Microwave investigation of sulfuric acid monohydrate

Article abstract of DOI:10.1021/ja012724w

The complex H₂SO₄-H₂O has been observed by rotational spectroscopy in a supersonic jet. A-type spectra for 18 isotopic forms have been analyzed, and the vibrationally averaged structure of the system has been determined. The complex forms a distorted, six-membered ring with the water unit acting as both a hydrogen bond donor and a hydrogen bond acceptor toward the sulfuric acid. One of the H₂SO₄ protons forms a short, direct hydrogen bond to the water oxygen, with an H···O distance of 1.645(5) A and an O-H···O angle of 165.2(4)°. Additionally, the orientation of the water suggests a weaker, secondary hydrogen bond between one of the H₂O hydrogens and a nearby S=O oxygen on the sulfuric acid, with an O···H distance of 2.05(1) A and an O-H ···O angle of 130.3(5)°. The experimentally determined structure is in excellent agreement with previously published DFT studies. Experiments with HOD in the jet reveal the formation of only isotopomers involving deuterium in the secondary hydrogen bond, providing direct experimental evidence for the secondary H···O interaction. Extensive isotopic substitution has also permitted a re-determination of the structure of the H₂SO₄ unit within the complex. The hydrogen-bonding OH bond of the sulfuric acid elongates by 0.07(2) A relative to that in free H₂SO₄, and the S=O bond involved in the secondary interaction stretches by 0.04(1) A. These changes reflect substantial distortion of the H₂SO₄ moiety in response to only a single water molecule, and prior to the proton transfer event. Spectral data indicate that the complex undergoes at least one, and probably more than one type of internal motion. Although the sulfuric acid in this work was produced from direct reaction of SO₃ and water in the jet, experiments with H₂¹⁸O indicate that about 2-3% of the acid is formed via processes not normally associated with the gas-phase hydration of SO₃.

Full text of DOI:10.1021/ja012724w

Published on Web 03/26/2002
Microwave Investigation of Sulfuric Acid Monohydrate
Denise L.Fiacco,† Sherri W. Hunt, and Kenneth R. Leopold*
Contribution from the Department of Chemistry, UniVersity of Minnesota, 207 Pleasant St., SE,
Minneapolis, Minnesota 55455
Received December 18, 2001
Abstract: The complex H2SO4-H2O has been observed by rotational spectroscopy in a supersonic jet.
A-type spectra for 18 isotopic forms have been analyzed, and the vibrationally averaged structure of the
system has been determined. The complex forms a distorted, six-membered ring with the water unit acting
as both a hydrogen bond donor and a hydrogen bond acceptor toward the sulfuric acid. One of the H2SO4
protons forms a short, direct hydrogen bond to the water oxygen, with an H‚‚‚O distance of 1.645(5) Å and
an O-H‚‚‚O angle of 165.2(4)°. Additionally, the orientation of the water suggests a weaker, secondary
hydrogen bond between one of the H2O hydrogens and a nearby SdO oxygen on the sulfuric acid, with an
O‚‚‚H distance of 2.05(1) Å and an O-H‚‚‚O angle of 130.3(5)°. The experimentally determined structure
is in excellent agreement with previously published DFT studies. Experiments with HOD in the jet reveal
the formation of only isotopomers involving deuterium in the secondary hydrogen bond, providing direct
experimental evidence for the secondary H‚‚‚O interaction. Extensive isotopic substitution has also permitted
a re-determination of the structure of the H2SO4 unit within the complex. The hydrogen-bonding OH bond
of the sulfuric acid elongates by 0.07(2) Å relative to that in free H2SO4, and the SdO bond involved in the
secondary interaction stretches by 0.04(1) Å. These changes reflect substantial distortion of the H2SO4
moiety in response to only a single water molecule, and prior to the proton transfer event. Spectral data
indicate that the complex undergoes at least one, and probably more than one type of internal motion.
Although the sulfuric acid in this work was produced from direct reaction of SO3 and water in the jet,
experiments with H218O indicate that about 2-3% of the acid is formed via processes not normally associated
with the gas-phase hydration of SO3.
Introduction
nucleation rates for aerosols involving sulfuric acid have been
notoriously difficult to predict.4,5 The gas-phase hydration of
Sulfuric acid/water aerosols play a vital role in the hetero-
geneous chemistry leading to the destruction of stratospheric
ozone.1,2 They have also demonstrated significantly high uptake
of nitric acid at temperatures at or near the frost point and are
believed to play an important role in the formation of polar
stratospheric clouds.1,3 Because of their importance, numerous
experimental and theoretical studies have been aimed at
investigating the nucleation of sulfuric acid and water vapor,4,5
but due to the strong tendency of H2SO4 to form hydrates,
sulfuric acid is thus of considerable interest with regard to
elucidating the details of sulfuric acid aerosol formation in the
atmosphere.
Bulk phase spectroscopic measurements on the sulfuric acid-
water system date back at least several decades6 and continue
to be a subject of active investigation today.7 In recent years,
spectroscopic and surface analytical techniques have also been
applied to H2SO4/H2O thin films,8 and infrared optical constants
have been measured for sulfuric acid-water mixtures as a
function of temperature, frequency, and composition.9 The
scattering of water molecules off liquid sulfuric acid surfaces
has been studied,10 and crystal structures for sulfuric acid,11 its
* To whom correspondence should be addressed. E-mail: kleopold@
chem.umn.edu.
† Present Address: Achillion Pharmaceuticals, 300 George St., New
Haven, CT 06511.
(1) Finlayson-Pitts, B. J.; Pitts, J. N., J. Chemistry of the Upper and Lower
Atmosphere. Theory Experiments and Applications; Academic Press: San
Diego, CA 2000.
(5) (a) Mirabel, P.; Katz, J. L. J. Chem. Phys. 1974, 60, 1138. (b) Heist, R.
H.; Reiss, H. J. Chem. Phys. 1974, 61, 573. (c) For additional references
prior to 1995, see: Laaksonen, A.; Talanquer, V.; Oxtoby, D. W. Annu.
ReV. Phys. Chem. 1995, 46, 489.
(6) See, for example: (a) Walrafen, G. E.; Dodd, D. M. Trans. Faraday Soc.
1961, 57, 1286. (b) Savoie, R.; Gigue´re, P. A. J. Chem. Phys. 1964, 41,
2698. (c) Palmer, K. F.; Williams, D. Appl. Opt. 1975, 14, 208.
(7) (a) Nash, K. L.; Sully, K. J.; Horn, A. B. J. Phys. Chem. A 2001, 105,
9422. (b) Tomikawa, K.; Kanno, H. J. Phys. Chem. A 1998, 102, 6082.
(8) (a) Roberts, J. T. Acc. Chem. Res. 1998, 31, 415. (b) Biermann, U. M.;
Luo, B. P.; Peter, Th. J. Phys. Chem. A 2000, 104, 783 and references
therein.
(2) See, for example: (a) Hallquist, M.; Stewart, D. J.; Baker, J.; Cox, R. A.
J. Phys. Chem. A 2000, 104, 3984. (b) Hanson, D. R.; Ravishankara, A. R.
J. Phys. Chem. 1994, 98, 5728. (c) Hanson, D. R.; Ravishankara, A. R. J.
Geophys. Res. 1991, 96, 17, 307. (d) Tolbert, M. A.; Rossi, M. J.; Golden,
D. M. Geophys. Res. Lett. 1988, 15, 847 and references therein.
(3) (a) Carslaw, K. S.; Luo, B. P.; Clegg, S. L.; Peter, Th.; Brimblecombe, P.;
Crutzen, P. J. Geophys. Res. Lett. 1994, 21, 2479. (b) Beyer, K. D.; Seago,
S. W.; Chang, H. Y.; Molina, M. J. Geophys. Res. Lett. 1994, 21, 871. (c)
Tabazadeh, A.; Turco, R. P.; Jacobson, M. Z. J. Geophys. Res. 1994, 99,
12897.
(4) See, for example: (a) Noppel, M. J. Chem. Phys. 1998, 109, 9052. (b)
Kusaka, I.; Wang, Z.-G.; Seinfeld, J. H. J. Chem. Phys. 1998, 108, 6829.
(c) Viisanen, Y.; Kulmala, M.; Laaksonen, A. J. Chem. Phys. 1997, 107,
920. (d) McGraw, R. J. Chem. Phys. 1995, 102, 2098 and references therein.
(9) (a) Niedziela, R. F.; Norman, M. L.; DeForest, C. L.; Miller, R. E.; Worsnop,
D. R. J. Phys. Chem. A 1999, 103, 8030. (b) Tisdale, R. T.; Glandorf, D.
L.; Tolbert, M. A.; Toon, O. B. J. Geophys. Res. 1998, 103, 25353 and
references therein.
(10) Govoni, S. T.; Nathanson, G. M. J. Am. Chem. Soc. 1994, 116, 779.
9
4504
J. AM. CHEM. SOC. 2002, 124, 4504-4511
10.1021/ja012724w CCC: $22.00 © 2002 American Chemical Society

Microwave Investigation of Sulfuric Acid Monohydrate
A R T I C L E S
monohydrate (H3O+HSO4-),11 and several higher hydrates12
have been published. Numerous vapor pressure and uptake
measurements involving sulfuric acid solutions have been
reported,13 and hydrated sulfuric acid has even been proposed
to form on interstellar dust grains present in circumstellar
envelopes.14a Aqueous sulfuric acid is also believed to comprise
the aerosol particles in the upper layer of the cloud cover over
Venus.14b
SO3 was introduced into the vacuum chamber through the pulsed valve
by passing Ar over solid, polymerized SO3 at a backing pressure of
∼2 atm. Water vapor was injected into the expansion by passing Ar
gas over a reservoir of liquid water at a backing pressure of 0.165 atm
and passing the resulting mixture through a 0.012 in. i.d. needle situated
slightly downstream of the nozzle orifice. Ideal conditions for the
production of H2SO4-H2O were obtained by clipping the needle to a
length of 0.11 in. and carefully placing its end in the central region of
the expansion, 0.21 in. below the nozzle orifice. Mixed isotopomers
were formed by adding D2O and H2O to the reservoir in proportions
that optimized the signal under investigation.
For the isolated hydrates of sulfuric acid, experimental,
spectroscopic observations appear limited to cryogenic matri-
ces,15 and our knowledge of these systems in the gas phase,
therefore, has been derived largely from computational results.16-19
Several studies, in particular, have investigated the structural
and energetic properties of isomeric forms of the lower hydrates
of the acid and have focused on the transition between neutral
and ionic species in the series H2SO4(H2O)n (n ) 0-7). On the
basis of this work, it appears that the neutral, hydrogen-bonded
forms are most stable for low n, but with increasing solvation,
the stability of the proton-transferred ion pair increases relative
to that of the hydrogen-bonded complex. Indeed, by n ) 5, the
lowest energy form is (HSO4-)(H3O+)(H2O)4, albeit by only
∼2 kcal/mol.16 However, even when proton transfer is energeti-
cally disfavored, the H2SO4 demonstrates a marked ability to
act as the proton donor in hydrogen-bonding interactions. For
example, in the theoretical structure for the monohydrate, the
sulfuric acid hydrogen bonds to the water unit with an
exceptionally short hydrogen bond length of only ∼1.6-1.7
Å.16-19
Rotational transitions of H2SO4-H2O and its isotopomers were
initially identified by their strong correlation with the intensity of the
110 r000 transition of H2SO4, HDSO4, or D2SO4 (predicted and observed
using published rotational constants25), as well as the nearly symmetric
triplet pattern observed for the a-type J ) 2 r 1 rotational transition.
This pattern is consistent with the near equivalent Kp ) 1 splitting about
the central Kp ) 0 transition predicted for a near prolate rotor. The
attainment and assignment of spectra of mixed isotopic species was
complicated by source conditions, and constant checking on the
110 r 000 transitions of HDSO4, D2SO4, and H2SO4 was necessary to
ascertain the chemical dependence of each transition. In addition, as
the B and C rotational constants are similar for several mixed
isotopomers, the a-type spectra were overlapping, initially precluding
unique spectral assignments for each of the observed a-type spectral
patterns. To overcome this obstacle, the dependence of each transition
on the ratio of H2O/D2O in the liquid reservoir was tested on several
independent occasions to aid in obtaining an initial assignment for each
isotopic species. Subsequent confirmation of these assignments came
from the ability to predict and observe transitions for a number of
isotopomers based on refined structural parameters.
The study of sulfuric acid monohydrate is also of fundamental
significance, as it represents the first stage in the hydration of
a simple, common mineral acid. Despite the variety of theoretical
calculations which now exist, a definitive gas-phase investigation
of the H2SO4-H2O adduct has not been carried out. Accord-
ingly, in this paper, we report the microwave spectrum and
structure of the 1:1 complex H2SO4-H2O.
As an additional check of the assignments of each transition to an
isotopomer of H2O-H2SO4, the Ar carrier gas was replaced with a
70% Ne/30% He mixture. The intensity of the assigned transitions
decreased significantly with the use of Ne/He yet the transitions
remained observable, ensuring the lack of dependence on Ar. The
spectra of all 18O-containing species were obtained by the addition of
H218O (95 atom %, Icon Services) to the liquid reservoir, while the
spectrum of the 34S-substituted H2SO4-H2O species was observed in
natural isotopic abundance.
Experimental Section
The estimated uncertainty in the measured transition frequencies is
2 kHz for the fully protonated forms. For isotopomers containing
deuterium, the hyperfine structure was not adequately resolved to
determine quadrupole coupling constants. Thus, an average linecenter
was estimated, with a corresponding increase of uncertainty, up to about
10 kHz for the fully deuterated derivative.
Rotational spectra were recorded on a Balle-Flygare Fourier
transform microwave spectrometer,20 the details of which have been
described previously.21 H2SO4-H2O was produced in situ via the
reaction between H2O and SO3, using an injection source similar to
that which we reported in previous studies on reactive species.22-24
Results
(11) Kemnitz, E.; Werner, C.; Trojanov, S. Acta Crystallogr. 1996, C52, 2665.
(12) Mootz, D.; Merschenz-Quack, A. Z. Naturforsch. 1987, 42b, 1231.
(13) See, for example: (a) Robinson, G. N.; Worsnop, D. R.; Jayne, J. T.; Kolb,
C. E.; Swartz, E.; Davidovits, P. J. Geophys Res. 1998, 103, 25,371. (b)
Marti, J. J.; Jefferson, A.; Cai, X. P.; Richert, C.; McMurry, P. H.; Eisele,
F. J. Geophys. Res. 1997, 102, 3725. (c) Zhang, R.; Wooldridge, P. J.;
Molina, M. J. J. Phys. Chem. 1993, 97, 8541 and references therein.
(14) (a) Scappini, F.; Smith, H.; Klemperer, W. Conf. Proc.-Ital. Phys. Soc.
2000, 67 (Workshop - Molecules in Space and in the Laboratory), 55. (b)
Encrenaz, T.; Bibring, J.-P.; Blanc, M. The Solar System, 2nd Corrected
and Revised Edition; Dunlap, S., Translator; Springer: Heidelberg, 1995.
(15) (a) Givan, A.; Larsen, L. A.; Loewenschuss, A.; Nielsen, C. J. J. Chem.
Soc., Faraday Trans. 1998, 94, 827. (b) Bondybey, V. E.; English, J. H. J.
Mol. Spectrosc. 1985, 109, 221.
(16) Re, S.; Osamura, Y.; Morokuma, K. J. Phys. Chem. A 1999, 103, 3535.
(17) Arstila, H.; Laasonen, K.; Laaksonen, A. J. Chem. Phys. 1998, 108, 1031.
(18) Bandy, A. R.; Ianni, J. C. J. Phys. Chem. A 1998, 102, 6533.
(19) Beichert, P.; Schrems, O. J. Phys. Chem. A 1998, 102, 10540.
(20) Balle, T. J.; Flygare, W. H. ReV. Sci. Instrum. 1981, 52, 33.
(21) (a) Phillips, J. A.; Canagaratna, M.; Goodfriend, H.; Grushow, A.; Almlo¨f,
J.; Leopold, K. R. J. Am. Chem. Soc. 1995, 117, 12549. (b) Phillips, J. A.
Ph.D. Thesis, University of Minnesota, 1996.
Spectral Observations. The 18 isotopomers observed in this
study are indicated in Table 1, and a listing of assigned
transitions is provided as Supporting Information. The atom
labeling scheme used in the tables is illustrated in Figure 1a,
and a representative spectrum, showing the JKpKo ) 212 r 111
transition of the parent form, is shown in Figure 2. As noted
above, in complexes containing deuterium, hyperfine structure
was poorly resolved and was not analyzed. For the complexes
of HOD, only species with the deuterium in the position closest
to the SdO oxygen of the sulfuric acid (O3) were observed.
For isotopomers containing only hydrogen, the a-type transi-
tions appeared as doublets. This is clearly seen for the parent
form in Figure 2. The splitting between components of these
(22) Canagaratna, M.; Phillips, J. A.; Goodfriend, H.; Leopold, K. R. J. Am.
Chem. Soc. 1996, 118, 5290.
(23) Ott, M. E.; Leopold, K. R. J. Phys. Chem. A 1999, 103, 1322.
(24) Fiacco, D. L.; Toro, A.; Leopold, K. R. Inorg. Chem. 2000, 39, 37.
(25) Kuczkowski, R. L.; Suenram, R. D.; Lovas, F. J. J. Am. Chem. Soc. 1981,
103, 2561.
9
J. AM. CHEM. SOC. VOL. 124, NO. 16, 2002 4505

A R T I C L E S
Fiacco et al.
Table 1. Spectroscopic Constants for Isotopic Forms of H2SO4-H2Oa
H1
H2
O1
O2
O3
O4
S
-−
H3
H4
O5
stateb
B (MHz)c
C (MHz)c
∆J (kHz)c
∆
JK (kHz)c
1
1
16
16
16
16
32
1
1
16
A
B
A
B
A
B
A
B
A
B
A
B
A
B
1899.1253(8)
1899.1131(8)
1894.8643(8)
1894.8532(8)
1798.2664(8)
1798.2589(8)
1782.3686(9)
1782.3752(9)
1792.9347(8)
1792.9117(8)
1787.0015(8)
1786.9700(8)
1758.277(1)
1758.2798(8)
1738.950(2)
1814.473(2)
1853.738(2)
1846.015(1)
1768.390(1)
1884.100(1)
1859.519(1)
1753.289(1)
1830.144(2)
1870.617(1)
1780.986(1)
1878.2435(8)
1878.2221(8)
1874.243(1)
1874.2238(8)
1779.5662(8)
1779.5493(8)
1747.5183(9)
1747.4815(9)
1765.0065(8)
1765.0069(8)
1769.942(1)
1769.9498(8)
1734.3217(8)
1734.3004(8)
1724.871(2)
1800.650(1)
1835.856(2)
1824.795(1)
1748.501(1)
1862.155(1)
1840.540(1)
1736.260(1)
1813.281(1)
1849.075(1)
1762.475(1)
0.94(4)
0.88(4)
0.83(5)
0.86(4)
0.85(4)
0.85(4)
0.86(7)
0.90(7)
0.86(4)
0.92(4)
d
13.0(4)
12.4(4)
d
12.5(4)
12.3(4)
11.9(4)
10(1)
1
1
1
1
1
1
1
1
1
1
1
1
16
16
16
18
16
16
16
16
18
16
16
16
16
16
16
16
18
16
16
16
16
16
16
18
34
32
32
32
32
32
1
1
1
1
1
1
1
1
1
1
1
1
16
18
18
18
18
18
11(1)
10.1(4)
9.6(4)
d
8.9(4)
11.7(4)
11.7(4)
11(1)
10.3(6)
7.5(7)
14.7(5)
10.1(8)
11.8(6)
11.9(5)
12.3(8)
12.6(6)
11.7(6)
11.7(5)
1.01(4)
0.70(5)
0.75(4)
0.8(1)
2
2
2
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
2
1
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
32
32
32
32
32
32
32
32
32
32
32
2
2
1
2
2
1
2
2
2
1
2
2
1
1
1
2
1
1
2
1
1
2
16
16
16
16
16
16
16
16
16
16
16
1.27(7)
0.32(7)
0.49(6)
0.84(8)
0.79(7)
0.72(6)
0.95(8)
0.87(7)
1.06(7)
0.85(5)
a Isotopic derivatives are specified by the approximate atomic masses (e.g., 2 for deuterium, 16 for 16O, etc.) according to the atom numbering scheme
of Figure 1. b Two states were observed only for the fully protonated forms. See text for discussion. c Uncertainties are one standard error in the least-
squares fit. d Not determined.
Figure 1. Four views of the sulfuric acid-water complex, emphasizing (a) bond lengths and bond angles within the monomers; (b) intermolecular parameters
specifying the relative orientation of the monomers (R is the O5-O1-S-O3 dihedral angle; a positive value of δ and a negative value of γ are drawn; see
text for discussion); (c) chemically interesting features of the experimentally determined structure; and (d) changes in the sulfuric acid monomer structure
upon complexation (value in H2SO4-H2O minus value in H2SO4 monomer).
doublets was generally on the order of 10-30 kHz in the J )
01 r 000 transition, and increased roughly in proportion to
(J′′ + 1), where J ′′ specifies the lower state of the transition.
with transitions due to state B at the lower frequency. These
states, if present, were not discernible for isotopomers contain-
ing deuterium, as the splitting is on the same order as that for
the hyperfine structure and may, therefore, have been obscured.
1
The corresponding states are labeled A and B in this paper,
9
4506 J. AM. CHEM. SOC. VOL. 124, NO. 16, 2002

Microwave Investigation of Sulfuric Acid Monohydrate
A R T I C L E S
H ) [(B + C)/2 - ∆JJ2]J2 + [A - (B + C)/2 - ∆JKJ2 -
∆KJz2]Jz2
+
2
2
[(B - C)/2 - 2δJJ2](Jx2 - Jy ) - δK[Jz2(Jx2 - Jy ) +
(Jx2 - Jy )Jz2] (1)
2
where A, B, and C are the rotational constants and ∆J, ∆JK, ∆K,
δJ, and δK are centrifugal distortion constants. Since the a-type
spectra are largely insensitive to A, and no b- and c-type
transitions were assigned, initial fits were performed with the
value of A held fixed at 4500 MHz for all 18 isotopomers. This
approach resulted in unacceptably large residuals for a number
of the isotopic species studied and thus the A constant was
allowed to float in a series of preliminary fits for each
isotopomer. In the final fit for each isotopic species, the A
constant was then fixed at the value obtained in the preliminary
fit, which resulted in much decreased residuals and improved
values for B and C. The values of B and C, however, were not
significantly affected by the choice of A. Moreover, the scope
of the data set dictated that of the centrifugal distortion constants,
only ∆J, and ∆JK were necessary to fit the spectrum. Thus ∆K,
δJ, and δK were constrained to zero. The residuals from all the
final fits were satisfactorily within the experimental uncertain-
ties, and the resulting spectroscopic constants are listed in Table
1. Values of B and C are seen to be determined with very small
standard errors. For the fully protonated forms, for which spectra
were split into doublets, separate fits were carried out for each
state.
18O Substitution. It is interesting to note from Table 1 that
the spectral assignments include isotopomers containing 18O in
both S-OH and SdO positions of the sulfuric acid. The latter
is somewhat surprising in light of the proposed mechanisms28-34
for the gas-phase reaction between H2O and SO3, which suggest
that the water oxygen should retain one of its hydrogens in the
final sulfuric acid product. As a check, therefore, the frequency
of the 110 r 000 transition for each of the two possible 18O-
substituted forms of the H2SO4 monomer was predicted from
experimentally determined structural parameters.25 The transi-
tions for both species were readily located (9940.519 MHz for
the Sd18O form and 9929.341 MHz for the S-18OH form) and
are shown in Figure 3. In addition, to ensure that these transitions
were indeed due to H2SO4, (rather than lines from other species,
fortuitously situated at similar frequencies) the same transition
of the 34S partner to each isotopomer was also predicted and
observed (9938.278 MHz for 34Sd18O; 9925.891 MHz for 34S-
18OH). These results provide unambiguous evidence that both
18O derivatives of sulfuric acid are present in the jet. Though
not immediately apparent from Figure 3, however, the S-
18OH transition was about 30-40 times more intense than that
of Sd18O, indicating that sulfuric acid formed is at least richer
in the expected product. While the formation of the Sd18O form
Figure 2. The 212 r 111 transitions of H2SO4-H2O, where the A and B
states are apparent. Total data collection time for the spectrum was
approximately 39 s.
Moreover, the spectra for mixed species (e.g., those containing
HDSO4 and D2SO4 with H2O) were relatively weak, hence the
less intense component, if present, may not have been observable
in some cases. The intensity ratios for states A and B were not
carefully measured, but appeared somewhat variable, ranging
from about 3:1 to as much as 16:1 in some spectra. However,
these ratios are sensitive to a variety of experimental conditions,
including the offset between the molecular frequency and the
center frequency of the microwave cavity, and this type of
variability is not unprecedented on our spectrometer.
Extensive searches for c-type transitions were also carried
out for the parent and fully deuterated forms. These searches
were guided by using calculated H2SO4-H2O structures to
provide estimates of the A rotational constant. However, instead
of a single, assignable c-type line, numerous transitions were
observed which were dependent on both SO3 and either H2O
or D2O. For example, in experiments with the fully protonated
form, a congested pattern of lines spread over an 80 MHz region
was observed near the predicted 312 r 202 transition. Similar
results were obtained for the fully deuterated form. For this
reason, no c-type transitions were assigned in this work. Separate
searches for b-type spectra were not conducted.
In addition to the dense spectra above, a number of other
unassigned transitions were observed. These lines also displayed
a chemical dependence on SO3 and either H2O, H2O/D2O, or
D2O, but were not assignable on the basis of rigid rotor
predictions. As a sizable assortment of species is likely formed
under the experimental conditions detailed above, a large number
of additional spectra are not particularly surprising. Moreover,
as discussed below, the H2SO4-H2O complex likely undergoes
at least one, and perhaps more than one type of internal motion,
the spectral signatures of which may add additional non-rigid-
rotor transitions to the spectrum. Nevertheless, the rigid-rotor,
a-type spectra of all 18 isotopomers investigated were well
behaved, and it is the analysis of these transitions that forms
the focus of this paper. The frequencies and approximate
intensities of all unassigned lines, as well as details of the
chemical dependencies of some of them, have been documented
elsewhere.26
(28) Morokuma, K.; Muguruma, C. J. Am. Chem. Soc. 1994, 116, 10316.
(29) (a) Jayne, J. T.; Po¨schl, U.; Chen, Y.; Dai, D.; Molina, L. T.; Worsnop, D.
R.; Kolb, C. E.; Molina, M. J. J. Phys. Chem. A 1997, 101, 10000. (b)
Kolb, C. E.; Jayne, J. T.; Worsnop, D. R.; Molina, M. J.; Meads, R. F. J.
Am. Chem. Soc. 1994, 116, 10314.
(30) Lovejoy, E. R.; Hanson, D. R.; Huey, L. G. J. Phys. Chem. 1996, 100,
19911.
Spectral Fits. The observed a-type transitions for each of
the 18 isotopic species studied were fit to Watson’s A-reduced
Hamiltonian for a distortable asymmetric rotor,27 viz.,
(31) Larson, L. J.; Kuno, M.; Tao, F.-M. J. Chem. Phys. 2000, 112, 8830.
(32) Hoffman, M.; Schleyer, P. v. R. J. Am. Chem. Soc. 1994, 116, 4947.
(33) Reiner, T.; Arnold, F. J. Chem. Phys. 1994, 101, 7399.
(34) Hoffmann-Sievert, R.; Castleman, A. W., Jr. J. Phys. Chem. 1984, 88, 3329.
(26) Fiacco, D. L., Ph.D. Thesis, University of Minnesota, 2001.
(27) Gordy, W.; Cook, R. L. MicrowaVe Molecular Spectra; John Wiley and
Sons: New York, 1984.
9
J. AM. CHEM. SOC. VOL. 124, NO. 16, 2002 4507

A R T I C L E S
Fiacco et al.
Figure 3. The 110 r 000 transitions of two isotopomers of 18O-substituted H2SO4 formed in the free jet expansion.
is surprising, it is also fortunate, as complexation of the acid
with water then allows for a full set of substitution experiments
within the sulfuric acid portion of the complex. Further
discussion of these observations is given in a later section.
for “light”, weakly interacting systems in which the monomer
distortions are truly small (because the interaction is weak), and
the moments of inertia of the complex are dominated by a
pseudodiatomic term (to which the monomer internal mass
distributions provide only small corrections). In short, the
unusually strong interaction in this complex and the concentra-
tion of mass in one of the monomer units conspire to render
the usual approach untenable.
A subset of the structural parameters used to define the atomic
positions is indicated in Figure 1a,b. Figure 1a focuses primarily
on bond lengths and bond angles within the monomers, while
Figure 1b describes the orientation of the water unit. Only a
subset of the parameters used has been indicated to reduce
clutter. A full listing appears in Table 2. In Figure 1b, the
position of the H2O unit with respect to H2SO4 is determined
by placing the oxygen atom in the O1-SdO3 plane at a distance
RO1-O5 from O1, and forming and angle O5-O1-S. The line
joining O1 and O5 is then rotated out of the plane, maintaining
the O5-O1-S angle (amounting to a rotation about the S-O1
bond). Thus, R is the O5-O1-S-O3 dihedral angle, with
positive R corresponding to rotation of the O5-O1 segment
toward the O2 side of the O1-S-O3 plane, as drawn in Figure
1b.
The symmetry of the water unit is broken by allowing the
two O-H bond lengths in the water unit to differ (Figure 1a).
The orientation of the water is determined by locating the F
axis (Figure 1b) with respect to the O1-S-O3 plane through
two angles labeled by δ and γ as shown in Figure 1b. δ ) γ )
0 correspond to the orientation when the line designating the
height of the O5-H3-H4 triangle coincides with the z axis,
which is parallel to the line segment connecting S and O3.
Positive δ corresponds to a rotation of F toward the sulfuric
acid unit in the plane of the page, while positive γ corresponds
to a counterclockwise rotation of the water molecule, as viewed
from a point on the positive z axis. A negative value of γ is
drawn in the figure. Once F is in position, two angles are used
to locate the position of the water hydrogens: the H-O-H
angle and an angle labeled θ, which sets the tilt of the water
molecule with respect to the F axis.
For the sulfuric acid portion of the complex, the dihedral angle
H1-O1-S-O3 is given by â while H2-O2-S-O3 is mea-
sured by φ. â ) 0 corresponds to the orientation in which H1
is in the O1-S-O3 plane with the O-H1 bond eclipsed to the
S-O3 bond, while φ ) 0 corresponds to that in which H2 lies
in the O2-S-O3 plane, eclipsed to the S-O3 bond. Positive
â indicates that the O1-H1 bond must be rotated clockwise to
eclipse the S-O3 bond, when viewed down the O1-S axis with
O1 closer to the observer. Positive φ indicates that the H2-O2
Structure Determination
A preliminary analysis of the rotational constants yielded a
structure similar to that obtained from previous ab initio19 and
DFT16-18 calculations. The complex forms a distorted six-
membered ring in which the water unit acts as both a proton
acceptor and a proton donor in its interaction with H2SO4. The
main structural features are highlighted in Figure 1. In the
primary interaction, the H2SO4 portion of the complex donates
a proton to the water unit to form a short, direct hydrogen bond
with an O-H distance on the order of 1.6 Å and an O-H-O
angle of ∼165°. A distance of ∼2.1 Å between a hydrogen on
the water unit and an SdO oxygen in H2SO4 is close to the
predicted value of ∼2.2 Å.
Twenty four structural parameters are needed to uniquely
specify the geometry of the complex. This presents a formidable
problem, and although it is common in situations of this type
to reduce the number of degrees of freedom by constraining
monomer geometries to their free-molecule values, such an
approach, in this case, is neither necessary nor appropriate.
Because 36 rotational constants have been determined, and since
each atom has been substituted at least once, many of the internal
degrees of freedom of the monomers are, in principle, determin-
able. This is fortunate, because calculations indicate that the
H2O-H2SO4 interaction is strong enough to produce significant
deformations of the interacting monomers. For example, in the
sulfuric acid unit, the calculated structures16-19 span a range of
0.02-0.05 Å for the lengthening of the O-H bond involved in
the primary hydrogen bond, and a range of 0.03-0.04 Å for
the contraction of the corresponding S-O single bond. Likewise,
the SdO distance is predicted to increase by as much as 0.01-
0.02 Å as a result of the secondary interaction with a water
proton. For the water portion of the complex, the calculated
H-O-H angle increases by about 1.4°.18
While these predicted changes are not enormous in absolute
terms, some of them have a significant effect on the moments
of inertia of the complex. In particular, with a heavy sulfuric
acid, and a light water molecule nearby, the H2SO4 unit itself
contributes substantially to the moments of inertia of the
complex. The result is that changes in its internal structure
cannot be ignored, and indeed early attempts to fit only the
intermolecular structural parameters without allowing relaxation
of the monomer internal degrees of freedom were unsuccessful.
Thus, the present situation is unlike that normally encountered
9
4508 J. AM. CHEM. SOC. VOL. 124, NO. 16, 2002

Microwave Investigation of Sulfuric Acid Monohydrate
A R T I C L E S
Table 2. Structural Parameters for H2SO4-H2Oa
between the two SdO bonds (O3-S-O4) is not predicted to
change from that in free H2SO4 and was fixed at the experi-
mental value of 123.3°.25 On the other hand, although the
experimental O2-H2 distance in free H2SO4 is 0.97(1) Å, the
value of 0.95 Å was found to minimize ø-squared in a series of
preliminary fits in which RO2-H2 was constrained to various
values in the neighborhood of 0.97 Å. Hence, RO2-H2 was
constrained to 0.95 Å all subsequent fits. The magnitude of the
O3-S-O4 angle was also tested in a similar series of
preliminary fits and supported the choice of 123.3° noted above.
On the basis of theoretical calculations, both the H2O and
the S-O1-H1 angles are expected to shift somewhat from their
free monomer values (1.4° for (HOH)17 and 0.4-0.5° for
(S-O1-H1)17,18), and thus appropriate values for these
parameters were also obtained from a series of preliminary fits.
In the minimization process, the H2O angle was allowed to vary
between 106 and 107°, while the S-O1-H1 angle was allowed
to vary between 108.5 and 109.0°. The range for the water angle
was chosen by considering the large distortion of this angle
predicted by theoretical calculations of the H2SO4-H2O com-
plex. As a verification of the chosen range, values closer to the
water angle in free H2O were tested and indeed resulted in much
larger residuals. The optimal values based on these preliminary
fits were 107° and 108.6° for the H-O-H and S-O1-H1
angles, respectively.
The final values for all 19 freed parameters are given in Table
2. The quoted uncertainties arise predominantly from those in
the H2O and S-O1-H1 angles, and the quoted values reflect
the spread of fitted parameters obtained by using the ranges of
these angles described above. Overall, the quality of the
structural fit was quite good, with the largest residual among
the fitted rotational constants only 560 kHz. The experimentally
determined structure of the complex is depicted in Figure 1c,
which highlights some of the more chemically interesting
features. A table of atomic Cartesian coordinates is provided
as Supporting Information.
H SO
H SO
2
4
2
4
parameter
exptl
theorb
monomerc
distortiond
fitted parameters:
RO1-O5
2.67(1)
100.2(6)
15.3(4)
38.7(6)
-11.4(8)
56(1)
2.64
99.9
17.7
32.9
0.7
S-O1-O5
R
δ
γ
θ
53.7
RO1-H1
RO2-H2
RS-O1
1.04(1)
1.009
0.975
1.603
1.636
1.466
1.458
108.4
108.0
109.1
104.5
122.9
107.5
102.7
-20.3
-165.0
0.971
0.968
107.2
0.97(1)
0.97(1)
0.07(2)
0.95e
1.567(1)
1.578(3)
1.464(1)
1.410(4)
108.6f
1.574(10)
1.574(10)
1.422(10)
1.422(10)
108.5(15)
108.5(15)
108.6(5)
106.4(5)
123.3(10)
106.4(5)
-0.007(11)
0.004(13)
0.042(11)
-0.012(14)
RS-O2
RS-O3
RS-O4
S-O1-H1
S-O2-H2
O1-S-O3
O2-S-O3
O3-S-O4
O1-S-O4
O1-S-O2
â
108.5e
106.71(6)
104.71(9)
123.3e
106.7(4)
101.8(2)
-13.7(5)
-163.4(5)
0.98(1)
0.98(1)
107f
-1.9(5)
-1.7(5)
0.8(9)
101.3(10)
-20.9(10)g
-155.1(10)g
0.5(12)
7.2(15)
-8.3(15)
æ
RH3-O5
RH4-O5
H3-O5-H4
calculated from fitted parameters:
RO3-H3
RH1-05
O1-H1-O5
O5-H3-O3
2.05(1)
2.230
1.651
165.9
122.8
1.645(5)
165.2(4)
130.3(5)
a All distances in Å. All angles in degrees. b Values taken from ref 16
or calculated from Cartesian coordinates provided by the authors of ref 16.
c Reference 25. d Value in complex minus value in monomer. e Held fixed
in fit. f Determined from a series of preliminary fits; held fixed in final fit.
See text for discussion. g The monomer value is calculated from the inertial
frame coordinates given in ref 25. A (1° uncertainty in the monomer values
is assumed based on uncertainties reported for other torsional angles reported
therein.
bond must be rotated clockwise to eclipse the S-O3 bond when
viewed down the S-O2 bond from a point closer to O2. Both
angles are indicated in Figure 1a.
Discussion
A nonlinear least-squares analysis of the observed B and C
rotational constants (36 constants in all) was carried out with
use of the 24 structural parameters listed in Table 2. Separate
fits were conducted with state A and state B data for the fully
protonated forms, and an average was taken to determine the
“final” value of each fitted parameter. In the process of fitting
the rotational constants, the sensitivity of the data to each
parameter was carefully tested. From this process, it was
concluded that five of the structural parameters could not be
freed in the final fits without resulting in singular matrices which
terminated the routine. Thus, their values needed to be con-
strained in some reasonable way. The five parameters are as
follows: (1) S-O1-H1, the angle between the sulfur, O1, and
H1; (2) S-O2-H2, the same angle except involving the free
H2SO4 hydrogen; (3) O3-S-O4, the angle between the two
SdO bonds; (4) RO2-H2, the O-H bond distance for the free
H2SO4 hydrogen; and (5) H3-O5-H4, the water angle.
Appropriate values for the constrained parameters were
determined from a comparison of the theoretical structure of
H2SO4-H2O with those of the free monomers. As the geometry
near the free H2SO4 hydrogen appears to remain essentially
unchanged upon complexation,16,17,19 the S-O2-H2 angle was
fixed at its free monomer value of 108.5°.25 Similarly, the angle
As is evident from the above discussion, the H2O unit of the
sulfuric acid-water complex positions itself so as to form a
distorted, nonplanar, six-membered ring with one-half of the
H2SO4 molecule. In doing so, the water acts as a hydrogen bond
acceptor in the complex, forming a short, somewhat direct
hydrogen bond characterized by a 1.645(5) Å O‚‚‚H distance
(2.663 Å O‚‚‚O distance) and a 165.2(4)° O-H‚‚‚O angle. The
orientation of the water also suggests a weaker, secondary
interaction between the H2O proton and a nearby SdO oxygen,
with a much longer O‚‚‚H distance of 2.05(1) Å and a highly
bent O-H‚‚‚O angle of 130.3(5)°. While weak, however, this
interaction appears to provide some real stability for the
complex, as is indicated by the lack of deuterium substitution
at the free water hydrogen position in the HOD containing
species. Such a preference for deuterium substitution in weak
hydrogen bonds has been observed in several complexes
involving water and is thought to arise from the reduction in
zero point energy associated with substitution by a heavier
isotope.35
(35) See, for example: (a) Leung, H. O.; Marshall, M. D.; Suenram, R. D.;
Lovas, F. J. J. Chem. Phys. 1989, 90, 700. (b) Canagaratna, M.; Phillips,
J. A.; Ott, M. E.; Leopold, K. R. J. Phys. Chem. A 1998, 102, 1489.
9
J. AM. CHEM. SOC. VOL. 124, NO. 16, 2002 4509

A R T I C L E S
Fiacco et al.
The experimentally determined structure agrees well with the
published computational studies.16-19 It should be noted, of
course, that the experimental parameters represent average
values for the ground vibrational state, while the computed
results correspond to equilibrium structures. Nevertheless, listed
in Table 2 are structural parameters computed by Re et al.,16
which are seen to reproduce the experimental bond lengths and
bond angles typically to within about 0.05 Å and a few degrees,
respectively. The results of the other reported computational
studies,17-19 though not listed, are overall of similar quality.
We note that in the experimental structure, the two H2SO4
hydrogens optimize in a trans configuration, consistent with the
lower energy form of the sulfuric acid monomer,25 and the
lowest energy conformation of the complex predicted by Re et
al.16
The re-determination of many of the monomer structural
parameters within the complex also offers an unusual op-
portunity to examine the degree of structural deformation of a
simple acid resulting from the first step in its hydration. The
structure of free sulfuric acid has been determined by microwave
spectroscopy in the gas phase25 and direct comparison between
complexed and uncomplexed forms, therefore, is possible.
Ironically, the uncertainties in the reported monomer structural
parameters are somewhat larger than those determined here,
quite likely due to the absence of any 18O substitution data in
the set of rotational constants analyzed for free H2SO4. As a
result, changes in only six of the structural parameters are
determined to better than the experimental uncertainty (two bond
lengths, two bond angles, and the two OH bond torsional angles,
â and æ). These changes are listed in Table 2 and highlighted
in Figure 1d.
As expected, the most significant changes in the H2SO4
structure occur in the region in close proximity to the water
molecule. Of particular interest are the 0.07(2) Å bond length
increase in the hydrogen bonding OH group and the 0.04(1) Å
elongation of the S-O3 bond. The former, clearly, suggests
the beginning of proton transfer while the latter may be viewed,
in chemical terms, as the earliest stages in the partial loss of
double bond character. Such loss is expected as the proton
transfers since the S-O3 bond of the bisulfate ion participates
in resonance structures with single bond character. While a 0.04
Å change seems small in absolute terms, it is interesting to note
that the S-O and SdO bond lengths in free sulfuric acid are
1.574(10) and 1.422(10) Å, respectively. Thus, the 0.04 Å
change represents a stretching of the S-O3 bond by ap-
proximately 25% of the difference between the single and double
sulfur-oxygen bonds in sulfuric acid.
The O5-H1 hydrogen bond distance observed for the
H2SO4-H2O marks perhaps the shortest gas-phase hydrogen
bond length for a complex involving water, with a value nearly
0.1 Å shorter than that in HF-H2O36 and 0.134(38) Å shorter
than that in HNO3-H2O.35b The short hydrogen bond distance
implies a very strong interaction between H2SO4 and H2O,
consistent with the calculated binding energy of 12.5 kcal/mol
obtained at the MP2 level in ref 19. This, together with the
measurable lengthening of the O1-H1 bond distance, marks
the onset of a proton-transfer event, and the H2SO4-H2O
complex can reasonably be regarded as an intimation of the
earliest stage in the changes that lead to (H3O+)(HSO4-) ion
pair formation. Interestingly, calculations indicate that such ion
pairs also form directly during the bulk phase hydration of SO3.37
Even with the addition of only one water molecule to H2SO4-
H2O, however, a further lengthening of the O1-H1 bond by
0.03 Å and an additional shortening of the hydrogen bond
distance by 0.127 Å are predicted.16 Clearly, further high-
resolution spectroscopic studies of even slightly higher hydrates
of sulfuric acid would be of interest with regard to gas-phase
proton transfer.
There is also evidence for internal motion within the complex.
The small splittings observed in the a-type spectra of the fully
protonated forms are reminiscent of the proton interchange-type
motions typical of hydrogen bonded complexes of water.38 For
example, in HNO3-H2O,35b the 202 r 101 transition is split by
30 kHz, an amount not too different from the 66 kHz observed
for H2SO4-H2O. In the former case, this observation was
attributed to proton interchange involving a 180° rotation of
water either about its C2 axis or about an axis perpendicular to
the HOH plane. Although the intensity ratios for the A and B
states do not conform to the 1:3 ratio expected for such motions
on the basis of nuclear spin statistics, reservations concerning
the variability of the observed ratios noted above leave open as
a reasonable possibility that some motion of this nature is
operative in the sulfuric acid complex as well. We note,
however, that while 180° rotation about the C2 axis of water
directly produces an equivalent configuration, rotation about the
perpendicular axis must be accompanied by a simultaneous
rotation about the secondary hydrogen bond to leave the
complex unchanged. A similar coupling of rotation about a weak
hydrogen bond and a water wag has been suggested in C2H4-
H2O.39 Another intriguing possibility involves the observation
that the complex is chiral at the sulfur and that a fairly simple
motion involving an exchange of the roles of the free and bound
sulfuric acid protons can interchange the enantiomeric forms.
Clearly, there is no shortage of possible tunneling pathways
which can account for the observed non-rigid-rotor features in
the spectrum. Further analysis, however, is not possible on the
basis of the observed a-type spectra alone.
Finally, the observation of 18O incorporation in the SdO
positions of the sulfuric acid raises some interesting mechanistic
questions about the formation of H2SO4 in the jet. Both
theoretical28 and experimental29,30 studies indicate that the gas-
phase reaction of SO3 and H2O to produce sulfuric acid may
proceed via at least one of two possible reactions, viz.,
SO3 + (H2O)2 f H2SO4 + H2O
(2)
(3)
H2O-SO3 + H2O f H2SO4 + H2O
In either case, calculations indicate participation by a (H2O)2-
SO3 intermediate, which then undergoes a concerted proton
transfer to produce the final sulfuric acid product. The result of
such a mechanism is that the added oxygen (which originates
in the water) assumes one of the S-OH positions in the H2SO4,
and does not incorporate into the SdO position of the molecule.
Similarly, in the aqueous phase, calculations predict37 that
the initial formation of the new S-O bond is accompanied
(37) Meijer, E. J.; Sprik, M. J. Phys. Chem. A 1998, 102, 2893.
(38) Fraser, G. T. Int. ReV. Phys. Chem. 1991, 10, 189.
(39) Andrews, A. M.; Kuczkowski, R. L. J. Chem. Phys. 1993, 98, 791.
(36) Bevan, J. W.; Kisiel, Z.; Legon, A. C.; Millen, D. J.; Rogers, S. C. Proc.
R. Soc. London 1980, A372, 441.
9
4510 J. AM. CHEM. SOC. VOL. 124, NO. 16, 2002

Microwave Investigation of Sulfuric Acid Monohydrate
A R T I C L E S
by proton transfer to a neighboring water solvent molecule,
directly producing bisulfate ion, and again leaving the water
oxygen in a single-bonded position in the molecule. Thus, while
the relative intensities of the two 18O substituted forms of the
H2SO4 monomer (Figure 3) establish that the sulfuric acid
produced in the expansion is indeed 30-40 times richer in the
expected product, it appears that 2-3% of the sulfuric acid
observed in these experiments has formed via alternate or
subsequent processes.
The specific nature of these processes is not clear. One
possibility may involve chemistry occurring on the stainless steel
surfaces of the nozzle and/or injection needle. However, while
such a scenario cannot be rigorously excluded, it seems unlikely
in view of previous observations that the same molecular source
does not scramble protons when forming H2O-DNO3 or D2O-
HNO3 in the jet.35b Another possibility involves participation
by larger water clusters in the expansion and raises the
interesting question as to how large a cluster must be before
the proton scrambling prevalent in aqueous phase becomes
viable. Interestingly, Tao and co-workers31 conclude that SO3-
(H2O)4 is the first cluster to be unstable with respect to formation
of (HSO4-)(H3O+)(H2O)2, though this, in itself, does not address
the question of proton scrambling after initial ion pair formation.
It is also worth noting that the SO3 + H2O system is well-
known to produce sulfuric acid aerosol, and thus, heterogeneous
chemistry associated with microdroplets formed during the early
phases of the expansion remains another plausible possibility.
We have, however, made no attempt to model the nucleation
under these conditions.
Sizable changes in the internal structure of the sulfuric acid
unit within the complex are observed. These include a 0.07(2)
Å elongation of the hydrogen-bonded OH group and a 0.04(1)
Å lengthening of the SdO bond involved in the secondary
interaction with the water. The ability to measure the structural
distortion of a monomer within a complex is unusual, but is
made possible in this system due to the appreciable strength of
the interaction, the large contribution that the H2SO4 itself makes
to the moments of inertia of the complex, and the large amount
of isotopic data collected. The observed changes reveal a
significant effect on the sulfuric acid of only a single water of
hydration. Together with the extremely short hydrogen bond,
the geometry of the complex intimates the earliest stages of
proton transfer, though certainly, the number of solvent mol-
ecules is insufficient to stabilize appreciable charge separation.
Nevertheless, these results suggest that the infrared spectrum
of the monohydrate, as well as any of the higher hydrates of
sulfuric acid, might show measurable shifts relative to the free
monomer, and should be of considerable interest. Published
calculations support this conjecture.16
The formation of H2SO4 in the jet appears to involve a small
contribution from processes not generally associated with the
gas-phase reaction of SO3 and H2O. Evidence for such pathways
comes from experiments with 18OH2, in which the 18O is
incorporated in the SdO position of free sulfuric acid, and both
SdO positions in the H2SO4-H2O complex. While the occur-
rence of surface reactions in the nozzle cannot be rigorously
excluded as a possible explanation, a scenario involving larger
clusters seems more likely. The contribution from these ad-
ditional pathways, however, is small under the conditions used
in these experiments, with the bulk of the sulfuric acid produced
incorporating the 18O into the S-OH position.
Summary
The zero point averaged ground-state structure of H2SO4-
H2O has been determined from microwave spectroscopy in a
supersonic jet, with the sulfuric acid produced in situ from the
reaction of SO3 and water. The system forms a cyclic, doubly
hydrogen bonded complex with a very short (1.645 ( 0.005
Å) primary hydrogen bond between one of the sulfuric acid
hydrogens and the water oxygen. A second, longer (2.05 ( 0.01
Å), and presumably weaker hydrogen bond is formed between
a water hydrogen and one of the doubly bonded oxygens on
the sulfuric acid moiety. Though weak, this secondary interac-
tion appears to provide some stability for the complex, as
evidenced by the observation that complexes with HOD are only
formed in the jet with deuterium in the hydrogen-bonded
position. Spectral evidence further indicates that the system
undergoes at least one, and quite possibly more than one type
of internal motion. The structure obtained from fitting the
observed moments of inertia is in excellent agreement with
published DFT and ab initio calculations.16-19
Acknowledgment. This work was supported by the National
Science Foundation, the Petroleum Research Fund, and the
University of Minnesota through the Doctoral Dissertation
Program (D.L.F.). We would also like to thank Drs. Arstila,
Re, and Morokuma for providing us with the Cartesian
coordinates corresponding to their calculated H2SO4-H2O
geometries.
Supporting Information Available: Tables of transition
frequencies and assignments for H2SO4-H2O and its isoto-
pomers and atomic Cartesian coordinates for the fitted structure
(PDF). This material is available free of charge via the Internet
at http://pubs.acs.org.
JA012724W
9
J. AM. CHEM. SOC. VOL. 124, NO. 16, 2002 4511