FTIR and computational studies of pure and water containing SO3 species in solid argon matrices

Article abstract of DOI:10.1016/j.molstruc.2006.06.027

The FT infrared spectrum in the 4000-400 cm^-1 range of SO₃ vapors, matrix isolated in argon and in water doped argon solid layers, is reported. Vibrational bands are assigned to pure SO₃ monomeric and polymeric species and to SO₃?H₂O complexes, on the basis of theoretical B3LYP and MP2 calculations employing the aug-cc-pVTZ basis sets. The spectroscopic evidence suggests that in addition to the monomer, both the dimeric and the cyclic trimeric (SO₃)_n complexes are the only other SO₃ forms present in the matrix. The spectra also indicate the presence of the 1:1 and the 1:2 SO₃·H₂O complexes as well as traces of H₂S₂O₇ and water complexed H₂SO₄, but no evidence for a stable 2:1 SO₃?H₂O complex was found. The occurrence of the various species is discussed in the light of their calculated energies.

Full text of DOI:10.1016/j.molstruc.2006.06.027

Journal of Molecular Structure 830 (2007) 21–34
www.elsevier.com/locate/molstruc
FTIR and computational studies of pure and water containing
SO3 species in solid argon matrices
a
a,
b
a
Aharon Givan , Aharon Loewenschuss *, Claus J. Nielsen , Mark Rozenberg
a
Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
b
Department of Chemistry, University of Oslo, Blindern, N-0315 Oslo, Norway
Received 2 May 2006; received in revised form 15 June 2006; accepted 21 June 2006
Available online 4 August 2006
Abstract
The FT infrared spectrum in the 4000–400 cmꢀ1 range of SO3 vapors, matrix isolated in argon and in water doped argon solid layers,
is reported. Vibrational bands are assigned to pure SO3 monomeric and polymeric species and to SO3ꢁ ꢁ ꢁH2O complexes, on the basis of
theoretical B3LYP and MP2 calculations employing the aug-cc-pVTZ basis sets. The spectroscopic evidence suggests that in addition to
the monomer, both the dimeric and the cyclic trimeric (SO3)n complexes are the only other SO3 forms present in the matrix. The spectra
also indicate the presence of the 1:1 and the 1:2 SO3ÆH2O complexes as well as traces of H2S2O7 and water complexed H2SO4, but no
evidence for a stable 2:1 SO3ꢁ ꢁ ꢁH2O complex was found. The occurrence of the various species is discussed in the light of their calculated
energies.
Ó 2006 Elsevier B.V. All rights reserved.
Keywords: SO3 (sulfur trioxide); SO3 (sulfur trioxide) polymers; SO3 (sulfur trioxide)–water complexes; Matrix isolation; Ab-initio and DFT calculations
1. Introduction
transition state – the (SO3)Æ(H2O) adduct, and that the
energy barrier between this transition state and the reac-
tants may be as high as approximately 30 kcal/mol. This
value gradually decreases with the increasing number of
water molecules participating in the hydrolysis process
increases [8,16–18]. For the formation of the (SO3)Æ(H2O)4
adduct no such energy barrier exists any more, and H2SO4
is readily formed. This obviously holds true for the
calculated stabilization energies of the adducts of SO3
and even larger numbers of water molecules. Moreover,
these calculations indicate that the hydrolysis of SO3 with
an excess of water molecules may result in H2SO4 hydrates
– (H2SO4)Æ(H2O)n (n P 1) species. Although polymeric SO3
molecules exist in SO3 vapors [19], we found no parallel
theoretical work on the hydrolysis of (SO3)n (n > 1) species.
The infrared spectrum of pure SO3 vapors was investi-
gated previously in the gas phase [19,20], as well as in neon,
argon and xenon matrices [21] and bands attributed to SO3
monomers and polymers were observed. SO3 infrared
absorption lines were also discerned in the spectrum of
the vapors over liquid H2SO4 (which due to the prevalent
SO3 is an intermediate in the chain of reactions by which
atmospheric sulfuric acid – a prominent constituent of
aerosols [1] and acid rain [2], is formed. This chain starts
with gaseous SO2 molecules of both anthropogenic and
natural origins, and proceeds to the acid formation, via
what can be crudely regarded as a two step mechanism.
The first step is the oxidation of SO2 by agents such as
hydroxyl radicals and oxygen molecules. This step may
take place in a variety of pathways with SO3 as their com-
mon final product [3–7]. Subsequently, gas phase hydroly-
sis of SO3 forms sulfuric acid:
SO3 þ H2O ! H2SO4
The theoretical aspects of the last reaction were studied
extensively [8–16]. They all indicate that the reaction be-
tween SO3 and a single water molecule passes through a
*
Corresponding author. Tel.: +972 2 658 5313; fax: +972 2 658 5319.
E-mail address: loewena@chem.ch.huji.ac.il (A. Loewenschuss).
0022-2860/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2006.06.027

22
A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
equilibrium, contain significant amounts of SO3 and H2O)
trapped in argon matrices [22], in experiments involving the
photooxidation products of H2S in oxygen matrices [23]
and in studies of the photolysis of mixtures of SO2, O3
and H2O in nitrogen matrices [24].
While adding water impurities to SO3 samples trapped
in neon [21], nitrogen [24] and oxygen [23] matrix resulted
in the observation of additional bands, assigned to the
(SO3)Æ(H2O) complex, this complex could not be stabilized
during the annealing of an argon matrix containing SO3
and H2O [24] or be clearly detected in the infrared spec-
trum of sulfuric acid vapors [22]. With the exception of sev-
eral polymeric (SO3)n bands recorded in the neon matrix
experiment [21], no infrared spectrum of either matrix
trapped (SO3)n species or (SO3)n(H2O)m (n > 1) polymers
was found.
The argon matrix gas, either pure or premixed with
water vapors (ratios in the range of 1:50–1:2000), was
deposited through a surrounding the central nozzle from
which the SO3 vapors were emanating. The estimated
SO3 guest:argon ratios in the matrix on the central CsI win-
dow, kept at 17–20 K, are estimated to be in the 1:100–
1:1000 range. Cooling was provided by an Air Products
CSW 202A Heliplex cryostat. Typical deposition times
were 1–3 h, depending upon sample dilution, while deposi-
tion rates of argon gas were of several mmol hꢀ1. Temper-
ature cycling of the samples was conducted by slow
warming up to 38–40 K, followed by fast recooling to
17 K.
Infrared spectra were recorded on a Bruker Equinox 55
spectrometer, employing a DTGS detector, coadding 32 to
128 scans at resolutions of 0.5–2 cmꢀ1
.
The aim of the present study is twofold:
3. Calculations
The spectroscopic characterization of pure SO3 species –
monomers, dimers and higher polymers in argon matri-
ces free of significant amounts of water impurities.
The production and identification of (SO3)nÆ(H2O)m spe-
cies in the matrix, both by varying the water content of
argon matrix gas and by post deposition controlled
annealing of the solid samples.
MP2 and DFT calculations employing the B3LYP func-
tional [33] were carried out using Gaussian 03 [34]. The
geometries of SO3, H2O, S2O6, S3O9, H2S2O7, and the var-
ious complexes were optimized and the frequencies of
vibration including infrared intensities were calculated.
Dunning’s correlation consistent aug-cc-pVTZ basis set
[35–37], which includes both diffuse and polarization func-
tions, was chosen to obtain a reasonably accurate geometry
of the isolated molecules and the complexes bonding.
The energy of the complex minus the monomer energies
is the directly calculated energy of complex formation,
DEcomplex = E(Aꢁ ꢁ ꢁB) ꢀ E(A) ꢀ E(B), which is subsequent-
ly corrected for the Basis Set Superposition Error (BSSE)
by the Counterpoise (CP) correction [38,39].
As pointed out above, hydrolysis of SO3 with an
excess of water may produce not only free sulfuric acid
molecules but also (H2SO4)Æ(H2O)n (n P 1) hydrates.
Identification and assignment of bands to such species,
may shed some light on the problematic case of the
infrared spectrum of the 1:1 (H2SO4)Æ(H2O) complex,
which has an important role in the vapor phase nucle-
ation of aerosols. While several theoretical and experi-
mental studies [25–32] predict an intense OH stretch
absorption in the 3100–2800 cmꢀ1 infrared frequency
region for this species, no such band was detected in
the infrared spectrum of sulfuric acid vapors trapped in
solid argon [22].
3.1. Structure and vibrational frequencies of the monomeric
species
The optimized structures and energies of SO3 and H2O
were calculated to serve as references for the possible mole-
cules and complexes formed in the matrix isolation experi-
ments. For comparison we only quote the structural results
from B3LYP/aug-cc-pVTZ calculations: SO3 (D3h),
2. Experimental
˚ ˚
The source of SO3 vapors was a small quantity of
K2S2O7 or Na2S2O7 crystals (Aldrich 99%) placed in a
quartz tube ending in a nozzle facing the cold surface of
the cryostat and covered with a water absorbing P2O5 solid
layer. The quartz tube temperature was controlled by a sur-
rounding a heating bath. Argon gas (99.9997%), was sup-
plied by AGA. Water vapors were taken from deionised
water that has previously been submitted to several degas-
sing cycles.
Prior to deposition, several short degassing cycles were
performed by heating the bath up to about 140 °C, (slightly
below the bath temperature needed to decompose K2S2O7),
with the deposition window still at room temperature and
turned away from the nozzle. For deposition, the bath tem-
perature was raised to 160–180 °C.
rS@O = 1.43974 A (re = 1.4175 A [40]); H2O (C2v), rO–
˚
˚
H = 0.961854 A (re = 0.9579205 A [41]), \HOH = 105.079
(\e = 104.500 [41]). That is, the method reproduces the
water structure satisfactorily but systematically overesti-
mates the experimental p-bonds of SO3 by as much as
˚
0.02 A. This is also reflected in the calculated frequencies
of vibration which deviate slightly from the observed funda-
mental transitions. For water the calculated wave numbers
are too high by 3.7% partly due to the neglect of anharmonic-
ity. For SO3, however, the calculated wave numbers are too
low by 2.6% due to basis set limitations (a basis set of at least
quintuple zeta quality is necessary to reproduce the experi-
mental SO3 frequencies of vibrations). A scaling of the har-
monic force fields, involving two and three parameters for
H2O and SO3, respectively, was therefore applied to obtain

A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
23
an agreement between observed and calculated wave num-
bers of the free molecules. The force fields were scaled
for the fundamental vibrational modes of S2O6, S3O9 and
H2S2O7 are included in Tables 1a and 1b. For the sake of
pffiffiffiffiffiffiffiffiffiffiffi
according to the procedure F
¼ F
ꢁ
ai ꢁ aj, where
brevity we have excluded wave numbers below 400 cmꢀ1
the limit of our experimental results.
,
scaled
i;j
calc:
i;j
ai and aj are scaling parameters for the valence coordinates
i and j, respectively. We have previously reported a similar
scaling of the harmonic force field of H2SO4 involving six
parameters [42]. There are obviously minor differences in
results obtained from B3LYP and MP2 calculations. How-
ever, after proper scaling of the force fields the normal coor-
dinates resulting from the two models are virtually
indistinguishable. The calculated and scaled wave numbers
(for all modes above 400 cmꢀ1) resulting from B3LYP/
aug-cc-pvTZ calculations, including infrared intensities, of
the (SO3)n species are collected in Table 1a while Table 1b
summarizes the results for the (SO3)nÆ(H2O)m species (scaling
factors are included as a footnote). It should be pointed out
that the described frequency scaling has the advantage of
being more mode specific than the application of a uniform
scaling factor. However, actual assignments rely more on
the experimental observations than on the use of a particular
scaling method.
3.3. SO3 dimeric and trimeric complexes
A scan of the potential surface of the SO3 dimeric com-
plex produced a single minimum energy structure of C2h
symmetry as illustrated in Fig. 2A. The enthalpy of reac-
tion of the SO3 dimeric complex is predicted to be
ꢀ10.6 kJ molꢀ1 at 298 K from CP-corrected MP2/aug-cc-
pVTZ calculations, Table 2a. However, the complex is dis-
favored by entropy and only becomes exogenic below
110 K. The magnitude of the dispersion forces in this com-
plex is illustrated by the difference between the DFT and
MP2 results for the reaction enthalpy, ꢀ0.5 and
ꢀ10.6 kJ molꢀ1, respectively. In any case, the formation
of the SO3 dimeric complex itself from the monomeric spe-
cies is close to being thermo neutral.
The formation of a cyclic SO3 trimeric complex with C2-
symmetry (Fig. 2B) is clearly exothermic (Table 2a). The
calculations also suggest the existence of a trimeric chain
complex (Fig. 2C) but as this complex is less favored ener-
getically (Table 2a) we do not consider this form further in
the present context.
3.2. S2O6, S3O9 and H2S2O7
The calculated structures of S2O6 (D2h), S3O9 (C2) and
H2S2O7 (C2) are illustrated in Fig. 1A, B, C, respectively,
and their energies relative to free SO3 and H2O are collect-
ed in Table 2a ((SO3)n species) and 2b ((SO3)nÆ(H2O)m spe-
cies). The results for S2O6 and H2S2O7 are comparable to
those recently reported by Johnson and Panas [43], while
for S3O9, our results do not support a minimum energy
structure of C3v-symmetry but rather a twisted C2-struc-
ture. There exists two studies of the S3O9 crystal structure
(P21nb, with four molecules in the cell) presenting C3v-like
structures [44,45]. Both studies have S–O ring distances of
3.4. (SO3)nÆ(H2O)m complexes
For the (SO3)Æ(H2O) dimeric complex a single minimum
energy structure of Cs symmetry (Fig. 3A) was found with
DrH° = ꢀ28 kJ molꢀ1 and to be exogenic already at 260 K.
Three 1:2 (SO3)Æ(H2O)2 complexes were identified from
the calculations – two cyclic and one open chain form
(Figs. 3B, C, D, respectively). Of these three, the open
chain form is around 30 kJ molꢀ1 higher in energy and
probably irrelevant to the present experiments.
Both DFT and MP2 calculations suggest the existence
of a stable 2:1 (SO3)2Æ(H2O) complex in which the water
molecule lone pairs form bonds to the two sulfur atoms
of SO3 (Fig. 3E). A search for other 2:1 complexes invari-
ably resulted in a structural relaxation to form H2S2O7.
In summary, the theoretical calculations suggest that a
water doped noble gas matrix of dispersed SO3 also may
contain 1:1, 1:2, 1:n SO3ꢁ ꢁ ꢁH2O and 2:1 SO3ꢁ ꢁ ꢁH2O com-
plexes, in addition to polymeric water and traces of
H2SO4 and H2S2O7.
˚
around 1.63 A, which agrees with the theoretical predic-
tions, but unreasonably large differences between the axial
˚
˚
and equatorial S@O bond lengths (1.37 A ax; 1.43 A eq;
˚
theoretical 1.42 A). Most likely the unit cell is disordered
and the structural analysis not valid.
H2S2O7 crystallizes in the space group C2/c with 16 mol-
ecules of C2-symmetry in the cell [46]. The B3LYP predict-
ed SO-bond distances are systematically longer than the
experimental values for SO3 as described above. For
H2S2O7 we also find a local minimum with C1-symmetry,
but as the energy of this conformer is about 20 kJ molꢀ1
higher, we do not consider it of relevance here. Finally,
we note that the B3LYP calculations, contrary to the
MP2 ones, do not predict S2O6 to be a stable molecule
3.5. Vibrational frequencies of the molecular complexes
`
vis-a-vis SO3.
For S2O6 and H2S2O7 the normal coordinates resulting
from the scaling of the B3LYP and MP2 force fields, apply-
ing the scaling factors derived for SO3 and H2SO4, are vir-
tually the same. For S3O9 (C2-symmetry) the available
hardware did not allow an MP2/aug-cc-pVTZ calculation
of the vibrational frequencies, but we suggest that the same
consistency should exist here. The predicted wavenumbers
The scaling factors derived for the monomeric species
were subsequently applied to the calculated harmonic force
fields of the complexes, while the scaling factors linked to
the intermolecular valence coordinates were constrained to
unity. Changing the latter scaling constants naturally affects
the low-lying vibrations, but the effect on the molecular
vibrations, including the OH stretching modes, is small.

24
A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
Table 1a
Calculated (B3LYP/aug-cc-pVTZ) and observed vibrational frequencies of SO3 monomer, dimer and trimer species (cmꢀ1
)
Species
No.
Description
Observed frequency
1385.2, 1388.9 (site)
Scaled frequencya
Scaled intensity
SO3
SO3
SO3
SO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 ring
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
SO3ÆSO3ÆSO3 chain
S2O6
m3(E0)
m1(A01)
m4(E0)
m2(A020)
m7(Au)
Antisym. SO3 stretch
Sym. SO3 stretch
SO3 bend
1385.2
1065.0
527.2
490.3
1400.0
1394.4
1374.9
1373.6
1061.9
1061.6
529.0
527.4
526.6
524.1
488.3
485.6
1412.1
1404.8
1404.2
1373.4
1370.5
1366.4
1066.3
1064.9
1063.6
537.0
530.1
529.0
527.2
526.3
525.3
482.0
479.9
474.7
1400.7
1396.9
1393.6
1375.6
1374.1
1371.2
1057.3
1055.6
1055.5
528.9
528.4
527.5
527.1
524.4
522.9
488.6
487.6
479.9
1310.9
815.4
687.4
351.4
1506.7
401.5
568.3
349.2
371.7
219.4
962.2
343.5
190
Inactive
25
32
334
Inactive
Inactive
418
Inactive
3
43
Inactive
46
Inactive
Inactive
94
386
84
12
322
254
157
4
4
4
46
13
4
26
29
7
105
101
4
364
101
2
25
88
446
1
1
3
9
31
47
24
0
527.2
490.3
1400.4
SO3 out-of-plane
SO3 antisym. stretch
SO3 antisym. stretch
SO3 antisym. stretch
SO3 antisym. stretch
SO3 sym. stretch
SO3 sym. stretch
OSO deformation
OSO deformation
OSO deformation
OSO deformation
OSO out-of-plane bend
OSO out-of-plane bend
Asym. SO3 stretch
Asym. SO3 stretch
Asym. SO3 stretch
Asym. SO3 stretch
Asym. SO3 stretch
Asym. SO3 stretch
Sym. SO3 stretch
Sym. SO3 stretch
Sym. SO3 stretch
SO3 bend
m
11(Bg)
m1(Ag)
14(Bu)
m2(Ag)
15(Bu)
m
1370.5, 1367.0
m
m8(Au)
m3(Ag)
535.1
525.0
m
m
16(Bu)
12(Bg)
m4(Ag)
17(Bu)
m
486.6
1413.5
1404.3
t1
t2
t3
t4
t5
t6
t7
t8
1370.5b
1367.0b
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
t1
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
m1(Ag)
m2(Ag)
m3(Ag)
m4(Ag)
541.6
SO3 bend
SO3 bend
SO3 bend
SO3 bend
SO3 bend
SO3 out-of-plane bend
SO3 out-of-plane bend
SO3 out-of-plane bend
Antisym. SO3 stretch
Antisym. SO3 stretch
Antisym. SO3 stretch
Antisym. SO3 stretch
Antisym. SO3 stretch
Antisym. SO3 stretch
Sym. SO3 stretch
Sym. SO3 stretch
Sym. SO3 stretch
SO3 bend
481.7
479.0
SO3 bend
SO3 bend
SO3 bend
SO3 bend
SO3 bend
1
0
23
136
SO3 out-of-plane bend
SO3 out-of-plane bend
SO3 out-of-plane bend
Sym. S@O2 stretch
Ring breathing
Ring deformation
Sym O@S@O bend
Antisym. S@O2 stretch
SO2 rock
SO2 wag
Ring deformation
SO2 twist
SO2 twist
SO2 wag
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
Inactive
182
S2O6
S2O6
S2O6
S2O6
S2O6
S2O6
S2O6
S2O6
m5(B1g
m6(B1g
m7(B2g
m8(B2g
m9(B3g
)
)
)
)
)
S2O6
S2O6
S2O6
m
m
m
10(Au)
11(B1u
12(B1u
)
)
SO2 torsion
5

A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
25
Table 1a (continued)
Species
No.
Description
Observed frequency
Scaled frequencya
Scaled intensity
S2O6
S2O6
S2O6
S2O6
S2O6
S2O6
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
S3O9
m
m
m
m
m
m
m
13(B2u
14(B2u
15(B2u
16(B3u
17(B3u
18(B3u
16(B)
)
)
)
)
)
)
Antisym. S@O2 stretch
SO2 rock
1522.2
567.8
88.5
387
38
1
Ring puckering
Sym. S@O2 stretch
Ring deformation
Antisym. O@S@O bend
Antisym. S@O2 stretch
Antisym. S@O2 stretch
Antisym. SO2 stretch
Sym. SO2 stretch
Sym. SO2 stretch
Sym. SO2 stretch
SO stretch
SO stretch
SO stretch
SO stretch
Ring bending
SO stretch
O@S@O bend
Ring bending
O@S@O bend
1256.5
783.1
514.4
1501.4
1484.9
1478.0
1266.4
1226.4
1226.3
834.9
829.2
786.8
763.0
680.9
668.4
662.2
589.1
562.6
548.7
490.8
462.7
409.7
450
549
61
415
50
75
13
224
303
711
744
66
0
0
2
2
33
73
124
24
8
m1(A)
17(B)
m
m2(A)
m3(A)
m
m
18(B)
19(B)
m4(A)
20(B)
m
m5(A)
m6(A)
m
21(B)
m7(A)
22(B)
m8(A)
23(B)
m9(A)
m
m
O@S@O bend
Concerted deformation
Concerted deformation
Concerted deformation
m
m
24(B)
10(A)
3
a
Scaling factors (see text): aS@O = 1.0325, aOSO = 1.078, aSO out-of-plane = 1.0625. H2O: aOH = 0.918193, aHOH = 0.955017.
Essentially dimer bands.
3
b
4. Spectroscopic results
site which is more stable than the one giving rise to the
1385.0 cmꢀ1 band, even though the latter is of a higher
initial intensity. These monomeric frequencies fit best
those recorded by us in the infrared spectra of sulfuric
acid vapors trapped in solid argon [22] at 1385.1 and
1389.8 cmꢀ1. Bondybey [21] assigned only a single absorp-
tion at 1385.9 cmꢀ1 to the t3 antisymmetric SO3 mode,
while Schriver et al. [24] report four absorptions for this
monomeric mode, 1392.2 (s), 1391.7 (s), 1391.5 cmꢀ1
(m) and 1389.7 cmꢀ1 (w).
Tables 1a and 1b summarize our spectroscopic results in
comparison with the relevant computed values. Table 1a
lists the pure (SO3)n species in order of increasing n, while
Table 1b summarizes the values for the molecular and com-
plexation species produced by the interaction of SO3 and
water molecules. The text of this section follows the same
order and discusses their mode assignments in order of
decreasing frequency.
In the bending mode region (Fig. 5b) two bands of
monomeric behavior were observed at 527.1 and
490.3 cmꢀ1 and assigned to the t4 in-plane and the t2 out
of plane bending of 32SO3, respectively. These bands were
also found for argon matrix isolated sulfuric acid vapors
[22] and, with similar frequencies, reported [21,24] in previ-
ous argon matrix studies.
To clarify the spectral differences between our experi-
ments and the previous work of Schriver et al. [24], a few
percent of N2 and water were added to the matrix gas with
the resulting spectra in the relevant regions reproduced
Fig. 5a–c. The effect of contaminating the argon matrix
with nitrogen is clearly reflected in the spectral features
of the isolated water molecules [48,49]: the rotational free-
dom of the H2O monomers in the matrix becomes blocked
by the N2 molecules, and the H2O frequencies recorded at
3730.6, 3641.8 and 1599.6 cmꢀ1 (Fig. 5a, trace B) are those
of the N2ÆH2O complex isolated in argon [49]. Parallel to
the changes in the H2O bands, the t3 doublet in pure argon
at 1385.0 and 1388.9 cmꢀ1 (Fig. 5b) blue shifts by 7.4 cmꢀ1
4.1. A. Pure SO3 samples
4.1.1. Monomeric SO3
Gas phase SO3 is essentially composed of monomers
[47]. Typical spectra of argon isolated SO3 in the antisym-
metric SO3 stretch region and in the bending modes region
are reproduced in Fig. 4a and b, respectively. The spectra
also show bands of SO2 monomer remnants (1354.9,
1351.0, 1156.7, 1147.2 and 517.3 cmꢀ1) [24].
The relative intensities of monomer bands (1385.0 cmꢀ1
(s), 1388.9 cmꢀ1 (m), 1375.8 cmꢀ1 (w)) decrease as a result
of annealing (Fig. 4a, trace B) as well as in samples pro-
duced at higher deposition rates (Fig. 4a, trace C). We
assign the two stronger bands to the t3 antisymmetric
SO3 stretch of 32SO3 monomer trapped in two different
matrix sites, whereas the weak 1375.8 cmꢀ1 band is
assigned to the 34SO3 isotopomer (9.2 cmꢀ1 shift vs.
12.5 cmꢀ1
,
calculated). The 1388.9 cmꢀ1 band loses
intensity at a slower rate indicating its assignment to a

26
A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
Table 1b
Calculated (B3LYP/aug-cc-pVTZ) and observed vibrational frequencies of H2S2O7, H2SO4 molecules and of the SO3ÆH2O, SO3ÆH2OÆH2O, and
H2OÆSO3ÆH2O complexes (cmꢀ1
)
Species
No.
Description
Observed frequency
3215.9
Scaled frequencya
Scaled intensity
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
H2S2O7
m15(B)
OH stretch
OH stretch
Antisym. SO2 stretch
Antisym. SO2 stretch
SOH bend
3370.3
3355.8
1473.3
1437.2
1239.0
1215.8
1189.8
1184.8
922.9
895.2
753.1
722.5
637.2
578.9
567.8
549.8
513.7
484.4
473.9
453.9
388.3
73.3
210.6
282.9
153.5
22.4
70.5
480.7
91.2
153.7
41.6
458.3
2.5
50.4
231.4
39.2
6.9
20.1
64.7
1
m1(A)
m2(A)
1474.7
1443.1
1237.8
m
m
16(B)
17(B)
m3(A)
m4(A)
SOH bend
Sym. S@O2 stretch
Sym. S@O2 stretch
S–OH stretch
m
18(B)
m5(A)
19(B)
m6(A)
20(B)
m7(A)
1205.0
929.0
909.5
m
S–OH stretch
Sym. S–O–S stretch
Antisym. S–O–S stretch
OSO3 deformation
O@S@O bend
OSO3 deformation
O@S@O bend
m
793.3, 787.3
m
m
21(B)
22(B)
575.2
566.8, 564.3
m8(A)
H2S2O7
H2S2O7
H2S2O7
H2S2O7
m
m
23(B)
24(B)
O–H torsion
OSO3 deformation
OSO3 deformation
O–H torsion
486.0
m9(A)
10(A)
m
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
H2SO4
SO3ÆH2O
SO3ÆH2O
SO3ÆH2O
SO3ÆH2O
SO3ÆH2O
SO3ÆH2O
SO3ÆH2O
SO3ÆH2O
SO3ÆH2O
m1(A)
m9(B)
Sym. O–H str
3570.8
3566.7
1458.7
1214.0
1156.8
1138.0
886.3
828.2
561.9
550.9
501.3
427.9
377.2
283.1
218.0
3701.2
3604.6
1581.2
1392.0
1377.5
1062.8
552.1
46
Antisym. O–H str
Antisym. S@O2 str
Sym. S@O2 str
Antisym. SOH bend
Sym. SOH bend
Antisym. S–O stretch
Sym. S–O stretch
O@S@O rock
O@S@O bend
SO4 wag
3566.7
1452.4
1216.1
1156.9
1135.9
881.7
831.4
558.0
548.1
506.0
421.7
378.5
287.7
224.0
204
288
163
86
m
10(B)
m2(A)
11(B)
m3(A)
12(B)
m4(A)
13(B)
m5(A)
14(B)
m
74
m
322
107
22
36
40
13
1
56
m
m
m6(A)
m7(A)
SO4 twist
O–S–O bend
m
15(B)
m8(A)
10(A00)
Antisym. OH torsion
Sym. OH torsion
Antisym. OH stretch in H2O
Sym. OH stretch in water
HOH bend in water
Antisym. SO3 stretch
Antisym. SO3 stretch
Sym. SO3 stretch
SO3 bend
103
108
50
m
m1(A0)
m2(A0)
m3(A0)
3598.1
1583.4
1390.6
77
213
215
5
22
52
m
11(A00)
m4(A0)
12(A00)
m
m5(A0)
m6(A0)
SO3 bend
SO3 out-of-plane bend
Water rotation
528.7
486.0
537.7
489.3
474.1
434.0
160
3
SO3ÆH2O
SO3ÆH2O
m
13(A00)
m7(A0)
m1
Water rotation
151
124
114
130
947
48
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(A)
SO3ÆH2OÆH2O(B)
Antisym. OH stretch in HOHꢁ ꢁ ꢁOSO2
Free OH in HO(H)ꢁ ꢁ ꢁSO3
Sym. OH stretch in HOHꢁ ꢁ ꢁOSO2
H-bonded OH in HO(H)ꢁ ꢁ ꢁSO3
HOH bend in HO(H)ꢁ ꢁ ꢁSO3
HOH bend in HOHꢁ ꢁ ꢁOSO2
Antisym. SO3 str
Antisym. SO3 str
Sym. SO3 str
Intermolecular
Intermolecular
Intermolecular
Intermolecular
3703.9
3649.3
3556.9
3114.0
1615.4
1586.3
1389.6
1351.5
1058.9
962.0
683.5
535.9
529.9
519.9
508.8
457.9
3700.9
m2
m3
m4
m5
m6
m7
m8
m9
m10
m11
m12
m13
m14
m15
m16
m1
69
238
252
21
66
123
25
21
141
70
239
127
920.1
Intermolecular
Intermolecular
Intermolecular
Antisym. OH in HOHꢁ ꢁ ꢁOSO2

A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
27
Table 1b (continued)
Species
No.
Description
Observed frequency
Scaled frequencya
Scaled intensity
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆH2O(B)
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
SO3ÆH2OÆSO3
m2
m3
m4
m5
m6
m7
m8
m9
m10
m11
m12
m13
m14
m15
m16
t1(A1)
t2(A1)
t3(A1)
t4(A1)
t5(A1)
t6(A1)
t7(A1)
t8(A1)
t9(A1)
Free OH in H2Oꢁ ꢁ ꢁSO3
Sym. OH in HOHꢁ ꢁ ꢁOSO2
H-bonded OH in H2Oꢁ ꢁ ꢁSO3
HOH bend in HO(H)ꢁ ꢁ ꢁSO3
HOH bend in HOHꢁ ꢁ ꢁOSO2
Antisym. SO3 str
Antisym. SO3 str
Sym. SO3 str
Intermolecular
Intermolecular
Intermolecular
Intermolecular
Intermolecular
Intermolecular
Intermolecular
Sym. OH stretch
HOH bend
Antisym. SO3 stretch
Sym. SO3 stretch
SO3 deformation
SO3 out-of-plane bend
SO3 rotation
3644.9
3560.0
3091.0
1590.9
1579.0
1400.3
1347.3
1065.2
1041.3
704.7
555.7
527.5
519.8
479.1
453.7
3589.8
1585.0
1399.8
1064.0
531.1
489.6
157.0
83.0
116
122
1020
40
71
238
262
65
26
121
24
69
118
78
146
49
77
309
0
39
20
0
0
0
Inactive
Inactive
Inactive
Inactive
3582.1
3150
1343.2
1058.1
Sym. Sꢁ ꢁ ꢁOꢁ ꢁ ꢁS stretch
Sꢁ ꢁ ꢁOꢁ ꢁ ꢁS bend
21.5
t10(A2)
t11(A2)
t12(A2)
t13(A2)
t14(A2)
t15(B1)
t16(B1)
t17(B1)
t18(B1)
t19(B1)
t19(B1)
t20(B2)
t21(B2)
t22(B2)
t23(B2)
t24(B2)
Antisym. SO3 stretch
SO3 deformation
H2O rotation
1379.7
539.3
465.7
96.2
SO3 rotation
SO3 rotation
Antisym. OH stretch
SO3 deformation
H2O rotation
6.7
Inactive
3681.1
1382.7
532.9
301.0
126.2
16.6
1393.0
1064.0
546.2
495.6
468.9
37
14
5
3
1
SO3 rotation
SO3 rotation
Antisym. SO3 stretch
Sym. SO3 stretch
SO3 deformation
H2O rotation
SO3 out-of-plane bend
Antisym. Sꢁ ꢁ ꢁOꢁ ꢁ ꢁS stretch
0
14
11
5
5
5
a
Scaling factors (see text) SO3: aS@O = 1.0325, aOSO = 1.078, aSO out-of-plane = 1.0625; H2O: aOH = 0.918193, aHOH = 0.955017; H2SO4: aO–
3
H = 0.906115, aS–O = 1.114194, aS@O = 1.044299, aOSO = 1.117991, aSOH = 0.976356, aOH tors = 0.851695.
shift in the nitrogen contaminated sample (Fig. 5b, traces A
and B) to 1392.4 and 1396.3 cmꢀ1, respectively. The two
latter bands are hence attributed to SO3 interacting with
the N2 contaminants in the matrix. While the
1385.0 cmꢀ1 absorption completely disappears in the nitro-
gen contaminated sample, the weaker 1388.9 cmꢀ1 is less
affected (Fig. 5b), in support of its assignment to a more
stable argon site.
the polymeric bands are far more dominant in the spec-
tra of matrix samples produced by faster deposition
(trace C), than in those recorded after annealing of layers
formed by low rate depositions (trace B). The non-mono-
meric bands which were found to be most sensitive to
the SO3 concentration of the deposited gas are attribut-
able to dimers.
Theoretical calculations (Tables 1a and 2a) indicate two
possible stable dimeric species. A cyclic S2O6 of D2h sym-
metry (Fig. 1) the DrEelec of which is calculated to be
8.0 kJ molꢀ1 (B3LYP) and ꢀ20.3 kJ molꢀ1 (MP2) (Table
2a) and a more loosely bonded SO3ÆSO3 complex with sim-
ilar structure and symmetry (Fig. 2A) the DrEelec of which
is ꢀ6.3 kJ molꢀ1 (B3LYP) and ꢀ20.5 kJ molꢀ1 (MP2)
(Table 2a).
4.2. The dimer (SO3)2 and trimer (SO3)3
As dimers are not initially present at low partial pres-
sure in the SO3 gas phase and given the low mobility of
these monomers in the argon matrix, we conclude that
bands attributed to dimers or to higher polymers, are
due to species formed during the actual deposition of
the matrix layers and not by temperature induced migra-
tion. This is well demonstrated in Fig. 4a and b, where
The calculated S2O6 main absorptions are at
1522.2 cmꢀ1 (asym. S@O2 stretch), 1256.5 cmꢀ1 (sym.
S@O2 stretch), 962.2 cmꢀ1 (SO2 wag) and 783.1 cmꢀ1

28
A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
Fig. 1. Calculated structures of SO3 related molecular species. (A) The S2O6 dimer molecule (D2h). (B) The S3O9 trimer molecule (C2). (C) The H2S2O7
molecule (C2).
Table 2a
Energies of reaction of various (SO3)n molecules and complexes from their monomeric constituents calculated using the aug-cc-pVTZ basis set
Method
B3LYP
SO3ÆSO3
SO3ÆSO3ÆSO3 (cyclic)
SO3ÆSO3ÆSO3 (chain)
S2O6 (D2h
8.0
)
S3O9 (C2)
DrEelec
ꢀ6.3
0.8
ꢀ0.5
ꢀ0.071
20.6
ꢀ23.2
2.2
ꢀ10.6
ꢀ0.199
48.8
ꢀ12.3
1.6
ꢀ3.1
ꢀ0.184
51.9
ꢀ26.4
BSSEa/kJ molꢀ1
DrH/kJ molꢀ1
DrS/J molꢀ1 Kꢀ1
DrG298/kJ molꢀ1
13.8
ꢀ14.9
ꢀ0.344
87.6
ꢀ0.175
66.0
MP2
DrEelec
ꢀ20.5
4.7
ꢀ10.6
ꢀ0.095
17.5
ꢀ58.6
12.4
ꢀ35.8b
ꢀ0.2b
23.5b
ꢀ20.3
ꢀ88.6
BSSEa/kJ molꢀ1
DrH/kJ molꢀ1
DrS/J molꢀ1 Kꢀ1
DrG298/kJ molꢀ1
ꢀ13.8
ꢀ0.176
38.5
ꢀ76.5a
ꢀ0.343a
20.6a
a
BSSE: Basis Set Superposition Error, Refs. [38,39]. The BSSE is included in DrH and DrG.
Thermal corrections from B3LYP/aug-cc-pVDZ calculation.
b
Table 2b
Energies of reaction of various SO3/H2O complexes from their monomeric constituents calculated using the aug-cc-pVTZ basis set
Method
B3LYP
SO3ÆH2OÆSO3
SO3ÆH2O
SO3Æ(H2O)2
A
SO3Æ(H2O)2
B
SO3Æ(H2O)2
C
H2S2O7 (C2)
DrEelec
ꢀ46.8
1.7
ꢀ32.7
ꢀ0.203
27.8
ꢀ32.7
0.8
ꢀ25.0
ꢀ0.106
6.6
ꢀ75.7
1.5
ꢀ59.4
ꢀ0.250
15.1
ꢀ77.9
1.5
ꢀ61.4
ꢀ0.251
13.3
ꢀ43.9
1.5
ꢀ29.6
ꢀ0.179
23.8
ꢀ120.4
BSSEa/kJ molꢀ1
DrH/kJ molꢀ1
DrS/J molꢀ1 Kꢀ1
DrG298/kJ molꢀ1
ꢀ106
ꢀ0.328
ꢀ8.4
MP2
DrEelec
ꢀ66.5
8.3
ꢀ46.0
ꢀ0.213
17.5
ꢀ39.2
4.3
ꢀ28.0
ꢀ0.106
3.5
ꢀ89.6
10.7
ꢀ63.6
ꢀ0.258
13.4
ꢀ91.2
10.6
ꢀ65.3
ꢀ0.256
11.1
ꢀ159.1
BSSEa/kJ molꢀ1
DrH/kJ molꢀ1
DrS/J molꢀ1 Kꢀ1
DrG298/kJ molꢀ1
ꢀ143.5
ꢀ0.333
ꢀ44.3
a
BSSE: Basis Set Superposition Error, Refs. [38,39] The BSSE is included in DrH and DrG.
(ring deformation). None of these bands were found in
the infrared spectra of water free SO3 samples. On the
other hand, Table 1a lists three observed bands in the
t3 SO3 asymmetric stretch region which resemble calculat-
ed frequencies for the loose complex SO3ÆSO3:
1400.4 cmꢀ1 (calculated at 1400 cmꢀ1) and a doublet
1370.5 and 1367.0 cmꢀ1 (calculated at 1373.6 cmꢀ1). In
neon matrices an analogous absorption was found at
1373.4 cmꢀ1 [21]. These bands shift to 1407.3 cmꢀ1 (a
6.9 cmꢀ1 shift), 1377.8 cmꢀ1 (a 7.3 cmꢀ1 shift) and
1374.6 cmꢀ1 (a 7.5 cmꢀ1 shift) in argon matrices with a
few percents of nitrogen impurities (Fig. 1B), the shifts
being similar to those observed for monomeric absorp-
tions in such matrices.

A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
29
Fig. 2. Calculated structures of SO3 complex species. (A) The SO3ÆSO3 dimeric complex (C2h). (B) The cyclic SO3ÆSO3ÆSO3 complex (C2). (C) The open
chain SO3ÆSO3ÆSO3 complex.
Fig. 3. Calculated structures of SO3/H2O complex species. (A) Structure of the H2OÆSO3 complex (Cs). (B) Structure of the (H2O)2ÆSO3, Form A complex.
(C) Structure of the (H2O)2ÆSO3, Form B complex. (D) Structure of the (H2O)2ÆSO3, open complex. (E) Structure of the H2OÆ(SO3)2 complex.
In the t4 bending mode region, dimeric bands are
observed at 535.1 cmꢀ1 (calculated at 529.0 cmꢀ1) and
525.0 cmꢀ1 (calculated at 526.6 cmꢀ1), with the neon
matrix band at 538.2 cmꢀ1 [21]. In the vicinity of the mono-
meric t2 out of plane bending mode, a dimeric band was
found at 486.6 cmꢀ1 (calculated at 485.6 cmꢀ1) and
observed at 493.8 cmꢀ1 in the neon matrix [21].
Bands attributable to higher polymers, which grow in
prominence in layers with higher SO3 concentration
(Fig. 4a, trace C, and Fig. 5a, trace C), were recorded at
1422.1, 1413.5, 1404.3, 541.6, 481.7 and 479.0 cmꢀ1 and
are close to those found in neon matrices: 1421.6, 1407.2,
544.9, 489.8, and 485.1 cmꢀ1 [21]. These observed polymer-
ic band frequencies deviate considerably from the main fre-

30
A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
a
b
0.1 a.u.
0.1 a.u.
C
B
C
B
A
A
1420
1400
1380
1360
1340
560
540
520
500
480
460
440
wavenumber/cm-1
wavenumber/cm-1
Fig. 4. Annealing and deposition rate effects on the spectrum of SO3 in argon matrices. (A) As deposited (17 K). (B) Sample A annealed to 38 K. (C) As
deposited at 17 K – faster deposition rate. (a) S–O antisymmetric stretch region. (b) Bending mode region.
a
b
c
0.05 a.u.
0.05 a.u.
B
0.1 a.u.
B
B
A
A
A
1420
1400
1380
1360
1340
560
540
520
500
480
-1
460
440
3800
3750
3700
3650
3600
-1
3550
3500
-1
wavenumber/cm
wavenumber/cm
wavenumber/cm
Fig. 5. N2 doping effect on the spectrum of an SO3/H2O/argon matrix. (A) Water free sample. (B) Few percents of N2 + 1% H2O in the sample. (a) OH
stretch region. (b) SO3 antisymmetric stretch region. (c) Bending mode region.
quencies calculated for the cyclic (Fig. 5) S3O9 trimer
(Table 1a) at 1501.4, 1226.4, 834.9 and 829.2 cmꢀ1. On
the other hand, the observed bands fit almost exactly the
calculated frequencies of the more loose centrosymmetric
(Fig. 2B) SO3ÆSO3ÆSO3 complex at 1412.4, 1404.9, 541.9,
483.6, and 480.2 cmꢀ1. In addition, the calculated SO3Æ-
SO3ÆSO3 bands at 1372.1 and 1370.7 cmꢀ1 may contribute
to the intensity of the 1370.5 cmꢀ1 band assigned in the
previous paragraph to the SO3ÆSO3 complex.
In summary, bands attributable to monomers as well as
to loosely bonded dimeric and trimeric SO3 species were
recorded. No spectroscopic evidence to the presence of
molecular S2O6 and S3O9 species was discerned.
and C) and of annealing the water doped matrices
(Fig. 6, trace D).
4.3.1. O–H stretch region
The spectrum (Fig. 6a, trace A) consists mainly of
bands previously attributed to the antisymmetric and
symmetric OH stretches of H2O rotating and non-rotating
monomers (3776.9, 3756.2, 3711.3, 3670.7, 3653.4, and
3637.9 cmꢀ1), of (H2O)2 dimers (3707.1, 3632.8,
3573.2 cmꢀ1
) and higher polymers (3539.4, 3515.5,
3372.9 and 3325.4 cmꢀ1) [48,50–56]. Four additional SO3
related bands are recorded in this region. Two sharp
bands at 3598.1, 3582.1 cmꢀ1 and two broad absorptions
at 3215.9 and 3150 cmꢀ1. All their intensities increase with
increasing water concentrations in the matrix (Fig. 6a,
traces B and C). Upon annealing (Fig. 6a, traces C and
D) only minor intensity changes occur: The 3598.1 cmꢀ1
band remains unchanged or even slightly loses intensity,
while the 3582.1 cmꢀ1 absorption somewhat increases its
intensity. The intensity changes of the 3215.9 and
3150 cmꢀ1 bands are masked by the underlying broad
O–H stretch ice absorption.
4.3. B. Water doped samples
To investigate the effects of doping the matrices with
water vapors, 2–0.05% of H2O vapors were introduced
into the argon matrix gas. The addition of water is reflect-
ed in new bands in essentially all spectral regions. Their
assignments are based on the spectral effects of varying
the water concentration in the matrix (Fig. 6, traces B

A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
31
a
b
c
0.1 a.u.
0.1 a.u
D
D
D
C
0.1 a.u.
C
C
B
A
B
A
B
A
3700
3500
3300
3100
2900
1700
1650
1600
1550
1500
1500
1450
1400
1350
1300
-1
-1
-1
wavenumber/cm
wavenumber/cm
wavenumber/cm
e
f
d
0.05 a.u
0.1 a.u.
0.05 a.u.
D
D
C
D
C
C
B
B
A
B
A
A
600
550
500
-1
450
1250
1200
1150
1100
1050
1000
950
900
850
800
-1
750
700
-1
wavenumber/cm
wavenumber/cm
wavenumber/cm
Fig. 6. Water fraction and annealing effects on the SO3 spectrum in Ar/H2O matrices. (A) No water in the sample, as deposited at 17 K. (B)
Argon:H2O = 300:1, as deposited at 17 K. (C) Argon:H2O = 150:1, as deposited at 17 K. (D) Layer C temperature cycled to 35 K. (a) OH stretch region.
(b) H2O bending mode region. (c) SO3 antisymmetric stretch region. (d) Symmetric stretch region. (e) S–O stretch region. (f) Bending mode region.
As pure SO3 species do not absorb in this region, these
new bands must be due to (SO3)m(H2O)n species. We assign
the sharp weak absorption at 3598.1 cmꢀ1 to the m1 sym-
metric O–H stretch of the 1:1 (H2O)Æ(SO3) complex, pro-
duced during deposition and not by temperature induced
migration (as suggested by Schriver et al. [24]) as it does
not intensify during the annealing processes. The observed
band frequency fits well the calculated value, 3604.6 cmꢀ1
(Table 1b), and resembles previous results observed in
neon, oxygen and nitrogen matrices [21,23,24], cf. Table
3. We note the low intensity of this band indicating its
low concentration in the sample. This is probably due to
the fact that, while this complex is lower in energy relative
to the reactants producing it, it is also the (H2O)nÆ (SO3)
species of highest energy (Table 2b and ref [16]). The
absence of H2SO4 bands in the spectrum may be related
to the result that the 1:1 (H2O)Æ(SO3) complex also has
the highest barrier to the transition state through which
it rearranges to H2SO4 [16].
More tentatively, the absorption at 3150 cmꢀ1 may repre-
sent the m4 stretch of the H-bonded OH mode of
(H2O)2Æ(SO3) (calculated value 3091.0 cmꢀ1 (Table 1b)).
This assignment is uncertain due to the underlying ice
band.
Other mixed trimeric species which may absorb in this
region are the (H2O)Æ(SO3)2 complex (Fig. 3E) with calcu-
lated OH stretch mode frequency 3589.8 cmꢀ1 and low
intensity of I = 49 (Table 1b) and H2S2O7 (Fig. 1C) for
which the OH stretch frequencies are calculated (Table
1b) at 3370.3 cmꢀ1 (m15(B) I = 388.3) and 3355.8 cmꢀ1
(m1(A), I = 73.3). We assign the weak broad band at
3215.9 cmꢀ1 to the m15(B) OH stretch mode of H2S2O7.
4.4. H–O–H bending mode region
The majority of bands in this region (Fig. 6b, trace B)
bands are due to bending modes of both rotating and
non-rotating water monomers (1661.9, 1637.8, 1623.9,
1608.3 and 1572.5 cmꢀ1 and higher water polymers
(1616.8, 1610.8, and 1593.1 cmꢀ1) [48,50–56]). A single,
additional weaker band, not much affected by annealing
to 35 K (Fig. 6b, traces C and D) is recorded at
1583.4 cmꢀ1. It is assigned here to the t2 H2O bending
mode of the 1:1 (H2O)Æ(SO3) complex, calculated at
1581.2 cmꢀ1 (Table 1b) and close to the frequency mea-
sured in a neon matrix at 1591.4 cmꢀ1 (Table 3 and ref.
[21]).
The 3582.1 cmꢀ1 band which increases slightly during
annealing was previously recorded by us in the infrared
spectrum of sulfuric acid vapors isolated in argon [22],
and assigned there to the (H2O)2Æ(H2SO4) complex. It is
more plausible to assign this band to the (H2O)2Æ(SO3)
complex, which is significantly lower in energy than the
1:1 (H2O)Æ(SO3) complex (Table 2b and ref [16]). The calcu-
lated band frequency for the most stable configuration B of
this complex (Form B, Fig. 2C) is 3560.0 cmꢀ1 (Table 1b).

32
A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
Table 3
(H2SO4) species observed by us in the infrared spectrum
of sulfuric acid vapors trapped in argon matrices [22]. Also,
two similar absorptions, for SO3 species trapped in neon
matrix [21], at 1482.4 and 1448.6 cmꢀ1, were attributed to
the (H2O)Æ(H2SO4) complex. However, the assignment to
H2S2O7 is preferred.
Infrared absorptions of the 1:1 (SO3)Æ(H2O) complex in various matrices
(cmꢀ1
)
Nea
N2
O2
Ard
b
c
m3(H2O)
m1(H2O)
m2(H2O)
m3(SO3)
m1(SO3)
m4(SO3)
m2(SO3)
a
3648.8
3562.7
3678
3562.8
3612.9
1591.4
1401.4
3598.1
1583.4
1390.6
The third band, 1343.2 cmꢀ1, remained essentially
unchanged by annealing to 35 K (Fig. 6c, traces C and
D). Its position is in good accordance with the calculated
value at 1347.3 cmꢀ1 (Table 1b) for the m8 SO3
antisymmetric stretch mode of (H2O)2Æ(SO3) in its type B
form (Fig. 3C). The second SO3 antisymmetric stretch of
this species, calculated at 1400.3 cmꢀ1 (Tables 1a and 1b)
may be masked by the 1400.4 cmꢀ1 (SO3)2 band (Table 1b).
Upon annealing of the water containing samples
(Fig. 6c, traces C and D) the frequency of the t3 antisym-
metric SO3 stretch of monomeric SO3 trapped in its stable
site shifts from 1388.9 to 1390.6 cmꢀ1. This shift may be
the result of the emergence of (H2O)Æ(SO3) complex species,
which is calculated to absorb at 1392.0 cmꢀ1 (Table 1b).
The second antisymmetric SO3 stretch of this species, with
a calculated frequency of 1377.5 cmꢀ1, is probably masked
by the absorption of the same mode of (SO3)2 species at
1390, 1399
1079
1397.0
545.8, 549.4
488.5
528.7
486.0
490.9
Ref. 21.
Ref. 24.
Ref. 23.
This work.
b
c
d
4.5. Antisymmetric SO3 stretch region
Three bands additional to those of monomeric and poly-
meric SO3 species, discussed above, were observed at
1474.1, 1443.1 and 1343.2 cmꢀ1 (Fig. 6c, trace B). All three
bands gain intensity with higher water concentrations in
the matrices (Fig. 6c, traces A, B and C) and are thus
attributed to water containing SO3 species. The two higher
frequency absorptions at 1474.1 and 1443.1 cmꢀ1 slightly
lose intensity upon annealing to 35 K (Fig. 6c, traces C
and D) and almost exactly fit the calculated values for
the antisymmetric SO2 stretches of H2S2O7 – 1473.3 cmꢀ1
[t2(A)] and 1437.2 cmꢀ1 [t16(B)] (Table 1b). Raman and
infrared results from oleum samples showing a peak at
1430 cmꢀ1 (Table 4, ref. [57,58]) support these assignment.
The 1443.1 cmꢀ1 band frequency, similar to the
3582.1 cmꢀ1 absorption, also resembles that of (H2O)2Æ
1370.5 cmꢀ1
.
4.6. Symmetric SO2 and SO3 stretch region
The most prominent sharp bands of this region at 1237.8
and 1205.0 cmꢀ1 (Fig. 6d, traces A, B and C) increase upon
raising water concentration and show the same behavior
during annealing as the 1474.1 and the 1443.1 cmꢀ1 bands
of the previous region – a slight loss of intensity. These
bands are consequently assigned to the SOH bend (calcu-
lated value – 1239.0 cmꢀ1 (Table 1b)) and the symmetric
SO2 stretch of H2S2O7 (calculated value – 1184.8 cmꢀ1
(Table 1b)). Similar frequencies (1200 cmꢀ1 (57) and
1182 cmꢀ1(58)) are observed for SO2 symmetric stretch of
H2S2O7 in oleums (Table 4).
Table 4
Vibrational frequencies of H2S2O7 in oleums as compared to monomers
isolated in argon (cmꢀ1
)
Mode
Argon matrix infrareda
Oleum
Calculatedd
Infraredb
Ramanc
1430
m15(B)
3215.9
3370.3
3355.8
1473.3
1437.2
1239.0
1215.8
1189.8
1184.8
922.9
895.2
753.1
722.5
637.2
578.9
567.8
549.8
513.7
484.4
473.9
The weak, broad band at 1058.1 cmꢀ1 which increases
upon annealing (Fig. 6d, traces C and D) may be related
to t1 symmetric stretch of SO3 in type B (H2O)2Æ(SO3) (cal-
culated value – 1065.2 cmꢀ1 (Table 1b)).
Except for the absorptions at 1150.0, 1152.3 and
1143.0 cmꢀ1 which are due to t1 symmetric stretch mode
of SO2 monomers trapped in different argon sites [24], all
other bands, 1219.8, 1192.8, 1189.3, 1179.5 and
1039.8 cmꢀ1, most likely belong to higher polymeric
(H2O)n (SO3)m – they are broad and grow during anneal-
ing. An absorption band at 1192.8 cmꢀ1 was previously
noted by us in the infrared spectrum of sulfuric acid vapors
trapped in argon [22] and assigned to the (H2O)2Æ(H2SO4)
complex.
m1(A)
m2(A)
1474.7
1443.1
1237.8
m
m
16(B)
17(B)
1430
m3(A)
m4(A)
1250
1182
960
m
18(B)
m5(A)
19(B)
m6(A)
20(B)
m7(A)
1205.0
929.0
909.5
1200
965
m
806
728
618, 640
m
793.3, 787.3
740
m
m
21(B)
22(B)
575.2
566.8, 564.3
m8(A)
m
m
23(B)
24(B)
516
476
486.0
495
470
m9(A)
4.7. Single S–O bond stretch region
a
This work.
Ref. [57].
Ref. [58].
(B3LYP/aug-cc-pVTZ).
b
c
Several bands in this region increase in intensity with the
water concentration in the matrix (Fig. 6e, traces A, B and
d

A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
33
C). Of these, the sharp bands at 929.0 and 909.5 cmꢀ1 as
well as the doublet at 793.3 and 787.3 cmꢀ1 lose intensity
upon annealing (Fig. 6e, traces C and D) and are assigned
to the t5(A) and t19(B) S–OH, stretches of H2S2O7, respec-
tively. The first two observed band frequencies resemble
the calculated values 922.9 and 895.2 cmꢀ1 (Table 1b),
but their intensity ratio I(929.0) > I(909.5) is opposite to
the calculated one (Table 1b). The splitting (20 and
6 cmꢀ1) may be due to different trapping sites but intensi-
ties are too low to observe the differences in annealing
effects. For H2S2O7 in oleums ([57,58] Table 4) the t5(A)
the t24(B) OSO3 deformation of H2S2O7. This is further
supported by the 495.0 cmꢀ1 frequency recorded in the
Raman spectrum of oleums [58] (Table 4).
The 575.2 cmꢀ1 band is attributed to the t21(B) O@S@O
bend of H2S2O7 (calculated value, 567.8 cmꢀ1), while the
sharp doublet at 566.8 and 564.3 cmꢀ1 are assigned to
the t22(B) OSO3 deformation of H2S2O7 (calculated value
– 578.9 cmꢀ1). The 528.7 cmꢀ1 band is assigned to the t5
SO3 bend of (H2O)Æ(SO3) (calculated value – 537.7 cmꢀ1).
The broad 554.6 and 357.6 cmꢀ1 bands are assigned to
higher (H2O)nÆ(SO3)m polymers.
mode is recorded at 960 cmꢀ1
.
The doublet at 793.3 and 787.3 cmꢀ1 is assigned to the
t20(B) S–O–S antisymmetric stretch of H2S2O7, although
the calculated value (Table 1b) is about 10% lower –
5. Concluding remarks
Theoretical calculations suggest that a water doped
noble gas matrix of dispersed SO3 may contain 1:1, 1:2
and even higher SO3ꢁ ꢁ ꢁH2O complexes as well as the 2:1
SO3ꢁ ꢁ ꢁH2O complex, in addition to polymeric water and
traces of H2SO4 and H2S2O7. The spectroscopic study indi-
cates the presence of the 1:1 and the 1:2 SO3ꢁ ꢁ ꢁH2O com-
plexes as well as both H2SO4 and H2S2O7, but there is no
evidence for a stable 2:1 SO3ꢁ ꢁ ꢁH2O complex. We therefore
suggest that any 2:1 SO3ꢁ ꢁ ꢁH2O complex formed during the
deposition stage of the experiment may readily convert to
H2S2O7.
In principle polymeric chain like complexes of the form
SO3Æ(H2OÆSO3)nÆH2O could also form during deposition
and extrapolation of the bonding energetics (Table 2b) sug-
gests that such complexes should be exogenic under matrix
isolation conditions. We again tentatively propose that
such complexes will readily convert to H2SO4 and/or
H2S2O7 during the deposition phase.
The theoretical calculations also suggest SO3 dimeric as
well as cyclic and chain like SO3 trimeric complexes to be
exogenic under matrix isolation conditions. It is tempting
to extrapolate the bonding energy of the dimeric and the
chain like trimeric SO3 complex to longer chain lengths,
ca. 6 kJ molꢀ1 (B3LYP) and ca. 20 kJ molꢀ1 (MP2) per
additional SO3 unit, Table 2a. However, the bonding
enthalpy is more than counteracted by the disfavorable
entropy, which is also reflected by the difference in melting
points of the c- and b-allotropes of SO3 [59]. Indeed, the
spectroscopic evidence suggests that both the dimeric and
the cyclic trimeric complexes are the only ones present in
the matrix. Moreover, the calculations suggest that the tri-
meric chainlike complex is of higher energy than the cyclic
form. We, therefore, argue that polymer chains of SO3 will
not form during the matrix isolation deposition phase.
722.5 cmꢀ1
.
The only absorption growing upon annealing and
matching a calculated frequency (962.0 cmꢀ1) of the second
possible mixed trimer (H2O)2Æ(SO3) (type A, in this case) is
found at 920.1 cmꢀ1. We assign it to the t10 mode of
(H2O)2Æ(SO3), type A.
Additional water concentration and annealing sensitive
absorptions were observed at 963.6, 960.5, 944.5, 946.5,
845.3, 837.4, 833.4, 903.1, 898.2, 738.4, and 731.6 cmꢀ1
.
Several bands of similar frequencies were recorded for
SO3 trapped in neon [21] at 959.6, 946.2, 928.8, 924.9,
913.4, 850.7, 842.9, 794.7, 738.8 cmꢀ1. The 928.8, 924.9
and 842.9 cmꢀ1 bands were attributed there to the
(H2O)Æ(H2SO4) complex. Most of these bands were also
observed by us in the spectrum of sulfuric acid vapors iso-
lated in argon [22]. There the 956 and 950 cmꢀ1 bands were
tentatively assigned to metastable (H2O)nÆ(SO3)mÆ(H2SO4)p
species, the 929 and 920 cmꢀ1 bands to (H2O)nÆ(H2SO4)m
polymers and the 847.5 cmꢀ1 line to the (H2O)2Æ(H2SO4)
trimer. As noted in the above discussion of the higher spec-
tral regions, we found no evidence for the existence of sul-
furic acid monomers in the sample. However, the
conversion of (H2O)nÆ(SO3) species to H2SO4 [16], which
is distinctly more probable for the higher water complexes,
allows the possibility of the presence of some H2SO4 com-
plex species.
4.8. SO3 and SO2 bends and deformations
Water concentration dependent new bands were record-
ed at 575.2, 566.8, 564.3 (doublet) 554.9 (broad), 537.6, and
528.7 cmꢀ1 (Fig. 6f, traces A, B and C). In addition, the
dimeric (SO3)2 486.6 cmꢀ1 band shifts to 486.0 cmꢀ1 and
its intensity grows by about a factor of four when less than
1% of water is added to the argon matrix gas. Its intensity
decreases upon annealing to 35 K – a behavior typical to
both (H2O)Æ(SO3) and H2S2O7 species. The calculated fre-
quencies of SOn deformations for these species are 489.3
and 484.4 cmꢀ1, respectively (Table 1b). The observed
486.0 cmꢀ1 absorption has, therefore, contributions from
the t17(Bu) O–S–O out of plane bend of the (SO3)2 dimer,
from the t6 SO3 out of plane bend of (H2O)Æ(SO3) and
Acknowledgements
Preliminary experiments were performed at the Univer-
sity of Regensburg and A.L. gratefully acknowledges the
support of the Humboldt Foundation and the help of Prof.
B. Dick and Ms. T. Schaefer. The Norwegian High Perfor-
mance Computing Consortium is acknowledged for grants
of computing time.

34
A. Givan et al. / Journal of Molecular Structure 830 (2007) 21–34
[34] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb,
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