Ultrafast dynamics of hydrogen bond exchange in aqueous ionic solutions

Article abstract of DOI:10.1021/jp9016739

The structural and dynamical properties of aqueous ionic solutions influence a wide range of natural and biological processes. In these solutions, water has the opportunity to form hydrogen bonds with other water molecules and anions. Knowing the time sca

Full text of DOI:10.1021/jp9016739

J. Phys. Chem. B 2009, 113, 7825–7835
7825
Ultrafast Dynamics of Hydrogen Bond Exchange in Aqueous Ionic Solutions
Sungnam Park,†,§ Michael Odelius,‡ and Kelly J. Gaffney*,†
PULSE Institute, SLAC National Accelerator Laboratory, Stanford UniVersity, Stanford, California 94305, and
Fysikum, AlbaNoVa UniVersity Center, Stockholm UniVersity, SE-106 91 Stockholm, Sweden
ReceiVed: February 23, 2009
The structural and dynamical properties of aqueous ionic solutions influence a wide range of natural and
biological processes. In these solutions, water has the opportunity to form hydrogen bonds with other water
molecules and anions. Knowing the time scale with which these configurations interconvert represents a key
factor to understanding the influence of molecular scale heterogeneity on chemical events in aqueous ionic
solutions. We have used ultrafast IR spectroscopy and Car-Parrinello molecular dynamics (CPMD) simulations
to investigate the hydrogen bond (H-bond) structural dynamics in aqueous 6 M sodium perchlorate (NaClO4)
solution. We have measured the H-bond exchange dynamics between spectrally distinct water-water and
water-anion H-bond configurations with 2DIR spectroscopy and the orientational relaxation dynamics of
water molecules in different H-bond configurations with polarization-selective IR pump-probe experiments.
The experimental H-bond exchange time correlates strongly with the experimental orientational relaxation
time of water molecules. This agrees with prior observations in water and aqueous halide solutions, and has
been interpreted within the context of an orientational jump model for the H-bond exchange. The CPMD
simulations performed on aqueous 6 M NaClO4 solution clearly demonstrate that water molecules organize
into two radially and angularly distinct structural subshells within the first solvation shell of the perchlorate
anion, with one subshell possessing the majority of the water molecules that donate H-bonds to perchlorate
anions and the other subshell possessing predominantly water molecules that donate two H-bonds to other
water molecules. Due to the high ionic concentration used in the simulations, essentially all water molecules
reside in the first ionic solvation shells. The CPMD simulations also demonstrate that the molecular exchange
between these two structurally distinct subshells proceeds more slowly than the H-bond exchange between
the two spectrally distinct H-bond configurations. We interpret this to indicate that orientational motions
predominantly dictate the rate of H-bond exchange, while translational diffusion must occur to complete the
molecular exchange between the two structurally distinct subshells around the perchlorate anions. The 2DIR
measurements observe the H-bond exchange between the two spectrally distinct H-bond configurations, but
the lifetime of the hydroxyl stretch precludes the observation of the slower molecular exchange. Our 2DIR
experiments and CPMD simulations demonstrate that orientational motions predominantly equilibrate water
molecules within their local solvation subshells, but the full molecular equilibration within the first solvation
shell around the perchlorate anion necessitates translational motion.
I. Introduction
The hydroxyl stretch frequency of water provides an excellent
sensor for local H-bond structure, which ultrafast infrared (IR)
Aqueous ionic solutions lubricate the chemical machinery of
natural and biological systems. While the unique and incom-
pletely understood properties of water receive significant and
justified attention,1 natural and biological processes also depend
critically on the ionic species present in solution.2 While the
dissolution of ions in water requires the solvation of the ions
by water molecules, leading to a disruption of the hydrogen
bond (H-bond) network, the extent to which dissolved ions
spectroscopy has harnessed to monitor H-bond dynamics.3,6-14
A variety of molecular dynamics simulations12,15,16 and time-
resolved IR experiments have been performed to characterize
the dynamics of water10-13,17 and various ionic solutions.3,9,14,16,18,19
For the study of H-bond structural dynamics, polarization-
selective IR pump-probe experiments have been used to
measure the orientational relaxation dynamics while two-
dimensional infrared (2DIR) spectroscopy has been employed
to determine the spectral diffusion dynamics. Orientational
relaxation and spectral diffusion dynamics provide an effective
monitor of H-bond dynamics in water and the influence of
dissolved ions on these dynamics. All studies to date demon-
strate that dissolved ions slow down H-bond structural dynamics
in highly concentrated aqueous ionic solutions,9,14 but the nature
of this dynamical transformation has yet to be determined.
Bakker and co-workers have emphasized the heterogeneity of
the dynamics in aqueous ionic solutions, particularly in aqueous
perchlorate (ClO4-) solutions by comparing the dynamics of
hydroxyl groups H-bonded to ClO4- anions and those H-bonded
disturb the structure of liquid water remains unresolved.2-5
A
full description of ionic solutions requires a detailed understand-
ing of the structure and dynamics of water molecules in different
H-bond configurations, the rate of H-bond exchange between
these H-bond configurations, and the rate of molecular exchange
within and between ionic solvation shells.
* To whom correspondence should be addressed. E-mail: kjgaffney@
slac.stanford.edu.
† SLAC National Accelerator Laboratory.
‡ Stockholm University.
§ Present address: Department of Chemistry, Korea University, Seoul,
136-701, South Korea.
10.1021/jp9016739 CCC: $40.75  2009 American Chemical Society
Published on Web 05/12/2009

7826 J. Phys. Chem. B, Vol. 113, No. 22, 2009
Park et al.
to another water molecule.3 From the orientational anisotropy
measurements, they attribute the slowing of the water dynamics
in aqueous ionic solutions to water molecules H-bonded to
ClO4- and conclude that ions only weakly modify the dynamics
of all other water molecules in aqueous solutions.3 More
recently, ion-water exchange dynamics have been studied with
aqueous NaBF4 solutions with 2DIR.20 They observe that the
exchange between water-water and water-anion H-bonds
occurs more slowly than the rate of orientational relaxation. As
will be discussed, we observe a stronger correlation between
the H-bond exchange time and the orientational relaxation time.
II. Methodology
A. Ultrafast Infrared (IR) Spectroscopy. The laser system
employed in the experiments was built based on a design that
has been described in detail elsewhere.21 Briefly, 800 nm pulses
were generated by a Ti:Sapphire oscillator (KM Laser) and
regenerative amplifier (Spitfire, Spectra-Physics) laser system
at 1 kHz. The 800 nm pulses with 45 fs duration and ∼0.8 mJ
per pulse were used to pump an optical parametric amplifier
(OPA, Spectra-Physics) to produce near-IR pulses at ∼1.3 and
∼2.0 µm which were utilized to generate mid-IR pulses at ∼4
µm in a 0.5 mm thick AgGaS2 crystal by difference frequency
generation (DFG). The power spectrum of the mid-IR pulses
had a Gaussian envelope with a ∼270 cm-1 bandwidth (full
width at half-maximum). After generation, the mid-IR pulses
propagate through an experimental setup purged with dry and
CO2 scrubbed air. We measured the pulse chirp with frequency-
resolved optical gating (FROG) measurements in a transient
grating geometry.21 We used CaF2 plates with different thick-
nesses to compensate for the linear dispersion introduced by
other dielectric materials in the setup, particularly a Ge Brewster
plate. This setup produced transform-limited mid-IR pulses with
an intensity fwhm of ∼55 fs at the sample.
Here, we have used concentrated aqueous NaClO4 solutions
as a model system to study the H-bond structural dynamics of
water in aqueous ionic solutions. Unlike most aqueous salt
solutions, aqueous NaClO4 solutions have two spectrally distinct
hydroxyl stretch peaks that correspond to two distinct H-bond
configurations: (1) water molecules H-bonded to other water
molecules and (2) those H-bonded to perchlorate ions and non-
H-bonded. We have used 2DIR spectroscopy to study the
H-bond exchange dynamics between these two spectrally distinct
subensembles and the spectral diffusion dynamics of each
subensemble. Polarization-selective IR pump-probe spectros-
copy has been performed to measure the orientational relaxation
and vibrational population relaxation dynamics of each suben-
semble. We have also performed Car-Parrinello molecular
dynamics (CPMD) simulations on aqueous 6 M NaClO4
solution. A comprehensive description of the H-bond structure
and dynamics of aqueous NaClO4 solutions emerges based on
the relative time scales of the orientational relaxation, spectral
diffusion, and H-bond exchange between spectrally distinct
H-bond configurations, and molecular exchange between struc-
turally distinct molecular configurations within the first solvation
shell of the perchlorate anions.
The experimental details and principles of two-dimensional
infrared (2DIR) spectroscopy have been described in detail
elsewhere.14,21-23 Briefly, we focus three mid-IR pulses with
an off-axis parabolic mirror (fl )150 cm) onto the sample in a
noncollinear geometry and collimate the beams after the sample
with another off-axis parabolic mirror (fl )150 cm). The spot
size of the IR beams at the sample position is approximately
50 µm in diameter. We control the relative time of these three
pulses with computer controlled translation stages. The sample
emits the signal in a unique phase-matched direction, which
we overlap with a local oscillator pulse for heterodyne detection.
A grating in a spectrometer disperses the heterodyned signal
onto the top stripe of a dual 32 × 2 element mercury-cadmium-
telluride (MCT) array detector with high speed data acquisition
electronics (Infrared Associates and Infrared Systems Develop-
ment Corp.). A portion of the IR beam that does not go through
the sample is sent to the bottom stripe of the array and used as
a reference beam. In 2DIR experiments, there are three
experimental time variables. The delay between the first and
second pulses corresponds to the evolution time (τ), the delay
between the second and third pulses corresponds to the waiting
time (Tw), and the delay between the third pulse and the emitted
signal corresponds to the detection time (t). We measure the
2DIR signal by scanning τ at fixed Tw and frequency resolving
the heterodyned signal onto the pixel array detector. To construct
the 2DIR spectra, we must Fourier transform the τ and the t
time periods. The spectrometer performs the detection time (t)
Fourier transform to generate the ωm axis, while we numerically
Fourier transform the τ time period after collecting the τ-de-
pendent interferogram for each value of ωm. This Fourier
transformation provides the ωτ axis. 2DIR spectra are displayed
with initial frequency ωτ and final frequency ωm at a fixed Tw
time. We generate purely absorptive 2DIR spectra with the dual
scan method in which nonrephasing and rephasing 2DIR spectra
are measured separately by two different input pulse sequences
and added.24
The structural analysis relies predominantly on the spatial
distribution function (SDF) extracted from the CPMD simula-
tions, rather than relying solely on the radial distribution function
(RDF) for structural information. The SDFs clearly show that
in aqueous 6 M NaClO4 solution the first solvation shell around
the anions in solution consists of two radially and angularly
distinct subshells. These structurally distinct subshells cor-
respond to (1) water molecules that predominantly donate a
H-bond to another water molecule and a perchlorate anion
(WWP) and (2) water molecules that predominantly donate two
H-bonds to other water molecules (WWW). The analysis of the
structural dynamics shows that the H-bond exchange rate
strongly correlates with the orientational relaxation rates, as seen
previously in MD simulations of water and aqueous sodium
chloride solutions.17,18 These simulation results have been
interpreted with an orientational jump model that attributes
H-bond exchange to prompt and large angular rotations.17,18
Comparison of the experimental and CPMD simulation results
lead us to attribute the H-bond exchange predominantly to
orientational relaxation of water molecules. The final stage of
H-bond structural relaxation involves the molecular exchange
between the two structurally distinct subshells within the first
solvation shell of the perchlorate anion. This molecular exchange
necessitates center-of-mass translational motion and proceeds
more slowly than the orientational relaxation that leads to
H-bond exchange between spectrally distinct H-bond configura-
tions. The MD simulations indicate that this molecular exchange
occurs too slowly to be observed prior to vibrational relaxation
of the OD stretch.
In IR pump-probe experiments, an IR pump pulse excites a
molecular system to the first vibrational excited state (υ ) 1),
and subsequently the time evolution of the molecular system is
measured by a time-delayed IR probe pulse. The details of the
IR pump-probe experiments have been described elsewhere.23,25
Mid-IR pulses are split into the pump and probe beams with a

Hydrogen Bond Exchange in Aqueous Ionic Solutions
J. Phys. Chem. B, Vol. 113, No. 22, 2009 7827
relative intensity of 9:1 and are focused onto the sample. The
probe beam is collimated after the sample and is dispersed
through a spectrometer onto the MCT array detector. The
wiregrid polarizers are placed in the pump and probe beam
before the sample and in front of the spectrometer. The parallel,
S|(t), and perpendicular, S⊥(t), components of the pump-probe
signals at each frequency are measured with the polarization of
the pump beam parallel and perpendicular to the probe beam,
respectively.
D2O and NaClO4 salt were purchased from Sigma-Aldrich
and were used as received. An isotopically mixed water solution
of 5% HOD in H2O was prepared by mixing 2.5 wt % D2O
with H2O. Aqueous NaClO4 solution was prepared by directly
dissolving NaClO4 salt in the isotopically mixed water solution.
This dilute isotopically mixed water solution of 5% HOD in
H2O was used for 2DIR and IR pump-probe measurements to
avoid undesired vibrational excitation transfer (Fo¨rster resonant
excitation transfer26,27 of the OD stretch mode which would
interfere with other dynamics of interest). For simplicity, the
isotopically mixed water sample without NaClO4 salt will be
referred to as neat water in the remainder of the paper. The
samples were housed in cells containing two CaF2 windows (3
mm thick) and a Teflon spacer with a thickness adjusted to
obtain optical density of ∼0.3 including the H2O background
absorption for all solutions studied. A range of 2340-2700 cm-1
was measured with a frequency resolution of ∼6 cm-1. 2DIR
spectra of HOD in aqueous 6 M NaClO4 solution were collected
at Tw ) 0.2, 0.4, 0.6, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, 7.0, and 9.0 ps.
All experiments were conducted at 22 °C.
Figure 1. FTIR spectra of the OD stretch of HOD in aqueous, 3, and
6 M NaClO4 solutions. The H2O background has been subtracted. FTIR
spectrum of the OD stretch of HOD in isotopically mixed water is
shown for comparison. In aqueous NaClO4 solutions, the lower
frequency peak results from the ODW subensemble while the higher
frequency peak results from the ODP subensemble. The dotted black
line is the linear spectrum obtained from the response function
calculation. See the text for more detail.
the simulation of 6 M NaClO4 with 46 DOH (9 ps) to obtain
the IR spectrum to get an appreciable OD component in the
total electric dipole and to validate a local mode description of
the hydroxyl stretch band. For reference, we also performed
simulations of pure liquid water at 1.0 g/cm3 and 350 K with
either 64 DOH (11 ps) or 64 H2O (18 ps) molecules.
III. Results
B. Ab Initio Molecular Dynamics Simulations. Ab initio
Car-Parrinello molecular dynamics (CPMD) simulations28 were
performed to characterize the structural and dynamical properties
of aqueous 6 M NaClO4 solution. The CPMD simulations give
an accurate description of many-body effects in concentrated
aqueous ionic solutions, against which classical force fields can
be evaluated,29,30 since CPMD calculates the forces on the fly
with periodic density functional calculations using a gradient-
corrected density functional, BLYP.31,32 However, since the
computationally taxing CPMD methodology limits the system
size to 7 Na+ and 7 ClO4- ions dissolved in 46 water molecules
and simulation duration to 20 ps, we also performed 100 times
longer duration and 8 times larger simulations with a classical
force field (parameters for the ions were taken from Heinje et
al.29 and water is described by the flexible SPC force field33)
that confirmed that the size and duration limits of the CPMD
calculation do not distort the local structure and dynamics. The
periodic density functional theory (DFT) calculations used
pseudopotentials in combination with an 85 Ry kinetic energy
cutoff for the plane wave expansion of the Kohn-Sham wave
functions. For hydrogen, a local pseudopotential parametrized
with one Gaussian was used. The pseudopotential for oxygen
was of Troullier-Martins type34 expressed in the Kleinman-
Bylander form,35 and were nonlocal in the l ) 0 channel.
Goedecker pseudopotentials were used for sodium and chlo-
rine.36,37 We model the aqueous 6 M NaClO4 solution in the
NVT ensemble with a 1.446 g/cm3 density and use a 0.1 fs
time-step and a fictitious electron mass of 500 au. We set the
Nose-Hoover thermostat38-40 to 350 K to compensate for the
lack of a quantum treatment of the hydrogen atoms and the
limitations of density functionals employed.41,42 We initialized
the 6 ps equilibration trajectory with the classical MD simulation
and simulated two different deuterated systems. We used the
simulation of 6 M NaClO4 with 1:45)DOH:H2O (20 ps) to
study the H-bond structural and reorientational dynamics and
A. FTIR Spectroscopy. Molecular dynamics simulations
have shown that the hydroxyl stretch frequency depends linearly
on the electric field projected along the hydroxyl bond measured
at the position of the hydrogen atom.10,43,44 This makes the
frequency of the hydroxyl stretch vibration very sensitive to its
H-bond configuration in both neat water and aqueous ionic
solutions.44 In general, H-bond structural changes lead to
changes in the projected electric field and manifest themselves
in the peak position and width of the hydroxyl stretch spectrum
of water.23 Figure 1 displays the OD stretch region of the FTIR
spectra of HOD in neat water and aqueous 3 and 6 M NaClO4
solutions. The OD spectrum of HOD in aqueous NaClO4
solutions has two spectrally distinct OD peaks that can be
accurately fit with the sum of two Gaussian peaks. As NaClO4
concentration increases, the low frequency peak blue shifts and
widens, while the high frequency peak blue shifts slightly and
increases in amplitude. The high frequency peak is associated
with water molecules in the anionic hydration shell of perchlo-
rate ions. Water molecules in the cationic hydration shell cannot
be distinguished from those in bulk water because cations
interact mostly with the oxygen atom of water and have little
effects on the hydroxyl stretch frequency.
As will be shown in Section III.F, molecular dynamics
simulations corroborate our assignment of the two spectrally
distinct hydroxyl stretch peaks in aqueous 6 M NaClO4 solution.
The low frequency OD peak at 2534 cm-1 results from water
molecules that donate a H-bond to a water molecule, while the
high frequency OD peak at 2633 cm-1 results from water
molecules that donate a H-bond to an anion or do not donate a
H-bond. The CPMD simulation shows that the non-H-bonded
hydroxyl groups are extremely short-lived, as observed previ-
ously for isotopically mixed water.12 As a result, it is assumed
that the non-H-bonded hydroxyl groups do not contribute to
the dynamics occurring on picosecond time scales. Our analysis
of experimental and simulation results emphasizes the H-bond

7828 J. Phys. Chem. B, Vol. 113, No. 22, 2009
Park et al.
Figure 2. 2DIR spectra for a series of Tw shown with 10% contour lines. (A) Experimental spectra of the OD stretch measured from 5% HOD in
H2O with 6 M NaClO4. The high frequency peak at ωτ ) ωm ) 2633 cm-1 corresponds to the ODP configuration with an anharmonicity of 100
cm-1. The low frequency peak at ωτ ) ωm ) 2534 cm-1 corresponds to ODW configuration with an anharmonicity of 153 cm-1. (B) Calculated
spectra with a response function formalism that includes a two-species exchange kinetics. (C) Calculated spectra without H-bond exchange (kP-W
) kW-P ) 0). Clearly, H-bond exchange must be included to accurately reproduce the experimental spectra.
structural dynamics occurring on picosecond time scales and
thus we focus mainly on the H-bond dynamics of the stable
water-perchlorate (ODP) and the water-water (ODW) H-bond
configurations. This will be discussed in greater detail in
Sections III.E and III.F.
approximately 2 times shorter than that of ODP. As a result,
the broad diagonal peak at ωτ ) ωm ) 2534 cm-1 decays faster
as Tw increases. The peak shape is diagonally elongated at short
Tw times and becomes symmetrical as Tw increases. This is a
signature of spectral diffusion, which will be discussed later in
detail. A cross peak at ωτ ) 2534 cm-1 and ωm ) 2633 cm-1
gradually increases in amplitude with increasing Tw. The Tw-
dependent cross peak amplitude in the 2DIR spectra provides
the spectroscopic signature for H-bond exchange between the
ODP and ODW configurations. By monitoring the Tw-dependent
rise of this cross peak amplitude, the exchange rate between
ODP and ODW can be determined. The cross peak at ωτ ) 2534
cm-1 and ωm ) 2633 results from ODW switching to ODP. Since
this exchange occurs at equilibrium, the exchange process from
ODP to ODW will also generate a cross peak at ωτ ) 2633 cm-1
and ωm ) 2534 cm-1 with an equal probability. Experimentally,
the υ ) 1f2 transition of ODP is negative and obscures this
cross peak. Switching from ODP to ODW however does result
in a cross peak between the υ ) 1f2 transitions at ωτ ) 2633
cm-1 and ωm ) 2370 cm-1 as clearly seen in the 2DIR spectrum
at Tw ) 9.0 ps in Figure 2A.
C. IR Pump-Probe Spectroscopy. The orientational and
vibrational population relaxation dynamics can be determined
by performing polarization-selective IR pump-probe spectros-
copy on the OD stretch of HOD in 6 M NaClO4 solution. As
mentioned in the previous section, in aqueous 6 M NaClO4 the
υ ) 0f1 transition (2533 cm-1) of the OD stretch in ODW is
significantly overlapped with the υ ) 1f2 transition of the OD
stretch in ODP. Thus, we measured the pump-probe signals at
probe frequencies of 2630 cm-1 for ODP and 2371 cm-1 for
ODW. Pump-probe signals of the hydroxyl stretch of HOD in
aqueous solutions relax to a constant offset in several picosec-
onds. This offset results from the deposition of heat in the
sample following vibrational population relaxation. When the
excited state molecules relax to the ground state, their vibrational
B. 2DIR Spectroscopy. The hydroxyl stretch spectrum in
aqueous NaClO4 solution consists of two spectrally distinct
H-bond configurations that thermally interconvert on the
picosecond time scale. This fact makes aqueous NaClO4
solutions an ideal model system for 2DIR studies of H-bond
exchange dynamics. 2DIR spectroscopy monitors thermal equi-
librium dynamics occurring on the picosecond time scale45-48
by vibrationally labeling molecules with their initial hydroxyl
(OD) stretch frequencies and then correlating these initial
frequencies (ωτ) with the final frequencies (ωm) of the molecules
after an experimentally controlled waiting time (Tw). Thus, 2DIR
spectroscopy can determine when an initially frequency-labeled
ODW hydroxyl stretch switches to an ODP hydroxyl stretch after
a given Tw.
Figure 2A displays 2DIR spectra at a series of Tw times
measured on HOD in aqueous 6 M NaClO4 solution. The
positive peaks shown in red along the diagonal (ωτ ) ωm) result
from the fundamental vibrational transition (υ ) 0f1). The
negative peaks appearing in blue below the diagonal arise from
the υ ) 1f2 transition with the value of ωm red shifted relative
to ωτ by the vibrational anharmonicity. The Tw-dependent 2DIR
spectra reflect a variety of dynamical processes. Vibrational
population decay and orientational relaxation result in Tw-
dependent peak amplitudes, spectral diffusion results in Tw-
dependent peak shapes, and population exchange between
subensembles results in Tw-dependent cross peak amplitudes.
In the 2DIR spectra shown in Figure 2A, the narrow diagonal
peak at ωτ ) ωm ) 2633 cm-1 results from ODP while the broad
diagonal peak at ωτ ) ωm ) 2534 cm-1 results from ODW. As
will be shown below, the vibrational lifetime of ODW is

Hydrogen Bond Exchange in Aqueous Ionic Solutions
J. Phys. Chem. B, Vol. 113, No. 22, 2009 7829
Figure 4. Vibrational population decays of the OD of HOD in two
subensembles in aqueous 6 M NaClO4 solution. Vibrational population
decay for ODW subensemble was measured at the υ ) 1 f2 transition
(2371 cm-1). Vibrational population decay of the OD of HOD in
isotopically mixed water measured at 2509 cm-1 (υ ) 0f1 transition)
is shown for comparison.
Figure 3. Orientational anisotropy decay, r(t). r(t) for ODP suben-
semble (black square) was measured at ωm ) 2630 cm-1 (υ ) 0f1
transition). The υ ) 1f2 transition of the OD stretch in the ODP
subensemble is overlapped with the υ ) 0f1 transition of the OD
stretch in ODW subensemble. r(t) for ODW (red circle) subensemble
was measured at ωm ) 2371 cm-1 (υ ) 1f2 transition). r(t) for
isotopically mixed water was measured with the υ ) 1f2 transition
at ωm ) 2388 cm-1 (green triangle). The exponential fits to r(t) are
shown with solid lines.
TABLE 1: Orientational Relaxation Parameters
center
freq (cm-1
)
a1
τor1 (ps)
a2
τor2 (ps)
6 M NaClO4 2630 (ODP) 0.15 ( 0.01 1.0 ( 0.3 0.19 ( 0.01 7.3 ( 0.5
energy dissipates into the bath leading to rapid local heating of
the sample. In IR pump-probe experiments, the transient OD
spectrum gets blue shifted gradually as the vibrational population
relaxation proceeds. Similarly, FTIR absorption spectra of the
hydroxyl stretch of water blue shift with increasing temperature.
We subtract this heating contribution from the pump-probe
signals to get accurate orientational anisotropy and population
decay dynamics.49-51 It should be noted that the heating
contribution in the pump-probe signal gets smaller as the salt
concentration increases.
2371 (ODW)
2510
2388
0.34 ( 0.01 5.0 ( 0.5
0.35 ( 0.01 2.6 ( 0.2
0.31 ( 0.02 3.3 ( 0.5
water
TABLE 2: Population Relaxation Parameters
center
freq (cm-1
)
A
T1S (ps) 1 - A T1L (ps)
5.2 ( 0.1
6 M NaClO4 2630 (ODP)
1
2371 (ODW) 0.61 ( 0.01 1.8 ( 0.1
2509
2388
0.39
3.9 (0.1
water
1
1
1.8 ( 0.1
1.8 ( 0.1
We measure the pump-probe signal with the probe beam
polarization parallel, S|(t), and perpendicular, S⊥(t), to the pump
beam polarization. The orientational anisotropy, r(t), equals
slowly than that of the OD stretch of HOD in water measured
at 2509 cm-1 52
.
D. Numerical Calculation of 2DIR Spectra. The linear IR
spectrum and Tw-dependent 2DIR spectra can be numerically
calculated by using the response function formalism with input
parameters based on diagrammatic perturbation theory. Con-
versely, all parameters in the response function formalism can
be determined from the linear and nonlinear experimental
results.53 Kwak et al. have described the response function
formalism with two-species chemical exchange and the numer-
ical calculation of 2DIR spectra in great detail,54 which we
briefly outline here to facilitate the presentation of our results.
Tw-dependent 2DIR spectra with the interconversion between
ODP and ODW subensembles can be calculated using the
following scheme
S|(t) - S⊥(t)
2
5
r(t) )
)
Cor(t)
(1)
S|(t) + 2S⊥(t)
where Cor(t) is the second-order Legendre polynomial of the
transition dipole correlation function, 〈P2[µ(t)·µ(0)]〉. The
vibrational population decay, P(t), equals
P(t) ) S|(t) + 2S⊥(t)
(2)
Figures 3 and 4 display the orientational anisotropy, r(t), and
the vibrational population decay, P(t), measured at 2630 cm-1
for ODP and 2371 cm-1 for ODW in aqueous 6 M NaClO4
solution. The orientational anisotropy decays has been fit to a
biexponential
TP1,τPor,CPFFCF
kP-W
TW1 ,τWor,CWFFCF
r(t) ) a1 exp(-t/τor1) + a2 exp(-t/τor2
)
(3)
r
ODP a ODW
f
evolve
kW-P
evolve
where τor2 > τor1. Table 1 lists the fit results. When compared
with neat water, ODP and ODW have significantly slower
anisotropy decay reflecting the effect of the dissolved NaClO4
salt. The normalized vibrational population decays have been
fit to a biexponential
where kP-W and kW-P are the forward and backward exchange
rate constants, TW1 and T1P are the vibrational lifetimes, τoWr and
τPor are the orientational relaxation times, and CFWFCF and CPFFCF
are the frequency-frequency correlation functions (FFCFs) of
ODW and ODP subensembles, respectively. The equilibrium
constant is given by
P(t) ) A exp(-t/T1S) + (1 - A)exp(-t/T1L)
(4)
where T1L g T1S. Table 2 lists the fit results. The vibrational
population of neat water at 2509 cm-1 decays monoexponen-
tially with a lifetime of 1.8 ps. The vibrational population decay
of ODW and ODP in aqueous 6 M NaClO4 solution occur more
[ODW]eq
[ODP]eq
kP-W
Keq
)
)
(5)
kW-P
where [ODW]eq and [ODP]eq are the equilibrium concentrations.

7830 J. Phys. Chem. B, Vol. 113, No. 22, 2009
Park et al.
Taking only the interconversion between two subensembles
into account, the rate equations can be written by
also be addressed when the pulses are temporally overlapped.58
Here, the pulses used in the calculations have an intensity fwhm
of 55 fs, as determined experimentally.
d[ODP]
The vibrational lifetimes (T1) and orientational relaxation
times (τor) for ODP and ODW subensembles have been directly
determined by polarization-selective IR pump-probe experi-
ments and used as input parameters for the response function
calculations. We discuss the limitations in used pump-probe
derived population and orientational relaxation times in section
IV.A. We use two Kubo terms to model the FFCFs for both
the ODP and ODW configurations, CFFCF ) ∆21 exp(- t/τ1) +
∆22 exp(-t/τ2). The second Kubo term generates an inhomoge-
neously broadened line width that obscures the motionally
narrowed first Kubo term in the calculated linear absorption
spectrum (the dotted line) shown in Figure 1. We used the center
line slope (CLS) method to determine the second Kubo term
time constants (τ2) for the ODP and ODW subensembles.14,23,59
We iteratively fit all other parameters in the response function
formalism by minimizing the difference between the numerically
calculated linear IR absorption spectrum and Tw-dependent 2DIR
spectra and the experimental results. The iterative fit varied the
ratios of transition dipole moments (µ01,W/µ01,P), the equilibrium
) -kP-W[ODP] + kW-P[ODW]
dt
(6)
d[ODW]
) kP-W[ODP] - kW-P[ODW]
dt
These rate equations can be analytically solved with the
boundary condition, [ODP] + [ODW] ) constant, and the peak
intensities in Tw-dependent 2DIR spectra are directly associated
with the concentrations that are determined by the two-species
exchange kinetics55
kW-P + kP-W exp(-kexTw)
[OD]PP(Tw) ) [ODP]eq
kex
kP-W + kW-P exp(-kexTw)
[OD]WW(Tw) ) [ODW]eq
kex
kP-W(1 - exp(-kexTw))
[OD]PW(Tw) ) [ODP]eq
kex
kW-P(1 - exp(-kexTw))
[OD]WP(Tw) ) [ODW]eq
kex
concentrations (CW/CP), the H-bond exchange rate (kW-PCW
)
(7)
kP-WCP), and the ∆1, ∆2, and τ1 parameters in the FFCF. Figure
2B and Figure 1 display the 2DIR spectra and the linear IR
absorption spectrum of the OD stretch of HOD in aqueous 6 M
NaClO4 solution, respectively, calculated from the response
function formalism with the best fit parameters summarized in
where kex ) kP-W + kW-P is the exchange rate constant,
[OD]PP(Tw) and [OD]WW(Tw) are the concentrations of the
diagonal peaks, and [OD]PW(Tw) and [OD]WP(Tw) are the
concentrations of the cross peaks. The integrated intensity of
the cross peaks in Tw-dependent 2DIR spectra depend on the
Table 3. Most significantly, we extract H-bond forward and
-1
backward exchange rate constants, (kP-W
(kW-P
(kP-W + kW-P
)
) 9 ( 2 ps and
exchange rate constant, kex ) kP-W + kW-P
.
)
-1 ) 17 ( 4 ps, as well as a total exchange rate of τex
)
The numerical calculation includes all of the dynamical
features that are observed in the 2DIR spectra. As Tw increases,
the amplitudes of peaks decay due to both vibrational population
relaxation and orientational relaxation while the peak shapes
change from diagonally elongated to symmetrical as a result of
spectral diffusion that is quantified by the FFCF. In addition,
the interconversion causes the cross peaks to grow in with
increasing Tw. As mentioned in Section III.A, the OD spectrum
of HOD in aqueous 6 M NaClO4 solution is reasonably well
described by a sum of two Gaussian functions. Accordingly,
we calculate the linear and third-order nonlinear response
functions for ODP and ODW in aqueous 6 M NaClO4 solution
by assuming that the fluctuations of ODP and ODW follow
Gaussian statistics (second-order cumulant approximation) and
that the transition dipole moment of the OD stretch does not
depend on the frequency (Condon approximation). While prior
studies have demonstrated the limitations of these approxima-
tions with respect to the hydroxyl stretch of pure water, a more
sophisticated theoretical treatment resides outside the scope of
this paper.56,57 The harmonic approximation is used to scale
-1
)
) 6 ( 2 ps. The calculated 2DIR spectra
without H-bond exchange (kP-W ) kW-P ) 0) appear in Figure
2C for comparison. Clearly, the cross peak intensity observed
experimentally in the 2DIR spectra requires H-bond exchange
between the ODP and ODW subensembles.
E. CPMD Simulations of the Structure of Aqueous 6 M
NaClO4 Solution. We use a standard geometric H-bond criterion
to analyze the H-bond structure: ROO < 3.5 Å, RHO < 2.5 Å, and
θHOO < 30°. Using this criterion, water molecules in aqueous 6 M
NaClO4 solution donate an average of 1.6 H-bonds. The simulations
indicate that the solution consists of predominantly two different
water species: (1) water molecules that donate two H-bonds to other
water molecules (WWW, 34%) and (2) water molecules that donate
one H-bond to a water molecule and the other H-bond to a ClO4-
ion (WWP, 27%). In addition, a large fraction of transient water
species donate only a single H-bond to either a water molecule
(WWN, 21%) or a ClO4- ion (WNP, 9%). While short-lived, these
species show up in the instantaneous sampling of the structure of
aqueous 6 M NaClO4 solution.
j
Radial distribution functions (RDFs), g(r), and spatial dis-
tribution functions (SDFs) extracted from the CPMD simulations
for the 6 M NaClO4 solution appear in Figures 5 and 6. The
results from classical MD simulations also appear in Figure 5A
and show a reasonable structural similarity between the two
simulations. Because of the high ionic concentration, the g(r )
the transition dipole moments, µ01/µ12 ) ꢀ2. In addition, the
finite pulse duration needs to be considered for the calculation
because the fwhm of the OD stretch spectrum is comparable to
the bandwidth of the input IR pulses and thus the IR pulses are
no longer in the impulsive limit. The finite pulse duration and
the pulse interaction orders within the finite pulse duration must
TABLE 3: Parameters Used for Numerical Calculation of Linear IR Spectrum and Tw-Dependent 2DIR Spectraa
T1(ps)
τor (ps)
∆1 (cm-1
)
τ1 (ps)
∆2 (cm-1
)
τ2 (ps)
µ01
conc
ODW
ODP
2.54
5.24
5.0
4.6
57.3
27.6
0.17
0.36
37.4
9.21
3.50
4.24
1.36
1
1.98
1
a The numerical calculation use single exponential decays for the population and the orientational relaxation. The values listed for T1 and τor
correspond to the best fits of the experimental data to single exponential decays.

Hydrogen Bond Exchange in Aqueous Ionic Solutions
J. Phys. Chem. B, Vol. 113, No. 22, 2009 7831
Figure 7. Linear IR spectra of the OD stretch of HOD in different
H-bond configurations extracted from the CPMD simulation of aqueous
6 M NaClO4 solution. The low-frequency broad peak results from the
OD groups that donate a H-bonded to other water molecules (ODW).
The high frequency narrow peak results from the non-H-bonded OD
groups and the OD groups that donate a H-bonded to a perchlorate
anion (ODP). The qualitative agreement between the FTIR spectrum
of the OD stretch of HOD in aqueous 6 M NaClO4 solution shown in
Figure 1 and the CPMD simulation results strongly support the
spectroscopic assignments used in our analysis of the experimental data.
Figure 5. Radial distribution functions (RDFs) and spatial distribution
function (SDF) in aqueous 6 M NaClO4 solution. (A) The simulated
RDF, restricted to atoms in water. (B) The SDF surrounding the water
molecules in solution. The SDF is graphically displayed with the
Molekel software.67 Perchlorate (ClO4-): oxygen (red) and chlorine
(green). Water: oxygen (blue) and hydrogen (gray).
ClO4- anion is divided into two structurally distinct subshells,
(1)
WW
(1)
WP
which we denote W
and W . The SDF shown in Figure
6B clearly shows that the first solvation shell around the
perchlorate anion contains two radially and angularly distinct
subshells, with one subshell dominated by water molecules that
(1)
WW
donate two H-bonds to other water molecules (W ) and the
other subshell being dominated by water molecules that donate
one H-bond to a water molecule and one to an anion (W(W1)P).
(1)
WP
As shown in Figure 6B, the OW of W water molecules peak
parallel to the O-Cl-O angle bisector, while the maxima in
(1)
WW
the OW density of W
water molecules has a tetrahedral
structure, with the peaks occurring antiparallel to the Cl-O
-
Figure 6. Radial distribution functions (RDFs) and spatial distribution
function (SDF) in aqueous 6 M NaClO4 solution. (A) The Cl-OW and
Cl-HW RDF. (B) The SDF of the oxygen atoms of water molecules
oriented about the ClO4- anion. The SDF is graphically displayed with
the Molekel software.67 The distribution in purple corresponds to oxygen
atoms from WWP and WWN water molecules. The distribution in blue
corresponds to oxygen atoms from WWW water molecules.
bonds on the opposite side of the ClO4 ion.
F. CPMD Simulations of the Linear IR Spectrum. We
calculate the IR spectra by Fourier transforming the total electric
dipole time correlation function, M(t)60-63
∞
4πω tanh(ꢀpω/2)
R(ω)·n(ω) )
-∞ dte-iωt〈M(t)·M(0)〉
∫
3pcV
(8)
OW - OW) in Figure 5A does not show a well-defined minimum
between the first and second solvation shells, but the SDF in
Figure 5B clearly shows that the roughly tetrahedral ordering
observed in water persists in concentrated NaClO4 solution. In
order to present the average symmetry around the water
molecule, we orient the coordinate system of the water
where V is the volume, T is the temperature, ꢀ ) 1/kT, n(ω) is
the refractive index, and c is the speed of light in vacuum.
To assign the two OD peaks of HOD in aqueous 6 M NaClO4
solution, we partition the CPMD simulation result into 1 ps time
intervals and the OD spectra of HOD in different H-bond
configurations are calculated in each time interval. Figure 7
displays the OD stretch spectra of HOD in different H-bond
configurations. We have scaled the frequency axis so that the
simulated gas phase vibrational frequency matches the experi-
mental value. When compared with the OD stretch peaks in
the experimental IR spectrum in Figure 1, the peaks in the
simulated IR spectrum are broader and the relative intensity of
the high and low frequency OD peaks is different. While the
CPMD simulation does not quantitatively reproduce the ex-
perimental FTIR spectrum, it clearly corroborates the assignment
of the OD peak at 2534 cm-1 to ODW subensemble and the
OD peak at 2633 cm-1 to ODP subensemble. The high frequency
narrow peak results from the OD groups that do not donate a
-
molecules so that the closest oxygen atom of the ClO4 ion to
the H-bond donor occurs around the left-most OH group. As a
consequence, the distribution of other water molecules pre-
dominantly appears around the right-most OH group, although
water molecules that donate two H-bonds to other water
molecules also generate a significant density of water along the
left OH group. Since the oxygen atom of water is not H-bonded
perfectly along the Cl-O bond, there is a broad spatial
distribution of Cl atoms.
Figure 6 displays RDF and SDF of different water configura-
-
tions oriented about the ClO4 anion in solution. As shown in
Figure 6A, the peak in the g(r ) ClP - OW) for WWW water
molecules occurs at a larger radius than for WWP water
molecules. This occurs because the first solvation shell of the
-
H-bond (ODN) or donate a H-bonded to a ClO4 ion (ODP),

7832 J. Phys. Chem. B, Vol. 113, No. 22, 2009
Park et al.
Figure 8. Orientational correlation functions, Cor(t) ) 〈P2[µ(t)·µ(0)]〉,
for ODP (black line) and ODW (red line) subensembles in aqueous 6
M NaClO4 solution as well as isotopically mixed water (green) obtained
from the CPMD simulations. The dashed lines are biexponential fits
toCor(t).
Figure 9. The H-bond exchange time cross correlation function,
GTCCF(t), between ODP and ODW (black line), the H-bond lifetime
autocorrelation function, GTACF(t), of non-H-bonded OD groups (green
line), and between WWW and WWP (red line) obtained from the CPMD
simulations. The dashed lines are biexponential fits to G(t).
while the low frequency broad peak results from OD groups
that donate a H-bond to another water molecule (ODW). It turns
out that both ODN and ODP subensembles contribute to the OD
peak at the high frequency in the IR spectrum. However, as
will be shown in Section III.G, the ODN subensemble is short-
lived and does not contribute to the H-bond structural dynamics
occurring on picosecond time scales observed in the CPMD
simulations or ultrafast IR experiments.
addition, the H-bond lifetime correlation function of each
individual species can be obtained by calculating the TACF.
For example, the H-bond lifetime TACF of ODW subensemble
equals
〈nW(0)nW(t)〉 - 〈nW〉2
GTWACF(t) )
(11)
〈n2W〉 - 〈nW〉2
G. CPMD Simulations of Hydrogen Bond and Orienta-
tional Dynamics in Aqueous 6 M NaClO4 Solution. We use
the second-order Legendre polynomial of the transition dipole
orientational time correlation function (TCF), Cor(t) )
〈P2[µ(t)·µ(0)]〉, to calculate the orientational anisotropy for the
ODW and ODP subensembles. The 2 ns long classical simulations
provide sufficient statistics to confirm that the orientational
relaxation of the OD group in HOD does not differ from the
orientational relaxation of OH groups. In the calculation of the
orientational time correlation functions for ODW and ODP, we
restrict the sampling to cases in which the OD group has retained
or recovered the same H-bond configuration. We divide the
resulting TCF by the appropriate H-bond lifetime time auto-
correlation function (TACF) to generate the correct orientational
TCF. Furthermore, for the calculation of orientational dynamics
we reduce the influence of fast H-bond dynamics by neglecting
H-bond fluctuations occurring faster than a picosecond. The
second-order orientational correlation functions, Cor(t), appear
in Figure 8.
This TACF represents the configurational memory of a water
molecule that initially resides in the ODW configuration before
switching to the ODP configuration.
We plot three TCFs in Figure 9. Clearly, the H-bond lifetime
correlation function of the non-H-bonded hydroxyl groups in 6
M NaClO4 solution decays extremely fast. This concurs with
the short-lived non-H-bonded species observed in MD simula-
tions of isotopically mixed water.12 Consequently, the inclusion
or exclusion of the non-H-bonded species has no impact on the
slower relaxation dynamics observed in the simulations. Here,
we need to emphasize two types of exchanges; (1) H-bond
exchange between ODW and ODP configurations and (2)
molecular exchange between WWW and WWP configurations. The
TCCF between ODW and ODP configurations exhibits the time
scale for the H-bond exchange between the spectrally distinct
H-bond configurations which results predominantly from ori-
entational relaxation. The decay of the slowest component of
the TCCF between WWW and WWP molecular configurations
emphasizes the time scale for exchange of water molecules
between the structurally distinct subshells, which requires center-
of-mass translational motion. The RDF and SDF displayed in
Figure 6 clearly show the distinct radial and angular distribution
of these two molecular configurations (WWW and WWP). In
aqueous 6 M NaClO4 solution, nearly all water molecules reside
in the first solvation shell of the perchlorate anion. So the final
exchange between these structurally distinct configurations leads
to the full equilibration of the solution structure.
We calculate time correlation functions for both spectrally
distinct hydroxyl stretch configurations (ODW and ODP) and
structurally distinct molecular configurations (WWW and WWP).
The H-bond exchange dynamics between ODW and ODP can
be extracted by calculating the time cross correlation function
(TCCF)17,18
〈nP(0)nW(t)〉
〈nP〉〈nW〉
GTP-CCWF(t) ) 1 -
(10)
A critical point regarding the analysis of the chemical
exchange dynamics based on these correlation functions must
be understood, before proceeding to the Discussion. The WWP
and ODP configurations correspond to predominantly the same
-
where nP is 1 when OD is H-bonded to ClO4 ions or not
H-bonded and 0 otherwise, and nW is 1 when OD is H-bonded
TCCF
to other water molecules and 0 otherwise. Here, G (t)
P-W
represents the H-bond exchange dynamics between ODP and
molecules since both configurations reside almost exclusively
(1)
ODW subensembles. The fluctuation-dissipation theorem pre-
in the W first solvation subshell around the perchlorate anion.
WP
TCCF
64
dicts G (t) = exp(- kext) with kex ) kP-W + kW-P
.
Here,
This is distinct from the ODW configuration, which has
contributions from WWP and WWW water molecules. Full
equilibration of the aqueous NaClO4 solution requires not only
P-W
the simulated H-bond exchange time, τex )(kex)-1, corresponds
to the slow exponential decay component of G (t). In
TCCF
P-W

Hydrogen Bond Exchange in Aqueous Ionic Solutions
J. Phys. Chem. B, Vol. 113, No. 22, 2009 7833
the H-bond exchange between the spectrally distinct ODW and
ODP configurations within the first anionic solvation shell, but
also the molecular exchange between the structurally distinct
WWP and WWW configurations.
of 4.4 ( 0.5 ps, the Cor(t) for the ODW subensemble decays
nearly monoexponentially with a time constant of 3.2 ( 0.4
ps, and the Cor(t) for neat water decays with a time constant of
2.2 ( 0.3 ps. While the simulated orientational relaxation decays
faster than the experimental orientational relaxation, the ratios
sim
of the slowest orientational relaxation time constants (τeoxrp/τ
or
IV. Discussion
) 1.7 ( 0.3 for ODP and τeoxrp/τ ) 1.6 ( 0.3 for ODW) obtained
from the CPMD simulation and polarization-selective IR
sim
or
We have investigated the orientational relaxation, spectral
diffusion, and H-bond exchange dynamics in aqueous 6 M
NaClO4 solution with ultrafast IR spectroscopy and ab initio
molecular dynamics simulations. The studies have been per-
formed to characterize the influence of dissolved ions on H-bond
structural dynamics in aqueous ionic solution. Concentrated
aqueous perchlorate solution represents an excellent model
system for examining the influence of ions on H-bond structural
dynamics in water because the hydroxyl stretch spectrum of
water in aqueous 6 M NaClO4 solutions is separated into two
spectrally distinct peaks with the lower frequency peak corre-
sponding to hydroxyl groups that donate a H-bond to another
water molecule and the higher frequency peak corresponding
to hydroxyl groups that do not donate a H-bond or donate a
H-bond to a perchlorate anion. This provides the opportunity
to experimentally measure the orientational relaxation and
spectral diffusion dynamics of these individual subensembles
independently with ultrafast IR spectroscopy, as well as the
exchange dynamics between them.
A. Orientational Dynamics. As indicated in Figure 3, the
orientational anisotropy of both ODW and ODP subensembles
of water in aqueous 6 M NaClO4 solution decays more slowly
than that of water molecules in isotopically mixed water. In
aqueous 6 M NaClO4 solution, the orientational anisotropy decay
of ODP subensemble occurs more slowly than that of ODW
subensemble The slow component of the orientational anisotropy
for the ODP subensemble decays with a time constant of 7.3 (
0.6 ps. This agrees with the 7.6 ps time constant measured by
Bakker and co-workers.3 We attribute the fast component of
the orientational relaxation to the non-H-bonded OD groups that
absorbs at 2633 cm -1. However, for the ODW subensemble,
we get a time constant of 5.0 ( 0.5 ps, significantly slower
than the 3.2 ps value reported by Bakker and co-workers. This
represents an important distinction between our experiment and
that of Bakker and co-workers, since we do not observe the
same orientational relaxation times for ODW subensemble, as
we do for isotopically mixed water.
For isotopically mixed water, we probed the orientational
anisotropy decay at 2509 cm-1 (υ ) 0f1) and 2388 cm-1 (υ
) 1f2). The orientational relaxation time measured at 2388
cm-1 exceeds the orientational relaxation time measured at 2509
cm-1 by a factor of ∼1.3, which is in agreement with previously
reported results from Bakker and co-workers in isotopically
mixed water.3 Our results, however, differ significantly from
those of Bakker and co-workers for the orientational anisotropy
decay of ODW subensemble in aqueous 6 M NaClO4 solution
as mentioned above.3 While Bakker and co-workers observed
that the orientational anisotropy decay of both ODW and OHW
subensembles in aqueous NaClO4 and Mg(ClO4)2 solutions is
indistinguishable from that of isotopically mixed water, we
measure the orientational anisotropy decay of the ODW suben-
semble to be significantly slower than that of isotopically mixed
water.
pump-probe experiments agree within experimental error. The
significant difference in the orientational correlation function
of neat water and the ODW subensemble extracted from the
CPMD simulations supports our conclusion that the ions in
concentrated aqueous NaClO4 solution change the average
dynamics of all water molecules, independent of their H-bond
configuration.
The origin of the discrepancy between our experimental
results and those previously reported by Bakker and co-workers
has yet to be definitively determined. The poorly resolved nature
of the two peaks in the absorption spectrum and the different
experimental designs limits the value of a direct comparison
between the experimental findings. Bakker and co-workers used
a two-color mid-IR pump-probe setup, while we utilizes a
identical pump and probe pulse and achieved spectral resolution
with a spectrometer. For either implementation, separating the
contributions of the two configurations proves difficult because
of the non-negligible spectral overlap and may account for the
different experimental observations.
Independent of the spectral overlap between the ODP and the
OPW configurations, polarization-selective pump-probe does
not measure the orientational relaxation of pure H-bond
configurations. The pump-probe signal at a given ωm frequency
equals the ωτ-integrated signal measured at the same ωm in the
2DIR spectra. In the pump-probe configuration, the cross peak
observed in the 2DIR spectra, contributes to the pump-probe
signal, meaning that the observed pump-probe signal results
from all molecules that possess the same frequency at the time
of probe absorption, independent of their prior history (their
initial frequencies). The orientational anisotropy measured at a
probe frequency for the ODP (ODW) configuration will reflect
the orientational memory of (1) molecules that started in the
ODP (ODW) configuration and remained, as well as (2)
molecules that started in the ODW (ODP) configuration and
exchanged to the ODP (ODW) configuration. Since the orienta-
tional anisotropy measures both contributions simultaneously
at a given probe frequency, the orientational relaxation of each
contribution cannot be separated in pump-probe spectroscopy.
In principle, the modeling of the 2DIR spectra can address this
issue at least in part but in practice such an analysis proves
difficult to perform robustly.
The mixing of H-bond configurations in the experimental
pump-probe data also limits the comparison to simulation
results, since the simulated orientational relaxation only includes
hydroxyl groups that reside in the same H-bond configuration
at time t as they possessed initially. Despite this complication,
we believe it reasonable to assume that the cross peak contribu-
tion to the ODW signal will not have a slower orientational decay
than the ODW molecules that did not exchange H-bond
configurations. If this proves true, the conclusion that concen-
trated ionic solutions change the dynamics of water molecules
even if they do not donate a H-bond to a perchlorate anion
should also prove robust.
The orientational anisotropy decay obtained from the IR
pump-probe experiments agrees with the trends in the orien-
tational correlation functions, Cor(t), extracted from MD simula-
tions as shown in Figure 8. The Cor(t) for the ODP subensemble
decays biexponentially with a slow exponential time constant
B. Spectral Diffusion Dynamics. We utilize Tw-dependent
2DIR spectra to extract the spectral diffusion dynamics of the
ODP and ODW subensembles. Under thermal equilibrium

7834 J. Phys. Chem. B, Vol. 113, No. 22, 2009
Park et al.
conditions, the H-bond structure in aqueous ionic solutions
evolves by changing the H-bond lengths and angles as well as
switching H-bond partners resulting in the evolution of the OD
stretch frequency. The OD stretch frequency evolution within
each subensemble causes the peak shape to change, while the
exchange between spectrally distinct ODW and ODP suben-
sembles as well as between structurally distinct WWW and WWP
molecular configurations will lead to growth in the cross peak
intensity. We monitored these spectral diffusion dynamics by
inspecting the Tw-dependence of the ODP and ODW peak shapes
residing along the diagonal in the 2DIR spectrum. The widths
of these peaks projected onto the diagonal axis reflect the
inhomogeneous distribution of the OD stretch frequencies within
each H-bond configuration. The inhomogeneity in the OD stretch
frequency leads to initial and final frequencies which remain
strongly correlated for small values of Tw and generate
diagonally elongated peaks, as shown in Figure 2. As the waiting
time increases, spectral diffusion leads to the loss of frequency
memory, which results in symmetric contours in the 2DIR
spectrum. In the response function formalism, these spectral
diffusion dynamics result from decay of the frequency-frequency
correlation function (FFCF), C(t) )〈δω(0)δω(t)〉. By utilizing
the diagonal peaks in the 2DIR spectra to measure the spectral
diffusion dynamics, we can ensure that the observed dynamics
do not contain the contribution from the cross peaks present in
the orientational anisotropy. This represents a clear advantage
of 2DIR measurements of spectral diffusion over time-resolved
hole burning7 or homodyne photon echo techniques.65 Table 3
lists the slowest decay component of the FFCF for ODW water
(3.5 ( 0.5 ps), ODP water (4.2 ( 0.6 ps), and neat water (∼1.5
ps).11,66 We emphasize the slow decay because it will not be
influenced by the dynamics of non-H-bonded configurations.
C. H-bond Exchange Dynamics. The dynamics of water
molecules within a given H-bond configuration can be accessed
by measuring the orientational and spectral diffusion dynamics,
but such dynamics cannot provide a complete description of
the H-bond structural dynamics of aqueous ionic solutions. A
thorough description of the H-bond structural dynamics requires
understanding the mechanism and time scale for the intercon-
version between distinct molecular and H-bond configurations.
ODP subensemble. We get a ratio between the measured and
exp sim
simulated H-bond exchange times, τ /τ ) 1.4 ( 0.5, similar
HB HB
to that observed for the orientational relaxation times. The
consistently faster dynamics observed in the CPMD simulations
may result from the 350 K temperature used in the simulation.
The use of an elevated temperature represents a common method
designed to compensate for the classical treatment of the proton
motion in the simulation.41 While this precludes the direct
quantitative comparison of experiment to simulation, the
comparison of trends remains valuable. The slow component
of the molecular TCCF between WWW and WWP subensembles
emphasizes the exchange of water molecules between the first
(1)
(1)
WW
solvation subshells W and W
.
WP
Experimentally, the off-diagonal cross peak intensities will
contain all of the dynamics that lead to the full equilibration in
aqueous 6 M NaClO4 solution and complete loss of configu-
rational memory. The simulation results indicate that we should
see biexponential exchange dynamics. We have looked for
biexponential exchange dynamics in the response function
calculations of the experimental data, but the vibrational lifetime
of the OD stretch does not allow the observation of the
molecular exchange between the first solvation subshells around
the perchlorate anion.
V. Concluding Remarks
We have investigated H-bond structural dynamics in aqueous
6 M NaClO4 with ultrafast IR spectroscopy and Car-Parrinello
molecular dynamics simulations. The aqueous NaClO4 solution
has two spectrally distinct hydroxyl stretch peaks. The lower
frequency peak corresponds to hydroxyl groups that donate a
H-bond to another water molecule, while the higher frequency
peak corresponds to hydroxyl groups that do not donate a
H-bond or donate a H-bond to a perchlorate ion. This spectro-
scopic distinction between hydroxyl groups in different H-bond
configurations allows us to measure the orientational and spectral
dynamics of each H-bond configuration independently, as well
as the time scale for interconversion between these configura-
tions. The dynamics extracted from ultrafast IR experiments
and CPMD simulations have allowed us to construct a detailed
account of the H-bond structural dynamics in this solution.
The orientational anisotropy decay and H-bond exchange
dynamics extracted from ultrafast IR experiments and CPMD
simulations occur with similar time constants. Such behavior
has been seen in MD simulations of neat water and aqueous
chloride solution and been attributed to large orientational jumps
that lead to both H-bond exchange and orientational anisotropy
decay.18 The observation of a similar correlation in the orien-
tational anisotropy decay and H-bond exchange dynamics in
both ultrafast IR experiments and CPMD simulations suggests
that the same orientational jump model may apply to the aqueous
NaClO4 solution. Conclusive assignment of the orientational and
H-bond dynamics to orientational jumps awaits further detailed
analysis of the CPMD simulation results.
Here, we determined the H-bond exchange time between
spectrally distinct ODP and ODW subensembles as well as the
molecular exchange between structurally distinct WWW and WWP
configurations in aqueous 6 M NaClO4 solution by using 2DIR
spectroscopy and CPMD simulations. The H-bond exchange
between ODP and ODW subensembles occurs with a time
constant of 6 ( 2 ps, very similar to the orientational relaxation
time constants of the ODP and ODW subensembles measured
in polarization-selective IR pump-probe experiments. The same
correlation between the H-bond exchange and orientational
relaxation times has been seen in MD simulations of water and
aqueous chloride solutions and described by a jump diffusion
model for the H-bond exchange.17,18 We also extract the H-bond
and molecular time cross correlation functions from the CPMD
simulations, as shown in Figure 9. The H-bond TCCF between
spectrally distinct ODP and ODW subensembles has been fit to
a biexponential function with a slow time constant of 4.4 (
0.5 ps, while the molecular TCCF between structurally distinct
WWW and WWP subensembles has been fit to a biexponential
with a slow time constant of 10 ( 2 ps. The slow component
The radial and spatial distribution functions extracted from
the CPMD simulations also present a clear picture of radial and
angular segregation of water molecules that donate two H-bonds
to other molecules (WWW) and water molecules that donate one
H-bond to a water molecule and one to a perchlorate anion
(WWP). The CPMD simulations show that the molecular
exchange between structurally distinct WWW and WWP configu-
rations proceeds more slowly than the H-bond exchange between
the spectrally distinct ODW and ODP configurations because it
requires center-of-mass translation of water molecules.
of the H-bond TCCF between ODP and ODW subensembles
(1)
WP
emphasizes the H-bond exchange predominantly within the W
solvation subshell around the perchlorate ions and occurs on a
similar time scale as the orientational anisotropy decay of the
Our complementary use of ultrafast IR spectroscopy and
CPMD has provided a detailed qualitative description of the

Hydrogen Bond Exchange in Aqueous Ionic Solutions
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of Energy and the W. M. Keck Foundation for financial support,
M. D. Fayer for the illuminating discussion of 2DIR spectros-
copy and water dynamics, K. Kwak for initial 2DIR calculation
source code, and J. Sung for experimental assistance. M.O.
thanks the Swedish Research Council (VR) for support and
gratefully acknowledges generous grants of computer time at
the Swedish National Supercomputer Center (NSC) and Center
for Parallel Computing (PDC).
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