Molecular-Level Mechanisms of Vibrational Frequency Shifts in a

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Molecular-Level Mechanisms of Vibrational Frequency Shifts in a Polar Liquid Christine M. Morales† and Ward H. Thompson*,‡ † ‡

Department of Chemistry, University of Wisconsin-Eau Claire, Eau Claire, Wisconsin 54702, United States Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States ABSTRACT: A molecular-level analysis of the origins of the vibrational frequency shifts of the CN stretching mode in neat liquid acetonitrile is presented. The frequency shifts and infrared spectrum are calculated using a perturbation theory approach within a molecular dynamics simulation and are in good agreement with measured values reported in the literature. The resulting instantaneous frequency of each nitrile group is decomposed into the contributions from each molecule in the liquid and by interaction type. This provides a detailed picture of the mechanisms of frequency shifts, including the number of surrounding molecules that contribute to the shift, the relationship between their position and relative contribution, and the roles of electrostatic and van der Waals interactions. These results provide insight into what information is contained in infrared (IR) and Raman spectra about the environment of the probed vibrational mode.

1. INTRODUCTION Vibrational spectroscopy is extensively applied to characterize molecules in a wide variety of environments. Frequently, the vibrational spectrum is used to infer details about the molecularlevel structure and interactions around the molecule or mode of interest. Yet, the quality of such inferences is not always clear. Typically, they are based on vibrational frequency shifts and peak narrowing or broadening—that is, limited pieces of information in comparison to the details required to describe a molecule’s dynamics and structural environment. Theoretical approaches can be a powerful tool for improving our understanding of the relationship between vibrational spectral features and molecularlevel properties.112 In this article, this issue is further examined by providing a detailed molecule-by-molecule picture of the mechanism of vibrational frequency shifts in a polar liquid, namely, the CN stretching mode of neat liquid acetonitrile. Acetonitrile is an important polar solvent that is also of interest because of the potential usefulness of the nitrile moiety as a vibrational probe of environment. Nitrile-containing molecules, albeit usually not acetonitrile itself, have been investigated as probes in biomolecules and materials.1331 Their suitability as reporters of the local environment is due to the sensitivity of the CN stretching frequency to intermolecular interactions and the position of this mode in an uncrowded region of the IR spectrum. The origin of CN frequency shifts in complex condensed-phase environments is still a topic of current study. A key issue involves the effect of hydrogen bonding to the nitrogen of the nitrile group, which results in a blue shift of the CN stretching frequency.2739 This result runs counter to a purely electrostatic picture of the hydrogen bond, which would predict a red shift in the nitrile frequency. Consequently, a quantum mechanical description of the nitrile group is required to reproduce the blue shift upon hydrogen bonding.32,33 A number of groups have r 2011 American Chemical Society

developed approaches for describing this effect within otherwise classical molecular dynamics simulations.24,2731,39 In the acetonitrile liquid considered in this work, hydrogen bonding, and hence this blue shifting, is absent, and the focus is on the influence of the less specific Coulombic and van der Waals interactions. In this study, the contributions present in the neat liquid are examined at a molecular level of detail. The questions addressed include: How many molecules contribute to the frequency shift? What intermolecular arrangements lead to the largest shifts? What are the relative contributions of the electrostatic and van der Waals interactions? What determines the infrared line width? The answers provide important insight into the vibrational spectroscopy of polar liquids in general, as well as a baseline for understanding the role of hydrogen-bonding interactions in nitrile frequency shifts, which will be considered elsewhere. The IR and Raman spectra of liquid acetonitrile have been well-studied. The CN stretching, ν2, mode, which has a frequency of 22662267 cm1 in the gas phase,4043 is redshifted in the neat liquid IR and Raman spectra by 1314 cm1.34,36,40,44,45 The features of this CN stretching peak in the liquid are obscured by the presence of an overlapping hot band. However, deconvolution of the spectra give the full width at half-maximum (fwhm) for the ν2 fundamental peak as 5.9 cm1 (IR)45 and 3.6 cm1 (Raman).46 The deconvoluted line shape has been used to extract reorientational and vibrational relaxation times. Among the findings are a temperature-independent vibrational relaxation time of about 3.5 ps. 45,4749 It should be noted that, in contrast, Deak et al. have reported the Received: February 17, 2011 Revised: April 28, 2011 Published: May 24, 2011 7597

dx.doi.org/10.1021/jp201591c | J. Phys. Chem. B 2011, 115, 7597–7605

The Journal of Physical Chemistry B vibrational lifetime of the CN stretch to be 80 ( 20 ps.50 The temperature-dependent reorientation time obtained from IR spectra, that is, from the Æμ(t) 3 μ(0)æ correlation function, was 3.7 ps, which is largely consistent with time scales extracted from Raman and NMR measurements.45 The vibrational properties of acetonitrile were previously modeled by molecular dynamics simulations in a few studies.45,51,52 Westlund and LyndenBell calculated the frequency shifts and vibrational dephasing times for several acetonitrile vibrational modes in the liquid using a perturbation theory approach.51 They obtained CN stretching frequency shifts of 0.9 or 1.7 cm1, depending on the model used. These results are in qualitative agreement with experimental measurements in that they predict a red shift, but do not properly reproduce the magnitude of the shift. Their results indicate that the red shift is due to the electrostatic forces on the CN bond, partially canceled by the effect of the Lennard-Jones interactions. Hashimoto et al. calculated the reorientational times from MD simulations for comparison with those obtained from analysis of the measured IR line width.45 Their times were in good agreement with the experimentally derived values, and they found that the electrostatic interactions had a dominant effect on the temperature dependence of the reorientational times. The vibrational frequency of the CN stretch of acetonitrile has also been studied using electronic structure calculations with a dielectric continuum model.53 Mennucci and da Silva calculated the CN frequency in acetonitrile monomers and dimers, with and without a polarizable continuum model, using density functional theory.53 They obtained frequency shifts in the neat liquid of 14 cm1 compared to an isolated molecule, in excellent agreement with the experimental data. Their calculations indicated no particular role for the acetonitrile dimer, which is often speculated to be important in the liquid structure.34,36,48,54,55 A key issue with this type of modeling is the lack of statistical sampling of liquid conformations, which is typically computationally expensive.8,9,56,57 Rather, the electronic structure calculations involve geometries optimized for one, or a few, molecules, whereas a spectrum arises from a thermal distribution of configurations. This limits the information that such calculations can provide regarding spectral line widths, including dynamical contributions, and molecular-level mechanisms, which can be fully evaluated only in the context of the distribution of liquid intermolecular interactions. Classical MD simulations do provide the statistical sampling necessary for obtaining such detailed mechanistic insight. However, the interactions affecting the vibrational frequencies are not as well described. Fortunately, even rather simple force fields can reasonably reproduce the spectral properties for acetonitrile (vide infra) and other liquids. Additionally, significant progress has been made in recent years in the development of electronic structure-based mapping of vibrational frequency shifts in MD simulations,24,5860 when this is not the case. A key motivation for understanding the connections between the vibrational spectra and the liquid structure and dynamics is the increasing interest in liquids in complex environments. These include biological systems, liquidliquid and liquidsolid interfaces, and liquids confined on the nanometer length scale. In these systems, the approximations and inferences frequently applied to bulk liquid simulations often fail, leading to incorrect deductions about the molecular-level properties.31 Infrared and Raman spectroscopies are commonly used as experimental probes of the structure and dynamics of complex systems. A faulty microscopic picture arising from the interpretation of these

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spectra can have significant consequences, for example, for the development of design principles for the use of porous materials in particular applications. As one example, the effects of confinement in porous materials such as reverse micelles and solgels on the vibrational spectra of liquids and solutes dissolved therein have been the subject of a number of studies,6183 yet a better understanding of the molecular-level mechanisms determining the vibrational spectra is still needed to fully interpret the measured spectra. The approaches described in this article can provide this insight into these mechanisms by allowing the assignment of the solvent structural arrangements and motions that give rise to vibrational frequency shifts and dephasing. Such an analysis is currently underway for acetonitrile confined in hydrophilic (OH-terminated) amorphous silica pores. The remainder of this article is organized as follows: The approach for simulating the frequency shifts and determining the contributions of each surrounding acetonitrile molecule is described in section 2. The results of the simulations are presented in section 3, where the origin of the vibrational line shift distribution is examined from a number of angles. Finally, some concluding remarks are given in section 4.

2. METHODS We previously presented a number of methods for analyzing the results of vibrationally adiabatic mixed quantum-classical molecular dynamics (MD) simulations.5 We applied these methods to two test systems, I2 and ICl in liquid Xe, and showed how they provide a detailed, molecular-level picture of the origin of vibrational frequency shifts.5 The mixed quantum-classical approach used in that work has a number of advantages, among which are the following: (1) feedback between the solute and solvent is included by allowing the solute vibrational wave function to influence the solvent dynamics and vice versa, (2) extremely accurate instantaneous frequency shifts are obtained,8486 and (3) a clear connection is provided between those frequency shifts and the solvent positions and dynamics. However, such an approach is not feasible for the liquid CH3CN system considered here because of the large number of coupled quantum degrees of freedom that would be required. At the same time, the approach for analyzing the mechanisms of the vibrational frequency shifts can be adapted in a straightfoward manner to a perturbation theory description of the nitrile vibrations, which is computationally feasible. Moreover, this more approximate description should be more than adequate for a vibrational mode such as CN, which, because of its strength, does not exhibit significant modulations in the bond distance. 2.1. Model for Vibrational Frequencies and IR Spectra. To model the instantaneous vibrational frequency of the CN stretching (ν2) mode of acetonitrile in the liquid, we used a perturbation theory expression within classical molecular dynamics simulations. In particular, a first-order perturbation theory expansion87 was used to obtain the frequency ω(t) along the oscillator coordinate Q in terms of the classical forces ∂V(t)/∂Q from the MD trajectory pωðtÞ ¼ pω0 ½Æψ1 jQ jψ1 æ Æψ0 jQ jψ0 æ

DV ðtÞ þ ... DQ

ð1Þ

where ψ0 and ψ1 are the ground-state and first-excited-state vibrational eigenfunctions and ω0 is the 0 f 1 vibrational frequency for the isolated molecule. We note that this firstorder expansion neglects higher-order derivatives as well as 7598

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The Journal of Physical Chemistry B

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interactions between the ν2 stretch and other vibrational normal modes. Further, we use a fully localized CN stretch as a model of the ν2 vibrational normal mode. The force along the bond is therefore obtained as88,85 DV μ μ ¼ FC FN 3 ^r CN ð2Þ DQ mC mN

interactions to provide detailed insight into the mechanism of the shifts. The shift in the (fundamental) vibrational frequency relative to the gas phase is, within the first-order perturbation theory approximation μ μ F F ð7Þ ^r CN ΔE01 ¼ ðQ11 Q00 Þ mC C mN N 3

where FC and FN are the total forces on the carbon and nitrogen atoms of the molecule, respectively, due to the rest of the liquid and ^r CN is the unit vector along the CN bond. The matrix elements Qnn = Æψn|Q|ψnæ are obtained for a one-dimensional oscillator with cubic anharmonicity

However, because the interactions between molecules in the simulation model (and most molecular dynamics simulation models) are pairwise, for example, Lennard-Jones and Coulombic, the forces can be decomposed by site or by molecule. For example, the force on the carbon atom of the molecule labeled 1 is

UðQ Þ ¼

1 f μω0 2 Q 2 þ Q 3 2 6

ð3Þ

to model the unperturbed ν2 stretch of CH3CN. It can be shown87 that, for such an oscillator, the required matrix elements are easily obtained as Q11 Q00 ¼ ½Æψ1 jQ jψ1 æ Æψ0 jQ jψ0 æ f p 2 ¼ 2pω0 μω0

ð4Þ

For the CN stretching mode, the cubic anharmonicity constant89 is f = 5.566 1030 cm4, and the unperturbed frequency4043 is taken as ω0 = 2266 cm1. We note that the approach used here determines only the frequency shifts in the liquid relative to the isolated molecule; the unperturbed frequency itself is not determined. Althugh the focus in this article is on the molecular-level mechanisms of frequency shifts, it is also instructive to consider the infrared line shape for liquid acetonitrile,31 obtained from the Fourier transform of the semiclassical correlation function,90,91 φ(t) Z 1 ¥ dt eiΔωt φðtÞ IðΔωÞ ¼ ð5Þ 2π ¥ where φðtÞ ¼

*

"Z ^ ð0Þ 3 μ ^ ðtÞ exp i μ

t

FC ¼

δωðτÞ dτ

ejtj=2T1

ð6Þ

Here, δω(t) ω(t) Æωæ, and μ^ is the 0 f 1 (fundamental) transition dipole vector for the CN oscillator. For the 0 f 1 (fundamental) transition of the ν2 vibration in rigid bulk liquid CH3CN, μ^ is accurately modeled within the Condon approximation in which it reduces to a unit vector along the molecular axis—that is, the line shape is a convolution of the spectral diffusion and molecular reorientation. There is some disagreement in the literature regarding the vibrational lifetime (see section 1). Based on the most recent report,50 it appears to be sufficiently long (∼80 ps) that its effects can be neglected in calculating the line shape. On the other hand, several earlier reports based on line shape analyses estimated it to be around 3.5 ps.45,4749 In analyzing the origin of the vibrational line shape in section 3.3, we use the latter lifetime; we note that this choice affects only the magnitude of the line width, not the conclusions about the contributions of the surrounding molecules. 2.2. Mechanistic Analysis. The frequency shifts in the 0 f 1 vibrational fundamental transition at each time step can be decomposed into contributions from particular intermolecular

M

3

ð8Þ

and similarly for FN. Here, M is the number of CH3CN molecules; R indexes the three interaction sites on each molecule; f jR C is the force on the carbon atom due to site R on molecule j; F Cj is the total force on the carbon atom due to all sites on molecule j; and FlrC is the force due to the long-range electrostatics, for example, the periodic-image contributions in an Ewald sum. From this expression, it is clear that the total frequency shift can be decomposed in terms of the contributions from each of the other molecules in the minimum-image simulation box of the liquid and a long-range electrostatic term ΔE01 ¼ where

M

∑ ΔEj01 þ ΔElr01 j¼2

j ΔE01

μ ¼ ðQ11 Q00 Þ F mC

and

j C

μ F mN

ð9Þ

j N

3 ^r CN

μ lr μ FC FlrN 3 ^r CN mC mN

ð10Þ

ΔElr01 ¼ ðQ11 Q00 Þ

#+

0

M

jR f C þ FlrC ¼ ∑ F jC þ FlrC ∑ ∑ j¼2 R¼1 j¼2

ð11Þ

Analysis of these contributions can yield considerable information about the mechanism of the frequency shifts. 2.3. Simulation Details. Classical molecular dynamics (MD) simulations were carried out using the DL_POLY_2 software92 with modifications to calculate the frequencies and obtain mechanistic information as described in sections 2.1 and 2.2. Liquid acetonitrile was simulated using 256 molecules in a cubic box of length 28.3736 Å on a side, giving a density of F = 0.764 g/cm3. The acetonitrile interactions were modeled using the three-site, rigid ANL potential.93 Lennard-Jones interactions were evaluated with a cutoff of 15 Å. Long-range electrostatic interactions were included using three-dimensional periodic boundary conditions with a smoothed particlemesh Ewald summation using an Ewald parameter of R = 0.23464, a 6 6 6 k-point grid for fast Fourier transforms, and a cutoff of 15 Å. Simulations of bulk CH3CN were initiated from an fcc lattice and begun with a 1-ns equilibration stage with 2-fs time steps, during which velocity rescaling was used to achieve a simulation temperature of approximately 300 K. Data were then collected over two separate 2-ns trajectories with 2-fs time steps in the NVE ensemble. The reported mean and variance for each variable of interest were obtained by simple block-averaging over 7599



Figure 1. Distribution of vibrational frequency shifts relative to the gasphase value. Results are shown for the total frequency shift (black line), the shift due to molecules in the minimum-image simulation box (red line), and long-range electrostatic contributions (blue line).

four blocks, two from each trajectory. Error bars were calculated at a 95% confidence level using the Student t distribution.94

3. RESULTS AND DISCUSSION In this section, we address a number of fundamental questions about the mechanisms of vibrational frequency shifts through the approaches described in section 2.2: What are the relative effects of long- and short-range interactions? How many surrounding molecules determine the ν2 frequency shift? What configurations are most effective for shifting the ν2 frequency to the blue (higher frequency) or to the red (lower frequency)? 3.1. Distribution of Instantaneous Vibrational Frequencies. A key way to decompose the effects of individual molecules

as well as long-range interactions is through their contributions to the normalized distribution P(Δω) of instantaneous vibrational line shifts relative to the in vacuo frequency, Δω = ω ω0. This distribution is plotted in Figure 1. It shows that the ν2 stretching frequency is red-shifted for the vast majority of acetonitrile molecules in the neat liquid. The distribution peaks around Δω = 13 cm1 and yields an average frequency shift of 11.5 cm1. This is in reasonable agreement with the 1314 cm1 red shift observed in the IR and Raman spectra.34,36,40,44,45 We note that the infrared line shape, discussed in section 3.3 and in ref 31, is motionally narrowed because of rapid spectral diffusion and, hence, differs in shape from the frequency distribution. However, the shape of the distribution reflects the variation in perturbations felt by the molecules in the liquid and contributes strongly to the spectral peak position and line shape. The distribution displays distinct asymmetry as it tails off more slowly toward higher frequencies. In the following sections, we probe the makeup of this distribution in terms of both collective and individual molecule contributions. 3.1.1. Long-Range Electrostatics. In analyzing the mechanism of the frequency shifts, we distinguish between the contributions due to specific intermolecular interactions between each CH3CN and the other molecules in the minimum-image simulation box (eq 10) and the long-range Coulomb interactions as represented in the Ewald sum (see eq 11). The distribution of frequency shift contributions due to the former is shown as the red line in Figure 1. These minimum-image contributions to the ν2 stretching frequency average 7.8 cm1, that is, shifted by 3.7 cm1 to

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Figure 2. Distributions of the jth-ranked individual contributor to the vibrational frequency shifts, P(Δω(j)). The distributions for, from top to bottom j = 15; j = 610; j = 1115; and j = 20, 25, 30, 35, and 50 are shown in each panel. Within each group, the colors black, red, blue, violet, and brown represent increasing values of j.

the blue compared to the distribution of the total frequency shifts. Indeed, this additional red shift is clearly seen in the distribution of the long-range Ewald terms, which is sharply, and nearly symmetrically, peaked around Δω = 3.7 cm1. In contrast, the distributions of the total shift and minimum-image contributions are asymmetric and broader, with fwhm values of 11 and 9.2 cm1, respectively, compared to 3.1 cm1 for the long-range terms. Whereas the long-range interactions are almost exclusively red shifting, the minimum-image contributions are blue shifting about 7.5% of the time, which leads to roughly 4% of the total shifts being blue shifts. The asymmetry and the existence of both red-shifting and blue-shifting intermolecular interactions suggest that distinct subpopulations might underlie the shape and width of the distribution. Moreover, it indicates that competing mechanisms might be at play at the molecular level, as it is difficult to imagine a single mechanism giving rise to both red- and blue-shifting contributions. 3.1.2. How Many Molecules Determine the Distribution? In this section, we address the important question: How many of the CH3CN molecules in the surrounding liquid are involved in determining the CN stretching frequency shift? As described in section 2, at every 20th time step (every 40 fs) in the MD simulation, the instantaneous line shift in the fundamental frequency, Δω = ω ω0, is calculated. The contribution to Δω for a chosen molecule due to another molecule in the liquid labeled j is then given by Δω(j) = ΔE(j) 01 /p in eq 10. These individual molecular contributions were calculated for each acetonitrile molecule and ranked in descending order Δωðrank 1Þ g Δωðrank 2Þ g 3 3 3 g Δωðrank N 1Þ

ð12Þ

To understand how molecules contribute to the total line shift, these individual, ranked frequency shifts are collected into distributions, P(Δω(j)), obtained over the MD trajectory for each rank j. The distributions for j = 115, 20, 25, 30, 35, and 50 are shown in Figure 2. The distributions for j = 115 are all bimodal, with peaks corresponding to both red- and blue-shifting interactions, indicating significant and competing effects. In particular, the j = 1 7600



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Figure 3. (Left) Average frequency shift, ÆΔω(j)æ, due to the jth-ranked contributing molecule (top, violet line) and the total shift due to the top n contributors, ÆΔΩ(n)æ (bottom, red line) plotted against the contributor rank (j or n). (Right) Residual, P(ΔΩ(N1)) P(ΔΩ(n)), for different n values between the total minimum-image frequency shift distribution and the distribution using n contributors. Results are shown for n = 1 (solid black line), 2 (solid red line), 3 (solid blue line), 4 (solid violet line), 5 (solid brown line), 6 (dashed black line), 7 (dashed red line), and 8 (dashed blue line).

distribution (i.e., the strongest contributor at each time step) clearly shows that CH3CN molecules generally experience a single, strong intermolecular interaction that shifts the vibrational frequency either toward the blue or toward the red by about 4 cm1 on average. The asymmetry of the distribution shows that this strongest interaction is more than three times more likely to be red shifting than blue shifting. The distributions for j = 27 look qualitatively similar but change in two distinct ways as j increases: the magnitude of the red and blue frequency shifts lessen, and the asymmetry between red- and blue-shifting interactions decreases. It is interesting to note, however, that the smaller frequency shifts and decreased asymmetry lead to greater net red-shifting contributions for the second- and third-ranked molecules on average than for j = 1 (see below). The asymmetry favoring red shifting decreases until j = 8, where the distribution is nearly symmetric. For the molecules ranked between 9 and 15, the net effect is to blue shift the vibrational frequency, whereas for j > 15, the molecules all produce a small red-shifting contribution on average. We can address the question of how many molecules determine the total distribution by using these distributions. An examination of the frequency distributions obtained from summing the frequency shift from the first n largest molecular contributions ΔΩðnÞ ¼

n

∑ ΔωðjÞ j¼1

ð13Þ

is particularly instructive. In particular, its convergence with increasing n to the total minimum-image contribution, ΔΩ(N1), where N is the number of molecules simulated, quantitatively addresses the question of the number of molecules involved in the shifts. This convergence is illustrated in Figure 3, where ΔΩ(n) as a function of n is compared with ΔΩ(N1). What is apparent from this plot is that the frequency shifts (excluding long-range electrostatics) are essentially converged by n = 6. This suggests that the frequency shift arising from individual molecular interactions is largely described by the effects of only six surrounding molecules. This is further indicated by the average frequency shift for different numbers of contributors, where ÆΔΩ(n)æ = 1.5, 3.7, 5.4, 6.6, 7.3, and 7.8 cm1 for n = 16, respectively, which can be compared with the total shift due to the minimum-image contributors of 7.8 cm1. To place

this analysis in context, the contributions for j g 7 effectively cancel each other out such that the average frequency shift, ÆΔΩ(n)æ, oscillates by less than 0.25 cm1 as it converges to the total minimum-image result. Indeed, the individual molecule contributions are quite small for the lower-ranked contributors; for example, ÆΔω(j)æ is 0.2 cm1 for j = 7 and less than 0.08 cm1 for j > 7. It is not only the average frequency shift due to individual intermolecular interactions that converges with roughly six contributing molecules, but also the distribution of frequency shifts, as illustrated in Figure 3. The right panel of that figure shows the difference in the distributions obtained by including different numbers of contributors in the determination of the frequency shift (using only minimum-image contributions). Specifically, the distribution from the top n contributors, P(ΔΩ(n)), is subtracted from the distribution of total minimum-image shifts, P(ΔΩ(N1)), shown as the red line in Figure 1. The distribution using the top six contributing molecules, n = 6, is reasonably close to the final distribution. The largest error in the n = 6 distribution is less than 15%, and the main effect of the lower-ranked (j g 7) contributors is to narrow the distribution slightly. 3.2. Spatial Distributions of Contributing CH3CN Molecules. A detailed picture of the origin of the ν2 frequency shifts for the liquid CH3CN molecules can be constructed from the distribution of positions of the surrounding molecules and their corresponding contributions to the shift. Based on the analysis of the frequency shifts in section 3.1.2 that found six dominant individual contributors, we focus particularly on those molecules. Distributions of the center-of-mass positions of the six strongest contributing molecules are shown in Figure 4, with colors indicating the average frequency shift associated with a given position relative to the affected CH3CN molecule. In addition, the frequency shifts are decomposed into contributions from the Coulombic and van der Waals interactions. A number of interesting features are readily apparent from Figure 4. This includes some of the information obtained from the frequency shift distributions plotted in Figure 2. For example, the red-shifting interactions dominate over the blue-shifting ones for these strongest contributing molecules, and the magnitudes of frequency shifts decrease steadily with increasing rank. However, considerable additional insight is also provided by these 7601



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Figure 4. Contour plots of the center-of-mass position distribution, projected onto a plane, of the surrounding CH3CN molecules contributing most strongly to the ν2 frequency shift; the color indicates the average frequency shift for a given position. The x and y axes are positions in angstroms, with the affected CH3CN molecule center of mass at the origin and the N atom pointing toward positive x. The total (Coulomb plus van der Waals) minimumimage contribution to the line shift (left column) is shown, along with its decomposition into the Coulombic (center column) and van der Waals (right column) interaction contributions. Results in each panel represent the jth-strongest contributor from j = 1 (top panel) to j = 6 (bottom panel).

plots. In particular, the origin of blue-shifting interactions can be clearly identified. The only molecules that provide a blue-shifting contribution are those that lie at the nitrogen end of the affected acetonitrile molecule. It is evident from the plot of the van der Waals contribution that these molecules exhibit repulsive, shortranged interactions that tend to compress the CN bond, resulting in an increased vibrational frequency. In contrast, red-shifting contributions result from longer-range interactions, both Coulombic and van der Waals, with contributors occupying a much broader array of positions around the molecule. The short-range nature of the blue-shifting interactions limits the potential regions in which surrounding molecules can effect a blue shift in the CN stretch. Recall that, for the strongest contributor, the magnitudes of the red- and blue-shifting interactions are comparable; see Figure 2. Thus, the geometric effect due to the long-range nature of the red-shifting interactions accounts for their dominance. The decomposition of the frequency shifts into Coulombic and van der Waals contributions shows both competition and

cooperation. The strong blue shifts associated with the van der Waals interactions with the nitrogen end of the acetonitrile molecule are canceled in part by corresponding red shifts due to the Coulombic interactions. This cancellation is greater for the more weakly interacting molecules. Indeed, for these contributors, the blue shifts due to the van der Waals interactions with the nitrogen end of the molecule are nearly completely negated by the Coulombic interactions. This competition between the two interactions is a key component that makes those molecules less effective in shifting the ν2 frequency. Such a partial cancellation of the electrostatic red shifts due to van der Waals interactions was also reported for the average frequency shifts by Westlund and Lynden-Bell.51 Surrounding molecules can effect a red shift in the CN frequency from a wide range of locations. However, the position right around the center of mass, near the central carbon, gives particularly strong red shifts. Like the blue-shifting interactions, this is most conspicuous for the strongest two or three contributing molecules, for which this location gives strong red shifts 7602



Figure 5. Infrared line shapes based on the top n-ranked individual contributor to the vibrational frequency shifts. The line shapes for n = 110 (solid lines ordered as black, red, blue, violet, brown) are compared with the full line shape (dashed black line). The long-range corrections, reorientational dynamics, and vibrational relaxation (using T1 = 3.5 ps) are included to obtain each line shape, independent of n.

with contributions from both Coulombic and van der Waals interactions. Molecules positioned on the methyl side of the molecule of interest uniformly give a red shift due to electrostatic interactions. A broad range of such red-shifting locations is seen, but this is more prevalent for the lower-ranked contributors, for example, third-ranked and beyond, indicating the naturally weaker nature of these longer-range interactions. Finally, we note that, not surprisingly, the top six contributors, which account for virtually all of the net frequency shift, are primarily associated with what would be described as the first solvation shell (which is roughly defined by a radius of ∼6 Å between centers of mass and contains approximately 10 molecules). That is, they are immediately adjacent to the acetonitrile molecule of interest. However, lower-ranked contributors are also located in the first solvation shell, as well as more distant locations. Thus, although location is a prerequisite for influence on the CN frequency, it is not a guarantee. 3.3. Infrared Spectrum. To this point the analysis has focused on the frequency and its distribution. It is also instructive to examine how the infrared line shape converges with the number of liquid molecules contributing to the frequency shift. This is shown in Figure 5. The line shapes are obtained using eqs 5 and 6, with δω(t) replaced by ΔΩ(n)(t) plus the long-range corrections, which are independent of n; the vibrational lifetime is taken to be T1 = 3.5 ps based on experimental data,45,4749 which affects the magnitude of the line width, but not the convergence with the number of contributing molecules. Thus, the convergence shown is based on how the average frequency shift (i.e., the peak position) and the spectral diffusion change with different numbers of contributors. The effect of the vibrational lifetime and the reorientational dynamics of the molecule of interest on the line shape are included in the same way for all n. We note that the primary result of including the long-range electrostatic terms is to shift the spectrum by 3.7 cm1 to the red, with only a slight broadening. We first note that the maximum in the infrared peak of the full line shape (including all contributors) is shifted by 11.7 cm1 from the gas-phase frequency, compared to the 1314 cm1 red shift observed experimentally from the IR spectrum34,36,40,44,45 and the 13 cm1 shift found in the frequency distribution (see

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section 3.1). The line width (fwhm) for the calculated spectrum is 6.1 cm1, compared to 5.9 cm1 obtained for the CN stretching peak in the IR spectrum after deconvolution with an overlapping hot band.45 Thus, the features in the simulated spectrum are in quite good agreement with the available experimental data.95 Given that the acetonitrile interactions used in this work, which involve only a three-site model,93 have not been optimized in any way for spectroscopic simulations, this agreement is highly encouraging. It suggests that the model is a reasonable representation of the liquid acetonitrile properties that determine the CN stretching spectral features. It can be seen from Figure 5 that the line shape with the inclusion of the six strongest contributors is in good agreement with the full result. The effect of the remaining, more weakly interacting acetonitrile molecules is to slightly narrow the spectrum. It is important to note that the convergence behaviors of the line shape and frequency distribution are essentially the same. This supports the use of the frequency distribution in the above examination of the qualitative and quantitative contributions of molecules to the frequency shift. The vibrational dynamics, as measured by the fwhm of the line shape, show relatively modest changes with the number of contributors included in the calculation. (Recall that the effects of rotational dynamics and vibrational relaxation are included in the same way for each n.) The fwhm is 5.7 cm1 if only the acetonitrile molecule making the strongest contribution is used to determine the frequency shift compared to 6.1 cm1 for the full line shape. As the number of contributors is increased, the line shape broadens, reaching a broad maximum of ∼6.4 cm1 for n = 610 before declining as the remaining contributing molecules used in the calculations are included. This suggests that the vibrational dynamics as represented by the spectral diffusion, that is, the fluctuations in the vibrational frequency with time, δω(t), are not strongly dependent on the number of contributors.

4. CONCLUSIONS We have analyzed the molecular-level origin of the vibrational frequency shifts in the CN stretching (ν2) mode of acetonitrile in the bulk liquid. The perturbation theory description of the vibrational frequency gives shifts relative to the isolated molecule of 13 and 11.7 cm1 for the maximum in the frequency distribution and the IR spectrum, respectively. These are in good agreement with the measured 1314 cm1 red shifts reported in the literature.34,36,40,44,45 The calculated IR line width of 6.1 cm1 for the CN stretch is likewise in accord with the observed value of 5.9 cm1 obtained after accounting for the effect of an overlapping hot band.45 These results indicate that the CH3CN model used here, although simple and not optimized for spectral simulations, represents the CN stretching properties well in the neat liquid. The key observations from the mechanistic analysis include the following: (1) Long-range electrostatic interactions, those beyond the minimum-image simulation cell, are important but not dominant, contributing about a third of the overall average red shift for the ν2 mode in liquid acetonitrile compared to the gas phase. (2) Beyond these long-range interactions, roughly six surrounding molecules account for the total average frequency shift and, more importantly, the distribution of 7603


The Journal of Physical Chemistry B instantaneous frequencies. This clearly eliminates a picture of the frequency shifts as arising from a large number of small interactions of similar size. (3) Blue-shifting contributions arise from molecules interacting at short range with the nitrogen end of the nitrile group, whereas the red-shifting contributions originate from a broad distribution of positions all around the molecule, including from around the methyl end. Thus, molecules must necessarily occupy a limited region in space to effect a blue shift, but the same is not true for the molecules exerting a red-shifting influence. The strongest contributors are therefore significantly more likely to have red-shifting interactions than blue-shifting ones. (4) Even though Coulombic interactions are important in determining the frequency shift, the molecules in the minimum-image simulation box that determine the shift are almost exclusively located in the first solvation shell. Other molecules within and outside this solvation shell have no net effect on the average frequency shift and only small effects on the frequency distribution and infrared line shape. It is interesting to note that the picture that emerges for the CN stretching mode in acetonitrile differs in important ways from that recently established for the OH stretching mode in water.24,5860 In the latter case, the OH frequency is strongly correlated with the electric field along the bond. This empirical relationship is sometimes taken as an indication that the frequency shifts are dominated by the fluctuations in the electrostatic environment of the molecule.4,58,60 In contrast, for acetonitrile, the short-ranged van der Waals interactions play an important role, giving rise to blue-shifting contributions that are not observed from electrostatic interactions. However, this is in general agreement with simulations of CN in water by Rey and Hynes.85 They found that the average frequency shift was determined by a cancellation of red-shifting Coulombic interactions by even larger blue shifts induced by repulsive van der Waals forces. The generality of the above conclusions to other polar liquids and other environments for acetonitrile is not yet clear, but is an important issue for current and future investigations. To aid in interpreting measurements using the nitrile frequency as a probe of environment, further investigations should clarify the effect on frequency shifts and line shapes of a hydrogen-bonding donor that blue shifts the CN frequency. Indeed, additional studies are warranted into how the lessons learned by examining the shifts of a particular mode in one environment can be extended to others.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the National Science Foundation (Grants CHE-0518290 and CHE-1012661). ’ REFERENCES (1) Møller, K. B.; Rey, R.; Hynes, J. T. J. Phys. Chem. A 2004, 108, 1275–1289. (2) Corcelli, S. A.; Lawrence, C. P.; Skinner, J. L. J. Chem. Phys. 2004, 120, 8107–8117.

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Molecular-Level Mechanisms of Vibrational Frequency Shifts in a

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