Intermolecular Vibrations and Diffusive Orientational Dynamics of Cs

ARTICLE pubs.acs.org/JPCA

Intermolecular Vibrations and Diffusive Orientational Dynamics of Cs Condensed Ring Aromatic Molecular Liquids Hideaki Shirota* Department of Nanomaterial Science, Graduate School of Advanced Integration Science & Department of Chemistry, Faculty of Science, Chiba University, 1-33 Yayoi, Inage-ku, Chiba 263-8522, Japan

bS Supporting Information ABSTRACT: The ultrafast dynamics, including the intermolecular vibrations and the diffusive orientational dynamics, of the neat Cs symmetry condensed ring aromatic molecular liquids benzofuran, 1-fluoronaphtalene, and quinoline were investigated for the first time by means of femtosecond Raman-induced Kerr effect spectroscopy. To understand the features of these Cs condensed ring aromatic molecular liquids, reference singular aromatic molecular liquids, furan, fluorobenzene, pyridine, and benzene, were also studied. High quality low-frequency Kerr spectra of the aromatic molecular liquids were obtained by Fourier-transform deconvolution analysis of the measured Kerr transients. The Kerr spectra of the Cs condensed ring aromatic molecular liquids are bimodal, as are those of the reference singular aromatic molecular liquids. The first moment of the intermolecular vibrational spectrum and the peak frequencies of the high- and low-frequency components in the broad spectrum band were compared with their molecular properties such as the rotational constants, molecular weight, and intermolecular (bimolecular) force. The comparisons show that the molecular volume (related to molecular weight and rotational constants) is a dominant property for the characteristic frequency of the entire intermolecular vibrational spectrum. The observed intramolecular vibrational modes in the Kerr spectra of the aromatic molecular liquids were also assigned on the basis of the ab initio quantum chemical calculation results. In their picosecond diffusive orientational dynamics, the slowest relaxation time constant for both the condensed ring and singular aromatic molecular liquids can be accounted for by the simple StokesEinsteinDebye hydrodynamic model.

1. INTRODUCTION Understanding the intermolecular vibrations in molecular liquids is a fundamental issue in chemistry because the collective fluctuation of the solvent plays a key role in the elementary steps of chemical reactions and in the solvent reorganization processes in solution.115 Intermolecular vibrations in solutions and liquids typically take place within the frequency range of approximately 1150 cm1. In fact, the techniques used to gain insight into to the molecular motions in this frequency region are rather limited. The recent significant advancement of ultrafast laser technology has provided a means for the observation of ultrafast dynamics in solutions and liquids. Femtosecond Raman-induced Kerr effect spectroscopy (RIKES)1618 and terahertz time-domain spectroscopy1921 can probe the molecular motions in this unique frequency region with a higher degree of sensitivity and with a better access to the lower frequency region than conventional steady-state Raman and far-infrared spectroscopic methods. In particular, the femtosecond RIKES typically permits the detection of molecular motions within the frequency range as wide as 0.5700 cm1. This spectroscopic technique is now used to investigate not only simple molecular liquids2227 but also more complex molecular systems and condensed phases,28 e.g., biological molecules and mimics or cooperative hydrogenbonding molecular systems,2934 micelle solutions,3538 confined solvents in nanoporous glasses,3948 polymer liquids49,50 r 2011 American Chemical Society

and solutions,35,49,5153 and room temperature ionic liquids.5465 This technique is not, however, straightforward enough to understand and assign the line shape of the broad intermolecular vibrational spectra of molecular liquids. Molecular dynamics (MD) simulations have been widely acknowledged as offering insight into the molecular-level aspects of the low-frequency Kerr spectrum for several molecular liquids,6679 as well as for room temperature ionic liquids.80,81 Thus, there is no doubt that these methods complement one another in offering us a better and deeper understanding of the intermolecular dynamics in molecular liquids. Among femtosecond RIKES studies of molecular liquids, one of the most extensive targets is aromatic molecular liquids.20,21,8297 Previous studies of aromatic molecular liquids have suggested that the contribution of the phenyl ring librational motion is substantial in the low-frequency Kerr spectrum. In particular, the Kerr spectra of aromatic molecular liquids are well represented by a sum of the BucaroLitowitz function (or the Ohmic function, which is the simplest form of the BucaroLitovitz function), which is empirically used to express the depolarized scattering that takes place in low-density atomic and molecular fluids,98 and Received: August 31, 2011 Revised: October 16, 2011 Published: November 07, 2011 14262

dx.doi.org/10.1021/jp208389n | J. Phys. Chem. A 2011, 115, 14262–14275

The Journal of Physical Chemistry A the antisymmetrized Gaussian functions, which are assumed to be inhomogeneously broadened vibrational modes.99 The line shape for the Kerr spectra of most aromatic molecular liquids is bimodal and is often assumed as the translational (or interactioninduced) motion (expressed by the BucaroLitovitz function) and the librational (expressed by the antisymmetrized Gaussian function) motion. Recently, some groups have attempted to gain a detailed understanding of the line shape for the Kerr spectra of aromatic molecular liquids. Fourkas and co-workers have investigated liquids of benzene and its four different isotopomers, C6D6, 1,3,5-C6H3D3, 13C6H6, and 13C6D6.100 They found a good correlation between the first moment of the high frequency component (treated as the ring libration) in the anisotropic intermolecular vibrational band and the inverse square root of the moment of inertia I1/2 for the four liquid benzenes. Heisler and Meech studied the isotropic intermolecular vibrational spectra of aromatic molecular liquids by femtosecond RIKES based on the polarization condition of isotropic (magic angle between the pump polarization and analyzer polarization) and found a linear correlation between the first moment of an isotropic vibrational spectrum and the inverse square of the molecular weight, MW1/2.101 They attributed this correlation to the fact that isotropic vibrational motion is translational in character. More complicated aromatic molecular liquids, however, have not yet been explored much. Quitevis and co-workers studied liquid biphenyl.93 In their study, they reported that the lowfrequency Kerr spectrum of liquid biphenyl is rather similar to that of liquid benzene, though the molecular properties of the two liquids, such as molecular shape, polarizability volume, and moment of inertia, are different. Tao and Stratt performed MD simulations of liquid biphenyl and benzene and compared the calculated Kerr spectra with the experimental Kerr spectra obtained by Quitevis and co-workers.67 The results obtained by Tao and Stratt clarified that the time scale of the librational dynamics is largely controlled by the Einstein frequency for libration about the three principle axes, and the Einstein frequency is proportional to the ratio of the mean-square torque and the moment of inertia, which depend on the molecular size and shape in similar ways. In the case of planar molecules, both quantities are proportional to the same radius of gyration. Thus, the factors of shape and size cancel one another out in the case of similar molecules. In addition to liquid biphenyl, we also reported upon the Kerr spectrum of neat 1,3-diphenylpropane.96 Compared with benzene and alkylbenzenes, such as toluene, ethylbenzene, and cumene, the spectral intensity in the low frequency region in less than 30 cm1 of 1,3-diphenylbenzene is small compared to that found in other aromatic molecular liquids. This fact was attributed to there being less activity of the translational motion due to the connection of the two phenyl rings. In this study, the intermolecular vibrations of condensed ring aromatic molecular liquids are investigated for the first time, using femtosecond Raman-induced Kerr effect spectroscopy. The target Cs condensed ring aromatic molecular liquids are 1-fluoronaphtalene, 2,3-benzofuran, and quinoline (Figure 1). These liquids are compared to their reference singular aromatic molecular liquids, 1-fluorobenzene, furan, pyridine, and benzene (Figure 1). The primary purposes of this study are (i) to obtain high quality intermolecular vibrational spectra of the Cs condensed ring aromatic molecular liquids as new data and (ii) to find the unique feature of the intermolecular vibrational spectra of the Cs condensed ring aromatic molecular liquids.

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Figure 1. Structures and abbreviations of the aromatic molecular liquids used in this study.

2. EXPERIMENTAL AND QUANTUM CHEMICAL CALCULATION METHODS 2,3-Benzofuran (Aldrich), 1-fluoronaphthalene (Wako Pure Chemical), quinoline (Aldrich), furan (Kanto Chemical), fluorobenzene (Wako Pure Chemical), pyridine (Wako Pure Chemical), and benzene (Kanto Chemical) were used as received. The shear viscosities (η) of the sample liquids were measured at 294 ( 0.2 K using a reciprocating electromagnetic piston viscometer (Cambridge Viscosity, ViscoLab 4100) with a circulating water bath (Yamato, BB300). The surface tensions (γ) of the liquids were measured using a du No€uy tensiometer (Yoshida Seisakusho) at 294.0 ( 0.5 K. The liquid densities (d) were obtained using a 5 mL volumetric flask at 294.0 ( 0.5 K. The femtosecond optical heterodyne-detected RIKES setup used in this study was essentially the same as a previously reported one,26,96 except for the light source, which was a Ti: sapphire laser (KMLabs Inc., Griffin) pumped by a Nd:VO4 diode laser (Spectra Physics, Millennia Pro 5sJ). The output power of the Ti:sapphire laser was approximately 380 mW. The typical temporal response, which is the cross-correlation between the pump and probe pulses as measured using a 200-μm-thick KDP crystal (type I), was 37 ( 3 fs (full-width at half-maximum). Scans with a high time resolution of 2048 points at 0.5 μm/step were performed for a short time window (6.8 ps). Longtime-window transients with data acquisition of 10.0 μm/step (condensed ring aromatic molecular liquids) or 5.0 μm/step (singular aromatic molecular liquids) were also captured. Pure heterodyne signals were obtained by recording scans for both +1.5 and 1.5 rotations of the input polarizer; they were then combined to eliminate the contribution of the homodyne signal. In each input polarization rotation, 3 scans were averaged for the short-time-window transients and 5 scans were averaged for the longer ones. The sample liquids were injected into a quartz cell with an optical path length of 3 mm (Tosoh Quartz) via a 0.2 μm Anotop filter (Whatman) prior to the femtosecond OHD-RIKES measurements. All the OHD-RIKES measurements were performed at 294 ( 1 K. The optimized structures and their normal modes of the target aromatic molecules were determined from ab initio quantum chemical calculations based on the B3LYP/6-311++G(d,p) level of theory, which were carried out using the Gaussian03 program suite.102 The obtained atom coordinates, polarizability tensor elements, and energies of the optimized neutral form and the cation form of the molecules are summarized in the Supporting Information. The energy of the cation form was obtained from the single point energy calculation, based on the optimized neutral form. 14263

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The Journal of Physical Chemistry A

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Table 1. Molecular Weights MW and Liquid Properties, Liquid Density d, Molar Volume Vm, Molecular Radius rm, Shear Viscosity η, and Surface Tension γ, at 294 K for Aromatic Molecular Liquids MW

d (g/mL)a

Vm (mL/mol)a

rm (Å)a

η (cP)b

γ (mN/m)b

2,3-benzofuran

118.1

1.086

108.7

2.96

1.834

38.9

1-fluoronaphthalene quinoline

146.2 129.2

1.122 1.084

130.3 119.2

3.14 3.05

2.190 3.990

39.7 46.0

furan

68.1

0.931

73.1

2.59

0.386

24.1

fluorobenzene

96.1

1.013

94.9

2.83

0.563

27.9

pyridine

79.1

0.972

81.4

2.69

0.924

37.4

benzene

78.1

0.869

89.9

2.78

0.645

29.5

liquid

a

(2%. b (3%.

3. RESULTS 3.1. Bulk Properties. Table 1 summarizes the molecular weights (MW) and bulk properties, such as liquid density (d), shear viscosity (η), and surface tension (γ), of the aromatic molecular liquids at 294 K. The molar volumes (Vm = MW/d) and the molecular radii (rm = (3Vm/4πNA)1/3, where NA is Avogadro’s constant) are also listed in the table. Some data for the liquids at 293 K have been tabulated in the CRC handbook,103 and their values are close to those in the present data, except for the surface tension of quinoline. The value of the surface tension estimated here is quite close to the value recently reported by Anantharaj and Banerjee,104 instead of the CRC handbook. As shown in Table 1, the shear viscosities and surface tensions of the Cs condensed ring aromatic molecular liquids are much larger than those of the reference singular aromatic molecular liquids. These physical properties will be compared to the data for the ultrafast dynamics in a later section of this article. 3.2. Diffusive Orientational Dynamics. Figure 2 shows the logarithmic plots of the Kerr transients for (a) 2,3-benzofuran and furan, (b) 1-fluoronaphtalene and fluorobenzene, (c) quinoline and pyridine, and (d) benzene. For the longest time scale in the Kerr transients, a multiexponential function is used to fit the data from 3 ps. The multiexponential fits are also shown in Figure 2. The fitting parameters for all the sample liquids studied herein are listed in Table 2. As shown in Figure 2 and Table 2, the slowest relaxation time for the condensed ring aromatic molecular liquids is much slower than that for the reference singular aromatic molecular liquids. 3.3. Intra- and Intermolecular Vibrations. Figure 3 shows the low-frequency Kerr spectra of the Cs condensed ring aromatic molecular liquids within the frequency range of 0700 cm1. The low-frequency Kerr spectra of the Kerr transients were obtained by means of standard Fourier-transform deconvolution analysis, as established by McMorrow and Lotshaw.83,105 For the purpose of comparison, the Kerr spectra of the comparative singular aromatic molecular liquids are shown in Figure 4. The Kerr spectra without the contributions of the overdamped picosecond relaxation processes (the second and third exponential components in the cases of the Cs condensed ring aromatic molecular liquids; the second exponential component in the cases of fluorobenzene, pyridine, and benzene; and the exponential component in the case of furan) are also shown in order to highlight the vibrational contributions: these spectra were used for the line shape analysis, following the method of traditional RIKES experiments. The contribution of the overdamped picosecond relaxation processes to each aromatic molecular liquid is also shown in Figures 3 and 4. The Kerr spectra are well represented

up to approximately 700 cm1, as can be seen in the figures. Besides the broad band below approximately 200 cm1, which is due to the intermolecular vibrations, sharp intramolecular vibrational modes were also observed in the Kerr spectra. The observed intramolecular vibrational modes of the aromatic molecular liquids are summarized in Table 3. The broad spectral bands below 200 cm1 for the aromatic molecular liquids were further carried out in the line shape analysis in order to reproduce and characterize the broad and complicated spectral shape. The fit function for the low-frequency Kerr spectra used in this study is a sum of Ohmic (eq 1) and antisymmetrized Gaussian functions (eq 2)99 IO ðωÞ ¼ aO ω expð ω=ωO Þ # 2ðω ωG, i Þ2 IG ðωÞ ¼ aG, i exp ΔωG, i 2 i¼1 " #) 2ðω þ ωG, i Þ2 aG, i exp ΔωG, i 2 3

∑

(

ð1Þ

"

ð2Þ

where aO and ωO are the amplitude and characteristic frequency parameters of the Ohmic line shape, respectively; and where aG,i, ωG,i, and ΔωG,i are the amplitude, characteristic frequency, and bandwidth parameters for the i-th antisymmetrized Gaussian function, respectively. A Lorentzian function (eq 3) was used when a clear intramolecular vibrational band was observed in the Kerr spectra aL ð3Þ IL ðωÞ ¼ ðω ωL Þ2 þ ΔωL 2 where aL, ωL, and ΔωL are the amplitude, peak frequency, and bandwidth parameters for the Lorentzian function, respectively. Figure 5 shows the results of the line shape analysis of the lowfrequency Kerr spectra of the condensed ring aromatic molecular liquids. The results of the line shape analysis of the low-frequency Kerr spectra of the reference singular aromatic molecular liquids are also shown in Figure 6. The fit parameters are summarized in Table 4. In the table, the first spectral moments (M1) of the lowfrequency Kerr spectra without the contributions of intramolecular vibrational modes and picosecond overdamped relaxation for the ILs are also listed. M1 of the spectrum is defined as, Z Z ωIðωÞdω= IðωÞdω ð4Þ M1 ¼ where I(ω) is the frequency-dependent spectral intensity. Since the parameters of the fit functions (eqs 1 and 2) are covariant and 14264



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is assigned as the high-frequency component to distinguish the frequency regions in the broad spectrum, and they are also shown in Figures 5 and 6. The peak frequencies of the low- and high-frequency components for the present samples are summarized in Table 4. 3.4. Ab Initio Quantum Chemical Calculations. The physical properties, dipole moment μ, mean polarizability volume α0, polarizability anisotropy volume αanis, and rotational constants Bx, By, and Bz, of the optimized aromatic molecules were obtained by the ab initio quantum chemical calculations based on the B3LYP/ 6-311++G(d,p) level of theory, and they are summarized in the Supporting Information. The values of the molecular properties will be compared with the intermolecular vibrational spectra later. In the ab initio quantum chemical calculations, the Ramanactive normal modes of the target aromatic molecules were also estimated. The calculated spectra of the molecules within the frequency range of 0700 cm1 are shown in Figures 3 and 4. The vibrational frequencies of the calculated Raman spectra and their assignments are summarized in Table 3.

4. DISCUSSION 4.1. Intermolecular Vibrational Spectrum. 4.1.1. Spectral Line Shape. The line shape of the low-frequency Kerr spectrum of

Figure 2. Loglog plots of Kerr transients for (a) 2,3-benzofuran and furan, (b) 1-fluoronaphtalene and fluorobenzene, (c) quinoline and pyridine, and (b) benzene. Multiexponential fits to the Kerr transients are indicated by black lines.

the broad spectrum has no clear peak, except for the intramolecular vibrational modes, the fit parameters include relatively large errors, as shown in Table 4. The part of the sum of the Ohmic components is assigned as the low-frequency component, and the part of the sum of the antisymmetrized Gaussian components

most singular aromatic molecular liquids, such as benzene, toluene, etc., is bimodal.26 This is also true for the Cs condensed aromatic molecular liquids studied here, as shown in Figure 5: the line shapes of the low-frequency Kerr spectra of the Cs condensed ring aromatic molecular liquids are clearly bimodal. Recently, Manfred et al. analyzed the Kerr spectra of liquids of benzene and its four different isotopomers and found a good correlation between the first moment of the high frequency component (assumed as the ring libration) in the anisotropic intermolecular vibrational band and the inverse square root of the moment of inertia I1/2 for the four liquid benzenes.100 Here, we tentatively distinguish the low-frequency component (sum of the Ohmic functions) from the high-frequency component (sum of the antisymmetrized Gaussian functions), which are assumed to be the translational (or interaction-induced) and librational motions at the first stage, respectively. In Table 4, the peak frequencies of the low-frequency and high-frequency components of the low-frequency Kerr spectra are summarized. As can clearly be seen in Table 4 and Figures 5 and 6, the high-frequency component in the Cs condensed ring aromatic molecular liquids is of a higher frequency than that in the reference singular aromatic molecular liquids. The more clearly bimodal spectral line shape of the Cs condensed ring aromatic molecular liquids than that of the reference singular aromatic molecular liquids, is the result of there being a larger difference between the peak frequencies of the high- and low-frequency components (antisymmetrized Gaussian and Ohmic components) for the Cs condensed ring aromatic molecular liquids as compared to the reference singular aromatic molecular liquids. Previously, we reported that most (singular) aromatic molecular liquids, except for heavier atom substituted benzenes such as hexafluorobenzene, show bimodal spectral features, but the spectral shape is rather dependent in the case of nonaromatic molecular liquids: some nonaromatic molecular liquids show a monomodal spectral shape but the others show a bimodal spectral shape.26 Thus, the bimodal spectral feature of aromatic molecular liquids is rather general, even in the Cs condensed ring aromatic molecular liquids. Below, we will compare the characteristic frequencies of the low-frequency spectra caused by the intermolecular vibrations with the molecular 14265



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Table 2. Fit Parameters for the Orientational Relaxation Processes in Aromatic Molecular Liquids liquid

a1

τ1 (ps)

a2

τ2 (ps)

a3

τ3 (ps)

2,3-benzofuran

0.0373 ( 0.0009

1.24 ( 0.06

0.0162 ( 0.0011

4.23 ( 0.32

0.0272 ( 0.0005

16.11 ( 0.13

1-fluoronaphthalene

0.0335 ( 0.0012

1.73 ( 0.08

0.0157 ( 0.0006

7.28 ( 0.27

0.0242 ( 0.0002

36.74 ( 0.15

0.0098 ( 0.0005

9.21 ( 0.57

0.0140 ( 0.0002

43.92 ( 0.37

quinoline

0.0230 ( 0.0007

2.05 ( 0.12

furan

0.0707 ( 0.0016

1.13 ( 0.01

fluorobenzene

0.0597 ( 0.0045

1.25 ( 0.07

0.0700 ( 0.0011

4.18 ( 0.03

pyridine

0.0552 ( 0.0008

1.56 ( 0.03

0.0442 ( 0.0007

4.46 ( 0.03

benzene

0.0562 ( 0.0028

1.19 ( 0.06

0.0448 ( 0.0015

3.09 ( 0.03

Figure 3. Fourier-transform Kerr spectra within the frequency range of 0700 cm1 in the condensed ring aromatic molecular liquids: (a) 2,3benzofuran, (b) 1-fluoronaphtalene, and (c) quinoline. Red lines denote the entire spectrum, blue lines denote the component of the overdamped picosecond relaxation component, and black lines denote the spectrum without the component of the overdamped picosecond relaxation. Raman spectra calculated for gas-phase (d) 2,3-benzofuran, (e) 1-fluoronaphtalene, and (f) quinoline at the B3LYP/6-311++G(d,p) level of theory.

properties and the bulk properties in order to discover the features of the intermolecular vibrational spectra of the Cs condensed ring aromatic liquids. 4.1.2. Comparison with Rotational Constants and Molecular Weight. Figure 7 shows plots of the first moment M1 and the peak frequency of the high-frequency component ωG of the

intermolecular vibrational spectrum vs the square roots of the rotational constants, Bx, By, Bz, and Bav. Bav is the average rotational constant, which is defined as (Bx + By + Bz)/3. Note that the rotational constants are estimated using the quantum chemical calculation results (Supporting Information), and the z axis here is set at the perpendicular coordinate to the aromatic 14266



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Figure 4. Fourier-transform Kerr spectra within the frequency range of 0700 cm1 in the singular aromatic molecular liquids: (a) furan, (b) fluorobenzene, (c) pyridine, and (d) benzene. Red lines denote the entire spectrum, blue lines denote the component of the overdamped picosecond relaxation component, and black lines denote the spectrum without the component of the overdamped picosecond relaxation. Raman spectra calculated for gas-phase (e) furan, (f) fluorobenzene, (g) pyridine, and (h) benzene at the B3LYP/6-311++G(d,p) level of theory.

plane. Thus, the comparison of M1 with the rotational constants could indicate the relationship between the entire intermolecular vibrational spectrum and the ring librations, but the comparison of ωG with the rotational constants would indicate the relationship between the high-frequency component (which is assumed due to the ring librations) of the intermolecular vibrational spectrum and the ring librations. The comparisons in Figure 8

are essentially based upon a report by Manfred et al.100 Instead of the moment of inertia, the rotational constant, which is obtained by the ab initio quantum chemical calculations, is used in this study. As shown in Figure 8, there are moderate correlations between M1 and the rotational constants with the similar standard deviations for the fits. However, comparisons of ωG with the rotational constants show very poor correlations. 14267



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Table 3. Observed and Calculated Intramolecular Vibrational Modes for 2,3-Benzofuran, 1-Fluoronaphtalene, Quinoline, Furan, Fluorobenzene, Pyridine, and Benzenea condensed ring aromatic molecular liquids benzofuran

1-fluoronaphthalen

exptl

calcd

mode

exptl

226

215

buf

158

144

257

250

TTR

183

175

422 540

429 548

Ph-ring bd (op) skel br

269 415

570

577

skel def

585

595

furan-ring tor

611

622

skel def (ip)

quinoline

calcd

mode

exptl

calcd

mode

TTR

192

173,182

buf, TTR

buf

392

401

sym BdTR (op)

266,268 423

F-Nap bd (op), cw sym BdTR (op)

521

528,531

skel br, skel def (ip)

460

465

F-Nap bd (ip)

474

479

skel def (ip)

530

539

skel br

568

577

stagger BrTR

singular aromatic molecular liquids furan

fuluorobenzene

exptl

calcd

mode

602

610,619

ring tor, ring bd (op)

exptl

calcd

pyridine

mode

exptl

calcd

benzene mode

exptl

calcd

mode

607

622

ring br, ring def (ip)

241

236

F-Ph bd (op)

407

418

ring bd (op)

408 500

404 505

F-Ph bd (ip) ring bd (op)

603 652

617 669

ring br ring def (ip)

518

524

ring br

613

627

ring def (ip)

a

TTR, torsion of two rings against each other; BdTR, bendings of two rings; BrTR, breathings of two rings; bf, butterfly; cw, cogwheel; bd, bend; def, deformation; br, breathing; tor, torsion; sym, symmetric; skel, aromatic skeleton.

In Figure 8, the plots of M1 and the peak frequency of the lowfrequency component ωO of the intermolecular vibrational spectrum vs the inverse square root of the molecular weight MW1/2 are also shown. Previously, Heisler and Meech showed that M1 of an isotropic Kerr spectrum was linearly proportional to MW1/2 for six different aromatic molecular liquids: benzene, pyridine, toluene, 2,4,6-trimethylpyridine, 1,3,5-trifluorobenzene, and hexafluorobenzene.101 Thus, this comparison should essentially be valid for the translational motion, not the librational motion. As shown in Figure 8, the molecular weight moderately correlates with M1 but not with ωO. From Figures 7 and 8, it becomes clear that the entire intermolecular vibrational spectrum (M1) shows a better correlation with the molecular properties (rotational constants and molecular weight) than with the (assumed) corresponding components of the intermolecular vibrational spectrum (ωG and ωO). The moderate correlations of M1 of the entire intermolecular vibrational spectrum with the square roots of the rotational constants and the inverse square root of the molecular weight have also been reported in the C3v CXY3 molecular liquids CHCl3, CHBr3, CFBr3, and CBrCl3.106 Thus, this feature is also true for aromatic molecular liquids, including Cs condensed ring aromatic molecular liquids. It should be noted, however, that the intermolecular force (or interaction energy) is not taken into consideration. Notwithstanding this, there are moderate correlations, and these imply that the molecular volume, which is related to both MW and B, is a dominant property in the characterization of the frequency of the intermolecular vibrational spectrum. However, it was also found that the peak frequencies of the (assumed) high- and low-frequency components of the intermolecular vibrational spectrum do not correlate well with the

rotational constants and the molecular weight, respectively. There are two plausible reasons for this. First, the intermolecular vibrational spectrum cannot be readily distinguished from the components of the librational and translational motions. Indeed, current MD simulations have pointed out these motions are well overlapped (in particular the low-frequency region) in time (and frequency as well) and are also coupled.6679 Second, the effect of the intermolecular force is not included. In the present results, however, the moderate correlations for M1 with the entire intermolecular vibrational spectrum are confirmed. Accordingly, the first reason is more likely to be responsible for the poor correlation. 4.1.3. Comparison with Intermolecular Interaction Energy. In Section 4.1.2, the new results in this study showed that the molecular volume (moment of inertia or rotational constants) has a critical effect upon the intermolecular vibrational spectrum. Nonetheless, it could be worthwhile to take the intermolecular interaction into consideration as a factor in the intermolecular vibrational spectrum. Here, the bimolecular interaction energy is simply considered as it was in a previous report.106 Figure 9a shows M1 and ωG vs the square root of the value of the negative intermolecular interaction energy (Ur0) divided by the molecular surface area (Am) and the molecular weight (MW), i.e., [Ur0/(AmMW)]1/2, on the basis of a previous report.106 The intermolecular interaction energy of two identical neutral molecules in the LennardJones potential expression is written as107,108 UðrÞ ¼

Crep 1 ðCdd þ Cdid þ Cdisp Þ r 12 r 6

ð5Þ

where r is the distance between molecules, and Crep, Cd‑d, Cd‑id, and Cdisp are the coefficients for the repulsion, dipoledipole 14268



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Figure 5. Low-frequency Kerr spectra within the frequency range of 0200 cm1 and their fit functions for condensed ring aromatic molecular liquids: (a) 2,3-benzofuran, (b) 1-fluoronaphtalene, and (c) quinoline. Black dots denote the data, red solid lines denote the complete fits, green areas denote the Ohmic functions (eq 1), blue areas denote the antisymmetrized Gaussian functions (eq 2), and orange areas denote the Lorentzian functions (eq 3) for the intramolecular vibrational modes. Green solid lines denote the sums of the Ohmic functions (lowfrequency component), and blue solid lines denote the sums of the antisymmetrized Gaussian functions (high-frequency component).

interaction, dipoleinduced dipole interaction, and dispersion interaction, respectively. The coefficients for the attractive term are given by107,108 Cdd ¼

2μ4 3ð4πε0 Þ2 kB T

ð6Þ

Cdid ¼

2α0 μ2 ð4πε0 Þ2

ð7Þ

Cdisp ¼

2

3 Iα0 4 ð4πε0 Þ2

ð8Þ

Figure 6. Low-frequency Kerr spectra within the frequency range of 0200 cm1 and their fit functions for singular aromatic molecular liquids: (a) furan, (b) 1-fluorobenzene, (c) pyridine, and (d) benzene. Black dots denote the data, red solid lines denote the complete fits, green areas denote the Ohmic functions (eq 1), and blue areas denote the antisymmetrized Gaussian functions (eq 2). Green solid lines denote the sums of the Ohmic functions (low-frequency component) and blue solid lines denote the sums of the antisymmetrized Gaussian functions (highfrequency component).

where ε0 is the permittivity of a vacuum. Here, we discuss the equilibrium intermolecular interaction energy (Ur0), which is the energy at the equilibrium distance between the two molecules (r0 = 2rm). Since the repulsion coefficient is often treated as an 14269


58.4

benzene

1-fluoronaphthalene quinoline

liquid

52.7

61.1

fluorobenzene

pyridine

56.4

62.2

quinoline

56.9 48.8

2,3-benzofuran 1-fluoronaphthalene

furan

M1 (cm1)

liquid

16.0 5.8

0.318 ( 0.151 0.330 ( 0.058

2.3 ( 0.1 15.7 ( 0.1 3.5 ( 0.8 2.7 ( 0.3 5.5 ( 0.1

0.220 ( 0.162

0.408 ( 0.069

0.422 ( 0.001

ωL1 (cm1) 157.9 ( 0.1 191.7 ( 0.2

13.69 ( 0.07 39.06 ( 0.22

7.1 ( 1.5

6.9 ( 1.9

10.9 ( 0.5

aL1

0.195 ( 0.002

0.719 ( 0.309

0.423 ( 0.222

0.480 ( 0.288

0.968 ( 0.05

0.257 ( 0.040

0.290 ( 0.007 0.222 ( 0.014

aG1

7.3 ( 0.1 24.8 ( 0.5

ΔωL1 (cm1)

intramolecular vibrations

5.6

5.0

7.3

8.2 7.0

0.383 ( 0.004

11.4 ( 0.2 10.4 ( 0.2

0.115 ( 0.001

0.151 ( 0.002 0.234 ( 0.002

3.3 ( 0.4 2.5 ( 0.1

ωO2 (cm1) ωO (cm1)

0.179 ( 0.001 0.375 ( 0.002

aO2

ωO1 (cm1)

aO1

intermolecular vibrational band

10.8 ( 5.2

19.4 ( 6.0

16.9 ( 7.3

54.3 ( 0.3

31.8 ( 1.3

33.6 ( 0.2 33.1 ( 0.5

3.41 ( 0.10

aL2

34.3 ( 2.4

32.5 ( 4.3

34.7 ( 4.5

94.4 ( 0.3

32.7 ( 1.6

37.6 ( 0.5 30.8 ( 0.7

ωG1 (cm1) ΔωG1 (cm1)

Table 4. Fit Parameters and First Moments M1 for Low-Frequency Kerr Spectra in Molecular Liquids

48.2 ( 0.4

58.9 ( 0.3

50.3 ( 0.3

69.9 ( 0.1

72.1 ( 0.2 63.1 ( 0.1

183.1 ( 0.1

89.7 ( 0.3

87.7 ( 0.3

77.9 ( 0.3

59.7 ( 0.1

59.1 ( 0.1 53.5 ( 0.1

8.8 ( 0.1

ΔωL2 (cm1)

45.2

56.1

40.9

60.6

66.9

65.7 58.0

ωG2 (cm1) ΔωG2 (cm1) ωG (cm1)

ωL2 (cm1)

1.591 ( 0.009

1.483 ( 0.005

1.416 ( 0.007

1.042 ( 0.003

0.869 ( 0.003 0.914 ( 0.005

aG2

The Journal of Physical Chemistry A ARTICLE

Figure 7. Plots of the first moment of the low-frequency Kerr spectrum (M1: red circles) and the peak frequency of the highfrequency component (ωG: blue squares) vs the square roots of the rotational constants, (a) Bx (M1 = 0.000213((0.000075) Bx1/2 + 41.79((5.34), χ2 = 49.82), (b) By (M1 = 0.0001536((0.000051) By1/2 + 47.68((3.21), χ2 = 46.81), (c) Bz (M1 = 0.0002471((0.000081) B z1/2 + 45.73((3.77), χ2 = 45.95), and (d) average rotational constant Bav (M1 = 0.0002044((0.000066) Bav1/2 + 44.66((4.01), χ2 = 44.56). The z axis is set perpendicular to the aromatic ring plan. Linear fits for M1 are indicated by the solid lines.

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Figure 8. Plots of (a) the first moment of the low-frequency Kerr spectrum (M1: red circles) and (b) the peak frequency of the lowfrequency component (ωO: blue squares) vs the inverse square roots of the molecular weight. Linear fits for M1 are indicated by the solid lines. The fit function is M1 = 256.0((86.9) MW1/2 + 30.62((8.90), and χ2 is 47.86.

adjustable parameter,108,109 we have estimated the equilibrium intermolecular interaction energy as follows. At the equilibrium distance (r0), the differential value of U(r) by r is 0. Accordingly, we can calculate the equilibrium intermolecular interaction energy as Ur0 ¼

1 ðCdd þ Cdid þ Cdisp Þ 2r0 6 6

6

ð9Þ

6

The values of Cd‑d/r0 , Cd‑id/r0 , Cdisp/r0 , and Ur0 for the 7 aromatic molecules studied here are summarized in the Supporting Information. The molecular surface area was estimated from the molecular radius (Am = 4πrm2). This relationship is simply considered the intermolecular vibration to be the harmonic oscillator. As shown in Figure 9a, there is a moderate correlation between the two quantities. However, Figure 9b shows the plots of M1 and ωG vs the square root of the value of the square of the negative intermolecular interaction energy (Ur0) per molecular surface area (Am) divided by the molecular weight (MW), i.e., [(Ur0/Am)2/ MW)]1/2, according to the libration model of Tao and Stratt.66 They analyzed the time scales of the librational dynamics of aromatic molecular liquids as the Einstein frequencies of libration about the three principle axes and found that these libration Einstein frequencies were proportional to the ratio of the mean square of the torque and the moment of inertia.67 sffiffiffiffiffiffiffiffiffiffiffiffi ÆTα 2 æ ð10Þ ωα ¼ Iα kB T where ωα is the librational frequency for axis α, Iα is the inertia moment about axis α, kB is the Boltzmann constant, T is the

Figure 9. Plots of the first moment of the low-frequency Kerr spectrum (M1: red circles) vs the square roots of the values of (a) the negative interaction energy (Ur0) at the equilibrium distance (r0) divided by the molecular surface area (A m ) and the molecular weight (MW) [Ur0/(AmMW)]1/2 (harmonic oscillator model) (M1 = 3380((1590) [Ur0/(AmMW)]1/2 + 40.51((7.74), χ2 = 68.98), and (b) the square of the negative interaction energy (Ur0) at the equilibrium distance (r0) divided by the molecular surface area (Am) divided by the molecular weight (MW) [(Ur0/Am)2/MW)]1/2 (libration model) (M1 = 29310((2270) [(Ur0/Am)2/MW)]1/2 + 49.94((5.45), χ2 = 98.17). Linear fits for M1 are indicated by the solid lines.

absolute temperature, and Tα is the torque about axis α. In eq 10, Tα is the torque about axis α, which is defined as ÆTα 2 æ ¼ f^ 2

N

αi 2 ∑ i¼1

ð11Þ

where f^ is the magnitude of the fluctuating force for the libration to the aromatic plane. The Einstein frequency for libration is then given by100 sffiffiffiffiffiffiffiffiffiffiffi f^ 2 ωα ¼ ð12Þ mkB T where m is the mass of the target molecule. In this study, f^ is simply assumed that it is related to the bimolecular interaction energy Ur0 (ignoring the many-body interaction effect for the simplicity), and the right-hand side of eq 12 is simply assumed to be proportional to [(Ur0/Am)2/MW)]1/2. The plots shown in Figure 9b are poorer than the plots based on the harmonic oscillator model (Figure 9a) based on the fit analysis (Figure 9b shows the larger standard deviation than Figure 9a). This implies that the intermolecular vibrational spectrum includes both the librational and translational motions, not just the librational motion since the MD simulation of liquid benzene by Ryu and Stratt showed an overlap between the 14271



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Figure 10. Plots of the first moment of the low-frequency Kerr spectrum (M1) vs the square root of the surface tension divided by density (γ/d)1/2. Linear fit is indicated by the solid line. Red squares denote the aromatic liquids investigated in this study, open squares denote aromatic molecular liquids, open circles denote nonaromatic molecular liquids reported in ref 26, and filled circles denote C3v CXY3 molecular liquids reported in ref 106. The fit function is M1 = 11.15((0.95) (γ/d)1/2 9.12((5.13).

translational and librational motions in the frequency region and the coupling motions (so-called cross-term).66 The present results might result from the complex properties of the intermolecular vibrations: the actual spectral line shapes of the translational and librational motions are not simply expressed by Ohmic and antisymmetrized Gaussian functions, and the intermolecular vibrational band is not just the sum of the components of these individual motions probably due to the coupling motions. 4.1.4. Comparison with Bulk Properties. Previously, we reported the linear correlation between M1 and the square root of the value of the surface tension divided by the liquid density (γ/d)1/2 in 40 aprotic molecular liquids, comprised of 20 aromatic molecular liquids and 20 nonaromatic molecular liquids.26 This result indicates that the intermolecular vibrational spectrum reflects the bulk properties. Figure 10 plots M1 vs (γ/d)1/2 for the present results. To see the entire feature, the previous data for the 40 aprotic molecular liquids are also shown,26 as well as recent results for 4 C3v molecular liquids, CHCl3, CHBr3, CFBr3, and CBrCl3.106 As can be seen in Figure 10, the data for the present molecular liquids, including the condensed ring aromatic molecular liquids, moderately conform to the overall linear relationship between M1 and (γ/d)1/2. However, if we focus closely on the data in this study, the data points are rather scattered. As discussed in Section 4.1.3, there is a moderate correlation between M1 vs [Ur0/(AmMW)]1/2. In fact, the idea conveyed in the plots in Figure 9a is similar to that in the plots in Figure 10, using the molecular weight instead of the liquid density, except that the plots in Figure 10 are for a microscopic bimolecular system. It can therefore be expected that the qualities of the two correlations are likely to be similar. Nonetheless, the correlation for the plots in bulk quantities for the present 7 aromatic molecular liquids is poorer than that for the plots in microscopic quantities. This result might be attributed to the fact that the surface tension does not very well reflect the microscopic intermolecular interaction, which is sensitive to the intermolecular vibration. Since the present 7 molecules have flat-plane shapes, they are anisotropic on a microscopic level (intermolecular vibration),

Figure 11. Plots of (a) the slow relaxation time τslow vs the product of the molar volume and shear viscosity Vmη, and (b) the slow relaxation time relative to that of quinoline τslow/τslow,quinoline vs the relative value of the product of the molar volume and shear viscosity to that of quinoline Vmη/Vm,quinolineηquinoline. The solid line in panel a is a linear fit (τslow = 0.1041((0.011) Vmη 1.822((2.57)), and that in panel b is a line with a slope of 1.

and thus, the bulk liquid property, which is isotropic, could be rather insensitive to this microscopic feature. However, we would like to point out again that there is a moderate correlation between M1 and (γ/d)1/2 for aprotic molecular liquids in whole. 4.2. Diffusive Orientational Dynamics. The rotational time constant τrs of a single molecule in solution has been amply discussed based on the StokesEinsteinDebye (SED) hydrodynamic model.110112 According to the SED model, the simplest τrs is given by τrs ¼

Vη kB T

ð13Þ

where V is the solute volume, η is the shear viscosity of the medium, kB is the Boltzmann constant, and T is the absolute temperature. In fact, by using RIKES, a collective reorientation correlation time in liquids was observed but not a single molecule reorientation.113 However, this model can be a good guide for understanding diffusive orientational relaxation in neat liquids. Figure 11a shows the plots of the slowest relaxation time τslow vs the product of the molar volume and the shear viscosity Vmη. The fit function by a linear function is also shown. The relationship between τslow and Vmη is linear, as shown in Figure 11a. Figure 11b shows the relationship between τslow and Vmη relative to that for quinoline, whose diffusive orientational relaxation is the slowest among the present 7 aromatic molecular liquids, (τ2,quinoline and Vm,quinolineηquinoline) to see more precisely. The line in Figure 11b is not the linear fit; rather, it indicates a direct 14272


The Journal of Physical Chemistry A linear comparison between the two quantities (in that the slope is 1). As shown in Figure 11b, the present aromatic molecular liquids, including condensed ring aromatic molecular liquids, show a linear correlation between τslow/τ2,quinoline and Vmη/ Vm,quinolineηquinoline. Therefore, the diffusive orientational relaxation time in aromatic molecular liquids, including condensed ring aromatic molecular liquids, can be accounted for by the simplest SED model. This is probably the case because (i) the molecular shape of all the aromatic molecules studied here is oblate, and thus, the shape factors are possibly similar, and (ii) the relative size of the solute and solvent molecules is uniform since the present systems are neat, and thus, the boundary conditions of the present 7 aromatic molecular liquids can be expected to be similar.

5. CONCLUSIONS The intermolecular vibrations and the diffusive orientational dynamics of the Cs condensed ring aromatic molecular liquids benzofuran, 1-fluoronephtalene, and quinoline were investigated together with the reference singular aromatic molecular liquids, furan, fluorobenzene, pyridine, and benzene, using femtosecond Raman-induced Kerr effect spectroscopy. The high quality lowfrequency spectra of the Cs condensed ring aromatic molecular liquids were reported here, for the first time. The line shapes of the low-frequency Kerr spectra of the condensed ring aromatic molecular liquids are clearly bimodal, as compared to the reference singular aromatic molecular liquids. The first moment of the intermolecular vibrational spectrum for the present 7 aromatic molecular liquids is moderately correlated with the square roots of the rotational constants and the inverse square root of the molecular weight. Thus, the molecular volume is a primary property of the characteristic frequency of the intermolecular vibrational spectrum. However, taking the intermolecular force estimated from the simple LenardJones model and the ab initio quantum chemical calculation results into consideration of the intermolecular vibrational spectrum indicated a better correlation for the harmonic oscillator model than the libration model. This fact indicates that the intermolecular vibrational spectrum in the present aromatic molecular liquids includes the contributions of both the translational and librational motions and that their respective contributions to the entire intermolecular vibrational spectra are hardly distinguishable. Regarding the diffusive orientational dynamics, the slowest relaxation time constant in both the condensed ring and singular aromatic molecular liquids is well expressed by the simple StokesEinsteinDebye hydrodynamic model. This is probably the case because the 7 molecules are all oblate, and the targets are neat, not solutions, so it is possible that the shape factor and the boundary condition are uniform for all the molecular liquids. ’ ASSOCIATED CONTENT

bS

Supporting Information. Ab initio quantum chemical calculation results (atom coordinates, polarizability tensor elements, and energies of the optimized neutral form and the cation form of the molecules); the list of the attractive energies (dipoledipole interaction, dipoleinduced dipole interaction, and dispersion; and bimolecular interaction energies based on eqs 59 for the 7 aromatic molecules; calculated molecular properties, dipole moment μ, mean polarizability volume α0, polarizability anisotropy volume αanis, rotational constants Bx, By,

ARTICLE

and Bz, and average rotational constant Bav, of aromatic molecules on the basis of the B3LYP/6-311++G(d,p) level of theory. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was partially supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan (Grant-in-Aid for Young Scientists (A), 21685001), the Inamori Foundation, and the Shimadzu Science Foundation. ’ REFERENCES (1) Barbara, P. F.; Jarzeba, W. Adv. Photochem. 1991, 15, 1–68. (2) Maroncelli, M. J. Mol. Liq. 1993, 57, 1–37. (3) Heitele, H. Angew. Chem., Int. Ed. 1993, 32, 359–377. (4) Yoshihara, K.; Tominaga, K.; Nagasawa, Y. Bull. Chem. Soc. Jpn. 1995, 68, 696–712. (5) Fleming, G. R.; Cho, M. Annu. Rev. Phys. Chem. 1996, 47, 109–134. (6) de Boeij, W. P.; Pshenichnikov, M. S.; Wiersma, D. A. Annu. Rev. Phys. Chem. 1998, 49, 99–123. (7) Bagchi, B.; Biswas, R. Adv. Chem. Phys. 1999, 109, 207–433. (8) Nandi, N.; Bhattacharyya, K.; Bagchi, B. Chem. Rev. 2000, 100, 2013–2045. (9) Ohta, K.; Tominaga, K. Bull. Chem. Soc. Jpn. 2005, 78, 1581– 1594. (10) Raineri, F. O.; Friedman, H. L. Adv. Chem. Phys. 1999, 107, 81–189. (11) Horng, M. L.; Gardecki, J. A.; Papazyan, A.; Maroncelli, M. J. Phys. Chem. 1995, 99, 17311–17337. (12) Stratt, R. M.; Maroncelli, M. J. Phys. Chem. 1996, 100, 12981–12996. (13) Biswas, R.; Bagchi, B. J. Phys. Chem. 1996, 100, 1238–1245. (14) Kashyap, H. K.; Biswas, R. J. Phys. Chem. B 2010, 114, 254–268. (15) Nagasawa, Y. J. Photochem. Photobiol., C 2011, 12, 31–45. (16) McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. IEEE J. Quantum Electron. 1988, 24, 443–454. (17) Lotshaw, W. T.; McMorrow, D.; Thantu, N.; Melinger, J. S.; Kitchenham, R. J. Raman Spectrosc. 1995, 26, 571–583. (18) Righini, R. Science 1993, 262, 1386–1390. (19) Schmuttenmaer, C. A. Chem. Rev. 2004, 104, 1759–1779. (20) Ronne, C.; Jensby, K.; Loughnane, B. J.; Fourkas, J.; Faurskov Nielsen, O.; Keiding, S. R. J. Chem. Phys. 2000, 113, 3749–3756. (21) Beard, M. C.; Lotshaw, W. T.; Korter, T. M.; Heilweil, E. J.; McMorrow, D. J. Phys. Chem. A 2004, 108, 9348–9360. (22) Kinoshita, S.; Kai, Y.; Ariyoshi, T.; Shimada, Y. Int. J. Mod. Phys. B 1996, 10, 1229–1272. (23) Castner, E. W., Jr.; Maroncelli, M. J. Mol. Liq. 1998, 77, 1–36. (24) Smith, N. A.; Meech, S. R. Int. Rev. Phys. Chem. 2002, 21, 75–100. (25) Zhong, Q.; Fourkas, J. T. J. Phys. Chem. B 2008, 112, 15529–15539. (26) Shirota, H.; Fujisawa, T.; Fukazawa, H.; Nishikawa, K. Bull. Chem. Soc. Jpn. 2009, 82, 1347–1366. (27) Turton, D. A.; Hunger, J.; Stoppa, A.; Thoman, A.; Candelaresi, M.; Hefter, G.; Walther, M.; Buchner, R.; Wynne, K. J. Mol. Liq. 2011, 159, 2–8. (28) Hunt, N. T.; Jaye, A. A.; Meech, S. R. Phys. Chem. Chem. Phys. 2007, 9, 2167–2180. 14273


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Intermolecular Vibrations and Diffusive Orientational Dynamics of Cs

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