Nitric acid-water complexes: Theoretical calculations and comparison to experiment

Article abstract of DOI:10.1021/jp020257e

The formation of HNO₃·(H₂O)_n complexes is studied both theoretically and experimentally. First principles electronic structure calculations were used to produce minimum structures and harmonic vibrational frequencies of HN

Full text of DOI:10.1021/jp020257e

7628
J. Phys. Chem. A 2002, 106, 7628-7635
Nitric Acid-Water Complexes: Theoretical Calculations and Comparison to Experiment†
Patrick R. McCurdy, Wayne P. Hess, and Sotiris S. Xantheas*
William R. Wiley EnVironmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory,
P.O. Box 999, MS K8-91, Richland, Washington 99352
ReceiVed: January 28, 2002; In Final Form: March 21, 2002
The formation of HNO3‚(H2O)n complexes is studied both theoretically and experimentally. First principles
electronic structure calculations were used to produce minimum structures and harmonic vibrational frequencies
of HNO3‚(H2O)n and DNO3‚(H2O)n complexes (n ) 0-4). They also provide insight into the ionization of
HNO3 in water, predicting that ionization in isolated clusters occurs for n ) 4 or larger. Vibrational absorption
spectra of matrix isolated nitric acid/water complexes were obtained using an FTIR spectrometer-based
instrument. By incrementally increasing the amount of H2O in the matrix, we have been able to study nitric
acid/water complexes and the ionization of HNO3. New spectral assignments, the first ones for the n ) 2 and
3 complexes, are suggested on the basis of the results of the electronic structure calculations.
I. Introduction
ion pair becomes important. A significant splitting in the
asymmetric stretch (∆ν3) of the NO3- ion was noted that varied
with the degree of solvation. In a later study of solid H2O-
HNO3 mixtures,21 the same authors suggested as many as three
water molecules may be required to ionize the HNO3 molecule.
However, no definitive conclusions were drawn, and no direct
evidence for the existence of higher order molecular species
other than the 1:1 complex was presented. Barnes et al.3 have
also previously studied HNO3‚H2O complexes in Ar matrixes
using FTIR spectroscopy. Their study focused on the H-ONO2
stretching region of the complex in 1:1:200 HNO3:H2O:Ar
matrixes.
In the present study we investigate the formation of HNO3‚
(H2O)n complexes from first principles electronic structure
methods and compare our findings to new and previously
reported experimental results. The calculations yielded optimized
ground-state structures and harmonic vibrational frequencies for
the HNO3‚(H2O)n (n ) 0-5) clusters and their DNO3 analogues.
We also present new FTIR data and discuss spectral assignments
in light of the new theoretical results. The calculated results
aid in the interpretation of the matrix isolated FTIR spectra,
indicating that dissociation occurs for cluster sizes greater than
n ) 4.
Proton transfer is an important aspect of acid-base equilibria,
electrochemistry, and various processes in biological systems
such as enzymatic catalysis, photosynthesis, and transport across
membranes. It has been established that proton transfer does
not occur for 1:1 complexes of even strong acids and water
(e.g., HCl‚H2O1 and HNO3‚H2O2). Instead, acidic proton transfer
is a process involving several solvent water molecules acting
together to stabilize the proton-anion pair. Water molecules can
stabilize proton transfer between other acceptor donor systems.
For example, the nitric acid-ammonia complex has been shown
to be molecular when isolated in a matrix or in the gas-phase,
but in an aqueous environment, the NH4+-NO3- pair becomes
the more stable form.3-5 Extensive theoretical work on processes
related to proton transfer in polar solvents has been reported.4-11
Despite this effort, the mechanism of solvation and ionization
of acids remains unclear due to the complexity of solution phase
reactions, and proton tunneling effects.
Nitric acid and its hydrates play an important role in
atmospheric chemistry.12 In the stratosphere, nitric acid hydrates
are the primary components of the type I polar stratospheric
cloudssa key player in the seasonal depletion of polar ozone.
Alternatively, the relative stability of HNO3 allows transport to
the troposphere where it gives rise to acid rain. The macroscopic
properties of the binary nitric acid - water system are an
essential element of a multicomponent thermodynamic model
that describes atmospheric processes. To this end, extensive
studies of the binary system’s properties such as thin film
crystallization kinetics,13,14 vapor pressure measurements,15
nucleation,16 phase transitions,17 and its role in heterogeneous
atmospheric reactions18 have been reported. Furthermore, the
formation, stability19 and reactions20 of aqueous clusters of nitric
acid were studied in molecular beam experiemnts that provided
molecular level information. Ritzhaupt and Devlin2 have previ-
ously studied HNO3‚H2O complexes in Ar matrixes using FTIR
spectroscopy. They concluded that at low concentrations of
water in the matrix (<3%) HNO3‚H2O exists primarily as a
molecular complex, and above this concentration the solvated
II. Theoretical and Experimental Methods
First principles electronic structure calculations were per-
formed to determine structures and vibrational frequencies for
the HNO3(H2O)n, n ) 0-4 clusters. We obtained optimal
structures and computed harmonic vibrational frequencies for
these clusters and their deuterated DNO3 analogues at the
second-order perturbation level22 of theory (MP2) using the
augmented correlation consistent polarized valence double-ú
(aug-cc-pVDZ) orbital basis set.23 This level of theory has been
chosen as a compromise between accuracy and feasibility of
the calculations especially for the larger clusters as it has been
previously shown to produce reliable results for the structures
and frequencies of hydrogen bonded neutral24 clusters as well
as clusters of water with positive25 and negative ions.26
Additional calculations at the same level of theory were
performed to obtain structures and frequencies for H2O, D2O,
† Part of the special issue “G. Wilse Robinson Festschrift”.
10.1021/jp020257e CCC: $22.00 © 2002 American Chemical Society
Published on Web 05/14/2002

Nitric Acid-Water Complexes
J. Phys. Chem. A, Vol. 106, No. 33, 2002 7629
Figure 1. Optimal geometries of H2O, NO3-, HNO3 and HNO3(H2O). Bond distances are in Å, and bond angles in degrees.
TABLE 1: Calculated Structural Parameters for the Nitric
and (H2O)2 and (D2O)2 complexes. The calculations were
performed using the Gaussian-9427 and NWChem28 suites of
electronic structure codes. The calculations do not explicitly
account for the effect of the matrix (Ar).
Acid-Water Cluster and Comparison with Previous
Calculations and Experimental Resultsa
theoretical
experimentally fitted32
Experiments were conducted using a matrix-isolation FTIR
apparatus described previously.29 Argon solutions of HNO3 and
H2O or their deuterated analogues (DNO3 and D2O) were co-
deposited from separate nozzles onto KBr substrates cooled to
12 K by a closed-cycle helium cryostat. For annealed samples,
FTIR spectra were taken at 12 K after annealing for 5 min at
the indicated temperature. Thin films were vapor deposited to
a thickness of approximately 40 µm over a period of ap-
proximately 2 h. HNO3 vapor was collected from a 1:2 (by
volume) mixture of fuming HNO3 (99.5) and H2SO4 (96%)
designed to reduce the minor NO2 vapor component. DNO3 was
produced by reacting D2SO4 (98%) with KNO3 (99%). Delivery
lines were passivated overnight with D2O before delivery of
DNO3 to minimize hydrogen isotope exchange. Thin film
growth was monitored by recording the interference fringes of
a reflected helium-neon laser beam aligned at a near-normal
incidence to the substrate. FTIR spectra of condensed samples
this fully distorted “preferred”
parameter
ref 31 work monomers
structure
R(Hb-Ow), Å
R(O1-Hb-Ow), deg
â(Hb-Ow-Hwb), deg
1.707 1.713
176.4 174.7
101.3 97.2
1.812
170.4
93.4
30.3
2.27
1.779
174.5
92
30
2.30
119.3
γ[Hwf-(Ow-Hb-O1)], deg 49.9 42.8
R(Hwb-O2), Å
q(O2-Hwb-Ow), deg
2.49 2.39
108 113.0
118.9
a The labeling of the atoms used to define the structural parameters
is shown in Figure 1.
harmonic zero-point corrections are included). This value is
about twice that of the hydrogen bond in the water dimer.33,34
The slight deviation from linearity is similar to that in the water
dimer (the Ow-Hb-O1 angle is 174.7° vs 171.3° in the water
dimer34), while the separation between the two heavy atoms
participating in the hydrogen bond (Ow and O1 in Figure 1) is
2.708 Å, about 0.208 Å shorter than the corresponding one in
the water dimer at the same level of theory (MP2/aug-cc-
pVDZ).34 The strong hydrogen bond results in an elongation
of the hydrogen bonded OH bond length by 0.021 Å with respect
to the isolated nitric acid fragment, a value that is three times
larger than the corresponding bond lengthening of 0.007 Å in
the water dimer. This, in turn, is expected to induce a large red
shift in the corresponding stretching frequency,35 as a conse-
quence of Badger’s rule.36 Indeed, the harmonic frequency of
the hydrogen bonded O1-Hb stretch in HNO3‚(H2O) is 3284
cm-1, a decrease of 420 cm-1 from the calculated harmonic
frequency of 3704 cm-1 for the nitric acid monomer.
Our value for the binding energy is slightly larger than the
9.5 kcal/mol value reported by Tao et al.31 Our computed MP2/
aug-cc-pVDZ structural parameters for the 1:1 complex together
with the theoretical result of Tao et al.31 and the parameters
obtained from the fitting of the microwave spectra32 are listed
in Table 1. Two sets of data are shown for the experimentally
fitted structure. The first one uses fully distorted monomers
(using the theoretically predicted changes in the fragment
were collected for 256 scans at a resolution of 1 cm-1
.
III. Results
a. Minimum Energy Structures. The optimal geometries
of H2O, NO3-, HNO3 and the HNO3(H2O) cluster at the MP2/
-
aug-cc-pVDZ level of theory are shown in Figure 1. The NO3
anion has D3h symmetry, whereas the symmetry of HNO3 is
Cs. The lowest energy conformation of the HNO3(H2O) cluster
corresponds to a cyclic, homodromic30 arrangement in which
the water molecule acts as a proton acceptor from nitric acid’s
hydrogen atom, in agreement with previous calculations31 and
the structure obtained from the fitting of the microwave
spectra.32 The system forms a quasi-planar, six-membered ring
with the free atom of the water molecule lying above the
molecular plane. The path corresponding to the wagging motion
of this atom above and below the plane passes via a planar
transition state with a barrier31 of 83 cm-1
.
The strength of the HNO3‚(H2O) hydrogen bond with respect
to the separated fragments is 10.3 kcal/mol (8.1 kcal/mol when

7630 J. Phys. Chem. A, Vol. 106, No. 33, 2002
McCurdy et al.
TABLE 2: Calculated Harmonic Frequencies (cm-1) for the Various Complexes. Symmetric and antisymmetric OH stretches
are indicated by “ss” and “as”, respectively
HNO3
[DNO3]
HNO3‚H2O
HNO3‚(H2O)2 HNO3‚(H2O)3
(HNO3)2
[(DNO3)2]
H2O
[D2O]
(H2O)2
[(D2O)2]
species
mode
[DNO3‚H2O] [DNO3‚(H2O)2] [DNO3‚(H2O)3]
HNO3 [DNO3] ν1 OH str
3704 [2696] 3284 [2397]
1861 [1848] 1831 [1807]
1349 [1040] 1504 [1140]
1321 [1321] 1335 [1334]
3050 [2235]
1809 [1786]
1507 [1140]
1348 [1348]
974 [972]
2887 [2121] 3465 [2525] as
3410 [2490] ss
1809 [1776] 1816 [1791] ss
1809 [1790] as
1556 [1179] 1468 [1115] ss
1449 [1104] as
1354 [1354] 1363 [1364] as
1312 [1312] ss
ν2 asym
NO2 str
ν3 NOH
bend
ν4 sym
NO2 str
ν5 N-O str
878 [878]
653 [649]
578 [541]
763 [762]
487 [360]
940 [938]
687 [683]
637 [607]
775 [776]
869 [642]
987 [985]
699 [694]
663 [638]
787 [787]
999 [720]
959 [954] as
956 [955] ss
702 [670] as
688 [684] ss
623 [592] as
620 [587] ss
790 [773] as
772 [771] ss
745 [551] as
689 [498] ss
ν6 NO2
698 [694]
scissors
ν7 ONO2
in plane
ν8 ONO2
640 [608]
778 [780]
out of plane
ν9 NO-H
torsion
981 [724]
H2O [D2O]
H2O [D2O]
ν1 OH str
3906 [3906]as 3903 [3903] as
3770 [3769]ss 3876 [3876] ss
3756 [3756] asa
3938 [2885] as 3925 [2876] as
3804 [2743] ss 3904 [2855] ss
3796 [2738] asa
3516 [3512] ssa
3704 [2678] ssa
ν2 HOH bend
1615 [1613]
1654 [1651]
1618 [1617]
1622 [1187]
1643 [1200]
1624 [1190]
a Participating in H-bond.
the formation of these rings37 is evident from the large
elongation of nitric acid’s hydrogen bonded OH. It amounts to
1.011 Å for n ) 2 and 1.020 Å for n ) 3 (cf. Figure 2), resulting
in lengthenings of 0.034 and 0.043 Å and corresponding red
shifts of 654 and 816 cm-1 in the OH stretching frequencies
with respect to isolated HNO3. Our FTIR data (Vide infra)
provide evidence to support this prediction as we have tenta-
tively identified nitric acid’s O-H stretch bands corresponding
to clusters with 1, 2, and 3 water molecules. The O-H stretch
band of the n ) 3 cluster is weak and highly broadened. As
regards the hydrogen bonding between water molecules, the
fragment containing two water molecules of the n ) 2 cluster
corresponds to a “compact” water dimer having an O-O
separation of 2.737 Å, viz. 0.179 Å shorter than the correspond-
ing one in the gas-phase water dimer. This trend continues for
the larger n ) 3 cluster where the O-O separation is now 0.08
Å shorter than the corresponding one in the cyclic water trimer.38
Our calculations further indicate that the HNO3(H2O)3 cluster
does not support a stable “ion pair” configuration.
The first stable ion-pair configuration is encountered as a local
minimum for n ) 4. Indeed for this cluster we locate two stable
structures, a global HNO3‚(H2O)4 minimum and a local
H3O+(H2O)3NO3- minimum lying just 0.4 kcal/mol above the
global minimum. These are shown in Figure 3. Zero-point
energy corrections increase the separation between the two
minima to 1.5 kcal/mol. The corresponding binding energies
of the two minima with respect to the (HNO3 + 4 H2O)
asymptote are 40.5 (31.4) kcal/mol and 40.1 (29.9) kcal/mol,
respectively.
Figure 2. Optimal geometries of HNO3(H2O)n, n ) 2, 3. The values
of the hydrogen bonded OH stretches and the interoxygen distances
between water molecules (Å) are shown.
geometries) as well as the average of the intermolecular
structural parameters obtained from fits using the undistorted
and fully distorted monomer geometries, denoted as “preferred”
structure in Table 1. Our results are closer to the experimentally
obtained structural parameters than the previous calculation31
and the remaining differences can be attributed both to the basis
set and to the effect of large-amplitude motion that is contained
in the fitting of the experimental data. A previously unexplored
arrangement, in which the water molecule acts primarily as a
proton donor to nitric acid (cf. Figure 1), corresponds to a local
minimum lying 7.3 kcal/mol above the global minimum (6.3
kcal/mol with zero-point energy corrections). This is a conse-
quence of the fact that HNO3 in the gas phase is a stronger
acid than water. The harmonic frequencies of the HNO3‚(H2O)n
and DNO3‚(H2O)n up to n ) 3, as well as for the (H2O)2 and
(D2O)2 dimers are given in Table 2.
The structural motif of homodromic rings that incorporate
water molecules continues for the larger clusters HNO3‚(H2O)n,
n ) 2, 3. The optimal structures for these clusters are shown in
Figure 2. The corresponding binding energies are 20.6 (16.2)
kcal/mol and 30.4 (23.7) kcal/mol for the n ) 2 and 3 clusters,
respectively, where numbers in parentheses include zero-point
energy corrections. The strong cooperative effect that drives
b. FTIR Spectra. The spectra of HNO3:H2O:Ar and
DNO3:H2O:Ar matrixes were obtained at various dilution factors
and compared with the measured spectra of equivalent HNO3:
Ar and H2O:Ar mixtures. Spectra of HNO3:H2O:Ar matrixes
show several distinct features that do not correlate to either
HNO3 or H2O species and therefore are assigned to nitric acid-
water complexes. Table 3 includes various experimental band
assignments for these complexes from the present work and
that of previous studies.3,39

Nitric Acid-Water Complexes
J. Phys. Chem. A, Vol. 106, No. 33, 2002 7631
TABLE 3: Measured Frequencies (cm-1) for the Various Complexes in Ar Matrix
mode
HNO3
3522a
HNO3‚H2O
HNO3‚(H2O)2
(HNO3)2
3235a
3216a
DNO3
2601b
DNO3‚H2O
DNO3‚(H2O)2
(DNO3)2
ν1 OH str of HNO3
ν2 + ν4
3025a
3126a
2980a
2784a
1694a
1412a
1308a
931a
2600
2292
2017
2415
2395
ν2 + ν3
2ν4
2161
1644
1096
ν2 NO2 asym str
ν3 NOH bend
ν4 NO2 sym str
ν5 N-O str
1699a
1304a
1321
897a
1670
1680a
1380a
1315a
938a
1678b
1013b
1310b
894b
1637
1115
1638
1070
1322
936
950
960
930
948
959
944
ν6 NO2 scissors
656a
588a
764a
451a
650b
548b
763b
ν7 ONO2 in plane
ν8 ONO2 out of plane
ν9 HON torsion
770a
776
780
770
693a
a Reference 3. b Reference 39.
TABLE 4: Calculated and Measured Frequency Shifts
(cm-1) for Deuterated Nitric Acid/Water Complexesa
∆ν1
measd
∆ω1
calcd
∆ν5
measd
∆ω5
calcd
∆ν3
measd
∆ω3
calcd
n
DNO3(H2O)n
1
2
3
-309
-440
-575
-299
-462
-586
43
61
72
60
90
107
83
100
100
139
101
HNO3(H2O)n
1
2
3
-496
-734
-907
-420
-654
-817
34
54
65
62
94
109
107
109
131
155
158
207
a See Table 3 for the assignment of the modes.
attributed to “Fermi resonances” with overtones and combination
bands: 2ν4 at 2784 cm-1; (ν2 + ν3) at 2981 cm-1; and (ν2 +
ν4) at 3130 cm-1. The remaining band at 3024 cm-1 was
assigned3 to the ν1 O-H stretch of the HNO3(H2O) complex.
In our spectra an additional broad feature centered at 2613
cm-1 is observed. If we assume that the band centered at 3024
cm-1 is assigned correctly as the HNO3‚(H2O) O-H stretch,
then the calculated frequency shifts indicate that the absorptions
centered at 2784 and 2613 cm-1 should be assigned as O-H
stretch modes for the HNO3‚(H2O)2 and HNO3‚(H2O)3 com-
plexes, respectively. Table 4 presents a comparison between
the calculated and experimentally determined frequency shifts
for the ν1, ν3, and ν5, bands. The broad absorption feature and
sharp bands observed above 3150 cm-1 are attributable to water
clusters. Although we expect the integrated band intensity of
the isolated HNO3 O-H stretch feature to be small and that
nearly all HNO3 forms complexes with water molecules, spectral
interference currently prevents confirmation of this assertion.
Figure 5a shows the FTIR spectra of the DO-NO2 stretch
region for DNO3:H2O:Ar matrixes as a function of increasing
H2O ratio. The prominent peak at 887 cm-1 in the upper trace
is assigned to ν5, the DO-NO2 stretch of the monomer, while
the peak at 1013 cm-1 is due to the D-O-NO2 bending mode.
As expected, these peaks decrease in intensity as the concentra-
tion of H2O in the matrix is increased, and the spectra displays
features associated with hydrated DNO3 species. The top trace
Figure 3. Global HNO3(H2O)4 and local H3O+(H2O)3NO3 minima
for the n ) 4 cluster.
-
Figure 4 displays the spectra from DNO3:H2O:Ar matrixes
between 1900 and 2650 cm-1, a region relatively free of
interference due to overlapping bands. The O-D stretching
bands associated with DNO3(H2O)n clusters up to n ) 3 are
apparent as the water concentration is increased (cf. Figure 4).
The strongest feature in the low water concentration matrix
(1:5:200) is the O-D stretch of the DNO3 monomer at 2601
cm-1 seen in Figure 4a. In the higher water concentration
spectrum, two strong bands centered at 2292 and 2161 cm-1
are evident, as is a strong broad feature near 2017 cm-1. These
bands are shifted from the DNO3 monomer O-D stretch
frequency by -309, -440, and -586 cm-1, respectively, which
compares very well with the calculated harmonic shifts of -299,
-461, and -575 cm-1 for the DNO3(H2O)n clusters, n ) 1, 2,
3. The integrated band intensity of the isolated DNO3 O-D
stretch feature decreases sharply in the high water concentration
spectrum indicating that nearly all DNO3 forms a complex with
water. The integrated band intensities of the features at 2292
and 2161 cm-1 also decrease with increasing water concentra-
tion, while the broad feature at 2017 cm-1 increases.
Figure 4b displays matrix spectra of HNO3 and HNO3(H2O)n
clusters in the H-ONO2 stretch region between 2400 and 3850
cm-1. Unlike the DNO3 spectra of Figure 4a, the H-ONO2
stretch region suffers from interference due to overlapping bands
of water and larger (H2O)n clusters. The O-H stretching bands
associated with HNO3(H2O)n clusters up to n ) 3 can nonethe-
less be identified. The strongest feature in the 1:5:200 matrix
is again the (offscale) O-H stretch fundamental of the nitric
acid monomer. In the region where the two OH stretches of the
HNO3‚(H2O) and HNO3‚(H2O)2 complexes are expected, we
observe four bands. These four bands, centered at 2784, 2981,
3024, and 3131 cm-1, were assigned by Barnes et al.3 as arising
from the HNO3(H2O) complex. Three of the bands were
of Figure 5a shows a series of peaks between 920 and 950 cm-1
.
The sharp band centered at 930 cm-1 is present only in mixtures
containing both DNO3 and H2O and is assigned to the DNO3‚
H2O complex. Two additional broad weak bands centered at
948 and 960 cm-1 are apparent. We assign these two peaks to
the DNO3‚(H2O)2 and DNO3‚(H2O)3 complexes. The relative
integrated absorption of the 948 and 960 cm-1 bands is greatest
in the 1:20:200 sample.
Very little isolated DNO3 is detected in the 1:20:200 sample,
as shown by the loss of the DO-NO2 band at 894 cm-1, and

7632 J. Phys. Chem. A, Vol. 106, No. 33, 2002
McCurdy et al.
Figure 5. FTIR absorption spectra of the O-N stretch bands for (a)
DNO3:H2O:Ar matrixes and (b) HNO3:H2O:Ar matrixes at 1:5:200
(upper trace) and 1:20:200 (lower trace) gas precursor ratios.
Figure 4. FTIR absorption spectra of the O-D and O-H stretch bands
for (a) DNO3:H2O:Ar matrixes and (b) HNO3:H2O:Ar matrixes at
1:5:200 (upper trace) and 1:20:200 (lower trace) gas precursor ratios.

Nitric Acid-Water Complexes
J. Phys. Chem. A, Vol. 106, No. 33, 2002 7633
thus increases the percent water (and nitric acid) concentration
of the matrix. The relative degree of anion solvation is apparent,
indicated by the splitting of the ν3a and ν3b bands, ∆ν3, which
decreases from ∼130 to ∼75 cm-1. For comparison, the
calculated splitting and band intensities of the NO3- bands for
the ion-pair complexes with 4 and 5 water molecules, is also
displayed in Figure 6. We note that the calculated band splittings
for the incremental solvation of the H3O+(H2O)3NO3- ion-pair
complex reproduce the trend observed experimentally quite
accurately.
IV. Discussion
The frequency shifts calculated for the D-ONO2‚(H2O)n
clusters (n ) 1-3) show quantitative agreement with the
measured FTIR data. In particular, the O-D stretch spectral
region displays bands separated by frequency intervals rather
accurately predicted by our calculations. Qualitative agreement
is also found for the O-H spectral region of the HNO3‚(H2O)n
system and the N-OD stretch and N-O-D bend spectral regions
of the DNO3‚(H2O)n system. On the strength of the cor-
respondence between the calculated and experimental results,
we may tentatively assign the measured bands for the nitric
acid-water clusters up to n ) 3 (cf. Table 3).
Given the fact that the computed frequencies are obtained at
the harmonic approximation, we choose to compare the
calculated frequency shifts, ∆ω, rather than their absolute values,
to the experimentally obtained frequency shifts, ∆ν. This
correspondence has been previously successfully used to assign
IR bands for negative ion-water clusters.26 The difference
between the harmonic and observed frequencies is strongly
mode dependent with the OH stretching modes usually display-
Figure 6. FTIR spectra of a 1:5 HNO3:H2O matrix (top), and a 1:20
HNO3:H2O matrix. The argon component was removed from the
initially prepared matrix by annealing at 40 K for 10 min.
ing the greatest discrepancy due to the large (>150 cm-1
)
anharmonicities of these high-frequency modes. For instance,
the calculated harmonic frequency of 3704 cm-1 for the
H-ONO2 stretch mode is significantly larger than the observed
gas-phase frequency of 3551 cm-1 and the Ar matrix isolated
value of 3522 cm-1. Modes with smaller anharmonicities can
show much better correspondence between calculated and
measured frequencies, such as the calculated frequency of 653
cm-1 for the ν6 NO2 scissors mode, which is very close to the
measured gas-phase value of 650 cm-1. When using frequency
shifts to guide spectral assignment, we assume that, for each
particular mode, the anharmonicities are similar even for clusters
of different sizes and therefore the frequency shifts, to first order,
are independent of error due to the harmonic approximation.
We regard our band assignments as tentative due to some
ambiguities apparent in the experimental results and discrep-
ancies with the interpretations of results published by other
researchers. The most likely cause for the discrepancies is the
effect of the argon matrix environment. The formation of clusters
within the argon matrix cannot be controlled ideally by simply
changing the deposition conditions. We have no control over,
or indeed much knowledge of, the distribution of various clusters
within the matrix. The cluster distribution depends on the
backing pressure and concentration of precursor gases, the
deposition rate, the temperature of the substrate and the anneal
history of the sample. Although all these factors are controllable,
there is no clear extrapolation from any particular set of growth
conditions to the actual cluster distribution. Furthermore, any
particular cluster could occupy a variety of matrix environments
or configurations. The exact effects of varying the deposition
conditions and anneal history are not known. Since the cluster
distribution is unknown, we can only expect integrated band
intensities to reflect differences in growth conditions in a
qualitative fashion.
the greatly diminished D-O-NO2 bend at 1013 cm-1. Figure
5b displays the analogous spectra and assignments for HNO3‚
(H2O)n complexes. Band assignments are presented in Table 3
and the comparison between calculated and observed frequency
shifts is shown in Table 4. The peaks at 939 and 943 cm-1 are
also observed when no water is present in the matrix. The
predicted band center for the DNO3 dimer is 955 cm-1 and we
assign these bands to the DO-NO2 stretch of (DNO3)2. At the
highest water concentration, the 939 and 943 cm-1 bands can
no longer be distinguished in the spectrum indicating that DNO3
dimer species are hydrated.
Interestingly, at this high water concentration one would
expect an abundance of species of higher order than the DNO3‚
(H2O)3 complex to be formed. However, the spectrum shows
no unambiguous features attributable to higher order DNO3‚
(H2O)n (n > 3) species. The most likely cause for the lack of
discernible higher order hydrates is the dissociation of DNO3
-
to a partially hydrated ion pair. The strongest NO3 modes
observed in the 1:20:200 spectrum are the degenerate ν3
vibrations between 1250 and 1500 cm-1. As concluded by
Ritzhaupt and Devlin,21 these bands are assigned to the
asymmetric stretch of the NO3- anion that is hydrogen bonded
-
to a hydronium ion. When the NO3 is in contact with a
counterion, this degeneracy is lifted and a splitting into the ν3a
and ν3b bands occurs. As the contact ion pair is increasingly
solvated, the splitting of the NO3- ν3 vibrations decreases. These
bands have also been recently observed40 during FTIR spec-
troscopic studies of water uptake on R-Al2O3 particles previously
reacted with HNO3. Figure 6 shows the spectra of 1:5:200 versus
1:20:200 (HNO3:H2O:Ar) samples annealed at 40 K for 10 min.
The annealing process evaporates argon from the matrix and

7634 J. Phys. Chem. A, Vol. 106, No. 33, 2002
McCurdy et al.
If a set of absorption bands is identified as arising from a
particular species (e.g., DNO3‚H2O) then it is normally assumed
that the relative integrated intensity of the associated bands will
be constant regardless of the species concentration. Conversely,
if two absorption features display constant relative integrated
band intensities, regardless of matrix concentration, then they
are likely derived from the same species. This reasoning
previously led Barnes et al.3 to conclude that the four bands
centered at 2784, 2981, 3024, and 3131 cm-1, observed in
HNO3:H2O:Ar matrixes, are assigned to the HNO3‚H2O com-
plex. Since we also observe that the relative band intensities of
these features are nearly constant as the water concentration is
varied, we are tempted to make the same conclusion. However,
on the strength of the results of the ab initio calculations, we
tentatively assign the band centered at 2784 cm-1 to the HNO3‚
(H2O)2 complex and the band centered at 2613 cm-1 to the
HNO3‚(H2O)3 complex. This latter band displays the expected
increase in integrated intensity with water concentration. This
assignment is further strengthened by the qualitative agreement
of the ab initio results with the observed spectral features for
several vibrational modes of the n ) 2 and 3 clusters.
In our experiments Ar acts as a solvent, providing some
degree of stabilization to ionic species. Even though the
calculations indicate that dissociation into ion pairs requires at
least four water molecules to stabilize the isolated clusters, it
may require less than four water molecules to produce a matrix
isolated ion pair if the solid argon solution provides sufficient
stabilization. Matrix-isolated species (solute) can be regarded
as molecules in a solution of matrix (solvent) molecules.
Theoretical models used to account for the solvent effects on
vibrational spectra interpret frequency shifts in terms of specific
solute/solvent interactions (electrostatic) superimposed on non-
specific (inductive and dispersive) contributions. It is known
that molecular vibrational frequencies are shifted in an argon
matrix environment because of this effect.41,42
vibrational modes of the HNO3‚H2O complex. The fact that only
two analogous peaks are observed in the corresponding portion
of the FTIR spectrum for the DNO3/H2O/Ar matrix support this
explanation for at least two of the peaks seen in the HNO3/
H2O/Ar spectrum. Still, no combination of frequencies for the
DNO3‚H2O complex match the observed frequency and hence
we assign the band centered at 2162 cm-1 to the DNO3(H2O)2
complex. Figure 4a also shows a broad peak at ∼2015 cm-1
.
This peak is not observed in very low water concentration
spectra (not shown here) but is clearly observed in the 1:5:200
spectrum. The integrated absorption intensity of the band
centered at ∼2015 cm-1 increases with water concentration and
the band broadens further. We assign this band to the DNO3‚
(H2O)3 complex.
V. Conclusions
We present the results of ab initio calculations for the
structures and vibrational spectra of the HNO3‚(H2O)n
(n ) 0-4) complexes and their deuterated analogues in an effort
to provide insight into the ionization of HNO3 in an aqueous
environment and aid in the assignment of the experimental FTIR
spectra obtained in a matrix environment. The calculations
predict the appearance of ion-pair configurations in the gas phase
for n ) 4. These results were used to interpret matrix isolation
spectra of HNO3‚(H2O)n complexers. While HNO3:H2O:Ar
matrixes have been studied previously, we present the first
spectroscopic evidence for the existence of the HNO3‚(H2O)2
and HNO3‚(H2O)3 complexes in these environments. Interest-
ingly, spectra for larger clusters were not observed. The
experimental assignments are in agreement with the results of
our cluster calculations that indicate that four water molecules
are needed to stabilize ion pair configurations. This finding is
consistent with the one of Ritzhaupt and Devlin21 in their
previous study of H2O/HNO3 solid mixtures where they mainly
observed molecular species in low ratio mixtures and concluded
“perhaps as many as three waters of hydration are required to
stabilize the ionized form.” Our results for the n ) 1 cluster
are largely consistent with Barnes et al.3 although we tentatively
reassign one band to the n ) 2 complex rather than a
combination band of the n ) 1 complex on the basis of the
cluster calculations presented in this study.
The O-H stretch of HNO3 in the gas-phase is observed at
3551 cm-1 43
while in an Ar matrix this stretch is red-shifted
,
by 29 cm-1 to 3522 cm-1. To illustrate the effect of the argon
matrix on molecules and their complexes, let us consider the
vibrational spectrum of methanol and its dimer. In the gas phase,
the OH stretch of the proton donating molecule of the dimer is
red-shifted by 107 cm-1 from the monomer value,44 while in
an Ar matrix the OH stretch is red-shifted by 135 cm-1 from
the monomer.42 This indicates that H-bonded complexes in
matrix environments can experience significantly large fre-
quency shifts with respect to their monomers than their gas-
phase counterparts (see for example ref 45)
Acknowledgment. This work was performed in the William
R. Wiley Environmental Molecular Sciences Laboratory (EMSL)
under the auspices of the Division of Chemical Sciences, Office
of Basic Energy Sciences, U.S. Department of Energy under
Contract DE-AC06-76RLO 1830 with Battelle Memorial In-
stitute, which operates the Pacific Northwest National Labora-
tory. The EMSL is a national user facility funded by the Office
of Biological and Environmental Research in the U.S. Depart-
ment of Energy. Computer resources were provided by the
Division of Chemical Sciences, U.S. Department of Energy.
Figure 4a shows two peaks (2292 and 2161 cm-1) in the
region where the OD stretch of the DNO3‚H2O complex is
expected. The ratio of their integrated intensities as a function
of H2O concentration is nearly constant, suggesting they could
be derived from the same species. While it is clear that the band
centered at 2292 cm-1 is due to the O-D stretch of the DNO3‚
H2O complex, the second band is shifted by -440 cm-1 from
O-D stretch of the isolated monomer, which compares remark-
ably well (-462 cm-1) to the calculated shift in the DNO3-
(H2O)2 complex. The assignment of this band to the DNO3-
(H2O)2 complex is also supported by the similar behavior of
the band assigned to the DNO3(H2O)2 complex for the DO-
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