Real-Time Probing of Hydrogen-Bond Exchange Dynamics in

Article pubs.acs.org/JPCB

Real-Time Probing of Hydrogen-Bond Exchange Dynamics in Aqueous NaPF6 Solutions by Two-Dimensional Infrared Spectroscopy Hyewon Son,† Dayoung Nam,† and Sungnam Park*,†,‡ †

Department of Chemistry, Korea University, Seoul 136-713, Korea. Multidimensional Spectroscopy Laboratory, Korea Basic Science Institute, Seoul 136-713, Korea.

‡

ABSTRACT: Ultrafast two-dimensional infrared (2DIR) spectroscopy was used to study H-bond exchange dynamics in aqueous NaPF6 solutions. Interestingly, there are two spectrally distinct hydrogen-bond (H-bond) configurations in aqueous NaPF6 solutions: water molecules that are Hbonded to PF6− (ODA) or other water molecules (ODW). These two spectrally distinct subsets of water in aqueous NaPF6 solutions provide an opportunity to study the individual dynamics of water in two H-bond configurations as well as interconversion dynamics between them. Most significantly, we have successfully measured H-bond exchange dynamics between two spectrally distinct H-bond configurations in real time by ultrafast 2DIR spectroscopy. In aqueous 5.0 M NaPF6 solution, water molecules switch their H-bond partners from PF6− to water molecule (ODA → ODW) with a time constant of 12.0 ps and from water molecule to PF6− (ODW → ODA) with a time constant of 21.6 ps at room temperature. H-bond exchange dynamics in aqueous NaPF6 solution were found to be relatively slower than those in aqueous NaBF4 and NaClO4 solutions which were studied previously, which was attributed to the asymmetric potential energy curve for the H-bond exchange process based on the orientational jump mechanism.

I. INTRODUCTION Hydrogen-bond (H-bond) structures in aqueous solutions are rearranged on a picosecond time scale by breaking and reforming H-bonds under thermal equilibrium conditions.1−4 Such fast rearrangements of H-bond structures may facilitate proton transfer, ion transports, and chemical reactions occurring in aqueous solutions.5,6 H-bond structures and dynamics of aqueous solutions are found to be substantially influenced by dissolved ions, which, thus, significantly change the properties of aqueous ionic solutions.3,7 Furthermore, the dissolved ions play an important role in determining the 3D structure of proteins in aqueous solutions by either directly interacting with the polar or charged residues of the proteins or changing the H-bond structures of water.8−10 In addition, the dynamics of water in the hydration shells of charged surfaces of proteins are of critical importance to understand the structures and functions of given proteins.11−13 Advances in ultrafast IR spectroscopic methods and molecular dynamics (MD) simulations allow detailed investigations of the H-bond structural dynamics in various aqueous environments.2−4,14−25 IR pump−probe (IR PP) experiments have been used to investigate the vibrational relaxation and orientational relaxation dynamics of water in bulk,16,17,26 aqueous ionic solutions, 14,15,22,23,27 and reverse micelles,19,21,28,29 revealing that the vibrational population relaxation and orientational relaxation dynamics of water slow down substantially in the presence of ions and in nanoscopic environments. Two-dimensional IR (2DIR) spectroscopy has been a powerful tool to study H-bond structural dynamics in aqueous solutions.3,22,23,25,30 Fayer and co-workers have studied © 2013 American Chemical Society

the H-bond dynamics in aqueous NaBr solutions, reporting that spectral diffusion dynamics and orientational relaxation dynamics in aqueous NaBr solutions get slower with increasing NaBr concentration and they are well-correlated.3,29 In addition, H-bond switching dynamics in aqueous NaBF6 and NaClO4 solutions were directly measured by 2DIR spectroscopy, and H-bond exchange time constants were able to be experimentally determined.22,23 Recently, molecular dynamics simulation studies have proposed that in aqueous solutions water molecules switch their H-bond partners by orientational jump mechanism.18,20,31 Furthermore, Gaffney and co-workers have investigated the H-bond exchange dynamics in aqueous NaClO4 solution by polarization-controlled 2DIR spectroscopy and have proven that water molecules rotate by a relatively large angle when they exchange H-bond partners.24,32 The mechanism behind H-bond exchange processes in aqueous solutions has begun to be better understood on a molecular level. Along with recent progress, we have further investigated the H-bond structures and dynamics in aqueous NaPF6 solutions where there are two spectrally distinct H-bond configurations originating from water molecules either H-bonded to other water molecules or directly H-bonded to PF6−.33 Similar to BF4− and ClO4−, PF6− in aqueous solutions has been known to form weak H-bonds with water molecules and splits the Received: Revised: Accepted: Published: 13604

July 10, 2013 September 2, 2013 September 29, 2013 September 30, 2013 dx.doi.org/10.1021/jp406805c | J. Phys. Chem. B 2013, 117, 13604−13613

The Journal of Physical Chemistry B

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hydroxyl stretch band into two components.22,23 However, the splitting of the hydroxyl stretch band in aqueous PF6− solutions is larger than in aqueous BF4− and ClO4− solutions due to different H-bond strengths between water and anion.34 The Hbond strength between water and anion in aqueous ionic solutions is believed to play an important role in determining the time scales of H-bond exchange between water−water and water−anion configurations. Water molecules are found to be more weakly H-bonded to PF6− than BF4− and ClO4− so that the OD stretch peaks of HOD molecules H-bonded to PF6− appear at higher frequencies. In this work, we chose aqueous PF6− solution to investigate the effect of the H-bond strength between water and anion on the H-bond exchange dynamics. The H-bond structures in aqueous PF6− solutions were studied in detail by concentration-dependent FTIR experiments and quantum chemical calculations. Vibrational population relaxation and orientational relaxation dynamics of waters in two Hbond configurations were measured by polarization-controlled IR PP experiments. Most significantly, H-bond exchange processes between two H-bond configurations were successfully measured in real time by 2DIR spectroscopy, and their Hbond exchange time constants were determined. Finally, we compared our 2DIR experimental results with those of aqueous BF4− and ClO4− solutions, which were studied previously.

(full width at half-maximum, fwhm). The CaF2 plates with different thicknesses were used to compensate for the linear dispersion introduced by other dielectric materials in the setup including a Ge Brewster plate and ZnSe beam splitters. The mid-IR pulses were nearly transform-limited at the sample position. The principles and experimental details of 2DIR spectroscopy have been described elsewhere.29,36,37 Three mid-IR pulses are focused with a 90° off-axis parabolic mirror (focal length (fl) = 10 cm) onto the sample in a box-car geometry. After the sample, the beams are collimated with another 90° off-axis parabolic mirror (fl = 10 cm). The spot size of the IR beams at the sample position is less than 100 μm in diameter. The relative time delays among three incident IR pulses are varied with computer-controlled linear translational stages. The signal is emitted from the sample in a unique phase-matched direction and is overlapped with a local oscillator pulse for heterodyne detection. The heterodyned signal is dispersed through a spectrometer onto the 64-element mercury−cadmium−telluride (MCT) array detector with high-speed data acquisition electronics (Infrared Associates and Infrared Systems Development Corp.). A small portion of the IR beam is sampled before the sample and is used as a reference beam to correct the fluctuation of the laser intensity during the experiments. In 2DIR experiments, there are three experimental time variables that can be controlled. The time delay between the first and second pulses is the coherence evolution time (τ), the time delay between the second and third pulses is the waiting time (Tw), and the time delay between the third pulse and the emitted signal is the detection time (t). The heterodyned 2DIR signal, S(τ,t;Tw), is collected by scanning τ at a fixed Tw, frequency-resolved by a spectrometer, and detected by the 64element array detector. To obtain the 2DIR spectra at a given Tw, S(ωτ,ωt;Tw), a Fourier transformation of the signal with respect to τ and t time periods should be performed. The spectrometer essentially performs the Fourier transform of the detection time (t) to generate the ωt-dependent spectrum, while another Fourier transform is numerically performed for the evolution time (τ) after collecting the τ-dependent interferogram for each value of ωt. This Fourier transformation provides the ωτ-dependent spectrum. Two-dimensional IR spectra, S(ωτ,ωt;Tw), are therefore displayed with respect to the initial excitation frequency ωτ and final emission frequency ωt at a given Tw. A purely absorptive 2DIR spectrum is obtained by using the dual scan method in which nonrephasing and rephasing 2DIR signals are measured separately by two different pulse sequences and are added together.38 For IR PP experiments,29,39 the IR pulses were split into the pump and probe beams with a 9:1 intensity ratio and were focused onto the sample. The probe beam was collimated after the sample and was dispersed through a spectrometer onto the 64-element MCT array detector. The IR PP signal S(t) was collected by measuring the transmission of the probe beam through the sample by chopping the pump beam at 500 Hz. For a given delay time t, the IR PP signal was defined by S(T) = [Tpump‑on − Tpump‑off](t)/Tpump‑off = ΔT(t)/T, where T is the transmission of the probe beam. For polarization-controlled IR PP experiments, the wire grid polarizers were placed in the pump and probe beam pathways before the sample and their polarization states were set to be 0 and 45° with respect to the normal to the optical table, respectively. A wire grid analyzer polarizer on a motorized rotational stage was placed after the sample, and the parallel and perpendicular polarizations of the

II. EXPERIMENTAL METHODS A. Sample Preparation. Sodium hexafluorophosphate (NaPF6, 98%) and deuterium oxide (D2O, 99.9%) were purchased from Sigma-Aldrich and used as received. Isotopically mixed HOD/H2O solution was prepared by mixing D2O and H2O with a volume ratio of 4:96, producing 8% HOD in H2O. All NaPF6 solutions were prepared by directly dissolving NaPF6 salt in 8% HOD in H2O. For IR experiments, the sample solutions were housed in a homemade IR cell with two 3 mm thick CaF2 windows. The optical path length of the sample cell was set to be 25 μm by Teflon spacers. B. FTIR Spectroscopy. All FTIR spectra were measured by a Varian 640-IR spectrometer with a 1 cm−1 resolution. For temperature-dependent FTIR experiments, the cell was connected to a temperature controller (PIKE Technologies, Madison, WI, USA) which can raise the temperature of the sample by the minimum unit of 1 °C. Temperature-dependent FTIR spectra were measured from 25 to 50 °C with an interval of 5 °C. At a given temperature, the cell was kept for at least 15 min before the FTIR spectrum was taken to make sure the thermal equilibrium was established. After the temperaturedependent FTIR experiments were finished, the sample cell was quickly cooled to the initial temperature (25 °C) by using a fan and the FTIR spectrum was measured to compare with the FTIR spectrum we measured before the experiment to check any undesired degradation of the sample. C. 2DIR and IR PP Spectroscopy. Our femtosecond laser system and time-resolved spectrometers have been described in detail elsewhere.3,35 Briefly, a train of 800 nm pulses with ∼45 fs duration and ∼1.0 mJ/pulse was generated by a Ti:sapphire oscillator (Tsunami, Spectra-Physics) and regenerative amplifier (Spitfire, Spectra-Physics) laser system operating at 1 kHz. The 800 nm pulses were used to pump an optical parametric amplifier (OPA, Spectra-Physics) to produce near-IR pulses which were used to generate mid-IR pulses centered at 2610 cm−1 in a 0.5 mm thick AgGaS2 crystal (type II) by difference frequency generation. The power spectrum of the mid-IR pulses had a Gaussian envelope with a ∼260 cm−1 bandwidth 13605

dx.doi.org/10.1021/jp406805c | J. Phys. Chem. B 2013, 117, 13604−13613


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in aqueous solutions. PF6− in aqueous solutions are solvated by forming H-bonds with the surrounding water molecules while Na+ are preferentially solvated by the oxygen atom of water. The dissolved ions disturb the H-bond network of water, especially, at high salt concentrations. The effect of dissolved salts on the H-bond structure of water is manifest in the spectral change in the OD stretch band. In Figure 1B, the OD stretch band of 8% HOD in H2O (0.0 M) peaks at ∼2510 cm−1 and its bandwidth is about ∼160 cm−1 in fwhm. Such broad bandwidth results from a wide distribution of H-bond configurations in terms of the strengths and the number of H-bonds. It is well-understood that the OD stretch frequency tends to be more red-shifted when HOD molecule makes stronger and more H-bonds with H-bond acceptors. As shown in Figure 1B, the broad low-frequency peak gets blue-shifted gradually as the concentration of NaPF6 salt is increased. In contrast, the narrow high-frequency peak at ∼2670 cm−1 grows with increasing the concentration of NaPF6 salt. FTIR experimental results indicate that the narrow high-frequency peak at ∼2670 cm−1 results from the OD stretch band of HOD that is H-bonded to hexafluorophosphate ion (ODA) while the broad low-frequency peak at ∼2530 cm−1 is associated with the OD stretch band of HOD that is H-bonded to other water molecules (ODW). The quantum chemical calculations were carried out by using the GAUSSIAN 09 package with density functional theory (DFT) method (B3LYP) and DGDZVP basis set employed.40,41 The HOD−PF6− cluster containing PF6− and seven HOD molecules was optimized using tight optimization criteria, and the vibrational frequencies of HOD molecules were calculated with the anharmonic corrections as shown in Figure 1A. The optimized structure of the HOD−PF6− cluster in Figure 1A consists of HOD molecules that are H-bonded to PF6− and other HOD molecules. A HOD molecule in the first hydration shell around PF6− can make up to two H-bonds with PF6− by donating two hydroxyl groups to PF6−. In addition, the HOD molecule in the first hydration shell of PF6− forms Hbonds with neighboring water molecules in the first hydration shell or those in the second hydration shell. In these quantum chemical calculations, we simply tried to calculate the OD stretch frequencies of two different H-bond configurations in the optimized HOD−PF6− cluster. The calculated OD stretch frequency of HOD···OH2 (ODW) was ∼2530 cm−1, and the calculated OD stretch frequency of HOD···PF6− (ODA) was ∼2650 cm−1. These calculation results agreed reasonably well with the experimental data, as indicated in Figure 1. Both FTIR experiments and quantum chemical calculations indicate that there are two spectrally distinct H-bond configurations of water molecules in aqueous NaPF6 solutions: (1) water molecules that are H-bonded to other water molecules (ODW at ∼2530 cm−1) and (2) water molecules that are H-bonded to PF6− (ODA at ∼2670 cm−1). For the remainder of this paper, two Hbond configurations of water molecules are denoted ODW and ODA, respectively. Figure 1C shows the temperature-dependent FTIR spectra of aqueous 5.0 M NaPF6 solution. As the temperature is increased, the broad low-frequency peak (ODW) is gradually blue-shifted and its amplitude gets smaller. In the case of the high-frequency peak (ODA), its peak position and amplitude are not significantly varied with increasing temperature. The blue shift of the ODW peak at higher temperatures results from the thermally induced weakening of the H-bonds between water molecules. In other words, the H-bonds between water

probe beam were selectively measured by setting the analyzer polarizer to be 0 and 90° by the computer-controlled motorized rotational stage. The parallel and perpendicular IR PP signals, S∥(ωpr,t) and S⊥(ωpr,t), were consecutively measured for every two scans with the polarization of the probe beam parallel and perpendicular to that of the pump beam, respectively. Twodimensional IR and IR pump−probe experiments were conducted at 22 °C. FTIR spectra of the sample solution were measured before and after each experiment to check any photodegradation or thermal degradation of the sample during the experiments. We found that there was no significant degradation of the sample.

III. RESULTS AND DISCUSSION A. FTIR Study. Figure 1 displays normalized FTIR spectra measured with aqueous NaPF6 solutions at different concentrations of NaPF6 salt. NaPF6 salt dissociates into Na+ and PF6−

Figure 1. H-bond configurations in aqueous NaPF6 solutions: (A) optimized structure of HOD−PF6− cluster by the quantum chemical calculations; (B) normalized FTIR spectra measured with aqueous NaPF6 solutions at different concentrations of NaPF6 salts dissolved in 8% HOD in H2O (HOD···OH2 (ODW) and HOD···PF6− (ODA) are two spectrally distinct H-bond configurations that are present in aqueous PF6− solution); (C) temperature-dependent FTIR spectra of aqueous 5.0 M NaPF6 solution. 13606



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Figure 2. IR PP signals measured with aqueous 5.0 M NaPF6 solution: (A) parallel and perpendicular IR PP signals, S∥(t) and S⊥(t); (B) normalized S∥(t) of ODW and ODA at different probe frequencies; (C) analysis of the isotropic IR PP signal of ODW measured at ωpr = 2530 cm−1. The isotropic IR PP signal of ODW, Siso(t), is represented by the sum of the population relaxation, P(t), and the heating contribution, G(t).

molecules get longer and weaker at higher temperatures due to thermal energies leading to the blue shift of the OD stretch band. In addition, the smaller amplitude of the ODW peak at higher temperatures is caused by the decrease in the transition dipole moment at higher temperatures. Such a temperaturedependent spectral property of the ODW peak is important in understanding the IR PP signal as presented in the next section. B. IR PP Study. In IR pump−probe experiments, a molecule system is excited to υ = 1 state by the IR pump pulse, the relaxation of the excited molecular system is monitored by a time-delayed IR probe pulse. The IR pump−probe signal decays due to vibrational population relaxation and orientational relaxation of the excited molecules. To separately measure the vibrational lifetime (T1) and orientational relaxation time (τor) of ODW and ODA, polarization-controlled IR PP experiments were used.42 Figure 2A shows the parallel and perpendicular frequency-resolved IR PP signals, S∥(t;ωpr) and S⊥(t;ωpr), measured with aqueous 5.0 M solution. In Figure 2A, the IR PP signals at ωpr = 2668 and 2530 cm−1 result from the fundamental (υ = 0↔1) transition of ODA and ODW, respectively, and are analyzed to obtain P(t) and r(t) of ODA and ODW. Figure 2B displays the parallel IR PP signals of ODW and ODA at two probe frequencies (dashed lines in Figure 2A). IR PP signals of ODA decay to zero as shown in Figure 2A,B. The standard analytical procedure was used to obtain P(t) and r(t) of ODA,.35,42,43 In contrast, the IR PP signal of ODW decays to a constant resulting from a heating effect which has been wellunderstood in studying the population relaxation of HOD in water.16,17,19 To analyze the IR PP signal of ODW, the parallel and perpendicular IR PP signals, S∥(t) and S⊥(t), measured at ωpr = 2530 cm−1 are expressed by

⎛ ⎞ 4 S∥(t ) = P(t )⎜1 + C2(t )⎟ + G(t ) ⎝ ⎠ 5

(1)

⎛ ⎞ 2 S⊥(t ) = P(t )⎜1 − C2(t )⎟ + G(t ) ⎝ ⎠ 5

(2)

where P(t) represents the vibrational population decay and C 2 (t) is the orientational correlation function and is represented by the second-order Legendre polynomial of the transition dipole correlation function, C2(t) = ⟨P2[μ(t)·μ(0)]⟩. The isotropic IR PP signal, Siso(t), is given by Siso(t ) =

S∥(t ) + 2S⊥(t ) 3

= P(t ) + G(t )

(3)

In eqs 1−3, the vibrational population decay is modeled as the first-order kinetics, P(t) = A exp(−t/T1), and the heating contribution, G(t), is given by G (t ) =

Aα [k r(1 − exp( −k bt )) kr − kb + k b( −1 + exp(−k rt ))]

(4)

where kr = 1/T1 and kb is the rate constant for relaxation of an intermediate state to a hot ground state leading to the offset at long times, α. Detailed analyses were described elsewhere.16,17,19 Vibrational population decay and orientational anisotropy decay of ODW can be obtained by P(t ) = 13607

S∥(t ) + 2S⊥(t ) 3

− G (t )

(5)


The Journal of Physical Chemistry B r (t ) =

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orientational relaxation time constant of 2.4 ± 0.2 ps. However, r(t) of ODW and ODA was well-represented by a biexponential function. As shown in Table 1, the short time components (τor1) of r(t) were not much different while the long time components (τor2) were found to be 5.7 and 8.7 ps for ODW and ODA, respectively. The biexponential behavior of the orientational anisotropy decay is more often interpreted by two sequential orientational diffusion processes of HOD in aqueous solutions.19 At short times, orientational diffusion of HOD occurs within the intact H-bond frame without breaking the Hbond. At long times, the HOD molecule undergoes full orientational relaxation by breaking the H-bond. Therefore, the long time component of r(t) is believed to be closely related to the H-bond exchange time scale in aqueous solutions. Our IR PP results indicate that the vibrational relaxation and orientational relaxation dynamics of HOD around PF6− are significantly slower than those in bulk, which are consistent with many previous experimental studies performed with aqueous solutions. C. 2DIR Study. Two-dimensional IR experiments were performed with aqueous 5.0 M NaPF6 solution, and Figure 4A displays 2DIR spectra measured with increasing waiting time (Tw). In our 2DIR spectra, the ωτ axis (horizontal axis) is associated with the initial molecular frequencies labeled at the evolution time (τ) while the ωt axis (vertical axis) is associated with the final molecular frequencies recorded at the detection time (t).37,44 At a given Tw time, the 2DIR spectrum, S(ωτ,ωt;Tw), is plotted with the initial and final frequencies (ωτ and ωt) and can be thought of as a correlation map between the initial and final frequencies of the molecules. Twodimensional IR spectra evolve as a function of Tw due to microscopically occurring molecular events. By analyzing the Tw-dependent 2DIR spectra, all dynamic information on the molecular system under study can be extracted.45−47 In the 2DIR spectrum at Tw = 0.2 ps shown in Figure 4A, the narrow high-frequency peak at ωτ = ωt = 2668 cm−1 comes from ODA while the broad low-frequency peak at ωτ = ωt = 2530 cm−1 results from ODW (see the FTIR spectrum shown in the upper panel in Figure 4A). The red peaks result from the ground-state bleach (GSB, υ = 0→1) and stimulated emission (SE, υ = 0←1) while the blue peak comes from the excitedstate absorption (ESA, υ = 1→2). The blue peaks are redshifted by the vibrational anharmonicities along the ωt-axis. It should be noted that the ESA contribution of the ODW peak is not clearly observed in Figure 4A because it is red-shifted from the GSB and SE contributions (∼2530 cm−1) along the ωt axis by ∼120 cm−1. All dynamic features are observed in Tw-dependent 2DIR spectra. The individual peaks in 2DIR spectra decay due to vibrational population relaxation and orientational relaxation as Tw is increased. It should be mentioned that 2DIR spectra in Figure 4A were normalized to show relative changes in peak amplitudes at a given Tw. In addition, the peak shapes change with increasing Tw as a result of spectral diffusion. In other words, the peaks in 2DIR spectra at short Tw are diagonally

S∥(t ) − S⊥(t ) S∥(t ) + 2S⊥(t ) − 3G(t )

(6)

Here, the heating contribution in eqs 5 and 6 was only included for the analysis of the IR PP signal of ODW, which is shown in Figure 2C. Siso(t) of ODW at ωpr = 2528 cm−1 is decomposed into P(t) and G(t) with kr = 1/T1 = (2.4 ps)−1 and kb = (1.5 ps)−1 in eq 3. Figure 3A and 3B display the vibrational

Figure 3. IR PP experimental results: (A) population relaxation decays, P(t), and (B) orientational anisotropy decays, r(t), of HOD in pure water (black line) and aqueous 5.0 M NaPF6 solution.

population decays, P(t), and orientational anisotropy decays, r(t), of HOD in pure water and ODW and ODA in aqueous 5.0 M NaPF6 solution, respectively. P(t) and r(t) were fit by a single-exponential or biexponential function, respectively. The exponential fit results are summarized in Table 1. In general, P(t) was well-represented by a single exponential as shown in Figure 3A. The vibrational lifetime of HOD in pure water was measured to be T1 = 1.7 ± 0.1 ps, which agrees well with the literature value.16 In aqueous 5.0 M NaPF6 solution, the vibrational lifetime of ODA (T1 = 6.7 ± 0.2 ps) is almost three times longer than that of ODW (T1 = 2.4 ± 0.2 ps). Our experimental results indicate that the vibrational lifetime of HOD gets longer when the peak is blueshifted (i.e., the H-bond strength gets weaker). r(t) of HOD in pure water was well-fit by a single-exponential function with

Table 1. Exponential Fit Results of Vibrational Population Decays, P(t), and Orientational Anisotropy Decays, r(t)

HOD in H2O ODW ODA

ωpr (cm−1)

T1 (ps)

b1

τor1 (ps)

b2

τor2 (ps)

2510 2530 2668

1.7 ± 0.2 2.4 ± 0.2 6.7 ± 0.2

0.34 ± 0.03 0.07 ± 0.02 0.14 ± 0.02

2.5 ± 0.2 0.52 ± 0.06 0.47 ± 0.05

0.29 ± 0.03 0.18 ± 0.03

5.7 ± 0.5 8.7 ± 0.5

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Figure 4. Tw-dependent 2DIR spectra: (A) 2DIR spectra measured with aqueous 5.0 M NaPF6 solution at Tw = 0.2, 1.0, 3.0, 5.0, and 7.0 ps; (B) simulated 2DIR spectra obtained by the response function calculations including the two-species chemical exchange kinetic model with the H-bond exchange time constant of τex = 7.7 ps; (C) simulated 2DIR spectra without H-bond exchange (τex ≈ ∞). See the text for details.

Figure 5. Schematic illustration of H-bond exchange dynamics observed in Tw-dependent 2DIR spectra measured with aqueous 5.0 M NaPF6 solution. The cross-peaks grow as Tw is increased. The upper left cross-peak is produced by the H-bond exchange from ODW to ODA, while the lower right cross-peak comes from the H-bond exchange from ODA to ODW. See the text for details.

elongated but become symmetrical as Tw is increased. Spectral diffusion dynamics are quantified by the frequency−frequency correlation function, CFFCF(t) = ∑iΔi2 exp(−t/τi). Most interestingly, the cross-peaks between ODW and ODA peaks grow gradually in 2DIR spectra with increasing Tw in Figure 4A.

As illustrated in Figure 5, the upper left cross-peak appears when HOD molecule exchanges its H-bond partner from water to PF6− (ODW → ODA), while the lower right cross-peak appears when HOD molecule exchanges its H-bond partner from PF6− to water (ODA → ODW). Here, we directly observed 13609



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Table 2. Parameters Used for Response Function Calculation of Tw-Dependent 2DIR Spectra ODW ODA

T1 (ps)

τor. (ps)

μ01

concn (M)

Δ1 (cm−1)

τ1 (ps)

Δ2 (cm−1)

τ2 (ps)

Δ3 (cm−1)

τ3 (ps)

2.4 6.7

5.7 8.7

1.9 1

1.8 1

70.6 25.0

0.1 0.1

4.7 6.7

0.5 4.0

36

3.5

the H-bond exchange processes in aqueous 5.0 M NaPF6 solution in real time by 2DIR spectroscopy. By analyzing how fast the cross-peaks grow as a function of Tw, the H-bond exchange rate constants can be extracted from the Twdependent 2DIR spectra, which will be presented in the next section. D. Numerical Calculation of Tw-Dependent 2DIR Spectra. Tw-dependent 2DIR spectra can be numerically calculated by using the response function formalism with input parameters based on diagrammatic perturbation theory.48,49 Kwak et al. have described the response function formalism with two-species chemical exchange kinetics and the numerical calculation of 2DIR spectra in great detail,50 which will be briefly outlined in this section. Tw-dependent 2DIR spectra measured with aqueous 5.0 M NaPF6 solution are numerically calculated in the following kinetic scheme, T1, τor , C FFCF

k WA

T1, τor , C FFCF

decay

kAW

decay

←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯OD W HoooI ODA ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→

[ODA ]eq [OD W ]eq

=

k WA kAW

(7)

(8)

where [ODW]eq and [ODA]eq are the equilibrium concentrations. Taking only the H-bond exchange between ODW and ODA into account, the differential rate equation can be written by23 ⎛ ⎞ 1 ⎜ c WW(Tw ) c WA(Tw )⎟ dTw ⎜⎝ cAW(Tw ) cAA(Tw ) ⎟⎠ ⎛−k WA kAW ⎞⎛ c WW(Tw ) c WA(Tw )⎞ ⎟ ⎟⎟⎜⎜ = ⎜⎜ ⎟ ⎝ k WA −kAW ⎠⎝ cAW(Tw ) cAA(Tw ) ⎠

k WA + kAW exp( −kexTw ) kex

cAA(Tw ) = [OD W ]eq

kAW + k WA exp( −kexTw ) kex

c WA(Tw ) = [ODA ]eq

k WA[1 − exp(−kexTw )] kex

cAW(Tw ) = [OD W ]eq

kAW[1 − exp(−kexTw )] kex

(10)

where kex = kWA + kAW is the exchange rate constant. In Twdependent 2DIR spectra, the cross-peaks grow with the exchange rate constant, kex = kWA + kAW. The numerical calculation includes all of the dynamical features that are observed in Tw-dependent 2DIR spectra. As Tw is increased, 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. Most prominently, the H-bond exchange causes the cross-peaks to grow in with increasing Tw. In the numerical calculation, it is assumed that the fluctuations of ODW and ODA follow Gaussian statistics (second-order cumulant approximation) and the transition dipole moment of the OD stretch does not depend on the frequency (Condon approximation). The harmonic approximation is used to scale the transition dipole moments, μ01 = √2μ12. In the kinetic scheme in eq 7, the vibrational lifetimes (T1) and orientational relaxation times (τor) for ODW and ODA were directly determined by polarization-controlled IR PP experiments and used as input parameters for the numerical calculations. Kubo terms were used to model the FFCF, CFFCF(t) = ∑iΔi2 exp(−t/τi) for both ODW and ODA. The first Kubo term in the FFCF represents the motionally narrow contribution for which τ1 = 0.1 ps was used. The center line slope (CLS) method was used to determine the time constants (τ2 and τ3) of the FFCF for ODW and ODA.3,29,51 With all predetermined parameters fixed, 2DIR spectra were numerically calculated to fit the experimental 2DIR spectra in Figure 4A by iteratively varying all other parameters such as the ratios of transition dipole moments (μ01,W/μ01,A) and equilibrium concentrations ([ODA]eq/[ODW]eq), H-bond exchange rate constants (k WA and k AW ), and Δ i in the FFCF. All predetermined and fitted parameters used for the response function calculations are summarized in Table 2. Mostly significantly, the forward and backward rate constants kWA−1 = τWA = 21.6 ± 2 ps for ODW → ODA and kAW−1 = τAW = 12.0 ± 1 ps for ODA → ODW were determined from the numerical calculations. In addition, the H-bond exchange rate constant was (kWA + kWA)−1 = τex = 7.7 ± 1 ps, which is associated with the time constant for the cross-peak growth in the Twdependent 2DIR spectra. Figure 4B displays the simulated 2DIR spectra with the best fit parameters (τex = 7.7 ps) which agree well with the experimental 2DIR spectra in Figure 4A. For comparison, the simulated 2DIR spectra without H-bond

where kWA and kAW are the forward and backward exchange rate constants, T1 and τor are the vibrational lifetime and orientational relaxation time, and CFFCF represents the frequency−frequency correlation function (FFCF) for ODW and ODA, respectively. The equilibrium constant is given by Keq =

c WW(Tw ) = [ODA ]eq

(9)

where cWW(Tw) and cAA(Tw) are the concentrations of the diagonal peaks, and cWA(Tw) and cAW(Tw) are the concentrations of the cross-peaks. The volumes of diagonal peaks and cross-peaks in Tw-dependent 2DIR spectra are directly associated with the concentrations that are determined by the two-species exchange kinetics in eq 9. The differential rate equation in eq 9 is analytically solved, 13610



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exchange (i.e., τex ≈ ∞) are shown in Figure 4C. It is clearly shown in Figure 4 that the cross-peaks in Tw-dependent 2DIR spectra are produced by the H-bond exchange processes in aqueous 5.0 M NaPF6 solution. E. Comparison with Previous Work. Prior to our current work, H-bond exchange dynamics were previously investigated in aqueous NaBF4 and NaClO4 solutions.22−24 In such aqueous ionic solutions, weakly H-bond accepting anions (i.e., BF4−, ClO4−, and PF6−) split the hydroxyl stretch band into two components associated with water−water (HOD···OH2) and water−anion (HOD···A−) H-bond configurations. The H-bond exchange time constants measured with three different aqueous ionic solutions are summarized in Table 3. First, it is

relatively slower in aqueous 5.0 M NaPF6 solution than in aqueous 5.5 M NaBF4 solution. The water molecule is more weakly bound to PF6− than BF4−, indicating that the energy difference between two H-bond configurations is larger in aqueous 5.0 M NaPF6 solution than aqueous 5.5 M NaBF4 solution. It is conceivable that the slower H-bond exchange time is associated with the potential energy curve for the Hbond exchange process. Recent molecular dynamics simulation studies suggest that the H-bond exchange should occur by orientational jump mechanisms in which a H-bond donor rotates by a large angle to exchange its H-bond acceptors by breaking and re-forming the H-bond in a concerted manner.18,20 As illustrated in Figure 6, a H-bond donor (HOD molecule) is simultaneously bound with two H-bond acceptors in a bifurcated structure on the transition state. In the orientational jump mechanism, the H-bond donor would exchange its H-bond acceptors most efficiently when the energy required for breaking the H-bond would be exactly matched by the energy released from the newly forming Hbond. In this sense, the H-bond exchange between water−water and water−water configurations in pure water would occur most efficiently in a symmetric double-well potential energy curve. On the other hand, the H-bond exchange between water−water and water−anion configurations in aqueous ionic solutions would be slower because it occurs in an asymmetric double-well potential energy curve. In this case, the energy required for H-bond breaking (HOD···OH2) is larger than the energy released from H-bond re-forming (HOD···A−) and vice versa. In addition to the H-bond strength between water and anion, the sizes and structures (octahedral vs tetrahedral) of the anions might be also important in determining the H-bond exchange dynamics in aqueous ionic solutions. Further systematic studies are required to provide deeper understanding of H-bond exchange dynamics in aqueous solutions.

Table 3. Comparison of H-Bond Exchange Time Constants Measured with Different Aqueous Ionic Solutions

NaBF4a NaClO4b NaPF6c a

peaks (cm−1)

concn (M)

τAW (ps)

τWA (ps)

τex (ps)

2526, 2646 2534, 2633 2530, 2668

5.5 6.0 5.0

7±1 9±2 12 ± 1

24 ± 3 17 ± 4 21.6 ± 2

5.4 ± 0.8 6±2 7.7 ± 1

Reference 22. bReference 23. cThis work.

worthwhile noting that τWA = kWA−1 is always larger than τAW = kAW−1 in three aqueous solutions in Table 3. This results from the fact that Keq = [ODA]eq/[ODW]eq = kWA/kAW < 1. In other words, water−water H-bond configuration is energetically more stable than water−anion H-bond configuration in three aqueous solutions, as illustrated in Figure 6. The activation

IV. SUMMARY AND CONCLUDING REMARKS In this work, we have studied the H-bond structures and dynamics in aqueous NaPF6 solution by FTIR, IR PP, and 2DIR spectroscopies. Concentration-dependent FTIR spectroscopy combined with the quantum chemical calculations has revealed that there are two spectrally distinct H-bond configurations in aqueous NaPF6 solutions. The broad lowfrequency peak results from water molecules that are H-bonded to other water molecules (ODW), while the relatively narrow high-frequency peak comes from water molecules that are Hbonded to PF6− (ODA). Vibrational population relaxation and orientational relaxation dynamics of waters in two distinct Hbond configurations were investigated by IR PP experiments. The vibrational lifetime of water molecules around PF6− (ODA) was almost three times longer than that of water molecules that are H-bonded to other water molecules. The orientational anisotropy decays of ODW and ODA were well-described by a biexponential function and were found to be much longer than that of pure water. Most importantly, we successfully measured H-bond exchange dynamics in aqueous NaPF6 solution in real time by 2DIR spectroscopy and determined the H-bond exchange time constant to be τex = 7.7 ± 1 ps, which was found to be longer than the H-bond exchange time constants in aqueous NaBF4 and NaClO4 solutions. As shown here, aqueous PF6− solution is an excellent model system because the two hydroxyl stretch bands are spectrally well-separated (∼140 cm−1 apart) so that their H-bond dynamics can be distinctly studied. This fact provides a great

Figure 6. Schematic potential energy curve in the H-bond exchange process between HOD−water and HOD−anion (denoted A−). On the transition state, a HOD molecule (H-bond donor) is bound with water and anion (two H-bond acceptors) in a bifurcated structure at the same time.

barrier for the forward H-bond exchange process (ODW → ODA) is higher than that for the backward H-bond exchange process (ODA → ODW), and thus τWA > τAW. Second, it is clearly seen from Table 3 that the H-bond exchange time constants are dependent on anions. Direct comparison of the results from three aqueous solutions in Table 3 may not be quite correct because H-bond exchange dynamics in aqueous solutions are known to be dependent on the concentration of salts, temperature, solution viscosity, and so on. However, one possible explanation should be given by comparing aqueous 5.0 M NaPF6 and 5.5 M NaBF4 solutions because both aqueous solutions have similar concentrations and fluorinated anions. In Table 3, the H-bond exchange dynamics are found to be 13611



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(15) Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. J. Negligible Effect of Ions on the Hydrogen-Bond Structure in Liquid Water. Science 2003, 301 (18), 347−349. (16) Steinel, T.; Asbury, J. B.; Zheng, J.; Fayer, M. D., Watching Hydrogen Bonds Break: A Transient Absorption Study of Water. J. Phys. Chem. A 2004, 108 (50). (17) Rezus, Y. L. A.; Bakker, H. J. On the Orientational Relaxation of HDO in Liquid Water. J. Chem. Phys. 2005, 123, 114502. (18) Laage, D.; Hynes, J. T. A Molecular Jump Mechanism of Water Reorientation. Science 2006, 311, 832−835. (19) Piletic, I.; Moilanen, D. E.; Spry, D. B.; Levinger, N. E.; Fayer, M. D. Testing the Core/Shell Model of Nanoconfined Water in Reverse Micelles Using Linear and Nonlinear IR Spectroscopy. J. Phys. Chem. A 2006, 110, 4985−4999. (20) Laage, D.; Hynes, J. T. Reorientational dynamics of water molecules in anionic hydration shells. Proc. Natl. Acad. Sci. U. S. A. 2007, 104 (27), 11167−11172. (21) Levinger, N. E.; Swafford, L. A. Ultrafast Dynamics in Reverse Micelles. Annu. Rev. Phys. Chem. 2009, 60, 385−406. (22) Moilanen, D. E.; Wong, D.; Rosenfeld, D. E.; Fenn, E. E.; Fayer, M. D. Ion−water hydrogen-bond switching observed with 2D IR vibrational echo chemical exchange spectroscopy. Proc. Natl. Acad. Sci. U. S. A. 2009, 106 (2), 375−380. (23) Park, S.; Odelius, M.; Gaffney, K. J. Ultrafast dynamics of hydrogen bond exchange in aqueous ionic solutions. J. Phys. Chem. B 2009, 113, 7825−7835. (24) Ji, M.; Odelius, M.; Gaffney, K. J. Large Angular Jump Mechanism Observed for Hydrogen Bond Exchange in Aqueous Perchlorate Solution. Science 2010, 328, 1003. (25) Nicodemus, R. A.; Ramasesha, K.; Roberts, S. T.; Tokmakoff, A. Hydrogen Bond Rearrangements in Water Probed with TemperatureDependent 2D IR. J. Phys. Chem. Lett. 2010, 1, 1068−1072. (26) Woutersen, S.; Emmerichs, U.; Bakker, H. J. Femtosecond midIR pump−probe spectroscopy of liquid water: Evidence for a twocomponent structure. Science 1997, 278, 658−660. (27) Lawrence, C. P.; Skinner, J. L. Ultrafast infrared spectroscopy probes hydrogen-bonding dynamics in liquid water. Chem. Phys. Lett. 2003, 369, 472. (28) Tan, H.-S.; Piletic, I. R.; Fayer, M. D. Orientational dynamics of water confined on a nanometer length scale in reverse micelles. J. Chem. Phys. 2005, 122, No. 174501(9). (29) Park, S.; Moilanen, D. E.; Fayer, M. D. Water Dynamics: The Effects of Ions and Nanoconfinement. J. Phys. Chem. B 2008, 102, 5279−5290. (30) Cowan, M. L.; Bruner, B. D.; Huse, N.; Dwyer, J. R.; Chugh, B.; Nibbering, E. T. J.; Elsaesser, T.; Miller, R. J. D. Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O. Nature 2005, 434, 199. (31) Laage, D.; Stirnemann, G.; Sterpone, F.; Rey, R.; Hynes, J. T. Reorientation and Allied Dynamics in Water and Aqueous Solutions. Annu. Rev. Phys. Chem. 2011, 62, 395−416. (32) Ji, M.; Gaffney, K. J. Orientational relaxation dynamics in aqueous ionic solution: Polarization-selective two-dimensional infrared study of angular jump-exchange dynamics in aqueous 6M NaClO4. J. Chem. Phys. 2011, 134 (4), 044516. ́ (33) Smiechowski, M.; Gojło, E.; Stangret, J. Ionic Hydration in LiPF6, NaPF6, and KPF6 Aqueous Solutions Derived from Infrared HDO Spectra. J. Phys. Chem. B 2004, 108, 15938−15943. (34) Stangret, J.; Gampe, T. Ionic Hydration Behavior Derived from Infrared Spectra in HDO. J. Phys. Chem. A 2002, 106, 5393−5402. (35) Kim, H.; Park, S.; Cho, M. Rotational dynamics of thiocyanate ions in highly concentrated aqueous solutions. Phys. Chem. Chem. Phys. 2012, 14, 6233−6240. (36) Zheng, J.; Kwak, K.; Fayer, M. D. Ultrafast 2D IR vibrational echo spectroscopy. Acc. Chem. Res. 2007, 40, 75−83. (37) Park, S.; Kwak, K.; Fayer, M. D. Ultrafast 2D-IR vibrational echo spectroscopy: A probe of molecular dynamics. Laser Phys. Lett. 2007, 4, 704−718.

advantage for studying the H-bond dynamics in a wide range of aqueous environments. Currently, we are also investigating other aqueous solutions, such as reverse micelles, nanoscopic water channels, and hydrothermal solutions.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korean government (MEST) (Grant Nos. 2013R1A1A2009991, 20110002122, 20110020033, and 20100020209) and the KETEP Grant (No. 20104010100640) to S.P.

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ABBREVIATIONS FTIR, Fourier transform infrared; IR PP, infrared pump− probe; 2DIR, two-dimensional infrared REFERENCES

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Real-Time Probing of Hydrogen-Bond Exchange Dynamics in

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