Article pubs.acs.org/JPCB
Hydration Dynamics of Cyanoferrate Anions Examined by Ultrafast Infrared Spectroscopy Pengyun Yu,†,‡,§ Fan Yang,†,§ Juan Zhao,† and Jianping Wang*,† †
Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Molecular Reaction Dynamics, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China ‡ University of Chinese Academy of Sciences, Beijing 100049, P. R. China ABSTRACT: In this work, we carried out steady-state IR absorption, transient IR pump−probe, and waiting-time-dependent two-dimensional (2D) IR measurements on ferrocyanide and ferricyanide ions solvated in water and deuterated water. These two anions are highly symmetric and have distributed cyano groups with IR-active stretching modes in the 5 μm wavelength region. The line width of their linear IR spectra and the initial value of the vibrational frequency−frequency correlation function extracted from their 2D IR spectra indicate water molecules in the hydration shell of the ferro-species are more inhomogeneously distributed but more tightly bound to the cyano groups than those of the ferri-species. Different charges and their distributions in the two anions cause different hydrogen bonding strengths with solvent. The frequency correlation relaxes somewhat slower in ferrocyanide, agreeing with stronger solute−solvent hydrogen-bonding interaction in this case. Mechanisms of the solvent isotope effect on the vibrational relaxation dynamics of the cyano stretching mode are discussed. These results also suggest that in the hydration shell the ferro-species breaks more water structure than the ferri-species, which is opposite to the situation of the bulk water region (beyond the hydration shell) reported previously. This work demonstrated that combined IR methods can be very useful for understanding the molecular details of the structure and dynamics of the hydrated ions.
1. INTRODUCTION In aqueous solutions, ions are hydrated. The interactions between ions and water are two-fold:1 on one hand, the electrostatic field due to the ions causes the rearrangement of nearby dipolar water molecules to form the hydration layer; on the other hand, such a hydrated complex can further exert longrange influences on bulk water, leading to well organized or less organized water structures. Ions causing more structured or less structured bulk water are thus termed as water “structure maker” or “structure breaker”.2 Small and multiply charged ions are believed to be structure makers, while large, monovalent ions are believed to be structure breakers.3 Thus, understanding the hydration structure of ions is a crucial prerequisite for understanding the effect of the hydrated ions on bulk water. Conventionally, information on the structure of the ionic hydration layer has been obtained mainly by static X-ray and neutron diffraction measurements.4 The hydration structure of ions is usually described in terms of the first neighbor ion− water distances and the number of nearest neighbor water molecules around the ions. Because water molecules in the hydration shell of ions are constantly exchanging with those in the bulk, the knowledge of the dynamical aspect of the hydration shell is particularly important.4 Such knowledge is also relevant to the water-structure-breaking or -making abilities of ions. One way to address this is to examine the solute and solvent interactions in real time.3 The dynamics of ionic © 2014 American Chemical Society
hydration can be examined using conventional methods. For example, NMR spectroscopy has been used to determine rotational correlation times of water molecules in the hydration shell of ions.5 However, because the dynamics of water and ions occur on the picosecond time scale, structural methods with ultrafast time resolutions are needed. In recent years, timeresolved infrared spectroscopy including two-dimensional infrared (2D IR) has been used to unravel the ultrafast structural dynamics of ionic hydration.6−9 In particular, several case studies were presented and the results suggested that the reorientation dynamics of water molecules in the ionic hydration layer and those in the bulk are very similar.8,10−13 Frequency response of ions can be correlated with the structural dynamics in the solvation shell.14 This is because the ion solvation process must involve solvent reconfiguration (deformation vibrations and rotations),3 which can be reflected by the frequency response of the ion. Femtosecond polarized infrared pump−probe spectroscopy can yield vibrational relaxation dynamics, as well as anisotropy dynamics. The 2D IR method can yield the molecular details of the vibrational frequency of given IR vibrators, particularly in terms of the frequency−frequency correlation functions. In the past decade, Received: October 27, 2013 Revised: February 27, 2014 Published: February 28, 2014 3104
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used to generate a 70 fs, 5 μJ mid-IR pulse by differencefrequency-mixing in a 0.5 mm thick type-II AgGaS2 nonlinear crystal. The obtained IR pulse was tuned to a center frequency at 2050 cm−1 with a fwhm of ca. 250 cm−1. The mid-IR pulse was then split into three excitation beams (ca. 400 nJ each) for the 2D IR experiment and a weak beam (local oscillator, LO) for heterodyne detection. The delay time between the first and second pulses (k1 and k2) is the coherence time (τ), and that between the second and third pulses is the waiting time (T). The three excitation pulses were focused on the solution sample by a parabolic mirror with 100 mm focal length, and the emitted photon echo signal was detected in the −k1 + k2 + k3 phase-matching direction. Four laser pulses were set to vertical polarization for parallel 2D IR measurement (denoted as zzzz). An IR monochromator equipped with a 64-element liquidnitrogen-cooled mercury−cadmium−telluride array detector was used to collect the 2D IR signal using the spectral interferometry approach. Numerical Fourier transform (FT) along the τ-axis yielded the frequency domain 2D IR spectra. In the 2D IR experiments, τ was scanned typically in a 2 ps time window at a step of 5 fs, for a fixed T. A series of T-dependent 2D IR spectra were collected. The projection of the 2D IR spectra on the detection frequency, in comparison with the IR pump−probe signal that was collected using k3 (pump) and an attenuated k1 (probe), was used for the 2D IR spectral phasing. Equally weighted rephasing (−k1 + k2 + k3) and non-rephasing (+k1 − k2 + k3) 2D IR spectra yield the so-called pure absorptive spectra. The vibrational population relaxation time constants were measured with the femtosecond IR pump−probe experiment at the magic angle (54.7°) condition. A perpendicular polarization pump−probe experiment was also carried out in order to obtain the anisotropy signal: r(T) = 1 − S⊥(T)/SM(T). Data acquisition steps were 100 fs in H2O and 300 fs in D2O. All nonlinear IR measurements were carried out at room temperature (22 °C). 2.3. Quantum Chemical Calculations. The vibrational properties of [Fe(CN)6]3− and [Fe(CN)6]4− in the gas phase were examined at the level of the density functional theory (DFT) using Gaussian 09.46 The calculations were performed using the B3LYP functional with the 6-31+G(d) basis set for carbon and oxygen and the lanl2dz pseudopotential for iron. The first hydration layer was added to the anions by randomly coordinating 12 water molecules to each anion. Harmonic transition frequencies and transition intensities for these systems were obtained for the cyano (CN) stretching mode. In addition, natural population analysis (NPA)47 was used to calculate atomic charges and orbital populations of the molecular wave function based on the construction of a set of natural atomic orbitals (NAOs).
these nonlinear IR spectroscopies have proved to be very useful structural methods for condensed-phase molecular structures and dynamics.15−36 The structural and dynamical sensitivities of the 2D IR method lie in its ability to obtain a series of diagonal and off-diagonal 2D peaks in a compact two-frequency plot, from which one can derive the frequency−frequency time correlations out of the diagonal and off-diagonal signals.37 Coordinating compounds often have several identical ligands that are IR active. The unique chemical composition and structure of such compounds enable them to serve as distributed structural probes for solvent22,36,38 and protein local environment.39,40 In particular, ferrocyanide ([Fe(CN)6]4−) and ferricyanide ([Fe(CN)6]3−) are two coordinating complexes with identical chemical composition and similar octahedral structure (Oh geometry with a central iron atom) but different charges. They are believed to be two chaotropic anions with the ability to break water structure.1 However, a subtle difference exists between the two anions in their waterstructure-breaking abilities, with that of [Fe(CN)6]3− being slightly stronger.1,41 Even though the vibrational lifetimes and rotational dynamics of these two anions in aqueous solutions have been examined in recent years,42−44 the structures of their hydration shells in light and heavy water are not fully understood. In this work, we examined the hydration dynamics of [Fe(CN)6]4− and [Fe(CN)6]3− solvated in H2O and D2O by means of steady-state linear IR and time-resolved nonlinear IR methods. The vibrational frequency distributions of the CN stretching modes were first examined via linear IR spectroscopy. Vibrational and rotational dynamics of the CN stretching modes in the two anions were then examined by polarized IR pump−probe experiments. Spectral diffusion dynamics was investigated by waiting-time-dependent 2D IR experiments. Quantum chemistry computations were carried out to obtain molecular details of the hydration structures of the two anions. The isotope effect on linear IR and 2D IR spectra and on the extracted hydrational and structural dynamics for the ferro- and ferri-species was discussed.
2. MATERIALS AND METHODS 2.1. Sample Handling and FT-IR Measurement. Potassium ferricyanide K3Fe(CN)6 was purchased from Sigma-Aldrich and used as received. The compound was dissolved into H2O or D2O at a concentration of ca. 0.58 M. Hydrated potassium ferrocyanide (K4Fe(CN)6·3H2O) was purchased from Sinopharm Chemical and heated up to 75 °C for 0.5 h for dehydration. The dehydrated compound was dissolved into H2O or D2O at a concentration of ca. 0.075 M. Then, the solutions of K3Fe(CN)6 and K4Fe(CN)6 in H2O were mixed at a 1:1 volume ratio, with final concentrations set to ca. 0.29 and 0.038 M, respectively. The mixed sample solution in D2O was prepared similarly. The sample solutions were contained between two 25 mm diameter 2 mm thick CaF2 windows separated by a 6 μm spacer. FT-IR spectra were collected using a Nicolet 6700 spectrometer (Thermo Electron) at 1 cm−1 resolution. All experiments were performed at room temperature (22 °C). 2.2. 2D IR Experiments. A home-built 2D IR spectrometer45 was used to collect 2D IR spectra. Briefly, a commercial ultrafast Ti:sapphire laser amplifier which generated a 3 mJ, sub-35 fs, 800 nm pulse at a repetition rate of 1 kHz was used to pump an optical parametric amplifier (OPA). The signal and idler pulses in the near IR region produced by the OPA were
3. RESULTS 3.1. Linear IR Spectra and Band Assignment. Shown in Figure 1 is the linear IR (FT-IR) absorption spectra of the [Fe(CN)6]4− and [Fe(CN)6]3− anions in the cyano stretch region in H2O and D2O, respectively. The inset of Figure 1 shows the optimized structure of [Fe(CN)6]4−. The structure of [Fe(CN)6]3− is similar. Here two anions are dissolved together in one solvent at a time. The observed IR band comes from the triply degenerate (T1u) CN stretches.48 It is noted that the band of ferrocyanide is broader than that of ferricyanide in both H2O and D2O. The ferro-species appears at ca. 2039.0 cm−1 with a full width at half-maximum (fwhm) of 3105
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3.2. Magic-Angle Pump−Probe Spectra. The magicangle pump−probe spectra of the [Fe(CN)6]4− and [Fe(CN)6]3− anions in the cyano stretch region in H2O (upper panels) and D2O (lower panels), respectively, are shown in Figure 2. These spectra were presented in identical frequency scale to show proportional spectral line widths. Here the highfrequency signals (red) arise because of vibrational ground-state bleaching (v = 0 → 1, where v is the vibrational quantum number), while the low-frequency signals (blue) arise because of the first excited-state absorption (v = 1 → 2). These transient signals appear at different frequency positions because of anharmonicity; i.e., the energy gap of the 1 → 2 is less than that of the 0 → 1 transition. These signals decay as a function of the delay time between the pump and probe pulses, and relax faster in H2O than in D2O, clearly showing the solvent isotope effect. This is found to be true for both anions. At a given frequency position, the kinetic trace under the magic-angle condition can be obtained to evaluate the population relaxation time constant without the influence of orientational contributions. The results are given in Figure 3 for the [Fe(CN)6]4− and [Fe(CN)6]3− anions solvated in H2O (upper panels) and D2O (lower panels), respectively. They are the vibrational bleach recoveries probed at the peak positions of the 0 → 1 transitions. The obtained vibrational lifetime parameters in terms of double exponentials are listed in Table 3. Clearly, each curve can be fitted reasonably well using two time constants, suggesting two-component characteristics of the vibrational population relaxation process for the cyano stretching mode. The measured vibrational lifetimes from previous studies using either the magic-angle pump−probe44 or transient grating method42,43 are also shown in Table 3 for comparison. It is seen that our results are in general agreement with previous measurements with two fitting components. However, we also find that one-exponential decay can also roughly fit the relaxations (data not shown), as also was reported in certain cases (Table 3). In addition, the variation of the measured values listed in Table 3 from different laboratories is also noted, which is probably due to the application of different methods. Our results are generally more close to the one-component fitting results,44 which were also obtained by using the pump−probe method. A detailed discussion on the vibrational relaxation is given in section 4.2. 3.3. Anisotropic Measurement. The anisotropies r(T) of the [Fe(CN)6]4− and [Fe(CN)6]3− anions in the cyano stretch region in H2O (upper panels) and D2O (lower panels), respectively, are shown in Figure 4. They are computed at the same frequency position as the vibrational population relaxation dynamics shown in Figure 3. The anisotropy trace in each case starts roughly at 0.4 and decays within a few ps. The results of single-exponential decay fitting in each case are listed in Table 4. Values from previous studies are also listed for comparison. It seems that [Fe(CN)6]4− rotates only slightly faster than [Fe(CN)6]3−, which is found to be the case in both solvents. Such a charge-dependent anisotropy is similar to what has been
Figure 1. Linear IR spectra of the CN stretch of [Fe(CN)6]4− (left peak) and [Fe(CN)6]3− (right peak) in H2O and D2O. The inset shows the structure of [Fe(CN)6]4−.
15.9 cm−1 in both H2O and D2O, while the ferri-species appears at 2115.6 cm−1 with a fwhm of 7.7 cm−1 in H2O and 8.2 cm−1 in D2O. The overall spectral profile of the ferri-species appears to be a Lorentzian function, while that of the ferro-species appears to be a Gaussian function. Spectral fitting parameters are given in Table 1. Because the concentration of ferricyanide is roughly 7 times higher than that of ferrocyanide in both solvents, the ratio of the transition dipole strength of ferrocyanide to ferricyanide is determined to be ca. 7.2:1, using integrated IR peak area. This means that the ferro-species has a much stronger transition dipole for the cyano stretch. The difference in the transition dipole strength of the cyano stretch in ferri- and ferro-species has been observed earlier by Drew.49 Such a difference is caused by the charge of ferro- versus ferri-ions, as well as by the quadrupole interactions, as has been explained by Stanghellini.50 In addition, for each species, the solvent isotope effect on the IR absorption profile is not significant: there is only slight broadness in D2O as compared with H2O in the case of ferricyanide and only slight red shift of the peak position in D2O with respect to H2O in the case of ferrocyanide. Table 2 lists the harmonic vibration transition frequencies and intensities of the six CN stretches in each case. The gasphase results show that the two anions have Oh symmetry and exhibit a triply degenerate T1u mode that is IR active as expected. The order of frequency for the two species by ab initio computations is in agreement with the IR experimental observation. Because experimentally one observes three IRactive T1u modes in linear IR together, we compute the sum of transition dipoles of the three degenerate transitions by using the equation51 |Δμ| = (0.3989 × I /ω)1/2 , where I and ω are the transition intensity and frequency, respectively (see Table 2). The computed transition dipole moment of the two species is found to be 0.59 and 0.26 D, respectively, with a dipole strength ratio of 5.1, which is in general agreement with the measured ratio from the FTIR experiments (7.2 in both D2O and H2O).
Table 1. Fitting Parameters of the Linear IR Spectra of the CN Stretch of [Fe(CN)6]4− and [Fe(CN)6]3− in H2O and D2O solute 4−
[Fe(CN)6]
[Fe(CN)6]3−
solvent
area
fwhm (cm−1)
peak (cm−1)
height
concentration (M)
H2O D2O H2O D2O
3.01 3.04 3.39 3.31
15.9 15.9 7.7 8.2
2039.4 2038.9 2115.6 2115.6
0.15 0.15 0.33 0.33
0.038 0.038 0.29 0.29
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Table 2. Transition Frequencies (ωi, in cm−1) and Transition Intensities (I, in km/mol) of the Six Harmonic CN Stretching Vibrations in [Fe(CN)6]3− and [Fe(CN)6]4− in the Gas Phase ωi I ωi I
[Fe(CN)6]3− [Fe(CN)6]4−
T1u
T1u
T1u
Eg
Eg
A1g
2182.2 198.3 2086.5 597.8
2182.5 84.0 2086.5 597.8
2182.5 84.0 2086.5 597.8
2183.5 0 2088.9 0
2185.1 0 2088.9 0
2194.2 0 2116.3 0
excitation absorption (v = 1 → 2 transition). The relationship between 2D IR and pump−probe spectra is that the projection of a 2D IR spectrum at a certain waiting time T along the detection frequency (ωt) is equivalent to a pump−probe spectrum at the same delay time between the pump and probe pulses. Similarly as in pump−probe spectra, the 1 → 2 transition in a 2D IR spectrum appears to be shifted along the ωt axis due to vibrational anharmonicity. The data of [Fe(CN)6]4− and [Fe(CN)6]3− in each solvent were collected simultaneously but plotted independently in Figures 5 and 6 in proper spectral windows. There are a few important observations from the 2D IR results. First, it is observed that the overall 2D IR spectral features of the [Fe(CN)6]4− ion solvated in H2O and D2O are quite similar at identical T times (Figure 5). This is also true for the [Fe(CN)6]3− ion solvated in H2O and D2O (Figure 6). In other words, the solvent isotope effect on the 2D IR line shape is insignificant, which agrees with FTIR results shown in Figure 1. Second, it is observed that the 2D IR signals are elongated along the diagonal at small T values, in both Figures 5 and 6. Such an elongation is a demonstration of the presence of the inhomogeneous broadening in the line width. The elongated 2D IR spectra at early T times indicate a larger degree of frequency−frequency correlation between pairs of vibrational transition frequency distributions. As T increases, the 2D signals become more vertically tilted for both the 0 → 1 and 1 → 2 transitions due to the well-known vibrational spectral diffusion. At very long T times, the correlation between pairs of vibrational frequencies would diminish. The change of the shape of the joint distribution between pairs of vibrators as a function of the T time can be used to extract frequency− frequency correlation functions (see below). 3.5. Spectral Diffusion. From the line shape analysis, one can quantify the degree of elongation of the 2D IR signal and how the elongation evolves as a function of T. To this end, we utilized an approach proposed by Tokmakoff and co-workers52 and used by other research group.39 Waiting-time-dependent rephasing and non-rephasing 2D IR spectra were used to compute the inhomogeneity index that is defined as
Figure 2. Time-resolved pump−probe spectra of [Fe(CN)6]4− (left) and [Fe(CN)6]3− (right) in the CN stretching region in H2O (upper) and in D2O (lower).
Figure 3. Population relaxation dynamics and exponential decay fitting for [Fe(CN)6]4− (left, at 2039 cm−1) and [Fe(CN)6]3− (right, at 2116 cm−1) in the CN stretching region in H2O (a and c) and in D2O (b and d). The probing frequency positions are marked by dashed lines in Figure 2.
C(T ) =
44
A re − A nr A re + A nr
(1)
Here, Are and Anr refer to the absolute values of frequencydomain rephasing and non-rephasing 2D IR spectra, respectively. The values of Are and Anr can be either the integration of the entire rephasing and non-rephasing 2D IR spectra39,52 or only a small integrated area centered at the peak position. In the present work, for the ferro-species, a small square centered at the peak position (ωt = 2034 cm−1 and ωτ = 2039 cm−1) with side length set to the fwhm (16 cm−1, obtained from the FTIR spectrum) is used. For the ferrispecies, the peak position is ωt = 2106 cm−1 and ωτ = 2116 cm−1 and the fwhm is 8 cm−1. Because the ferro- and ferrispecies were solvated in the same solvent, we were able to
seen previously. This can be explained by a relatively tight and compact solvation layer of the [Fe(CN)6]4− anion, as suggested by the quantum chemistry computations (see below). 3.4. Waiting-Time-Dependent 2D IR Spectra. Figures 5 and 6 display the absorptive 2D IR spectra of [Fe(CN)6]4− and [Fe(CN)6]3− in the CN stretching region in H2O and D2O, respectively, at selected waiting times. The observed 2D IR signal comes from the triply degenerate (T1u) CN stretches. There are two peaks in each spectrum: the positive (red) peak arises from vibrational ground-state bleaching (v = 0 → 1 transition), and negative (blue) peaks arise from the first 3107
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Table 3. Vibrational Lifetime and Relative Amplitude (in Parentheses) Extracted as Double Exponential Functions for [Fe(CN)6]4− and [Fe(CN)6]3− in the CN Stretching Region in H2O and D2O, Probed Using the Vibrational Ground-State Bleaching Signalsa [Fe(CN)6]4−
[Fe(CN)6]3−
1
T12
solvent
T1 (ps)
H2O
1.2 ± 0.1 (32.3%)
D2O
0.60 (20%)c 2.0 ± 0.1 (11.5%) 0.70 (27%)d
T11
(ps)
5.5 ± 0.1 (67.7%) 4.4 ± 1b 3.7 (80%)c 30.0 ± 0.1 (88.5%) 24 ± 3b 23.0 (73%)d
(ps)
T12 (ps)
0.9 ± 0.1 (32.3%)
7.3 ± 0.2 (67.7%) 7.0 ± 1b
2.6 ± 0.3 (33.3%)
12.1 ± 0.4 (66.7%) 8.0 ± 1.5b
Results from previous works are also listed for comparison. The probe frequency is set to 2039 cm−1 for [Fe(CN)6]4− and 2116 cm−1 for [Fe(CN)6]3−. bResults from ref 44. cResults from ref 43. dResults from ref 42.
a
frequency distribution is a straight line along the diagonal, while a completely uncorrelated case is a 2D Gaussian random distribution. From Figure 7 and Table 5, it is clear that there is more inhomogeneous contribution in the case of ferrocyanide than in the case of ferricyanide, in both H2O and D2O. The initial values of C(T) are ca. 0.25−0.32 for the ferro-species and ca. 0.15−0.20 for the ferri-species. However, because of the limitation of the method, there are fluctuations in the obtained C(T) values. This makes it difficult to ascertain the isotope effect on the C(T) curves. On the other hand, judging from the 2D IR spectra shown in Figure 5 or 6, the solvent isotope effect on the 2D IR line shape is not obvious either. As for the dynamics, it is seen that the C(T) relaxes with a time constant of ca. 1.6 ps for the ferrocyanide anion case in both H2O and D2O. The C(T) relaxes somewhat faster (1.1− .5 ps) in the case of ferricyanide anion solvated in both solvents within experimental errors. The relaxation time constant of the FFCF can be used to differentiate the solute−solvent interactions for the ferro- and ferri-species. Longer FFCF relaxation time implies stronger solute−water interactions, meaning tighter solvation layers. This is probably the case of ferrocyanide. In the ferri-species, the anion−water interaction is not as strong as that in the ferro-species, thus causing faster memory loss.
Figure 4. Anisotropy dynamics and resulting fits of ferrocyanide and ferricyanide: (a) ferrocyanide in H2O; (b) ferrocyanide in D2O; (c) ferricyanide in H2O; (d) ferricyanide in D2O.
Table 4. Single-Exponential Parameters for the Anisotropic Dynamics for [Fe(CN)6]4− and [Fe(CN)6]3− in the CN Stretching Region in H2O and D2O, Probed at Their IR Absorption Peak Positions Indicated in Figure 2 solute Fe(CN)6
4−
Fe(CN)63−
a
solvent
Aa
H2O
0.33
D2O
0.18
H2O
0.31
D2O
0.32
τ (ps) 3.0 ± 2.1 ± 2.0c 2.8 ± 1.9 ± 2.6d 3.1 ± 3.3 ± 3.8 ± 4.0 ±
0.1 0.5b 0.1 0.5b
4. DISCUSSION 4.1. Hydration Structures. The Gaussian line shape of the linear IR spectra for the ferro-species strongly suggests a more inhomogeneous environment around the anion, which implies a weaker interaction between cyano groups and water molecules, thus a loosely organized hydration layer. Quantum chemistry computations are used to reveal molecular details of the hydration. Figure 8 shows a comparison of the two anions interacting with 12 water molecules; however, for simplicity, it only focuses on one ligand branch interacting with one water molecule. The bond lengths of the FeC, CN, and N···H bonds are listed. The bond lengths of FeC and CN in the absence of the water cluster are also listed for comparison. Table 6 lists the NPA charges for gas-phase [Fe(CN)6]4− and [Fe(CN)6]3−. The NPA analysis shows that, because of ligandto-metal charge transfer in these two hexacyanometalate complexes, the originally positively charged iron atoms (Fe(II) and Fe(III)) and six negatively charged cyanide groups change their atomic partial charges. However, overall the atoms in ferrocyanide are either higher in positive charge (C) or higher in negative charge (Fe and N) than those in ferricyanide. Using the computed bond lengths shown in Figure 8, the size of the ferro-species (assumed to be spherical) in the gas phase is
0.3 0.5b 0.6 0.5b
Amplitude from fitting. bResults from ref 44. cResults from ref 43. Results from ref 42.
d
compute the inhomogeneous indices for the two species from the same 2D IR data set. The results are given in Figure 7, and their fittings with a single-exponential decay function are listed in Table 5. The values obtained earlier are also listed in Table 5. The inhomogeneous index is a measure of the frequency− frequency correlation functions (FFCF) of the transitions involved, which is a quantitative description of the vibrational spectral diffusion.53 The inhomogeneous index is an approximation of the FFCF under moderate inhomogeneous broadening conditions.52 This is because the nature of the 2D IR spectra is a manifestation of joint frequency distributions and the inhomogeneous index can reflect the change of the joint distributions. For example, a completely correlated joint 3108
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Figure 5. Waiting-time-resolved absorptive 2D IR spectra of the CN stretch of [Fe(CN)6]4− in H2O (upper) and in D2O (lower). The spectral window is [ωt = 1975−2080 cm−1 and ωτ = 2000−2080 cm−1]. Diagonal lines are shown in each panel. 2D IR spectra are intensity normalized.
Figure 6. Waiting-time-resolved absorptive 2D IR spectra of the CN stretch of [Fe(CN)6]3− in H2O (upper) and in D2O (lower). The spectral window is [ωt = 2070−2140 cm−1 and ωτ = 2095−2135 cm−1]. Diagonal lines are shown in each panel. 2D IR spectra are intensity normalized.
Table 5. Fitting Parameters for the Inhomogeneous Indices by Single-Exponential Function for the CN Stretching of [Fe(CN)6]4− and [Fe(CN)6]3− Solvated in H2O and D2Oa solute [Fe(CN)6]
4−
solvent
C(0)
H2O
0.25
τSD1 (ps) 0.08b
D2O
0.33 0.08b
[Fe(CN)6]3−
H2O D2O
0.15 0.20
τSD2 (ps) 1.6 ± 1.4b 1.6 ± 1.5b 1.1 ± 1.5 ±
0.2 0.2 0.4 0.2
a
Values of FFCF dynamics from the literature are also listed for comparison. bResults from ref 43.
Figure 7. Inhomogeneous indices and their fits of ferrocyanide and ferricyanide in the CN stretching region: (a) ferrocyanide in H2O; (b) ferrocyanide in D2O; (c) ferricyanide in H2O; (d) ferricyanide in D2O.
energy in H2O to be −10.4 and −6.9 kcal/mol for the ferroand ferri-species, respectively; both are, however, quite stronger than that in pure water (−3.9 kcal/mol, estimated from a water dimer, which is nearly a factor of 2 of the typical value of bulk water, −1.9 kcal/mol54,55). Although our calculated results are not properly scaled, they reveal the relative hydrogen-bond strengths in the two hydrated anions. The result indicates that because the net charge in the ferro-species (4−) is larger than that in the ferri-species (3−), even though the charge is distributed, as shown in Table 6, the first solvation layer is more
estimated to be only 5% larger than that of the ferri-species, and the size difference between two anions becomes negligibly small upon solvation. However, the ionic hydrogen-bond length (N···H) is clearly shorter in the ferro-species, and the associated water molecule is more polarized (larger OH bond length and smaller HOH angle). Computations at the same level yield the average N···H hydrogen bonding stabilization 3109
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species. Thus, the water molecules in the hydration shell of the ferro-species are more tightly bound and more inhomogeneously arranged. Electrolytes may exist as dissociated ions that are hydrated when dissolved in water. Thus, water molecules in the hydration shell(s) could be structurally different from those beyond the hydration shell, i.e., the bulk water. The difference of the ferro- and ferri-species in terms of their abilities to affect the bulk water structure has been examined previously.1,41 Steady-state estimation of the average number of hydrogen bonds from light to heavy water (i.e., from H2O to D2O) has been carried out. It was found that [Fe(CN)6]4− and [Fe(CN)6]3− are weak water-structure breakers, with the latter being slightly stronger. While it is generally agreed that the water structure in the hydration shell of an ion will be altered from that of the bulk, our results suggest that water molecules in the hydration shell are less organized in the case of the ferrospecies than the ferri-species. This means that in the hydration shell, instead of the ferri-species, it is the ferro-species that breaks more water structure, which is different from the situation of the bulk. 4.2. Vibrational Relaxations. In polyatomic systems, the vibrational relaxation of an excited solute mode generally undergoes two steps, an intramolecular energy transfer process that is usually very rapid plus an intermolecular energy dissipation process that is relatively slow. This can be regarded as a “two-step vibrational relaxation” in general. For the cyano stretching mode of [Fe(CN)6]4− and [Fe(CN)6]3− in H2O and in D2O, the vibrational relaxation indeed shows a fast component and a slow component in each case (Figure 3 and Table 3). The origin of the fast-decaying component in the case of [Fe(CN)6]4− in H2O and in D2O has been discussed extensively.42 It involves population equilibration between the IR-active T1u mode and the Raman-active Eg and A1g modes, which is an intramolecular process. The finite energy splitting among these modes can be seen in Table 2. In polyatomic systems, if the vibrational lifetime of a solute mode often changes when the solvent is changed,57−62 the relaxation process is most likely to involve the intermolecular vibrational energy transfer process. In this case, the energy transfer rate depends on the Coulomb interaction between solute and solvent.63−67 The involvement of solvent modes can be confirmed by the solute’s lifetime dependence on the isotope composition of the solvent.68 Because the isotopic replacement in solvent alters the energy-accepting modes as well as the coupling strength between solute and solvent modes, it changes the intermolecular energy transfer rate. For the cyano stretching mode of [Fe(CN)6]4− and [Fe(CN)6 ]3− in H2O and in D2O, the slow-decaying component can be attributed to the vibrational energy dissipation process into solvent. Even though the linear IR spectra of their cyano stretches are very similar in H2O and D2O and show no significant isotope effect on the line shape for the two anions, their vibrational lifetimes (T1) differ substantially in the two solvents, mainly for the slow-decaying component. This observed isotopic effect of the T1 times for the two anions in H2O and D2O suggests the vibrational relaxation of the cyano stretch in these cases is indeed an intermolecular process. The largest difference is found in the case of ferro-species. It is noted that the slow component of the population relaxation process of [Fe(CN)6]4− in H2O is ca. 6 times accelerated with respect to that in D2O (5.5 ps versus 30.0 ps). The vibrational excitation energy of the cyano
Figure 8. Geometry and bond length parameters in [Fe(CN)6]4− (left) and [Fe(CN)6]3− (right) clustered with 12 water molecules included. For simplicity, only one FeCN branch and one water molecule are shown. The bond lengths of FeC and CN are listed (first row, in Å). The values of the two anions in the absence of water are listed in the second row. The hydrogen bond lengths (N···H) and water structure parameters are also given.
Table 6. NPA Charge Analysis for Gas-Phase [Fe(CN)6]4− and [Fe(CN)6]3− Fe C2 C3 C4 C5 C6 C7 N8 N9 N10 N11 N12 N13
[Fe(CN)6]4−
[Fe(CN)6]3−
−1.25341 0.33028 0.33028 0.33028 0.33028 0.33028 0.33028 −0.78804 −0.78804 −0.78804 −0.78804 −0.78804 −0.78804
−0.87795 0.29161 0.29161 0.29161 0.29094 0.29161 0.29094 −0.66514 −0.63502 −0.63502 −0.63502 −0.66514 −0.63502
tightly bound to the ferro-species than to the ferri-species. These results suggest a stronger interfacial interaction between water and cyano groups and hence larger perturbation to water structure in the hydration shell of the ferro-species. On the other hand, for the ferri-species, there is comparatively less perturbation to the water structure in the hydration shell, and the CN group experiences a more or less homogeneous H2O environment, so as to show a Lorentzian-like IR line shape for the CN stretching mode (Figure 1). This picture of hydrated anions is in accordance to the observed differences in the anisotropic measurements (see discussion in the next section). When molecular rotation occurs, molecules can rotate together with the first hydration layer. Because ferrocyanide has a stronger hydrogen bonding interaction with the first hydration layer, it forms a smaller and more compact hydrated complex that generally rotates faster. It is well-known that for the CN group the formation of a hydrogen bond blue shifts its stretching frequency.56 Thus, the hydrogen bonding strength can be evaluated from the amount of frequency shift from the gas phase to the solution phase. In the gas phase, it is already shown in the ferri-species that the CN stretches at higher frequency than that in the ferrospecies, for the vibrational frequency is inversely proportional to the bond length (Figure 8). From the bond length change from gas phase to solution phase, the blue shift is found to be more in [Fe(CN)6]4− (22 cm−1) than in [Fe(CN)6]3− (13 cm−1), indicating stronger hydrogen bonding in the ferro3110
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However, for the ferri-species, it seems to be difficult to explain the observed lesser acceleration in H2O versus that in D2O (7.3 ps versus 12.1 ps), even though the transition energy gap (2115.6 cm−1) appears to better match that of the solvent combination band of H2O at 2128 cm−1 in comparison with that of the ferro-species (2039.4 cm−1 in Figure 9, upper panel). Here, a more appropriate question to ask is why vibrational relaxation of [Fe(CN)6]3− does not slow down in D2O. This is likely due to the presence of the OD stretching mode that has an extended low-frequency tail (down to 2100 cm−1 or even lower at high concentration) and overlaps with the CN stretching frequency (2115.6 cm−1). This is clearly seen in Figure 9 (lower panel). Thus, reaching up to the OD stretch mode could be an alternative relaxation channel for the CN excited state. However, for the ferro-species, this channel is not as efficient as that for the ferri-species because the CN stretching frequency of the latter is located at an even lower frequency side (2038.9 cm −1 ). The interplay of the combination band in H2O and OD stretching band in D2O in this region has been discussed in previous studies of the ferro-species.43,44 Additionally, as shown in Table 3, in H2O, the slow T1 component of the ferro-species is only slightly shorter than that of the ferri-species. This is likely due to the differences in the hydrogen-bonding interactions for the two species. As shown in Figure 8, [Fe(CN)6]4− forms a stronger cyano−water hydrogen bond. Strong solute−solvent coupling may facilitate vibrational energy relaxation. Further, because the anisotropy relaxation time constant is generally larger than that of the fast-decaying component, which is true in four cases, the observed anisotropy decay is more likely to be associated with the physical rotation of the hydrated complexes, rather than pseudo rotations induced by the solvent. However, as discussed previously, there are other mechanisms for the anisotropy relaxation for both degenerate and nondegenerate modes.44 We are currently investigating the structural (including rotational) dynamics with the aid of molecular dynamics simulations. 4.3. Structural Dynamics. The FFCF dynamics can be extracted from waiting-time-dependent 2D IR spectra via the inhomogeneous index.39,52 The value of C(T) can be viewed as a “dynamical” measure of the inhomogeneous broadening contribution, because it evolves with T times. The evolution of the inhomogeneous broadening has been known as vibrational “spectral diffusion”.71 However, the motional narrowing process, which is the ultrafast switching process in the frequency response, on the other hand, is not sensed by the FFCF measurement. Figure 7 and Table 5 show that there is more inhomogeneous contribution in the case of ferrocyanide than in ferricyanide, in both H2O and D2O. This result is in agreement with the linear IR line width analysis shown in Table 1. However, linear IR can only provide “static” assessment of the inhomogeneous line broadening. From linear IR and 2D IR results, it can be concluded that there is more inhomogeneous broadening contribution in ferrocyanide than in ferricyanide. Further, the frequency correlation relaxes somewhat faster in the case of the ferri-species, suggesting weaker hydrogenbonding interactions, which is supported by the quantum chemistry computations. The FFCF dynamics is closely related to the reconfigurational motion of solvent. Weaker hydrogen bonding interaction, which is the case of the ferri-species, would allow relatively easier randomization of water molecules, causing a faster memory-loss process, i.e., a faster FFCF
stretching will unlikely relax to the FeC stretching directly, even though its frequency is quite low (ca. 300−400 cm−1). This is not an efficient vibrational energy dissipation channel for the CN excitation because of the location of the FeC group in the molecular structure. The energy relaxation in this system was known to be an intermolecular process and involves solvent modes.44 To examine the vibrational energy accepting modes, we compare the broadband linear IR spectra of [Fe(CN)6]4− and [Fe(CN)6]3− in H2O and in D2O. The results are given in Figure 9, along with those of the pure solvents. In H2O (panel
Figure 9. FTIR spectra of pure H2O (panel A, black curve), ferrocyanide (with Fe(II)), and ferricyanide (with Fe(III)) anions solvated in H2O (A, red), pure D2O (panel B, black), and the two anions solvated in D2O (B, red).
A), a sharp peak appears at 1645 cm−1 (the HOH bending), a broad band appears at around 3450 cm−1 (the O H stretching), and a weak peak appears at 2128 cm−1. This is due to the combination transition of the HOH bending motion and liberational motion at 483 cm−1, which is frustrated rotational and translational motions.69 The stretching modes of CN in ferrocyanide (2039.4 cm−1) and ferricyanide (2115.6 cm−1) overlap with the combination band. In D2O, the D OD bending mode appears at 1209 cm−1, the OD stretching is at around 2500 cm−1, while the combinational band of the bending and librational modes is around 1551 cm−1. In this solvent, it is seen that the CN stretching absorption band of either ferrocyanide (2038.9 cm−1) or ferricyanide (2115.6 cm−1) sits on the low-frequency tail of the OD stretching mode. For the ferro-species, the observed speed-up in H2O with respect to that in D2O can be explained as the solvent effect that is associated with the combination band of H2O at 2128 cm−1. Such speed-up has also been reported and explained earlier.43,44 The extinction coefficient of this combination band was estimated to be 3 M−1.70 This intermolecular vibrational relaxation is a cubic interaction process,62 in which the initial vibration excitation (the CN stretch) is annihilated at the cost of two newly created excitations of solvent modes (the HOH bending plus the low-frequency liberational motion of H2O). In D2O, the vibration relaxation occurs much slower, suggesting inefficient intermolecular energy transfer processes. 3111
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to compare isotope and charge effects on structural and dynamical aspects of ion solvation, in particular on those of the hydration shell of ions, using a combination of infrared spectroscopic methods.
dynamics. A tighter hydrogen bonding structure with stronger solute−solvent coupling, which is the case of the ferro-species, will lead to a relatively slow FFCF dynamics. In addition, the obtained time constants for C(T) in the case of [Fe(CN)6]4− are in reasonable agreement with previous reported values43 that are listed in Table 5 for comparison, where an integrated three-pulse photon echo method was used and the first moment of peak-shift was used to describe the FFCF. Furthermore, no significant isotope effect is seen from the spectral diffusion dynamics, suggesting a similar solvation structure in H2O and D2O for each anion. The obtained anisotropy, on the other hand, can be used for the reorientational dynamics of the hydrated anions in the aqueous environment. The reorientational dynamics can be influenced by solvent friction, thus also reflecting the solvent structural dynamics. The results suggest that [Fe(CN)6]4− rotates only slightly faster than [Fe(CN)6]3−, similar to what has been seen previously.44 This is in agreement with the discussion above that the solvation layer of the [Fe(CN)6]4− anion is relatively tight and compact (so it rotates faster). However, no obvious solvent dependence is observed. The reorientational time constants of the four systems are found to be on a similar time scale as the rotational time of bulk water, which was found to be 2.5 ps.4,72
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AUTHOR INFORMATION
Corresponding Author
*Phone: (+86)-010-62656806. Fax: (+86)-010-62563167. Email:
[email protected]. Author Contributions §
These authors contributed equally.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Knowledge Innovation Program (Grant No. KJCX2-EW-H01) and the Hundred Talent Fund from the Chinese Academy of Sciences. The support from the National Natural Science Foundation of China (91121020, 21103200, and 21173231) was also acknowledged. The work was also supported by the NSFC instrumentation fund (20727001).
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5. CONCLUSION In this work, we studied the structure and dynamics of the cyanoferrate anions solvated in light and heavy water (H2O versus D2O) using linear IR, pump−probe IR, and waitingtime-dependent 2D IR measurements. The structural distributions of water molecules within the hydration shell of the [Fe(CN)6]4− and [Fe(CN)6]3− ions are reflected by the linear IR and 2D IR spectral line shapes. The vibrational frequency distributions of the triply degenerate CN stretching modes are examined in H2O and in D2O, respectively. It turns out that, in both solvents, the linear IR line shape of the CN stretching modes in ferrocyanide is more Gaussian-like, while that in ferricyanide is more Lorentzian-like, suggesting more structural inhomogeneity in the former. Even though the two anions have a very similar size, a stronger interfacial interaction between water and cyano groups is found for the ferro-species because of the higher negative charge, which suggests more tightly packed water structure in the hydration shell. This implies that in the hydration shell the ferro-species breaks more water structure, which is clearly different from the situation of the bulk water region (beyond the hydration shell) reported previously. The presence of solute−solvent interaction is reflected from the vibrational relaxation, anisotropy relaxation, as well as frequency correlation relaxation dynamics. In particular, a significant solvent isotope effect on the vibrational relaxation time constant is observed, indicating solvent-involved vibrational energy relaxation pathways. More inhomogeneous contribution to the frequency−frequency time correlation function is seen in the initial value of the FFCF in the case of ferrocyanide than in ferricyanide, in both H2O and D2O, and the frequency correlation relaxes somewhat faster in the case of the ferricyanide. This is also in agreement with the conclusion that the hydrogen bonds are weaker in the hydration layer of ferricyanide than in ferrocyanide. These results are supported by the quantum chemistry computations. In addition, no significant isotope effect is seen on the dynamics of FFCF, or on the anisotropy relaxations. This study provides an example
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