Atom Substitution Effects of - American Chemical Society

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J. Phys. Chem. B 2009, 113, 9840–9851

Atom Substitution Effects of [XF6]- in Ionic Liquids. 2. Theoretical Study Tateki Ishida,*,† Keiko Nishikawa,‡ and Hideaki Shirota*,‡ Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, 38 Nishigo-Naka Myodaiji, Okazaki 444-8585, Japan, and Department of Nanomaterial Science, Graduate School of AdVanced Integration Science, Chiba UniVersity, 1-33 Yayoi, Inage-ku, Chiba 263-8522, Japan ReceiVed: NoVember 10, 2008; ReVised Manuscript ReceiVed: March 30, 2009

Following the preceding spectroscopic study, we further investigate atomic mass effects of [XF6]- in 1-butyl3-methylimidazolium cation ([BMIm]+) based ionic liquids (ILs) on dynamical natures by a computational approach in this study. We carry out the molecular dynamics simulations for 1-butyl-3-methylimidazolium cation based ILs ([BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6]) with the development of the force fields of [AsF6]- and [SbF6]- by an ab initio calculation. We have calculated density of state (DOS) and velocity autocorrelation function (VACF) profiles, polarizability time correlation function (TCF) and Kerr spectra, intermediate scattering functions, and dynamical structure factors. The decomposition analysis has been also carried out to understand the ion species and types of motion. From these computational studies, we find that the contribution of the reorientation of cations and anions mainly governs the Kerr spectrum profile in all three ILs, while the contribution of the collision-induced and cross terms, which are related to translational motions including coupling with librational motion, is not large at higher frequencies than 50 cm-1. It is suggested that, with the atom substitution effects of anion units on interionic interactions, many properties in ILs are controllable. In addition, it is emphasized in this study that atomic mass effects in ILs are accessible through a complementary approach of both experimental and theoretical approaches. 1. Introduction We can use various strategies to extract and understand the characteristics of ionic liquids (ILs). One of those is to observe differences in physical or chemical properties, changing an ionic species with a counterion unchanged. Many studies using this strategy have been reported.1-8 However, there have been few accounts of research on the comparison of ILs with the replacement of not an ionic species (or unit) but an atomic element in it. Recently, Shirota and Castner9 have discovered the large magnitude of decrease in shear viscosities by the replacement of the 1-methyl-3-neopentylimidazolium cation [C-mim]+ with the 1-methyl-3-trimethylsilylmethylimidazolium cation [Si-mim]+ in the conversion of the neopentyl group to the trimethylsilylmethyl group of the cation. Their results indicated that both the bulk property and the interionic interaction in ILs can be sensitive to the change even in the small atomic part of the ionic species. Thus, it is considered to be important to pursue the differences in bulk properties caused by an atomic-level distinction for studying the interaction among ions in ILs at a molecular level. In the preceding paper (DOI 10.021/jp809880j), we have focused on the relation between the mass effect in anion species and the differences in the interionic vibration, which seems to be one of the observable properties for specifying the molecular-level intermolecular interaction in the condensed phase. We have focused on the mass effects of the anion species on the bulk properties, such as shear viscosity and density, and interionic vibration, which would specify the microscopic interionic interaction in ILs. The interionic vibrational dynamics of 1-butyl-3-methylimidazolium hexaflu* To whom correspondence should be addressed. E-mail: ishida@ ims.ac.jp (T.I.) and [email protected] (H.S.). † Institute for Molecular Science. ‡ Chiba University.

oropentelate ([BMIm][XF6])(X ) P, As, and Sb) has been investigated with the femtosecond optically heterodynedetected Raman-induced Kerr effect spectroscopy (OHDRIKES) technique. We have found out that the difference in the spectrum profiles of ILs could be seen clearly depending on the mass of a center atom in an anion: in particular, in the frequency region less than 50 cm-1, where the interactioninduced motions10,11 of the ion species dominantly affect the vibrational spectrum. From these findings, the subjects we need to study further are (1) how we can resolve the experimentally observed spectrum into a contribution from each ionic component and extract the roles of the cation and anion, (2) how or to what degree the variation of atomic mass actually influences the motions of cation and anion species, and (3) how atomic mass effects emerge on the dynamical properties of ILs. To complement the many difficulties in extracting the detailed information of interionic dynamics only from spectroscopic data with femtosecond laser experiments,9,12-20 molecular dynamics (MD) simulation is one of the promising procedures for investigating the molecular motions governed by specific interaction and the property related to it with high resolution. Therefore, it is expected that a theoretical study collaborating with experimentalists can expand and improve our view and understanding of ILs.21 On the IL studies, there have been MD simulation researches22 and some trials for studying ILs by the comparison of relevant spectroscopic experiments with MD simulation works.23-29 Urahata and Ribeiro26 carried out the MD simulations for [BMIm][PF6] and [MOIm][PF6] and compared their result with the experimental result of Wynne and coworkers.19 From their studies, it was shown that the interionic vibrational spectrum of ILs includes the contribution from the interionic interaction among ion species and that important information on the motion of the cation and anion in ILs is

10.1021/jp8098818 CCC: $40.75  2009 American Chemical Society Published on Web 06/25/2009

Atom Substitution Effects. 2. Theoretical Study

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provided by the comparison of the density of states (DOS) profile with the spectrum by an OHD-RIKES experiment. Also, Hu et al.30 reported a MD study of the Kerr spectra of an IL, 1-methoxyethylpyridinium dicyanoamide. They compared computed Kerr spectra with the experimental data12 and studied intermolecular dynamics in the IL. Their results indicated that the Kerr spectrum profile depends on the intermolecular interactions between cation and anion molecules. In this paper, we investigate the atomic substitution effect on the interionic interaction and dynamics in ILs, [BMIm][XF6] (X ) P, As, and Sb) with the MD simulations. For executing MD simulations for a series of [XF6]-, we newly develop the force fields of the [AsF6]- and [SbF6]- anions and propose them. We discuss the results of the DOS and velocity autocorrelation function (VACF) profiles referring to the experimental data shown in the preceding paper (DOI 10.021/jp809880j) and investigate the atomic substitution effect on the motion of ions under an interionic interaction which is specific to ILs. Also, we carry out the computation of the polarizability time correlation function (TCF) of three IL systems, employing the dipoleinduced-dipole (DID) approximation,10 and calculate the Kerr spectrum profile of the systems. Then, we compare the calculated Kerr profiles with the experimental data reported in the preceding paper (DOI 10.021/jp809880j) and investigate the contributions of interionic dynamics and molecular motions to the Kerr spectra with the decomposition analysis of the total Kerr signal into each component of polarization anisotropy relaxation related to ion dynamics. In addition, dynamical properties such as an intermediate scattering function and a dynamical structure factor are calculated, and the mass effects on these properties are also studied. Finally, we will consider how mass effects influence the motion of ions and the interionic interaction at molecular level. 2. Computational Details 2.1. Force Field Parameter Determination for [AsF6]- and [SbF6]-. We can utilize the force field parameters for [BMIm]+ and [PF6]- reported by Lopes et al.;31,32 however, to our best acknowledgment, force field parameters of [AsF6]- and [SbF6]anions have not been reported, yet. Therefore, it is desired to develop intramolecular potential parameters for the [AsF6]- and [SbF6]- anions. Here, we describe the scheme for determining those parameters. Employing an ab initio calculation, we first optimized the geometry of the anion by preparing start geometry for each anion to fit potential functions. The Gaussian 03 program package33 was used for all of the quantum chemistry calculations. We used the DFT/B3LYP34,35 level theory, and the cc-pVDZ36,37 and ccpVDZ-PP38 basis sets were employed for F and P and for As and Sb, respectively. All of the degrees of freedom in the anion were optimized. On the basis of these optimized geometries, the determination of force field parameters was carried out. For the fitting of potential functions, we employed the following expressions of potential functions considering contributions from intramolecular bond stretching and angle bending:

Vbond ) k1(r - r0)2

(1)

Vbend ) k2(θ - 90°)2 + k3(φ - 180°)2

(2)

where r0 is a bond length at the optimized structure and θ and φ represent bending angles in a plane and out of a plane,

Figure 1. Definitions of the bending angle in [XF6 ]-.

TABLE 1: Force Field Parameters of [PF6]-, [AsF6]-, and [SbF6]k1 (kJ/(mol Å2)) k2 (kJ/(mol rad2)) k3 (kJ/(mol rad2)) r0 (Å) a

[PF6]-a

[AsF6]-b

[SbF6]-b

1550.00 582.50 145.5 1.606

1225.51 533.54 84.86 1.799

1153.57 406.19 31.58 1.964

From refs 31 and 32. b Fitted parameters.

TABLE 2: LJ Parameters and Atomic Charges for [PF6]-, [AsF6]-, and [SbF6]LJ Parameters ε (kJ/mol) P As Sb

0.8368 1.715b 2.301b

σ (Å)

a

3.740a 3.697b 3.875b

Atomic Charges q (e) P F ([PF6]-) As F ([AsF6]-) Sb F ([SbF6]-) a

1.3400a -0.3900a 1.1690c -0.3615c 1.5164c -0.4194c

From refs 31 and 32. b From ref 39. c Fitted parameters.

respectively (see Figure 1). In the calculation of potential energy surfaces, bond lengths, and bending angles were varied as follows. For bond stretching, the bond length was changed in a range of (∆R, (2∆R, and (4∆R (∆R ) 0.05 Å), and also, for bending, an angle was varied in a series of (∆θ and (2∆θ or (∆φ and (2∆φ (∆θ or ∆φ ) 5°). With the combination of these bond and angle variations with respect to the optimized structure, an electronic structure calculation has been performed for each conformation. In total, about 1560 points were collected for fitting. In Table 1, the obtained force field parameters for [AsF6]- and [SbF6]- are shown. Also, Table 2 includes the Lennard-Jones (LJ) parameters and atomic charges we used. The LJ parameters were adopted from sets in the computer simulation.39 Atomic charges were determined with the ChelpG charge fitting procedure.40 Tables 1 and 2 include the parameters used for [PF6]- for comparison.31,32 With these obtained parameters, we examined the availability of the derived force field of [AsF6]- and [SbF6]- anions with a MD simulation procedure. In the MD simulation, we utilized the DL_POLY MD suite41 for implementing newly developed force fields and executing simulation. In all the simulations, the model of anions was fully flexible, and the cation model was also flexible except for the C-H bonds.31 The C-H bonds in the cation were constrained.31 In each IL system examined, 125 ion pairs (4000 atoms) were set in a cubic box, and the

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TABLE 3: Density Comparison between Experimental (at 297 K) and Calculated (at 298 K) Liquid Densities of [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6] [BMIm][PF6] [BMIm][AsF6] [BMIm][SbF6]

exptl (g/mL)

calcd (g/mL)

1.368 1.540 1.690

1.322 1.481 1.618

periodic boundary condition was applied. A section of 12 Å was taken as cutoff length. The time step was 0.5 fs. The longrange Coulomb term was treated using Ewald’s summation technique.42 MD simulations for determining force fields were carried out referring to the literature31 as follows. At first, all of the systems were equilibrated at 600 K for 15 ns in the microcanonical system (under controlled volume and total energy (NVE) conditions where N is the number of particles) and then gradually cooled to 298 K to ensure proper equilibration. Then, a 250 ps NVE run for equilibration was carried out at 298 K with velocity scaling. After these equilibration runs, a 1 ns NPT simulation (under controlled pressure and temperature conditions) with the Nose´-Hoover thermostats and barostats was performed for calculating densities under 298 K and 1 atm. The time constants of temperature and pressure were set to be 0.1 and 0.5 ps, respectively.31 It should be noted that production runs in the NPT simulation were started after 300 ps equilibrations referring to the literature.31 Table 3 shows the calculated densities from simulation data and the experimental data shown in the preceding paper for comparison. As seen in Table 3, the simulated density results are slightly smaller than the experimental ones, but our simulation results are in good accord with the observed data and reproduce the tendency for the densities of the three ILs (DOI 10.021/jp809880j). Also, with additional 5 ns simulation data, we examined dynamical properties such as diffusion coefficients and viscosities in comparison with the experimental results. Assuming the Stokes-Einstein relation can be applied to the systems we studied, self-diffusion coefficients, D, and viscosities, η, are related to the radius of an ion as follows: Dη ∝ kBT/r, where r represents an ionic radius and kB and T mean the Boltzmann constant and temperature, respectively. Then, we can estimate the ratio of viscosities for each system relative to that for a reference system (we chose [BMIm][PF6] as the reference) as follows

ηIL D[BMIm][PF6] r[BMIm][PF6] ) · η[BMIm][PF6] DIL rIL

(3)

where IL ) [BMIm][AsF6] or [BMIm][SbF6], D[BMIm][PF6] ) (D[BMIm] + D[PF6])/2, and DIL ) (D[BMIm] + D[AsF6])/2 or (D[BMIm] + D[SbF6])/2. From the MD simulation results, we calculated self-diffusion coefficients for cations and anions using the Einstein relation43

D ) lim tf∞

1 〈|r (t) - ri(0)| 2〉 6t i

(4)

where ri is the position vector of the center of mass of the ion i. Then, we evaluated the ratio ηIL/η[BMIm][PF6] with the molar volume results shown in the preceding paper (DOI 10.021/ jp809880j). Table 4 indicates our results of the diffusion coefficients and the comparison of the ratios, ηIL/η[BMIm][PF6], with the ratios calculated with the experimental data in the

TABLE 4: Calculated Self-Diffusion Coefficients and Comparison of the Estimated Ratio of Viscosities between Experimental (at 297 K) and Calculated (at 298 K) Results of [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6] cation

anion

IL

DCation × 10-8 (cm2/s)

DAnion × 10-8 (cm2/s)

calcd

exptla

[BMIm][PF6] [BMIm][AsF6] [BMIm][SbF6]

2.1 2.4 2.4

1.4 2.1 2.6

1.00 0.737 0.655

1.00 0.787 0.461

a

ηIL/η[BMIm][PF6]

Estimated from the results in the preceding paper.

preceding paper (DOI 10.021/jp809880j). The calculated results of the diffusion coefficients for the [BMIm][PF6] system (2.1 × 10-8 cm2/s for the cation and 1.4 × 10-8 cm2/s for the anion) are in the same order of magnitude as the reported experimental data (6.8 × 10-8 cm2/s for the cation and 4.0 × 10-8 cm2/s for the anion).44 The calculated ratios are in good accord with the experimental results, though the difference between the calculation and the experiment in [BMIm][SbF6] tends to be larger than that in [BMIm][AsF6] because of the force field we parametrized. In addition, as seen in Table 4, while the diffusion coefficient of cation is slightly modified depending on the system, the diffusion coefficients of the anion increase with the mass of a center atom in the anion. It is considered that these results indicate the decrease of interionic interactions between the cation and the anion, depending on the center atom in the anion. Therefore, though we could improve the agreement of computed densities, self-diffusion coefficients, and ratios of viscosities with experiments by adjusting parameters, the difference between our fitting results and experimental data is not of sufficient magnitude to warrant further refinement and is small enough to discuss the qualitative trend of static and dynamical features for the three ILs. 2.2. MD Computational Details for DOS’s and Dynamical Properties. With the newly developed sets of force field parameters for [AsF6]- and [SbF6]- anions, MD simulations have been carried out. The same pairs of ion species as in the force field determination were set inside a cubic box, using the configuration at the end of the NPT production run as the initial configuration. With the results of the NPT run mentioned above, the length of the cubic box size was set to be 35.47 Å for [BMIm][PF6], 35.87 Å for [BMIm][AsF6], and 36.38 Å for [BMIm][SbF6], respectively, in all of the simulation runs. We carried out canonical ensemble (under controlled volume and temperature (NVT) conditions) simulations at 298 K for 10 ns for equilibration. All of the other conditions were the same as in the force field determination described above. After the equilibration run, the production run for 5 ns was performed for each target system. Simulation data were recorded every 10 fs and collected during production runs. 2.3. Polarizability TCF and Kerr Spectra. 2.3.1. Theoretical Background. The Kerr response for OHD-RIKES with the typical polarization setup is connected with the relaxation of the polarizability anisotropy of the system. Therefore, to investigate comparing it with the experimentally observed Kerr spectra, it is required to calculate the TCF of off-diagonal elements of the total polarizability of the system.10 Here, the theoretical background of the polarizability TCF is summarized. The total polarizability of the system, Π(t), is represented as the sum of the molecular polarizability, ΠΜ(t), and the interaction-induced polarizability, ΠΙΙ(t), as follows,



Π(t) ) ΠM(t) + ΠII(t)

(5)

where t indicates the time dependence and the superscripts M and II represent the molecular part and the interaction-induced part, respectively. The molecular part is the sum of the polarizability tensors of isolated gas phase molecular polarizability in the laboratory frame, N

ΠM(t) )

∑

Ri(t)

(6)

φ(t) ) 〈Tr[(βM(0) + βII(0)) · (βM(t) + βII(t))]〉 ) 〈Tr(βM(0) · βM(t))〉 + 〈Tr(βII(0) · βII(t))〉 + 〈Tr(βM(0) · βII(t))〉 + 〈Tr(βII(0) · βM(t))〉 ) φ (t) + φind(t) + φcross(t) mol

(10) where

φmol(t) ) 〈Tr(βM(0) · βM(t))〉

i)1

φind(t) ) 〈Tr(βII(0) · βII(t))〉 where N is the number of molecules and Ri denotes the polarizability tensor of molecule i. The interaction-induced part comprises the modulation of the molecular polarizabilities due to the intermolecular interactions and the contributions from the inducedmultipole components. For the computation of the interactioninduced part, we employed the DID model approximation,10,45 which assumes that the molecular polarizabilities are modulated because of a dipolar coupling and that the influence of higher order multipoles is not considered. Also, it should be noted that the DID model used in this study is a center-center DID model, where it recognizes the polarizability as concentrated in the center of mass of the molecule. The interaction-induced polarizability in the DID approximation is represented as follows, N

ΠII(t) )

φcross(t) ) 〈Tr(βM(0) · βII(t))〉 + 〈Tr(βII(0) · βM(t))〉 The nuclear response function, R(t), due to motion of the nuclei, is related to the time derivative of the polarizability TCF, φ(t),

R(t) ) -

1 ∂ φ(t) kBT ∂t

(11)

The Kerr signal in the frequency domain, R(ω), is provided by the imaginary part of the Fourier transform of the R(t), and the R(ω) is represented as, including quantum corrections to the classically obtained spectrum,46,47

N

∑ ∑ Ri(t) · Tij(t) · R˜ j(t)

(7)

i)1 j*i

where Tij means the dipole interaction tensor between molecules i and j. R˜ i(t) is the effective polarizability for molecule i defined by the following equation including the interaction-induced effects,

∑ Ri(t) · Tij(t) · R˜ j(t)

(8)

j*i

Equation 8 can be solved by the calculation procedure which is called the all-orders DID approximation.45 The total polarizability of the system, Π(t), can be reorganized, separating it into the isotropic, (1/3)Tr(Π(t))I, and anisotropic, βM(t) and βII(t), components as follows,

{

1 - e-pω/kBT 1 + e-pω/kBT

∫0∞ sin(ωt) R(t) dt

}

{

(13)

where Rmol(ω), Rind(ω), and Rcross(ω) denote the Kerr spectra components for the molecular part, the interaction-induced part, and the molecular-interaction-induced cross-correlation part contributions, respectively. ILs are composed of cations and anions. Therefore, the total polarizability of the system can be decomposed into the cationic and anionic components,30

Π(t) ) ΠC(Cation)(t) + ΠA(Anion)(t)

1 1 Π(t) ) Tr(Π(t))I + ΠM(t) - Tr(ΠM(t))I + 3 3 1 ΠII(t) - Tr(ΠII(t))I 3 1 ) Tr(Π(t))I + βM(t) + βII(t) 3

(12)

where p ) h/2π and h means the Planck constant. With eqs 10, 11, and 12, the R(ω) can be separated into three components,

R(ω) ) Rmol(ω) + Rind(ω) + Rcross(ω)

N

R˜ i(t) ) Ri(t) +

R(ω) ) 2 ×

(14)

Referring to eqs 5, 6, and 7, the ΠC(t) and ΠA(t) are represented as follows,

}

ΠC(t) )

(9) where I is the unit tensor, βM(t) ) {ΠM(t) - (1/3)Tr(ΠM(t))I}, and βII(t) ) {ΠII(t) - (1/3)Tr(ΠII(t))I}. Therefore, the TCF of the off-diagonal elements of the total polarizability, φ, can be rewritten and separated into three parts: a molecular part, φmol, an interaction-induced part, φind, and a molecular-interactioninduced cross-correlation part, φcross, as follows,

(t) + ∑ RC(II) (t) ∑ RC(M) k k

(15)

∑ RlA(M)(t) + ∑ RlA(II)(t)

(16)

k)1

ΠA(t) )

l)1

k)1

l)1

where the indices k and l go over all cations and anions, respectively. Then, the total polarizability of the system, Π(t), can be rewritten in the similar form to eq 9,

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1 Π(t) ) Tr(ΠC(t) + ΠA(t))I + 3 1 1 ΠC(t) - Tr(ΠC(t))I + ΠA(t) - Tr(ΠA(t))I 3 3 1 ) Tr(ΠC(t) + ΠA(t))I + βC(t) + βA(t) 3 (17)

{

} {

}

where βC(t) ) {ΠC(t) - (1/3)Tr(ΠC(t))I} and βA(t) ) {ΠA(t) - (1/3)Tr(ΠA(t))I}. The polarizability TCF, φ, can be rewritten as follows,

φ(t) ) 〈Tr[(βM(0) + βII(0)) · (βM(t) + βII(t))]〉 ) 〈Tr[(βR(0) + βCI(0)) · (βR(t) + βCI(t))]〉 ) 〈Tr(βR(0) · βR(t))〉 + 〈Tr(βCI(0) · βCI(t))〉 + 〈Tr(βR(0) · βCI(t))〉 + 〈Tr(βCI(0) · βR(t))〉 ) φR(t) + φCI(t) + φR-CI(t)

(22) where

φR(t) ) 〈Tr(βR(0) · βR(t))〉

φ(t) ) 〈Tr[(βC(0) + βA(0)) · (βC(t) + βA(t))]〉 ) 〈Tr(βC(0) · βC(t))〉 + 〈Tr(βA(0) · βA(t))〉 +

φCI(t) ) 〈Tr(βCI(0) · βCI(t))〉

〈Tr(βC(0) · βA(t))〉 + 〈Tr(βA(0) · βC(t))〉 ) φ (t) + φA(t) + φC-A(t) (18) C

φR-CI(t) ) 〈Tr(βR(0) · βCI(t))〉 + 〈Tr(βCI(0) · βR(t))〉 The Kerr signal in the frequency domain, R(ω), can be rewritten as follows,

where

φC(t) ) 〈Tr(βC(0) · βC(t))〉

R(ω) ) RR(ω) + RCI(ω) + RR-CI(ω)

φA(t) ) 〈Tr(βA(0) · βA(t))〉

where RR(ω), RCI(ω), and RR-CI(ω) denote Kerr spectra components for the reorientational part, the collision-induced part, and the reorientational collision-induced cross-correlation part contributions, respectively. 2.3.2. Calculation Details for Polarizability TCF. In Figure 2, the body-fixed coordinate axes we set in the cation and the anion are shown. For the calculation of gas-phase molecular polarizability tensors of the cation and the anion, we used the Gaussian 03 program package.33 We employed the DFT/B3LYP34,35 level with the cc-pVDZ36,37 basis sets for [BMIm]+, F, and P and the cc-pVDZ-PP38 basis sets for As and Sb. Table 5 displays the computed molecular polarizability tensor elements of the cation and the anion. For the calculation of the molecular polarizability, eq 8 was solved iteratively by the efficient iteration scheme proposed by Kiyohara et al.49 under the all-orders DID approximation. We also employed the Thole’s model50 in a simplified way for avoiding the nonphysical divergence of the polarization50 in the computation of dipole interaction tensors. In our calculation, we considered the distance and vector between the centers of mass of distinct molecules in the dipole interaction tensor, T ) (I - 3rˆrˆ)/r3, where rˆ ) r/r. Therefore, the range of the attenuation of dipolar interactions at short distances, s, was evaluated with the definition50 s ) 1.662(Ai Aj)1/6, where Ai and Aj denote the molecular polarizabilities set at the centers of mass of the molecules i and j, respectively. It should be noted that, only in determining the range of attenuation of dipolar interactions, both the Ai and the Aj were taken as isotropic and scalar in our model and that, for the molecular polarizabilities, Ai and Aj, we used 14.372 Å3 for [BMIm]+, 3.1602 Å3 for [PF6]-, 3.8635 Å3 for [AsF6]-, and 4.5745 Å3 for [SbF6]-, on the basis of the ab initio calculations (see Table 5). The dipole interaction tensor we used is given by50

φC-A(t) ) 〈Tr(βC(0) · βA(t))〉 + 〈Tr(βA(0) · βC(t))〉 Corresponding to eq 13, the Kerr signal in the frequency domain, R(ω), is given by three components,

R(ω) ) RC(ω) + RA(ω) + RC-A(ω)

(19)

where RC(ω), RA(ω), and RC-A(ω) denote Kerr spectra components for the cation contribution, the anion contribution, and the cation-anion cross-correlation part contribution, respectively. While the separation of βM(t) and βII(t) enables us to distinguish the molecular contribution from the interactioninduced contribution, it is required to use the separation procedure which describes dynamics in ILs, such as the librational and reorientational dynamics, of molecular ions. To investigate the dynamics in three ILs further, it is important to extract the interaction-induced effect due to the reorientation from the interaction-induced polarizability part, βM(t) + βII(t) (see eq 9). Therefore, we employ the projection scheme for the separation of the reorientational part from the collision-induced part as proposed in previous works.10,48 To carry out the projection scheme, the interaction-induced polarizability part in eq 9 can be rewritten as

βM(t) + βII(t) ) (1 + f)βM(t) + (βII(t) - fβM(t)) ) βR(t) + βCI(t)

(20) where the projection factor, f, is defined as

f)

Tr(βII · βM) Tr(βM · βM)

T ) (I - 3rˆrˆ)/r3

(21)

and the subscripts R and CI denote reorientational and collisioninduced contributions, respectively. Then, the polarizability TCF, φ, can be represented as follows,

(r > s)

T ) [(4V3 - 3V4)I - 3V4rˆrˆ]/r3 where V ) r/s.

(23)

(24) (r e s)

(25)



Figure 2. Definitions of body-fixed coordinate axes for [BMIm]+ and [XF6 ]-. In [BMIm]+, the Y direction is along the line connecting two nitrogen (blue colored) atoms in the ring, and the Z direction is set perpendicular to the ring plane and the Y direction axis. The X direction is set in the ring plane orthogonal to both the Y and the Z axes. In [XF6]-, the X, Y, and Z direction axes are set equivalently.

TABLE 5: Components of the Molecular Polarizability Tensor Elements from an Ab Initio Calculation for [BMIm]+, [PF6]-, [AsF6]-, and [SbF6]- (Units in Å3) [BMIm]+ [PF6][AsF6][SbF6]a

RXXa

RXYa

RYYa

RXZa

RYZa

RZZa

13.625 3.1602 3.8635 4.5745

0.64676 0.00000 0.00000 0.00000

18.741 3.1602 3.8635 4.5745

-0.27918 0.00000 0.00000 0.00000

-1.5650 0.00000 0.00000 0.00000

10.763 3.1602 3.8635 4.5745

X, Y, and Z directions are set as shown in Figure 2.

3. Results and Discussion In this section, first, we show and discuss the profiles of DOS and VACF, referring to the OHD-RIKES experimental results. Then, we carry out the direct comparison of computed Kerr spectra with the experimentally obtained Kerr spectra. Finally, the discussion of dynamical properties of ILs will be given. 3.1. DOS and VACF Profiles. 3.1.1. DOS and VACF Calculations. With MD simulation results, we calculated VACFs, 〈Vi(0) · Vi(t)〉, where Vi(t) is the velocity of ith ionic species, and obtained the vibrational DOS’s with the Fourier transformation of VACFs. All of the DOS spectra are calculated as area normalized spectra,

∫

IDOS(ω) ) I(ω)/ I(ω) dω

(26)

where IDOS(ω) represents the frequency dependent area normalized DOS intensity and I(ω) is the calculated DOS from MD simulation. In this study, we calculated the time correlation of the total velocity which includes the velocities of all of the atoms in each system (hereafter, denoted as total (anion and cation) DOS), and also the TCFs were calculated for cation and anion species, respectively. Figure 3 displays the total, cation, and anion DOS results in [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6], respectively, including the low-frequency spectrum by the OHD-RIKES experiment indicated in the preceding paper (note that Figure 3d is also area normalized spectra from the experiment; DOI 10.021/jp809880j). 3.1.1a. Total (Anion and Cation) DOS and VACF Profiles. Figure 3a shows that the peak frequency shifts toward the lowfrequency region, depending on the mass of the center atom in [XF6]-. Our MD simulation results agree with the spectral feature that the broad peak appears at around 100 cm-1 in the experimental Kerr spectrum (Figure 3d), while the broad peak seen at low frequencies does not appear clearly in the calculation results.

Figure 3. Comparison of calculated DOS profiles with the Kerr spectra: (a) total DOS, (b) cation DOS (thin line), imidazolium ring contribution (thick line), and butyl chain contribution (dotted), (c) anion DOS, and (d) the Kerr spectra ([BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6]). All are area normalized spectra.

The total VACF profiles for the three ILs (Figure 4a) include the oscillatory behavior similar to the VACFs of the cation (Figure 4b). As seen in Figure 4c, however, each anion VACF shows the first minimum after 0.40 ps and does not include an oscillatory behavior. For the difference between the calculation (Figure 3a) and the experiment (Figure 3d), there are several aspects that are accessible to us. First is the possibility of the many-body interaction effects such as a three-body interaction inside ILs, which could be attributed to the accuracy of the potential functions used in MD simulations. The second aspect is the polarization effect due to the many-body interaction effects,

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Figure 5. Comparison of the calculated Kerr spectra for [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6] with the experimental Kerr spectra: (a) the calculated (area normalized) Kerr spectra up to 120 cm-1 and (b) the experimental Kerr spectra.

Figure 4. VACFs for (a) total (anion and cation), (b) cation, and (c) anion. The insets in (a) and (b) show magnification of the time region between 0.10 and 0.75 ps.

which could govern interaction-induced effects10,11 remarkably seen at the low-frequency domain.51-53 3.1.1b. Cation DOS and VACF Profiles. The normalized DOS’s of the cation in Figure 3b indicate some of the same general trends as the corresponding Kerr profiles observed in the experiment shown in Figure 3d; namely, the PF6 profiles show relatively greater intensity at low and high frequencies relative to the AsF6 and SbF6 profiles. This trend is evident in the DOS’s calculated from only the imidazolium ring atoms but not those from the butyl group, which are similar in all three ILs. Figure 4b shows that each VACF for the cation clearly shows an oscillatory behavior similar to the cage effect which has been observed in simulation studies of alkali halides.54 This oscillation can be ascribed to a short-time rattling motion of the lighter [BMIm]+ inside a cage in which heavier anions form.54 In addition, the overall shapes of cation DOS’s in Figure 3b are similar to those of the experimental data shown in Figure 3d, corresponding to the fact that, in the OHD-RIKES experiment, the Kerr spectrum has been generated with the signals from the asymmetric cation species. 3.1.1c. Anion DOS and VACF Profiles. Figure 3c indicates the clear differences from the cation profiles (Figure 3b). Each peak is sharper than that in the cation DOS and does not indicate broad features. With the increase of the mass of the anion, the

spectral width becomes narrow, and the peak position shifts toward the lower-frequency region. The profile of VACFs (Figure 4c) shows that the decay of VACF to its first minimum becomes slow as the mass of the anion increases (0.16 ps for [PF6]-, 0.19 ps for [AsF6]-, and 0.22 ps for [SbF6]- by fitting VACF results with a single exponential function in the range between t ) 0 and the time at the first minimum), corresponding to the decreasing tendency of the spectral width in the DOS profiles. 3.2. Kerr Spectra from Polarizability TCF and Comparison with OHD-RIKES Experimental Results. 3.2.1. Total Kerr Spectrum Profile. We show the computation results of the Kerr spectra for [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6] including the experimental result in the preceding paper in Figure 5. As seen in Figure 5a, calculated Kerr spectra include characteristic large intensities at less than 100 cm-1, and the Kerr profiles at between 100 and 120 cm-1 show relatively broad features different from the experimental results. These results indicate that the force field parameters we used are likely to include intra- and intermolecular (interionic) vibrational motions at frequencies that do not exactly correspond to those in the experimental results. As reasons for these results, we can consider several aspects. The first is that the broad spectral features at higher frequencies than 50 cm-1 in our calculation are related to the approximate model treatment that does not include the effect of the polarizability change depending on intramolecular vibrational motion attributed to high-frequency regions. The second aspect is that the DID interaction model used in this study is not the atomic site-site DID interaction model, which provides a more realistic representation of the charge distribution of molecular ions and is completely consistent with the molecular polarizability calculation. Third, it should be noted that our force field was not optimized to describe interionic interactions quantitatively. It is clear that the calculation results could capture characteristic features of interest at lower-frequency regions than 100 cm-1 as shown in the experimental result (DOI 10.021/jp809880j). Therefore, we



Figure 6. Decomposition of the computed Kerr spectra (R(ω)) into the molecular (cation + anion) and interaction-induced polarizations and the cross-correlation component: (a) [BMIm][PF6], (b) [BMIm][AsF6], and (c) [BMIm][SbF6].

Figure 7. Decomposition of the computed Kerr spectra (R(ω)) into the cation and anion contributions and the cation-anion crosscorrelation component: (a) [BMIm][PF6], (b) [BMIm][AsF6], and (c) [BMIm][SbF6].

consider that the improvement of reproducing spectrum profiles at higher frequencies than 100 cm-1 is left to further refinements of force field parameters. We focus on the spectral feature at the lower-frequency region, below. In Figure 5a, our calculation results indicate that the intensity of [BMIm][PF6] at between 10 and 50 cm-1 is larger than that of other ILs, while it becomes smaller comparing with the intensity of [BMIm][AsF6] or [BMIm][SbF6] at higher frequencies than 50 cm-1. These features are consistent with the experimental result shown in Figure 5b, except for the magnitude of the intensity at frequencies after 50 cm-1. To investigate the contributions of the modulation of total polarizabilities of the system to Kerr profiles, we show the decomposition analysis in Figure 6. The separation into the molecular and interaction-induced polarizations shows that the interaction-induced part has a dominant contribution to the total Kerr profile in all three ILs. The interaction-induced polarization has a large effect on the Kerr spectra at the frequency region lower than 50 cm-1, indicating that this polarization is attributed to interionic interactions, whereas the contribution of the molecular polarization that can be related to molecular motions is very small compared with the contribution from interionic dynamics. Also, Figure 6 shows interesting features of the cross-correlation effect, that the contribution of the cross part to the Kerr spectra increases

as the mass of a center atom in the anion becomes large and that it has the almost same contribution as what the induced parts in [BMIm][AsF6] and [BMIm][SbF6] provide. Thus, these features indicate both the translational and the rotational motions of ions become important in determining the Kerr spectrum profile by the substitution of the center atom of the anion with a heavier atom than phosphorus. 3.2.2. Cation and Anion Contributions to Kerr Spectrum Profile. Figure 7 shows the calculation results for the decomposition analysis of the Kerr spectra of three ILs. In [BMIm][PF6] (Figure 7a), it is found that the degree of the contribution of the cation is almost the same as that of the anion at the frequency region lower than 100 cm-1. Corresponding to this, the cation-anion cross correlation mainly contributes to the Kerr spectra at the lower-frequency region, whereas at the frequency region higher than 100 cm-1, the cation contribution becomes larger than that of anion, and the cross correlation is reduced. Thus, at the higher region, the cation component dominantly contributes to the Kerr spectrum profile. These indicate that the interionic interactions between the cation and the anion play an important role at the low-frequency region in the Kerr spectrum profile of [BMIm][PF6]. On the other hand, in both [BMIm][AsF6] and [BMIm][SbF6] (Figures 7b,c), the cation component has a dominant contribution at the whole frequency region, while the anion contribution is very small.

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Figure 9. Rotational correlation function (C(t)) of body-fixed coordinate axes (see Figure 2) for [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6]: (a) cation, X (dotted), Y (solid), and Z (dashed)directions, and (b) anion.

Figure 8. Decomposition of the computed Kerr spectra (R(ω)) into the reorientational and collision-induced components and the cross term contribution: (a) [BMIm][PF6], (b) [BMIm][AsF6], and (c) [BMIm][SbF6].

Therefore, it is considered that, among three IL systems we studied, the interionic interactions between the cation and the anion in [BMIm][PF6] are quite larger than those in other two ILs, partly because of the difference of the size of the anion as discussed in the preceding paper (DOI 10.021/jp809880j). Also, this consideration is consistent with the decrease of viscosity in [BMIm][AsF6] and [BMIm][SbF6] in comparison with that in [BMIm][PF6]. 3.2.3. Effects of Ionic Motions on Kerr Spectra. Figure 8 displays the computation results for the decomposition of the Kerr spectra of three ILs into MD components. As seen in Figure 8a, in [BMIm][PF6], the contribution of reorientation is dominant though the collision-induced and cross parts show a small contribution. In Figure 8b,c, the reorientational component has a dominant contribution to the Kerr spectra. From these results, it is considered that the Kerr spectrum profile is mainly determined by the molecular reorientation. On the collisioninduced and cross components, it is found that their contribution to the Kerr spectrum profile largely decreases as the mass of the anion species becomes larger than [PF6]-. With these results, the interionic interactions between the cation and the anion seem to be changed because of the mass effect on the motion of anion molecules in three ILs. Thus, in these three ILs, the contribution of translational motion and its coupled motion with librational motion can be reduced as the mass of a center atom in the anion

becomes larger, and then, the reorientational components increase in the total Kerr spectrum profile in comparison with [BMIm][PF6]. These considerations indicate that the contribution of reorientational motion to the Kerr spectra can be mainly attributed to those of the cation and are consistent with the results in Figure 7 that the cation component is dominant as discussed above. 3.2.4. Reorientations of the Cation and the Anion. We further examined the rotational correlation functions of the unit vectors along with the body-fixed coordinate axes shown in Figure 2 with the definition of the rotational correlation function as C(t) ) 〈ni(t) ni(0)〉, where ni (i ) X, Y, or Z) corresponds to the unit vector. The rotational correlation functions for the cation and anion were calculated and shown in Figure 9. We fitted calculation data with a biexponential function. In Table 6, fitted decay time parameters for the cation and anion in three ILs are shown. For the cation, the fast relaxation components (τ1) of the unit vectors are not different from each other compared to the slow components (τ2) in three ILs. The slow component for the unit vector perpendicular to the imidazolium ring (Z direction) is close to the decay time of another unit vector (X direction) which is in the ring plane and perpendicular to the Z direction axis, while the relaxation of the third unit vector (Y direction) is almost more than six times slower. Also, the component along the Y direction in [BMIm][PF6] is larger than that in [BMIm][AsF6] and [BMIm][SbF6]. On the other hand, both the fast and the slow components for the anion are much smaller than those for the cation and increase depending on the mass of a center atom in the anion. In addition, all of the slow components for the anion are almost the same as or faster than the fast components for the cation. Therefore, these results indicate that the reorientation can be governed mainly by the rotational relaxation of cation. 3.3. Calculations of the Dynamical Structure Factor and the Intermediate Scattering Function. Dynamical properties are required to study spatial relaxation processes. For the



TABLE 6: Fitted Decay Time Parameters for Rotational Correlation Functions of Body-Fixed Coordinate Axes for the Anion and Cation in [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6] Cationa IL

axisb

τ1 (ps)

τ2 (ns)

[BMIm][PF6]

X Y Z X Y Z X Y Z

79.0 59.9 78.6 66.5 78.3 68.6 106 62.1 123

2.52 12.6 2.34 1.64 8.26 1.68 1.89 8.52 1.92

[BMIm][AsF6] [BMIm][SbF6]

Figure 10. Dynamical structure factor, S(k,ω), at k ) 1.00 and 2.00 Å-1 for [BMIm][PF6].

Aniona

-

[PF6] [AsF6][SbF6]a

τ1 (ps)

τ2 (ps)

4.37 9.18 14.4

15.8 37.1 62.8

Fitted with a biexponential function. b See Figure 2.

intermediate scattering function, we use the definition of that as

F(k, t) )

〈∑ ∑ N

N

i

j

eik · {ri(0)-rj(t)}

〉

Figure 11. Comparison of S(k,ω) at k ) 2.00 Å-1: [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6].

(27)

where ri(t) is the position of ionic species i at time t. The dynamical structure factor, S(k,ω), is obtained with the Fourier transform of F(k,t). F(k,t) represents the decay (or loss) of correlation among local densities of the molecules (or atomic sites) through the relative motions of ionic species. Also, S(k,ω) corresponds to a spectrum in the frequency region of F(k,t). 3.3.1. Dynamical Structure Factor and Spectral Broadening in ILs Depending on WaWenumber Vectors. In investigating dynamical properties, it is important for us to remember the relation between the wavenumber vector, k, and the momentum, p, that is, p ) hk (where h is the Plank constant). Thus, the larger the k becomes, the greater the magnitude of momentum. Then, it is expected that the variation of velocity distribution can cause a spectral broadening in observed dynamical properties. Experimentally, such a spectral broadening has been observed and reported for [BMIm][PF6] by Triolo et al.55 They have shown the broadening of spectral width depending on the increase of momentum in the S(k,ω) profile of [BMIm][PF6] at k ) 1.4 and 2.2 Å-1 at 300 K. Figure 10 indicates that S(k,ω) for [BMIm][PF6] at k ) 2.00 Å-1 has a slightly broader spectral width in comparison with that at k ) 1.00 Å-1 in the region between ω ) 0 and ω ) 50 cm-1. Also, the value of half width at half-maximum (HWHM) increases (from 10 cm-1 at k ) 1.00 Å-1 to 12.5 cm-1 for k ) 2.00 Å-1) corresponding to the trend in the experimental results.55 This is considered to be caused by the change of the distribution of frequencies related to interionic vibrational motion among ion species, depending on the increase of the magnitude of momentum. 3.3.2. Mass Effects on the Dynamical Structure Factor and the Intermediate Scattering Function. In Figure 11, we show the result of S(k,ω) at k ) 2.00 Å-1 to discuss the mass effect on S(k,ω). At ω ) 0-100 cm-1, the spectral width of S(k,ω)

Figure 12. Comparison of F(k,t) at k ) 1.00 and 2.00 Å-1: [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6].

becomes broad with the replacement of the center atom of the anion. This feature indicates that the change of spatial distribution of the ions depends on the mass of the anion. Also, we investigated F(k,t) at k ) 2.00 Å-1 comparing with F(k,t) at 1.00 Å-1. Corresponding to the profiles of the S(k,ω) (Figure 11), the F(k,t) at 2.00 Å-1 indicate the change of decay behavior depending on the mass of the anion (Figure 12), consistent with the fact that the correlation function of the anion, which moves slowly, tends to decay steadily. At k ) 1.00 Å-1, however, the profiles of decaying for the three ILs are very similar. Therefore, it is indicated that the mass effects on F(k,t) at the short distance range, around k ) 2.00 Å-1, are larger than those at the long distance range, around k ) 1.00 Å-1. This is related to the consideration that the motion of the ions at long distances is diffusive but that, at short distances, it is influenced largely by the interionic interactions. As seen in F(k,t) at k ) 2.00 Å-1 for the anions and cation for the three ILs (Figure 13), the decay of F(k,t) becomes fast as the mass increases for both the cation and the anion. In particular, for both the anion and the cation, the behavior of decay in F(k,t) does not show a large difference among the three ILs until about 0.5 ps. On the other hand, after 0.5 ps, the

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Ishida et al. the relaxation of cation motion is likely to be different from anion relaxation more largely at the long-time region than at the short-time region. The third aspect is that, at short-distance ranges, the reorientation of cations and anions is likely not to play a large role in the relaxation of the ions. 4. Conclusions

Figure 13. Calculated F(k,t) at k ) 2.00 Å-1 for the anion and cation. (a) Anion ([PF6]-, [AsF6]-, and [SbF6]-) and (b) cation ([BMIm]+ in [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6]).

TABLE 7: Fitted Decay Time Parameters for the Intermediate Scattering Functions for the Anion and Cation and Experimentally Determined Parameters in [BMIm][PF6], [BMIm][AsF6], and [BMIm][SbF6] IL

aniona

cationa

exptlb

IL

τ1 (ps)

τ2 (ps)

τ1 (ps)

τ2 (ps)

τ1 (ps)

τ2 (ps)

[BMIm][PF6] [BMIm][AsF6] [BMIm][SbF6]

0.265 0.277 0.304

9.00 6.25 4.46

0.277 0.296 0.307

5.44 4.95 4.68

0.517 0.679 0.684

4.49 3.80 3.31

a Fitted with a biexponential function. b From the quadruple-exponential fit of the Kerr transients in the preceding paper (DOI 10.021/jo809880j).

difference of the decay feature for the anion remarkably appears among the three ILs, comparing with the results of the cation. Thus, it is indicated that the mass effects on F(k,t) at k ) 2.00 Å-1 are larger for anions than those for cations and that the difference of these effects can be seen not at a short-time region (t < 0.5 ps) but at a long-time region (t g 0.5 ps). Table 7 shows the biexponential fitting results for Figure 13, including the short (τ1) and long (τ2) decay times and experimentally determined parameters for the Kerr transients in the preceding paper (DOI 10.021/jp809880j). As seen in Table 7, the trends of the fitted parameters are consistent with the experimental results. In particular, the results of the cation in Table 7 are in qualitatively good accord with the experimentally fitted data for the Kerr transients, which mainly consisted of signals from the cation. In addition, while the decay time in the reorientational correlation function of the anion shown in Table 6 increases dependently on the increase of anion mass, the decreasing tendency of the long-time components (τ2 in Table 7) for the cation and anion is seen as the mass of a center atom in the anion increases. Thus, at short-distance ranges, the relaxation of the ionic species is likely to be different from that related to reorientation. It is considered that there are several aspects for the anion-cation correlation with their motions. First is that cation relaxation is not largely different from anion relaxation at the short-time region. The second aspect is that

In this study, we have developed the force field of [AsF6]and [SbF6]-, employing the ab initio calculation, and carried out the MD simulations for [BMIm][XF6] (X ) P, As, and Sb) systems to complement the understanding of atomic mass effects on ILs at the molecular level in collaboration with experimental study. In the study of DOS and VACF profiles, from the results of anion, it has been seen that both the spectral shift and the decay constant of VACF depend on the mass of the center atom in the anion both at low- and high-frequency regions consistently. From the DOS analysis, it has been found that the double peak structure in the cation DOS can be mainly attributed to the cation ring contribution. Also, it has been found that each VACF shows the oscillatory behavior that is similar to the cage effect seen in MD simulation studies of molten salts.54 In total (anion and cation) DOS, our simulation results included the appearance of the broad peak at high frequencies, consistent with the experimental data (DOI 10.021/jp809880j), while the broad spectral shape seen at low frequencies in the experiment did not agree with the present MD simulation result. In the direct comparison of calculated Kerr spectra with the experimental data, it has been found that the interionic interaction between the cation and the anion is still strong in [BMIm][PF6], but it decreases as the mass of the center atom of the anion increases, indicating that the interionic interaction tends to decrease depending on the increase of ion volume, consistent with the results shown in the preceding paper (DOI 10.021/jp809880j). Also, from the decomposition analysis of the computed Kerr spectra, it has been found that the cation-anion cross correlation component is mainly dominant in [BMIm][PF6] by the strong interionic interactions, while the cation contribution becomes dominant in [BMIm][AsF6] and [BMIm][SbF6] indicating the weakening of interionic interactions. In addition, it has been found that the contribution of the reorientation of cations and anions mainly governs the Kerr spectrum profile in all three ILs, while the collision-induced and cross terms, which are related to translational and librational motions, do not show a large contribution to the total Kerr spectrum profile at high frequencies. Therefore, the anion mass effects on the Kerr spectrum profile we have pursued with theoretical investigations suggest that interionic properties in ILs are also effectively controllable by the substitution of an atomic unit with a different atom in an ion unit in addition to a combination of cations and anions. In the analysis of dynamical properties, the broadening of spectral width caused by momentum transfer in [BMIm][PF6] has been observed to be consistent with the experimental data in the literature.55 Also, it has been found out that, at shortdistance ranges, the relaxation of ionic species is likely to be different from that related to reorientation. It is desired to study the strength and behavior of couplings between ionic motions through ionic interactions further, and the research on this point is now in progress. Acknowledgment. This work was supported in part by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan (No. 20031027, Grant-in Aid Scientific

Atom Substitution Effects. 2. Theoretical Study Research for Priority Area “Science of Ionic Liquids” (T.I.); 17073002, Grant-in Aid Scientific Research for Priority Area “Science of Ionic Liquids” (K.N.); 19559001, Grant-in Aid for Scientific Research (C) (H.S.)). This work was also partially supported by Izumi Science and Technology Foundation (H.S.). References and Notes (1) Ionic Liquids in Synthesis, 2nd ed.; Wasserscheid, P.; Welton, T., Eds.; Wiley-VCH: Weinheim, 2008. (2) Rogers, R. D., Voth, G. A. Special Issue on Ionic Liquids. Acc. Chem. Res. 2007, 40 (11). (3) Electrochemical Aspects of Ionic Liquids; Ohno, H., Ed.; WileyInterscience: Hoboken, 2005. (4) Wasserscheid, P.; Keim, W. Angew. Chem., Int. Ed. 2000, 39, 3773. (5) Castner, E. W., Jr.; Wishart, J. F.; Shirota, H. Acc. Chem. Res. 2007, 40, 1217. (6) Weingaertner, H. Angew. Chem., Int. Ed. 2007, 47, 654. (7) Wishart, J. F., Castner, E. W., Eds. Special Issue on Physical Chemistry of Ionic Liquids. J. Phys. Chem. B 2007, 111 (18). (8) Maginn, E. J. Acc. Chem. Res. 2007, 40, 1200. (9) Shirota, H.; Castner, E. W., Jr. J. Phys. Chem. B 2005, 109, 21576. (10) Frenkel, D.; McTague, J. P. J. Chem. Phys. 1980, 72, 2801. (11) Ladanyi, B. M.; Skaf, M. S.; Liang, Y. Q. Interaction-induced contributions to spectra of polar liquids. In Collision- and InteractionInduced Spectroscopy; Tabisz, G. C., Neuman, M. N., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1995; p 143. (12) Shirota, H.; Castner, E. W., Jr. J. Phys. Chem. A 2005, 109, 9388. (13) Shirota, H.; Funston, A. M.; Wishart, J. F.; Castner, E. W., Jr. J. Chem. Phys. 2005, 122, 184512. (14) Xiao, D.; Rajian, J. R.; Hines, J. L. G.; Li, S.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. B 2008, 112, 13316. (15) Xiao, D.; Rajian, J. R.; Cady, A.; Li, S.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. B 2007, 111, 4669. (16) Xiao, D.; Rajian, J. R.; Li, S. F.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. B 2006, 110, 16174. (17) Rajian, J. R.; Li, S. F.; Bartsch, R. A.; Quitevis, E. L. Chem. Phys. Lett. 2004, 393, 372. (18) Hyun, B. R.; Dzyuba, S. V.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. A 2002, 106, 7579. (19) Giraud, G.; Gordon, C. M.; Dunkin, I. R.; Wynne, K. J. Chem. Phys. 2003, 119, 464. (20) Shirota, H.; Wishart, J. F.; Castner, E. W., Jr. J. Phys. Chem. B 2007, 111, 4819. (21) Hunt, N. T.; Jaye, A. A.; Meech, S. R. Phys. Chem. Chem. Phys. 2007, 9, 2167. (22) Refer to section 4 in ref 1 and references therein. (23) Hu, Z. H.; Margulis, C. J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 831. (24) Hu, Z.; Margulis, C. J. Acc. Chem. Res. 2007, 40, 1097. (25) Hu, Z. H.; Margulis, C. J. J. Phys. Chem. B 2006, 110, 11025. (26) Urahata, S. M.; Ribeiro, M. C. C. J. Chem. Phys. 2005, 122, 024511. (27) Bhargava, B. L.; Balasubramanian, S. J. Phys. Chem. B 2007, 111, 4477. (28) Bhargava, B. L.; Balasubramanian, S. J. Chem. Phys. 2007, 127, 114510. (29) Bhargava, B. L.; Balasubramanian, S.; Klein, M. L. Chem. Commun. 2008, 3339.

J. Phys. Chem. B, Vol. 113, No. 29, 2009 9851 (30) Hu, Z.; Huang, X.; Annapureddy, H. V. R.; Margulis, C. J. J. Phys. Chem. B 2008, 112, 7837. (31) Lopes, J. N. C.; Deschamps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 2038. (32) Lopes, J. N. C.; Deschamps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 11250. (33) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. GAUSSIAN 03; Gaussian, Inc.: Pittsburgh, PA, 2003. (34) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (35) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (36) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (37) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358. (38) Peterson, K. A. J. Chem. Phys. 2003, 119, 11099. (39) Mayo, S. L.; Olafson, B. D.; Goddard, W. A., III. J. Phys. Chem. 1990, 94, 8897. (40) Brenneman, C. M.; Wiberg, J. J. Comput. Chem. 1987, 8, 894. (41) Smith, W.; Forster, T. R. The DL_POLY_2 User Manual; Daresbury Laboratory: Daresbury, U.K., 2001. (42) Smith, W. Comput. Phys. Commun. 1992, 67, 392. (43) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, U.K., 1987. (44) Tokuda, H.; Hayamizu, K.; Ishii, K.; Abu Bin Hasan Susan, M.; Watanabe, M. J. Phys. Chem. B 2004, 108, 16593. (45) Geiger, L. C.; Ladanyi, B. M. J. Chem. Phys. 1987, 87, 191. (46) Cho, M.; Du, M.; Scherer, N. F.; Fleming, G. R.; Mukamel, S. J. Chem. Phys. 1993, 99, 2410. (47) Bursulaya, B. D.; Kim, H. J. J. Chem. Phys. 1998, 109, 4911. (48) Stassen, H.; Dorfmu¨ller, T.; Ladanyi, B. M. J. Chem. Phys. 1994, 100, 6318. (49) Kiyohara, K.; Kamada, K.; Ohta, K. J. Chem. Phys. 2000, 112, 6338. (50) Thole, B. T. Chem. Phys. 1981, 59, 341. (51) Yan, T.; Burnham, C. J.; Del Popolo, M. G.; Voth, G. A. J. Phys. Chem. B 2004, 108, 11877. (52) Jiang, W.; Yan, T.; Wang, Y.; Voth, G. A. J. Phys. Chem. B 2008, 112, 3121. (53) Ishida, T.; Shirota, H. In preparation. (54) Hansen, J.-P.; McDonald, I. R. Theory of Simple Liquids, 3rd ed.; Academic Press: Amsterdam, 2006. (55) Triolo, A.; Russina, O.; Arrighi, V.; Juranyi, F.; Janssen, S.; Gordon, C. M. J. Chem. Phys. 2003, 119, 8549.

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