 2
of [5]. Briefly, the ground state N–H separation is
[21] and the meadetermined as r0 ¼ 1:0236 A
sured fundamental frequencies of the degenerate
asymmetric N–H stretch, the out-of-plane (umbrella) bend, and the degenerate asymmetric N–H
bend are m3 ðe0 Þ ¼ 3388:65 cm1 [21], m2 ða002 Þ ¼
903:39 cm1 [22], and m4 ðe0 Þ ¼ 1507:1 cm1 [27],
respectively. Available experimental frequencies
for the symmetric N–H stretch fundamental are
less certain and scatter largely between m1 ða01 Þ ¼
2742 40 [24], 3150 100 [25], 3258 56 [28],
and 3404 40 cm1 [29], depending on the correct
interpretation of the photoelectron spectra. The
currently best value based on experimental evidence is derived in the present work from the
1
NHþ
(Section
3 –Ar spectrum as 3234 15 cm
3.1.1), in good agreement with recent theoretical
values ð3180–3240 cm1 [5,32,33,35]). As the normal modes of NHþ
3 are not significantly affected by
Ar complexation [5], the nomenclature describing
the normal modes of NHþ
3 –Arn refers to the four
intramolecular vibrations of NHþ
3 ðmi ; i ¼ 1–4Þ,
and the intermolecular stretching and bending
modes ðms and mb Þ.
Several reactive complexes of NHþ
3 with neutral
ligands, NHþ
–L,
are
discussed
as
intermediates
in
3
ion–molecule reactions [36–39]. Some NHþ
–L
3
complexes with inert ligands are unreactive in the
ground electronic state (e.g., L ¼ CO2 , O2 , and the
rare gas atoms Rg ¼ Ne, Ar, Kr, and Xe [37,40]).
Although NHþ
3 –Rg complexes have been observed
in electron-impact mass spectra of NH3 =Rg mixtures [40], no spectroscopic studies have been
performed to characterize their interaction potentials. Hence, the spectrum of NHþ
3 –Ar reported in
the present work provides the first high-resolution
spectroscopic information about the structure and
stability of NHþ
3 –L dimers. Accurate knowledge of
NHþ
–L
interaction
potentials are required to im3
prove our understanding of ion–molecule reactions of NHþ
3 . Such reactions play a major role in
88
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
the chemistry of N and H containing plasmas,
such as N2 =H2 discharges [23], planetary atmospheres [19] and interstellar media [19,41–43]. In
addition, the NHþ
3 –Ar interaction may be considered as a prototype interaction between a charged
amino group of a biological molecule ðRNHþ
2 Þ and
a nonpolar solvent. Thus, the NHþ
3 –Arn interaction may also be of interest for biophysical phenomena.
2. Experimental
Mid-IR photofragmentation spectra of mass
selected NHþ
3 –Arn complexes (n ¼ 1–6) are recorded in a tandem mass spectrometer apparatus
described in detail elsewhere [6]. The NHþ
3 –Arn
complexes are produced in a cluster ion source
which combines a pulsed and skimmed supersonic
expansion with electron impact ionization. The gas
mixture employed contains NH3 , He, and Ar in a
ratio of 1:10:100 at stagnation pressures between 3
and 8 bars. As expected, higher backing pressures
shift the distribution of NHþ
3 –Arn complexes to
larger cluster sizes. Close to the nozzle orifice the
expansion is crossed by 100 eV electron beams
emitted from two heated tungsten filaments.
Electron impact and Penning ionization processes
close to the nozzle orifice are followed by ion–
molecule and clustering reactions leading to the
formation of weakly bound NHþ
3 –Arn complexes.
The ion–molecule chemistry of a NH3 containing
He plasma has been described previously [21,23].
Similarly, NHþ
3 –Rg dimers have been produced in
electron-impact mass spectra of NH3 /Rg mixtures
[40]. The production of NHþ
3 in a microwave discharge of a NH3 /Ne mixture is discussed in [31].
The central part of the expanded plasma is extracted through a skimmer into a quadrupole mass
spectrometer which is tuned to the mass of the
NHþ
3 –Arn complex under study. After deflection
by 90°, the mass selected parent ion beam is injected into an octopole ion guide where it is intersected by a counterpropagating tunable IR laser
pulse. Resonant excitation of NHþ
3 –Arn into predissociating rovibrational levels lying above the
lowest dissociation limit results in ligand evaporation according to the following process:
H
þ
NHþ
3 –Arn þ hmIR ! ðNH3 –Arn Þ
! NHþ
3 –Arm þ ðn mÞAr
ð1Þ
No other reaction channel after photoexcitation is
observed. The produced NHþ
3 –Arm fragment ions
are selected by a second quadrupole mass spectrometer and monitored by a Daly ion detector.
The IR photodissociation spectrum of NHþ
3 –Arn is
obtained by measuring the yield of the NHþ
3 –Arm
fragment ions as a function of the IR laser frequency ðmIR Þ. To separate the contribution of
fragment ions produced by laser-induced dissociation from the background signal, which mainly
arises from metastable decay of hot parent complexes or dissociation caused by collisions with
residual gas in the octopole region, the ion source
is triggered at twice the laser frequency, and the
laser-off signal is subtracted from the laser-on
signal. In cases where for a given parent complex
(n) more than one fragment channel (m) is observed, spectra are recorded for the two most
probable channels. In agreement with previous
studies on related AHþ –Arn complexes the
photofragmentation spectra do not significantly
depend on the fragment channel m [6,7,10,15,16].
Tunable IR laser radiation is produced by a
Nd:YAG laser pumped optical parametric oscillator (OPO) laser which is characterized by the
following parameters: 0:02 cm1 bandwidth,
2500–6900 cm1 tuning range, 0.5–5 mJ/pulse intensity, 5 ns pulse width, and 20 Hz repetition rate.
The laser frequency is calibrated by optoacoustic
spectra of ammonia [44] recorded simultaneously
with the idler output of the OPO. Interpolation
between reference lines is accomplished by etalon
fringes of the OPO oscillator. In addition, rotational line positions of the NHþ
3 –Ar dimer spectrum are corrected for the Doppler shift
ð0:049 0:005 cm1 Þ arising from the kinetic energy of the ions in the octopole ð5:5 1 eVÞ. The
absolute accuracy of rotational line positions is
limited to 0:01 cm1 due to a combination of the
laser bandwidth and the uncertainty in the ion
kinetic energy. All spectra are normalized for laser
intensity variations recorded with an InSb IR detector assuming a linear power dependence. To
avoid saturation broadening, the rotationally re-
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
solved spectra of the dimer are recorded at reduced
laser intensities (from typically 101 down to
103 mJ=mm2 ).
3. Results and discussion
3.1. NH3þ –Ar dimer (n ¼ 1)
3.1.1. Overview spectrum and vibrational assignments
Fig. 2 reproduces the overview spectrum of
NHþ
in the range between 3160 and
3 –Ar
3460 cm1 recorded in the NHþ
3 fragment channel.
Four vibrational transitions are observed at
3177:4 1, 3305:5 2, 3336:0 1, and 3396:26 0:13 cm1 and they can unambiguously be assigned to the m1 , m1 þ ms , m3 ða1 Þ, and m3 ðb2 Þ vibrations of a H-bound NHþ
3 –Ar dimer structure with
89
C2v symmetry, respectively. The assignments are
based on their positions, intensities, and rotational
structures and are strongly supported by the ab
initio calculations described in [5]. The latter predict the H-bound geometry to be the global minimum on the intermolecular potential determined
at the HF and MP2 levels. If not stated otherwise,
the experimental dimer data are compared in this
section to the results obtained at the MP2/aug-ccpVTZ# calculations (Table 1). The reader is referred to Figs. 1 and 3 of [5] for the calculated
geometry and normal modes of the H-bound
NHþ
3 –Ar dimer.
In the spectral range of the strongly IR active,
doubly degenerate asymmetric N–H stretch fun1
damental of bare NHþ
[21],
3 ðm3 ¼ 3388:65 cm
indicated by an arrow in Fig. 2), two strong
transitions with comparable intensities are found
in the NHþ
3 –Ar spectrum. As discussed in [5],
complexation of NHþ
3 with Ar at the H-bound
binding site reduces the symmetry from D3h to C2v
and splits the doubly degenerate m3 ðe0 Þ fundamental of NHþ
3 into two components of a1 and b2
symmetry. The lower frequency parallel component ðDKa ¼ 0Þ is observed at m3 ða1 Þ ¼ 3336:0 1 cm1 and the higher frequency perpendicular
component ðDKa ¼ 1Þ is centered at m3 ðb2 Þ ¼
3396:26 0:13 cm1 . The deduced complexation
Table 1
Comparison between experimental and theoretical spectroscopic and structural parameters of H-bound NHþ
3 –Ar
Parameter
1
Fig. 2. Overview of the mid-IR photodissociation spectrum of
þ
NHþ
3 –Ar recorded in the NH3 fragment channel. The m1 ða1 Þ,
m1 þ ms ða1 Þ, and m3 ða1 Þ bands are parallel transitions of a nearly
symmetric prolate top. The m3 ðb2 Þ vibration is a perpendicular
transition and the assignments of the Q branches of the
Ka0
Ka00 subbands are given. The arrows above the wavenumber scale indicate the estimated and measured positions of
the m1 ða01 ) and m3 ðe0 Þ transitions of bare NHþ
3 at 3234 15 and
3388:65 cm1 , respectively. The origin of the m3 ðb2 Þ band of
NHþ
3 –Ar is also indicated by an arrow. As the spectrum is
composed of several separate scans, only intensities of closely
spaced transitions are reliable. In particular, two different
mirror sets ( 6 and P 3240 cm1 ) are used in the OPO laser to
record the full spectrum.
m1 ðcm Þ
Dm1 ðcm1 Þ
m3 ðb2 Þ ðcm1 Þ
Dm3 ðb2 Þ ðcm1 Þ
m3 ða1 Þ ðcm1 Þ
Dm3 ða1 Þ ðcm1 Þ
ms ðcm1 Þ
ks (N/m)
A ðcm1 Þ
B ðcm1 Þ
)
Rcm (A
)
RH–Ar (A
a
Expa
Calcb
3177.4(10)
3139.4
)70.5
3395.9
7.2
3323.3
)65.4
133.2
12.4
10.84
0.1313
3.2487
2.2224
3396.26(13)
7.6
3336(1)
)53
128c
11.5c
10.87
0.1282
3.300(1)
2.268(1)
Intermolecular parameters for the ground vibrational state
are averaged over the A2 and E tunneling components.
b
MP2/aug-cc-pVTZ# calculations for the H-bound equilibrium structure [5].
c
Values for the m1 excited state.
90
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
shifts, Dm3 ða1 Þ ¼ 52:7 cm1 and Dm3 ðb2 Þ ¼ þ 7:6
cm1 , agree with the theoretical values of )65.4
and +7.2 cm1 , respectively [5]. Accordingly, the
experimental and calculated m3 splittings compare
favorably (60.3 vs 72:6 cm1 ). Moreover, the calculations predict the IR oscillator strength of
m3 ða1 Þ to be approximately twice that of m3 ðb2 Þ
(ratio 1:8), consistent with the experimental
observations (ratio 2:1). The magnitude and
direction of the observed m3 frequency shifts as well
as the relative IR intensities can be rationalized by
considering the normal mode analysis of the Hbound NHþ
3 –Ar structure (Fig. 3 in [5]). The m3 ða1 Þ
mode involves a significant stretching motion of
the bound N–H bond and experiences thus a large
red shift and an enhancement in its IR intensity
upon complexation. Both effects are typical signs
of H-bonding. On the other hand, m3 ðb2 Þ corresponds mainly to the asymmetric N–H stretch
mode of the two free N–H bonds and features thus
only a small blue shift and a weak reduction in its
IR intensity upon complexation. The vibrational
frequencies, shifts, splitting, and IR intensities of
the two m3 components observed in the IR spectrum of NHþ
3 –Ar can only be explained by a Hbound equilibrium structure (Fig. 1) which is the
calculated global minimum [5]. For example, no
splitting in m3 occurs for a p-bound structure with
C3v symmetry which is calculated to be a less stable
isomer. Moreover, for a planar side-bound geometry with C2v symmetry, calculated to be a lowlying transition state, the predicted shifts of the
two m3 components are in opposite direction and
the splitting is much smaller ð8:8 cm1 Þ compared
to the experimental spectrum.
The parallel transition at 3177:4 1:0 cm1 is
attributed to the m1 fundamental of the H-bound
NHþ
3 –Ar dimer. This mode is IR forbidden for
bare NHþ
3 and its frequency is not well determined
experimentally. Photoelectron studies with the
correct interpretation yield approximate frequencies of m1 3150 100 [25] and 3258 56 cm1
[28], consistent with all theoretical estimates from
(rovibrational) calculations on scaled ab initio
PESs (m1 ¼ 3212 30 [32], 3232 [33], 3233 [35],
and 3210 cm1 [5]). Photoelectron studies with an
alternative interpretation of the adiabatic ionization potential arrive at either significantly lower or
higher frequencies (m1 ¼ 2742 40 [24] and
3404 40 cm1 [29]). Similar to the m3 ða1 Þ component, the ab initio calculations for H-bound
NHþ
3 –Ar predict a large red shift of Dm1 ¼
70:5 cm1 upon complexation [5] because the m1
mode in the dimer involves also a large elongation
in the bound N–H bond. Similar to m3 ða1 Þ the
calculations are assumed to overestimate the m1 ða1 Þ
complexation shift by 20%. Scaling the calculated shift by 0:8 ðDm1 ¼ 70:5 ! 56:4 cm1 Þ,
the m1 frequency of bare NHþ
3 can be estimated as
3234 15 cm1 from the experimental m1 frequency of the dimer ð3177:4 cm1 Þ. Despite the
assumed conservative error of 15 cm1 , this estimate is currently the most accurate available m1
value derived from experimental evidence. The m1
mode becomes IR allowed in H-bound NHþ
3 –Ar
and its predicted IR oscillator strength is comparable to those of the intense m3 components [5].
Indeed, the calculated intensity ratio of the two
parallel bands m3 ða1 Þ and m1 ða1 Þ of 1.7 is in good
agreement with the experimental spectrum in Fig.
2 (ratio 2:1). The large m1 intensity and red shift
are not compatible with side-bound and p-bound
NHþ
3 –Ar structures and confirm the assignment of
the transition to the H-bound isomer.
The parallel band at 3305:5 2 cm1 is assigned to the combination band m1 þ ms , where ms is
the intermolecular stretching mode. The rotational
structure of the band is compatible with such an
assignment and the derived intermolecular
stretching frequency in the m1 state of ms ¼
128 cm1 is in excellent agreement with the value
calculated for the ground vibrational state
ðms ¼ 133 cm1 [5]). Moreover, such combination
bands are typical for H-bonding and have previously been observed in the IR spectra of related
H-bound AHþ –Ar dimers [6,7,10,15,20,45]. Approximating the NHþ
3 –Ar dimer as a pseudodiatomic, the harmonic force constant of the
intermolecular stretching frequency can be estimated as ks 11:5 N=m. Apart from m1 and m3 , the
only other intramolecular state of bare NHþ
3 that
falls in the spectral range between 3100 and
3500 cm1 is the doubly degenerate m4 þ 2m2 mode
with predicted frequencies of 3361 [35] and
3327 cm1 [33]. Neglecting cross anharmonicities,
the m4 þ 2m2 frequency of bare NHþ
3 is estimated as
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
3350 cm1 from the measured frequencies of
2m2 ¼ 1843:161 cm1 [22] and m4 ¼ 1507:1 cm1
[27]. As both the m2 and m4 frequencies show
modest complexation shifts [5], m4 þ 2m2 may be
considered as an alternative assignment for the
3305.5 cm1 band. However, m4 þ 2m2 has not
been observed in the IR spectrum of NHþ
3 recorded in a Ne matrix [31], indicating that its IR
intensity is small. Moreover, for H-bound
NHþ
3 –Ar the m4 IR intensity is predicted to be low
and m4 þ 2m2 should split into a parallel and perpendicular component (with a1 and b2 symmetry)
with similar intensities [5]. In contrast, the experimental spectrum features a single, relatively
strong parallel band. Consequently, the assignment of the 3305:5 cm1 band to m1 þ ms is strongly
favored.
All four vibrational bands in the spectrum of
Fig. 2 are attributed to the H-bound NHþ
3 –Ar dimer which is predicted to be the global minimum on
the intermolecular potential (De ¼ 1133 cm1 ,
D0 ¼ 897 cm1 [5]). No spectral signature of a
p-bound geometry is observed which is calculated
to be a slightly less stable isomer (De ¼ 866 cm1 ,
D0 ¼ 672 cm1 [5]). The small population of the
p-bound isomer under the present experimental
conditions is attributed to low isomerization barriers (< 30 cm1 [5]) toward the H-bound minimum.
3.1.2. Rotational analysis
Three vibrational bands in the IR spectrum in
Fig. 2, namely m1 ða1 Þ, m1 þ ms ða1 Þ, and m3 ða1 Þ, have
the rotational structure appropriate for a parallel
transition of a (near) symmetric prolate top, with
heavily overlapping DKa ¼ 0 subbands. In contrast, the m3 ðb2 Þ band displays clearly resolved rotational structure appropriate for a perpendicular
transition, with well-separated DKa ¼ 1 subbands. Similar to the related H2 Oþ –Rg dimers
[15,46,47], a standard Hamiltonian appropriate for
a semirigid, near prolate symmetric top in a doublet electronic state is considered for the analysis
of the rovibrational structure [48,49]. It is
composed of three terms to account for vibration,
rotation and centrifugal distortion, and spin–
rotation interaction:
H^ ¼ H^vib þ H^rot þ H^sr ;
ð2Þ
H^vib ¼ m0 ;
91
ð2aÞ
H^rot ¼ BN^ 2 þ ðA BÞN^z2 14ðB CÞN^ 2 dKa 1
DN N^ 4 DNK N^ 2 N^z2 DK N^z4 ;
ð2bÞ
H^sr ¼ a0 ðN^x S^x þ N^y S^y þ N^z S^z Þ
þ að2N^z S^z N^x S^x N^y S^y Þ:
ð2cÞ
The vibrational Hamiltonian, H^vib , reduces to a
band origin, m0 . The rotational Hamiltonian, H^rot ,
includes quartic centrifugal terms. The 1=
4ðB CÞN^ 2 dKa 1 term accounts for the small
asymmetry splitting of each rotational level in
Ka ¼ 1 states into c and d parity doublets ðdKa 1 ¼ 1
for Ka ¼ 1 and dKa 1 ¼ 0 otherwise) and B ¼
ðB þ CÞ=2. Because the asymmetry parameter, j,
of H-bound NHþ
3 –Ar is close to )1 (je ¼
0:99970, Be Ce ¼ 0:0016 cm1 [5]), the asymmetry splitting may only be resolved for Ka ¼ 1 at
the present experimental resolution ð0:02 cm1 Þ.
The Hamiltonian for spin–rotation interaction,
H^sr , is appropriate for a symmetric top in a doublet
electronic state [49]. According to Hund’s case (b),
the electron spin S^, couples to the rotational momentum N^ , to form the total angular momentum
(excluding nuclear spin), J^ ¼ N^ þ S^. Thus, in a
doublet electronic state, the spin of the unpaired
electron (S ¼ 1=2) splits each rotational level with
N > 0 into two components with J ¼ N þ 1=2 ðF1 Þ
and J ¼ N 1=2 ðF2 Þ, respectively. The selection
rules for allowed transitions are F1 $ F1 ,
F2 $ F2 , DJ ¼ 0; 1, and DN ¼ DJ . Additional
selection rules for the parallel a-type bands are
DKa ¼ 0; þþ $ þ, and þ $ , whereas
transitions in the perpendicular b-type band connect levels with DKa ¼ 1, þþ $ , and
þ $ þ, respectively [48,50]. The three spin–
rotation parameters a0 , a, and b (b ¼ 0 for a
symmetric top) can be transformed into an
equivalent set of eii parameters (i ¼ a; b; c) [49],
which are more convenient for comparison with
the corresponding constants of free NHþ
3 (ebb ¼ ecc
and eaa ¼ ebb for prolate and oblate symmetric
tops, respectively).
First, the rotational structure of the perpendicular m3 ðb2 Þ band is considered. Adjacent Q
92
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
branches of the DKa ¼ 1 subbands are spaced by
approximately 2ðA0 B0 Þ 21 cm1 . This spacing
is only compatible with semirigid NHþ
3 –Ar dimer
structures with C2v symmetry in which solely two
protons are not lying on the N–Ar axis, such as the
H-bound or side-bound geometries (Fig. 1 in [5]).
For both structures, the calculated rotational
constants of Ae 11 cm1 and Ae Be Ce 0:13 cm1 are compatible with the observed
spacing [5]. In contrast, the spacing expected for
the p-bound local minimum is of the order of
2ðA BÞ 10:5 cm1 [5], in disagreement with the
experimental spectrum.
For a nearly symmetric prolate top molecule
with C2v symmetry and two equivalent protons
(fermions with nuclear spin I ¼ 1=2), the nuclear
spin statistical weights are 1:3 for rovibronic levels
with A ðA1 ; A2 Þ and B ðB1 ; B2 Þ symmetry, respectively [48]. As the vibronic symmetry of the
ground vibrational state in the 2 B1 electronic
ground state of H-bound NHþ
3 –Ar is Celec Cvib ¼ B1 a1 ¼ B1 , rotational levels with even
(odd) Ka quantum numbers have B (A) rovibronic
symmetry. Hence, Ka ¼ even and Ka ¼ odd levels
have different nuclear spin functions and
Ka ¼ even levels have three times higher nuclear
spin statistical weights than Ka ¼ odd levels. The
Ka ¼ even and Ka ¼ odd levels correspond to
the ortho- and para-modification of H-bound
NHþ
3 –Ar, respectively, and interconversion between them (for example by collisions in the early
part of the expansion) are unlikely on the time
scale of the experiment [50]. The intensity alternation of the Ka ¼ even=odd levels arising from
the nuclear spin statistical weights is clearly evident in the experimental spectrum (Fig. 2) where
the populations of the Ka00 ¼ 0 and Ka00 ¼ 2 levels
are enhanced compared to the Ka00 ¼ 1 level, bearing in mind that the population decreases exponentially for increasing Ka00 due to the Boltzmann
factor. Consequently, the Ka ¼ 1
0 Q branch is
by far the most intense one and Q branches from
subbands with Ka ¼ 3 are below the detection limit
because of their low thermal population. Thus, all
para-complexes cool during the expansion into the
Ka00 ¼ 1 state, whereas the cooling for the orthocomplexes is incomplete leading to significant
population of the Ka00 ¼ 0 and 2 states. Simulations
of the Q branch intensities yield a temperature of
TKa 50 10 K for the population of Ka00 levels.
Closer inspection of the intense Ka ¼ 1
0
subband of the m3 ðb2 Þ transition (Fig. 3) shows that
individual rotational lines in the P and R branches
are discernible. Moreover, each rotational P and R
branch line and also the unresolved Q branch is
split into two components, denoted A2 and E. The
A2 series is roughly two times more intense than
the E series. The spacings between adjacent lines in
the P and R branches of both the A2 and E series
are of the order of 2B 0.25–0.26 cm1 , consistent
with the calculated rotational constants of the H1
bound NHþ
[5].
3 –Ar structure, Be ¼ 0:1313 cm
The splitting between the A2 and E series is of the
order of 0:15 0:02 cm1 for unperturbed transitions originating from levels with small N
ðN < 10Þ and decreases slightly to 0:07 0:03 cm1 as N increases (for unperturbed transitions involving N ¼ 20–40).
A splitting of single rotational lines in the rotation–vibration spectrum of a nonrigid, near
prolate symmetric top molecule in a doublet electronic state may be caused by several reasons, including K-type doubling, spin–rotation splitting,
and tunneling splitting. K-type doubling arising
Fig. 3. Expanded view of the Ka ¼ 1
0 subband of the m3 ðb2 Þ
transition of H-bound NHþ
3 –Ar. The inset shows part of
spectrum in the P branch along with assignments. The tunneling
splitting of each rotational line into a doublet (with A2 and E
symmetry) is attributed to hindered internal rotation.
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
from nonvanishing asymmetry ðB C 6¼ 0Þ splits
each rotational N level of a prolate symmetric top
(B ¼ C) with Ka 6¼ 0 into a c and d parity doublet.
For small asymmetry, the splitting is proportional
K
to ðB CÞ a , i.e., it is zero for Ka ¼ 0, largest for
Ka ¼ 1, and much smaller and negligible at the
present
resolution
for
Ka > 1 ðBe Ce ¼
0:0016 cm1 for H-bound NHþ
–Ar
[5]). Thus, for
3
the Ka ¼ 1
0 subband the lower state N 00 levels
are not split, whereas the upper state N 0 levels are
split. As the selection rules are such that the P/R
and Q branch lines terminate at different parity
levels (c and d, respectively) individual rotational
transitions in the P/R and Q branches are not split
but only displaced by the asymmetry. Hence, the
splitting observed in Fig. 3 cannot arise from
asymmetry.
Another possible source for the splitting arises
from spin–rotation interaction in the 2 B1 electronic
state of H-bound NHþ
3 –Ar. For example, such
splittings have been resolved in the IR spectra
of the isoelectronic H2 Oþ –Ar complex [15] and
also the related H2 Oþ –He=Ne dimers [46,47].
Under the realistic assumption that the electromagnetic properties of the electronic wavefunction
2 00
of NHþ
3 in its A2 ground electronic state are only
little affected upon Ar complexation, the spin–rotation constants of H-bound NHþ
3 –Ar can be estimated from those of bare NHþ
3 by scaling them
with the ratios of the moments of inertia [49].
Moreover, the transformation of the inertial axis
system upon Ar complexation has to be taken into
account. This procedure reliably predicted the
spin–rotation constants of isoelectronic H-bound
H2 Oþ –Ar from those of H2 Oþ [15]. Using the experimental rotational and spin–rotation parameters of NHþ
(A00 ¼ B00 ¼ 10:644 cm1 , C 00 ¼
3
1
5:246 cm , eaa ¼ ebb ¼ 0:040 cm1 , ecc ¼ 0 [21])
and the ab initio rotational constants of H-bound
1
NHþ
3 –Ar (Ae ¼ 10:84 cm , Be Ce Be ¼ 0:13
1
cm [5]), the following spin–rotation parameters
are estimated for NHþ
3 –Ar assuming a prolate
symmetric top structure: eaa ¼ 0:041 cm1 ,
jebb j ¼ jecc j < 5 104 cm1 , a ¼ a0 ¼ 0:0137 cm1 ,
and b ¼ 0. Under the realistic assumption that the
spin–rotation constants are similar for the ground
and m3 ðb2 Þ excited states (because of similar rotational constants), the spin–rotation splitting in the
93
m3 ðb2 Þ band can be estimated using the energy level
expressions given in [49]. The evaluated splitting is
largest for the R(0) and P(2) lines ð0:031 cm1 Þ
and decreases rapidly as N increases with a 1=N
dependence [49] to 102 cm1 for N > 10. Thus,
the magnitude of the expected spin–rotation
splitting is roughly one order smaller or less than
the observed splitting ( 0:15 cm1 for small N).
Moreover, the F1 =F2 spin–rotation splitting
strongly depends on N with similar intensities for
both components [15,49]. Both observations are
inconsistent with the experimental spectrum,
where the A2 =E splitting is only weakly dependent
on N and the A2 series is twice as intense as the E
series. Consequently, the observed splitting is attributed to tunneling splitting arising from hindered internal rotation of NHþ
3 within the dimer
and a detailed analysis is presented in Section
3.1.3. Similar tunneling splittings have been observed in the m3 band of the related NHþ
4 –Ar dimer
[12,13]. For the subsequent rotational analysis of
the NHþ
3 –Ar dimer spectrum, the spin–rotation
Hamiltonian (2c) is set to zero.
The rotational line positions of both the A2 and
E tunneling components in the Ka ¼ 1
0 subband of m3 ðb2 Þ are listed in Table 2. In total, 77
transitions are assigned to P(3–41) and R(1–38) of
the A2 component and 78 transitions to P(2–41)
and R(2–39) of the E component. The P and R
branch lines of both components are fit separately
to Hamiltonian (2) to derive the corresponding
molecular constants, B; DN , and m0 in the ground
and m3 ðb2 Þ vibrational states. All other parameters
are set to zero. Initial fits revealed significant local
perturbations in the m3 ðb2 Þ state for N 0 ¼ 9–23 of
the A2 component and N 0 ¼ 34–37 of the E component, leading to deviations of up to 0:12 cm1
between experimental and simulated transition
frequencies. These perturbations cause irregular
spacings between adjacent rotational lines and intensity anomalies that are clearly evident in the P
and R branches of the Ka ¼ 1
0 subband shown
in Fig. 3. Thus, the rotational and centrifugal
distortion constants of the unperturbed ground
vibrational state, B00 and D00N , are determined by
least-squares fitting the ground state combination
differences, D2 F00 ðN Þ, for each tunneling component to Hamiltonian (2) [50]. The constants
94
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
Table 2
Rotational line positions (in cm1 ) of P and R branch lines observed for the A2 and E tunneling components of the Ka ¼ 1
subband of the m3 ðb2 Þ vibration of H-bound NHþ
3 –Ar
A2 component
N
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
a
P(N)
3406.131
3405.839
3405.598
3405.353
3405.075
3404.820
3404.549
3404.288a
3404.031a
3403.773a
3403.569a
3403.144a
3402.890a
3402.637a
3402.375a
3402.119a
3401.879a
3401.596a
3401.326a
3400.874a
3400.651a
3400.342a
3400.070
3399.778
3399.510
3399.185
3398.900
3398.619
3398.320
3398.022
3397.734
3397.433
3397.146
3396.847
3396.545
3396.236
3395.964
3395.661
3395.345
0
E component
3
D 10
0
)31
)9
10
)2
10
8
17
31
46
116
)34
)11
14
31
56
98
97
111
)56
8
)14
2
)1
21
)13
)6
5
0
)4
2
)3
6
3
)2
)13
12
8
)10
3
R(N)
D 10
3407.422
3407.643
3407.917
3408.178
3408.411
3408.661
3408.904
3409.159a
3409.409a
3409.679a
3409.966a
3410.060a
3410.325a
3410.572a
3410.816a
3411.074a
3411.344a
3411.587a
3411.802a
3411.882a
3412.158a
3412.352a
3412.568
3412.795
3413.030
3413.206
3413.416
3413.640
3413.830
3414.040
3414.259
3414.454
3414.663
3414.865
3415.059
3415.257
3415.457
3415.653
9
)22
2
14
0
5
4
17
27
58
108
)33
)2
13
27
56
99
116
107
)35
21
)4
)6
6
27
)10
)11
4
)14
)11
4
)5
2
4
)1
)1
3
4
P(N)
D 103
R(N)
D 103
3406.220
3405.976
3405.696
3405.456
3405.190
3404.915
3404.659
3404.392
3404.126
3403.853
3403.592
3403.313
3403.040
3402.776
3402.497
3402.223
3401.929
3401.658
3401.387
3401.117
3400.823
3400.530
3400.262
3399.986
3399.689
3399.419
3399.139
3398.846
3398.558
3398.258
3397.966
3397.673
3397.377
3397.094a
3396.808a
3396.413a
3396.149a
3395.864
3395.557
3395.254
)5
10
)10
11
7
)4
4
3
3
)2
6
)2
)4
4
)1
)1
)19
)13
)6
4
)10
)21
)7
1
)10
6
14
10
13
4
5
7
6
20
33
)62
)24
)6
)9
)5
3407.510
3407.760
3408.007
3408.246
3408.505
3408.751
3408.988
3409.241
3409.477
3409.704
3409.966
3410.189
3410.430
3410.667
3410.886
3411.119
3411.356
3411.602
3411.834
3412.037
3412.271
3412.480
3412.701
3412.931
3413.141
3413.354
3413.568
3413.783
3413.985
3414.204
3414.415
3414.624a
3414.840a
3414.948a
3415.159a
3415.372
3415.561
3415.774
9
8
5
)5
6
5
)3
7
0
)13
9
)6
)2
0
)14
)13
)6
11
16
)6
4
)9
)7
4
)2
)3
)1
4
)3
10
17
25
41
)48
)31
)11
)11
14
The deviations (D) between observed and calculated positions using the constants listed in Table 3 are also given.
These perturbed lines are excluded from the fits.
derived from fitting 39 (37) combination differences of the A2 (E) component are listed in Table
3. The standard deviations of the fits, r 6 0:01
cm1 , are consistent with observed line width
ð0:02–0:08 cm1 Þ and the accuracy of the cali-
bration ð0:01 cm1 Þ. The constants listed in Table
3 reproduce all combination differences to within
0:016 cm1 . A list of the experimental and calculated combination differences is available upon
request.
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
Table 3
Molecular constants (in cm1 ) of the Ka ¼ 1
0 subband of the m3 ðb2 Þ vibration of H-bound NHþ
3 –Ar
Ka ¼ 0; v ¼ 0a
Ka ¼ 1; v3 ðb2 Þ ¼ 1b
A2
E
A2
E
0.128265(29)
5.48(13)
39
39
6.8
0.128198(35)
5.04(17)
37
37
8.0
3406.9049(29)
0.1274781(95)
5.082(64)
77
47
10.2
3406.7387(20)
0.1275993(72)
5.502(47)
78
70
8.6
c
m0
B
DN (107 )
Assigned data
Used data
r (103 )
95
Standard deviations are listed in parentheses.
Constants determined by fitting ground state combination differences, D2 F00 ðN Þ, to Hamiltonian (2).
b
Constants determined by fitting the transition frequencies listed in Table 2 to Hamiltonian (2) and keeping the lower state constants
fixed at values derived from the analysis of D2 F00 ðN Þ.
c
Absolute accuracy of the calibration is 0:01 cm1 . These m0 values differ by A0 from the band origin of m3 ðb2 Þ.
a
The P and R branch transitions listed in Table 2
are least-squares fitted to Hamiltonian (2) to determine the upper state constants B, DN , and m0 of
both tunneling components of the m3 ðb2 Þ Ka ¼
1
0 subbands. All other constants are set to
zero. In these fits the rotational constants of the
lower state are fixed to the values derived from the
analysis using combination differences (Table 3).
Moreover, transitions to the perturbed upper state
levels mentioned above are excluded from the fits.
In total 47 (70) transitions are used to derive the
upper state constants of the A2 (E) component
summarized in Table 3 and the residuals
(D ¼ exp calc) are listed in Table 2. The residuals
are less than 0:03 cm1 for transitions into unperturbed levels and up to 0:12 cm1 for transitions into perturbed levels. Although the
interacting ‘‘dark’’ states could not be identified,
they significantly affect the intensities of the P and
R branch lines of the ‘‘bright’’ transitions. Despite
these perturbations, the rotational temperature
corresponding to the population of the N 00 rotational levels in the Ka00 ¼ 0 state can be estimated as
TN 60 20 K from simulations of the
Ka ¼ 1
0 subband. This value is in good agreement with the temperature describing the population of the Ka00 levels, TKa ¼ 50 10 K. As expected,
the m0 origins of the A2 and E components derived
from the fits of the P and R branch lines (Table 3)
are close to the Q branch heads, because of the
small asymmetry (B–C). Moreover, the origins are
only slightly below the Q branch maxima reported
in Table 4 as the difference in the rotational constants of both vibrational states ðB0 B00 Þ is small.
Fig. 4 shows expanded views of the unresolved
Q branches of all five observed Ka0
Ka00 subbands
of the m3 ðb2 Þ transition. Each Q branch is split into
several components which may arise from tunneling, spin–rotation splittings and sequence transitions, and their positions and widths are listed in
Table 4. Although some of the P and R branch
lines of the weaker Q branches arising from Ka00 > 0
are clearly discernible, low signal-to-noise ratios
and congestion prevent a detailed rotational
analysis. The positions of the Q branch components of each Ka0
Ka00 subband are averaged
(Table 4) and least-squares fitted to Hamiltonian
(2) to roughly estimate the A rotational constants
in the ground and m3 ðb2 Þ vibrational states as well
as the band origin of m3 ðb2 Þ. The resulting constants are m0 ¼ 3396:26 ð13Þ cm1 , A0 B0 ¼
10:522ð29Þ cm1 and A00 B00 ¼ 10:742ð56Þ cm1 ,
respectively. All other constants are set to zero in
the fit. The standard deviation of the fit,
r ¼ 0:13 cm1 , is consistent with the overall
breadth of the Q branches ranging from 0.4 to
0:9 cm1 . Using B00 B0 0:128 cm1 (Table 3),
the A rotational constants in both vibrational
states are estimated as A00 ¼ 10:87 and A0 ¼
10:65 cm1 , respectively. As expected, the A constant decreases slightly upon m3 ðb2 Þ excitation,
mainly due to an increase in the averaged N–H
bond lengths. The derived complexation-induced
blue shift of the m3 ðb2 Þ frequency, Dm3 ðb2 Þ ¼
96
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
Table 4
Maxima (in cm1 ) and widths (FWHM) of the components of the unresolved Q branches of the Ka0
vibration of H-bound NHþ
3 –Ar
Ka0
Ka00
Average
1
2
0
1
1
0
2
1
Ka00 subbands of the m3 ðb2 Þ
3
2
3363.61(6)
3363.82(6)
3363.95(14)
3364.18(6)
3385.23(10)
3385.38(10)
3385.48(7)
3406.61(8)
3406.77(12)
3406.95(20)
3427.70(5)
3427.83(10)
3447.56(12)
3447.73(6)
3447.87(13)
3448.02(8)
3448.34(17)
3363.89
3385.36
3406.77
3427.77
3447.90
Fig. 4. Expanded view of the Q branches of the Ka0
7:6 cm1 , agrees with the calculated value of
7:2 cm1 [5].
Although the three parallel bands m1 ða1 Þ,
m1 þ ms ða1 Þ, and m3 ða1 Þ with overlapping DKa ¼ 0
subbands display rotational fine structure, congestion arising from tunneling, asymmetry and
spin–rotation splitting, and possible perturbations
prevents a detailed analysis similar to that of the
perpendicular m3 ðb2 Þ transition. Fig. 5 shows expanded views of the m1 ða1 Þ and m3 ða1 Þ transitions.
Clearly, higher resolution spectra are desired for
definitive rotational assignments. Nonetheless,
some conclusions can be derived from the coarse
structure of the three parallel bands supporting
their vibrational assignments. The m1 ða1 Þ band is
centered at 3177:4 1 cm1 and features a P
branch head near 3169 cm1 . The occurrence of a
P branch head indicates that the rotational B
constant increases upon vibrational excitation,
Ka00 subbands of the m3 ðb2 Þ transition of H-bound NHþ
3 –Ar.
consistent with a shorter and stronger intermolecular bond. Such bond contractions are typical
for excitation of proton donor stretch vibrations in
AHþ –Rg complexes (Section 3.1.4). In contrast,
the m1 þ ms band centered at 3305:5 2 cm1 features a head in the R branch near 3308:5 cm1 .
Additional excitation of the intermolecular stretch
vibration in the m1 state causes an increase in the B
constant, because the lengthening of the intermolecular bond upon ms excitation overrides the effect
of bond shortening due to m1 excitation. Similarly
to m1 ða1 Þ, the m3 ða1 Þ band with band origin at
3336:0 1 cm1 is slightly shaded to the blue.
However, as the bond contraction is less pronounced, no prominent head in the P branch occurs for the range of N levels observed.
The widths of individual lines observed in the
spectrum in Fig. 2 range from 0.02 to 0:08 cm1 .
Partly unresolved tunneling, spin–rotation, and
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
Fig. 5. Expanded views of the parallel m1 ða1 Þ and m3 ða1 Þ transitions of H-bound NHþ
3 –Ar. The inset shows an expanded part
of the m3 ða1 Þ spectrum. A definitive assignment of the rotational
structure is prevented by congestion arising from the overlapping DKa ¼ 0 subbands and splittings due to tunneling, spin–
rotation interaction, asymmetry, and possible perturbations.
asymmetry splittings give rise to the observed
broadening of many lines. However, several isolated rotational lines in all four bands are limited
by the laser bandwidth of 0:02 cm1 , giving rise to
a lower limit of the upper state lifetime,
s > 250 ps. A firm upper limit for the time scale of
the fragmentation process is provided by the
quantitative observation of dissociation during the
ions’ passage through the octopole ion guide
ð102 lsÞ.
3.1.3. Tunneling
As discussed in Section 3.1.2, the observed
A2 =E splitting in the Ka ¼ 1
0 subband of m3 ðb2 Þ
is attributed to a tunneling motion of NHþ
3 –Ar
which connects the three equivalent H-bound
minima on the PES via hindered internal rotation
of NHþ
3 through potential barriers. This tunneling
motion splits each rovibronic level of A1 , A2 , B1 ,
and B2 symmetry in the molecular symmetry
group G4 of the rigid complex into two components with A01 þ E0 , A001 þ E00 , A002 þ E00 , and A02 þ E0
symmetry in the molecular symmetry group G12
for the nonrigid complex, respectively [51]. The G4
and G12 molecular symmetry groups are isomorphic to the C2v and D3h point groups, respectively.
97
Alternating rotational N levels in the Ka ¼ 0 state
of the vibrational ground state of NHþ
3 –Ar have
B1 and B2 symmetry in C2v (MS) and are split into
A002 þ E00 and A02 þ E0 levels in D3h (MS), respectively (abbreviated by A2 þ E in the following
discussion). The selection rules for allowed transitions are A01 $ A001 , A02 $ A002 , E0 $ E00 and the
nuclear spin statistical weights are 0, 4, and 2 for
levels with A1 , A2 , and E symmetry in D3h (MS) for
a molecule with three equivalent protons, respectively [51]. Indeed, a 4:2 intensity alternation for
the (unperturbed) A2 and E levels is clearly observed in the spectrum (e.g., see inset in Fig. 3) and
supports the assignments given in Fig. 3 and Table
2. The magnitude of the tunneling splitting observed in the m3 ðb2 Þ Ka ¼ 1
0 subband is of the
order of 0:15 0:02 cm1 (small N). For example,
the difference in the band origins of the A2 and E
components derived from fitting the P and R
branch lines is 0:17 cm1 (Table 3), whereas the
maxima of the corresponding Q branches are
separated by 0:18 cm1 (Table 4).
The selection rules prevent the separate determination of the tunneling splitting in each vibrational state from the observed spectra. In order to
estimate the tunneling splitting in the ground vibrational state of NHþ
3 –Ar, D0 , the one-dimensional
(1-D) minimum energy path for in-plane NHþ
3
internal rotation is considered. Ab initio calculations predict a threefold barrier of V3 ¼ 320 cm1
(MP2 level) occurring at the three side-bound
structures [5]. Approximating the effective internal
rotor constant by the C rotational constant of
NHþ
in the ground vibrational state (C0 3
5:25 cm1 [22]), the 1-D Schr€
odinger equation is
solved to obtain the eigenvalues of the two lowest
energy levels [52]. The ground state tunneling
splittings derived from this 1-D model are
D0 ¼ 0:96, 0.16, 0.03, and 0.01 cm1 for V3 ¼ 100,
200, 300, and 400 cm1 , respectively. The splitting
depends sensitively on the barrier height and is
comparable to the observed splitting for barriers
of Vb 200 cm1 which is somewhat smaller than
the calculated barrier V3 ¼ 320 cm1 . The 1-D
model is expected to somewhat underestimate the
tunneling splittings owing to several approximations. First, full 3-D rovibrational calculations are
likely to produce larger splittings on the same 3-D
98
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
intermolecular PES, because the zero-point energy
contributions from the additional intermolecular
degrees of freedom reduce the effective barrier [53].
Second, in addition to the lowest energy tunneling
path assumed in the 1-D calculation, there is another competing low-energy path on the 3-D PES
which connects the three H-bound global minima
via the p-bound local minima. Although this outof-plane path is slightly longer than the in-plane
path, the barrier is comparable (Vb 310 cm1 Þ,
indicating that a 3-D tunneling path needs to be
considered for calculating reliable tunneling splittings. Although such calculations have previously
been performed for related dimers, such as
þ
NHþ
4 –Rg [12,13,54] and CH3 –Rg [53], they are
beyond the scope of the present work. The results
of such 3-D calculations are also required for a
firm assignment of the Q branch components of
the m3 ðb2 Þ Ka0
Ka00 subbands in Fig. 4 and Table 4
(other than the assigned Q branches of the
Ka ¼ 1
0 subband with A2 and E symmetry).
Neglecting the small tunneling splittings, the IR
spectrum of NHþ
3 –Ar in Fig. 2 is similar to that
expected for a semirigid H-bound NHþ
3 –Ar dimer,
indicating that the complex is closer to the limit of
a semirigid bender than to free internal rotation.
This situation is expected because both the NHþ
3
rotational constants (< 11 cm1 [22]) and the zeropoint level are well below the hindered rotation
barriers ( 300 cm1 ) [55].
In general, the tunneling splitting may sensitively depend on the vibrational state and the Ka
quantum number [13,46,56]. Unfortunately, from
the available spectral information it is not obvious
whether the splitting observed in Fig. 3 ð 0:15
cm1 Þ corresponds to the sum or the difference of
the tunneling splittings in both vibrational states.
Usually, for isolated noninteracting vibrational
states, the doubly degenerate E tunneling component of a threefold XY3 internal rotor is lying
above the nondegenerate A component (noninverted case) [57]. Assuming this scenario for both
the ground and m3 ðb2 Þ vibrational states and neglecting the Ka dependence of the splitting, the
observed splitting of 0:15 cm1 corresponds to the
decrease of the tunneling splitting upon m3 ðb2 Þ
excitation. Such a decrease is expected as the vibrational energy in the excited state has to be ex-
changed between the N–H bonds during the
tunneling motion. This situation is, for example,
observed in the case of the related H2 Oþ –Rg dimers with Rg ¼ He [47] and Ne [46]. Also in the
related NHþ
4 –Ar dimer, the tunneling splitting
arising from NHþ
4 internal rotation decreases from
1:8 cm1 in the ground vibrational state
(Ka ¼ 0) to 1:0 cm1 in the perpendicular component of the m3 vibrational state ðKa ¼ 1Þ [12,13].
In addition to vibrational excitation, apparently
also rotational excitation reduces the tunneling
splitting in NHþ
3 –Ar. On the other hand, for
strongly interacting vibrations, the E tunneling
component of a threefold XY3 internal rotor may
be lower in energy than the A component (inverted
case) [57]. Such a situation occurs for CH3 internal
rotation in the asymmetric C–H stretching fundamentals of CH3 OH [56] because of the strong
coupling between the torsion and the three C–H
stretching modes. As the CH3 internal rotation in
CH3 OH is very similar to the NHþ
3 hindered rotation in NHþ
–Ar
with
respect
to
the
internal ro3
tation barriers and the coupling strengths between
the intramolecular stretching states, the internal
rotation splitting in the m3 ðb2 Þ fundamental of
NHþ
3 –Ar may also be inverted. Following this
scenario, the observed tunneling splitting in Fig. 3
of 0:15 0:02 cm1 (small N) would correspond to
the sum of the splittings in both vibrational states
implying that the ground state splitting is of the
order of 0:12 0:05 cm1 . As a splitting of this
magnitude is compatible with the ab initio PES,
further spectroscopic or theoretical information is
required to definitively decide whether the tunneling splitting is regular or inverted in the m3 ðb2 Þ
vibrational state of NHþ
3 –Ar.
3.1.4. Discussion
The detailed rovibrational analysis of the midIR spectrum of NHþ
3 –Ar, including vibrational
frequency shifts and splittings, IR intensities, rotational constants, nuclear spin statistical weights,
is only consistent with a H-bound equilibrium
structure, in agreement with the ab initio PES
calculated at the MP2 level [5]. All spectral features are assigned to this isomer and no spectral
evidence of the predicted, shallow local p-bound
minimum is observed.
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
The molecular constants of H-bound NHþ
3 –Ar
are used to estimate the structural parameters of
the intermolecular bond in the ground vibrational
state (v ¼ 0, Ka ¼ 0). The rotational constants in
Table 3 indicate that the intermolecular interaction is very similar in both the A2 and E tunneling
states. Assuming that the NHþ
3 structure is not
affected by Ar complexation (rN–H ¼ r0 ¼
derived from B0 ¼ 10:64399 cm1 [21]),
1:0235 A
the intermolecular center-of-mass separation is
, yielding a H–Ar
estimated as Rcm ¼ 3:300ð1Þ A
. The ab initio calculaseparation of 2.2765(10) A
tions predict a small elongation of the bound N–H
). Corbond upon Ar complexation (by 0.0082 A
recting for this deformation, the H–Ar separation
in the ground
is estimated as R0 ¼ 2:268ð1Þ A
vibrational state. This value is compatible with the
[5]. As expected,
ab initio value of Re ¼ 2:2224 A
the equilibrium separation (Re Þ is slightly smaller
than the ground state separation (R0 Þ because of
the anharmonicity of the intermolecular stretching
motion. According to the ab initio calculations,
the Ae rotational constant increases slightly upon
complexation ðDAe 0:1 cm1 [5]), mainly due to
a decrease in the HNH bond angle of the free
N–H bonds. This trend is confirmed by the experimental rotational constants ðDA0 0:2 cm1 Þ.
Using a pseudodiatomic approach [58], the harmonic force constant and frequency of the intermolecular stretching mode in the ground
vibrational state can be estimated from the rotational and centrifugal distortion constants:
ks ¼ 11:3 0:7 N=m and xs ¼ 126 5 cm1 .
These values compare favorably to the ab initio
data (12.4 N/m, 133 cm1 ) and the values derived
from the m1 þ ms combination band (11.5 N/m,
128 cm1 ). Table 1 compares the salient molecular
parameters derived from the spectroscopic data
with the ab initio properties derived for the
H-bound equilibrium structure. As can be seen,
the agreement between experiment and theory is
nearly quantitative.
The dissociation energy of the dimer in the intramolecular ground vibrational state is calculated
as D0 900 cm1 [5]. The modest m3 ðb2 Þ blue shift
upon complexation, Dm3 ðb2 Þ ¼ 7:6 cm1 , reflects
the relatively small decrease in the intermolecular
binding energy upon vibrational excitation (<1%).
99
The small influence of m3 ðb2 Þ excitation on the intermolecular bond is expected, as this mode corresponds mainly to the asymmetric N–H stretch
vibration of the two free N–H bonds (Fig. 3 in [5]).
Consequently, the parameters of the intermolecular bond are expected to be similar in both vibrational states. Indeed, the analysis of the rotational
constants of the A2 and E components in the
m3 ðb2 Þ vibrational state (using rN–H ¼ r3 ¼
derived from B3 ¼ 10:51793 cm1 [21])
1:0297 A
yield structural and vibrational parameters very
similar to the ground state values: Rcm ¼
, RH–Ar ¼ 2:259ð1Þ A
, ks ¼ 10:9 0:5
3:297ð1Þ A
N=m, xs ¼ 124 0:4 cm1 . The decrease in the A
rotational constant upon m3 ðb2 Þ excitation ( 0:2
cm1 or 2%) is mainly due to an increase in the
vibrationally averaged N–H separations. A similar
effect is observed in the bare monomer, where the
A rotational constant decreases by 0:13 cm1
(1.2%) [21].
In contrast to m3 ðb2 Þ, excitation of m1 ða1 Þ and
m3 ða1 Þ have a larger effect on the intermolecular
interaction. The normal coordinates of the latter
two modes are very similar for the elongation of the
bound N–H bond adjacent to the intermolecular
H–Ar bond (Fig. 3 in [5]). Consequently, the calculated complexation shifts are also very similar:
Dm3 ða1 Þ ¼ 65:4 and Dm1 ða1 Þ ¼ 70:5 cm1 . Experimentally, only Dm3 ða1 Þ is determined (as m1 of
NHþ
3 is not known with sufficient accuracy), and
the derived shift of 53 cm1 is close to the theoretical value (Table 1). The red shifts imply that the
strength of the intermolecular interaction increases
by about 6% upon excitation of these two modes.
This effect is typical for the excitation of proton
donor stretch vibrations in proton-bound dimers
[4,59]. Excitation of the bound N–H bond in Hbound NHþ
3 –Ar leads to an enhanced proton shift
from NHþ
3 toward the Ar ligand, leading to a
shorter and stronger intermolecular bond. The
contraction of the H–Ar bond explains the formation of the head in the P branch of the m1 ða1 Þ
transition (because B00 < B0 ). Both the m1 ða1 Þ and
m3 ða1 Þ bands are clearly shaded to the blue and may
contain additional signal in the blue wings arising
from sequence transitions of the type m1=3 ða1 Þ þ
mx
mx (where mx are intermolecular vibrations).
Such transitions are often accompanying the
100
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
excitation of proton donor stretch fundamentals
in H-bound dimers. The sequence bands occur to
the blue of the fundamentals, because the intermolecular interaction is stronger and more anisotropic in these intramolecular excited states
(leading to higher intermolecular bending and
stretching frequencies) [4,10,15,20,45]. Hence, the
intermolecular stretching frequency in the m1 excited state, derived from m1 þ ms and m1 as
128 cm1 , is slightly larger than that expected for
the ground state. For example, in the related
SiOHþ –Ar dimer (which has a similar binding
energy) the intermolecular stretching frequencies
are 103 and 116 cm1 in the ground and m1 excited
states, respectively [10]. The m1 þ ms band is clearly
shaded to the red (with a sharp head in the R
branch), as the large effective bond lengthening
upon ms excitation overcompensates for the minor
bond contraction upon m1 excitation (leading to
B00 > B0 ).
The lifetimes of the vibrationally excited states
estimated from the linewidths of the most narrow
spectral features are larger than 250 ps for all
observed vibrations. The relatively long lifetimes
with respect to both predissociation and intracomplex vibrational energy redistribution are
consistent with the weak coupling of the excited
states to other intra- and intermolecular degrees of
freedom. The weak intermolecular bond in
1
NHþ
3 –Ar ðDe ¼ 1133 cm Þ causes only weak
coupling between intra- and intermolecular modes,
leading to small complexation-induced frequency
shifts ðjDm1;3 j < 70 cm1 Þ and long predissociation
lifetimes ðs1;3 > 250 psÞ. In contrast, the much
stronger bond in isoelectronic H-bound H2 Oþ –Ar
ðDe ¼ 2484 cm1 Þ induces strong coupling between the proton donor stretch ðm1 Þ and the dissociation continuum, leading to a large red shift
ðDm1 ¼ 541 cm1 Þ and a short lifetime ðs1 ¼ 10 5 psÞ [15].
3.1.5. Comparison to related systems
In this section, the properties of the NHþ
3 –Ar
dimer derived from the IR spectra are compared to
those of related systems. The following discussion
focuses mainly on the experimental results,
whereas corresponding theoretical data are compared in [5].
Several proton-bound AHþ –Ar dimers have
recently been studied by the same experimental and
theoretical tools. All of them feature (nearly) linear
H-bonds and their properties are compared in
Table 5. The table includes dissociation energies
calculated at the MP2/aug-cc-pVTZ# level (De Þ, as
well as the complexation-induced frequency shifts
of the A–H stretch vibration ðDm1 Þ, and harmonic
force constants (ks Þ and separations (RH–Ar Þ of the
intermolecular bond derived from rovibrational IR
spectra. The corresponding theoretical data for Dm1
and RH–Ar may be found in Table 6 of [5]. In general, the intermolecular bond strength in AHþ –Ar
is related to the proton affinity of the base A,
PA(A) [4,59]. As for all AHþ –Ar dimers in Table 5
PAðAÞ PAðArÞ ¼ 369 kJ=mol [18], they are essentially AHþ ions weakly perturbed by the relatively fragile intermolecular bond to the Ar ligand.
Complexation shifts the proton from A toward Ar
and results in a flattening of the potential for the
proton motion leading to a red shift in the A–H
stretching frequency, Dm1 . The following systematic
trend is observed: the lower PA(A), the stronger
and shorter the intermolecular bond (larger De and
ks , smaller RAr–H Þ, and the more pronounced the
delocalization of the proton (larger jDm1 jÞ. However, for some AHþ
k –Ar complexes with k equivalent protons (k > 1), jDm1 j is smaller than estimated
from PA(A). This is particularly true for the weakly
bound AHþ
k –Ar dimers with high PAðAHk1 Þ, such
as NHþ
–Ar
and NHþ
4
3 –Ar. In these systems the
weak intermolecular bond does not sufficiently
decouple the local A–H stretch modes. Thus, although the m1 normal mode is dominated by the
bound A–H stretch, it contains significant elongations of the free A–H bonds, leading to a reduced
effective Dm1 shift upon complexation. For example, the similar PAs of SiO and NH2 lead to similar
intermolecular interaction strengths in SiOHþ –Ar
and NHþ
3 –Ar but the m1 shift is much smaller for
NHþ
–Ar
(Table 5). In contrast, for strongly bound
3
AHþ
–Ar
dimers such as OHþ
2 –Ar, the intermoleck
ular perturbation is sufficiently strong to nearly
completely decouple the bound A–H stretch from
the free ones. Consequently, in strongly bound
AHþ
k –Ar complexes Dm1 provides a direct measure
of the intermolecular interaction energy (in contrast to the weakly bound dimers).
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
101
Table 5
Comparison of several properties of H-bound AHþ –Ar dimers
AHþ –Ar
H3 NHþ –Ara
SiOHþ –Arb
H2 NHþ –Ar
OCHþ –Arc
HNHþ –Ard
HOHþ –Are
OCOHþ –Arf
N2 Hþ –Arg
PA(A)
ðkJ=molÞh
De ðcm1 Þ
Dm1 ðcm1 Þ
ks (N/m)
)
RH–Ar (A
854
778
773
594
590
593
541
494
927
)22
6
2.34
1117
)217
13
2.19
1133
)70i
12
2.27
1551
)274
17
2.13
1773
300 50
20
2.06
2484
)541
29
1.93
2379
)704
2881
)728
38
1.90
a
Refs. [11,12].
Refs. [10].
c
Refs. [6,7].
d
Ref. [20].
e
Ref. [15].
f
Ref. [45].
g
Refs. [4,7,9,73].
h
Refs. [18,19]. PA(Ar) ¼ 369 kJ/mol.
i
Theoretical value (Ref. [5]).
b
Interestingly, the properties of the intermolecular interaction in NHþ
3 –Ar differs in several aspects from the one in isoelectronic H2 Oþ –Ar
[14,15]. The intermolecular bond is much stronger
and shorter in the latter complex (Table 5), due to
PAðOHÞ PAðNH2 Þ. Moreover, also the angular
anisotropy is larger in H2 Oþ –Ar and the higher
barriers to internal rotation lead to smaller tunneling splittings which could not be resolved at the
level of the present spectral resolution [15]. On the
other hand, spin–rotation splittings are larger and
resolved in H2 Oþ –Ar compared to NHþ
3 –Ar because the spin–rotation interaction in H2 Oþ is
larger than in NHþ
3 [15]. In both cases, the radical
character resulting from the unpaired electron in
the 2p orbital perpendicular to the molecular plane
does not significantly affect the intermolecular interaction strength of the H-bound dimer. Hence,
the properties of the H-bonds of the open-shell
dimers are roughly similar to those of corresponding closed-shell complexes with bases A of
similar PA (Table 5).
Calculations for XHþ
3 –Ar with X ¼ C, N, and
O predict a drastic effect of the electron density in
the 2pz orbital on the intermolecular PES [5]. The
vacant 2pz orbital in CHþ
3 is very electrophilic and
electron transfer from Ar into this orbital leads to
a rather strong intermolecular p-bond in
1
CHþ
3 –Ar ðDe ¼ 6411 cm Þ, in good agreement
with the experimental IR spectrum [16]. The 2pz
orbital in NHþ
3 is occupied with one electron which
largely reduces its electrophilic character. Consequently, NHþ
3 –Ar adopts a H-bound structure
which is more stable than the p-bound isomer.
Similarly, a H-bound equilibrium structure is observed in the IR spectrum of H3 Oþ –Ar, because
the Pauli exchange repulsion of the two electrons
in the 2pz orbital of H3 Oþ further destabilizes the
p-bound structure compared to the H-bound global minimum [60]. In general, increasing the electron density in the 2pz orbital of these XHþ
3 ions
causes the p-bond in XHþ
–Ar
to
become
weaker,
3
whereas the H-bond becomes stronger.
Comparison between the NHþ
k –Ar dimers with
k ¼ 2–4 shows the effects of the number of
equivalent protons on the properties of the intermolecular interaction, such as strength and anisotropy. The most stable structures of all three
dimers feature linear proton bonds and their interaction strengths are anticorrelated to PA
(NHk1 Þ. As PA(NHk1 Þ increases with k, the intermolecular bonds in NHþ
k –Ar become weaker
and longer, as can be seen from the values for De ,
ks , Dm1 , and RH–Ar in Table 5. Parallel to the
strength of the interaction, the anisotropy of the
PES decreases with increasing k. The calculations
predict diminishing barriers to internal rotation of
Vb 800, 300, and 200 cm1 for k ¼ 2–4, respectively. As at the same time the tunneling path
between equivalent H-bound minima becomes
102
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
shorter, the probability for tunneling in NHþ
k –Ar
þ
þ
increases in the order NHþ
2 < NH3 < NH4 (as the
effective internal rotor constants are similar). Indeed, the tunneling splittings observed in the IR
1
spectra of m3 of NHþ
[12]) are
4 –Ar ( 0:5–1 cm
þ
larger than those of m3 of NH3 –Ar ( 0:15 cm1 ).
The IR spectra of the N–H stretch fundamentals
of NHþ
2 –Ar lack tunneling splittings, i.e., they are
< 0:04 cm1 [20].
The intermolecular bond in neutral NH3 –Ar
[61,62] differs drastically from that in the NHþ
3 –Ar
cation demonstrating the pronounced effect of
ionization on the interaction. The additional
charge causes the intermolecular bond in NHþ
3 –Ar
to become much shorter and stronger compared to
). In addition, the
NH3 –Ar (Rcm ¼ 3:30 vs 3:57 A
anisotropy of the potential is much smaller in the
neutral dimer [62]: the small barriers to internal
rotation are comparable to the NH3 rotational
constants and as a result the complex is highly
nonrigid and close to the free internal rotation
limit.
3.2. Larger NH3þ –Arn complexes (n ¼ 2–6)
3.2.1. IR spectra
Fig. 6 compares the IR spectra of NHþ
3 –Arn for
n ¼ 1–6 recorded in the dominant NHþ
3 –Arm
fragment channel (indicated as n ! m). The maxima and widths of the observed transitions are
summarized in Table 6, along with their assignments. For the larger cluster sizes investigated
ðn > 3Þ, several fragment channels are possible
and the photofragmentation branching ratios observed for m3 excitation are summarized in Table 7.
The IR spectra of NHþ
3 –Arn display distinct vibrational frequency shifts and splittings as well as
intensity variations as a function of cluster size
which are used to characterize the microsolvation
process of NHþ
3 in argon. According to the ab
initio calculations at the MP2 level, the dimer PES
features three H-bound global minima ðDe ¼
1133 cm1 Þ and two less stable p-bound local
minima ðDe ¼ 866 cm1 Þ. Thus, in the most stable
NHþ
3 –Arn complexes the first three Ar ligands are
expected to form equivalent proton bonds,
whereas the next two Ar atoms are p-bound (Fig.
1), leading to highly symmetric cluster structures
Fig. 6. Mid-IR photodissociation spectra of NHþ
3 –Arn complexes recorded in the dominant NHþ
3 –Arm fragment channel
(indicated as n ! m). The intense bands in each spectrum are
assigned to the vibrations of the most stable isomers of each
cluster (Fig. 1). The asterisks indicate absorptions attributed to
less stable isomers. The arrows above the wavenumber scale
indicate the estimated and measured positions of the m1 ða01 Þ and
1
m3 ðe0 Þ transitions of bare NHþ
3 at 3234 15 and 3388:65 cm ,
respectively. As the n ¼ 1 and 2 spectra are composed of several
separate scans, only intensities of closely spaced transitions are
reliable. In particular, the latter spectra are recorded with two
different mirror sets ( 6 and P 3240 cm1 Þ.
with C2v ðn ¼ 1; 2Þ, D3h ðn ¼ 3; 5Þ and C3v ðn ¼ 4Þ
symmetry. The spectroscopic information extracted from the IR spectra in Fig. 6 strongly
support this scenario.
First, the m3 bands of NHþ
3 –Arn are considered.
As discussed in detail in Section 3.1.1, complexation of NHþ
3 with one Ar ligand reduces the
symmetry from D3h to C2v and causes the degenerate asymmetric N–H stretch vibration,
m3 ðe0 Þ ¼ 3388:65 cm1 (indicated by an arrow in
Fig. 6), to split into two components in the
H-bound NHþ
3 –Ar dimer ðn ¼ 1Þ, namely m3 ða1 Þ
with a large red shift (53 cm1 ) and m3 ðb2 Þ with a
small blue shift ðþ7:6 cm1 Þ. The experimental
shifts and relative IR intensities are in good
agreement with the calculations. The magnitude
and direction of the shifts are easily rationalized by
the corresponding normal mode pictures (Fig. 3 in
[5]). Similar to NHþ
3 –Ar, the m3 vibration of the
NHþ
–Ar
trimer
ðn
¼ 2Þ is split into two compo2
3
nents with a1 and b2 symmetry, consistent with a
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
103
Table 6
Band maxima (in cm1 ) and widths (FWHM, in parentheses) of the transitions observed in the IR spectra of NHþ
3 –Arn clusters
recorded in the NHþ
3 –Arm fragment channel along with the assignments to the most stable isomer (Fig. 1)
n
m
Transition
Assignment
Isomer
1b
0
3177:4 1
3305:5 2
3336:0 1
3396:26 0:13
m1 ða1 Þ
m1 þ ms ða1 Þ
m3 ða1 Þ
m3 ðb2 Þ
C2v
C2v
C2v
C2v
3172(20)
3279(6)
3305(5)
3376(12)
m1 ða1 Þ
m3 ðb2 Þ
m1 þ ms ðb2 Þc
m3 ða1 Þ
C2v
C2v
C2v
C2v
2
0
Dm3 a
)53
7.61
)110
)13
3
0
3306(10)
m3 ðe0 Þ
D3h
)83
4
0d
1
3326(35)
3319(14)
m3 (e)
C3v
)63
)70
5
1
2d
3332(20)
3330(8)
m3 ðe0 Þ
D3h
)57
)59
2
3338(17)
?
)51
6
m3
a
Band shifts with respect to the m3 frequency of bare
Band origins.
c
Uncertain assignment.
d
Minor fragment channel.
b
NHþ
3
1
ð3388:65 cm
[21]).
Table 7
þ
Photofragmentation branching ratios of NHþ
3 –Arn into NH3 –Arm and ðn–mÞAr atoms (Eq. (1)) for excitation at the m3 band maxima
n
1
2
3
4
5
6
m
0 (1.0)
0 (1.0)
0 (1.0)
0 (0.27)
1 (0.73)
0 (0.14)
1 (0.49)
2 (0.36)
2 (1.0)
1.0
2.0
3.0
3.27
3.74
4.0
hn mi
Only channels contributing more than 5% are listed. Uncertainties are estimated as 0.05.
C2v equilibrium structure. However, the m3 ða1 Þ
component at 3376 cm1 is higher in frequency
than the m3 ðb2 Þ component at 3279 cm1 ; consistent with the normal mode analysis [5]. The symmetric m3 ða1 Þ mode corresponds mainly to the
stretch of the free N–H bond, whereas the m3 ðb2 Þ
mode is predominantly an asymmetric stretch of
the two bound N–H bonds. Both measured frequencies of the trimer are in agreement with the
values calculated at the MP2 level (3373 and
3260 cm1 [5]). Similar to the dimer, the measured
splitting ð79 cm1 Þ is somewhat smaller than the
calculated one ð113 cm1 Þ. In addition, the calculations predict m3 ðb2 Þ of the trimer to be three times
more intense than m3 ða1 Þ, consistent with the ex-
perimental spectrum in Fig. 6. The assignments of
m3 ða1 Þ and m3 ðb2 Þ are also supported by the observed band profiles: m3 ða1 Þ is a broader parallel
band composed of overlapping DKa ¼ 0 subbands
leading to the appearance of single intense P and R
branches and a band gap at 3376:1 cm1 ; on the
other hand, m3 ðb2 Þ is a narrower symmetric perpendicular band which is mainly composed of
unresolved, closely spaced intense Q branches of
the DKa ¼ 1 subbands.
In contrast to the dimer and trimer with C2v
symmetry, the m3 band of the NHþ
3 –Ar3 tetramer
ðn ¼ 3Þ is not split. The appearance of a single intense peak at m3 ðe0 Þ ¼ 3306 cm1 is consistent with
the degenerate N–H stretch vibration of a planar
104
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
D3h symmetric structure featuring three equivalent
proton bonds (Fig. 1). The red shift with respect to
1
free NHþ
may be compared to the value
3 of 83 cm
1
of 130 cm calculated at the B3LYP level. Similar
to the tetramer, the IR spectra of the NHþ
3 –Arn
clusters with n ¼ 4–6 feature single intense m3 bands
indicating that the threefold structural symmetry is
strictly (n ¼ 4 and 5) or effectively conserved ðn ¼
6Þ. The geometries of the n ¼ 4 and n ¼ 5 complexes
are predicted to have C3v and D3h symmetry, with
one and two p-bound ligands attached to a (nearly)
planar NHþ
3 –Ar3 core, respectively (Fig. 1). The
single m3 bands of the n ¼ 4 and n ¼ 5 clusters occur
at m3 ðeÞ ¼ 3319 cm1 and m3 ðe0 Þ ¼ 3330 cm1 , implying nearly additive total blue shifts of 13 and
24 cm1 with respect to the n ¼ 3 complex. These
values compare favorably to calculations of the
p-bound dimer and trimer, for which total blue
shifts of 13.1 and 23:6 cm1 are predicted for complexation of bare NHþ
3 with one and two p-bound
Ar ligands, respectively [5]. Fig. 7 compares the
experimental m3 frequencies of NHþ
3 –Arn (n ¼ 0–5)
with those calculated at the HF level [5]. Although
the HF level underestimates the intermolecular interaction strength and thus the magnitude of shifts
and splittings in the intramolecular N–H stretching
frequencies, the overall pattern shows good qualitative agreement with the experimental data and
strongly supports the given assignments. A similar
conclusion was previously drawn for related
þ
AHþ
k –Arn clusters, such as H2 O –Arn [14,15],
þ
þ
NH4 –Arn [11], and CH3 –Arn [16].
Fig. 7. Comparison of experimental (a, Table 6) and theoretical
(b, Table 11 in [5], HF/aug-cc-pVTZ# level) frequencies of the
asymmetric N–H stretch fundamentals ðm3 Þ of NHþ
3 –Arn
ðn ¼ 0–5Þ.
In addition to the m3 bands, the m1 ða1 Þ fundamentals are observed for the n ¼ 1 and n ¼ 2
complexes at 3177.4 and 3172 cm1 , respectively.
As discussed in Section 3.1.1, the m1 mode of bare
NHþ
3 is IR forbidden and values from photoelectron spectra are rather inaccurate. Reduction of
symmetry from D3h to C2v makes the m1 fundamental IR allowed in H-bound NHþ
3 –Ar and
NHþ
–Ar
,
respectively.
The
m
band
in the IR
2
1
3
spectrum of NHþ
–Ar
is
rather
strong
and com3
parable in intensity to the m3 components. In contrast, for NHþ
3 –Ar2 the observed m1 IR oscillator
strength is about one order of magnitude smaller
than that of m3 ðb2 Þ, consistent with the theoretical
intensity ratio of 1:8.5 [5]. According to the MP2
calculations, m1 displays red shifts of )70.5 and
11:2 cm1 upon sequential Ar complexation at
the H-bound binding sites [5]. The first value has
been used to estimate the monomer frequency as
3234 15 cm1 (indicated by arrows in Figs. 2 and
6) and the second one is in qualitative agreement
with the experimental shift of 5 cm1 (bearing in
mind that the m1 band of NHþ
3 –Ar2 has a width of
20 cm1 ). The m1 range of the complexes with n > 2
has not been investigated, because this fundamental should either be IR forbidden or very weak
for these cluster sizes [5].
The magnitude and direction of the frequency
shifts and splittings of the N–H stretch vibrations
(m1 and m3 ) in NHþ
3 –Arn upon sequential Ar complexation are rationalized in detail in [5] by considering the effects of the intermolecular H-bonds
and p-bonds on the strength of the intramolecular
N–H bonds and their influence on the N–H stretch
normal coordinates. Briefly, formation of intermolecular proton bonds (n ¼ 1–3) causes the N–H
bonds on average to become weaker and longer,
and as a result the averaged N–H stretching frequency decreases almost linearly as a function of n.
The observation of this linear trend implies that
the intermolecular proton bonds have roughly
similar interaction energies (independent of n) and
three-body interactions are not very important.
For example, the averaged experimental m3 frequency decreases by 28 cm1 per Ar ligand from
3388:65 cm1 ðn ¼ 0Þ to 3306 cm1 ðn ¼ 3Þ. Calculations at the B3LYP and MP2 levels predict a
somewhat larger decrease of 43 and 36 cm1 per
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
Ar atom, respectively. In contrast, the HF level
clearly underestimates the interaction leading to a
too small shift of 12 cm1 per Ar atom. After
closure of the first subshell at n ¼ 3, further Ar
ligands form p-bonds to the 2pz orbital of
NHþ
3 –Ar3 which causes the N–H bonds to become
shorter and stronger again. Hence, the m3 frequency increases again by 12 cm1 per Ar atom
from 3306 cm1 ðn ¼ 3Þ to 3330 cm1 ðn ¼ 5Þ.
Again, the HF calculations for n ¼ 3–5 underestimate the blue shift, with a value of 9 cm1 per Ar
atom. The observation of the roughly additive blue
shifts upon sequential complexation at the pbound sites (13 and 11 cm1 Þ indicates that the
two equivalent p-bonds in NHþ
3 –Ar5 are only
slightly weaker than the one in NHþ
3 –Ar4 . Thus,
again the three-body contributions appear to be
small and noncooperative.
So far, the dominant features in the spectra of
NHþ
3 –Arn with n ¼ 1–5 are all explained by considering the most stable cluster structure for each
cluster size (Fig. 1, Table 6). As the binding energies for the H-bonds and p-bonds are not too
different (De ¼ 1133 and 866 cm1 , respectively),
the occurrence of less stable NHþ
3 –Arn isomers
may be expected in the expansion. However, no
sign of a p-bound dimer is visible in the spectrum
of NHþ
3 –Ar (Section 3.1.1). The unassigned band
at 3305 cm1 in the spectrum of NHþ
3 –Ar2 may at
first glance be attributed to a m3 component of a
less stable isomer. However, this transition cannot
be assigned to m3 ðe0 Þ of the pp isomer (two
p-bonds, D3h symmetry, Fig. 1f in [5]), because its
frequency should be higher compared to NHþ
3,
m3 ðe0 Þ ¼ 3388:65 cm1 , as p-bonds strengthen the
N–H bonds. For similar reasons, an assignment to
the Hp isomer (one H-bond and one p-bond, Cs
symmetry, Fig. 1g in [5]) can be excluded as the m3
components of this isomer should occur to the
blue of the m3 bands of the H-bound NHþ
3 –Ar dimer (i.e., m3 > 3336 cm1 [5]). Hence, the
3305 cm1 transition has to be attributed to a vibration of the most stable NHþ
3 –Ar2 isomer featuring two proton bonds [5]. The band contour is
similar to the one of m3 ðb2 Þ suggesting that it is a
perpendicular transition. One possible assignment
is to the m4 þ 2m2 ðb2 Þ combination band which may
acquire IR intensity by interacting with the
105
strongly IR active m3 ðb2 Þ level via a Fermi resonance. An alternative assignment is to the combination band of m1 with one of the two
intermolecular stretching modes, m1 þ ms . Similar
combination bands are observed for the NHþ
3 –Ar
dimer and also the related H2 Oþ –Arn clusters [15].
The antisymmetric ms ðb2 Þ frequency is predicted as
147 cm1 (MP2), i.e., the m1 þ ms ðb2 Þ frequency is
estimated as 3319 cm1 [5], in close proximity to
the observed 3305 cm1 band. Similar to the
m4 þ 2m2 ðb2 Þ vibration, this transition may gain IR
intensity from the m3 ðb2 Þ fundamental via a Fermi
resonance. At present, an assignment to m1 þ ms ðb2 Þ
is favored, as indicated in Fig. 6 and Table 6. The
broad low-energy shoulder of the m3 ðe0 Þ band of
the most stable HHH isomer of NHþ
3 –Ar3 (marked
by an asterisk in Fig. 6) may arise from a less
stable HHp isomer with two H-bonds and one
p-bond, because this absorption is shifted a few
cm1 to the blue of the m3 ðb2 Þ band of the HH
trimer. Such a small blue shift is expected for
formation of an additional p-bond. Moreover, the
p-bound Ar ligand in the HHp trimer may be
further stabilized by two Ar–Ar contacts. Likewise, the low-energy shoulder of the main m3 ðe0 Þ
transition of the most stable NHþ
3 –Ar4 complex
may be due to less stable isomers, such as the
HHpp pentamer.
According to the ab initio calculations and the
microsolvation model in Fig. 1, the first solvation
shell is closed at n ¼ 5, with three proton-bound
ligands in the first subshell and two p-bound ligands in the second subshell. The second solvation
shell is expected to start at n ¼ 6. The m3 band of
the NHþ
3 –Ar6 heptamer shows a single peak at
3338 cm1 which corresponds to a further blue
shift of 6 cm1 with respect to NHþ
3 –Ar5 . This
shift is approximately 50% of the one caused by a
p-bound ligand in the first shell ð13 cm1 Þ. Apparently, the m3 shift is not saturated after filling
the first shell at n ¼ 5. The total m3 shift of the
n ¼ 6 complex from the NHþ
3 monomer frequency
amounts to 51 cm1 . Low signal-to-noise ratios
prevented the spectroscopic investigation of clusters larger than n ¼ 6. So far, no Ar matrix isolation studies on NHþ
3 have been performed making
it impossible at the present stage to compare the
NHþ
3 –Arn cluster band shifts with the bulk limit
106
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
ðn ! 1Þ. The total m3 shift of the n ¼ 6 complex of
1.5% lies within the typical range of band shifts of
stable and unstable species in Ar matrices (<2%
[63]). Interestingly, the m3 band of NHþ
3 embedded
in a Ne matrix is shifted to higher frequency
compared to the gas phase value (by þ16 cm1 or
0.5% [31]). The preferred binding site of the 6th
ligand in NHþ
3 –Ar6 is not obvious and no calculations have been performed for clusters larger
than n ¼ 5 [5]. Assuming a van der Waals radius of
for Ar [64], the closest approach to the
1.9 A
charge of a rigid NHþ
3 –Ar5 core appears to be
along the side-bound orientation at a distance of
from the central N atom. At this binding
4:5 A
site, the 6th Ar ligand pushes on two H-bound Ar
ligands of the first shell and causes the corresponding H-bonds to deviate from linearity. As a
result, these H-bonds will become weaker and the
adjacent N–H bonds stronger. The latter effect is
compatible with the observed increase in the
asymmetric N–H stretching frequency, m3 . The
appearance of a single m3 band in the NHþ
3 –Ar6
spectrum implies that the effect of symmetry reduction on the local NHþ
3 environment caused by
the 6th ligand in the second shell is marginal.
Consequently, the splitting into two m3 components is small (< 10 cm1 ) and unresolved.
In contrast to the dimer, the transitions of the
larger NHþ
3 –Arn cluster ðn > 1Þ do not display
resolved rotational substructure, mainly because
the rotational constants are decreasing rapidly
with increasing n. For example, the calculated ro1
tational constants of NHþ
3 –Ar2 (Ae ¼ 0:42 cm ,
1
1
Be ¼ 0:026 cm , and Ce ¼ 0:025 cm [5]) are of
the order of the laser bandwidth of 0:02 cm1 ,
leading to heavily overlapping DKa ¼ 0 and
DKa ¼ 1 subbands in the parallel and perpendicular transitions, respectively. In addition, the
tunneling probability for internal NHþ
3 rotation is
also expected to decrease rapidly with increasing
number of Ar ligands, because the effective barrier
to internal rotation increases upon formation of
additional intermolecular bonds. For example,
neglecting three-body forces and assuming that the
proton bonds are equivalent in the NHþ
3 –Arn
clusters with n ¼ 1–3, the effective barrier is
Vb ðnÞ nVb , where Vb 320 cm1 is the barrier for
the dimer ðn ¼ 1Þ [5].
3.2.2. Dissociation energies
According to Eq. (1), vibrational excitation of
larger NHþ
3 –Arn clusters may lead to the observation of several competing fragment channels
(m < n). The observed fragmentation branching
ratios following m3 excitation are summarized in
Table 7. Up to the cluster size n ¼ 3, m3 excitation
exclusively leads to the evaporation of all ligands
(m ¼ 0). However, for n ¼ 4 and n ¼ 5 two major
fragment channels are observed. Similar to previous studies on related systems [6,7,10,15,16,65],
the range of m for a given n is rather narrow. As a
result, this information can be used to infer approximate values for incremental ligand binding
energies. For this purpose, a statistical approach is
adopted based upon following assumptions and
approximations. (1) The kinetic energy release as
well as the difference in the internal energies of the
parent and daughter ions are neglected. (2) Only
Ar atoms and no oligomers are evaporated. (3)
Ligands with smaller binding affinities are evaporated first. (4) Ligands at equivalent binding sites
have the same binding energy and three-body effects are neglected. (5) The Ar–Ar interactions are
ignored, as they are much weaker than the
NHþ
3 –Ar interactions. Within the framework of
this model, the absorbed photon energy
(m3 3300 cm1 ) must be larger than the sum of
the binding energies of the (n m) evaporated ligands but smaller than the sum of the (n m þ 1)
most weakly bound ligands. This model has been
applied to a variety of related cluster systems and
has yielded dissociation energies in satisfactory
agreement with ab initio calculations and thermochemical data [6,7,10,15,16,65,66]. In the case
of NHþ
3 –Arn , the ligands are classified into two
groups, namely H-bound and p-bound ligands
with dissociation energies D0 (H) and D0 (p) and the
additional assumption that D0 ðHÞ > D0 ðpÞ. The
restrictions derived from the data in Table 7 are
then 825 < D0 ðHÞ=cm1 < 1100 and 550 < D0 ðpÞ=
cm1 < 1100. Hence, both dissociation energies
are consistent with the ab initio values of D0 ¼ 900
and 670 cm1 for H-bound and p-bound NHþ
3 –Ar,
respectively [5]. The validity of this model implies
further that two photon processes are not observed
at the laser intensities employed (0.1 mJ/mm2 Þ.
The fact that the averaged number of evaporated
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
Ar ligands, hn mi, systematically increases with
cluster size implies that the incremental binding
energies of Ar ligands decreases as the cluster
grows (Table 7).
For those NHþ
3 –Arn clusters for which several
fragment channels are observed, the IR spectra
recorded in each channel differ slightly in the position and largely in the width of the m3 bands
(Table 6). For example, n ¼ 4 complexes can
evaporate either 3 or 4 Ar ligands upon m3 absorption and the corresponding m3 band maxima
(widths) are 3319 (14) and 3326 (35) cm1 for the
m ¼ 1 and m ¼ 0 fragment channel, respectively.
In general, parent clusters containing more internal energy prior to excitation can shed more ligands after absorption of the IR photon.
Consequently, the IR spectra recorded in the
smaller fragment channel correspond to the absorptions of warmer species. Hence, the m3 bands
are significantly broadened and somewhat shifted
due to additional contributions of sequence transitions m3 þ mx
mx compared to the spectra of
vibrationally colder species recorded in the higher
fragment channel. The IR spectra in Fig. 6 are
recorded in the dominant fragment channel,
whereas the analysis of the frequency shifts and the
branching ratios (to derive binding energies) are
based on the data of the colder NHþ
3 –Arn clusters.
3.2.3. Comparison to related systems
In general, the properties of the microsolvation
process of a Mþ cation in argon (such as the shape
and size of the primary solvation shells or the sequence of shell filling) depends sensitively on the
size, shape, and charge distribution of the central
ion which determines the Mþ –Ar dimer interaction
potential. Usually, the Mþ –Ar interaction is much
stronger than the Ar–Ar interaction ( 100 cm1
[64]). Hence, neglecting three-body effects it is clear
that the Mþ ion in large Mþ –Arn clusters is localized inside the Arn cluster rather than on the
surface. This is certainly also true for the
NHþ
3 –Arn system. For small atomic and molecular
ions with a nearly isotropic Mþ –Ar interaction,
the first solvation shell in Mþ –Arn complexes is
closed at n ¼ 12 leading to an icosahedral structure allowing for closed packing [67]. Magic
numbers observed in a variety of mass spectra of
107
Mþ –Arn [68,69] as well as photoelectron spectra of
O –Arn [70] confirm this view. Moreover, systematic band shifts observed in the IR spectra of
AHþ –Arn (A ¼ N2 [7], OC [6]) indicate that the
first solvation shell in these systems is also filled at
n ¼ 12 and composed of two staggered equatorial
five-membered rings around a linear Ar–AHþ –Ar
trimer core. In the latter examples, the closed-shell
core ions (N2 Hþ ; OCHþ ) have a similar size as Ar,
so that the n ¼ 12 clusters are only slightly distorted icosahedrons with a nearly ‘‘spherical’’ impurity in the center. However, the sequence of
filling the first solvation shell is slightly different
for the SiOHþ ion compared to HCOþ and N2 Hþ
owing to subtle differences in the charge distributions and molecular shapes of these isovalent ions
[6,7,10].
The cluster growth in AHþ
k –Arn systems in
which the central AHþ
ion
has
several equivalent
k
protons ðk > 1Þ differs qualitatively from that in
þ
AHþ –Arn and Arþ
n complexes. The AHk ions have
usually several distinct attractive centers for ligands created by the k protons and/or unpaired
electrons. For example, NHþ
3 offers three H-bound
and two p-bound sites. Consequently, the PESs of
AHþ
k –Ar dimers are of lower symmetry and usually more anisotropic than the PESs of AHþ –Ar
dimers with linear AHþ ions. Thus, the intermolecular bonds in AHþ
k –Arn are more directional
and the AHþ
ions
are
far from being a spherical
k
impurity within the icosahedral Arn clusters. In
general, in AHþ
k –Arn complexes whose dimer PESs
feature pronounced H-bound global minima, the
first k Ar ligands form equivalent proton bonds,
whereas further ligands (n > k) are attached to less
favorable binding sites. Examples of this type inþ
clude H2 Oþ –Arn [14,15], NHþ
4 –Arn [11], H3 –Arn
þ
[71,72], and NH3 –Arn . However, not all AHþ
k –Arn
systems belong to this class. For example, the
CHþ
3 –Ar potential features pronounced p-bound
global minima and only shallow H-bound local
minima [16,17]. Thus, in CHþ
3 –Arn the first two Ar
ligands form p-bonds, whereas further ligands are
attached to the protons [16].
The cluster growth in NHþ
3 –Arn is in many respects analogous to that in NHþ
4 –Arn [11]. The
solvation in NHþ
–Ar
also
begins
with the forman
4
tion of equivalent proton bonds (n ¼ 1–4, first
108
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
subshell) and proceeds then with solvation at the
four faces of the tetrahedral ion (n ¼ 5–8, second
subshell) leading to structures with high symmetry
[11]. The IR spectra of the N–H stretch vibrations in
NHþ
4 –Arn show frequency shifts and splittings as a
function of cluster size similar to those of NHþ
3 –Arn .
For example, the first four Ar ligands lead to a red
shift of the (averaged) triply degenerate asymmetric
1
N–H stretch vibration of NHþ
4 , m3 ðt2 Þ, of )9.4 cm
per Ar atom, whereas the face-bound ligands in the
second subshell cause a blue shift of +3.7 cm1 per
Ar atom [11]. These values are smaller than those
for H-bonds and p-bonds in NHþ
3 –Arn ()28 and
+12 cm1 Þ, as the interactions in NHþ
4 –Arn are
weaker than in NHþ
–Ar
.
For
example,
the calcun
3
lated binding energies for proton- and face-bound
1
NHþ
[12]) are lower
4 –Ar (De ¼ 927 and 723 cm
than those of proton- and p-bound NHþ
3 –Ar (1133
and 866 cm1 Þ, respectively. These theoretical
numbers are supported by the experimental
photofragmentation branching ratios. For example, NHþ
4 –Ar4 evaporates predominantly all Ar ligands upon m3 excitation [11], whereas NHþ
3 –Ar4
loses mainly three ligands owing to the stronger
proton bonds in the latter complex. The estimated
dissociation energies are 825 < D0 ðHÞ=cm1 <
1100 for NHþ
3 –Arn ðn ¼ 1–3Þ and D0 ðHÞ 825
cm1 for NHþ
4 –Arn ðn ¼ 1–4Þ [11].
The cluster growth in NHþ
3 –Arn is in certain
aspects also comparable to that in isoelectronic
H2 Oþ –Arn [14,15]. In H2 Oþ –Arn , the first two
H-bound Ar ligands cause a red shift in the averaged O–H stretch frequencies of 194 cm1 per Ar
atom, whereas the subsequent two p-bound ligands
lead to blue shifts of 80 cm1 per Ar atom [15].
These shifts are much larger than those of
1
NHþ
3 –Arn ()28 and þ12 cm ) because of the
much stronger interaction in H2 Oþ –Arn : De ¼ 2484
and 1939 cm1 for H-bound and p-bound
H2 Oþ –Ar, respectively [14]. As a consequence of
the larger interaction in H2 Oþ –Arn , the shifts
caused by complexation of Ar ligands at equivalent
binding sites decrease drastically as the cluster size
increases: e.g., the red shifts of the averaged O–H
stretch upon sequential proton solvation are )258
ðn ¼ 1Þ and )130 cm1 ðn ¼ 2Þ, respectively [15].
Hence, the nonadditivity of the interactions in
H2 Oþ –Arn is more pronounced than in the more
weakly bound NHþ
3 –Arn complexes leading to
significantly larger noncooperative three-body interactions in the former complexes.
4. Concluding remarks
The intermolecular interaction and microsolvation process of NHþ
3 with up to six Ar ligands
are investigated for the first time by high-resolution IR spectroscopy. The rotationally resolved
spectra of all three N–H stretch fundamentals of
the NHþ
3 –Ar dimer ðn ¼ 1Þ provide a wealth of
information about the details of the interaction
potential of this fundamental cation–ligand complex. The dimer features a H-bound planar equilibrium structure with C2v symmetry. Rotational
and centrifugal distortion constants of the ground
vibrational state are consistent with an intermo and a stretching
lecular H–Ar separation of 2.27 A
force constant of 12 N/m. Tunneling splittings
indicate low barriers for hindered internal rotation
of the NHþ
3 ion connecting the three equivalent
H-bound global minima via planar side-bound
transition states. Although the preliminary analysis of the tunneling process using a 1-D model
reported in the present work supports this interpretation, a quantitative description of this hindered internal motion requires the solution of the
rotation–vibration Schr€
odinger equation using the
3-D interaction potential (similar to the recent
study of CHþ
3 –He/Ne [53]). By comparison with
theoretical data, the frequency of the infrared (IR)
forbidden m1 fundamental of free NHþ
3 is estimated
from the NHþ
–Ar
spectrum
as
3234
15 cm1 ,
3
the currently most accurate value based upon experimental measurements. This example demonstrates that cluster ion spectroscopy may be used
to infer spectroscopic properties of the bare ion.
Although the IR spectra of larger NHþ
3 –Arn
complexes ðn ¼ 2–6Þ are not rotationally resolved,
the vibrational bands display distinct frequency
shifts and splittings of the N–H stretching modes
as a function of cluster size. The spectra are
compatible with cluster geometries in which the
first three Ar ligands fill a first subshell by forming
equivalent intermolecular proton bonds ðn ¼ 1–3Þ
leading to planar structures with either C2v or D3h
O. Dopfer et al. / Chemical Physics 283 (2002) 85–110
symmetry. The next two Ar ligands occupy a second subshell by forming equivalent p-bonds to the
two lobes of the 2pz orbital of NHþ
3 leading to
cluster structures with C3v ðn ¼ 4Þ and D3h symmetry ðn ¼ 5Þ. The first Ar solvation shell around
the interior NHþ
3 ion is closed at n ¼ 5 and the 6th
Ar ligand occupies a position in the second solvation shell. The dissociation energies of the Hbonds and p-bonds are estimated as D0 ðHÞ 950 150 cm1 and D0 ðpÞ 800 300 cm1 , respectively. In general, the intermolecular H-bonds
significantly weaken the intramolecular N–H
bonds, whereas the p-bonds slightly strengthen
them. Moreover, the effects are slightly noncooperative and become weaker as the cluster size increases.
In line with the topic of this Special Issue, the
combined spectroscopic and theoretical approach
reported in the present work and the accompanying article [5] demonstrates that the fruitful interplay between high-resolution spectroscopy and
quantum chemical calculations provides a very
powerful tool to further improve our knowledge of
fundamental ion–ligand interactions. In addition,
the present results on the NHþ
3 –Arn model system
may be useful for a better understanding of the
interaction between charged biomolecular amines
with nonpolar spherical solvent molecules.
Acknowledgements
This study is part of the project No. 2063459.00 of the Swiss National Science Foundation. The authors thank S.A. Nizkorodov for
valuable assistance during the experimental part of
this study. O.D. is supported by the Deutsche
Forschungsgemeinschaft via a Heisenberg Stipendium (DO 729/1-1).
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