Intermolecular Vibrational Spectra of C 3 v CXY3 Molecular Liquids

ARTICLE pubs.acs.org/JPCA

Intermolecular Vibrational Spectra of C3v CXY3 Molecular Liquids, CHCl3, CHBr3, CFBr3, and CBrCl3 Hideaki Shirota†,‡,* and Tatsuya Kato† †

Department of Nanomaterial Science, Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi, Inage-ku, Chiba 263-8522, Japan ‡ Department of Chemistry, Faculty of Science, Chiba University, 1-33 Yayoi, Inage-ku, Chiba 263-8522, Japan

bS Supporting Information ABSTRACT: We report the quality anisotropic intermolecular vibrational spectra within the frequency range 0.5
800 cm
1 of four C3v CXY3 molecular liquids, CHCl3, CHBr3, CFBr3, and CBrCl3, by means of femtosecond opticalheterodyne-detected Raman-induced Kerr effect spectroscopy. The results show that the first moment of the intermolecular vibrational spectrum is proportional to the square root of the value of the surface tension divided by the liquid density. This implies that the intermolecular vibrational spectrum reflects the bulk properties of the liquids. To understand the molecular-level aspects of the intermolecular vibrational spectra of the liquids, the spectra are compared with the molecular properties such as molecular weight, rotational constants, and bimolecular interaction energy. Overall, the first moment of the spectrum moderately correlates to the inverse square roots of both the molecular weight and the fast rotational constant. Therefore, the molecular properties are responsible for the intermolecular vibrational spectrum. Plots of the first moment of the intermolecular vibrational spectrum vs the square root of the value of the simple bimolecular interaction energy divided by the molecular surface area and the molecular weight show a linear correlation in the case of the oblate symmetric top molecular liquids, CHCl3, CHBr3, and CFBr3. However, CBrCl3, which is a prolate symmetric top molecular liquid, does not show the same correlation for the oblate molecular liquids.

1. INTRODUCTION The intermolecular dynamics in molecular liquids are of longstanding interest in chemistry. Since the rapid collective fluctuation of solvents affects the barrier-crossing processes in chemical reactions and biological dynamics in solution, such as electron transfer, proton transfer, and protein folding, studies of liquid dynamics are essential for a detailed understanding of these processes.1
9 Intermolecular vibrations, including collisions, librations, etc., in solutions typically occur within the frequency range of approximately 1
150 cm
1. Extensive studies have revealed the molecular level aspects in the intermolecular vibrations in liquids, which dictate the liquid dynamics and the solvation dynamics.10
27 Femtosecond optical heterodyne-detected Ramaninduced Kerr effect spectroscopy (OHD-RIKES) is a very useful spectroscopic technique to investigate the intermolecular vibrational dynamics and intermolecular interactions in simple molecular liquids28
35 because it provides high quality spectra within the frequency range 0.5
800 cm
1, which includes the intermolecular dynamics and vibrations. OHD-RIKES can also be used to obtain spectra of complex condensed phases36 such as polymer liquids37,38 and solutions,37,39
42 microemulsions,42
45 biological molecules and mimics,46
50 solvent molecules confined in nanoporous glasses,51
60 and room-temperature ionic liquids.61
70 To date, low-frequency Kerr spectra of simple molecular liquids have been reported and accumulated.29,31
35 However, r 2011 American Chemical Society

there are much less data regarding the intermolecular vibrational spectra of molecular liquids than that regarding the intramolecular vibrational spectra. Also, the details of the line shape of the broad intermolecular vibrational spectra of molecular liquids are not yet fully understood, though there are some challenges.35,71
74 Molecular dynamics (MD) simulation is a powerful and complementary method to understand the details of the low-frequency Kerr spectrum in molecular liquids, and thus several groups have calculated the Kerr spectra of some molecular liquids75
88 and room temperature ionic liquids89,90 using MD simulations. However, the number of the calculated molecular liquids is still limited. McMorrow and Lotshaw measured the low-frequency spectra of liquid benzene and pyridine by femtosecond OHD-RIKES.71 They pointed out that these aromatic liquids show a bimodal spectral feature, but some nonaromatic liquids such as CS2, CHCl3, CHBr3, and CH3CN show a monomodal spectrum. Recently, we obtained the low-frequency spectra of 40 aprotic molecular liquids including 20 aromatic and 20 nonaromatic molecular liquids and found that the spectral shapes of the aromatic molecular liquids are bimodal but the spectral line shape in the nonaromatic molecular liquids depends on the liquid: some are monomodal and some are bimodal.35 We also showed in the study that the first moment of the low-frequency Received: April 7, 2011 Revised: July 12, 2011 Published: July 12, 2011 8797

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Table 1. Calculated Molecular Properties, Dipole Moment μ, Mean Polarizability Volume r0, Polarizability Anisotropy Volume ranis, Rotational Constants Bx, By, and Bz, Short and Long Bond Lengths lC
X and lC
Y, and Ionization Energy Ie of C3v CXY3 molecules, CHCl3, CHBr3, CFBr3, and CBrCl3, on the basis of the B3LYP/6-311++G(d,p) Level of Theory liquid CHCl3

a

μ (Debye)

R0 (Å3)

Ranis (Å3)

Bxa (GHz)

Bya (GHz)

Bza (GHz)

lC
X (Å)

lC
Y (Å)

b

7.23

2.93

3.202

3.202

1.659

1.082

1.786

11.14 (11.37)c

b

1.197 (1.04)

Ie (eV)

CHBr3

0.966 (0.99)

10.34

4.59

1.203

1.203

0.611

1.081

1.952

10.14 (10.50)c

CFBr3

0.595

10.52

4.04

1.051

1.051

0.614

1.342

1.961

10.34 (10.67)c

CBrCl3

0.109

7.75

1.125

1.125

1.692

1.977

1.788

10.78 (10.6
11.05)c

1.22 b

c

Axis z sets along with the bond of C
Y. Reference 97. Reference 98.

spectrum correlates to the square root of the value of the surface tension divided by the liquid density, (γ/d)1/2.35 To understand the intermolecular vibrational spectrum at the molecular level, Fourkas and co-workers studied 5 aromatic molecular liquids having different shapes and dipoles and concluded the molecular shape and the electrostatic force are important to determine the intermolecular vibrational spectrum shape.72 Recently, Fourkas and co-workers also investigated benzene and its isotopomers73 and showed an excellent correlation between the high-frequency component assigned by an antisymmetrized Gaussian function in the anisotropic intermolecular vibrational spectrum and the inverse square root of the moment of inertia, I
1/2. They discussed this feature for the liquid benzenes based on the theoretical molecular-level approach reported by Tao and Stratt.76 Heisler and Meech focused on the isotropic intermolecular vibrational spectra of aromatic molecular liquids.74 They found a linear correlation between the first moment of an isotropic vibrational spectrum and the inverse square of the molecular weight, MW
1/2. They attributed this correlation to the fact that isotropic vibrational motion is translational in character. In this study, we have focused on C3v CXY3 molecular liquids, i.e., CHCl3, CHBr3, CFBr3, and CBrCl3. The C3v CXY3 molecular liquids are rather simple molecular liquids, but they are very different from the aromatic molecular liquids. Previously, Back et al. and Deuel et al. investigated liquid halogenated methanes.91,92 Back et al. measured liquid CHCl3, CHBr3, CFBr3, and CBrCl3 by femtosecond OHD-RIKES based on the depolarized polarization condition and confirmed that the observed low-frequency intramolecular vibrational modes were anisotropic.91 The later work by Deuel et al. characterized the low-frequency Kerr spectra by an Ohmic function and found that the characteristic frequency shifted to a lower frequency in the order of CHCl3, CFCl3, CCl4, and CBrCl3.92 This work follows these studies but includes higher-quality Kerr spectra. In this study, the intermolecular vibrational spectra are compared with the bulk liquid and molecular properties to understand the molecular-level aspect of the intermolecular vibrational band.

2. EXPERIMENTAL PROCEDURES AND QUANTUM CHEMISTRY CALCULATIONS CHCl3 (Wako Pure Chemical), CHBr3 (Sigma-Aldrich), CFBr3 (Tokyo Chemical Industry), and CBrCl3 (Kanto Chemical) were used as received. The shear viscosities (η) of the sample liquids were measured at 295 ( 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

295.0 ( 0.5 K. The densities (d) of the liquids were obtained using a volumetric flask at 295.0 ( 0.5 K. Details of the femtosecond OHD-RIKES apparatus used in this study were already reported elsewhere.35,93 A titanium sapphire laser that was built from a laser kit (CDP Corp., TISSA-kit 20) and pumped by the second-harmonic-generated light of a Nd:VO4 laser (Spectra Physics, Millennia Pro Vs) was used as the light source for the femtosecond OHD-RIKES setup. The output power of the laser was approximately 370 mW. The typical temporal response, which was the cross-correlation between the pump and probe pulses measured using a 200 μm-thick KDP crystal (type I), was found to be approximately 33 ( 3 fs (full width at half-maximum). Scans for a short time window (13.65 ps) with a high time resolution of 0.5 μm/step (total of 4096 steps) were performed. Long time window transients with a data acquisition of 5.0 μm/step were also recorded up to 50 ps, except for CHCl3 (30 ps). Pure heterodyne signals were obtained by recording scans for both ∼+1
and ∼
1
rotations of the input polarizer, which were then added to delete the residual homodyne signal. The Kerr transient of the liquid CHCl3 in this paper was obtained from our previously reported data.35 The result of the data analysis of the Kerr transient of liquid CHCl3 done in this study was very similar to that of the previous analysis.35 The sample liquids were injected into a 3 mm optical path length quartz cell (Tosoh Quartz) via 0.2 and 0.02 μm Anotop filters (Whatman) prior to the femtosecond OHD-RIKES measurements. All of the OHDRIKES measurements were performed at 295 ( 1 K. Ab initio quantum chemical calculations at the B3LYP/6-311+ +G(d,p) level of theory94,95 with very tight convergence criteria were performed to obtain the optimized structures, dipole moments, normal modes, and polarizability tensor elements of CHCl3, CHBr3, CFBr3, and CBrCl3 using the Gaussian 03 program suite.96 The obtained atom coordinates are summarized in the Supporting Information.

3. RESULTS 3.1. Bulk and Molecular Properties of C3v CXY3 Molecules. First, we will give an overview of the four C3v CXY3 molecules. Table 1 lists the dipole moment (μ), mean polarizability volume (R0), polarizability anisotropy volume (Ranis), rotational constants (Bx,y and Bz), bond lengths (lC
X and lC
Y), and ionization energy (Ie) of CHCl3, CHBr3, CFBr3, and CBrCl3. These values, except for the molecular weights, were estimated from the optimized structures obtained by the quantum chemical calculations based on the B3LYP/6-311++G(d,p) level of theory. The ionization energy was calculated as the difference between the single point energy of the cationic form and the optimized energy of the neutral form. The single-point energy of the cationic form was estimated on the basis of the optimized neutral form. The 8798

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Table 2. Molecular Weights MW and Liquid Properties, Liquid Density d, Molar Volume Vm, Molecular Radius rm, Shear Viscosity η, and Surface Tension γ, at 295 K for C3v CXY3 Molecular Liquids, CHCl3, CHBr3, CFBr3, and CBrCl3 liquid

a

MW da (g/mL) Vma (mL/mol) rma (Å) ηb (cP) γb (mN/m)

CHCl3 119.38

1.471

81.16

3.181

0.521

27.84

CHBr3 252.73

2.873

87.97

3.267

1.792

48.09

CFBr3 270.72

2.742

98.73

3.340

1.396

33.13

CBrCl3 198.27

2.000

99.14

3.400

1.463

31.76

(2%. b (3%.

ionization energy values were used to estimate the interaction energies of the molecules (see section 4.4). Some reported standard data of the dipole moments97 and the ionization energies98 for the sample liquids are also shown for the comparisons. As shown in Table 1, all four molecules belong to the C3v point group, and their dipole moments are all along the X
CY3 bond. However, the magnitudes of the dipole moments of the four molecules are very different; for example, CHCl3 is much more polar than CBrCl3. The molecules also vary in their molecular shapes; CHCl3, CHBr3, and CFBr3 are oblate symmetric tops, but CBrCl3 is a prolate symmetric top. The bulk physical properties, liquid density (d), molar volume (Vm), molecular radius (rm), shear viscosity (η), and surface tension (γ), at 295 K of the four C3v CXY3 molecular liquids are also listed in Table 2. The molar volume was estimated from the liquid density and the molecular weight according to the following equation: Vm = MW/d. The radii of the molecules were obtained by the equation of rm = (3Vm/4πNA)1/3 where NA is Avogadro’s constant. Data for the liquid density, shear viscosity, and surface tension of CHCl3 and CHBr3 at 297 K are summarized in the CRC Handbook, and the values obtained in this study are in good agreement with the handbook’s values at a similar temperature.97 These properties will be referenced to discuss the results of the ultrafast dynamics in the four liquids below. 3.2. RIKES Experiments and Data Analysis. Figure 1a shows the long time window Kerr transients of liquid CHCl3, CHBr3, CBrCl3, and CFBr3. To characterize the overdamped feature, the Kerr transients were fitted by a biexponential function after 3 ps. The fits are also shown in Figure 1a, and the fit parameters are summarized in Table 3. Overall, the time constants obtained in this study are similar to reported values.91,99,100 The signal intensity due to the nuclear response for liquid CBrCl3 is minute because of its tiny dipole moment and polarizability anisotropy (Table 1). Figure 1b shows the Kerr transients of the sample liquids within the time range of
0.5
5.0 ps. Each Kerr transient in the four liquids includes a unique beat pattern. The Kerr transients were further analyzed by the Fourier-transform deconvolution procedure based on the method by McMorrow and Lotshaw101,102 to represent the low-frequency Kerr spectra. Parts a
d of Figure 2 display the Kerr spectra within the frequency range 0
800 cm
1. Note that the obtained spectra here correspond to the depolarized Raman spectra including the Bose
Einstein thermal occupation factor.103
105 As shown in parts a
d of Figure 2, two different kinds of vibrational bands were observed in each Kerr spectrum: (1) sharp intramolecular vibrational modes and (2) a broad band in the low frequency region of less than 100 cm
1. The low-frequency broad spectrum band in the spectra of the four liquids originates from

Figure 1. (a) Long time scale Kerr transients of liquid CHCl3 (black), CHBr3 (red), CFBr3 (blue), and CBrCl3 (green). The data are illustrated by dots, and the biexponential fits are shown by solid lines. (b) Short time scale Kerr transients of liquid CHCl3 (black), CHBr3 (red), CFBr3 (blue), and CBrCl3 (green). Offsets are made for clarification.

orientational dynamics and intermolecular vibrations but not intramolecular vibrational modes. The amplitude of the orientational dynamics component for liquid CBrCl3 is much smaller than that of the other three liquids because of its symmetric nature, which leads to a smaller dipole moment and polarizability anisotropy (Table 1). Figure 2e shows the calculated depolarized Raman-active normal mode spectra of the four molecules based on the B3LYP/6-311++G(d,p) level of theory. As can be seen by comparing parts a
d of Figure 2 with Figure 2e, the intramolecular vibrational modes in the experimentally obtained Kerr spectra are in good agreement with the calculated spectra. The observed and calculated intramolecular vibrational bands of the CXY3 molecules are summarized in Table 4. The assignments of the intramolecular vibrational bands were made on the basis of the present ab initio quantum chemical calculation results and reported studies.91,92 All of the intramolecular vibrational modes of the CXY3 molecules are Raman active. However, some intramolecular vibrational modes of the CXY3 molecules were not observed in the Kerr spectra. Since the Kerr spectra in this study capture the anisotropic Raman-active motions, an isotropic vibrational band such as the symmetric C
Y stretching mode is silent. Bands for the degenerate X
C
Y bending modes of CHCl3 and CHBr3 and the symmetric C
X stretching modes of CHCl3, CHBr3, and CFBr3 were also not observed because of the limitation of the detectable frequency range of the present OHD-RIKES apparatus (