Article pubs.acs.org/JPCB

Molecular Dynamics Investigation of the Vibrational Spectroscopy of Isolated Water in an Ionic Liquid Z. L. Terranova and S. A. Corcelli* Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States ABSTRACT: Experimental studies examining the structure and dynamics of water in ionic liquids (ILs) have revealed local ion rearrangements that occur an order of magnitude faster than complete randomization of the liquid structure. Simulations of an isolated water molecule embedded in 1-butyl-3-methyl imidazolium hexafluorophosphate, [bmim][PF6], were performed to shed insight into the nature of these coupled water−ion dynamics. The theoretical calculations of the spectral diffusion dynamics and the infrared absorption spectra of the OD stretch of isolated HOD in [bmim][PF6] agree well with experiment. The infrared absorption line shape of the OD stretch is narrower and blue-shifted in the IL compared to those in aqueous solution. Decomposition of the OD frequency time correlation function revealed that translational motions of the anions dominate the spectral diffusion dynamics.

1. INTRODUCTION Our understanding of water−ion interactions is derived primarily from studies of dilute aqueous salt solutions in which the ions are fully hydrated and water−water interactions are perturbed but still prevalent. Studying water at dilute concentrations in an ionic liquid (IL) reverses this scenario; the water is isolated in a sea of ions, and the water−water interactions are negated. The water/IL system provides a unique opportunity to investigate the dynamics of water in a highly electrolytic environment. Moreover, the isolated water molecule can serve as a reporter of the structure and dynamics of the IL. Despite their promise as environmentally friendly solvents and in clean and renewable energy applications,1−7 widespread industrial adoption of many ILs is plagued by their large viscosities.8 While impurities such as water are known to alter the physical properties and chemical reaction rates in hygroscopic ILs,9−11 the addition of this cosolvent is gaining in popularity as a means to reduce viscosity.12 Thus, understanding the behavior of water in ILs and how water alters the properties of ILs has important practical implications. Many ILs are hygroscopic, and complete removal of water is nearly impossible.13,14 A variety of experimental15−18 and computational19−23 studies have aimed to understand the influence of water on the properties of ILs. These studies suggest that some ILs have nanoscale structuring with polar and nonpolar regions.20,24−31 As the water concentration in these ILs increases, the polar domains collapse with the formation of larger water clusters stabilized by a hydrogen-bond network.20,32 Previous work examining isolated water in ILs determined that a water molecule is bridged by two anions in an IL, existing in an A···HOH···A complex. As a result of this proximity, the anions were assumed to be most responsible for influencing the OH stretch frequency.33−35 Investigations © 2014 American Chemical Society

varying the lengths of the cation alkyl chains in imidazoliumbased ILs suggest that the chains do not have an influence on the OH stretching frequency.33,36 X-ray scattering, NMR, and vibrational spectroscopy have been used to understand the structure in bulk ILs.37−40 Ultrafast two-dimensional infrared (2D IR) spectroscopy measurements of ILs have the potential to elucidate important dynamical motifs that differ from conventional solvents. 2D IR spectroscopy has already proven itself as a powerful technique for investigating the structure and dynamics of liquids by monitoring the response of a vibration to the evolution of its local environment, a process called spectral diffusion. The frequencies of vibrational reporters are exquisitely sensitive to changes in their local environment, particularly to changes in electrostatics, hydrogen bonding, and chemical processes. For example, the OH and OD stretch frequencies of HOD are known to depend on hydrogen bonding; an increase in hydrogen-bond strength red shifts the OH and OD stretch vibrational frequencies. The inhomogeneous IR absorption line shape of liquid water reflects the range of different hydrogenbonding environments present.41−44 The spectral diffusion time scales revealed by 2D IR have been shown to directly relate to hydrogen-bond rearrangement processes in liquid water.45−56 Recently, the dynamics of HOD isolated in an IL was investigated with vibrational spectroscopy.57 The linear IR absorption spectrum of the OD stretch frequency of dilute HOD in 1-butyl-3-methyl imidazolium hexafluorophosphate, [bmim][PF6], revealed a blue-shifted and a significantly narrowed vibrational line shape compared to the spectrum of Special Issue: James L. Skinner Festschrift Received: February 14, 2014 Revised: March 20, 2014 Published: March 20, 2014 8264

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vector between site i and the D atom. For calculations of EOD, the long-range electrostatic interactions were corrected with the damped shifted force (DSF) method.66 One motivation for utilizing the DSF method rather than traditional Ewald summation techniques67−70 is that DSF treats the interactions as a pairwise sum, thus lending itself to straightforward decomposition in terms of the contributions of the anions and cations in the IL. The empirical relationship that relates the OD vibrational stretch frequency, ωOD, to EOD was developed by Lin, Auer, and Skinner in HOD for aqueous NaBr solutions65

HOD in water. The blue shift suggests weaker OD interactions with the ionic environment and is characteristic of a relatively isolated OD stretch, for example, the free OD stretches at a liquid D2O/vacuum interface.58−60 The 2D IR measurements monitored spectral diffusion of the OD stretch of HOD in the IL. An important quantity accessible by both simulation and experiment is the frequency fluctuation time correlation function (FFCF), C(t) = ⟨δω(t)δω(0)⟩, where δω(t) is the deviation of the frequency from its equilibrium value, δω(t) = ω(t) − ⟨ω⟩. As a water molecule samples different molecular environments, the FFCF decays to zero. This can be approximately related to the spectral diffusion measurements quantified experimentally using the center line slope (CLS) method.61,62 Measurements of the amplitudes and time scales of the FFCF thus give information about the dynamics of the environment surrounding the HOD molecule. Two time scales were found, 6.9 ± 2.1 and 72 ± 20 ps. The faster of the two relaxation time scales was attributed to changes in the local structure of the anions bridged by the water and the subsequent motions of the cations. The slower relaxation time was assigned to orientational relaxation, though a discrepancy of approximately 1 order of magnitude exists between the 72 ps time scale and the 2.3 ns response in heterodyne-detected optical Kerr effect experiments in [bmim][PF6].31 The objective of this paper is to utilize molecular simulation to understand the factors responsible for the spectral diffusion time scales for HOD isolated in the [bmim][PF6] IL. In section 2, the theoretical methodology necessary to compute the linear IR absorption spectrum of HOD in [bmim][PF6], as well as the FFCF, is discussed. In addition, approaches to decompose the FFCF into contributions from specific motions of the anions and cations are presented. In section 3, results for the IR absorption spectrum, the FFCF, and its decompositions are shown and discussed. Finally, some concluding remarks can be found in section 4.

⎛ ⎛ cm−1 ⎞ cm−1 ⎞ 2 ωOD = 2762.6 cm−1 − ⎜3640.8 ⎟Eeff − ⎜56641 ⎟Eeff au ⎠ ⎝ ⎝ au 2 ⎠ (2)

Here, an effective electric field, Eeff, was introduced to account for the blue shifts in the OD stretch frequency observed experimentally with increasing salt concentrations Eeff = E H 2O + aEcat + bEan

where a and b are empirical parameters, 0.81379 and 0.92017, respectively. EH2O, Ecat, and Ean are contributions to EOD from water, cations, and anions, respectively. This spectroscopic map was designed to be applicable for all aqueous salt concentrations, and when no ions are present, the map is conveniently appropriate for HOD in H2O. The unequal weighting of the contributions for the cations and anions reproduces the smaller OD frequency shifts observed in electrolyte solutions. Because non-Condon effects are known to be important in the vibrational spectroscopy of water,64 calculations of the IR absorption spectrum of HOD also require a spectroscopic map for the magnitude of the transition dipole moment, μ′, for the OD stretch relative to its value in the gas phase, μ′g μ′ = 0.71116 + 75.591Eeff μg′

2. THEORETICAL METHODOLOGY A. Spectroscopic Maps. In order to calculate the IR absorption spectrum and the spectral diffusion dynamics of the OD stretch of isolated HOD in [bmim][PF6] within an MD simulation, one must have a model for relating the OD vibrational frequency and its transition dipole moment to the instantaneous solvent environment of the HOD molecule. We will adopt an approach that has shown considerable success in describing the vibrational spectroscopy of HOD in water44,63,64 and in electrolyte solutions,65 whereby the relevant spectroscopic quantities (i.e., the OD vibrational frequency and transition dipole moment) are empirically related to the electric field of the environment projected along the OD bond of interest. The motions of the environment cause the projected electric field, and thus the OD vibrational frequency, to fluctuate. From the vibrational frequency and transition dipole moment dynamics, the IR spectrum and FFCF can be calculated. The projection of the electric field along the OD bond axis, EOD, due to a collection of N solvent point charges, {qi}, is given in atomic units by N

EOD = rOD ̂ ·∑ i=1

(4)

It is important to emphasize that the spectroscopic maps given by eqs 2 and 4 were developed in the context of aqueous alkali halide salt solutions and not specifically for water in ILs. Comparisons of the results for the IR absorption spectrum and the FFCF for isolated HOD in [bmim][PF6] directly with experiment will both provide validation and reveal the extent to which the spectroscopic maps are transferable. B. Infrared Absorption Spectrum. The IR absorption spectra were computed from knowledge of the frequency and transition dipole moment trajectories using the semiclassical fluctuating frequency approximation (FFA)71,72 I(ω) =

∫0



t

dt e iωt ⟨μ ⃗ (t ) ·μ ⃗ (0)e−i ∫0 dτ δω(τ)⟩e−t /2T1

(5)

where ⟨...⟩ represents a classical ensemble average, δω(t) = ω(t) − ⟨ω⟩ is the fluctuation of the frequency from its average value, ⟨ω⟩, and μ⃗ (t) is the transition dipole moment vector

μ ⃗ (t ) = μ′x10rOD ̂

qiri ̂D ri2D

(3)

(6)

assumed to be in the direction of the OD bond, r̂OD . In eq 6, x10 = ⟨1|x̂|0⟩ is the matrix element of the position operator computed assuming Morse oscillator ground-, |0⟩, and first excited-state, |1⟩, vibrational wave functions. For convenience, x10 can also be related, empirically, to the OD stretch frequency

(1)

where r̂OD is the unit vector along the OD bond, riD is the distance between charge i and the D atom, and r̂iD is a unit 8265

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proceed to decompose CE(t) and assume that the physical insights are relevant for Cω(t). Because δE(t) can be expressed as a linear sum, eq 3, CE(t) can be decomposed into contributions from anions and cations using the same approach that has proven successful in unraveling the factors that influence solvation response functions in ILs,75,76 proteins,77 and DNA78−82

(7)

The FFA expression, eq 5, approximately captures the effects of inhomogeneous broadening, motional narrowing, rotational broadening, and non-Condon transition dipole moments on the vibrational line shape. The effects of lifetime broadening are captured empirically via the exp(−t/2T1) factor, where T1 is the vibrational population lifetime, 1.8 ps for the OD stretch of HOD in water.73 T1 has not been determined for HOD in [bmim][PF6]. For the calculation of the IR absorption spectrum of HOD in [bmim][PF6], the value 1.8 ps was assumed to be qualitatively representative of the population lifetime. C. Spectral Diffusion and Decomposition of the FFCF. Spectral diffusion of the OD stretch vibrational frequency of HOD is a sensitive reporter of the dynamics of its local solvation environment. These dynamics are often quantified in terms of the normalized FFCF Cω(t ) =

⟨δω(t )δω(0)⟩ Cω(0)

C E(t ) =

α

⟨δE(t )δE(0)⟩ C E(0)

C Eα(t ) = C E(0)

∑ α

⟨δE α(t )δE(0)⟩ C E(0)

(10)

where α represents the solvent component of interest. This method of decomposing CαE(t) and Cω(t) by proxy is rigorously consistent with the linear response approximation and has not previously been applied in the context of understanding vibrational spectral diffusion in multicomponent liquids. Each of the solvent component correlation functions, CαE(t), in eq 10 can also be further separated into contributions that arise from their respective translational and rotational motions. The translational contribution to Eα, Eα,trans, is calculated by regarding each relevant IL molecule as a single point charge located at its center of charge. The rovibrational contribution to Eα is then just the difference Eα,rovib = Eα − Eα,trans. These definitions allow the solvent component correlation functions for the cations and anions to be decomposed into their respective translational and rovibrational contributions

(8)

Cω(t) is accessible experimentally and can be computed from frequency trajectories obtained during MD simulations using, for example, the spectroscopic maps described in section 2A. The FFCF has been measured for HOD in water47,48 and in the [bmim][PF6] IL.57 For HOD in water, the long-time (∼1.5 ps) decay of the FFCF has been attributed to hydrogen-bond rearrangements. FFCFs computed using the spectroscopic maps developed by Skinner and co-workers generally have the same long-time decay rate as the hydrogen-bond time correlation function for a given empirical water model.43 The quantitative agreement of the long-time FFCF decay with experiment, however, varies by water model. Water models without electronic polarizability generally have FFCFs and hydrogen-bond time correlation functions that decay too quickly.74 For a multicomponent solution, like the [bmim][PF6] IL, it would be physically insightful to decompose the FFCF into contributions from the respective components (i.e., from the anions and the cations). A straightforward decomposition is somewhat hindered by the quadratic form of the empirical frequency map, eq 2, where the total frequency shift, δω, is not a simple sum of contributions from anions, δωan, and cations, δωcat, δω ≠ δωan + δωcat. However, the effective electric field, Eeff, from which the frequencies are computed is naturally a sum of contributions from the anions and cations, eq 3. Note that for isolated water in an IL, the contribution to the effective electric field from other water molecules can be ignored. Fortuitously, the normalized time correlation function of the electric field fluctuations C E(t ) =



C Eα(t ) = C Eα ,trans(t ) + C Eα ,rovib(t )

functions Cα,trans (t) E α,trans

(11)

Cα,rovib (t) E α,rovib

where the and are computed with eq 10, but with δE (t) and δE (t) in place of δEα(t). D. Molecular Dynamics Simulations. For our control calculations on dilute HOD in water, a cubic simulation box of 512 H2O molecules was constructed with periodic boundary conditions. The vibrational spectroscopy of neat water is complicated by intra- and intermolecular coupling of the OH stretches. Considering dilute HOD in H2O is preferable because the OD stretch is spectrally isolated from all other vibrational modes and limits intra- and intermolecular vibrational coupling. For our calculations of the vibrational spectroscopy of dilute HOD in H2O, we can regard each bond as the OD vibration of interest. Here, we are taking advantage of the fact that a single HOD molecule in H2O is indistinguishable from a neat H2O simulation. The atomiccentered partial charges and other force field parameters for the H2O molecule are from the SPC/E model.83 The cubic simulation box of ILs was constructed with 256 [bmim] cations, 256 [PF6] anions, and one D2O molecule with periodic boundary conditions. A D2O molecule was used because its dynamics are not particularly different from those of HOD, and both OD bonds could be considered as the vibration of interest, thus providing a 2-fold increase of our statistics. The MD simulations were performed using the Large-scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS) program.84 All molecules were modeled as fully flexible, except for covalent bonds containing hydrogen or deuterium, which were fixed at equilibrium lengths using the SHAKE algorithm.85,86 For the [bmim] molecules, force field parameters for the bonds, bends, dihedrals, and atomic-centered Lennard-Jones sites were adopted from the generalized Amber force field (GAFF).87 Minor dihedral angle modifications were made to better match density functional theory calculations carried out with a B3LYP functional and the aug-cc-pVDZ basis set. Parameters for [PF6] are not available in the GAFF and were obtained from Liu et

(9)

where δE(t) = Eeff − ⟨Eeff⟩ is the fluctuation of the effective electric field from its average value and is an excellent surrogate for Cω(t). For a linear relationship between the electric field and the vibrational frequency, the two normalized correlation functions are identical. For a quadratic relationship between the field and the frequency, the functions can differ. However, for HOD in [bmim][PF6], the normalized correlation functions are almost quantitatively identical (vide infra). Thus, we will 8266

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al.88 Atomic-centered partial charges for the IL molecules were calculated via the Merz−Singh−Kollman89 analysis of the electron density of the optimized geometry of the molecules obtained with DFT with a B3LYP functional and the aug-ccpVDZ basis set. In an attempt to more accurately model the dynamics of the system, the partial charges were empirically scaled by a factor of 0.84, as suggested by DFT calculations for a similar IL, [bmim][BF4].90 Treating the charge scaling factor as a tunable force field parameter to approximately describe the effects of electronic polarizability is commonly used as a means to more accurately capture diffusion in ILs.91 The long-ranged electrostatic interactions in the simulations were computed with the particle-mesh Ewald summation method with a 15 Å realspace cutoff.67 Out of concern for the long relaxation dynamics, we rely on a rigorous equilibration procedure identical to that in our previous work simulating ILs. In brief, the molecules are allowed to relax during a minimization procedure after which the temperature is slowly raised from 0 to 300 K and maintained at 300 K for 4 ns in the NPT ensemble controlled by a Nosé−Hoover thermostat and barostat.92 The size of the simulation box was isotropically scaled to reflect the average density and was then simulated in the NVT ensemble for 1 ns at 300 K, and the temperature was slowly raised to 600 K over 1 ns to destroy any pseudostable ionic cages that may have formed. Next, the temperature was reduced back to 300 K in 1 ns, followed by an NVT simulation for 1 ns at a constant temperature of 300 K. The final velocities were scaled to 300 K, and a preproduction NVE simulation was performed for 11 ns. A total of 50 ns of continuous dynamics for the D2O/IL system and 5 ns for the neat H2O system were collected in the NVE ensemble with a 2 fs integration time step and a collection resolution of 4 fs. Energy conservation was excellent with temperature stability within 1 K for the duration of the production runs. As a preliminary validation of the simulations and force fields, we calculated the orientational time correlation function for an OD bond in neat H2O and in the [bmim][PF6] IL, given as ⟨P2(r̂OD(0)·r̂OD(t))⟩, where P2(x) is the second-order Legendre polynomial (Figure 1). The oscillations below 1 ps are indicative of water librational motion and will be discussed in more detail in section 3B. The reorientational dynamics are clearly much faster in H2O than those in the IL. Experimental measurements of the OD anisotropy decay in [bmim][PF6] were collected out to 40 ps, and a biexponential fit revealed two

time constants of 2.4 and 24.7 ps.57 The calculated rotational correlation function was fit to a triexponential function for t ≥ 1 ps (Figure 1). The three time constants were 3.5, 19.4, and 85.6 ps. The first two time constants agree fairly well with experiment and serve as a validation of the simulations. The longer time decay (85.6 ps) would not be resolvable in the experiment because of the population lifetime of the OD vibrational reporter.

3. RESULTS AND DISCUSSION A. IR Absorption. The calculated IR absorption spectra for the OD stretch of dilute HOD in H2O and in [bmim][PF6] are shown in Figure 2. It is immediately apparent that the line

Figure 2. Vibrational line shapes for the OD stretch of dilute HOD in H2O and in the [bmim][PF6] IL. The spectra were arbitrarily scaled to have the same maximum intensity.

Table 1. Summary of the Theoretical and Experimental IR Absorption Line Shapes for the OD Stretch of HOD in H2O and in [bmim][PF6]a HOD in H2O HOD in [bmim][PF6]

theory exptb theory exptb

ωmax (cm−1)

fwhm (cm−1)

2548 2510 2712 2678

148 170 20 21

a ωmax is the frequency of maximum absorption, and fwhm is the fullwidth at half maximum absorption. bReference 57.

width is narrowed dramatically in the IL by 128 cm−1 and is blue shifted by 164 cm−1 (Table 1). Experimentally, the spectrum shifts by 168 cm−1 and narrows by 149 cm−1. The agreement between theory and experiment for the differences in the line shapes between the aqueous and IL environments is excellent, which validates both the simulations and the spectroscopic maps. Consistent with previous studies,44,64,65 the peak of the OD stretch spectrum of HOD in water is to the blue of experiment, and the spectrum is slightly too narrow. In the IL, the peak in the spectrum is again to the blue of experiment, but its width is almost exactly correct. As discussed previously, there is some ambiguity about the vibrational lifetime of HOD in the IL, and the spectrum in Figure 2 assumes T1 = 1.8 ps, the same value as HOD in H2O. However, the lifetime is likely longer because the HOD molecule is not hydrogen-bonding, and the 2D IR spectra were collected out to 40 ps, implying a T1 longer than 1.8 ps. Therefore, the 20 cm−1 width of the spectrum can be regarded as an upper bound. Taking T1 = ∞ provides a lower bound of 16 cm−1. The significant narrowing of the spectrum in the IL solvent relative

Figure 1. The orientational time correlation function for an OD bond in H2O (black) and in the [bmim][PF6] IL (turquoise). 8267

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to aqueous solution is a reflection of the absence of hydrogenbonding sites on the IL molecules and a reduction in the diversity of solvent environments to inhomogeneously broaden the line shape. Examining the distribution of electric fields present in water and in the IL is physically insightful for understanding the contributions to the IR absorption spectrum of HOD in these two liquids. Figure 3 shows distribution functions, F(E), for the

Figure 4. Normalized CE(t) for HOD in H2O and HOD in the [bmim][PF6] IL. Also shown is a comparison between Cω(t) (red) and CE(t) for HOD in the IL.

directly related to spectral diffusion measurements, CE(t) serves as an exemplary surrogate, and the two functions will be regarded as interchangeable for the remainder of the paper. As discussed in section 2C, CE(t) is amenable to decomposition strategies that can offer additional physical insight regarding the physical motions responsible for spectral diffusion. Immediately apparent in Figure 3 is a dramatic difference in the long-time decay of the FFCF for HOD in the aqueous environment, where the decay is complete in under 5 ps, versus that in the IL solvent, where the function persists beyond 100 ps. For HOD in water, CE(t) was fit to a triexponential function, which revealed three time scales, 37 fs, 297 fs, and 0.86 ps. In previous studies, the faster time scales were attributed to hydrogen-bond fluctuations, while the slowest time was related to hydrogen-bond rearrangement processes.47,48 Given that the viscosity of the [bmim][PF6] IL is ∼450 times larger than the viscosity of water,93 it is not surprising that more large-scale rearrangement of solvent structures takes considerably longer in the IL than that in aqueous solution, though the specific motions cannot be assigned until we consider physical decompositions of CE(t) below. A similar triexponential fit of CE(t) for HOD in the IL revealed time constants of 54 fs, 1.6 ps, and 38 ps. Experimentally, two time scales were identified for spectral diffusion, 6.9 and 72 ps.57 Spectral diffusion occurring on a ∼50 fs time scale, as predicted in our calculations, would be difficult to resolve experimentally; therefore, we cannot make a direct comparison. The other two calculated time constants are too fast compared to experiment by about a factor of 4 for the 1.6 ps time and a factor of 2 for the longest 38 ps time scale. For HOD in water, it has been established that spectral diffusion occurs too quickly in nonpolarizable water models, by about a factor of approximately 1.5−2.74,94 It is therefore likely that quantitatively reproducing the spectral diffusion time scales for HOD isolated in ILs would also require electronically polarizable force fields. Nonetheless, the qualitative agreement between experiment and theory is reasonable enough to proceed to decompose CE(t) for HOD in the IL to achieve additional physical insight. Already, the simple absence of nanosecond time scales in both simulation and experiment demonstrates that the OD vibrational reporter is insensitive to longer-time rearrangements that have been observed in both theoretical and experimental investigations of solvation dynamics in [bmim][PF6].76,95−99

Figure 3. Distribution functions, F(E), for the projection of the electric field projected along the OD of HOD in H2O (black) and in the [bmim][PF6] IL (turquoise). The distributions of electric fields in the IL resulting from cations (blue) and anions (red) are also shown. The distribution functions have all been scaled to have the same value at their maximum.

projection of the electric field along the OD bond of HOD in H2O and in [bmim][PF6]. In the IL, the electric field of interest is Eeff, as defined in eq 3. It is immediately apparent that the average electric field projected along the OD bond is about a factor of 3 smaller for HOD in the IL (0.010 au = 51.4 MV/ cm) compared to that of HOD in aqueous solution (0.032 au = 164.5 MV/cm). This is most likely due to the absence of a hydrogen-bonding partner for HOD in the IL. The electric field distribution for HOD in water exhibits a characteristic shoulder on the low-field side of F(E). These small values of the field correspond to frequencies on the blue side of the IR absorption spectrum, which have been attributed in previous studies to HOD molecules whose OD bond is not engaged as a hydrogenbond donor. The electric field distribution for HOD in the IL is significantly narrowed and is centered almost exactly at the same location of the shoulder in the water distribution. The difference in widths between the two distributions is consistent with the calculated and experimentally observed narrowing in the IR absorption spectrum and suggests that the origin of the change in width is mostly inhomogeneous in nature. Figure 3 also shows distribution functions for the effective electric fields from the cations and anions. Note that the distribution for the total effective field should not be a sum of the contributions from the cations and anions. Interestingly, the distribution of fields from the anions mimics the total, whereas the distribution function for the cations is narrow and centered almost at zero. These results confirm that the anions interact more strongly with the HOD molecule and are the dominant contributor to the IR absorption spectrum. B. Spectral Diffusion. Figure 4 shows the normalized electric field correlation function, CE(t), for the OD stretch of dilute HOD in H2O and isolated HOD in [bmim][PF6]. Also shown in Figure 3 is the FFCF, Cω(t), which is nearly identical to CE(t) at all times, particularly for t > 1 ps. While the FFCF is 8268

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Before progressing to decompositions of CE(t) for HOD in the IL, it is important to discuss the subpicosecond damped oscillation that is evident in the electric field correlation function for both HOD in water and HOD in the IL. Such oscillations have been experimentally verified for spectral diffusion of HOD in liquid water and assigned to a oscillatory stretching motion of the hydrogen bond between the OD vibrational reporter and a neighboring water molecule.49 The peak in the oscillation occurs at 120 fs for HOD in water but at 280 fs for HOD in [bmim][PF6]. Also, the oscillation is considerably more pronounced in the IL. The decompositions discussed below will reveal that the oscillation is related to translational motion of the water relative to the anions. Thus, the physical interpretation is similar in the IL; only now, it is an oscillatory stretch within a [PF6]···HOD···[PF6] complex. Experimentally, significant oscillations were observed for the spectral diffusion of D2O in the [bmim][PF6] IL having a period of 0.3 ps. However, these oscillations were assigned as quantum mechanical coherence oscillations due to anharmonic coupling between the symmetric and asymmetric stretches of D2O (i.e., the same oscillations were observed in the CLS of the diagonal and cross peaks of the symmetric and asymmetric stretches of D2O in the 2D IR spectra). Here, the OH and OD vibrational frequencies of HOD are too far out of resonance to support oscillations due to coherent energy transfer. Moreover, such an effect would also not be captured using the theoretical approach utilized in this paper for computing the spectral diffusion dynamics. Figure 5 shows results for decomposing CE(t) for the OD stretch of HOD in the IL in terms of contributions from the

diffusion process into contributions from translational and rovibrational motions of these molecules relative to the OD bond of interest (Figure 6). From this analysis, it is clear that

Figure 6. Decomposition of normalized CE(t) for the OD stretch of HOD isolated in the [bmim][PF6] IL in terms of the contributions from the translational (solid) and rovibrational (dashed) components from cations (blue) and anions (red).

the long-time spectral diffusion dynamics are dominated by translational motions of the anion relative to the OD bond. Translational and rotational motions are nearly equal contributors to the cation portion of the correlation function. The pronounced 280 fs oscillation in CE(t) is only present in the anion translational correlation function. Thus, we can now assign this feature to a vibrational motion between the HOD molecule and a neighboring [PF6] anion. A much smaller amplitude and higher frequency oscillation is also present in the total correlation function, which can now clearly be assigned to rovibrational motions of the anions.

4. CONCLUDING REMARKS A combined MD simulation and spectroscopic map approach has been utilized to investigate the vibrational spectroscopy and spectral diffusion dynamics of the OD stretch of HOD isolated in the [bmim][PF6] IL. Excellent agreement between experiment and theory was achieved for the dramatic shift and change in width of the IR absorption spectrum for the OD stretch of HOD in the IL relative to that in aqueous solution. This result served to validate the spectroscopic maps that were originally developed for aqueous electrolyte solutions. The spectral diffusion dynamics were calculated, and the agreement with experiment was more modest. The theoretical time scales were too fast compared to experiment, which is perhaps expected for the nonpolarizable force fields used in the MD simulations. In the future, we intend to investigate this effect using electronically polarizable force fields (e.g., using the SPC-FQ100 or TTM3-F101,102 water models, both of which have performed well in other vibrational spectroscopy applications). Decompositions of the total spectral diffusion dynamics in terms of contributions from anions and cations revealed that the anions dominate the response at all times. Further decompositions revealed that translational motions of the anions relative to the OD bond of interest were, by far, the most important component of the spectral diffusion dynamics. The decompositions also allowed us to assign a pronounced oscillation in the calculated FTCF to a OD···[PF6] vibrational motion. Overall, the results of this paper demonstrate the utility of the MD/spectroscopic map approach for determining unambigu-

Figure 5. Decomposition of normalized CE(t) for the OD stretch of HOD isolated in the [bmim][PF6] IL in terms of the contributions from the cations (blue) and anions (red).

[PF6] anions and the [bmim] cations. It is immediately apparent that the anions are the dominant contributor to spectral diffusion over all time scales; the cations never contribute more than ∼10% to CE(t). The long-time decays of both the anion and cation correlation functions are similar to the 38 ps decay of the total correlation function (36 ps for the anions and 43 ps for the cations). This suggest that the longtime decay is a collective process involving reorganization of both the anions and cations. The pronounced 280 fs oscillation in CE(t) is clearly visible only in the anion component; however both the anion and cation correlation functions have smaller amplitude vibrations superimposed upon the decay at short times. Additional physical insight can be obtained by further decomposing the anion and cation contributions to the spectral 8269

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ously the signature of physical motions in complex heterogeneous solvents in linear and 2D IR experiments.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported by the American Chemical Society Petroleum Research Fund (52648-ND6) and the Sustainable Energy Initiative at the University of Notre Dame. The authors are also thankful for high-performance computing resources and support from the Center for Research Computing at the University of Notre Dame.



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dx.doi.org/10.1021/jp501631m | J. Phys. Chem. B 2014, 118, 8264−8272

Molecular dynamics investigation of the vibrational spectroscopy of isolated water in an ionic liquid.

Experimental studies examining the structure and dynamics of water in ionic liquids (ILs) have revealed local ion rearrangements that occur an order o...
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