Isotope effects in the vibrational spectrum of perfluoroethane

Accepted Manuscript Isotope effects in the vibrational spectrum of perfluoroethane O.S. Golubkova, T.D. Kolomiitsova, D.N. Shchepkin, K.G. Tokhadze PII: DOI: Reference:

S0022-2860(13)00776-X http://dx.doi.org/10.1016/j.molstruc.2013.09.012 MOLSTR 20009

To appear in:

Journal of Molecular Structure

Received Date: Revised Date: Accepted Date:

24 May 2013 9 September 2013 9 September 2013

Please cite this article as: O.S. Golubkova, T.D. Kolomiitsova, D.N. Shchepkin, K.G. Tokhadze, Isotope effects in the vibrational spectrum of perfluoroethane, Journal of Molecular Structure (2013), doi: http://dx.doi.org/10.1016/ j.molstruc.2013.09.012

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Isotope effects in the vibrational spectrum of perfluoroethane O. S. Golubkova, T. D. Kolomiitsova, D. N. Shchepkin, and K. G. Tokhadze,

Physical Faculty, St. Petersburg State University, Peterhof, St. Petersburg, 198504 Russian Federation

2

Abstract IR spectrum of solution of perfluoroethane with the natural isotope composition in liquid N2 at T = 77 K is recorded. Relative intensities for the *ν1, *ν5, and *ν10 bands of the asymmetric isotopologue

13

C12CF6 have been determined. The ν5(A2u) and ν10(Eu)

bands of the C2F6 molecule were found to behave quite differently upon isotopic substitution. The ν10 band splits into two bands close in intensity, one of which falls within the spectral region of the main isotopologue. This fact explains the low (less than 1%) intensity of the *ν10 band. At the same time the isotopic substitution does not change intensity of the ν5 band, and the *ν5 band intensity corresponds to the natural isotope abundance (2%). This interpretation has been confirmed by a calculation performed for the C2F6 and 13C12CF6 molecules using the GF matrix formalism. Keywords: FTIR spectra; Gas phase; Cryosolutions; Frequencies and intensities of vibrational bands; Vibrational mode interactions; Isotope effects in the band intensities

Physical Faculty, St. Petersburg State University, 198504, Peterhof, St. Petersburg, Russian Federation. E-mail: [email protected]

3

I. Introduction In recent years the perfluoroethane molecule has been the object of many studies. First of all, the researchers are interested in optical properties of this inert, incombustible compound with a low (−78° C) boiling temperature. It is known that the C2F6 molecule can produce a stronger greenhouse effect than the CO2 molecule because the strong fundamental absorption bands of this molecule can gives rise to screening of the thermal radiation of the Earth, and the content of C2F6 in the atmosphere increased up to ~3 ppm in the past decades [1−4]. There are several papers devoted to the study of rotational structure of vibrational bands in the high-resolution IR spectra of the the spectrum of the

13

12

C2F6 molecule [5−7], information about

C12CF6 isotopologue is unavailable in the literature. At the same

time, in order to correctly interpret the vibration−rotation spectrum of perfluoroethane in the atmosphere, it is necessary to take into account the noticeable presence of the asymmetric isotopologue. The natural abundance of isotopologues is as follows: 0.9787 (12C2F6), 0.0212 (13C12CF6), and 0.00011 (13C2F6). It seems likely that, using modern measuring methods, the relative intensities of the bands of

13

C12CF6 can be easily

determined in view of the 2% natural abundance of this isotopologue; however, the interpretation of the rotational structure of 13C12CF6 is difficult even in the high-resolution spectra because the rotational constants of C2F6 are small (A0 = 0.0946542 cm−1 and B0 = 0.0615759 cm−1 [5]). First of all, exact information on the vibrational spectra of the 12C2F6 and 13C12CF6 molecules is required to solve this problem. Consequently, it is advisable to study the spectra of perfluoroethane in cryogenic solutions where each vibrational transition is associated with a relatively narrow band whose integral intensity is determined by the vibrational transition moment [8−10]. The vibrational spectrum of the C2F6 molecule was most completely interpreted in [11] where the frequencies and intensities were determined for 28 fundamental and combination bands in the gas phase spectrum at room temperature and in the spectrum of

4

solution in liquid Xe at T = 163 K. This interpretation is consistent, in the main, with the results of [12]. The vibrational transition moments were determined in [11] with allowance for the observed Fermi resonances. The measured values of frequencies and intensities are in agreement with the results calculated using the force field [13]. The authors of [11] were able to observe the bands *ν 5 , *ν 10 , and *(ν 2 +ν 10 ) belonging to the asymmetric isotopologue 13C12CF6. Here and below, the asterisk * denotes the frequencies of 13C12CF6. The disadvantage of the study of spectra in liquid Xe is the relatively large (5−16 cm−1) half-width of vibrational bands, which hinders their separation and increases the error of intensity determination. In this paper the absorption spectrum of a sample of C2F6 with the natural isotope composition was studied in solution of liquid N2 at 77 K, and the frequencies and relative intensities of bands in the spectra of the 12C2F6 and 13C12CF6 molecules were determined. The experience gained in the studies of spectra of a number of freons [8, 9, 14] dissolved in liquid nitrogen, argon, and oxygen allows us to assume that the half-widths of the bands will not exceed 1−1.5 cm−1. The essential narrowing of the bands will increase the accuracy of separation of the bands belonging to different isotopologues. In addition, in this work the integral absorption coefficients of the ν5, ν10, and *ν10 of perfluoroethane with the natural isotope composition were measured in the gas phase at room temperature, and a simple model was proposed that explained the anomalous low intensity of the *ν10 band. In interpreting the bands, we used the numbering of normal modes of the

12

C2F6

molecule of the D3d symmetry presented in Table 1. Note that other variants of numbering are also used in the literature [15].

2. Experimental The absorption spectra of C2F6 with a natural isotope abundance were recorded at room temperature in the gas phase with a Bruker IFS-28 Fourier spectrometer at a resolution of 1 cm−1 and in solution in liquid N2 at a temperature of 77 K with a Nicolet

5

6700 Fourier spectrometer at a resolution of 0.2 cm−1. We used gas cells and optical cryostats with BaF2 windows. The design of a cryostat with a vertical optic axis is described in [10 p.13], the thickness of a layer of liquid N2 above the window was varied in the interval [0.3−3] cm, the concentration of C2F6 in solution was c = (10−8−10−5) mol/cm3. The optical path length  was controlled using the induced absorption of nitrogen at ν = 2344 cm−1. The integral absorption coefficient of this band AN2 = 0.0258 km/mol was measured in a optical cryostat with BaF2 windows and the 4-cm thickness of a layer. In [5−7] the vibrational−rotational absorption spectrum of C2F6 was studied with the use of a sophisticated experimental technique including molecular beams at low temperatures and the laser spectroscopy at a resolution better than 0.001 cm−1. Unfortunately, the spectral region measured in such experiments is limited, and, therefore, information on the

13

C12CF6 spectrum was, in fact, not gained. In the present study the

integral absorption coefficients of the ν5 and ν10 strong fundamental bands of the C2F6 molecule in the gas phase were measured in a single-component system. The perfluoroethane pressure was varied in the interval P = 2−10 atm. At such pressures the rotational structure of bands is merged due to the self-broadening, and the integral intensities of bands can be measured with good accuracy. The procedure of such measurements was discussed in [16]. We used cells with optical path lengths  1 = 0.42 cm and  2 = 12 μm. In the second case, the cell thickness was measured using the interference fringes of equal inclination. The integration limit was (1285−1180) cm−1 for the ν10 band and (1160−1095) cm−1 for the ν5 band. For each of the bands the absorption coefficients measured at seven different pressures were averaged.

3. Results Figure 1 presents the absorption bands in the region of the ν5 (A, B) and ν10 (C, D) vibrations of the 12C2F6 and 13C12CF6 molecules in nitrogen solution in comparison with

6

the same bands in the gas phase spectrum at room temperature. Rotation of such molecules as C2F6 with rotational constants smaller than 0.1 cm−1 is totally hindered in solution in nitrogen at 77 K. Accordingly, narrow symmetric bands with a Lorentzian profile within 5−10 half-widths are recorded in the spectrum whose intensity is not perturbed by vibration−rotation interactions and is determined by the vibrational transition moments [10]. Since the bands in the cryogenic spectrum are symmetric, the isotope shifts and the relative intensities of the bands can be determined with high accuracy. The advantages of using a low-temperature solution show up in determining the *ν5 band intensity (see Fig. 1 (A, B)). In the gas phase spectrum the band of the

13

C12CF6

molecule (the transition frequency is shown by an arrow) falls within the region of a P branch of the ν5 vibrational−rotational band of the

12

C2F6 molecule. In solution in N2,

where the full width at half maximum (FWHM) of the ν5 band of both isotopologues equal 1.3 cm−1, it is easy to separate the bands and determine their relative intensities in a natural sample (see Table 2). Note that, for the ν5 band, the ratio of integral intensities B(*ν5)/B(ν5) = 0.022(1) coincides with the percentage of the

13

C12CF6 molecules in

natural samples. The FWHMs of the ν10 band in liquid nitrogen are also small (1.7 cm−1), the *ν10 and ν10 bands are easily separated, and the ratio of intensities B(*ν10)/B(ν10) = 0.008(1), i.e., it is anomalously small as compared to the analogous ratio for the ν5 vibration. Note that, due to the decrease in the band widths, the study of spectra in solutions in liquid nitrogen (T = 77 K) is preferred over the study of spectra in solutions in liquid xenon (T = 167 K) [11]. The spectral characteristics (frequencies, widths, and relative intensities) of bands of a perfluoroethane sample with the natural abundance of 13C12CF6 dissolved in liquid N2 are presented in Table 2. Assignment of the second-order bands of the C2F6 molecule coincides with that reported in [11], their relative intensities in the spectra in solutions in Xe and N2 coincide within the experimental error limits.

7

Intensities of the weak *ν10, *ν5, and *(ν2 + ν10) bands of the asymmetric isotopologue 13

C12CF6 and of the (ν2 + ν10) and (ν8 + ν11) bands of the 12C2F6 molecule in the spectrum

of a natural sample of perfluoroethane are determined with a large error. This error can be decreased by increasing the concentration of a sample in nitrogen solution (see Fig. 2 (a) and (b)) when the ν10 and ν5 absorption bands are completely saturated. The *ν1 and *ν7 bands in the spectrum of the asymmetric isotopologue become active in the electric dipole absorption. It is possible to measure the *ν1 band intensity, and, in accordance with the calculations discussed below, it appears to be extremely low. Unfortunately, the *ν7 band is not observed because it falls into the absorption region of the stronger ν10 vibration. Under the same conditions, it is possible to measure intensity of the (ν2 + ν10) sum band at a frequency of 2047.8 cm−1. The corresponding integral absorption coefficient A = 3.2(4) km/mol coincides within the experimental error with a value A = 2.6(3) km/mol obtained for liquid and gaseous

12

C2F6 in [8, 11]. For the asymmetric isotopologue, only an

estimate (~0.01(1) km/mol) can be obtained for intensity of the *(ν2 + ν10) band at 2003.0 cm−1. Table 3 presents the frequencies and integral absorption coefficients A(νk) for the ν10, *ν10, and ν5 bands of the perfluoroethane isotopologues measured in the gas at room temperature, as well as the integral absorption coefficients A(νk) for the ν10, *ν10, ν5, *ν5, and *ν1 bands measured in the spectrum of solution in liquid nitrogen. The integral absorption coefficients of a k-th band listed in Table 3 are defined as A(ν k ) = Bk / (  ⋅ c ) , where Bk is the integral intensity of an absorption band,  is the optical path length, c is the total concentration of a C2F6 sample with the natural composition of isotopes. The values of integral absorption coefficients for the fundamental ν10 and ν5 bands measured in this work in the gas phase spectrum at room temperature are in agreement with the data [2, 3]. According to the data of [2], the integral absorption coefficient of the ν10 band does not depend on temperature in the interval (203−293) K, and all the values measured at room temperature can be averaged. In [2] the combination bands (ν6 + ν8) and (ν2 + ν11) and

8 the *ν10 band of the isotopically substituted molecule fall into the integration limit (1170−1400) cm−1 used to determine the integral intensity A(ν10). According to data of Table 2, the relative intensity of the sum of these bands amounts to about 3%. A value of A(ν10) = 1010 (20) km/mol was obtained by averaging the corrected value of [2], the intensity [3], and the intensity measured in this work.The value of A(*ν10) = 8.7(8) km/mol in the gas phase measured in this work

was obtained with an optical path 0.42 cm and the perfluoroethane pressure 2 atm. Table 3 presents the absorption coefficients of bands in nitrogen solution averaged over variations of the thicknesses and concentrations. The integral absorption coefficient of the ν5 band in solution appeared to be smaller than the integral absorption coefficient in the gas phase because of the difference in temperature and the temperature dependence of intensity observed in [2]. It follows from the data of [2] that A(ν5) ≈ 240 km/mol at T = 0 K, which coincides with the value of Table 3. One of important experimental results of this paper is the determination of an absorption coefficient of the *ν5 band, A(*ν5) = 5.6 km/mol, and the ratio B(*ν5)/B(ν5) = 0.022(1), which corresponds, to within the experimental error, to the natural abundance of isotopes. In the spectral range of 1210−1190 cm−1, where the CF stretching vibrations of the E symmetry absorb, only the *ν10 band at 1200.3 cm−1 with a relative intensity lower than one per cent, B(*ν10)/B(ν10) = 0.008(1), can be assigned to the asymmetric isotopologue. To confirm the proposed interpretation, we also show in Table 3 the calculated values of frequencies and integral absorption coefficients Ao (ν k ) = Bk /( ⋅ ci ) , where ci is the 12

corresponding concentration of each of the isotopologues comparison

with

the

experimental

data,

the

integral

C2F6 and

13

absorption

C12CF6. For coefficients

A(ν k ) = Bk /( ⋅ c) calculated for the natural abundances of isotopologues are listed in the table. The calculation of the vibrational spectrum⎯the frequencies and intensities⎯for 12

C2F6 and

13

C12CF6 was carried out in [11], where for the

13

C12CF6 molecule the direct

problem was for the first time solved in the harmonic approximation with the use of the

9

force field [13] which describes the frequencies of a number of perfluoroparaffins. This force field was chosen because it provides the best description of frequencies of the C2F6 molecule with the root-mean-square deviation δ ≈ 1 cm−1. The advantage of a calculation using the data of [13] over ab initio calculations, e.g., [15], is that the parameters of the adopted force field can be used to calculate the asymmetric isotopologue of the molecule. In calculating the intensities in this work, the derivatives of the dipole moment were refined by using the latest experimental data on the integral absorption coefficients; the signs of first derivatives were taken from [13]. One can see in Table 3 that the intensities calculated for the

12

C12CF6 and

13

C12CF6 molecules satisfactorily describe the set of

experimental results. The *ν1 band intensity is rather low, which agrees with the experimental result. Comparison of the calculated spectrum of the 13C12CF6 molecule with the experimental spectrum recorded in nitrogen solution is shown in Fig. 3. In the calculation each band is described by a Lorentzian profile with the parameters of bands of the main isotopologue in the spectrum in nitrogen solution (see Table 2). The FWHM of 1.4 cm−1 characteristic of totally symmetric bands was taken for the *ν1 band, and a value of 1.7 cm−1 was taken for the *ν7 band. In Fig. 3 the integral intensity of each of the calculated bands was determined by the concentration of C2F6 in solution, the isotope composition of a sample, the thickness of a layer, and the corresponding absorption coefficient of 13C12CF6. The calculated spectrum was made coincident in frequency with the observed band of an isotopologue because each band is shifted on passage from the gas phase to solution. On the basis of the calculation (Table 3), the *ν7 band was shifted by δν relative to the *ν10 band. One can see in Fig. 3 that the calculated *ν7 band falls within the ν10 band shape of the main isotopologue, and its intensity is comparable to that of the *ν10 band. The calculated *ν1 band qualitatively describes the weak absorption experimentally recorded in the region of 1392−1400 cm−1.

4. Discussion

10

Consider first the unusual experimental effect observed in the vibrational spectrum of perfluoroethane⎯the anomalously low intensity of the *ν10 band of doubly degenerate stretching vibration of the asymmetric isotopologue. This effect can be explained within the framework of the scheme taking into account different behavior of the stretching vibrations of symmetries A and E in the C2F6 molecule on isotopic substitution. The main isotopologue of the C2F6 molecule (with the D3d symmetry) has two equivalent CF3 groups with the local C3v symmetry. Each group has a symmetric (A) and doubly degenerate (E) stretching vibrations, which have, in the zero approximation, the same frequencies ν ~ 1240 cm−1. When two CF3 groups are combined to give the C2F6 molecule, vibrations of the two groups begin to interact. The vibrations of the symmetry type A of the two CF3 groups interact via the C−C valence bond, and the coefficients of total interaction (D = GF) are governed by the force constants of the C−F and C−C bonds, which are relatively large and close in magnitude (FC−F = 9.79⋅106 cm−2 and FC−C = 7.67⋅106 cm−2 [13]). Accordingly, the splitting between the symmetric and antisymmetric under inversion vibrations should be large (ΔEA ~ 300 cm−1) and the frequencies are ν1(A1g) = 1417 cm−1 and ν5(A2u) = 1121 cm−1 (see Table 3). The vibrations of the symmetry type E of the two CF3 groups can only interact via the low-frequency bending vibrations because these vibrations correspond to motions perpendicular to the symmetry axis. The corresponding force constants are small (FF−C−C = 1.55⋅106 cm−2), and the splitting is insignificant in this case: ΔEE is smaller than 5 cm−1 and the frequencies are ν10(Eu) = 1250 cm−1 and ν7(Eg) = 1252 cm−1 (see Table 3). For the symmetric isotopologue, the energy levels and frequencies coincide in the zero approximation, and irrespective of the magnitude of interaction symmetric (g) and antisymmetric (u) vibrations take place. The absorption coefficients are strictly zero for the symmetric (ν 1 (A1g) and ν 7 (Eg)) bands. Of the stretching vibrations, only the ν5(A2u) and ν10(Eu) vibrations are active in the electric dipole absorption. On the

12

C/13C substitution in one of the groups, the groups are no longer identical.

This substitution gives rise to a decrease in the vibrational own frequencies of the 13CF3

11

group by ΔνA ~ 20 cm−1 for symmetric (A) vibrations and by ΔνE ~ 40 cm−1 for degenerate (E) vibrations. In the case of the A vibrations, the isotopic substitution virtually does not change the mixing coefficients of vibrations of different CF3 groups (the change in the own frequencies is much smaller than the harmonic splitting, ΔνA ~ 20 cm−1 << ΔEA ~ 300 cm−1), and the vibrations remain approximately symmetric (g) and antisymmetric (u). As a result, the ν5 band retains its intensity, and a weak absorption, which is practically two orders of magnitude weaker than the ν5 band, appears near the ν1 band (see Table 3). For the E vibrations, the isotopic change of frequencies of the two groups is larger than the characteristic magnitude of interaction between the groups, ΔνE ~ 40 cm−1 >> ΔEE ~ 5 cm−1. For this reason, the E vibrations of two groups (13CF3 and

12

CF3) are practically

independent. Upon lowering the symmetry, the total intensity of the ν10(Eu) band of the symmetric isotopologue is about evenly divided between the two bands, А(*ν10) ≈ А(*ν7) (Fig. 3 and Table 3), and the *ν7 band associated with the 12CF3 group is naturally under the contour of the ν10 band of the main isotopologue.

5. Conclusions The set of experimental data on the frequencies and intensities of the C2F6 absorption bands in solution in liquid N2 and in the gas phase allows us to ascribe the band at 1200.3 cm−1 (in nitrogen) to the *ν10 vibration in the asymmetric isotopologue 13C12CF6. For this reason, we conclude that the assignment of a band at 1206 cm−1 in the gas phase [12] to the difference (ν1 − ν12) transition and a band at 1199.7 cm−1 in solution in liquid Ar [8] to the third-order sum transition (ν8 + ν9 + ν12) is erroneous. On the symmetry violation with respect to the center of inversion resulting from the isotopic substitution in the equivalent groups of molecules, anomalies are possible in the band intensities of isotopologues. In the case of the C2F6 molecule (D3d), the totally symmetric (A) stretching vibrations retain an approximate symmetry upon isotopic substitution, while the E vibrations show the symmetry lowering to C3v.

12

It should be noted that the effect of an “anomalous change” of intensity upon isotopic substitution in the C2F6 molecule is not unique. A similar picture should be observed for molecules with the center of inversion in the presence of close in frequency symmetric and antisymmetric vibrations, for example, in the case of the C2F4 molecule (D2h). In the absorption spectrum of a natural sample one of the splitting components will be masked by absorption of the main isotopologue, and a band with an intensity of about 50% of that estimated from the natural abundance of the

13

C isotope will be observed within the

isotope shift. Acknowledgements. This study was supported by the Russian Foundation for Basic Research, Grant 09-03-0023. The authors thank RC «Geomodel» of St. Petersburg State University for the facilities in spectra recording.

References [1] J. Harnisch, R. Borchers, Geophys. Res. Lett. 23 (1996) 1099. [2] J. Ballard, R.J. Knight, D.A. Newnham, J.Q.S.R.T. 66 (2000) 1992. [3] Q. Zou, C. Sun, V. Nemtchinov, P. Varanasi, J.Q.S.R.T. 83 (2004) 215. [4] J. Muhle, A.L. Ganesan, B.R. Miller, C.M. Harth, B.R. Greally, M. Righy, L.W. Porter, L.P. Steele, C.M. Trudinger, P.B. Krummel, S.O’Doherty, P.J. Fraser, P.G. Simmonds, R.G.Prinn, and R.F. Weiss, Atmos. Chem. Phys. 10 (2010) 5145. [5] G.M. Hansford and P.B. Davies, J.Mol.Spectr. 180 (1996) 345. [6] M. Lorono, W. Henze, and P.B. Davies, J. Phys. Chem. A104 (2000) 6395. [7] K.M. Ward, G. Duxbury, M. Lorono, W. Henze, P.B. Davies, and D.A. Newnham, J. Mol. Spectr. 204 (2000) 268. [8] L.A. Zhigula, T.D. Kolomiitsova, S.M. Melikova, D.N. Shchepkin, J. Appl. Spectr. 64 (1997) 310. [9] L.A. Zhigula, V.A. Kondaurov, I.S. Fedorov, D.N. Shchepkin, Opt. Spectr. 103 (2007) 603.

13

[10] R.J.H. Clark, R.E. Hester (Eds.), Molecular Cryospectroscopy, Advances in Spectroscopy, vol.23, Wiley, Chichester, 1995. [11] O.S.Golubkova, V.N. Bocharov., A.P. Burtsev, D.N. Shchepkin, Opt. Spectr. 111 (2011) 357. [12] J. Rud Nielsen, C.M. Richards, H.L. McMurry, J. Chem. Phys. 16 (1948) 67. [13] L.N. Pirozhnaya, O.B. Zubkova, L.A. Gribov, J. Appl. Spectr. 43 (1985) 440. [14] T.D. Kolomiitsova, V.A. Kondaurov, D.N. Shchepkin, Opt. Spectr. 91 (2001) 203. [15] G.R. De Mare and Yu.N. Panchenko, J. Struct. Chem. 47 (2006) 232. [16] A.P. Burtsev, V.N. Bocharov, S.K. Ignatov, T.D. Kolomiitsova, P.G. Sennikov, K.G. Tokhadze, L.A. Chuprov, D.N. Shchepkin, and O. Schrems, Opt. Spectr. 98 (2005) 227.

14

Figure captions Fig.1. The ν5 (A, B) and ν10 (C, D) absorption bands of the isotopologues of C2F6 in the gas phase (1) at room temperature and in the solution in liquid N2 at 77 K (2). (A) and (B): (1) – с = 4.46 10-4 mol/cm3,  = 12 μm, (2) – с = 5 10-6 mol/cm3,  = 2.5 cm; (С): (1) – с = 1.8 10-4 mol/cm3,  =12 μm, (2) – с = 5 10-6 mol/cm3,  = 2.5 cm; (D): (1) – с = 8.9 10-4 mol/cm3,  = 0.42 cm, (2) – с = 5 10-6 mol/cm3,  = 2.5 cm. The arrows indicate the ν5 and ν10 bands of 13C12C12F6 in the gas phase and in solution. Fig.2 Absorption spectra of C2F6 in liquid N2 at 77 K: (a) – с = 2.5 10-7mol/cm3,  = 2.7 cm, (b) – с = 0.9 10-8 mol/cm3,  = 2.5 cm; (1) - *ν5, (2) - ν5, (3) – ν8 + ν11, (4) * ν10, (5) – ν10; The arrows indicate the positions of the vibrational bands of the C3F8 impurity molecule, ν3 of 13CF4, and 2ν4 of CF4. Fig.3 Absorption spectrum of

13

C12CF6. (1) in liquid N2 at 77 K, A - *ν5, B - *ν10,

с = 2.5 10-7 mol/cm3,  = 2.7 cm; С - *ν1, с = 2.5 10-5 mol/cm3,  = 2.5 cm; (2) the calculated spectrum in the regions of the ν1, ν5, ν7, ν10 and bands of the C13C12F6 molecule.

15

16

17

18

Table 1. Frequencies νi (cm−1) of normal vibrations of the С2F6 molecule. The symmetry types of vibrations are shown in parentheses [6] ν1

ν2

ν3

ν4

ν5

(A1g) (A1g) (A1g) (A1u) (A2u) 1417

807.4 348

65.3

ν6

ν7

(A2u) (Eg)

1116.9 714

ν8

ν9

ν10

(Eg) (Eg) (Eu)

1237 620

380

ν11

ν12

(Eu)

(Eu)

1250.5 522.5 216

19

Table 2. Experimental frequencies νi (cm−1), FWHM (cm−1), and relative integral intensities (Bi /B(ν10)) of some fundamental and combination absorption bands of 12

C12CF6 and 13C12CF6 (*) with the natural abundance of isotopes in liquid nitrogen,

T = 77 K

Assignment

νi,, cm−1

FWHM, cm−1

(Bi /B(ν10)) x 1000

ν10 ( Eu)

1244.8

1.7

1000

ν5 ( A2u)

1111.8

1.3

242(12)

*ν10 ( E)

1200.3

1.8

8.1(8)

*ν5 ( A1)

1097.6

1.3

5.6(5)

ν8 + ν11 ( A2u)

1139.0

1.4

10(1)

ν6 + ν8 (Eu)

1328.5

3.6

11(1)

ν2 + ν11( Eu)

1330.0

3.6

11(1)

*ν1 ( A1)

1396.3

1.4

0.05(1)

*(ν2 + ν10) (E)

2003.0

2.0

0.01(1)

ν2 + ν10 ( Eu)

2047.8

2.2

3,2 (4)

ν1 + ν10 ( Eu)

2657.8

2,9

1.5(2)

2ν6 + ν10 ( Eu)

2665.7

2.5

1.6(2)

20

Table 3. Comparison of calculated and experimental absolute intensities (A) in the gas phase and in liquid N2 (T =77 K) for 12C12CF6 and 13C12CF6 (*). The calculated and experimental frequencies (νi) are also presented Gas phase

Calculation

A (νi )

A (νi )

A (νi )

A0 (νi )

νi , cm−1

km/mol

km/mol

km/mol

km/mol

1250

1025(10) a

1000(20)

990

1010

1250

8.7(8) а

8.1(8)

9.2

460

1214

0

0

0

0

1252

9.0

450

1251

240(10)

240

245

1121

5.6(5)

5.2

244

1106

0

0

0

1416

0.04(1)

0.026

1.1

1392

Assignment ν10 (Eu)

Liquid N2

νi , cm−1

1050 [2] 985 [3] *ν10 (E)

1206

ν7 (Eg) *ν7 (E) ν5 (A2u)

1115

290 (10) a 292 [5] 283 [6]

*ν5 (A1) ν1 (A1g) *ν1 (A1) a

This work.

0