Vibrational spectroscopic studies and DFT calculations on tribromoacetate and tribromoacetic acid in aqueous solution

Spectrochimica Acta Part A 79 (2011) 1483–1492

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Vibrational spectroscopic studies and DFT calculations on tribromoacetate and tribromoacetic acid in aqueous solution Wolfram W. Rudolph a,∗ , Gert Irmer b a b

Medizinische Fakultät der TU Dresden, Institut für Virologie im MTZ, Fiedlerstr. 42, 01307 Dresden, Germany Technische Universität Bergakademie Freiberg, Institut für Theoretische Physik, Leipziger Str. 23, 09596 Freiberg, Germany

a r t i c l e

i n f o

Article history: Received 17 December 2010 Received in revised form 2 May 2011 Accepted 5 May 2011 Keywords: Tribromoacetate Tribomoacetic acid Raman- and infrared spectroscopy DFT calculations Aqueous solutions Anion hydration Acid dissociation

a b s t r a c t Aqueous solutions of sodium tribromoacetate (NaCBr3 CO2 ) and its corresponding acid (CBr3 COOH) have been studied using Raman and infrared spectroscopy. The spectra of the species in solution were assigned according to symmetry Cs . Characteristic bands of CBr3 CO2 − (aq) and the tribromoacetic acid, CBr3 COOH(aq), are discussed. For the hydrated anion, the CO2 group, the symmetric CO2 stretching mode at 1332 cm−1 and the asymmetric stretching mode at 1651 cm−1 are characteristic while the C O mode at 1730 cm−1 is characteristic for the spectra of the acid. The stretching mode, C–C at 912 cm−1 for CBr3 CO2 − (aq) is 10 cm−1 lower in the anion compared with that of the acid. These characteristic modes are compared to those in acetate, CH3 CO2 − (aq). Coupling of the modes are fairly extensive and therefore DFT calculations have been carried out in order to compare the measured spectra with the calculated ones. The geometrical parameters such as bond length and bond angles of the tribromoacetate, and tribromoacetic acid have been obtained and may be compared with the ones published for other acetates and their conjugated acids. CBr3 COOH(aq) is a moderately strong acid and the pKa value derived from quantitative Raman measurements is equal to −0.23 at 23 ◦ C. The deuterated acid CBr3 COOD in heavy water has been measured as well and the assignments were given. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Metal acetates are used in many industrial processes, in food preservation, as mordants for textile printing and dyeing, as additives in lubricating oils and greases, as catalysts and intermediates in organic reactions, and as pigments for ceramics, to name a few [1]. Furthermore, acetates and the haloacetates (the latter term refers to fluoro-, chloro- and bromo-acetates) exist widely in the biosphere. These compounds arise from photochemical degradation of halogenated hydrocarbons from direct anthropogenic emissions and also natural sources [2,3]. Recent interest in studying carboxylates and carboxylic acids in aqueous solution stems from their importance as constituents in biomolecules such as amino acids, fatty acids and surfactants among others [4]. Detailed studies aimed at the hydration, dissociation and ion-pair formation of these species in solution have been carried out by infrared [4–6] and dielectric relaxation spectroscopy (DRS) [7,8]. DRS studies are especially useful in determining hydration numbers and association constants in salt solutions forming ion pairs between anions and cations (solvent

∗ Corresponding author. Tel.: +49 351 458 6224. E-mail address: [email protected] (W.W. Rudolph). 1386-1425/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2011.05.004

shared-, solvent–solvent separated ion pairs and ion pairs without interposed water). Such studies have been carried out on aqueous solutions of sodium salts of dicarboxylates such as oxalate, malonate and succinate [7,8]. Although acetates and haloacetates have been studied quite frequently by vibrational spectroscopy [4–6,9] surprisingly, such is not the case for tribromoacetate and tribromoacetic acid. While one early vibrational spectroscopic study emphasized the investigation of potassium tribromoacetate and tribromoacetic acid in the solid state only a few incomplete solution spectra were given [10]. Infrared and Raman spectra of NaCBr3 CO2 in the solid state have been reported as part of a vibrational spectroscopic investigation of substituted acetates in Ref. [9]. As part of a speciation study on haloacetates and their corresponding acids in aqueous solution as well as the lack of complete data on the tribromoacetate and the tribromoacetic acid prompted us to report on the vibrational spectra of CBr3 COOH(aq) and its corresponding anion CBr3 CO2 − (aq). In order to compare the spectroscopic data of the characteristic modes (C–C, s CO2 and as CO2 ) for CBr3 CO2 − (aq) with the ones in the acetate, CH3 CO2 − (aq), several solutions of sodium acetate have been measured as well. The spectral assignments of the hydrated species are supplemented with DFT calculations in order to guide the assignments of the measured spectra. In addition, the DFT parameters such as bond length and bond angles of the tribromoacetic acid and its salt in

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the gas phase and with a continuum solvation sphere have been reported. A dilution series of tribromoacetic acid and the addition of HCl to aqueous solutions of tribromoacetic acid suppressing the dissociation allowed for the identification of the bands of CBr3 COOH(aq) in addition to the bands of the anion, CBr3 CO2 − (aq). Quantitative Raman data on the concentration dependence of the equilibrium of tribromoacetic acid dissociation as a function of dilution have been collected and the pKa value for the tribromoacetic acid dissociation has been calculated. Deuterated solutions of tribromoacetic acid solutions in heavy water have been measured in order to complement the spectroscopic assignments. 2. Experimental 2.1. Preparation of the solutions Preparation of a NaCBr3 CO2 stock solution started with a CBr3 COOH (Aldrich, 99.5%) solution and was neutralized with a slightly higher amount of carbonate free 18.45 M NaOH solution (ca. 2%) than needed. The crystalline acid was purchased from Aldrich (99.5%). The solution was concentrated in a vacuum apparatus and then cooled to 4 ◦ C. The precipitated crystal pulp was filtered through a suction filter and the white crystals were dried at 40 ◦ C for several hours. The solutions have been prepared from NaCBr3 CO2 and triply distilled water by weight. A stock solution NaCBr3 CO2 1.927 mol L−1 was prepared and the pH value of the solution pH was measured to ∼8.20. Two dilute solutions were prepared from the stock solution: (A) 0.964 mol L−1 and (B) 0.385 mol L−1 NaCBr3 CO2 solution. For purposes of comparison of the CO2 − modes in solutions of CH3 CO2 − (aq) with the ones of tribromoacetate, stock solutions of NaCH3 CO2 have been prepared from dried anhydrous NaCH3 CO2 (99.5% extra pure; Merck, Darmstadt, Germany) with triply distilled water by weight. The following NaCH3 CO2 solutions have been prepared: 1.209 mol L−1 , 0.810 mol L−1 and 0.161 mol L−1 . Aqueous stock solutions of CBr3 COOH, 1.880 mol L−1 , and 1.680 mol L−1 were prepared by weight. A CBr3 COOH solution with an excess of HCl was prepared in order to study the undissociated acid (repression of the dissociation). A dilution series of the tribromoacetic acid were prepared by weight and doubly distilled water. Furthermore, a tribromoacetic acid solution in heavy water was prepared from deuterated CBr3 COOD crystals and heavy water by weight. The deuterated tribromoacetic acid was prepared from the light acid which was dissolved in heavy water and subsequently crystallized. This procedure was carried out twice. The solution densities were determined with a pycnometer of 5.000 mL volume at (23 ± 0.1) ◦ C. 2.2. Raman spectra Raman spectra were measured in the macro chamber of the T 64000 Raman spectrometer from Jobin Yvon in a 90◦ scattering geometry at 23 ◦ C. These measurements have been described in detail elsewhere [11,12]. Briefly, however, the spectra were excited with the 487.98 nm line of an Ar+ laser at a power level of ∼1100 mW at the sample. After passing the spectrometer in subtractive mode, with gratings of 1800 grooves/mm, the scattered light was detected with a cooled CCD detector. IVV and IVH spectra were obtained with fixed polarisation of the laser beam by rotating the polarisator at 90◦ between the sample and the entrance slit to give the scattering geometries: I VV = I(Y [ZZ]X) = 45˛2 + 4 2

(1)

I VH = I(Y [ZY ]X) = 3 2

(2)

The isotropic spectrum, Iiso or I␣ is then constructed: I iso = I VV − (4/3)I VH

(3)

The depolarization ratio, , of the modes was determined according to Eq. (4)  = I VH /I VV = 3 2 /(45˛2 + 4 2 )

(4)

The polarization analyser was calibrated with CCl4 before each measuring cycle and adjusted if necessary. The depolarisation ratio of the 1 mode of CCl4 at 459 cm−1 was measured 15 times and a depolarization ratio equal to 0.0036 ± 0.0005 determined. The depolarization degree of the CCl4 modes at 217 cm−1 and 315 cm−1 (these modes are depolarised according to the theory) have been determined to 0.75 ± 0.02. The wavenumber positions have been checked with Neon lines and the peak positions for bands with smaller band width (full width at half height; FWHH) have been determined with an error of ±0.5 cm−1 and broader bands FWHH ≥25–30 cm−1 ) with a precision of ±1 cm−1 . The signal to noise ratio for the band at 1332 cm−1 of the spectra for a 0.402 mol L−1 has been determined to 370:1 and was much better for the modes in more concentrated solutions. Band intensities have been determined by fitting the bands using Gaussian–Lorentzian product functions on baseline corrected spectra. In the case of the tribromoacetic acid solutions, overlap between bands of the tribromoacetic acid and its corresponding salt, CBr3 CO2 − (aq) have been resolved by fitting the band profiles. Band intensities for CBr3 CO2 − (aq), CBr3 COOH(aq) and CBr3 COOD(D2 O) have been presented as relative integrated band intensities, Irel . The details of the band fitting procedure of the baseline corrected Raman- and infrared-bands has been described elsewhere [13]. Quantitative Raman measurements have been carried out to determine the dissociation constant of tribromoacetic acid according to an external quantification method previously described [14]. Raman spectra were measured with equipment described above at (23 ± 0.1) ◦ C and the solutions have been measured in quartz cuvettes from Helma. The spectra were excited with the 487.98 nm of an Ar+ laser at power levels ∼1100 mW and only the IVV scattering has been recorded. The stability of the apparatus has been checked, including the laser power, by measuring the 1 mode of SO4 2− of a 0.740 mol L−1 K2 SO4 solution during the measuring cycle of ∼1.5 h. The variation of the integrated band intensity of the external reference mode 1 SO4 2− at 981 cm−1 was better than ±1% during a measuring cycle. The analytical band of CBr3 CO2 − (aq) at 1332 cm−1 , s CO2 has been chosen because it does not overlap with modes of CBr3 COOH(aq) and can therefore be integrated quite easily. Five NaCBr3 COO solutions (0.0107, 0.0265, 0.0651, 0.1617 and 0.401 mol L−1 ) have been measured in the wavenumber range from 1154 to 1830 cm−1 and four CBr3 COOH solutions (0.402, 0.941, 1.680, and 1.800 mol L−1 ). The measuring cycle was as follows: first, measurement of the CBr3 COOH solution, second, the SO4 2− (aq) and then the NaCBr3 CO2 solution and so on. Two independent measurements have been carried out. The integrated band intensity, A1332 as a function of concentration has been established and from this calibration curve the equilibrium concentration of [CBr3 CO2 − ], and [CBr3 COOH] determined in the acid solutions (A1332 = 47046.0 · CCBr COO− ; R2 = 0.9998). 3 (The equilibrium species concentration i is denoted as [i].) The degree of dissociation ˛ of the acid has been calculated according to ˛ = [CBr3 CO2 − ]/cT with cT the total acid concentration in the solution. 2.3. Infrared spectra The infrared solution spectra were measured with the FT-IR spectrometer IFS66v (BRUKER OPTICS, Germany)[9] in the wave-

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Table 1 ˚ angles ˛ijk and dihedral angle d1237 Geometrical parameters: bond lengths aij (in A), of the CBr3 CO2 − anion (see Fig. 1). Molecule (with solvation sphere)

a12 a23 a24 a15 a16 a17 ˛324 ˛516 ˛517 ˛617 d1237 W (a.u.)

1.6510 1.2287 1.2271 1.9919 1.9919 1.9844 135.13◦ 108.17◦ 107.53◦ 107.53◦ 0◦ −7949.25774467

1.6032 1.2391 1.2367 1.9770 1.9770 1.9670 130.74◦ 109.11◦ 108.05◦ 108.05◦ 0◦ −7949.34232214

length range from 400 to 4000 cm−1 with a spectral resolution of 2 cm−1 in capillary thickness between AgCl disks. The spectra have been corrected by subtracting the spectra of the window (AgCl) material from the measured solution spectra. In order to evaluate the infrared bands quantitatively, the water spectrum has been subtracted from the spectra of the NaCBr3 CO2 solutions. 2.4. Density functional theory calculations The optimization of the molecule geometry and the calculation of the vibrational frequencies has been performed with the density functional theory (DFT) method B3LYP using the basis set 6-311++(3df,2pd) using Gaussian 03 [15]. Proper description of anions with electrons which are located, on average, relatively far from the nuclei, require diffuse orbitals and polarization basis sets. The CC-pVDZ basis set was also used. The optimization procedure led to the result that the geometry of the CBr3 CO− with the dihedral angle ϕ = 0◦ is stable and no imaginary frequencies appeared. DFT frequency calculations were performed for this stable configuration in the gas phase. A second geometry at the dihedral angle for ϕ ∼ 30◦ is a saddle point. Further details are discussed in Section 3. In addition to the calculations of the anion in the gas phase, calculations have also been performed in the presence of the solvent water by placing the solute within the solvent. The latter is modelled as an isotropic and homogeneous continuum, characterized by its dielectric properties. The frequencies were calculated with a floating cavity (a set of interlocking spheres attached to the solute atoms). The electrostatic solute–solution interaction is calculated introducing an apparent charge distribution spread on the cavity surface. The polarized continuum model (PCM) implemented in the Gaussian package was used in a version described in [16]. The orientational component of the solvent polarization is not able to follow the oscillating charge distribution connected with fast vibrations. Only the faster contributions to the solvation polarization are instantaneously equilibrated to the momentary charge distribution. In studies of nonequilibrium effects within the PCM it was found that nonequilibrium solvation has greater effects on the calculated Raman and IR intensities but little effect on the frequencies [17,18]. The frequencies, therefore, were calculated within the floating cavity model. A similar optimization procedure has been carried out for CBr3 COOH. The DFT frequencies have been calculated for the stable geometry with Cs symmetry in the gas phase and with a solvation sphere.

Fig. 1. The geometry of the CBr3 CO2 − anion for the conformational isomer with ϕ = 0◦ . The labeling of the atoms is as follows: no. 1 carbon atom of CBr3 group; no. 2 carbon atom of CO2 group; no. 5–7 the bromine atoms and no. 3 and 4 the oxygen atoms.

3. Results and discussion 3.1. DFT results and vibrational frequency calculations of CBr3 CO2 − The geometry of CBr3 CO2 − anion in the gas phase is stable with the dihedral angle ϕ = 0◦ (Cs symmetry, see Fig. 1). The corresponding stationary point on the potential surface is a local minimum which has all real frequencies. The geometrical parameters such as bond lengths and bond angles are presented in Table 1 for the gas phase anion and the anion with a solvation sphere. Another conformer with Cs symmetry at the dihedral angle ϕ ∼ 30◦ has been found and for this geometry a single imaginary frequency for the calculations of the normal-mode frequencies has been obtained. The geometry for ϕ ∼ 30◦ is therefore a saddle point on the potential surface. The energy difference between these two conformers is small (48 cal/mol) and in aqueous solution at room temperature an exchange between the conformers seems possible. Nevertheless, the results of the DFT calculation on the basis of the Cs symmetry (ϕ = 0◦ ) compare well with the measured frequencies of CBr3 CO2 − (aq). The Raman and infrared spectroscopic data on CBr3 CO2 − (aq) are discussed below.

0.70 0.60

Absorbance

Gas phase molecule

IR

0.50 0.40 0.30 0.20 0.10

12000

Intensity /a.u.

Parameter

Raman

10000 8000 6000 4000 2000 0

200

400

600

800

1000

1200

1400

1600

1800

Wavenumbers / cm-1 Fig. 2. Infrared (top) and Raman spectrum (Ipol and Idepol ) of an aqueous 1.927 mol L−1 NaCBr3 CO2 solution. The infrared spectrum starts at ≥400 cm−1 . Note, the very broad and strong mode at 685 cm−1 due to libration of water. The prominent mode at 1332 cm−1 in Raman and infrared is assigned to s CO2 . The mode at 1651 cm−1 assigned to as CO2 is very strong in infrared but with lower intensity in Raman (overlapped with ıH2 O at 1638 cm−1 ). The C–C mode at 912 cm−1 is of weak intensity in Raman and infrared. For further explanations see text.

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Table 2 Raman and infrared data of the CBr3 CO2 − (aq) anion measured in an aqueous 1.927 mol L−1 NaCBr3 CO2 solution at 23 ◦ C. Raman

max (cm−1 ) – – 141.7 179.2b 217.5 309 398 608 718 767 820.5 911.5 1332.5 1651

B3LYPa isolated molecule

B3LYPa (+ solvation sphere)

Intensity

 (cm−1 )

 (cm−1 )

2.165 1.480 2.294 0.250 0.230 8.614 19.704

17.0 120.3 125.7 161.9 163.8 188.8 240.0 351.6 542.3 660.4 670.4 744.4 798.3 1288.1 1799.4

28.9 125.9 134.6 171.0 176.4 198.5 272.5 362.2 544.2 689.3 691.4 812.2 832.9 1317.9 1692.3

Infrared



fwhh (cm−1 )

Intensity

max (cm−1 )

0.64 0.74

35 22.4

164.1 48.8

n.d. n.d. n.d. n.d.

0.036 0.004 0.72 0.74 0.010 0.74 0.68 0.64 0.18 0.69

24 22.1 22.1 33.5 27.5 23.5 18.4 16 16.2 60.4

276.7 372.9 27.4 93.9 110.2 73.3 28.8 9.5 100.0 77.2

n.d. n.d. n.d. 608 718.5 766.5 820.8 912 1331.5 1651.5

fwhh (cm−1 )

21.8 19.4 17.7 17 16 17.0 64

Symmetry

a a a a a a a a a a a a a a a

Assignment

CO2 ıCBr3 CBr3 /ıCBr3 CBr3 /ıCBr3 CBr3 /ıCBr3 ıs CBr3 s CBr3 s CBr as CBr3 s CBr3 /ıOCO ıCCO2 ıCCO2 CC s CO2 as CO2

n.d. due to the limit of our infrared spectrometer the peaks below 400 cm−1 could not be measured. a 6-311++g(3df,2pd); with solvation; symmetry is Cs . b Accidental degeneration.

3.2. Vibrational spectroscopic results for CBr3 CO2 − (aq) The Raman and infrared spectroscopic data for a 1.927 mol L−1 NaCBr3 CO2 aqueous solution has been summarized in Table 2 and a representative Raman and infrared spectrum is shown in Fig. 2. The 15 normal modes of the CBr3 CO2 − ion belong to the point group Cs and span the representation:  vib (Cs ) = 10 a (Ra, i.r.) + 5 a (Ra, i.r.).

All modes are Raman and i.r. active and the modes with the character a are partially polarized while the ones with symmetry a are depolarized. For vibrations with symmetry a the symmetry Cs with the mirror plane 1-2-3-7 (see Fig. 1) remains unaffected, however normal modes with symmetry a are depolarized. The anion in the gas phase shows free rotation of the C–C bond and it may be assumed to have C2v symmetry if the CBr3 group has a low

Fig. 3. Calculated (with solvation spheres) normal vibrations of the CBr3 CO2 − anion in solution, dihedral angle ϕ = 0◦ . Shown are the largest displacements of the atoms.

W.W. Rudolph, G. Irmer / Spectrochimica Acta Part A 79 (2011) 1483–1492

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Table 3 Summary of overtones and combination bands in Raman spectra of CBr3 CO2 − (aq). Peak position (cm−1 )



fwhh (cm−1 )

Intensity

542 1014.8 1165 1209 1435.5 1527 1817.5

0.023 0.112 0.58 0.155 0.455 0.056 0.016

16.5 24 47 28 20 34 19

2.8 0.93 5.44 7.0 1.27 9.7 2.4

Assignment ? 309 + 718 = 1027 398 + 767 = 1165 2 × 608 = 1216 2 × 718 = 1436 2 × 767 = 1534 2 × 911 = 1822

reorientation barrier around the C–C bond and if its rotation is fast. With this approximation, the symmetry species are classified according to  vib (C2v ) = 5a1 + a2 + 5b1 + 4b2 . In order to compare our model calculations with the species in the solution phase, a dielectric continuum shell around the CBr3 CO2 − has been calculated. In aqueous solution, though, the free rotation is strongly hindered and therefore the Cs symmetry of the anion CBr3 CO2 − (aq) may be favoured. Both the gas phase DFT results and the results with solvation shell have been presented in Table 2. For the assignment with the spectroscopic data in solution, CBr3 CO2 − (aq) only the DFT results with a dielectric continuum shell around the anion have been taken. DFT data for the anion in gas phase represents the anion with negligible forces in solution, similar to a molecular anion in an unpolar solvent. 3.2.1. Vibrational normal modes (see Fig. 3) The description for modes which lose their symmetry during vibration (depolarized), with respect to the mirror plane (a ), reduce to C1 symmetry and the projection of the strong displacement vectors are shown perpendicular to the mirror plane. Displacements also occur due to the invariance of the mass centre in the mirror plane but these projections are not shown. For modes with symmetry a , the polarized modes, the symmetry of the species during vibration remains and the displacements occur only in the mirror plane. 3.2.2. Vibrational spectra, and assignment of the normal modes Inspecting the spectra in Fig. 2 and data in Table 2 leads to the realization that two distinct vibrational ranges may be discussed. (A) the range from 100 to 850 cm−1 and (B) from 1300 to 1660 cm−1 . A: The vibrational modes are mixed on the potential energy surface and therefore the assignment of the normal modes is difficult. The normal mode with the lowest calculated frequency 28.9 cm−1 is a pure torsional motion of the CO2 group and could not be observed experimentally. Five bands are expected in the region from 100 to 300 cm−1 whose origin can reasonably be attributed

Fig. 4. Geometry of CBr3 COOH, conformational isomer with ϕ = 0◦ . The labeling of the atoms is as follows: no. 1 carbon atom of CBr3 group; no. 2 carbon atom of CO2 group; no. 5–7 the bromine atoms and no. 3 and 4 the oxygen atoms. In addition the H-atom is labeled no. 8.

to the deformational modes of the CBr3 group. The deformation mode at 126 cm−1 (DFT result) represents a deformation mode of the CBr3 group and could not be found in the Raman spectrum (our infrared data start from ≥400 cm−1 due to the wavenumber limit of the i.r. spectrometer). The Raman mode at 141.7 cm−1 with the theoretical value at 134.6 cm−1 may be assigned to a rocking mode of the CBr3 group (see Fig. 3). A similar assignment has been concluded for the Raman modes at 179.2 and 217.5 cm−1 . Due to the relatively large natural band width (FWHH of more than 20 cm−1 ) of the Raman bands small differences such as 171.0 and 176.4 cm−1 predicted theoretically, cannot be resolved experimentally. While the Raman band at 217.5 cm−1 could be assigned to the deformational vibration of CBr3 group, the strongly polarized Raman band at 309 cm−1 (depolarization degree at 0.004) is assigned to the symmetric stretching vibration of CBr3 group. This mode has the highest intensity in the Raman spectrum. The normal modes above ∼400 cm−1 are dominated by the stretching motion of the CBr3 group due to the large atomic mass of the Br atom but these modes are coupled with motions of the C–CO2 group of the anion. The Raman band at 398 cm−1 corresponds to symmetric stretching vibration of CBr3 combined with contributions from rocking of CO2 group lying in the mirror plane. The Raman and infrared bands at 608 cm−1 are assigned to an asymmetric vibration of CBr3 . The normal mode with symmetric CBr3 stretching in combination with CO2 deformations is associated with the Raman band at 718 cm−1 (infrared mode at 718.5 cm−1 ). The Raman band at 767 cm−1 (infrared mode at 766.5 cm−1 ) is due to the deformation of the whole C–CO2 unit. The Raman band at 911.5 cm−1 (infrared band 912 cm−1 ) has been assigned to the C–C stretching 12000

Table 4 ˚ angles aijk and dihedral angle Geometry of CBr3 COOH such as bond lengths aij (in A), d1237 (see Fig. 4). Separated molecule

Molecule (with solvation sphere)

a12 a23 a24 a15 a16 a17 a38 ˛324 ˛516 ˛517 ˛617 ˛238 d1237 d2381 W (a.u.)

1.5459 1.3380 1.1943 1.9652 1.9652 1.9403 0.9680 124.72◦ 110.42◦ 109.72◦ 109.72◦ 107.48 0◦ 0◦ −7949.78147189

1.5510 1.3205 1.2005 1.9654 1.9654 1.9455 0.9959 125.92◦ 110.28◦ 109.42◦ 109.42◦ 109.30 0◦ 0◦ −7949.34232214

8000 6000 4000

Intensity

Geometric parameter

10000

2000 0 3000 2500 2000 1500 1000 500 0

0

200

400

600

800

1000

1200

Raman shift / cm

-1

1400

1600

1800

Fig. 5. Comparison of the Raman spectra of aqueous tribromoacetic acid and its salt. Upper panel: 1.927 mol L−1 NaCBr3 CO2 , and lower panel: 1.880 mol L−1 CBr3 COOH. All three scattering components are given: polarized, depolarized and the isotropic spectrum.

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Table 5 Raman and infrared data of CBr3 COOH(aq) measured at 23 ◦ C in concentrated CBr3 COOH solution and in a solution with HCl added. Raman

max (cm−1 ) – – 139 180.4b 205.7 271 316.9 400 538 603 685 773 799 922 1203 1401 1730c ∼2920 a b c

B3LYPa isolated molecule

B3LYPa (+ solvation spheres)

Intensity

 (cm−1 )

 (cm−1 )

0.1 2.29 0.85 1.30 0.06 0.45 1.10 0.16 5.75 1.8

34.1 127.9 135.2 174.2 182.6 203.6 296.4 365.0 514.7 614.9 636.4 743.9 799.5 903.0 1159.4 1350.2 1827.0 3766.8

46.7 128.4 135.3 173.7 183.6 203.6 295.0 366.5 502.6 588.4 637.0 730.0 799.0 904.5 1154.4 1338.0 1776.0 3166.5

Infrared



0.74 0.75 0.14 0.09 0.006 0.51 0.5 0.4 0.024 0.41 0.39 0.37 0.10 0.06 0.08 0.1

fwhh (cm−1 )

16.3 14.4 14.5 50 27 41 34 23.5 33.7 2.3 25.3 19.4 54 72 38 90

max (cm−1 )

Intensity

fwhh (cm−1)

– – – –

31,766 6800 30,500 5670 53,311 8900 2000 28,290 25,413 23,267 15,350 4321 5185 4324 28,663 2000

– – – 530 604 686 774 800 922 1210 1405 1731 2840

26 18.5 31 17 12 18 34 30 48.5 70

Assignment

Symmetry

a a a a a a a a a a a a a a a a a a

COOH ıCBr3 CBr3 /ıCBr3 CBr3 /ıCBr3 CBr3 /ıCBr3 ıs CBr3 s CBr3 s CBr OH as CBr3 /OH s CBr3 /ıOCOH ıCCOOH ıBrCCOH CC ıCOH ıCOH/s OCOH C O OH

6–311++g(3df,2pd); with solvation; symmetry is Cs . Accidental degeneration. This mode shows an asymmetry at the low frequency side at ∼1709 cm−1.

vibration. For CBr3 CO2 − (D2 O), the anion in heavy water, C–C is found at 910 cm−1 . The value for the acetate anion in aqueous solution, CH3 CO2 − (aq) is found at 928.4 cm−1 with a FWHH = 11.45 cm−1 and the band is with  = 0.054 polarized [19]. B: Symmetric and asymmetric stretching modes of the CO2 group give rise to the Raman bands at 1332 cm−1 and 1651 cm−1 (infrared bands at 1332 cm−1 and 1651.5 cm−1 ). The Raman mode at 1332 cm−1 , the symmetric stretch of the CO2 has a depolarization ratio  = 0.18 and is therefore polarized. In heavy water this mode is positioned at 1334.5 cm−1 slightly higher than in water while the asymmetric stretching modes of the CO2 group is located at 1652 cm−1 . These slightly higher wavenumber positions for s CO2 and as CO2 for CBr3 CO2 − (D2 O) compared with the ones for CBr3 CO2 − (aq) reflects the different H-bonding strength between the anion and water respectively heavy water. This effect

700

A

600

has been observed recently for the PO4 3− in water and heavy water [11]. The vibrational modes of the CO2 group are prominent in all salts of carboxylic acids [4,16–18,25] (characteristic band). In the acetate spectrum, CH3 CO2 − (aq), the value of the symmetric stretch of the CO2 group has been assigned to max = (1415.4 ± 0.2) cm−1 with a FWHH = (25.50 ± 0.2) cm−1 . The antisymmetric stretch of the CO2 group at 1556 ± 0.5) cm−1 and with a FWHH = (36.40 ± 0.4) cm−1 is, with  = 0.60, also polarized but to a much lesser degree [19]. The antisymmetric stretching mode of the CO2 group is the strongest band in the infrared spectrum and is used as a diagnostic band in infrared. The oxygen atoms of the CO2 group are strongly hydrated and clusters of the acetate with water clusters of the form CH3 CO2 nH2 O have been calculated up to 7 water molecules [20]. The compari-

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Fig. 6. Raman spectra (polarized, depolarized and isotropic scattering) of tribromoacetic acid-d1 dissolved in D2 O (solution is 4.21 mol L−1 in CBr3 COOD). Panel A: wavenumber range from 80–1000 cm−1 ; panel B: wavenumber range from 1000 to 1850 cm−1 . The broad, weak mode at ∼1200 cm−1 is due to the deformation of D2 O.

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Fig. 7. Raman spectra (polarized, depolarized and isotropic scattering) of tribromoacetic acid-d1 dissolved in D2 O (solution is 0.545 mol L−1 in CBr3 COOD). Panel A: wavenumber range from 80 to 1000 cm−1 and panel B: wavenumber range from 1000 to 1850 cm−1 . The broad mode at 1205 cm−1 is due to the deformation mode of D2 O.

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Fig. 8. Calculated (with solvation spheres) normal vibrations of the CBr3 COOH in solution, dihedral angle ϕ = 0◦ . Shown are the largest displacements of the atoms.

Table 6 Raman spectroscopic data of a 4.21 mol L−1 CBr3 COOD solution in D2 Oa at 23 ◦ C. max (cm−1 )



fwhh (cm−1 )

Intensity

Symmetry

142.4 183 209 220 268 315.5 402 604 651 672 719.5 775.5 802 899 1064 1312 1545 1602.5 1731b 2196

0.75 0.70 0.22 0.068 0.005 0.014 0.66 0.70 0.13 0.162 0.10 0.68 0.67 0.44 0.2 0.265 0.12 0.5 0.09 0.2

15 12 13 20.9 33 23.5 31 26.8 35.5 38 18.2 19.7 21.5 21.3 45 27 50.1 30 40 70

8707 1220 6056 2817 1611 23,300 2245 6196 4883 1199 757.7 5830 2866 1215 791 1355.4 2179 270 10,405 1500

a a a a a a a a a a a a a a a a a a a a

a b

A broad weak mode at 1201 cm−1 (fwhh = 52 cm−1 ; integrated intensity = 2100;  ∼0.28) is due to D2 O, namely ıD2 O. This band shows an asymmetry at the low frequency at 1710 cm−1 .

Assignment CBr3 /ıCBr3 CBr3 /ıCBr3 CBr3 COOD CBr3 /ıCBr3 ıs CBr3 s CBr3 s CBr as CBr3 /OD Overtone s CBr3 /ıOCOH Overtone ıCCOOD ıBrCCOD C–C ıCOD/s OCOD ıCOD/s OCOD Overtone Overtone C O OD

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Table 7 Quantitative Raman data of the dissociation of CBr3 COOH(aq) at 23 ◦ C. cT (mol L−1 )

A1332

[CBr3 COO− ] (mol L−1 )

˛

Qa

pQa

0.065 0.162 0.402 0.941 1.680 1.880

2942 6920 14840 24680 25400 18240

0.0625 0.1471 0.3154 0.5246 0.5399 0.3877

0.962 0.908 0.785 0.558 0.321 0.206

1.586 1.451 1.149 0.6609 0.2335 0.1007

−0.200 −0.162 −0.061 0.180 0.632 0.997

son of the two stretching modes of CBr3 CO2 − in vacuo for s CO2 at 1288 cm−1 and for as CO2 at 1799 cm−1 with the species in solution, CBr3 CO2 − (aq) results in wavenumber values at 1332 cm−1 and at 1651 cm−1 , respectively (cf. data in Table 2). These big shifts of +44 cm−1 for s CO2 and −148 cm−1 for as CO2 in going from CBr3 CO2 − in vacuo to the hydrated species, CBr3 CO2 − (aq) are only explainable with the strong hydration of the CO2 group in aqueous solution. Weaker bands observed in the Raman and infrared spectrum were attributed to combinations and overtones and are presented in Table 3 together with tentative assignments. 3.3. DFT results and vibrational frequency calculations of CBr3 COOH The geometry of CBr3 COOH in the gas phase is stable with the dihedral angle ϕ = 0◦ (Cs symmetry, see Fig. 4). The corresponding stationary point on the potential surface is a local minimum which results in real frequencies for all modes. The DFT frequencies have been compared with the data measured by Raman and infrared spectroscopy. The geometrical parameters such as bond lengths, and bond angles are presented in Table 4 for the gas phase molecule and the tribromoacetic acid with solvation or in the case of water as solvent a hydration sphere. Unfortunately, to our knowledge no geometry parameters of the monomeric acid, CBr3 COOH(aq), have been published. However, for the crystalline CBr3 COOH geometrical parameters, such as bond length and bond angles for the acid dimer, have been published [21] and for the CBr3 group at least a useful comparison is possible. The published parameters and our DFT values agree quite well. 3.4. Vibrational spectroscopic results for CBr3 COOH(aq) The pure tribromoacetic acid, C2 HBr3 O2 , at room temperature, is a white solid and crystallizes in a monoclinic lattice (C2/c) with 8 formula units [21] The unit cell is comprised of carboxylic acid dimers (CBr3 COOH)2 . The acid dimer possesses C2h symmetry and therefore the molecule possesses an inversion centre which forces the mutual exclusion of the Raman and infrared modes. In highly concentrated aqueous solutions of carboxylic acids with a mole ratio acid: H2 O < 1:3 these carboxylic acids are no longer in their dimeric form but completely hydrated [22,23]. Subsequent dissociation takes place and increases with further dilution. It is fair to assume this holds true for CBr3 COOH(aq) as well. The formation of a hydrated acid monomer from the dimer results in the breakdown of the mutual exclusion rule. The 18 vibrational modes of CBr3 COOH corresponding to symmetry Cs have the representation:  vib (Cs ) = 12 a (Ra, i.r.) + 6 a (Ra, i.r.). All modes are Raman and i.r. active and the modes with the character a are partially polarized while the ones with symmetry a are depolarized. Tribromoacetic acid solutions at higher concentrations contain the monomeric acid but with increasing dilution the dissociation of the acid leads to the formation of its conjugated salt, CBr3 COO− (aq) (and hydrated protons). The tribromoacetic acid is a much stronger acid than the acetic acid and its acid strength falls into a range of those acids termed medium strong acids (−2 < pKa < 2 with

pKa = −log10 Ka ; cf. Ref. [23]). The dissociation scheme may be defined as follows: CBr3 COOH + H2 O  CBr3 CO2 − + H3 O+

(7)

The thermodynamic dissociation constant, Ka , of CBr3 COOH may be defined as follows: Ka =

[H3 O+ ] · [CBr3 OO− ] H3 O+ · CBr3 OO− · = Qa · Q CBr3 COOH [CBr3 OOH]

(8)

Raman spectroscopy does not measure activities but instead equilibrium concentrations and with the measured ˛-values (see further below) and the known total concentration of the acid (cT ) the concentration quotient, Qa , for the dissociation reaction (7) may be formulated as: Qa =

˛2 cT 1−˛

(9)

The pKa value of reaction (7) has been reported at 0.66 at 25 ◦ C [3,24] and therefore a Ka value is 0.22. (This is the preferred value according to Ref. [3] and quoted in Ref. [24].) In Fig. 5 the Raman spectrum of a 1.880 mol L−1 CBr3 COOH(aq) solution (lower panel) is compared to a solution of a 1.927 mol L−1 NaCBr3 COO solution (upper panel). The spectroscopic results for CBr3 COOH(aq) are given in Table 5. Due to the quite extensive dissociation of the acid both the undissociated acid and its conjugated salt are observed (lower panel of Fig. 5). The most prominent band of the acid is the mode at 1730 cm−1 assigned to C O of the COOH group, which may be used for analytical purposes. It is noteworthy that the modes of the CBr3 group are almost similar to the ones in its corresponding anion and because of their rather large half width they cannot be easily distinguished from the ones in CBr3 CO2 − (aq) (cf. results in Table 3). In Figs. 6 and 7 the Raman spectra of a 4.21 mol L−1 and 0.545 mol L−1 tribromoacetic acid in D2 O respectively are presented. The Raman spectroscopic results for CBr3 COOD(D2 O) are given in Table 6. In the very concentrated solution the equilibrium concentration of acid dominates and ∼95% of the total amount exists as CBr3 COOD(D2 O). The small amount of CBr3 COO− (D2 O) is barely observable by the band, s CO2 at 1335 cm−1 of CBr3 CO2 − (D2 O). In the more dilute solution 0.545 mol L−1 the band at 1334 cm−1 dominates and only ∼20% CBr3 COOD(D2 O) exist in equilibrium. Again, the band at 1731 cm−1 may be used for quantification. The modes of the OD group are especially sensitive to deuteration but the other modes also “feel” the deuterium because of the strong coupling of the modes. For instance the C–C stretch occurs 20 cm−1 lower in the deuterated acid, CBr3 COOD(D2 O) compared to the peak position in the CBr3 COOH(aq) (see results in Table 2 and Table 5). 3.4.1. Vibrational normal modes (see Fig. 8) The description for the 6 modes which lose its symmetry during vibration (depolarized) with respect to the mirror plane (a ) reduce to C1 symmetry and the projection of the strong displacement vectors are shown perpendicular to the mirror plane. Displacements occur due to the invariance of the mass centre in the mirror plane

W.W. Rudolph, G. Irmer / Spectrochimica Acta Part A 79 (2011) 1483–1492

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This C O mode has a small depolarization degree at 0.07 typical for all carboxylic acids (cf. Refs. [25,26]). The mode has a slight asymmetry at the low wavenumber side at ∼1710 cm−1 . As previously mentioned, the modes of the CBr3 group are not so different from the ones in its corresponding anion and because of their rather large half width cannot easily be distinguished from the ones in CBr3 CO2 − (aq). The modes of the CBr3 group were studied in solutions with additional HCl (suppression of dissociation). The prominent modes of the acid are the C–C stretch, C–(OH), and C O the so called characteristic vibrations. The stretching mode of O–H, OH, although prominent too, is, in dilute solution, broad and completely overlapped with the broad OH contour of water. The OH mode shifts by a factor of ∼0.752 to lower wavenumbers. The deformation mode of the CO–H group, ıCO–H is broad and of medium intensity and shifts considerably with deuteration as well (Compare results for the acids in Tables 5 and 6).

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Fig. 9. Isotropic Raman spectra of NaCBr3 COO the (A) 1.927 mol L−1 , (B) a 1.680 mol L−1 CBr3 COOH solution and (C) a 1.68 mol L−1 CBr3 COOH solution, with HCl added (1.21 mol L−1 ).

3.4.2. Quantitative Raman measurements In Fig. 10 a concentration plot of six different concentrations of CBr3 COOH is presented and quantitative Raman data for the dissociation of CBr3 COOH in aqueous solutions at 23 ◦ C are given in Table 7. These data confirm the moderately strong acid nature of CBr3 COOH in aqueous solution and the Ka value, data derived from extrapolating the Qa values to zero concentration lim Qa = Ka is c→0

Intensity

but these projections are not shown. For the 12 modes with symmetry a , the polarized modes, the symmetry of the species during vibration remains and the displacements occur only in the mirror plane. In Fig. 9 the Raman spectra of a 1.680 mol L−1 tribromoacetic acid with an excess of 1.21 mol L−1 HCl (panel C), a spectrum without additional HCl (panel B) are compared with the spectrum of a NaCBr3 CO2 solution (panel A). With the addition of HCl to the tribromoacetic acid, the band at 1332 cm−1 , s CO2 of CBr3 COO− (aq) declines in intensity by ca. 70% while the mode at 1730 cm−1 , C O increases in intensity by ca. 50%. CBr3 COOH(aq) without HCl has a dissociation degree of 0.321 but with HCl added the degree of dissociation lowers to 0.141. The most prominent band of the acid is the mode at 1730 cm−1 assigned to C O of the COOH group. 600 400 200 0 600 400 200 0 600 400 200 0 400 300 200 100 0 225 150 75 0 150 100 50

∼1.7 ± 0.1 (pKa = −0.23 ± 0.03) at 23 ◦ C. Our value constitutes the upper limit of the strength of the tribromoacetic acid and it is noticeable that the pKa values quoted in Refs. [3,24,27] range from −0.214 to 0.72 and reflect the difficulty in determining pKa values for these moderately strong acids. Nevertheless, it is obvious that the tribromoacetic acid is a much stronger acid than the acetic acid (pKa = 4.756 at 25 ◦ C). The reason is the well known electronwithdrawing effect of the –CBr3 group close to the –COOH group (−I effect). The bromine atoms pull the electron density away from the carbon to which they are attached and this C-atom is pulling on the C–C bond. The C-atom of the COOH group will thus pull on the electron density of the C–O bond, in turn, the oxygen atom is pulling on the electron density between O–H. This results in less electron density around the H in CBr3 COOH as compared to the H atom in acetic acid. Mullikan charges of CBr3 COOH and CH3 COOH are presented in supplementary section S1. Covington et al. [23] have extensively discussed and assessed the pKa values for similar trihaloacetic acids namely trichloro- and trifluro acetic acid and gave an (tentative) explanation for the quite large data scatter of these trihaloacetic acids. Their explanation is based on the assumption that the dissociation is a two step mechanism and that Raman spectroscopy can only detect the H3 O+ A− ion pair with the anion plus the fully dissociated anion [A− ] while conductivity or e.m.f. measurements detect only the equilibrium concentration of the fully dissociated anion [A− ]. As a result, the Ka value measured with the Raman method is larger (smaller pKa value) than the one from the conductivity method. 4. Conclusions

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Fig. 10. Concentration plot of isotropic Raman spectra of aqueous tribromoacetic acid solutions. Concentrations from top to bottom: 1.880, 1.680, 0.941, 0.402, 0.162 and 0.0651 mol L−1 . Note, that already at 0.162 mol L−1 of CBr3 COOH the mode at 1730 cm−1 assigned to C O (CBr3 COOH) has completely disappeared. The broad (isotropic) mode at 1628 cm−1 is due to the water bending mode ıH2 O.

Solutions of NaCBr3 CO2 and its corresponding acid, CBr3 COOH, were studied by Raman and infrared spectroscopy. The spectra in solution were assigned according to symmetry Cs . Characteristic bands of the CBr3 CO2 − (aq) spectrum and of the tribromoacetic acid are discussed. For the salt, the two modes of the CO2 group at 1332 cm−1 and 1651 cm−1 are characteristic while the C O mode at 1730 cm−1 is characteristic for the spectra of the acid. The stretching mode C–C for CBr3 COOH(aq) occurs at 922 cm−1 while that of the salt, CBr3 CO2 − (aq), is 10 cm−1 lower. Coupling of the modes are fairly extensive and therefore DFT calculations were carried out in order to compare the measured

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spectra with the calculated ones. The geometrical parameters such as bond length and bond angles of the tribromoacetate, and tribromoacetic acid have been given and may be compared with the ones published for other acetates resp. acetic acids. The geometrical parameters for the CBr3 group of CBr3 COOH(aq) and (CBr3 COOH)2 in the solid are quite similar. Tribromoacetic acid, CBr3 COOH(aq), is a moderately strong acid and a Ka value derived from quantitative Raman measurements is equal to ∼1.7 at 23 ◦ C. This value is higher than the thermodynamic value equal to 0.22 at 25 ◦ C. CBr3 COOD(D2 O) solutions have been measured, as well, and the assignments have been given. Acknowledgment WWR wishes to thank Frau B. Ostermay for her skilful technical assistance. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.saa.2011.05.004. References [1] [2] [3] [4] [5]

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[8] A. Tromans, P.M. May, G. Hefter, T. Sato, R. Buchner, J. Phys. Chem. B 108 (2004) 13789–13795. [9] E. Spinner, J. Chem. Soc. (1964) 4217–4226. [10] F. Márquez, M.I. Suero, J.C. Otero, J.I. Marcos, Spectrosc. Lett. 25 (1992) 821–830. [11] W.W. Rudolph, G. Irmer, Appl. Spectrosc. 61 (2007) 1312–1324. [12] W.W. Rudolph, D. Fischer, G. Irmer, Appl. Spectrosc. 60 (2006) 130–144. [13] W.W. Rudolph, Z. Phys. Chem. 194 (1996) 73–90. [14] W. Rudolph und, W.E. Steger, Z. Phys. Chem. 172 (1991) 49–59. [15] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford, CT, 2004. [16] M. Cossi, G. Scalmani, N. Rega, V. Barone, J. Chem. Phys. 117 (2002) 43–54. [17] C. Cappelli, S. Corni, R. Cammi, B. Mennucci, J. Tomasi, J. Chem. Phys. 113 (2000) 11270–11279. [18] C. Cappelli, S. Corni, J. Tomasi, J. Chem. Phys. 115 (2001) 5531–5535. [19] W.W. Rudolph, G. Irmer, Unpublished Results, TU Bergakademie Freiberg, 2010. [20] G.D. Markham, C.W. Bock, J. Mol. Struct. Chem. 7 (1997) 281–307. [21] P.G. Jones, V. Lozano, J. C. S. Faraday II 76 (1980) 14–25. [22] M. Leuchs, G. Zundel, J. C. S. Faraday II 76 (1980) 14–25. [23] A.K. Covington, J.G. Freeman, T.H. Lilley, J. Phys. Chem. 74 (1970) 3773–3780. [24] H.C. Brown, D.H. McDaniel, O. Häfliger, in: E.A. Brande, F.C. Nachod (Eds.), Determination of Organic Structures by Physical Methods, Academic Press, New York, 1962, pp. 567–662 (third printing). [25] S.K. Freeman, Applications of Laser Raman Spectroscopy, John Wiley & Sons, New York, 1974. [26] G. Köbrich, in: H. Volkmann (Ed.), Handbuch der Infrarot Spektroskopie, Verlag Chemie, Weinheim Bergstraße, 1972, pp. 329–376. [27] J.A. Dean, Langes’s Handbook of Chemistry, 15th ed., McGraw-Hill, Inc, 1999, Section 8, p. 1180.