Infrared E-type band shapes of the liquid CD3I and CD3CN:

Spectrochimica Acta Part A 54 (1998) 589 – 604

Infrared E-type band shapes of the liquid CD3I and CD3CN: Orientational diffusion and free rotation A.A. Stolov a,*, A.I. Morozov a, A.B. Remizov b a

Department of Chemistry, Kazan State Uni6ersity, Kremle6skaya st. 18, Kazan, 420008, Russia b Kazan State Technological Uni6ersity, Karl Marx st. 68, Kazan, 420015, Russia

Received 24 January 1997; received in revised form 26 September 1997; accepted 8 October 1997

Abstract Infrared absorption spectra of liquid methyl iodide-d3 (CD3I) and acetonitrile-d3 (CD3CN) have been studied in wide temperature ranges (212–317 K and 234–346 K, respectively). IR spectra in the regions of degenerate (E-type) bands belonging to CD3-stretching and deformational vibrations (n4, n5, n6 of CD3I and n6, n7 of CD3CN) were fitted by the sum of Cauchy-Gauss components. Each E-type band was reproduced by the sum of two components: the narrower (n) and the broader (b) ones. The different temperature behaviour of the components has been found: the integrated intensities of the narrower components (In) decrease with the temperature, while the intensities of the broader ones (Ib) increase. The narrower components of the bands belonging to deformational CD3-vibrations were interpreted within the framework of the orientational diffusion mechanism. The broader components of these bands were attributed to the unresolved gas-like vibration-rotational absorption of the molecules. The enthalpy differences between the molecules absorbing via two different mechanisms (DH) were determined from the dependencies of ln(In/Ib) upon T − 1: 0.5990.15 (CD3I) and 1.1090.20 koal mol − 1 (CD3CN). These values are close to those determined previously for nondeuterated methyl iodide and acetonitrile, respectively. The shape of the CD3-stretching E-type band of CD3I is assumed to be mainly due to interactions of the C – D stretching vibrations with single particle and collective motions of molecular dipoles. An attempt is made to separate the widths of the narrower components into the contributions of orientational and vibrational relaxation. Various experimental and theoretical approaches to molecular relaxation are considered in view of the obtained data. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Orientational diffusion; Free rotation; Acetonitrile; Methyl iodide; Vibrational relaxation; Infrared spectra

1. Introduction The rotation of several small molecules or small molecular fragments in liquid inert media is considered to be nearly free. This means that the * Corresponding author.

spectra of the systems under study contain the features of the free rotation. Thus, mid-infrared (IR) spectra of the hydrogen halogenides (HCl, HBr, HI and HF) dissolved in alkanes, benzene, carbon disulfide, haloforms and liquefied noble gases represent the wings which are similar to the vapour-phase spectra [1–5]. Other examples are CO and NO dissolved in CCl4, SnCl4 [1] and

1386-1425/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 1 3 8 6 - 1 4 2 5 ( 9 7 ) 0 0 2 6 3 - 1

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liquefied argon [6]; NH3, H2O and D2O dissolved in alkanes, CCl4 and aromatic solvents [7,8]. For all the above mentioned systems the molecules under study have relatively small moments of inertia and occupied volumes. As a rule, the conclusions about nearly free rotation were done on the basis of the mid- or far-infrared band shapes of the solutes. The orientational motion of the molecules having the general formula CH3X or CD3X (X = F, Cl, Br, I, CN) was an object of extensive study. These molecules represent symmetric tops with essentially different moments of inertia for spinning (rotation about the symmetry axis, ) and tumbling (rotation perpendicular to the symmetry axis, Þ) motions. It has been noted several times, that the spinning rotation of these molecules in the liquid phase can be considered as nearly free [2,9 –18]. The arguments in favour of such a conclusion are: (i) the similarity of IR spectra of the vapour and the liquid phase [2,9 – 13]; (ii) close to zero activation volume for spinning rotation [14,15]; and (iii) temperature dependence of the parallel diffusion constant, which is described by the free rotation model satisfactorily [16 – 18]. Normal vibrations of the CH3X (CD3X) molecules (which refer to the C36 point symmetry group) are subdivided into symmetric (A1-type) and double degenerate asymmetric (E-type) ones. The IR and Raman band shapes of the A1-type vibrations contain the information about the tumbling motions, while the E-type band shapes are due to both tumbling and spinning motions of CH3X (CD3X) [19,20]. In addition, the vibrational relaxation takes an important part in broadening of both A1- and E-type bands. It has been noted several times, that the IR E-type bands of CH3X (CD3X) molecules can not be represented by one Lorentzian or Cauchy – Gauss function, but consist of two components: the narrower and the broader one [9,13,21 – 23]. Two alternative explanations of these facts are known. Bulanin and Tonkov supposed [9], that the gas-like absorption retains in the IR spectra of the liquid methyl halides. Unresolved gas-like absorption is responsible for the broader components of the bands. The bands due to the gas-like absorp-

tion were assumed to have two maxima, which were denoted as P- and R-branches [9]. A similar semiquantitative explanation was given more recently for IR spectra of acetonitrile [13]. Though the presence of the gas-like spectra does not contradict with the results obtained for HCl, CO and other light diatomic molecules, the Bulanin’s concept has not been widely accepted. According to the alternative point of view, the broader components of the E-type bands are the result of the second order Coriolis coupling between A1- and E-type modes of the CH3X (CD3X) molecules [21–23]. This explanation was based on the correlations found for the E-type bands of CH3I [21]. It was noted that the broader component’s widths correlate with the separations between the degenerate bands and their non degenerate (A1-type) neighbours. The assignment of the broader components of the bands to the A1-E-type Coriolis coupling is not supported by any theory, and no experimental confirmation has been obtained so far. Therefore, further consideration of the IR spectra of CH3 –X top molecules seems to be necessary. Recently we have reinvestigated IR E-type band shapes of CH3I [24] and CH3CN [25]. The main results of these studies are the following. (i) The E-type bands, belonging to both stretching and deformational CH3-modes of the molecules, can be satisfactorily represented by the sum of two Cauchy–Gauss components: the narrower (n) and the broader (b) one. (ii) The broader components of the bands, belonging to deformational vibrations (i.e. n5, n6 of CH3I and n6, n7 of CH3CN), are very similar to the vapour phase spectra of the compounds. They were assigned to the unresolved gas-like absorption of the molecules. The narrower components represent the liquid-like ‘pure vibrational’ transitions. (iii) The temperature redistribution of the components intensities allowed to determine the enthalpy difference between molecules, absorbing via two different mechanisms: 0.809 0.10 and 1.269 0.15 and kcal mol − 1 for CH3I and CH3CN respectively. (iv) The broader components of the CH3stretching modes were attributed mainly to the combinational transitions between asymmetric vibrations and low-frequency motions of the molecules.

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Fig. 1. IR spectra of liquid CD3I in the region of n4 at (a) 212 and (b) 315 K. Here and below, circles denote the observed spectra, continuous curves, the calculated ones.

In the present work we apply the above approach [24,25] to the liquid CD3I and CD3CN. The results obtained are compared with those documented for their nondeuterated analogs.

The (dl/dg) ratio characterizes the band shape: the shape is close to Lorentzian when (dl/dg) 1, and to Gaussian when (dl/dg) 1.

3. Results and discussion 2. Experimental

3.1. Band fitting of the spectra Deuterated acetonitrile and methyl iodide were produced by Izotop (St. Petersburg, Russia). Their stated purity was not less than 99.5% and no further purification has been carried out. Carbon disulfide, was purified according to Ref. [26]. IR absorption spectra were measured with a SPECORD M-30 spectrometer combined with computer. The spectral slit width (1 cm − 1) was essentially smaller than the minimal band width determined (10 cm − 1). Therefore it was not necessary to account for apparatus distortions [27]. Other experimental details and the band fitting procedure were described previously [24]. It should mentioned, that the Cauchy-Gauss curves (multiplication of the Lorentzian and Gaussian functions with the widths dl and dg respectively) were used for fitting the spectra. Such functions were chosen since they have ‘Lorentzian’ center and ‘Gaussian’ wings similar to the band shapes predicted by the Kubo – Rothschild theory [28,29].

The bands of interest were those belonging to stretching and deformational asymmetric (E-type) vibrations of CD3-groups. Three such modes are observable in the IR spectrum of CD3I: n4 = 2290, n5 = 1038, and n6 = 665 cm − 1 [30]. Only two bands were observed in the spectrum of liquid CD3CN: n6 = 1064 and n7 = 847 cm − 1 [23]. The band belonging to asymmetric stretching vibrations (n5) is very weak, and its investigation is hardly possible [23]. IR spectra of liquid CD3I in the ranges of n4, n5 and n6 are shown in Figs. 1 and 2. In addition to the E-type bands several A1-type ones (n1 = 2139, n2 = 937 cm − 1) and combination bands (n1 + n3 = 2623, n3 + n5 + n6 = 2173, 2xn5 = 2072, n2 + n3 + n6 = 2063, n2 + n5 = 1973, 2xn2 = 1866, and 2xn3 = 981 cm − 1) fall in these regions. A very weak band at 1162 cm − 1 is, probably, due to the presence of an admixture (apparently CHD2I). All

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Fig. 2. IR spectra of liquid CD3I in the region of n5 and n6 at (a) 212 and (b) 315 K.

the E-type bands were reproduced by a sum of two Cauchy–Gauss functions: the narrower and the broader ones. Attempts to reproduce each of them by a single Cauchy-Gauss function failed. The values, characterizing the components of n4 – n6 are given in Table 1. Indexes n and b denote the narrower and the broader components respectively, (In/Ib) is the ratio of the integrated intensities of the components, dn and db are their full width at half height. Fig. 3 shows the IR spectra of CD3CN in the range of n6 and n7. The fundamentals n3 =1101 and n4 = 833 cm − 1, and the combinational band n4 + n8 = 1194 cm − 1 fall in this range. The bands at 1094 and 837 cm − 1 are probably due to the hot transitions: (n3 +n8) −n8 and (n4 +n8) −n8 respectively. It is seen from Fig. 3, that two components are necessary for fitting the band shape of n6. The representation of all the above mentioned E-type bands of CD3I and CD3CN by the sum of two Cauchy–Gauss functions seems reasonable, since these bands have very broad wings. However the wings of n7 of CD3CN are not so broad (Fig. 3). To examine the band shape of n7 we have measured the 1000 – 730 cm − 1 spectral region more thoroughly (Fig. 4). First, we tried to reproduce the band shape of n7 by only one Cauchy – Gauss curve. The best fit is shown in Fig. 4a. It is seen, that the experimental spectrum is poorly

described in the vicinity of the band maximum (i.e in the 870–840 cm − 1 range). However, the addition of one Cauchy–Gauss component improves the situation significantly (Fig. 4b, c). Thus, two components appeared to be necessary for fitting the band shape of n7. The parameters of the narrower and the broader components of n6 and n7 are given in Table 2. The existence of two components for all E-type bands belonging to the CD3-group vibrations is in accord with the results obtained for nondeuterated methyl iodide and acetonitrile [24,25]. In order to examine the origin of the broader components let us consider the spectra of the vapour phase of CD3I and CD3CN. These spectra are well known [31,32]. The E-type bands are represented mainly by Q-branches, reflecting the following selection rule: DJ = 0, DK = 9 1 (where J and K are the rotational quantum numbers). The frequencies of the Q-branches follow the relationship: n$ n0 + [A(1−2z)−B]9 2[A(1− z)− B]K (1) where n0 is the frequency of the ‘pure vibrational’ transition, A and B are the rotational constants for spinning and tumbling motions, respectively, z is the first order Coriolis coupling constant [32]. In the above relationship the terms with K 2 are omitted. The IR absorption intensities of the Qbranches obey the law [32]:

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Table 1 The parameters of the narrower and the broader components of E-type bands for liquid (212 – 317 K) and vapour (295 K) CD3I Band

n4

n5

T (K)

Vapour 212 295 317 Error Vapour 212 295 315

Error n6

Error a

Vapour 212 295 315

Narrower component (cm−1)

Broader component (cm−1)

In/Ib

nn

dn

d1/dg

nb

db

d1/dg

2288.1 2290.1 2290.7 90.4

23.6 38.7 43.1 92.2

0.17 0.28 0.30

2300 2290 2293 2294 93

88a 227 225 225 96

0.54 0.54 0.54

0.28 0.18 0.17 90.02

1037.8 1038.6 1038.8 90.2

19.7 26.6 28.5 90.6

0.31 0.41 0.45

1062 1055 1060 1062 92

98a 108 107 107 91

1.05 1.05 1.05

0.84 0.66 0.63 90.06

658.0 657.4 657.2 90.2

13.8 18.4 19.7 90.8

0.11 0.15 0.16

661 668 664 663 92

59a 92 86 85 92

1.04 1.07 1.08

2.10 1.19 1.06 90.31

The dyap value calculated by Eq. (3)

Intensityexp[− hcK 2(A − B)/kT]

(2)

where k and h are the Boltzman and Planck constants, respectively and c is the speed of light. According to Eqs. (1) and (2) the E-type band envelopes are Gaussian, and their widths (FWHM) are: dvap = 4[A(1− z)−B] · [kT ln2/hc(A −B)]1/2

(3)

The calculated magnitudes of dvap are given in Tables 1 and 2. Following our previous work [24] we will separate the results, obtained for the deformational and stretching vibrations. It is seen from Tables 1 and 2 that for n5, n6 bands of CD3I and n6, n7 of CD3CN, the dvap values correlate with the liquid-phase broader component’s band widths (db). Moreover, the vapour-phase band positions are also close to the nb values. The same has been found for the deformational E-type vibrations of CH3I [24], and CH3CN [25]. These facts make it possible to suggest that the broader components of the deformational degenerate vibrations of CD3-groups are really the result of the gas-like absorption in the liquid phase [9,13]. Fig. 5 shows the correlation between

db and dvap values obtained for CH3- and CD3asymmetric deformational vibrations of different compounds: CH3I [24], CH3CN [25], CH3Br [33], CD3I and CD3CN. Satisfactory linear correlation is observed, the tangent being close to 1: db = (0.9859 0.237) · dvap + (29.3923.1) r= 0.955,

n= 10

(4)

The value of the intercept shows the additional broadening of the E-type bands when going from the vapour phase to the liquid. The origin of such additional broadening needs a special theoretical investigation. To our knowledge, no theoretical work has been carried out to explain the gas-like wings of CH3-X top molecules. Nevertheless, numerous theoretical studies have been devoted to the spectra of light diatomic molecules in condensed phase (see, for example Refs. [34–36]), and some interpretation may be given within the framework of these investigations. It is obvious, that intermolecular interactions perturb the C36 symmetry of the molecules. As a result the ‘pure vibrational transition’ (which obey the selection rule: DJ = 0; DK = 0 [9]) becomes possible. This gives rise to the appearance of central peaks of the E-type bands. Secondly, an additional quan-

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Fig. 3. IR spectra of liquid CD3CN in the region of n6 and n7 at (a) 240 and (b) 348 K.

tum number should be introduced in order to describe the vibrational-rotational transitions [35]. Each transition becomes governed by three quantum numbers, and the transformation of each Q-branch takes place. Thirdly, the vibrational-rotational levels become broadened due to the distribution of intermolecular potential [35,36]. Finally, the Q-branch structure of the E-type band becomes totally blurred, and the width of the envelope increases. The results obtained for the CD3-stretching band of CD3I (n4) significantly differ from those for n5 and n6. It is seen from Table 1, that for this band the db value is substantially larger than dvap. Similar relationships were found for the stretching infrared bands of CH3I, CH3CN and CH3Br [24,25,33]. Therefore the gas-like absorption cannot be responsible (at least as the main mechanism of the band shape formation) for the broader component of n4. To considered the origin of the broader components of the CH3 (CD3) stretching bands we have examined IR spectra of several polar and nonpolar compounds in the ranges of CH-stretching and deformational vibrations. The data will be published elsewhere in detail (some of the data can also be found in Ref. [37]). The main results of this work are the following. (i) The broad bands (d 60–150 cm − 1) are present in the CH-stretch-

ing region of several dipolar compounds in the liquid phase: acetone, dimethyl sulfoxide, chloroform, bromoform, dichloromethane, 1,2-dichloroand 1,2-dibromaethane. Meanwhile, the CH-deformational regions do not contain the broad bands. (ii) The nonpolar compounds (alkanes, 1,4-dioxane) do not show the broad bands in either CH-stretching or deformational regions. These data provide the basis for considering the origin of the broader components of C–H bands. First, it follows that the broader components of CH-stretching modes and those of the deformational ones have different origins. Therefore, no correlations, including characteristics of both stretching and deformational broader components is to be expected. Secondly, the broader components of the C–H (C–D) stretching band of CH3-X (CD3-X) top molecules are not the result of the gas-like absorption only. Though the gas-like absorption may contribute to the band shape of the broader component, this is not the main mechanism of the C–H (C-D) stretching band shape formation. Thirdly, it follows that the broader components of the CH-stretching bands are not solely due to the second order Coriolis coupling. If it were so, then these components would be absent in IR spectra of polar molecules (like 1,2-dibromoethane), as the rotational motion of these

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Fig. 4. IR spectra of liquid CD3CN in the region of n7 at (a, c) 343 and (b) 240 K. (a) Shows the attempt to reproduce the spectrum by four individual components.

molecules is slow (in comparison with the spinning motion of CD3I). The results obtained for different compounds make it possible to suggest that the interaction of C – H stretching modes with some low-frequency motions give rise to the appearance of the broader components in the C – H stretching range. This conclusion is supported by the vapour-phase spectra of various compounds with hindered rotation of one or more methyl group [38]. The high- and low-frequency sides of the CH3-asymmetric IR bands contain combinations of these vibrations

with the methyl torsional modes. The latter modes were observed in the far infrared spectra [38]. It is well known, that far infrared spectra of liquids contain a broad band (Poley absorption) due to single particle and collective motions of molecular dipoles [39]. The intensity of this absorption depends on the permanent dipole moment of the molecule [40]. Nonpolar molecules, like 1,4-dioxane, have weak absorption bands in the far infrared spectra [40], while polar molecules, like dichloromethane or acetonitrile show intense bands [41,42]. Note, that the broader components

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Table 2 The parameters of the narrower and the broader components of E-type bands for liquid (234 – 346 K) and vapour (295 K) CD3CN Band

n6

T (K)

Vapour 234 295 346

Error n7

Error a

Vapour 242 295 346

Narrower component (cm−1)

Broader component (cm−1)

In/Ib

nn

dn

d1/dg

nb

db

d1/dg

1036.9 1037.4 1037.9 90.3

16.9 21.1 24.5 90.9

1.34 1.34 1.34

1046 1049 1047 1045 93

103a 116 115 115 95

0.79 0.79 0.79

0.40 0.24 0.18 90.04

849.8 849.5 849.2 90.3

10.2 13.4 16.1 91.0

0.17 0.17 0.17

850 855 851 847 910

35a 55 57 60 92

0.47 0.47 0.47

1.32 0.91 0.70 90.21

The dvap value calculated by Eq. (3)

of the CH-stretching bands are absent in the spectra of the investigated nonpolar molecules (1,4-dioxane, alkanes), and are present in the spectra of the polar ones. This correlation is in accordance with our assignment of the broader components.

3.2. Temperature dependencies of the intensity ratios The most noticeable changes are seen in redistribution of the narrower and the broader components’ integrated intensities: the (In/Ib) ratios essentially decrease with temperature (Figs. 1–4, Tables 1 and 2). These findings for the deformational C–H bands may be interpreted in terms of thermodynamic equilibrium between two ensembles of particles. The ‘immediate picture’ of the system contain the two types of independently absorbing molecules: one type of molecules absorb in accordance with the gas-like selection rule, the other type gives the liquid-like ‘pure vibrational’ central component of the band. It seems likely that the molecules giving the gas-like spectrum passes (on average) an additional kinetic energy, as their rotation is nearly free. Thus, according to the van’t Hoff equation: Ib/In = (ab/an) · exp[− (DH/RT)+ (DS/R)]

Fig. 5. The correlation between dvap and db for IR bands belonging to deformational CH3- and CD3-vibrations. The numbers of points correspond to (1) n5 of CH3I, (2) n6 of CH3I, (3) n6 of CH3CN, (4) n7 of CH3CN, (5) n5 of CD3I, (6) n6 of CD3I, (7) n6 of CD3CN, (8) n7 of CD3CN, (9) n5 of CH3Br, (10) n6 of CH3Br.

(5)

where an and ab are the integral absorption coefficients of the narrower and broader components in the liquid, DH and DS are enthalpy and entropy differences between the molecules obeying the two different laws of absorption. The dependencies of ln(In/Ib) upon T − 1 for the bands of CD3I and CD3CN are given in Figs. 6 and 7. The DH values, obtained for the bands,

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Fig. 7. The dependencies of ln(In/Ib) upon T − 1 for the E-type bands of liquid CD3CN: triangles n6, squares n7.

Fig. 6. The dependencies of ln(In/Ib) upon T − 1 for the E-type bands of (a) liquid CD3I and (b) its solution in CS2 (0.9 mol l − 1): circles n4, triangles n5, squares n6.

belonging to the deformational E-type modes, are listed in Table 3. It is tacitly assumed that the (ab/an) ratios are independent of the temperature. To check this assumption one can compare the results obtained for two different bands of the same compound. The only substantial difference is seen for the DH values determined for the neat CD3I. However, the values obtained for the solution in CD2 are close. The discrepancy found for neat CD3I can by attributed to different temperature effects on the (ab/an} ratios of n5 and n6. However, it should be kept in mind that there may be another origin of such discrepancy. It is

seen that the intensity ratios (In/Ib) are noticeably different for n5 and n6 bands of CD3I, and for n6 and n7 bands of CD3CN. It follows that the (In/Ib) ratio depends on the form of the normal vibration responsible for these bands. To put it in another way, there are certain conditions, under which a molecule exhibits the gas-like absorption for one of the E-type bands (for example for n5 of CD3I) and the liquid-like absorption for another E-type band (n6 of CD3I) simultaneously. It is clear that this factor can affect the slope of the (In/Ib)= f(T − 1) dependence as well. Thus, the physical meaning of the slope is more complex than simple enthalpy differences between the molecules, obeying the two different mechanisms of absorption. Nevertheless, the obtained slopes can be interpreted as the ‘effective’ enthalpy differences, following from IR experiments. Good agreement is seen for the DH values obtained for n6 and n7 bands of CD3CN (Table 3). To compare these results with those obtained previously Table 3 shows some of the DH data for nondeuterated methyl iodide and acetonitrile. One can see, that the average DH value obtained for CD3I (0.59 9 0.15 kcal mol − 1) is close to that for CH3I. Deuterated and nondeuterated acetonitrile also show close DH values, which appeared to be larger than those for methyl iodide.

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The dependence of ln(In/Ib) on T − 1 for CD3stretching band of CD3I (n4) is given in Fig. 6a. Though the slope (0.579 0.11) coincides with those obtained for n5 and n6, such agreement should be considered as fortuitous. Note that similar intensity redistribution was observed for CH-stretching ranges of the other studied polar molecules. Assuming the broader component of n5 to be mainly due to the combinations between CH3-stretching and low-frequency modes, one obtains Ib/In exp(−hcnFIR/kT)

(6)

where nFIR is the weight center frequency of the far-infrared absorption. Far infrared spectrum of the liquid acetonitrile shows a broad band (0 – 250 cm − 1) with the maximum at $60 cm − 1 and the half width $110 cm − 1 [43,44]. The slope of the dependence of ln(In/Ib) upon T − 1 predicted on the basis of Eq. (6) gives 0.17 kcal mol − 1 only. It is approximately three times smaller than the observed value. However, at least two more factors should take part in the intensity redistribution. First, there should be a contribution from the equilibrium between the gas- and liquid-like absorption. Second, there must be a strong temperature dependence of the (ab/an) ratio (see Eq. (5)) for the C–H stretching region of CD3I. The latter conclusion is based on the results of our previous Table 3 The slopes of the dependencies of ln(In/Ib) upon T−1 for the E-type bands of some CH3-X and CD3-X compounds DH (Eq. (5)) (kcal mol−1)

Ref.

n5 n6 n5 n6

0.359 0.09 0.869 0.24 0.499 0.08 0.649 0.10

This This This This

Neat Neat

n5 n6

0.769 0.12 0.829 0.07

[24] [24]

CD3CN

Neat Neat

n6 n7

1.189 0.16 1.029 0.31

This work This work

CH3CN

Neat Neat

n6 n7

1.199 0.15 1.339 0.11

[25] [25]

Compound

Solvent

CD3I

Neat Neat CSa2 CSa2

CH3I

a

Band

Concentration 0.9 mol l−1.

uork work uork uork

studies of the C–H-stretching region of CH3I [24,45]. It has been found that the (In/Ib) ratio strongly depends on the solvent’s basicity: the stronger the basicity of the solvent, the higher the ratio. Hence, it was proposed, that methyl groups of CH3I form hydrogen bonds with proton acceptor groups of the solvents [24,45]. It is well-known that the absolute integrated intensities of A–Hstretching bands in the A-H…B complexes strongly depend on the temperature [46,47]. Such dependencies were explained to be the result of strengthening of the H-bonds when the temperature is decreased [47]. Since strengthening of the H-bonds causes the enhancement of the (In/Ib) ratio for n4, it is obvious that the (an/ab) ratio in Eq. (5) should depend both on solvent and the temperature. Apparently, the contribution of the temperature variation of (an/ab) to the slope of the function ln(In/Ib)= f(T − 1) is predominant.

3.3. Widths of the narrower components. Orientational diffusion and 6ibrational relaxation Infrared band widths can be used for evaluating the spinning and tumbling diffusion constants of the molecules. The methods of determining the diffusion constants are based on the assumption of statistical independence of the vibrational and orientational relaxation processes [19,20]. This results in the additivity of the vibrational (dvib) and orientational (dor) contributions to the band width: d= dvib + dor

(7)

It follows from the above description that only the narrower components of the E-type bands can be used for the determination of D . Moreover, the C–H (C–D)-stretching range is hardly usable for this purpose, since the band shape mechanism is not understood well for this range. Nevertheless, for generality we consider both stretching and deformational E-type band widths below. It should be kept in mind that the narrower components do not represent the whole ensemble, but a certain part of it only. The lower the temperature, the larger the fraction of molecules contributing to the narrower component.

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Fig. 8. Spinning diffusion coefficients of liquid CD3CN measured by different methods: 1, NMR [14]; 2, NMR [56]; 3, NMR [53]; 4, NMR [52]; 5, NMR [17]; 6, Raman [17] and 7, Raman and IR [23].

Several works were devoted to the investigation of orientational dynamics of CD3I [16,48 – 52] and CD3CN [14,17,23,53 – 60]. Tumbling diffusion constants (DÞ) of the molecules were determined by NMR [14,17,48,53,54,57], IR [23], and Raman [17,23,49–51,60] methods, and these data are in good agreement with each other. However, the diffusion constants for spinning motion (D ) are determined with less accuracy [14,16,17,23, 48,50,51,53–55,57]. Fig. 8 illustrates the scatter of the D magnitudes obtained for CD3CN in different laboratories. No agreement is seen between the activation energies either. Different NMR, Raman and IR approaches use different assumptions, and this could be the main reason for such discrepancy. To determine the diffusion constants from the vibrational spectroscopic data it is necessary to separate the contributions of vibrational and orientational relaxation (Eq. (7)). The following approaches are used: (a) The use of both isotropic and anisotropic components of the Raman spectra [19,20]. Unfortunately, this method is not applicable to totally depolarized E-type bands of CD3I and CD3CN. (b) Extrapolation of the dependence d = f(T) to absolute zero (Rakov’s method [61,62]). Here d is

599

the total band width. It is believed that d(0)= dvib and this value is independent of the temperature. Though dvib is assumed in this method to be independent of the temperature, it is well known, that this is not so. To estimate possible errors resulting from such an assumption we made a statistical analysis of more than a hundred dependencies of dvib on T, obtained by Raman spectra for different bands of various organic compounds [16,17,50,52,58, 60,63–92]. Some of the dvib values were recalculated from the vibrational relaxation times (tv) The analysis of the ((dvib/dT) values shows that 95% of them fall within the (− 2.0 · 10 − 2 B ((dvib/ (T)B 2.4 · 10 − 2 cm − 1 K − 1) interval. It is also important to note that the dvib magnitudes usually do not exceed 10 cm − 1. The 95% of them fall into the (1.2B dvib B 9.5 cm − 1) region. The comparison between the dvib, dn values and their temperature derivatives will be made below. (c) To determine the dvib it has been proposed to extrapolate the dependence of d upon (T · h − 1) to T · h − 1 = 0 [93]. Here, h is the viscosity coefficient of the medium. This method is based on the Debye–Stokes–Einstein theory of orientational diffusion [94]. As in the above method, independence of dvib of temperature is assumed. It has been shown in [62] that the Debye– Stokes–Einstein theory is not applicable to rotational diffusion of methyl groups: the change of the viscosity coefficient from 10 − 1 to 1015 cP does not affect the spinning diffusion constant noticeably. Hence, this approach is not applicable here. (d) Attempts are made to calculate the dvib values on the basis of the existing theories of vibrational dephasing [95–97]. Unfortunately, all the theories contain several unknown parameters. Consequently, only the order of magnitude of dvib can be predicted reliably. Nevertheless, a semiempirical approach based on the Fischer–Laubereau IBC model [95] is wide spread. It has been proposed [16,17,23] to determine the dvib values for the E-type bands from the vibrational widths of nearest A1-type bands: dvib,E = dvib,A1 × (nA1/nE)2

(8)

Here nA1 and nE are the frequencies of the A1- and E-type bands under investigation. However, it

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Table 4 The orientational diffusion coefficients and IR-spectroscopic characteristics of CD3I and CD3CN Compound

Band

T (K)

dn (cm− 1)

D aÞ (1010 s−1) D b (1010 s−1)

D c (1010 s−1)

d dor (cm−1) d dvib (cm−1)

CD3I

n4

212 295 317 212 295 317 212 295 317

23.6 38.7 43.1 19.7 26.6 28.5 13.8 18.4 19.7

2.4 10.3 12.5 2.4 10.3 12.5 2.4 10.3 12.5

82 157 179 82 157 179 82 157 179

139 9 47 250 9 47 282 9 47 101 930 144 930 156 930 95 947 137 9 47 149 947

7.4 14.8 17.0 11.7 23.0 26.3 7.4 14.8 17.0

16.2 9 3.8 1.5 23.9 9 3.8 1.9 26.1+3.8 8.0 93.2 3.6 93.2 2.1 93.2 6.4 92.4 3.6 92.4 2.7 92.4

234 295 346 234 295 346

16.9 21.1 24.5 10.2 13.4 16.1

5.1 12.6 18.4 5.1 12.6 18.4

100 130 155 100 130 155

78 928 101 928 123 928 79 9 72 120 972 164 972

15.1 20.3 24.6 6.2 8.8 10.8

1.8 93.7 0.8 93.7 −0.193.7 4.0 92.1 4.6 9 2.1 5.3 92.1

n5 n6

CD3CN

n6 n7

d evib (cm−1)

8.4

6.3

a

Raman data obtained for CD3I in Ref. [16] and average over the Raman and NMR data obtained for CD3CN in Ref. [17]. b NMR data obtained for CD3I in Ref. [48] and NMR data for CD3CN, averaged over Refs. [14,17,53,54,57]. c The values calculated from Eqs. (7) and (9), assuming dvib = 5.49 4.1 cm−1. d The values calculated from Eqs. (7) and (9), assuming D equal to those determined by NMR. e Literature data (Ref. [16] for CD3I and Ref. [23] for CD3CN).

should be noted that the IBC model was developed for diatomic molecules and hence there is no solid basis for Eq. (8), where the bands are of different symmetry types. Moreover, the resulting dvib,E value depends on the choice of the neighbouring A1-type band. To illustrate this we calculated the vibrational widths of n6 (665 cm − 1, CD3I) using the Raman data for two different neighbouring A1-type bands: n2 =937 and n3 = 493 cm − 1 (Refs. [16,50,52]). The obtained dvib magnitudes are 1.7 and 7.3 cm − 1, respectively. A large discrepancy between these two values shows the low prediction ability of Eq. (8). Thus, no universal approach to determine the dvib magnitudes exists so far. The dvib values for the E-type bands of CD3I and CD3CN were obtained previously as follows. The IBC model in the form of Eq. (8) was applied in Refs. [16,17] to determine the dvibs of n4 (CD3I) and n5 (CD3CN). Isotropic band widths of the nearest A1-type modes (n1 for both CD3I and CD3CN) were used in calculations [16,17]. In Ref. [23] the dvib values of the E-type bands of CD3CN (n5 – n8) were determined from those of CH3CN by using the rela-

tionship similar to Eq. (8). The dvibs for the bands of CH3CN, in their turn, were determined by the Rakov’s method. In one of the studies (Ref. [51]) the contributions of the vibrational relaxation to the n4 band width of CD3I was neglected. In the cited work the Raman contour of n4 was fitted by two Lorentzian functions. The widths of these two components were used for evaluating the orientational diffusion coefficients. It should be noted, that the D values obtained in Ref. [51] were found to decrease with the temperature. These results seem, at least, very strange. Probably, they can be explained in view of the above mentioned complex mechanisms of the CH3- and CD3-band shape formation. To account for the vibrational relaxation it seems reasonable to use the above mentioned results of the statistical treatment. It seems reasonable to assume that the statistical data obtained for various vibrational bands can be extended to the E-type bands of CD3I and CD3CN. Thus the dvib values for all the bands under study are supposed to fall in the 1.2–9.5 cm − 1 region. The justification of this assumption

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Fig. 10. The dependencies of dn on T for neat CD3CN: triangles n6, squares n7.

Fig. 9. The dependencies of dn on T for (a) neat CD3I and (b) its solution in CS2 (0.9 mol l − 1): circles n4, triangles n6, squares n7.

will be done below, when comparing the data obtained by IR and NMR methods. The relationship between the orientational part of the band width (dor) and the diffusion constants (D , DÞ) is given by the equation proposed by Tanabe [23]: dor = (pc) − 1(DÞ +(1 −z) · D )

(9)

Eq. (9) was derived empirically and is not supported by any theory. This relationship differs from that derived in the Valiev’s theory of rotational diffusion [98] only in the respect that the D value is multiplied by (1 −z). Such modification follows from the necessity of accounting for the

Coriolis coupling and does not seem meaningless (compare with Eq. (3) which describes the E-type evelope’s widths in the vapour phase). To calculate the spinning diffusion constant from Eqs. (7) and (9) we took the Raman and NMR data on DÞ values, which were obtained in Refs. [16,17] with high accuracy. Table 4 shows the spinning diffusion coefficients obtained via different bands of CD3I and CD3CN. Relatively large errors (9 28– 9 72 · 1010 s − 1) are mainly due to the uncertainty in the vibrational part of the band widths (dvib = 5.49 4.1 cm − 1). It is seen that there is a good agreement between the data obtained via two different deformational bands of CD3I. The same should be said about the D values calculated for CD3CN. Such compatibility confirms the validity of Eq. (9). The orientational diffusion coefficients calculated from the band width of n4 of CD3I appeared to be too high in comparison with the other data. Such discrepancy is probably due to the complex band shape mechanism of the CD3-stretching band formation. Thus, it appears that the infrared C–H (C–D)-stretching range is hardly usable for evaluating the diffusion constants. Table 4 also shows the values of D obtained for CD3I and CD3CN by NMR method. Since the

602

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spinning diffusion of CD3CN has been studied several times (Figs. 8 – 10) we took the average D magnitudes obtained by NMR only [14,17,53,54,57]. The accuracy of the averaged D values is believed to be 920 · 1010 s − 1. We know only one work where the spinning diffusion constant of CD3I was determined from the NMR data (Ref. [48], Table 4). Unfortunately the exact errors of obtaining the spinning diffusion constants by NMR are not known [57]. Thus, we assume the above error limit ( 920 · 1010 s − 1) to be valid for CD3I also. It is seen that there is a good agreement between the D values calculated by Eqs. (7) and (9) and those obtained by NMR. This is the second argument in favour of the validity of Eq. (9). Though the estimated dvib values make it possible to calculate the spinning diffusion coefficients, the inverse problem seems to be nore interesting: the orientational diffusion constants of CD3I and CD3CN determined from the NMR data [14,17,48,53–55,57] can be used for the evaluation of dvibs. The uncertainty in the D values is the main factor responsible for the error determining the dvib. This uncertainty gives an error in the calculated dor magnitudes of approximately 92.0 cm − 1. The calculated dvibs are given in Table 4. It is seen that all of them (except those for n4 of CD3I) fall within the (1.2 B dvib B9.5 cm − 1) limits. This fact shows that the vibrational parts of the E-type band widths indeed are not exempt from the above mentioned statistics. If so, then the indicated upper and lower limits of dvib can be extended to E-type bands of other CH3-X (CD3-X) molecules when calculating their spinning diffusion constants. The last column of Table 4 shows the dvib values obtained previously by using the Fischer – Laubereau model [16,23]. The agreement is seen only for n6 of CD3CN. However, taking into account the limitations of the IBC model, such agreement can be considered as fortuitous only.

Acknowledgements This work was supported by the Russian Fund of Basic Research (programme No 96-03-32171a).

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