Photoelectron spectroscopy and theoretical calculations of so4- and HSO4-: Confirmation of high electron affinities of so4 and HSO4

Article abstract of DOI:10.1021/jp992726r

We present a combined photoelectron spectroscopic and theoretical study of SO₄^- and HSO₄^- and their corresponding neutral species in the gas phase. We measured very high electron affinities for SO₄ and HSO₄, which are 5.10(0.10) and 4.75(0.10) eV, respectively. Theoretical calculations of the neutral and anionic species using both density functional and ab initio molecular orbital theory confirm the high electron affinities of the two species. The theoretically predicted vertical and adiabatic detachment energies are in good agreement with the experimental measurements. We find that both SO₄^- and SO₄ have C_2v symmetry, whereas both HSO₄^- and HSO₄ have C_s symmetry. We predict significant geometry changes between the equilibrium geometries of the anion species and the neutral speeds for both systems that are consistent with the broad nature of the measured photoelectron spectra.

Full text of DOI:10.1021/jp992726r

504
J. Phys. Chem. A 2000, 104, 504-508
-
-
Photoelectron Spectroscopy and Theoretical Calculations of SO4 and HSO4 :
Confirmation of High Electron Affinities of SO4 and HSO4
Xue-Bin Wang,†,‡ John B. Nicholas,* and Lai-Sheng Wang*
,‡
,†,‡
Department of Physics, Washington State UniVersity, 2710 UniVersity DriVe, Richland, Washington 99352, and
W. R. Wiley EnVironmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, MS K8-88,
P.O. Box 999, Richland, Washington 99352
ReceiVed: August 2, 1999; In Final Form: NoVember 9, 1999
-
and HSO -
4
and HSO ,
We present a combined photoelectron spectroscopic and theoretical study of SO
4
4
and their
corresponding neutral species in the gas phase. We measured very high electron affinities for SO
4
which are 5.10(0.10) and 4.75(0.10) eV, respectively. Theoretical calculations of the neutral and anionic
species using both density functional and ab initio molecular orbital theory confirm the high electron affinities
of the two species. The theoretically predicted vertical and adiabatic detachment energies are in good agreement
-
with the experimental measurements. We find that both SO
4
4
and SO have C2V symmetry, whereas both
-
HSO
4
4 s
and HSO have C symmetry. We predict significant geometry changes between the equilibrium
geometries of the anion species and the neutral species for both systems that are consistent with the broad
nature of the measured photoelectron spectra.
I. Introduction
the calculated energetic information with the experimental data.
Our theoretical calculations predicted that the lowest energy
conformations of both SO4 and SO4 have C2V symmetry. We
found considerable changes in geometry between the anion and
neutral structures that were consistent with the broad PES
features observed. We predicted that both HSO4- and HSO4
have Cs symmetry.
SO4- and HSO4- are important anions in both the condensed
phase and the gas phase. It is believed that SO4 plays a large
role in the chemistry of the ionosphere. The SO4 molecule is
-
-
1
also known to be an intermediate in the reaction of sulfur
trioxide with atomic oxygen and is an important atmospheric
2
intermediate. The vibrational frequencies of SO4 were measured
3
The paper is organized in the following manner: In the next
section, the experimental aspects will be briefly described. In
section III, the theoretical methods are presented. We report
the experimental results in section IV, followed by the presenta-
tion of the theoretical results and discussion in section V. A
brief conclusion is given in section VI. Finally, detailed
using IR spectroscopy in a low-temperature matrix. Recently,
McKee predicted SO4 to be a C2V molecule with a very high
electron affinity (EA) of 5.28 eV. While many experimental
studies have dealt with the oxidative ability of SO4 in solution,
4
5,6
its gas-phase properties remain almost completely unknown. The
-
HSO4 anion is known to be thermodynamically stable in high-
-
7
,8
calculations for the various isomers of SO4 and SO4 at different
temperature acidic solutions. Vibrational spectral studies of
-
levels of theory are presented in the Appendix.
HSO4 have been carried out, and its ionic dissociation constant
is well-known.9
-11
HSO4 has also been theoretically investi-
-
gated and found to have Cs symmetry with the OSO3 unit having
II. Experiment
a local C3V symmetry.12 Viggiano et al. have investigated the
-
The experiments were carried out with an apparatus that
involves a magnetic-bottle TOF photoelectron analyzer and an
ESI source. Details of the experimental setup have been
protonation reactions of HSO4 in the gas phase and obtained
a very high electron affinity of 4.7(0.2) eV for HSO4. Recently,
13
-
-
we have studied the ion pairs NaSO4 and KSO4 , and their
1
5
dimers, in the gas phase.14 However, there have been no direct
published elsewhere. To produce the desired anions, we used
-
4
a 10 M solution of the corresponding salts (NaHSO4) at pH
7 in a water/methanol mixed solvent (2/98 ratio), spraying it
measurements of the EAs of SO4 and HSO4, and the EA of
SO4 is still unknown. The scarcity of experimental and theoreti-
cal studies of gaseous SO4 and HSO4 and their anions is
surprising.
∼
through a 0.01 mm diameter syringe needle at ambient
-
atmosphere and -2.2 kV high voltage. To generate SO4 , a
Na2S2O8 solution was used, in which the S2O8 dianions
dissociated to give SO4 . Negatively charged molecular ions
2-
In this paper, we report a photoelectron spectroscopy (PES)
-
-
-
study of SO4 and HSO4 , which were produced using an
emerging from a desolvation capillary were guided by an rf-
only quadrupole ion guide into an ion trap, in which the ions
were accumulated for 0.1 s before being pushed into the
extraction zone of a TOF mass spectrometer.
15
electrospray ionization (ESI) source. We directly measured
the EA’s and electronic structures of the corresponding neutral
species. We obtained for the first time the EA of SO4, which
we found to be 5.10(0.10) eV. We measured the EA of HSO4
to be 4.75(0.10) eV. We also carried out theoretical calculations
on both anions, and their corresponding neutrals, and compared
In each PES experiment, the anions of interest were mass-
selected and decelerated before being intercepted by a laser beam
in the detachment zone of the magnetic-bottle photoelectron
analyzer. For the current study, the 193 nm (6.424 eV) light
from an ArF excimer laser was primarily used. The photoelec-
†
‡
Washington State University
Pacific Northwest National Laboratory
1
0.1021/jp992726r CCC: $19.00 © 2000 American Chemical Society
Published on Web 12/29/1999

High Electron Affinities of SO4 and HSO4
J. Phys. Chem. A, Vol. 104, No. 3, 2000 505
TABLE 1: The Measured Adiabatic (ADE) and Vertical
-
-
Detachment (VDE) Energies for SO
4
and HSO
4
ADE (eV)
VDE (eV)c
-
5.10 (0.10)a
4.75 (0.10)a
5.4 (0.1)
SO
HSO
4
X
X
A
5.40 (0.10)
5.00 (0.10)
5.65 (0.10)
-
4
a
Also represents the adiabatic electron affinity of the neutral.
Figure 1. Photoelectron spectra of SO -
eV).
-
4
and HSO at 193 nm (6.424
4
trons were collected at nearly 100% efficiency by the magnetic-
bottle and analyzed in a 4 m TOF tube. Photoelectron TOF
spectra were measured and then converted to kinetic energy
-
spectra that were calibrated by the known spectra of I and
-
O . The binding energy spectra were obtained by subtracting
4
4 4
, (c) HSO
-,
Figure 2. Ground-state geometries of (a) SO
and (d) HSO
indicated. The numbers in the parentheses in (d) indicate the distribution
of the unpaired spin.
-, (b) SO
the kinetic energy spectra from the photon energy. The energy
4
, optimized at B3LYP/tzvp+. All bond lengths in Å are
resolution was ∼11 meV fwhm at 0.4 eV kinetic energy, as
-
measured from the spectrum of I at 355 nm, and deteriorated
at 193 nm and higher kinetic energies.
-
slightly narrower than that of SO4 , yielding an ADE and VDE
III. Theoretical Details
of 4.75(0.10) and 5.00(0.10) eV, respectively. The second
feature (A) of HSO4 overlaps feature X slightly. We estimate
an ADE of 5.4(0.1) eV and a VDE of 5.65(0.10). The energetic
data for SO4 and HSO4 are summarized in Table 1.
-
We used theoretical chemistry to determine the geometry and
-
-
electronic structure of SO4 , HSO4 , and the corresponding
neutrals, and as verification of our interpretation of the PES
spectra. All of the species were optimized with density
The ADE of the X feature in each spectrum should correspond
to the adiabatic EA of the neutral species. However, for cases
in which there are large structural changes between the anion
and neutral ground states, the ADE can only be viewed as an
upper limit of the EA, because the Franck-Condon factors for
the 0-0 transition may be negligible. The broad nature of the
PES spectra of SO4 and HSO4 suggests that there should be
significant geometry changes between the anion and neutral
ground states for the two molecules. As will be shown below,
this is indeed born out from the theoretical calculations.
functional theory (DFT).1
6,17
The optimizations used the hybrid
18,19
B3LYP exchange-correlation functional.
We used the tzvp+
basis set, which is derived from the DFT-optimized tzvp basis
set of Godbout and co-workers,20 with the addition of a diffuse
s (H, O, and S) and p (O and S only) function. The exponents
of the diffuse functions were derived from an even-tempered
expansion of the outermost functions in the original basis set.
Frequencies were calculated for all species to verify that the
geometries were minima on the potential energy surface.
Following the DFT optimizations, single-point energies were
obtained using coupled-cluster theory with perturbative triples
-
-
V. Theoretical Results and Discussion
(
CCSD(T)) and the 6-311+G* basis set. The vertical detachment
-
A. SO4 and SO4 . The lowest energy geometries of both
energy was taken as the difference in total energy between the
anion and the corresponding neutral molecule at the anion
geometry. The reported adiabatic detachment energy is the
difference in total energy between the optimized geometries of
the anion and neutral. All the theoretical calculations were
performed using Gaussian94.21
During the course of our work, we found that SO4 required
more extensive theoretical treatment. The details of this aspect
of the theoretical study are included in the Appendix.
SO4- and SO4 have C2V symmetry. The B3LYP/tzvp+ opti-
mized geometries of SO4 and SO4 are presented in Figure
, parts a and b, respectively. Although both the anion and neutral
have the same symmetry, there are considerable structural
changes. In the anion, the two types of S-O bonds are different
by only 0.064 Å, whereas they are different by almost 0.2 Å in
the neutral. This large geometry change between the anion and
neutral ground states is consistent with the broad PES spectrum
-
2
-
observed for SO4 . At the B3LYP/tzvp+ level, we obtain a
VDE of 6.67 eV and an ADE of 5.25 eV (Table 2). The large
difference between the predicted VDE and ADE is consistent
with the large equilibrium geometry changes between the anion
and the neutral. The predicted values reasonably compare to
the experimental ADE value of 5.10 eV and VDE value of 5.40
eV. While the predicted ADE is in good agreement with the
experiment, the VDE is much too high. This large disagreement
IV. Experimental Results
-
-
Figure 1 shows the 193 nm spectra of SO4 and HSO4 . We
-
observed one broad feature for SO4 (X) and two broad features
-
-
(
X and A) for HSO4 . The feature of SO4 yields an adiabatic
(ADE) and vertical (VDE) detachment energy of 5.10(0.10) and
-
5
.40(0.10) eV, respectively. The first feature (X) of HSO4 is

506 J. Phys. Chem. A, Vol. 104, No. 3, 2000
Wang et al.
TABLE 2: Calculated Adiabatic and Vertical Detachment
-
Energies for SO
4
ADE (eV)
VDE (eV)
B3LYP/tzvp+
5.25
4.71
4.82
4.95
4.79
5.10(0.10)
6.67
6.11
6.27
6.40
5.64
5.40(0.10)
a
MP2/6-311+G*
a
MP4(sdq)/6-311+G*
a
CCSD/6-311+G*
a
CCSD(T)/6-311+G*
exp
a
Calculated at the B3LYP/tzvp+ optimized geometry.
is corrected at the CCSD(T)/6-311+G*//B3LYP/tzvp+ level,
which predicts a VDE of 5.64 eV, much closer to the
experimental value. However, the CCSD(T) ADE of 4.79 eV
is in somewhat poorer agreement with the experimental value
than the B3LYP/tzvp+ value. Therefore, the theoretical calcula-
tions consistently predict a larger difference between the VDE
and ADE than the experimental measurements indicate. This
suggests that the experimentally measured ADE may not be
the true ADE because of the negligible Franck-Condon factor
for the 0-0 transition. Rather, the measured ADE should only
be viewed as an upper bound.
-
The ground state of SO4 is open shell with an unpaired
electron. The neutral SO4 is closed shell with a singlet ground
state. The considerable lengthening of two of the S-O bonds
upon electron detachment in the neutral SO4 suggests that the
-
unpaired electron in SO4 occupies a bonding molecular orbital
-
Figure 3. Geometries of various isomers of (a) SO
4
4
and (b) SO ,
primarily consisting of bonding interactions in these two S-O
bonds. The large geometry changes between the C2V anion and
C2V neutral are consistent with our experimental observation of
a broad band. As will be shown in the Appendix, three other
optimized at B3LYP.tzvp+. All bond lengths in Å are indicated.
TABLE 3. Calculated Adiabatic and Vertical Detachment
-
Energies for HSO
4
-
ADE (eV)
VDE (eV)
isomers of the SO4 anions with higher energies are also found
in our theoretical studies. We can rule out the D2d and C3V
isomers, because there is little geometry change between their
anions and neutrals (Figure 3), which would yield sharp
photodetachment features, inconsistent with our experimental
observation.
B3LYP/tzvp+
4.76
5.01
4.74
4.65
4.59
4.75(0.10)
4.99
5.68
5.42
5.09
4.93
5.00(0.10)
MP2/6-311+G*a
a
MP4(sdq)/6-311+G*
CCSD/6-311+G*a
a
CCSD(T)/6-311+G*
exp
-
-
B. HSO4 and HSO4 . Both HSO4 and HSO4 are found to
have Cs symmetry. The B3LYP/tzvp+ optimized geometries
of the two species are shown in Figure 2 parts c and d,
a
Calculated at the B3LYP/tzvp+ optimized geometry.
-
shown in Figure 2d, the electron spins are mainly localized on
respectively. Contrary to the result obtained for SO4 , the VDE
the two O atoms with the longer S-O bonds. Compared to the
obtained at the B3LYP/tzvp+ level was very close to that
predicted by CCSD and CCSD(T) single point calculations
-
geometry changes between SO4 and SO4, the geometry changes
-
between HSO4 and HSO4 are smaller. The smaller geometry
(
Table 3). Both B3LYP and CCSD(T) VDEs are within the
changes are also consistent with the relatively narrower ground-
state PES feature of HSO4 . The difference between the
predicted ADE and VDE of HSO4 is also smaller. The good
agreement between the predicted and experimental ADE and
VDE indicates that the experimentally measured ADE is the
true value for HSO4 . Our measured EA for HSO4 is in excellent
agreement with the value obtained previously by Viggiano et
al., and it is slightly more accurate.
experimental error. MP2 and MP4 VDEs are ∼0.5 eV higher
than those of B3LYP and CCSD(T) and are, consequently, in
poorer agreement with experiment. The predicted values of the
ADE vary less between the different levels of theory, although
the MP2 value again appears too large. The best agreement with
the experimental value was obtained from the B3LYP/tzvp+
calculations.
-
-
-
There are also substantial geometric changes between the
-
ground states of HSO4 and HSO4, which is consistent with
V. Conclusion
-
the broad ground-state PES feature (X) of HSO4 (Figure 1).
-
The structure of HSO4 is similar to that obtained from a
In conclusion, we present the first photoelectron spectra of
SO4- and HSO4 and a theoretical investigation of both the
anion and neutral species. We observe one broad feature in the
previous theoretical calculation.12 HSO4 has three nearly equal
S-O bonds and a much longer S-O bond between S and the
O bonded to the H. In the HSO4 neutral, the biggest change
occurs at the S-O bond in which the O is bonded to H; it is
shortened by nearly 0.1 Å, relative to the anion. The changes
in the S-O bonds of the SO3 moiety are similar to the SO4
case. The short S-O bond (1.441 Å) is identical to that in SO4,
but the two longer S-O bonds in HSO4 did not change very
-
-
-
PES spectrum of SO4 . Two broad features, separated by ∼0.65
-
eV, were observed in the PES spectrum of HSO4 . We measured
the electron affinity of SO4 for the first time in the gas phase
and found it to be very high (∼5.10 eV). We also measured a
more accurate electron affinity (4.75 ( 0.10 eV) for HSO4 that
compares well with a previous estimate using a thermodynami-
cal cycle. Theoretical calculations, which predicted C2V sym-
-
much, relative to the anion. Because HSO4 is closed shell, the
-
HSO4 neutral must be a doublet with an unpaired electron. As
metry for both SO4 and SO4, were performed. The predicted

High Electron Affinities of SO4 and HSO4
J. Phys. Chem. A, Vol. 104, No. 3, 2000 507
TABLE 4: Relative Energies (kcal/mol) and Number of
Imaginary Frequencies of the Various Symmetries of SO
at B3LYP/TZVP+, B3LYP/6-31+G*, and MP2/6-31+G*
TABLE 5: Energies (kcal/mol) of Various Symmetries of
-
-
4
SO
4
Relative to C2W from CCSD(T)/6-311+G*//B3LYP/
tzvp+ Calculations
B3LYP/tzvp+
B3LYP/6-31+G* MP2/6-31+G*
symmetry MP2
MP4(sdq)
CCSD
CCSD(T)
symmetry energy imaginary energy imaginary energy imaginary
D
2d 2A
2
-3.94
-3.52
0.0
8.39
3.75
0.0
9.68
4.56
0.0
5.88
2.85
0.0
2
C
C
C
3V
B
A
1
D
2d 2A
2
1.98
1.90
0.0
2
2
0
1
3.63
1.90
0.0
2
2
0
1
0.0
0.54
3.08
12.67
0
0
0
1
2
2
2V
2
C
C
C
3V
B
A
1
2A
12.59
6.20
2.80
2.59
2
s
”
2V
2
2A
1.65
1.64
s
”
TABLE 6: Relative Energies (kcal/mol) of the Various
Symmetries of SO at B3LYP/6-31+G* and MP2/6-31+G*
ADE and VDE values of SO4- were in good agreement with
the experimental values. However, the difference between the
calculated ADE and VDE was much larger than that which was
experimentally determined, at the highest level of theory carried
out, suggesting that the measured ADE may only represent an
upper limit of the real adiabatic electron affinity. Theory predicts
4
symmetry B3LYP/tzvp+ B3LYP/6-31+G* MP2/6-31+G*
D2d 1A1
28.20
33.78
0.0
27.11
32.71
0.0
0.0
12.47
17.53
1
C
C
3V
A
A
1
1
2V
2
TABLE 7: Relative Energies (kcal/mol) of the Various
Symmetries of SO
Calculations
-
that both HSO4 and HSO4 have Cs symmetry. The calculated
4
from CCSD(T)/6-311+G*//B3LYP/tzvp+
-
VDE and ADE for HSO4 are in excellent agreement with the
experimental values.
symmetry
MP2
MP4(sdq)
CCSD
CCSD(T)
D
2d 1A
1
-10.12
5.18
43.92
35.19
0.0
36.87
34.07
0.0
15.68
17.89
0.0
Acknowledgment. This work is supported by The U.S.
Department of Energy, Office of Basic Energy Sciences,
Chemical Science Division. Acknowledgment is also made to
the donors of the Petroleum Research Fund, administered by
the American Chemical Society, for partial support of this
research. The work was performed at the W. R. Wiley
Environmental Molecular Sciences Laboratory, a national
scientific user facility sponsored by DOE’s Office of Biological
and Environmental Research and located at Pacific Northwest
National Laboratory, which is operated for DOE by Battelle.
L.S.W. is an Alfred P. Sloan Foundation Research Fellow.
1
C
C
3V
A
A
1
1
2V
1
0.0
three levels of theory were in close agreement with each other,
despite the differing numbers of negative frequencies, we used
only our B3LYP/tzvp+ geometries. The relative CCSD(T)/6-
11+G* energies, including the MP2, MP4(sdq), and CCSD
predictions, also obtained from these single-point calculations,
are shown in Table 5.
Only the MP2/6-311+G* calculation predicts that the D2d
symmetry is lowest in energy. All of the more extensive
treatments of electron correlation predict the lowest energy for
the C2V geometry, which is consistent with the DFT results. The
difference in energy between the various states becomes less
when the triple excitations are included, but CCSD(T) still gives
larger relative energy differences than those given by B3LYP.
From these results, we tentatively concluded that the lowest-
3
Appendix
4
In a recent paper, McKee presented a theoretical study of a
-
variety of sulfur-containing complexes, including SO4 and SO4 .
B3LYP/6-31+G* and MP2/6-31+G* optimizations were re-
-
ported for SO4 and SO4 , with single-point energies calculated
-
at higher levels of theory. Frequencies were also obtained at
the B3LYP/6-31+G* level. The zero-point energies from these
frequency calculations were given, but no other details were
presented. McKee reported one geometry for SO4 (C2V) and three
energy geometry of SO4 has C2V symmetry. We still cannot
reach a firm conclusion, because the energy differences among
the various isomers of SO4 are not great enough (Table 5). In
-
principle, they might even be accessible at our experimental
conditions (room temperature). Frequency calculations at a
higher-order level of correlation (i.e., MP4) would be needed
to verify whether the D2d and C3V geometries are stable points.
Such studies are beyond the scope of the current investigation.
Extending this approach to SO4, we find that B3LYP again
predicts that the lowest energy isomer is that of C2V symmetry,
whereas MP2 predicts that the D2d isomer is the lowest in
-
for SO4 (D2d, C3V, and C2V). We found that the relative energies
-
of the three isomers of SO4 were different at the B3LYP/6-
3
1+G* level from those found at the MP2/6-31+G* level. To
-
obtain the ADE and VDE for SO4 , for comparison to the
experiment, we had to determine which of these three states to
choose as the anion ground state. Our optimizations and
frequency calculations at the B3LYP/tzvp+ level indicated that
the D2d and C3V geometries were not stable points. We thus
decided to duplicate the B3LYP/6-31+G* and MP2/6-31+G*
optimizations and frequency calculations to clarify the situation.
The relative energies and number of imaginary frequencies for
the various states are presented in Table 4. We were also able
to optimize a geometry of Cs symmetry. At the B3LYP/tzvp+
and B3LYP/6-31+G* levels; only the C2V geometry is a
minimum. The C2V molecule is also the lowest in energy. The
other isomers have one or two large imaginary frequencies.
However, at the MP2/6-31+G* level, only the Cs isomer has a
negative frequency. In this case, the D2d geometry is the lowest
in energy. The B3LYP/tzvp+ structures of the four symmetries
-
energy. However, contrary to the results for SO4 , both DFT
and MP2 predict that all the symmetries are stable points. In
addition, during attempts to optimize a Cs geometry, the
molecule reverted to C2V symmetry at both levels of theory.
The relative energies of the various isomers are given in Table
6, and the B3LYP/tzvp+ structures are shown in Figure 3b.
To again clarify the correct symmetry, we obtained CCSD-
(T)/6-311+G* single-point energies for each species. As before,
we used the B3LYP/tzvp+ geometries for the single point
calculations. The calculated energies, relative to those of the
C2V isomer, are shown in Table 7.
Once again, the MP2/6-311+G* single-point energy is the
lowest for the D2d geometry, whereas all the other results
indicate that the C2V geometry is the energy minimum. The
relative energies from the more extensive treatment of electron
correlation are not close to those obtained with DFT; CCSD-
(T) gives predictions of the relative energies that are ∼10 kcal/
-
of SO4 are shown in Figure 3a.
The only isomer that is a minimum at both levels of theory
is that of C2V symmetry. To verify which symmetry was the
lowest energy state, we obtained CCSD(T)/6-311+G* single-
point energies for each species. Although the geometries at all

508 J. Phys. Chem. A, Vol. 104, No. 3, 2000
Wang et al.
mol lower than those given by B3LYP. However, we can still
conclude that the lowest energy isomer of SO4 has C2V
symmetry.
(13) Viggiano, A. A.; Henchman, M. J.; Dale, F.; Deakyne, C. A.;
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S. J. Phys. Chem. A 1999, 103, 3423.
(
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