On the hydration and hydrolysis of carbon dioxide

Article abstract of DOI:10.1016/j.cplett.2011.08.063

The dissolution of carbon dioxide in water and the ensuing hydrolysis reactions are of profound importance for understanding the behavior and control of carbon in the terrestrial environment. The first X-ray absorption spectra of aqueous carbonate have been measured at three different pH values to characterize the evolution of electronic structure of carbonate, bicarbonate, carbonic acid and dissolved CO₂. The corresponding carbon K-edge core-level spectra were calculated using a first-principles electronic structure approach which samples molecular dynamics trajectories. Measured and calculated spectra are in excellent agreement. Each species exhibits similar, but distinct, spectral features which are interpreted in terms of the relative C-O bond strengths, molecular configuration, and hydration strength.

Full text of DOI:10.1016/j.cplett.2011.08.063

Chemical Physics Letters 514 (2011) 187–195
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
FRONTIERS ARTICLE
On the hydration and hydrolysis of carbon dioxide
Alice H. England a,b, Andrew M. Duffin , Craig P. Schwartz a,b, Janel S. Uejio a,b
,
a,b
c,
⇑
a,b,
⇑
David Prendergast , Richard J. Saykally
a
Department of Chemistry, University of California, Berkeley, CA 94720, USA
Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Available online 24 August 2011
The dissolution of carbon dioxide in water and the ensuing hydrolysis reactions are of profound impor-
tance for understanding the behavior and control of carbon in the terrestrial environment. The first X-ray
absorption spectra of aqueous carbonate have been measured at three different pH values to characterize
2
the evolution of electronic structure of carbonate, bicarbonate, carbonic acid and dissolved CO . The cor-
responding carbon K-edge core-level spectra were calculated using a first-principles electronic structure
approach which samples molecular dynamics trajectories. Measured and calculated spectra are in excel-
lent agreement. Each species exhibits similar, but distinct, spectral features which are interpreted in
terms of the relative C–O bond strengths, molecular configuration, and hydration strength.
Ó 2011 Elsevier B.V. All rights reserved.
1
. Introduction
influence of the aqueous carbonate system extends to the astro-
2 2
nomical realm. Upon irradiation, CO –H O deposits in outer space
The hydrolysis of carbon dioxide (CO
2
) to form carbonic acid
are converted to carbonic acid, which has also been identified as a
possible species present on several planetary surfaces [6].
Understanding the molecular-scale details of carbonate, bicar-
and the subsequent speciation to bicarbonate and carbonate is a
fundamental process that has been studied extensively. From a
geological perspective, carbonic acid is the most abundant terres-
trial acid, while bicarbonate and carbonate are the primary con-
tributors to total alkalinity in natural waters. These dissolved
carbonate species participate in numerous reactions that have vital
implications in rock weathering, mineral precipitation, ocean acid-
ification and climate change. New technologies are emerging to
mitigate global warming by exploiting methods for capture and
2
bonate, carbonic acid, and CO behavior in these various environ-
ments is critical to the development and success of future
strategies aimed at maintaining or mitigating these natural carbon
processes. The overall reactions [7] for carbon dioxide dissolution,
hydrolysis, and equilibrium are:
CO2ðgÞ þ H
2
O $ CO2ðaqÞ
ð1Þ
ð2Þ
ð3Þ
ð4Þ
storage of excess CO
MOFs) developed to selectively trap CO
into underground salt-water reservoirs [2].
2
, such as the metal-organic-frameworks
3
ꢂ
CO2ðaqÞ þ H
2
O $ H
2
CO
3
ðKeq ¼ 2:6 ꢀ 10ꢁ at 25 CÞ
(
2
gas [1] or pumping CO
2
ꢁ
H
2
CO
3
$ Hþ þ HCO3 ðpK ¼ 6:35Þ
Aqueous carbonate chemistry not only governs the terrestrial
carbon cycle, but it also maintains the delicate pH balance required
in mammalian biological systems. The carbonate/bicarbonate/CO
buffer system regulates blood pH, and is also responsible for CO
transport in the body and ion mobility across cell membranes.
The importance of calcium carbonate in biomineralization pro-
cesses has led to extensive study of its nucleation and precipitation
dynamics in supersaturated solutions [3,4]. Seawater carbonate
a
ꢁ
2ꢁ
ðpK ¼ 10:33Þ
2
a
2
There have been many studies addressing these species, with
research on carbonate solubility dating back to as early as 1902
[
8], and extensive characterization of this fundamental system
continuing throughout the past century to document the relevant
equilibria, kinetics, thermodynamics, and structural properties.
Notable areas include Raman and IR experiments of carbonate
species in solution [9–12], investigation into solubility and hydra-
tion mechanisms [13–15], and analysis of ion pairing [16–18].
More recently, theoretical studies of the aqueous carbonate system
have worked to elucidate mechanistic details of the equilibrium
reactions as well as hydration processes through molecular
dynamics simulations and quantum calculations [14,19–23].
2
chemistry dictates the uptake of CO in surface waters, and the
consequent carbonate saturation plays a major role in the calcifica-
tion of ocean organisms and ecosystems [5]. Furthermore, the
⇑
Corresponding authors. Address: Department of Chemistry, University of
California, Berkeley, CA 94720, USA. Fax: +1 510 642 8566 (R.J. Saykally).
E-mail addresses: dgprendergast@lbl.gov (D. Prendergast), saykally@berkeley.
edu (R.J. Saykally)
0
009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2011.08.063

1
88
A.H. England et al. / Chemical Physics Letters 514 (2011) 187–195
The nature of carbonic acid itself has been of central interest.
2.2. Molecular dynamics simulations
While its observation in the gas phase is well-documented, it
was long debated whether it exists as a short-lived intermediate
or only as a transition state that cannot be isolated. Earlier stud-
ies on the aqueous form were able to identify carbonic acid in
ice matrices via FT-IR spectroscopy, either as a result of bicar-
bonate protonation at low temperatures, or irradiation of solid
AMBER 9 [32] was used to perform classical MD simulations for
gaseous and dissolved CO , and Quantum Mechanic/Molecular
2
Mechanics (QM/MM) trajectories for carbonate, bicarbonate, and
carbonic acid. Classical MD calculations employed the default
ff99SB force field while the PM3 method was used for the semi-
empirical QM/MM calculations. For all systems, ꢃ90 TIP3P waters
were added and the MD simulations were run in periodic boundary
conditions for 10 ns. 100 uncorrelated snapshots were chosen from
each trajectory to represent a sufficient sampling of molecular mo-
tions. Additionally, first principles molecular dynamics (FPMD),
within the Born–Oppenheimer approximation, was performed on
carbonate to verify the accuracy of the QM/MM simulation. We
used the Quantum-ESPRESSO package [33], sampling the dynamics
of the electronic ground state for 2.5 ps using the Perdew–
Burke–Ernzerhof form of the generalized-gradient approximation
(PBE GGA functional) [34].
2 2
CO –H O ices [6]. More recent studies succeeded in spectro-
scopic detection of carbonic acid in water, including Raman mea-
surements [24] and ultrafast IR experiments [25]. Alternative
detection methods with clear spectral signatures for carbonic
acid are crucial to the future characterization of this short-lived
species.
Near edge X-ray absorption fine structure spectroscopy
(
NEXAFS), is an atom-specific probe of not only the electronic
structure of a molecule, but also of its local chemical environ-
ment, making it an ideal method for detailed characterization
of hydration interactions. Previous NEXAFS studies were re-
stricted to gaseous CO
2
[26], and carbonate adsorbed to a surface
[
27] or in various solid mineral forms [28], by the difficulties
2.3. First principles simulated spectroscopy
inherent in addressing liquid samples. Here we report the first
measurement of the carbon K-edge NEXAFS spectra for aqueous
carbonates, facilitated by the use of liquid microjet technology
X-ray absorption spectra were calculated within Fermi’s Golden
Rule, using DFT. The initial state was derived from a ground state
DFT calculation. The lowest energy final state was approximated
as the self-consistent electronic response of a given molecular con-
figuration to the presence of a core–hole on the excited carbon
atom (modeled using a suitably modified pseudopotential) and
the inclusion of an excited electron in the first available empty
state (excited state core hole (XCH) approximation) [35]. The
resulting excited state self-consistent field was used to generate
subsequent higher excited states non-self-consistently. Transition
matrix elements were computed using individual Kohn–Sham
states (the ground state 1s atomic orbital and the spectrum of
eigenvalues from the approximate final state). All DFT calculations
were obtained using the PBE GGA functional [34]. Plane–wave
pseudopotential calculations employed ultrasoft pseudopotentials
and a kinetic energy cut-off of 25 Ry. A modified form of the Quan-
tum-ESPRESSO package [33] was used to generate the Kohn–Sham
eigenspectrum while the Shirley interpolation scheme [36] was
employed to accelerate numerical convergence of computed
spectra. Because there is no absolute energy reference in pseudo-
potential calculations, further spectral alignment was necessary
for meaningful comparisons between chemically or structurally
different systems. Details of the alignment scheme are described
in the Results section. Isosurfaces were calculated with
Quantum-ESPRESSO and rendered in VMD [37].
[
29]. We combine molecular dynamics (MD) simulations with a
first principles density functional theory (DFT) method to model
and interpret the measured NEXAFS spectra [30,31], gaining new
and detailed insights into the nature of aqueous carbonate
species.
2
. Materials and methods
2.1. Experimental
Sodium carbonate was obtained commercially from Sigma–Al-
drich in the crystalline form of 99.0% purity. A 1 M solution was
prepared with 18 M /cm resistivity water, at an initial pH of 12.
X
To access the lower pH regions, the carbonate samples were
mixed with appropriate ratios of 1 M HCl in a dual syringe pump
system (Teledyne-Isco) by adjusting the relative flow rates. Based
on reactions (1)–(4) and associated equilibrium constants, the ini-
tial equilibrium composition as a function of pH was as follows:
pH = 12 (98% carbonate and 2% bicarbonate); pH = 8.5 (98%
2
bicarbonate and 2% carbonic acid/CO ); pH = 3 (100% carbonic
acid/CO ). Because the relevant reaction rates are not known, it
2
is not possible to reliably estimate the adjusted composition when
the liquid microjet is injected into vacuum. Moreover, to actually
measure these concentrations in situ would require a different
experiment.
3. Results and discussion
The NEXAFS experiments were conducted at Beamline 8.0.1. at
the Advanced Light Source (Lawrence Berkeley National Labs,
Berkeley, CA). A detailed description of the experiment has been
published previously [29]. Briefly, in the main vacuum chamber a
3.1. Carbon dioxide vs carbonic acid
A limitation of our experiment is the uncertainty as to the spe-
cies present in the acidic pH range. As the carbonate solution is
mixed in the microjet with HCl to form bicarbonate and carbonic
acid, it will quickly convert to dissolved carbon dioxide as shown
in reactions (1)–(4). Therefore, at pH = 3, our samples in the acidic
liquid microjet stream is produced by a 30 lm fused silica
capillary tip pressurized with the syringe pump. Shortly after
the sample leaves the jet tip, it is intersected with an intense,
tunable X-ray beam over the carbon K-edge energy range (280–
3
2
20 eV). The total electron yield (TEY) was collected with a
.1 kV biased copper electrode as representative of the bulk
range could potentially contain carbonic acid, dissolved CO
2
, and
gaseous CO escaping from the microjet. The experimental on-
2
liquid spectra. Similarly, the vapor phase spectra were obtained
by positioning the jet slightly above or below the incident
X-ray beam. In order to account for intensity fluctuations, the
and off-jet spectra are nearly identical after normalization, a strong
indication that we are primarily observing a gaseous species.
Furthermore, as shown in Figure 1, the spectra agree well with
TEY signal was normalized to an I
0
collected from a gold mesh lo-
previous electron energy loss measurements for CO
However, since there are no previous NEXAFS spectra for dissolved
CO or carbonic acid, we must rely on theoretical spectra to estab-
lish the dominant species in this pH range.
2
gas [38].
cated further up the beamline. The background vapor signals
were subtracted from the spectra, which were subsequently
area-normalized for comparison.
2

A.H. England et al. / Chemical Physics Letters 514 (2011) 187–195
189
inant species in our acidic pH experiment is CO
2
gas, but it is also
important to understand the chemical origin of this peak.
One would assume that the disappearance of the 3s
upon hydration is simply due to the presence of water. However,
slight changes in the shape of CO can also impact the position
g
r feature
2
and intensity of features in the computed spectrum. There were
negligible differences in the bond distances and angles between
gaseous and dissolved CO
versus molecular shape on the spectrum, additional fictitious
core-excited state calculations were performed on the CO mole-
2
, but to confirm the effect of hydration
2
cules with the effect of the water removed from the spectra. This
constrained model maintains the structural effects of the solvent
while removing the electronic confinement and hybridization ef-
fects. The constrained CO
is compared with its dissolved counterpart and the original gaseous
CO spectrum in Figure 2A. This indicates that the spectroscopic
disappearance of the 3s feature is a direct result of hydration,
while the small differences in molecular shape between CO gas
and its constrained form lead to a slight blue-shift in the position
of the 2
ꢄ. To gain further insight into the reason why the 3s
peak is only present in the gas phase, the states for corresponding
snapshots in the dissolved and constrained CO are imaged in Fig-
ure 2B–E. The 2
ꢄ state is very similar in each and localized on
the CO , therefore it should be unaffected by hydration. The 3s
2
gas spectrum for the 2
p
u
ꢄ and 3s
g
r states
2
r
g
2
p
u
r
g
2
p
u
2
r
g
state for the gas is very large and diffuse, but upon hydration it
hybridizes with the surrounding water to form a band of states that
have mixed CO 3sr and water character. The formation of this en-
2 g
ergy dispersive band, together with the reduced overlap with the
carbon 1s orbital due to its large spatial extent, leads to the eradica-
tion of the peak from the solvated phase spectrum.
g
Upon closer inspection of the final 3sr Rydberg state shown for
one CO gas snapshot (Figure 2C), there is electron density around,
2
but not actually on the carbon atom itself, which would imply that
there should be no feature observed for this state in the carbon K-
edge spectrum. The carbon 1s(
g g
r ) ? 3sr transition is dipole-for-
Figure 1. Experimental and calculated NEXAFS carbon K-absorption edge spectra
for acidic pH range. The experimental spectrum for the acidic region (B) is
bidden ( ) in the equilibrium molecular structure, but be-
g g
r ? r
comes dipole-allowed upon the inclusion of nuclear motion. We
have previously encountered this issue of sampling the nuclear de-
grees of freedom accessible, either from zero-point motion or finite
temperature, in order to accurately predict NEXAFS spectral fea-
compared with calculated spectra for the three possible components: CO
2
gas (C),
dissolved CO (D), and carbonic acid (E). The experimental ISEELS spectrum of CO
2
2
gas is also included (A) [38]. Each calculated spectrum represents the average of 100
individual spectra, with ± one standard deviation shown in the shaded areas.
tures [40,41]. Here, we found the appearance of the 3s
state for CO gas dependent on the bending vibration, which is con-
sistent with previous predictions in the literature [42–44]. Vibronic
coupling with the CO bending mode along with the intensity-
lending
ꢄ resonance makes this the strongest observed Rydberg
transition for CO . The correlation between O–C–O bond angle
and the 3s peak is illustrated in Figure 3A for all 100 snapshots
contributing to the average CO spectrum. As expected, those clo-
ser to 180° show little or no intensity, while those with smaller an-
gles display increasingly more intense peaks. This is due to
stronger vibronic coupling as the molecule bends and the linear
symmetry is broken. Furthermore, the spectra and isosurfaces for
three representative snapshots are shown in Figure 3B. These illus-
trate the increasing p-character on the carbon atom as the CO
2
molecule bends away from the linear configuration. This demon-
strates the importance of MD sampling in order to accurately pre-
dict the experimental spectrum. If only the relaxed linear CO
2
molecule was used for the gas phase calculation, then we would
be missing this important Rydberg feature that is not only sensitive
g
r Rydberg
The calculated spectra for CO
2
gas, dissolved CO
2
and carbonic
2
acid are compared to experiment in Figure 1. Due to the known
underestimation of band gaps and band widths by DFT, the energy
spacing between features will also be underestimated compared
to experiment. All spectra exhibit a sharp feature at about
2
p
2
2
90.7 eV, which represents the excitation of a carbon 1s electron
r
g
to the LUMO 2
sition of these
p
p
u
ꢄ antibonding molecular states. The shape and po-
2
ꢄ features are too similar to provide any insight into
which species are actually present in the experiment. However there
are distinct spectral differences in the higher energy range that pro-
vide the key to interpreting our experiments. Carbonic acid exhibits
two broad
experiment. Both CO
the 4
ꢄ resonance centered at 310 eV that match experiment, but
only gaseous CO exhibits the small peak observed at 292.3 eV, rep-
resenting the 3s Rydberg state. Furthermore, the peak positions
for the 2 , and 4 ꢄ peaks in the experimental spectra (Fig-
ꢄ, 3s
ure 1A and B) match extremely well with those observed in previous
CO gas electron-energy-loss spectra [39] and NEXAFS measure-
ments [26]. Transitions to additional 3p, 4s, and 4p Rydberg states
in CO gas are weakly detected in the 295–297 eV range, yet these
r
ꢄ resonances from 294 to 305 eV that are absent in the
2
species have broader
rꢄ features representing
r
u
2
r
g
p
u
r
g
r
u
2
2
to CO configuration but also to the presence of water.
2
3.2. Carbonate molecular structure effects
features are not resolved in our plane–wave supercell theoretical
spectra due to their diffuse nature. Calculations with a larger box
size will be necessary to resolve such fine structure for higher energy
Rydberg states. All of the above factors clearly indicate that the dom-
The basic and mid-range pH experiments are not nearly as com-
plicated because the speciation clearly indicates carbonate and
bicarbonate as the dominant species, respectively. However, we

1
90
A.H. England et al. / Chemical Physics Letters 514 (2011) 187–195
2
much flexibility in this carbon out-of-plane vibrational mode (m )
when using classical force fields [20,45]. Previous experimental let-
ter also indicates that the D3h symmetry of the unperturbed car-
bonate ion is at variance with its vibrational spectrum in
solution, indicating symmetry breaking of the planar structure
[
9,11]. Recently, Vchirawongkin et al. have calculated the degree
of symmetry breaking upon hydration and confirmed that the opti-
mized carbonate structure in water is not planar [21].
Rather than manipulate the force field parameters from the
classical simulations, we instead modeled carbonate using QM/
MM to better represent the appropriate flexibility of these small
molecules in water. Here, the carbonate ion was treated quan-
tum-mechanically to produce a more accurate model of the
m
2
rigidity, while the solvent was treated classically. This combination
allowed for a better representation of the molecular structure
while keeping the simulations tractable for the timescale needed
to sample enough uncorrelated snapshots. The average absolute
dihedral angle from the classical simulation was 16.5 ± 8.5°, while
QM/MM predicted a much smaller value of 2.5 ± 2.1°. For verifica-
tion of the structure, several MD trajectories were simulated using
FPMD, an ab initio DFT method. In all cases, the carbonate structure
equilibrated after 1 ps, with an overall average dihedral angle of
2
.4 ± 1.7°. Both QM/MM and FPMD predict that the solvated car-
bonate structure is still perturbed from the planar geometry, but
to a much less degree than predicted classically. The NEXAFS spec-
trum computed from the QM/MM trajectory is in excellent agree-
ment with the experimental spectrum (Figure 4A), indicating a
much more accurate sampling of the carbonate structure with re-
Figure 2. Spectra and isosurfaces for gaseous and dissolved CO
of the average calculated spectra for the carbon 1s transition to the 2
states for CO gas (solid line), constrained CO gas (dotted line), and dissolved CO
dashed line). Isosurfaces for a representative snapshot of constrained CO
plotted in B (2 ); and those for dissolved CO in D (2
ꢄ) and C (3s
3s ). Atom colors are aqua for carbon, red for oxygen, and white for hydrogen.
2
. Part A shows detail
p
u
ꢄ and 3s
r
2
g
2
2
(
2
gas are
u
p ꢄ) and E
gards to the
2
m vibrational mode. Furthermore, the bond lengths
p
u
r
g
2
predicted by QM/MM are also in better agreement with the litera-
ture for carbonate, bicarbonate and carbonic acid. The bicarbonate
spectra derived from classical MD and QM/MM are compared with
experiment in Figure 4B. While we did not encounter the same
(
r
g
found it necessary to employ quantum mechanical methods to
accurately model the structure and dynamics of carbonate, bicar-
bonate, and carbonic acid. In particular, the carbonate spectrum
calculated using classical MD did not agree with experiment (Fig-
ure 4A) as a direct result of excessive flexibility in the molecular
problem with planarity for the bicarbonate
ment with experiment was improved with QM/MM due to the
p
ꢄ feature, the agree-
more accurate prediction of bond lengths.
configuration. We found the LUMO
p
ꢄ feature in the individual
snapshots shifted to lower energy and weakened in intensity as
the planar symmetry was broken via the carbon out-of-plane
vibration, as measured by the C–O–O–O dihedral angle (Figure 5).
Further investigation into the ‘correct’ degree of planarity for
carbonate revealed that other groups have also encountered too
3.3. Spectral fingerprints of aqueous carbonate species
It is important to note that the calculated spectra are not simply
aligned empirically to the corresponding experimental absorption
onset energies, but, rather, relative to a simulated atomic carbon
Figure 3. CO
the peak intensity represented by rainbow color. Because this feature is vibronically coupled to the bending mode, the intensity increases as the CO
80°. Panel B shows three spectra representing snapshots over a range of CO linearity, with their bond angles indicated and corresponding isosurfaces plotted to the side. The
atom size in the isosurface plots has been minimized in order to see localization of electron density on the carbon atom.
2
3s
r
g
Rydberg vibronic state. In panel A, the 3s
r
g
feature for all 100 individual CO
2
gas spectra is plotted versus energy (x-axis) and O–C–O angle (y-axis), with
2
angle decreases from
1
2

A.H. England et al. / Chemical Physics Letters 514 (2011) 187–195
191
using periodic boundary conditions (in which the energy reference
is necessarily determined by the mathematical requirement that
the potential in each repeated cell must average to zero). To over-
come these limitations, we can shift the energy scale of the com-
puted DFT eigenvalues such that relative energies between
different systems are meaningful and such that we have alignment
with an experimental reference.
For a given chemical system X with a molecular configuration i
(
possibly sampled from a molecular dynamics trajectory), we shift
the energy scale used in the absorption cross section,
follows:
r
(E), as
XCH
C
E # E ꢁ
e
ðiÞ þ
D
E
ðiÞ þ
expt
D ;
ð5Þ
Nþ1
atomic
XCH
where
e
ðiÞ is the (N + 1)th eigenvalue of the lowest energy core-
Nþ1
excited state of configuration i, i.e., corresponding to the Kohn–
Sham eigenvalue of the first available state that the excited electron
C
could occupy above the existing N valence electrons;
D
E
ðiÞ is
atomic
the relative excitation energy of X(i) with respect to that of an iso-
lated C atom (we only consider carbon core-level excitations in this
letter), computed as:
h
i
h
i
C
XCH
tot
XCH
GS
tot
GS
D
E
ðiÞ ¼ E ðiÞ ꢁ EC ðiÞ ꢁ E ðiÞ ꢁ EC ðiÞ
ð6Þ
atomic
where these are DFT total energy differences between the total sys-
tem X and the isolated atom in ground and excited states. Note that
the dependence of the atomic energies on snapshot i is not neces-
sarily unique for each snapshot, but appears only through the same
choice of periodic boundary conditions (lattice vectors, cell volume,
etc.). Finally the alignment with experiment is performed once and
only once for a given reference calculation through the constant
Figure 4. Carbonate and bicarbonate spectra. The experimental spectrum for the
basic pH region is compared to the calculated spectra for carbonate (panel A), and
the mid-range pH to bicarbonate (panel B). Experimental spectra are plotted as
dotted lines, with the calculated spectra shown as solid lines (QM/MM = black and
classical MD = gray). All calculated spectra represent the average of 100 individual
spectra. For both carbonate and bicarbonate, the spectrum computed from QM/MM
is in better agreement with experiment than the classically derived spectrum.
2
Dexpt. In our case, only the spectrum of isolated CO was aligned
to the corresponding gas-phase experiment and all other simulated
spectra were aligned relative to that. A similar alignment approach
has been documented by Hamann and Muller for electron energy
loss near-edge spectra [46]. This is a key step towards using an effi-
cient first-principles theory to accurately predict X-ray absorption
spectra of novel condensed phases.
excitation energy. This allows us to accurately predict relative
spectral energy alignment, and provides accurate absolute energies
for aqueous carbonate species when aligned with an established
standard measurement, such as the position of the 2
p
u
ꢄ peak in
gaseous CO . Relative alignment of calculated spectra is a pervasive
2
Based on this scheme, the relative energy positioning in the cal-
culated carbonate spectra is in excellent agreement with the
problem both for simulations of isolated clusters when using
pseudopotentials (which neglect explicit calculation of core-elec-
tronic states) and for accurate simulations of condensed phases
experimental results, as shown in detail for the LUMO
p
ꢄ feature
Figure 5. Carbonate dihedral angle. Panel A shows the correlation between the carbonate
represented by rainbow color for all 100 individual classically-derived spectra. Panel B displays three representative spectra (solid lines) labeled with their corresponding
pꢄ energy (x-axis) and the dihedral angle (y-axis), with the peak intensity
dihedral angle, and the average of all 100 spectra (dotted line) which is also plotted in Figure 4A. The C–O
1
–O dihedral angle, h, is also defined in panel B as the angle
2
–O
3
between the planes formed by C–O
lower energies.
1
–O
2
and O
1
2
–O –O
3
. As the dihedral angle increases, the planar symmetry of the p
ꢄ final state is broken, resulting in less intense features at

1
92
A.H. England et al. / Chemical Physics Letters 514 (2011) 187–195
in Figure 6A. The relative ordering is reproduced correctly, and the
position of carbonate matches well. The bicarbonate
ꢄ feature is
3.4. Relative condensation energies
p
predicted to be 0.08 eV higher than experiment, but since the
experimental resolution is 0.1 eV, this difference is reasonable.
Given that the X-ray excitation is localized on the carbon atom,
the NEXAFS spectra are highly sensitive to its immediate surround-
ings, in particular to the nature of its bonds with oxygen. The C–O
bond length will have significant impact on the energies of bonding
and antibonding states in a molecule. A shorter bond will result in
a stronger bonding interaction and consequently a higher energy
antibonding state relative to a longer C–O bond. This correlation
between intramolecular bond lengths and the position of K-shell
NEXAFS spectroscopy is also sensitive to the local chemical envi-
ronment around the molecule, as found with the effect of hydration
on the 3s
g 2
r Rydberg transition for CO . It has already been shown
that CO , carbonic acid, bicarbonate, and carbonate all have differ-
2
ent degrees of interaction with water [19,22,23], but in order to ex-
tract detailed chemical insight from this experiment, DFT
calculations also need to be performed for the corresponding bare
molecules. Instead of computing the spectra for all snapshots, only
one representative snapshot was chosen for each system. The
waters were stripped away and the bare molecules were allowed
to relax before calculating the total energies, thereby removing both
the interactions with water and any intramolecular rearrangements
that occur as a result of hydration. Using the same atomic carbon
resonances (especially
r
ꢄ resonances) has been documented previ-
ously for a variety of gas phase molecules [47]. A thorough analysis
of the bond lengths in these molecules becomes critical to under-
standing the subtle differences in the spectra.
alignment scheme, the relative absorption onsets (
p
⁄ peak shifts)
There are two types of bonds present in these molecules: C@O
of the bare and hydrated systems were calculated with the follow-
ing ordering: carbonate (+3.16 eV) > bicarbonate (+1.22 eV) > car-
bonic acid (ꢁ0.067 eV) > carbon dioxide (ꢁ0.073 eV).
ꢁ
(
or C–O ) and C–OH. The ordering of the calculated average C@O
bond lengths follow the sequence: CO
(
2
(1.166 Å)
1.224 Å) < HCO3 (1.261 Å) < CO3 (1.285 Å), which correlates with
the relative positions of the LUMO
ꢄ carbonyl peaks (Figure 6A)
and the
ꢄ carbonyl peaks (Figure 4B, feature 1). Additionally, C–
OH bonds are present in bicarbonate (1.356 Å) and carbonic acid
1.339 Å), which introduces a third peak (Figure 6B, feature 2) in
the
2 3
< H CO
ꢁ
2ꢁ
These peak shifts encompass the difference between the inter-
actions of the ground and core-excited states with the solvent
(analogous to solvatochromism in UV–Vis spectroscopy). They
can be explained by estimating differences in condensation energy
between the states. Condensation energies for the ground and ex-
cited states were calculated by subtracting all of the individual en-
ergy components from total energy of the hydrated states:
þ
p
r
(
r
ꢄ range. The C–OH bonds are longer than the C@O bonds over-
all, so they appear at lower energies. All bond lengths are compiled
in Table 1. For further confirmation, the states of each feature were
imaged for individual snapshots to verify that they were indeed
cond
GS
total
bare
H
GS
2
O
Na
D
E
¼ EGS ꢁ EGS ꢁ NE
ꢁ MEGS
ð7Þ
localized on the C@O or C–OH bonds, with the appropriate
ꢄ character (Figure 7).
p
ꢄ or
þ
cond
total
bare
H
2
O
Na
r
D
E
XCH ¼ EXCH ꢁ EXCH ꢁ NEGS ꢁ MEGS
ð8Þ
Figure 6. Experimental and calculated NEXAFS spectra for all three pH regions. The experimental spectra are presented with the corresponding calculated spectra for
carbonate (blue), bicarbonate (red), and carbon dioxide gas (green). The calculated spectrum of carbonic acid (dotted black) is included for comparison. The figure is split to
show the detailed alignment of the
energy features. Features within the areas marked 1 and 2 in panel B represent transitions to
represent the average of 100 individual snapshots.
pꢄ features in panel A, and the rꢄ resonances in panel B. Panel B is plotted on a smaller scale y-axis for better visualization of the higher-
rꢄ states localized on the C@O and C–OH bonds, respectively. Calculated spectra

A.H. England et al. / Chemical Physics Letters 514 (2011) 187–195
193
total
total
XCH
Table 1
where EGS ; E
are the total energies of the hydrated system in the
Average C–O bond lengths. The bond lengths (Å) calculated for this work are the
averages of 100 snapshot MD trajectories with an error of one standard deviation. The
literature values for CO gas are experimental bond lengths, while those for the
2
bare
bare
XCH
ground and excited states, EGS ; E
bare molecules in the ground and excited states, E ; E
are the total energies of the
þ
H
GS
2
O
Na
GS
are the
total energies of a single water molecule or sodium ion, while N
and M are the number of waters and sodium ions for each system.
All energies were obtained from the DFT pseudopotential calcula-
tions using the PBE GGA functional [34]. The calculated relative con-
aqueous species are calculated at the B3LYP level using a polarizable continuum
model for the solvent.
This work
C@O (Å)
Literature
C–OH (Å)
C@O (Å)
C–OH (Å)
cond
GS
cond
XCH
densation energies (
D
H
E
;
D
E
) for each species in eV are: CO
2
a
ꢁ
CO2(g)
1.166 ± 0.021
1.162
1.162
1.167
1.167
(
ꢁ25.30, ꢁ25.37),
2
CO
3
(ꢁ31.85, ꢁ31.91), HCO3 (ꢁ33.96,
a
1
.165 ± 0.020
1.171 ± 0.021
.171 ± 0.024
2ꢁ
ꢁ
32.74), and CO (ꢁ35.76, ꢁ32.59). It should be noted that these
b
3
CO2 (aq)
b
‘condensation energies’, are not an absolute measure of hydration
energy, but rather, a description of the relative energetic effects of
the presence of water on the different carbonate species. The differ-
ence between the excited and ground state condensation energies
should yield the same relative alignment provided by Eq. (6).
If both the ground and excited states were stabilized by the sol-
vent to the same degree, then we would expect no peak shift be-
tween the bare and hydrated systems. However, we find that the
ground and excited states have differing degrees of interaction
with the surrounding water. The ground state of carbonate is the
most stabilized upon hydration and bicarbonate to a lesser degree.
1
b
1.335b
1.335b
1.397b
H
2
CO3(aq)
1.224 ± 0.021
1.342 ± 0.029
1.220
1
.336 ± 0.025
ꢁ
ðNaþ
b
HCO3
ðaqÞ
Þ
1.263 ± 0.021
1.356 ± 0.027
1.259
1.255
1.302
1.302
1.302
b
1.259 ± 0.022
CO23
ꢁ
ð2Naþ
Þ
1.293 ± 0.024
b
b
b
ðaqÞ
1
1
.284 ± 0.022
.279 ± 0.023
a
Ref. [50].
Ref. [19].
b
Figure 7. Isosurfaces for
species. The
ꢄ states correspond to the features in the calculated spectra shown in detail in Figure 6A, while the C@O and C–OH
B, designated in areas 1 and 2, respectively. Atom colors are aqua for carbon, red for oxygen, white for hydrogen, and blue for sodium. The
the surrounding water to create a large band of states, but some localization along the carbon–oxygen bonds can still be seen in the representative isosurfaces.
p
ꢄ or
r
ꢄ resonances of hydrated carbonate species. Isosurfaces illustrate the localization of
p
ꢄ or
r
ꢄ resonances along C@O or C–OH bonds for each
ꢄ states correspond to the features in Figure
ꢄ resonances are hybridized with
p
r
6
r
r

1
94
A.H. England et al. / Chemical Physics Letters 514 (2011) 187–195
This is expected, given the double and single overall negative
charge on these ions, respectively. The corresponding excited
states are less stabilized, given that the solvent is in equilibrium
with the solute ground state and cannot rearrange on the X-ray
absorption timescale. This difference in stabilization leads to an
opening of the gap between ground and excited states, resulting
in a blue-shift of the absorption onset. The neutral species, car-
For aqueous carbonate species, our measurements and analysis
indicate that NEXAFS is sensitive to subtle differences in both
chemistry and environment at the molecular scale and provide a
vital benchmark for further studies of this fundamental carbon
cycle.
Acknowledgements
2
bonic acid and CO , both exhibit comparatively weak interactions
with water. However, their diffuse and polarizable excited states
are more stabilized due to electronic screening by the solvent,
leading to a small overall red-shift.
This letter was supported by the Director, Office of Basic Energy
Sciences, Office of Science, US Department of Energy under Con-
tract No. DE-AC02-05CH11231 through Lawrence Berkeley Na-
tional Laboratory’s Chemical Sciences Division; experiments were
performed at the Advanced Light Source, with theory, interpreta-
tion, and analysis provided through a User Project at the Molecular
Foundry, and high performance computing resources provided by
the National Energy Research Scientific Computing Center. Addi-
tional computing resources were provided by the Molecular
Graphics and Computation Facility (College of Chemistry, Univer-
sity of California, Berkeley) under NSF grant CHE-0840505. A. H.
England acknowledges support from the Office of Civilian Radioac-
tive Waste Management Graduate Fellowship administered by Oak
Ridge Institute for Science and Education under a contract between
the US Department of Energy and the Oak Ridge Associated
Universities.
Furthermore, these energetic arguments are in accord with the
number of coordinating water molecules derived from radial dis-
tribution functions of the MD trajectories. The relative ordering
cond
2 2 3
values, CO > H CO > HCO3 > CO3 , representative of
GS
ꢁ
2ꢁ
of
DE
increasing hydration strength through the series, matches with
the number of coordinated waters up to 2.5 Å: CO
2
ꢁ
2ꢁ
(
2 3
0.56) < H CO (3.17) < HCO3 (4.26) < CO3 (5.55). This trend in
hydration strength and number of coordinating waters for each
species is in agreement with other theoretical studies [19,22,23]
as well as with experiment for carbonate [48]. It should be noted,
however, that our water coordination numbers are lower overall
for bicarbonate and carbonate when compared to the literature,
which is due to the inclusion of sodium counterions in our MD sim-
ulations. We found that both sodium ions were located closer to
carbonate than any waters, resulting in a large decrease in the
number of waters in the first solvation shell from (9.09 to 5.55).
For bicarbonate, the effect was less pronounced from (5.41 to
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Janel Uejio was born in Concord, MA, in 1983, but was
raised in Schenectady New York. She attended Carleton
College where she graduated magna cum laude, in 2005
with a degree in chemistry. Her doctoral work was
completed under Prof. Richard Saykally at the Univer-
sity of California Berkeley in 2010. She now resides in
Oregon, where she works for Intel, in process develop-
ment.
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960.
David Prendergast was born in Ireland in 1977. He
obtained his B.Sc. in Physics and Mathematics with First
Class Honors from University College Cork (UCC) in
Alice England was born in Salt Lake City in 1984. She
obtained her B.A. in Chemistry from Vassar College in
1999 and his Ph.D. in Physics in 2002 from the group of
Prof. Stephen Fahy at UCC. He has worked as a post-
doctoral fellow in the groups of Giulia Galli at Lawrence
Livermore National Laboratory and Steven G. Louie in
the Physics Department of University of California,
Berkeley. In 2007, he joined the Molecular Foundry at
Lawrence Berkeley National Laboratory as a Staff Sci-
entist where he works in the Theory of Nanostructured
Materials Facility.
2
006. She is currently a graduate student in the group of
Prof. Richard Saykally in the Chemistry Department of
the University of California, Berkeley.
Rich Saykally is a co-author of over 380 publications
that have been cited over 22,000 times and the recipient
of over 70 honors and awards from nine different
countries. He is a member of the National Academy of
Sciences and the American Academy of Arts and Sci-
ences, is a UC-Berkeley Distinguished Teacher, and has
been active at the national level in science education.
Over 150 students and postdocs have trained under his
direction, many of whom hold prominent positions in
academic, government, and industrial institutions.
Saykally currently holds The Class of 1932 Endowed
Chair in the Department of Chemistry at University of
Andrew M. Duffin graduated with a B.Sc. in Chemistry
from Brigham Young University. Afterwards he moved
to the University of California, Berkeley for graduate
work under the direction of Richard Saykally. While at
Berkeley he studied electrokinetic effects in liquid
microjets and x-ray spectroscopy of solvated boron
compounds. Andrew received his Ph.D. from Berkeley in
2
010 and is currently a postdoctoral researcher at
Pacific Northwest National Laboratory.
California, Berkeley.
Craig Schwartz was born in Wheaton, IL in 1983. He
obtained his B.A. in Chemistry from Northwestern Uni-
versity in 2004. He received his Ph.D. in Chemistry from
University of California, Berkeley in 2010 under the
supervision of Prof. Richard Saykally. Currently he
works as an Associate Predictive Modeler with AllState.