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Theoretical investigation of the torsional spectra of 2,2,2-trifluoroethanol
Chemical Physics 266 (2001) 19±32
www.elsevier.nl/locate/chemphys
Theoretical investigation of the torsional spectra of 2,2,2-tri¯uoroethanol M.L. Senent a,*, A. Perez-Ortega b, A. Arroyo b, R. Domõnguez-G omez c a c
Departamento de Quõmica y Fõsica Te oricas, Instituto de Estructura de la Materia, C.S.I.C., Serrano 113 bis, Madrid E-28006, Spain b Departamento de Quõmica, Facultad de Ciencias, Universidad de Burgos, Burgos 09001, Spain Departamento de Ingenierõa Civil, C atedra de Quõmica, E.U.I.T. Obras P ublicas, Universidad Polit ecnica de Madrid, c/Alfonso XIII, 3-5, 28014 Madrid, Spain Received 16 November 2000; in ®nal form 21 February 2001
Abstract The structure and the torsional spectra of various isotopic varieties of 2,2,2-tri¯uoroethanol (TFE) are investigated with MP4(SDQ)/cc-pVTZ ab initio calculations. The energy levels corresponding to the CF3 and the OH internal rotation modes, are calculated variationally. With the predicted frequencies and intensities, previous assignments are reviewed. The position of several combination bands are predicted. The most stable conformation of TFE has a gauche geometry which is stabilized by the formation of intramolecular F±H hydrogen bonds. A second trans conformer lies 681.5 cm 1 over the gauche form. The torsional barriers have gauche trans been calculated to be V3 1534:0 cm 1 , V3 1490:9 cm 1 , VOH a 34° 707:5 cm 1 and VOH a 180° 804:9 cm 1 . The fundamental bands of the gauche-TFE have been evaluated at 286.7 and 283.3 cm 1 (OH torsion) and 115.0 and 114.9 cm 1 (CF3 torsion) and their corresponding intensities to be 21:73 10 4 and 23:16 10 4 , and 0:009 10 4 and 0:002 10 4 , respectively. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: 2,2,2-Tri¯uoroethanol; Ab initio; Torsion; FIR
1. Introduction 2,2,2,-Tri¯uoroethanol (TFE, CF3 CH2 OH) is a polar organic solvent that is employed in protein folding investigations as an alternative to water, because both species behave as weak bases capable of forming hydrogen bonds [1]. The dierent properties of the two molecules confer value to TFE as an optional solvent. TFE is larger than
*
Corresponding author. Tel.: +34-91-561-6800; fax: +34-91564-5557. E-mail address: [email protected] (M.L. Senent).
water and has only a single OH group. The dielectric constant is one-third lower than for H2 O. Available studies [2±16] show the molecular spectra and the structure of some halogen derivatives of ethanol (mono-ethanols (CH3 CH2 OX) and trihalo-ethanols (CX3 CH2 OH). The vibrational spectra have been recorded in the gas phase [3,4,6± 8], in condensed phases [4,6] and in argon and nitrogen matrices [5]. Recently, Xu et al. [9] have published the microwave spectrum and Durig and Larsen [7] the far infrared spectra of TFE. From the spectroscopic point of view, TFE is of interest due to it shows two large amplitude motions that confer non-rigidity to the molecule: the torsion of
0301-0104/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 1 ) 0 0 3 1 1 - 1
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M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Fig. 1. The two conformers of TFE, gauche and trans.
the tri¯uoromethyl group (CF3 ) and the torsion of the hydroxyl group (OH). The number and relative energies of the TFE potential energy surface wells are controversy. It is well known that the most stable conformer (Fig. 1) corresponds to a cis±gauche geometry stabilized by the formation of an intramolecular hydrogen bond between one of the ¯uorine atoms and the hydroxyl hydrogen [2±10,15]. However, the existence of the second conformer is less clair. Some authors as Durig and Larsen [7] have analysed the spectra from the hypothesis of the existence of the second conformer. Barnes et al. [3], Perttil a [5], and Marco and Orza [8] suppose that the experimental mixture is almostful consists predominantly of the gauche form. Marco and Orza [8] conclude that the formation of dimers favours the stabilization of the trans conformation although the monomer adopts the gauche form. In second paper, Orza et al. [15] have studied the displacement of the infrared spectra with the formation of intermolecular hydrogen bonds between TFE and some chemical solvents, that stabilize a second conformer. In addition, dierent authors provide quite dierent enthalpies (DH ) between conformers. For example, Krueger and Mettee [2] have evaluated DH to be 1161 cm 1 (3.32 kcal/mol) from the spectral bands of the OH stretching region, whereas Durig and Larsen [7] gave 20 cm 1 from the far infrared band positions. In the case of monohalo-ethanols, the most stable geometry is the gauche conformer and the enthalpy has been evaluated to be 2.0 kcal/mol from ab initio calculations [16].
The polymerization of TFE, that favours the stabilization of the trans-structure [3,8], can aggravate the interpretation of the spectra [17]. In the liquid phase, TFE builds dimers and polymers. In the gas phase, some molecules can be polymerized [17,18] giving complicated additional bands. In this paper, we determine all the possible minimum energy geometries of the potential energy surface of the isolated molecule. We interpret the torsional spectra of TFE from the ab initio calculations of frequencies and intensities using ¯exible models in one (1D) and two (2D) dimensions [18±22]. The aim of the work is to add information concerning the features that are signi®cant for the assignments and for the molecular structure analysis. The experimental data we use are from Refs. [7,9] although some parameters vary in the two papers. The FIR assignment [7] has been performed under the supposition that the isolated TFE presents two conformers, gauche and trans. However, the microwave study considers a single gauche minimum. In addition, Xu et al. [9] have determined the gauche±gauche barrier (763 cm 1 ) from the torsional splitting to be higher than the one evaluated by Durig and Larsen [7] from the IR bands (603, 440, 590 and 455 cm 1 for the isotopic species CF3 CH2 OH, CF3 CH3 OD, CF3 CD2 OH and CF3 CD2 OD, respectively). The OH fundamental has been estimated to be 364 cm 1 with microwave spectroscopy from the torsional splittings [9] and it has been assigned to the bands at 281.0 and 272.0 cm 1 observed by far infrared spectroscopy [7]. The tunneling splitting is also dierent (5.9 GHz in Ref. [9] and 28 GHz in Ref. [7]). 2. The torsional Hamiltonian of TFE The roto-vibrational Hamiltonian may be de®ned as the sum of three terms: the vibrational Hamiltonian, Hv , the pure rotational Hamiltonian and the roto-torsional operator [19]. If it is assumed that the two torsional modes of TFE are independent from the remaining coordinates, the torsional terms HT of the vibrational Hamiltonian can be written as:
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
H^T
o o o o B11 B12 oh oh oh oa o o o o B12 B22 oa oh oa oa
V 0 h; a V h; a
1
where the two variables h and a are de®ned as functions of the two dihedral angles F4 C1 C2 O and HOC2 C1 (h 180° \F4 C1 C2 O and a 180° \HOC2 C1 ). V represents the potential energy surface (PES) and V0 is the pseudopotential given by: 2 X 2 1X o o ln g 0 Bkl V 4 k1 l1 oqk oql 2 X 2 o ln g o 1 X o ln g Bkl oqk oql 16 k1 l1 oqk o ln g q1 h; q2 a 2 Bkl oql where g is the determinant of the G 1 matrix [19]. B11 , B22 and B12 are the tri¯uoromethyl torsion, hydroxyl torsion and torsion±torsion interactions, kinetic energy parameters, respectively. They are related to the torsional elements g44 and g55 and g45 of the G matrix by the equations B11 h2 =2g44 , 2 2 B22 h =2g55 and B12 h =2g45 . The complete torsional Hamiltonian of TFE commutes with the symmetry operations of the G6 full-non-rigid Group [23,24] of ethanol-h6 [18]. Therefore, the analytic form for the potential, the pseudopotential, and the kinetic parameters B11 , B22 , and B12 can be described by the symmetry adapted Fourier series that transforms as the totally symmetric irreducible representation of G6 . The analytic expression for the potential energy surface is: XX V h; a Acc NL cos3N h cos La N 0 L0 Ass NL sin 3N h sin La
3
In this paper, the torsional levels are calculated variationally using models in 1D and 2D. In the case of the 1D models, the 1D Hamiltonians are obtained by eliminating the interaction terms from Eqs. (1) and (2). The employed trial functions are
21
series of solutions of the free rotor for the 1D calculations and series of solutions of the double free rotor for the 2D calculations. The intensities of the transitions between different vibrational states are determined with the oscillator strength equation de®ned in Refs. [18,20] for a two-torsional problem. The strength depends on the transition frequency and the dipole moment variation. It depends also on the radius of the internal rotors, the average of the kinetic parameter 1=2 B B11 B22 , the Boltzmann population of the two states, the nuclear statistical weight, q [25]. In the cases of CF3 CH2 OH and CF3 CH2 OD, the nuclear statistical spin weights q are 1 and 0.5 for the Ai and E irreducible representations [18] due to the odd number of particles in 19 F nuclei [25]. For the non-degenerate representations q has been taken equal to 1. For the E two-degenerate representations, the weights are multiplied by two and q has been taken equal to 1 0:5 2. 3. Computational details All the ab initio calculations have been performed with the G A U S S I A N 9 4 program [26] using the Dunning' correlation consistent triple zeta basis set [27] and the M oller±Plesset perturbation theory up to the four order incorporating single, double and quadrupole substitutions (MP4(SDQ)). All the valence electrons have been correlated. The geometry has been optimized in all the selected conformations with the MP2/cc-pVTZ approach. The kinetic parameters have been computed from the optimized geometries with the KNP.f program [28]. The band positions and the intensities have been calculated with the programs UNADIM.f and BIDIM.f [18] that incorporate symmetry conditions. 4. Results and discussion As was expected, the most stable geometry of TFE is a cis±gauche conformer placed at a 115:9° (or 115:9°), although a secondary minimum has been detected at a 0° (see Fig. 1). The two stable geometries can be classi®ed by the
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M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Table 1 Structural parametersa of the two conformers, calculated with MP2/cc-pVTZ C1C2 O3C2 F4C1 F5C1 F6C1 H7C2 H8C2 H9O3 O3C2C1 F4C1C2 F5C1C2 F6C1C2 H7C2C1 H8C2C1 H9O3C2 F4C1C2O3 F5C1C2F4 F6C1C2F4 H7C2C1O3 H8C2C1O3 a
gauche-TFE
trans-TFE
1.5113 1.4039 1.3400 1.3465 1.3339 1.0914 1.0860 0.9620 111.91 110.38 110.54 112.46 107.27 107.87 107.74 182.1 119.1 121.0 124.7 118.1
1.5087 1.4064 1.3437 1.3354 1.3354 1.0911 1.0911 0.9599 107.52 109.19 111.96 111.96 106.92 106.92 107.87 180.0 119.3 119.3 121.6 121.6
and angles are in degrees. Distances are in A,
C1 and Cs point groups. Table 1 shows the structural parameters calculated optimizing the geometry at the MP2/cc-pVTZ level. The largest torsional dependence corresponds to the O3C2C1 bending angle that changes by 4.4° during the OH group internal rotation, (from 111.91° at the gauche conformers to 107.52° at the trans geometry) as was ®rst observed for ethanol [18]. With the OH internal rotation, the CF3 group loses the C3v symmetry. The central bond C1C2 decreases from (gauche) to 1.5087 A (trans) where the 1.5113 A steric interactions are lower. The gauche-TFE parameters can be compared with the experimental ones of Ref. [9]. The torsional coordinate amin determined from the microwave measurements (amin 111° [9]) is 5.8° smaller than the calculated value (Table 2). Except for H9O3, the microwave bond distances are slightly larger than the theoretical ones. The MP2/cc-pVTZ vibrational kinetic parameters, the MP4(SDQ)/cc-pVTZ internal rotational barriers and potential parameters, and the rotational constants of the two conformers, are shown in Table 2. In agreement with experiments, the calculated gauche conformer is the most stable
Table 2 Kinetic and potential parameters of the two TFE conformersa a A B C j B11 B22 B12 V0
gauche-TFE
trans-TFE
115.9 5325.935 2842.173 2812.024 0.97629852 1.10325304 21.46799684 0.94878180 0.02953732
0.000 5346.683 2869.439 2824.998 0.96536335 1.09465528 21.50216697 0.513430049 0.00612807
Calculated
Experimental
1534.0 1490.9 707.5 804.9 681.5
1895 9 1161 10 622 606 19.5
Ref. [7] gauche
V3 trans V3 VOH a 34° VOH a 180° DH
Ref. [10]
763
a The rotational constants, A, B and C are in MHz; the torsional kinetic parameters Bii , the barriers and the pseudopotential V 0 are in cm 1 .
geometry, due to the formation of a hydrogen between the OH hydrogen bond of 2.5004 A and the neighbouring ¯uorine atom. The energy dierence between conformers (DH ) has been calculated to be 681.5 cm 1 , far away from the experimental data determined by Durig and Larsen [7] from the observed FIR frequencies (19.5 cm 1 ). However, the ab initio calculations predict a large dierence of stability between conformers which agrees with the suppositions in Refs. [3,4,8,15]. gauche The tri¯uoromethyl torsion barriers V3 trans and V3 have been evaluated to be 1534.0 and 1490.9 cm 1 , whereas the experimental values of CF3 CH2 OH obtained by a 1D treatment are 1895 9 and 1161 10 cm 1 [7]. The experimen gauche tal V3 of CF3 CH2 OD has been observed to be 1696 10 cm 1 [7]. The calculated hydroxyl torsion trans±gauche, gauche±trans and gauche± gauche barriers occur at a 34°, a 34° and a 180°, and their heights are 26.0, 707.5 and 804.9 cm 1 , respectively. They can be compared with the FIR parameters of 601, 622 and 603 cm 1 [7], respectively. The calculated gauche±gauche barrier is slightly larger than the one of Ref. [7], but coincides with the microwave data of Xu et al.
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
(763 cm 1 ) evaluated from the torsional splitting [9]. In an earlier paper [20], we found a similar behaviour for acetone where the ab initio barrier coincides with the one obtained from microwave data but disagrees with the FIR parameter. The gauche conformer is a near prolate symmetric top j 0:97629852. The calculated rotational constants for the gauche conformation are 5325.935, 2842.173 and 2812.024 MHz. The experimental values for the vibrational ground state are 5318.27299, 2827.6629 and 2798.5618 MHz [9]. The trans-form rotational constants are 5346.683, 2869.439 and 2824.998 MHz. TFE has eight large amplitude motions below 700 cm 1 . In Table 3, the MP2/cc-pVDZ harmonic frequencies of the two conformers, are shown. The gauche frequencies are compared with the experimental data of Ref. [3] and the four experimental trans values are from Ref. [7]. The harmonic approximation appears insucient for describing the OH torsional motion and some CF3 deformations but provides information that can help the assignments. For example, it permits to infer that the
23
spectral analysis requires to consider that two CF3 rocking modes (238 and 363 cm 1 ) and the CCO bending mode (415 cm 1 ) can interact with the two torsional frequencies. As was expected, the calculated gauche OH fundamental (334 cm 1 ) lies below the experimental value (280 cm 1 ). In the case of the trans form, the harmonic approximation predicts a value lower than the one assigned in Ref. [7]. Results obtained in 1D and 2D are compared for evaluating the interactions between the two torsions. The 1D and 2D potential energy surfaces have been calculated by ®tting the energies in Table 4. E h; a are the 2D energies obtained by freezing two coordinates during the geometry optimization. The 1D energies, E h and E a, have been evaluated by freezing only one variable. For this reason, the 1D and 2D selected conformations are not equivalent. The energies have been determined at the MP4(SDQ)/cc-pVTZ//MP2/cc-pVTZ level. The 2D potential energy surface, V h; a, was obtained by ®tting to Eq. (3) the E h; a energies of 26
Table 3 Harmonic frequencies of the two TFE conformers calculated with MP2/cc-pVDZ gauche-TFE m11 m20 m19 m18 m17 m16 m15 m14 m13 m12 m11 m10 m9 m8 m7 m6 m5 m4 m3 m2 m1
trans-TFE
Assignments
Calculated
Experimental [3]
Calculated
Experimental [7]
CF3 tor CF3 rock OH tor CF3 rock CCO bend CF3 def CF3 def CF3 def CC stretch CH2 rock CO stretch CH2 wag COH bend CF3 stretch CF3 stretch CF3 stretch CH2 twist CH2 bend CH2 stretch CH2 stretch OH stretch
121.2 225.9 334.0 406.1 429.6 538.7 554.1 670.4 843.9 965.0 1131.7 1179.5 1231.5 1298.3 1335.2 1413.3 1472.4 1494.1 2985.9 3194.3 3842.2
118 238 280 363 415 549 660 660 780 830 940 1080 1160 1160 1270 1270 1405 1453 2943 2990 3655
105.3 163.5 229.6 359.9 423.7 541.4 558.6 656.1 842.6 1000.6 1145.2 1190.7 1213.2 1282.6 1330.9 1336.7 1509.7 1521.8 3070.6 3130.9 3876.7
105 246 284 363
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M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Table 4 Relative energiesa (in cm 1 ) of the selected conformations in terms of h (CF3 torsion) and a (OH torsion) h
a
E
h
a
E
0 0 0
681.510 1373.253 2172.397
0 90 180
180 180 180
804.886 1321.944 1876.561
0 90 180 90
30 30 30 30
712.186 1512.920 2243.610 1342.513
0 90 180 90
150 150 150 150
434.558 918.359 1727.873 1209.474
0 90 180 90
60 60 60 60
603.783 1439.576 2167.801 1252.737
0 90 180 90
120 120 120 120
15.984 686.040 1539.421 833.470
0 90 180 90
90 90 90 90
198.427 981.390 1755.610 912.185
0 90 180 90
115.1 122.7 118.7 110.0
0.000c 681.096 1533.983 790.912
E ab 0.0 2.5 2.5 0.6
0 30 60 90
681.510 706.252 598.145 198.333
b
E h; a 0 90 180
E h gauche-TFE
trans-TFE 0 90 180 90
2.1 5.4 0.0
0.000d 659.095 1490.887 659.095
0.0 19.0 0.0 19.0
120 150 180
7.307 408.120 804.886
a
Calculated with MP4(SDQ)/cc-pVTZ. E gauche 452:178859 a.u. c E 452:178839 a.u. d E trans 452:175754 a.u. b
conformations selected using symmetry criteria. As is recommended in Refs. [29,30], the calculations have been performed for h 0°, 90°, 180° and 90°. The hydroxyl torsion coordinate has been ®xed at a 0°, 30°, 60°, 90°, 120°, 150° and 180°. The reference structure h; a 0°; 0° is the trans conformation with the methyl group staggered. Three 1D and one 2D surfaces have been determined. V trans h and V gauche h restrict the motion of the methyl group while the OH group remains at the trans or gauche positions. V a hinders the hydroxyl group motion. In this case, the tri¯uoromethyl group remains at its minimum. The three functions are:
V a 443:559 163:974 cos a 266:442 cos 2a 27:206 cos 4a 5:991 cos 6a V trans h 702:269
217:509 cos 3a 8:153 cos 5a in cm 1
745:443 cos 3h
43:174 cos 6h in cm 1 V gauche h 751:498
766:991 cos 3h
54:908 sin 3h 15:494 cos 6h
in cm 1
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
25
The 2D function is: V h; a 1164:534
729:352 cos 3h
15:881 cos 6h 220:828 cos a 199:768 cos 2a
187:749 cos 3a
0:805 cos 4a 1:340 cos 5a 2:115 cos 6a
72:578 cos 3h cos a
68:045 cos 3h cos 2a 28:440 cos 3h cos 3a 19:673 cos 3h cos 4a 3:755 cos 3h cos 5a 0:981 cos 3h cos 6a 7:137 sin 3h sin a 114:885 sin 3h sin 2a 31:646 sin 3h sin 3a Fig. 2. The calculated potential energy surface V h of TFE (g-TFE ±±; t-TFE ± ± ±).
18:340 sin 3h sin 4a 4:195 sin 3h sin 5a 9:522 cos 6h cos a 1:875 cos 6h cos 2a 0:831 cos 6h cos 3a 0:656 cos 6h cos 4a
in cm 1
Figs. 2 and 3 represent the V h and V a potentials, respectively. Fig. 2 shows two lines corresponding to the gauche (continuous line) and trans (dashed line). In Fig. 3, we compare the ab initio PES with the one ®tted by Durig and Larsen [7] from the experimental FIR frequencies. Both curves coincide in the gauche well but dier around the trans minimum showing an unusual behaviour that cannot be explained as a computational error. We have con®rmed that the trans conformer is the unique second minimum. For eliminating the possibility of the existence of a trans±gauche minima, the energies of four geometries, corresponding to values of h lying between 0° and 30°, have been calculated. Our experience [19±22] shows that calculations and experiments are always in very good agreement if the employed ab initio methods are accurate enough. However, the calculations are
Fig. 3. The potential energy surface V a of TFE (±±) compared with the one ®tted from the bands assigned in Ref. [7] (- - -).
performed on isolated molecules and fail when the intermolecular forces are not negligible. In
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M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
accordance with the measurements of Marco and Orza [8] and Orza et al. [15], the TFE behaviour could be explained by the polymerization of some molecules or by the binding of TFE and water molecules in the experimental mixture, that can stabilize the trans conformer. These authors have studied the infrared spectrum shifts caused by the production of TFE complexes with dierent bases by formation of intermolecular FH hydrogen bonds [15]. It can be concluded that some bands observed in Ref. [7] have to be assigned to the dimer spectrum or to the TFE±H2 O spectrum and cannot be attributed to the isolated molecule. The kinetic parameters of the torsional Hamiltonian have been determined with the KNP.f program [28] from the optimized geometries. Table 2 shows the vibrational parameters B11 , B22 , B12 , and V 0 of the two conformers. The values for each conformation have been ®tted to completely symmetric periodic functions. For CF3 CH2 OH the resulting functions are: B11 h; a 1:1239
0:0013 cos 3a
0:0021 cos 4a
0:0002 cos 5a
0:0063
cos 6h
0:7931 cos a 0:5517
cos 2a
0:1259 cos 3a 0:0038 cos 5a
0:0029 cos 6a 0:0620 cos 3h cos a 0:0937 cos 3h cos 2a 0:0482 cos 3h cos 3a 0:0346 cos 3h cos 4a
0:0156 cos 3h
cos 5a 0:0052 cos 3h cos 6a 0:0734 sin 3h sin a
0:0848 sin 3h
sin 2a 0:0553 sin 3h sin 3a 0:0295 sin 3h sin 4a 0:0123 sin 3h sin 5a 0:0044 cos 6h cos a
0:0003 cos 6h cos 2a
0:0003 cos 6h cos 3a 0:0011 cos 6h cos 4a
in cm 1
0:5519 0:0201 cos 3h 0:0022 cos 6h 1:0473 cos a
0:0430 cos a
0:0244 cos 2a
0:0125 cos 3h
0:0183 cos 4a
B12 h; a
0:0155 cos 3h
0:0024 cos 6h
B22 h; a 21:7374
0:0165 cos 2a 0:0196 cos 3a 0:0049 cos 4a 0:0010 cos 5a 0:0005 cos 3h cos a
0:0011 cos 3h cos a
0:0052 cos 3h cos 2a
0:0048 cos 3h cos 2a
0:0052 cos 3h cos 3a
0:0002 cos 3h cos 3a
0:0025 cos 3h cos 4a
0:0006 cos 3h cos 4a
0:0017 cos 3h cos 5a
0:0003 cos 3h cos 5a
0:0005 cos 3h cos 6a
0:0017 sin 3h sin a
0:0059 sin 3h sin a
0:0057 sin 3h sin 2a
0:0111 sin 3h sin 2a
0:0008 sin 3h sin 3a
0:0031 sin 3h sin 3a
0:0005 sin 3h sin 4a
0:0025 sin 3h sin 4a
0:0001 sin 3h sin 5a
0:0011 sin 3h sin 5a
0:0003 cos 6h cos a
0:0009 cos 6h cos a
0:0006 cos 6h cos 2a
0:0006 cos 6h cos 2a
0:0003 cos 6h cos 3a
0:0003 cos 6h cos 3a 1
0:0002 cos 6h cos 4a in cm
0:0003 cos 6h cos 4a in cm 1
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
The independent terms of B11 (tri¯uoromethyl torsion) and B22 (hydroxyl torsion) are 1.1239 and 21.7374 cm 1 close to the ones employed by Durig and Larsen [7] (1.0465 and 20.6949 cm 1 ) for the ®tting of the potential energy surfaces. We omit the transcription of the pseudopotential function V 0 h; a, since its order of magnitude is 1 cm 1 . The relations between cartesian and internal coordinates are also omitted (see Ref. [28]). 5. Assignments The 1D and 2D non-degenerate energy levels Ai of CF3 CH2 OH are compared in Table 5. The 2D gauche energies of the isotopic varieties CF3 CH2 OD, CF3 CD2 OH and CF3 CD2 OD are shown in Table 6. They are labelled using the vibrational quantum numbers (v and v0 ) and the irreducible represent of TFE. The tunnelling eect
27
between the gauche conformers causes a splitting of each gauche level into two sub-components labelled as v and v ; v represents a trans-level. Two properties have been calculated for the labelling of the states: the expectation values of the 1D Hamiltonians on the 2D wave functions and the probability integrals in the potential surface wells (see Ref. [18]). The tri¯uoromethyl barriers produces a splitting of each sub-component into three microstates, one non-degenerate Ai and two degenerate Ei levels, although the Ai E energy dierence is negligible. As a result, nine microstates corresponding to the nine wells of the potential energy surfaces, appear. All levels shown in Table 5 are referred to the calculated vibrational ground state calculated with each model. In gauche-CF3 CH2 OH, the 2D zero vibrational (213.750 cm 1 ) splits into two subcomponents v v0 0 0 and v v0 0 0 at 0.000 and 0.179 cm 1 whereas the energy dierence calculated in 1D is 0.205 cm 1 (Table 5). For
Table 5 Comparison between the non-degenerate energy levels (cm 1 ) of CF3 CH2 OH, calculated in 1D and 2D v v0
a b
Symmetry
1D
2D
Experimental [7]
OH
CF3
0.000a 0.205
0.000b 0.000
0.000c 0.179
0.0 0.95
114.6 114.6 227.3 227.3
115.0 115.0 228.0 228.0
119.8 119.8 238.9 238.9
283.5 286.7 497.2 519.8 698.4 861.5
272.2 281.0
0.0c 112.4 222.9 101.5 293.1
0.0 104.6 206.0 284.2
gauche-TFEa 0 0 00
A1 A2
CF3 torsion 10 1 0 20 2 0
A2 A1 A2 A1
OH torsion 0 1 01 0 2 02 03 04
A1 A2 A1 A2 A1 A2
277.0 280.4 492.4 513.6 692.1 844.3
trans-TFEb 00 10 20 01 02
A1 A2 A1 A2 A1
0.0a 92.9 278.5
0.0b 105.2 209.9
Zero vibrational a 149:5 cm 1 ; b 55:6 cm 1 ; c 213:8 cm 1 . Zero vibrational a 730:1 cm 1 ; b 52:8 cm 1 ; c 792:1 cm 1 .
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M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Table 6 Calculated energy levels of isotopic varieties of gauche-TFE (in cm 1 ) v v0 0 0 0 0 0 0 0 0 1 1 2 2 3 3 4 4 5 5 1 1 2 2 1 1
0 0 1 1 2 2 3 3 0 0 0 0 0 0 0 0 0 0 1 1 1 1 2 2
Symmetry
CF3 CH2 OH
CF3 CH2 OD
CF3 CD2 OH
CF3 CD2 OD
A1 A2 A1 A2 A1 A2 A2 A1 A2 A1 A2 A1 A1 A2 A2 A1 A1 A2 A2 A1 A1 A2 A2 A1
0.0 0.2 283.5 286.7 497.2 519.8 679.9 698.4 115.0 115.0 228.0 228.0 339.0 339.0 447.6 447.6 554.0 554.0 397.5 399.0 509.5 509.6 608.2 628.2
0.0 0.0 217.1 217.3 408.3 409.8 566.5 556.5 111.4 111.4 220.9 220.9 328.5 328.5 433.8 433.8 537.0 537.0 327.6 327.5 436.4 436.3 518.9 517.5
0.0 0.2 283.0 286.1 497.3 519.2 681.6 696.2 106.4 106.4 211.1 211.0 314.0 314.0 415.0 415.0 514.1 514.1 388.2 390.1 491.4 492.6 600.5 620.4
0.0 0.0 216.1 216.2 406.4 408.0 565.1 554.6 103.7 103.6 205.6 205.6 305.9 305.9 404.5 404.5 501.2 501.2 318.9 318.9 420.0 419.9 508.9 508.5
CF3 CH2 OD, CF3 CD2 OH and CF3 CD2 OD, the splitting was found to be 0.005, 0.177 and 0.005 cm 1 , respectively. Experimentally, the FIR values are 0.95 cm 1 (CF3 CH2 OH), and 0.21, 1.0 and 0.19 cm 1 , for the three deuterated varieties [7]. Our calculated splittings agree with those observed by microwave spectroscopy that are 0.2 cm 1 for CF3 CH2 OH and 0.007 cm 1 for CF3 CH2 OD [9]. As V3 is three times higher than the hydroxyl barriers, it produces really a small splitting. It is imperceptible at the lowest energy levels. The trans ground state v v0 0 0 lies at 578.4 cm 1 over the gauche ground state (213.8 cm 1 ) (Table 5). As is evident, the assignment of the levels over the gauche±trans barrier (707.5 cm 1 ) to the trans or gauche conformations is not simple because the eigenfunctions cannot be localized in the wells. The probability integrals around the two minima are identical. For example, the OH torsional level at 679.9 cm 1 could be identi®ed with the ®rst excited trans OH level ( v v0 0 1, Table 5) or with an excited gauche
OH level ( v v0 0 3 , Table 6). The probability integrals around the two minima are identical. The ®rst labelling, that is the most believable, implies the calculated trans OH fundamental 0 0 ! 0 1 to lie at 101.5 cm 1 , far away from the experimental data of Ref. [7] (284.2 cm 1 ). This discrepancy relates to the dissimilarity between our calculated trans±gauche barrier of 26 cm 1 (707.5± 681.5 cm 1 ) and the one arising from the assignment of Ref. [7] (601 cm 1 ). In the case of ethanol [18], the OH torsional mode behaves as an independent mode, whereas the CH3 torsion is aected by the interactions, due to the conditions imposed during the geometry optimization (the number of optimized coordinates is dierent in the 1D and the 2D calculations). In TFE, the dierences between OH levels calculated in 1D and 2D are larger than the CF3 group ones. The OH levels (0 1 ) and (0 1 ) have been determined to be 283.5 and 286.7 cm 1 in 2D and to be 277.0 and 280.4 cm 1 in 1D. The CF3 levels (1 0 ) and (1 0 ) have been determined to be
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
115.0 and 115.0 cm 1 in 2D, and to be 114.6 cm 1 in 1D. The comparison of the gauche levels of dierent isotopic varieties clari®es the assignments (Table 6). We omit the transcription of the trans levels where the dierences between calculations and available experimental data are too large. As in ethanol, the deuteration of the ±CH2 ± group imparts the largest eects on the CF3 levels, which shows the dependencies of the ¯uoromethyl group torsion in other vibrations (Table 5). The two fundamentals shift to 103.6 and 103.7 cm 1 and to 216.1 and 216.2 cm 1 when the molecule is fully deuterated. They are found at 111.4 and 111.4 cm 1 , and 217.1 and 217.3 cm 1 , for CF3 CH2 OD. The corresponding experimental values, assigned by Durig et al. [7], are 112.9 cm 1 (CF3 torsion), 194.8 and 189.4 cm 1 (OH torsion). The prominent Q branches observed in the experimental spectra [7] correspond to Type-C bands. Their intensities depend on the variation of the out-of-plane dipole moment component. For this reason, the dipole moments along the C principal axis of the selected conformations, have been ®tted to symmetry adapted periodic series. The ``in plane'' la , and lb components transform
29
as the totally symmetric representation A1 and the ``out of plane'' lc transforms as the antisymmetric non-degenerate A2 . The analytic form of lc h; a is, lc h; a
0:01746 sin 3h 1:15222 sin a 0:04723 sin 2a
0:09102 sin 3a
0:00157 sin 4a 1:51072 sin 5a 0:00304 cos 3h sin a 0:00083 cos 3h sin 2a 0:00026 cos 3h sin 3a 0:00251 sin 3h cos 2a 0:00011 sin 3h cos 3a 0:00132 sin 3h cos 4a 0:00276 sin 3h cos 5a 0:00171 sin 3h cos 6a
in Debyes
Absolute intensities are adimensional properties determined with the oscillator strength equation [18±20]. Tables 7±9 show the frequencies and intensities of the most prominent ¯uoromethyl torsional bands, hydroxyl torsional bands and
Table 7 Tri¯uoromethyl torsional frequencies (in cm 1 ) and absolute intensities of CF3 CH2 OH and CF3 CH2 OD v v ! v0 v0
a
Symmetry
CF3 CH2 OH
CF3 CH2 OD a
Frequencies
Intensities 10 4
Experimental
Frequencies
Intensities 10 4
trans ! trans 00 ! 10 10 ! 20 20 ! 30
A1 ! A2 A2 ! A1 A1 ! A2
112.4 110.4 108.2
0.073 0.032 0.007
104.6 102.9 99.4
110.7 109.8
0.173 0.515
gauche ! gauche 00 ! 10 00 ! 10 10 ! 20 10 ! 20 20 ! 30 20 ! 30 30 ! 40 30 ! 40 40 ! 50 40 ! 50
A1 A2 A2 A1 A1 A2 A2 A1 A1 A2
115.0 114.9 113.0 112.9 110.9 110.9 108.7 108.7 106.4 106.4
0.009 0.002 0.008 0.003 0.005 0.003 0.003 0.002 0.002 0.002
119.8
111.4 111.3 109.5 109.5 107.6 107.6 105.3 105.3 103.3 103.3
± ± ± ± ± ± ± ± ± ±
! A2 ! A1 ! A1 ! A2 ! A2 ! A1 ! A1 ! A2 ! A2 ! A1
Experimental data are from Ref. [7].
119.1 118.2 116.2 115.0
Experimentala
112.9 112.2 109.9 107.8 106.3
30
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Table 8 Hydroxyl torsional frequencies (in cm 1 ) and absolute intensities of CF3 CH2 OH and CF3 CH2 OD v v ! v0 v0
Symmetry
gauche ! gauche 00 ! 01 A1 ! A2 E!E 00 ! 01 A2 ! A1 E!E 01 ! 02 A2 ! A1 E!E 01 ! 02 A1 ! A2 E!E trans ! trans 00 ! 01 A1 ! A2 E!E 01 ! 02 A2 ! A1 E!E
CF3 CH2 OH
CF3 CH2 OD 4
a
Frequencies
Intensities 10
Experimental
Frequencies
Intensities 10 4
Experimentala
286.7 286.7 283.3 283.3 210.5 210.5 236.3 236.3
21.73 21.73 23.16 23.16 4.03 4.03 2.08 2.28
284.2
217.3 217.3 217.1 217.1 192.7 192.7 191.1 191.1
14.24 14.24 14.27 14.27 5.11 5.11 5.40 5.40
194.3
101.5 101.5 191.6 191.6
1.78 1.78 3.01 3.01
281.0 >200 and <250
54.4 54.4
194.8
185
0.308 0.308
Table 9 Frequencies (in cm 1 ) and absolute intensities of the combination bands CF3 CH2 OH and CF3 CH2 OD v v ! v0 v0
10 10 01 01 11 11 11 11 20 20 a
! 11 ! 11 ! 11 ! 11 ! 21 ! 21 ! 12 ! 12 ! 21 ! 21
Symmetry
A1 A2 A1 A2 A1 A2 A1 A2 A1 A2
! A2 ! A1 ! A2 ! A1 ! A2 ! A1 ! A2 ! A1 ! A2 ! A1
CF3 CH2 OH
CF3 CH2 OD
Frequencies
Intensities 10 4
Experimentala
Frequencies
Intensities 10 4
Experimentala
282.5 284.1 114.0 112.3 110.5 112.0 209.2 230.7 281.6 281.6
12.33 12.13 0.03 0.04 0.04 0.02 1.76 1.54 6.70 6.48
'284
216.3 216.1 110.5 110.4 108.8 108.8 191.3 189.9 215.4 215.5
7.07 7.07 ± ± 0.03 0.03 2.79 2.28 4.39 4.39
'194
<200 and >250 '284
'185 '194
Experimental data are from Ref. [7]. Bold numbers correspond to our predictions.
combination bands. Some E bands are excluded from the tables because the intensities of the Ai and E components of each transition are identical. The experimental frequencies shown in the tables are from Ref. [7]. The calculations allow to predict approximate band positions where the experimental spectra shows protuberances. The dipole moment c-component depends strongly on the hydroxyl torsion and slightly on the ¯uoromethyl torsional coordinate. For this reason, it may be expected that the OH internal rotation transitions yield the largest intensities.
5.1. The CF3 CH2 OH spectrum In Fig. 4, the calculated and experimental far infrared spectra of CF3 CH2 OH, are compared. The water spectra is shown on the top of the ®gure. The region of the weak tri¯uoromethyl group transitions has been ampli®ed. As was expected, the most intense bands correspond to the OH torsional mode which produces the largest variation of the dipole moment. The gauche±gauche bands of the CF3 mode (Table 7) are of very low intensity and the frequencies are in
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Fig. 4. The calculated far-infrared spectrum of CF3 CH2 OH (C) compared with the experimental one (A) recorded in Ref. [7] with an eective resolution of 0.10 cm 1 . The experimental CF3 torsional bands can be observed on the B spectrum.
good agreement with the experimental data [7]. The calculated CF3 trans±trans bands (Table 7) lies among the gauche±gauche bands whereas the corresponding assigned frequencies are lower. The OH torsional fundamental frequencies 00 ! 01 and 00 ! 01 have been calculated to be 286.7 and 283.3 cm 1 con®rming the assignment of Durig and Larsen [7] to the pattern observed near 280 cm 1 (Table 9) and refuting the assertion of Xu et al. [9] who predicted the OH fundamental to lie at 364 cm 1 using the torsional splittings. However, the calculated intensities of the two gauche-transitions are almost identical (21:73 10 4 and 23:16 10 4 ), and contradict the assignment of Durig and Larsen [7] to the two bands of dierent intensity observed at 281.0 and 272.0 cm 1 . In addition, the calculations do not predict strong bands around 270 cm 1 .
31
On the basis of the calculated potential shape, it can be proposed a new interpretation for the band observed at 284.2 cm 1 , that was assigned to the OH trans fundamental in Ref. [7]. It has to be taken into account that the trans fundamental has been calculated far away at 101.5 cm 1 (679:9 792:2 213:8 cm 1 ). The two bands observed at 284.2 and 281.0 cm 1 shows similar intensities and they can be related to the two components of the gauche OH fundamental, 00 ! 01 and 00 ! 01 . Two combinations bands have been calculated near the OH gauche fundamentals. The calculated intensities of the transitions at 10 ! 11 and 10 ! 11 at 282.470 and 284.1 cm 1 are 12:33 10 4 and 12:13 10 4 . The calculations provide sets of strong bands near 210 cm 1 and near 230 cm 1 , where some experimental patterns were observed but were not assigned. For example, the OH ®rst sequence 01 ! 02 and 01 ! 02 have been calculated at 210.5 and 236.3 cm 1 and two combination bands have been found at 209.2 and 230.7 cm 1 . There intensities are 4:03 10 4 , 2:08 10 4 , 1:76 10 4 , and 1:54 10 4 , respectively. The remaining bands are of low intensity. Two strong transitions 20 ! 21 and 20 ! 21 are calculated to be around 281 cm 1 . 5.2. The CF3 CH2 OD spectrum The calculated frequencies of the gauche±CF3 transitions (Table 7) con®rm previous assignments [7]. The strongest bands correspond to the OD torsional mode. The frequencies of the 00 ! 01 and 00 ! 01 transitions have been determined to be 217.3 and 217.1 cm 1 and the intensities of the nondegenerate components 14:24 10 4 and 14:27 10 4 . As in the case of the OH isotopomer, the two components show similar strength for this reason, they can be reassigned to the bands observed at 194.3 and 194.8 cm 1 , that are of the same intensity. Durig and Larsen [7] have assigned these two transitions to the two bands observed at 194.8 and 189.4 cm 1 . Some strong transitions are predicted near 190 cm 1 and may be assigned to the bands observed
32
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
near 185 cm 1 . The A transitions of 01 ! 02 and 01 ! 02 lie at 192.7 and 191.1 cm 1 and show intensities of 5:11 10 4 and 5:40 10 4 . The calculated intensities of the combination bands at 191.4 and 189.9 cm 1 are 2:79 10 4 and 2:28 10 4 , respectively. Two strong combination bands are calculated near 215 cm 1 in the region of the OH gauche fundamentals. In CF3 CH2 OD the pattern of strong intensity observed in the experimental spectra near 250 cm 1 has been assigned to a CF3 rocking mode that has been neglected in the calculations and can push the torsional band to the lower frequencies. This vibrational eect could explain why the differences between calculations and experiments are larger for the deuterated species. Acknowledgements This work has been supported by the ``Consejerõa de Educaci on y Cultura'' of the Castilla and Le on Community, Spain (BU07/97), and the ``Vicerectorado de Investigaci on y Relaciones Internacionales'' of the University of Burgos, Spain. M.L. Senent acknowledges Prof. J.M. Orza (C.S.I.C.) for all his useful help. References [1] H. Sticht, D. Willbold, P. R osch, J. Biochem. Struct. Dyn. 12 (1994) 019. [2] P.J. Krueger, H.D. Mettee, Can. J. Chem. 42 (1964) 340. [3] A.J. Barnes, H.E. Hallam, D. Jones, Proc. R. Soc. Lond. A 335 (1973) 97. [4] J. Travert, J.C. Lavalley, Spectrochim. Acta 32A (1975) 637. [5] M. Perttil a, Spectrochim. Acta 35A (1978) 585. [6] V.F. Kalansinsky, H.V. Anjaria, J. Phys. Chem. 84 (1980) 1940. [7] J.R. Durig, R.A. Larsen, J. Mol. Struct. 238 (1989) 195. [8] J. Marco, J.M. Orza, J. Mol. Struct. 267 (1992) 33. [9] Li.-H. Xu, G.T. Fraser, F.J. Lovas, R.D. Suenram, C.W. Gillies, H.E. Warner, J.Z. Gillies, J. Chem. Phys. 103 (1995) 9541.
[10] M.A. Natal-Santiago, J.A. Dumesic, J. Catalysis 175 (1998) 252. [11] R.G. Azrak, E.B. Wilson, J. Chem. Phys. 52 (1970) 5299. [12] K.S. Buckton, R.G. Azrak, J. Chem. Phys. 52 (1970) 5652. [13] C.L. Brummel, S.W. Mork, L.A. Philips, J. Chem. Phys. 95 (1991) 7041. [14] J.R. Durig, P. Klaebae, J. Liu, Zeitch. Phys. Chem. 191 (1995) 1. [15] J. Marco, J.M. Orza, J.L.M. Abboud, Vib. Spectrosc. 6 (1994) 267. [16] D.A. Dixon, B.E. Smart, J. Phys. Chem. 95 (1991) 1609. [17] M.L. Senent, R. Domõnguez-G omez, Y.G. Smeyers, in: J. Maruani et al. (Eds.), New Trends in Quantum Systems in Chemistry and Physics, vol. 1, 2001, p. 359. [18] M.L. Senent, R. Domõnguez-G omez, Y.G. Smeyers, M. Villa, J. Chem. Phys. 12 (2000) 5809. [19] M.L. Senent, J. Mol. Spectrosc. 191 (1998) 265. [20] Y.G. Smeyers, M.L. Senent, V. Botella, D.C. Moule, J. Chem. Phys. 98 (1993) 2754. [21] M.L. Senent, D.C. Moule, Y.G. Smeyers, J. Chem. Phys. 102 (1995) 5952. [22] M.L. Senent, Y.G. Smeyers, J. Chem. Phys. 105 (1996) 2789. [23] Y.G. Smeyers, Introduction to Group Theory for Non Rigid Molecules, in: P.O. Lowden (Ed.), Advances in Quantum Chemistry, vol. 24, Academic Press, New York, 1992, pp. 1±77. [24] Y.G. Smeyers, Group Theory for Three-Dimensional Nonrigid molecular problems, Application to the Double Equivalent C3v Rotation Plus Bending, Wagging or Torsion Mode, in: Y.G. Smeyers (Ed.), Structure and Dynamics of Nonrigid Molecular Systems, Kluwer, Dordrecht, 1994. [25] E. Bright Wilson Jr., J. Chem. Phys. 3 (1935) 276. [26] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, G A U S S I A N 9 4 , Revision E.2, Gaussian, Inc., Pittsburgh PA, 1995. [27] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007. [28] M.L. Senent, Chem. Phys. Lett. 296 (1990) 299. [29] Y.G. Smeyers, M. Villa, Chem. Phys. Lett. 235 (1995) 587. [30] M. Villa, Q.G. Herrera-Perez, Y.G. Smeyers, Chem. Phys. Lett. 306 (1999) 78.
www.elsevier.nl/locate/chemphys
Theoretical investigation of the torsional spectra of 2,2,2-tri¯uoroethanol M.L. Senent a,*, A. Perez-Ortega b, A. Arroyo b, R. Domõnguez-G omez c a c
Departamento de Quõmica y Fõsica Te oricas, Instituto de Estructura de la Materia, C.S.I.C., Serrano 113 bis, Madrid E-28006, Spain b Departamento de Quõmica, Facultad de Ciencias, Universidad de Burgos, Burgos 09001, Spain Departamento de Ingenierõa Civil, C atedra de Quõmica, E.U.I.T. Obras P ublicas, Universidad Polit ecnica de Madrid, c/Alfonso XIII, 3-5, 28014 Madrid, Spain Received 16 November 2000; in ®nal form 21 February 2001
Abstract The structure and the torsional spectra of various isotopic varieties of 2,2,2-tri¯uoroethanol (TFE) are investigated with MP4(SDQ)/cc-pVTZ ab initio calculations. The energy levels corresponding to the CF3 and the OH internal rotation modes, are calculated variationally. With the predicted frequencies and intensities, previous assignments are reviewed. The position of several combination bands are predicted. The most stable conformation of TFE has a gauche geometry which is stabilized by the formation of intramolecular F±H hydrogen bonds. A second trans conformer lies 681.5 cm 1 over the gauche form. The torsional barriers have gauche trans been calculated to be V3 1534:0 cm 1 , V3 1490:9 cm 1 , VOH a 34° 707:5 cm 1 and VOH a 180° 804:9 cm 1 . The fundamental bands of the gauche-TFE have been evaluated at 286.7 and 283.3 cm 1 (OH torsion) and 115.0 and 114.9 cm 1 (CF3 torsion) and their corresponding intensities to be 21:73 10 4 and 23:16 10 4 , and 0:009 10 4 and 0:002 10 4 , respectively. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: 2,2,2-Tri¯uoroethanol; Ab initio; Torsion; FIR
1. Introduction 2,2,2,-Tri¯uoroethanol (TFE, CF3 CH2 OH) is a polar organic solvent that is employed in protein folding investigations as an alternative to water, because both species behave as weak bases capable of forming hydrogen bonds [1]. The dierent properties of the two molecules confer value to TFE as an optional solvent. TFE is larger than
*
Corresponding author. Tel.: +34-91-561-6800; fax: +34-91564-5557. E-mail address: [email protected] (M.L. Senent).
water and has only a single OH group. The dielectric constant is one-third lower than for H2 O. Available studies [2±16] show the molecular spectra and the structure of some halogen derivatives of ethanol (mono-ethanols (CH3 CH2 OX) and trihalo-ethanols (CX3 CH2 OH). The vibrational spectra have been recorded in the gas phase [3,4,6± 8], in condensed phases [4,6] and in argon and nitrogen matrices [5]. Recently, Xu et al. [9] have published the microwave spectrum and Durig and Larsen [7] the far infrared spectra of TFE. From the spectroscopic point of view, TFE is of interest due to it shows two large amplitude motions that confer non-rigidity to the molecule: the torsion of
0301-0104/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 1 ) 0 0 3 1 1 - 1
20
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Fig. 1. The two conformers of TFE, gauche and trans.
the tri¯uoromethyl group (CF3 ) and the torsion of the hydroxyl group (OH). The number and relative energies of the TFE potential energy surface wells are controversy. It is well known that the most stable conformer (Fig. 1) corresponds to a cis±gauche geometry stabilized by the formation of an intramolecular hydrogen bond between one of the ¯uorine atoms and the hydroxyl hydrogen [2±10,15]. However, the existence of the second conformer is less clair. Some authors as Durig and Larsen [7] have analysed the spectra from the hypothesis of the existence of the second conformer. Barnes et al. [3], Perttil a [5], and Marco and Orza [8] suppose that the experimental mixture is almostful consists predominantly of the gauche form. Marco and Orza [8] conclude that the formation of dimers favours the stabilization of the trans conformation although the monomer adopts the gauche form. In second paper, Orza et al. [15] have studied the displacement of the infrared spectra with the formation of intermolecular hydrogen bonds between TFE and some chemical solvents, that stabilize a second conformer. In addition, dierent authors provide quite dierent enthalpies (DH ) between conformers. For example, Krueger and Mettee [2] have evaluated DH to be 1161 cm 1 (3.32 kcal/mol) from the spectral bands of the OH stretching region, whereas Durig and Larsen [7] gave 20 cm 1 from the far infrared band positions. In the case of monohalo-ethanols, the most stable geometry is the gauche conformer and the enthalpy has been evaluated to be 2.0 kcal/mol from ab initio calculations [16].
The polymerization of TFE, that favours the stabilization of the trans-structure [3,8], can aggravate the interpretation of the spectra [17]. In the liquid phase, TFE builds dimers and polymers. In the gas phase, some molecules can be polymerized [17,18] giving complicated additional bands. In this paper, we determine all the possible minimum energy geometries of the potential energy surface of the isolated molecule. We interpret the torsional spectra of TFE from the ab initio calculations of frequencies and intensities using ¯exible models in one (1D) and two (2D) dimensions [18±22]. The aim of the work is to add information concerning the features that are signi®cant for the assignments and for the molecular structure analysis. The experimental data we use are from Refs. [7,9] although some parameters vary in the two papers. The FIR assignment [7] has been performed under the supposition that the isolated TFE presents two conformers, gauche and trans. However, the microwave study considers a single gauche minimum. In addition, Xu et al. [9] have determined the gauche±gauche barrier (763 cm 1 ) from the torsional splitting to be higher than the one evaluated by Durig and Larsen [7] from the IR bands (603, 440, 590 and 455 cm 1 for the isotopic species CF3 CH2 OH, CF3 CH3 OD, CF3 CD2 OH and CF3 CD2 OD, respectively). The OH fundamental has been estimated to be 364 cm 1 with microwave spectroscopy from the torsional splittings [9] and it has been assigned to the bands at 281.0 and 272.0 cm 1 observed by far infrared spectroscopy [7]. The tunneling splitting is also dierent (5.9 GHz in Ref. [9] and 28 GHz in Ref. [7]). 2. The torsional Hamiltonian of TFE The roto-vibrational Hamiltonian may be de®ned as the sum of three terms: the vibrational Hamiltonian, Hv , the pure rotational Hamiltonian and the roto-torsional operator [19]. If it is assumed that the two torsional modes of TFE are independent from the remaining coordinates, the torsional terms HT of the vibrational Hamiltonian can be written as:
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
H^T
o o o o B11 B12 oh oh oh oa o o o o B12 B22 oa oh oa oa
V 0 h; a V h; a
1
where the two variables h and a are de®ned as functions of the two dihedral angles F4 C1 C2 O and HOC2 C1 (h 180° \F4 C1 C2 O and a 180° \HOC2 C1 ). V represents the potential energy surface (PES) and V0 is the pseudopotential given by: 2 X 2 1X o o ln g 0 Bkl V 4 k1 l1 oqk oql 2 X 2 o ln g o 1 X o ln g Bkl oqk oql 16 k1 l1 oqk o ln g q1 h; q2 a 2 Bkl oql where g is the determinant of the G 1 matrix [19]. B11 , B22 and B12 are the tri¯uoromethyl torsion, hydroxyl torsion and torsion±torsion interactions, kinetic energy parameters, respectively. They are related to the torsional elements g44 and g55 and g45 of the G matrix by the equations B11 h2 =2g44 , 2 2 B22 h =2g55 and B12 h =2g45 . The complete torsional Hamiltonian of TFE commutes with the symmetry operations of the G6 full-non-rigid Group [23,24] of ethanol-h6 [18]. Therefore, the analytic form for the potential, the pseudopotential, and the kinetic parameters B11 , B22 , and B12 can be described by the symmetry adapted Fourier series that transforms as the totally symmetric irreducible representation of G6 . The analytic expression for the potential energy surface is: XX V h; a Acc NL cos3N h cos La N 0 L0 Ass NL sin 3N h sin La
3
In this paper, the torsional levels are calculated variationally using models in 1D and 2D. In the case of the 1D models, the 1D Hamiltonians are obtained by eliminating the interaction terms from Eqs. (1) and (2). The employed trial functions are
21
series of solutions of the free rotor for the 1D calculations and series of solutions of the double free rotor for the 2D calculations. The intensities of the transitions between different vibrational states are determined with the oscillator strength equation de®ned in Refs. [18,20] for a two-torsional problem. The strength depends on the transition frequency and the dipole moment variation. It depends also on the radius of the internal rotors, the average of the kinetic parameter 1=2 B B11 B22 , the Boltzmann population of the two states, the nuclear statistical weight, q [25]. In the cases of CF3 CH2 OH and CF3 CH2 OD, the nuclear statistical spin weights q are 1 and 0.5 for the Ai and E irreducible representations [18] due to the odd number of particles in 19 F nuclei [25]. For the non-degenerate representations q has been taken equal to 1. For the E two-degenerate representations, the weights are multiplied by two and q has been taken equal to 1 0:5 2. 3. Computational details All the ab initio calculations have been performed with the G A U S S I A N 9 4 program [26] using the Dunning' correlation consistent triple zeta basis set [27] and the M oller±Plesset perturbation theory up to the four order incorporating single, double and quadrupole substitutions (MP4(SDQ)). All the valence electrons have been correlated. The geometry has been optimized in all the selected conformations with the MP2/cc-pVTZ approach. The kinetic parameters have been computed from the optimized geometries with the KNP.f program [28]. The band positions and the intensities have been calculated with the programs UNADIM.f and BIDIM.f [18] that incorporate symmetry conditions. 4. Results and discussion As was expected, the most stable geometry of TFE is a cis±gauche conformer placed at a 115:9° (or 115:9°), although a secondary minimum has been detected at a 0° (see Fig. 1). The two stable geometries can be classi®ed by the
22
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Table 1 Structural parametersa of the two conformers, calculated with MP2/cc-pVTZ C1C2 O3C2 F4C1 F5C1 F6C1 H7C2 H8C2 H9O3 O3C2C1 F4C1C2 F5C1C2 F6C1C2 H7C2C1 H8C2C1 H9O3C2 F4C1C2O3 F5C1C2F4 F6C1C2F4 H7C2C1O3 H8C2C1O3 a
gauche-TFE
trans-TFE
1.5113 1.4039 1.3400 1.3465 1.3339 1.0914 1.0860 0.9620 111.91 110.38 110.54 112.46 107.27 107.87 107.74 182.1 119.1 121.0 124.7 118.1
1.5087 1.4064 1.3437 1.3354 1.3354 1.0911 1.0911 0.9599 107.52 109.19 111.96 111.96 106.92 106.92 107.87 180.0 119.3 119.3 121.6 121.6
and angles are in degrees. Distances are in A,
C1 and Cs point groups. Table 1 shows the structural parameters calculated optimizing the geometry at the MP2/cc-pVTZ level. The largest torsional dependence corresponds to the O3C2C1 bending angle that changes by 4.4° during the OH group internal rotation, (from 111.91° at the gauche conformers to 107.52° at the trans geometry) as was ®rst observed for ethanol [18]. With the OH internal rotation, the CF3 group loses the C3v symmetry. The central bond C1C2 decreases from (gauche) to 1.5087 A (trans) where the 1.5113 A steric interactions are lower. The gauche-TFE parameters can be compared with the experimental ones of Ref. [9]. The torsional coordinate amin determined from the microwave measurements (amin 111° [9]) is 5.8° smaller than the calculated value (Table 2). Except for H9O3, the microwave bond distances are slightly larger than the theoretical ones. The MP2/cc-pVTZ vibrational kinetic parameters, the MP4(SDQ)/cc-pVTZ internal rotational barriers and potential parameters, and the rotational constants of the two conformers, are shown in Table 2. In agreement with experiments, the calculated gauche conformer is the most stable
Table 2 Kinetic and potential parameters of the two TFE conformersa a A B C j B11 B22 B12 V0
gauche-TFE
trans-TFE
115.9 5325.935 2842.173 2812.024 0.97629852 1.10325304 21.46799684 0.94878180 0.02953732
0.000 5346.683 2869.439 2824.998 0.96536335 1.09465528 21.50216697 0.513430049 0.00612807
Calculated
Experimental
1534.0 1490.9 707.5 804.9 681.5
1895 9 1161 10 622 606 19.5
Ref. [7] gauche
V3 trans V3 VOH a 34° VOH a 180° DH
Ref. [10]
763
a The rotational constants, A, B and C are in MHz; the torsional kinetic parameters Bii , the barriers and the pseudopotential V 0 are in cm 1 .
geometry, due to the formation of a hydrogen between the OH hydrogen bond of 2.5004 A and the neighbouring ¯uorine atom. The energy dierence between conformers (DH ) has been calculated to be 681.5 cm 1 , far away from the experimental data determined by Durig and Larsen [7] from the observed FIR frequencies (19.5 cm 1 ). However, the ab initio calculations predict a large dierence of stability between conformers which agrees with the suppositions in Refs. [3,4,8,15]. gauche The tri¯uoromethyl torsion barriers V3 trans and V3 have been evaluated to be 1534.0 and 1490.9 cm 1 , whereas the experimental values of CF3 CH2 OH obtained by a 1D treatment are 1895 9 and 1161 10 cm 1 [7]. The experimen gauche tal V3 of CF3 CH2 OD has been observed to be 1696 10 cm 1 [7]. The calculated hydroxyl torsion trans±gauche, gauche±trans and gauche± gauche barriers occur at a 34°, a 34° and a 180°, and their heights are 26.0, 707.5 and 804.9 cm 1 , respectively. They can be compared with the FIR parameters of 601, 622 and 603 cm 1 [7], respectively. The calculated gauche±gauche barrier is slightly larger than the one of Ref. [7], but coincides with the microwave data of Xu et al.
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
(763 cm 1 ) evaluated from the torsional splitting [9]. In an earlier paper [20], we found a similar behaviour for acetone where the ab initio barrier coincides with the one obtained from microwave data but disagrees with the FIR parameter. The gauche conformer is a near prolate symmetric top j 0:97629852. The calculated rotational constants for the gauche conformation are 5325.935, 2842.173 and 2812.024 MHz. The experimental values for the vibrational ground state are 5318.27299, 2827.6629 and 2798.5618 MHz [9]. The trans-form rotational constants are 5346.683, 2869.439 and 2824.998 MHz. TFE has eight large amplitude motions below 700 cm 1 . In Table 3, the MP2/cc-pVDZ harmonic frequencies of the two conformers, are shown. The gauche frequencies are compared with the experimental data of Ref. [3] and the four experimental trans values are from Ref. [7]. The harmonic approximation appears insucient for describing the OH torsional motion and some CF3 deformations but provides information that can help the assignments. For example, it permits to infer that the
23
spectral analysis requires to consider that two CF3 rocking modes (238 and 363 cm 1 ) and the CCO bending mode (415 cm 1 ) can interact with the two torsional frequencies. As was expected, the calculated gauche OH fundamental (334 cm 1 ) lies below the experimental value (280 cm 1 ). In the case of the trans form, the harmonic approximation predicts a value lower than the one assigned in Ref. [7]. Results obtained in 1D and 2D are compared for evaluating the interactions between the two torsions. The 1D and 2D potential energy surfaces have been calculated by ®tting the energies in Table 4. E h; a are the 2D energies obtained by freezing two coordinates during the geometry optimization. The 1D energies, E h and E a, have been evaluated by freezing only one variable. For this reason, the 1D and 2D selected conformations are not equivalent. The energies have been determined at the MP4(SDQ)/cc-pVTZ//MP2/cc-pVTZ level. The 2D potential energy surface, V h; a, was obtained by ®tting to Eq. (3) the E h; a energies of 26
Table 3 Harmonic frequencies of the two TFE conformers calculated with MP2/cc-pVDZ gauche-TFE m11 m20 m19 m18 m17 m16 m15 m14 m13 m12 m11 m10 m9 m8 m7 m6 m5 m4 m3 m2 m1
trans-TFE
Assignments
Calculated
Experimental [3]
Calculated
Experimental [7]
CF3 tor CF3 rock OH tor CF3 rock CCO bend CF3 def CF3 def CF3 def CC stretch CH2 rock CO stretch CH2 wag COH bend CF3 stretch CF3 stretch CF3 stretch CH2 twist CH2 bend CH2 stretch CH2 stretch OH stretch
121.2 225.9 334.0 406.1 429.6 538.7 554.1 670.4 843.9 965.0 1131.7 1179.5 1231.5 1298.3 1335.2 1413.3 1472.4 1494.1 2985.9 3194.3 3842.2
118 238 280 363 415 549 660 660 780 830 940 1080 1160 1160 1270 1270 1405 1453 2943 2990 3655
105.3 163.5 229.6 359.9 423.7 541.4 558.6 656.1 842.6 1000.6 1145.2 1190.7 1213.2 1282.6 1330.9 1336.7 1509.7 1521.8 3070.6 3130.9 3876.7
105 246 284 363
24
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Table 4 Relative energiesa (in cm 1 ) of the selected conformations in terms of h (CF3 torsion) and a (OH torsion) h
a
E
h
a
E
0 0 0
681.510 1373.253 2172.397
0 90 180
180 180 180
804.886 1321.944 1876.561
0 90 180 90
30 30 30 30
712.186 1512.920 2243.610 1342.513
0 90 180 90
150 150 150 150
434.558 918.359 1727.873 1209.474
0 90 180 90
60 60 60 60
603.783 1439.576 2167.801 1252.737
0 90 180 90
120 120 120 120
15.984 686.040 1539.421 833.470
0 90 180 90
90 90 90 90
198.427 981.390 1755.610 912.185
0 90 180 90
115.1 122.7 118.7 110.0
0.000c 681.096 1533.983 790.912
E ab 0.0 2.5 2.5 0.6
0 30 60 90
681.510 706.252 598.145 198.333
b
E h; a 0 90 180
E h gauche-TFE
trans-TFE 0 90 180 90
2.1 5.4 0.0
0.000d 659.095 1490.887 659.095
0.0 19.0 0.0 19.0
120 150 180
7.307 408.120 804.886
a
Calculated with MP4(SDQ)/cc-pVTZ. E gauche 452:178859 a.u. c E 452:178839 a.u. d E trans 452:175754 a.u. b
conformations selected using symmetry criteria. As is recommended in Refs. [29,30], the calculations have been performed for h 0°, 90°, 180° and 90°. The hydroxyl torsion coordinate has been ®xed at a 0°, 30°, 60°, 90°, 120°, 150° and 180°. The reference structure h; a 0°; 0° is the trans conformation with the methyl group staggered. Three 1D and one 2D surfaces have been determined. V trans h and V gauche h restrict the motion of the methyl group while the OH group remains at the trans or gauche positions. V a hinders the hydroxyl group motion. In this case, the tri¯uoromethyl group remains at its minimum. The three functions are:
V a 443:559 163:974 cos a 266:442 cos 2a 27:206 cos 4a 5:991 cos 6a V trans h 702:269
217:509 cos 3a 8:153 cos 5a in cm 1
745:443 cos 3h
43:174 cos 6h in cm 1 V gauche h 751:498
766:991 cos 3h
54:908 sin 3h 15:494 cos 6h
in cm 1
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
25
The 2D function is: V h; a 1164:534
729:352 cos 3h
15:881 cos 6h 220:828 cos a 199:768 cos 2a
187:749 cos 3a
0:805 cos 4a 1:340 cos 5a 2:115 cos 6a
72:578 cos 3h cos a
68:045 cos 3h cos 2a 28:440 cos 3h cos 3a 19:673 cos 3h cos 4a 3:755 cos 3h cos 5a 0:981 cos 3h cos 6a 7:137 sin 3h sin a 114:885 sin 3h sin 2a 31:646 sin 3h sin 3a Fig. 2. The calculated potential energy surface V h of TFE (g-TFE ±±; t-TFE ± ± ±).
18:340 sin 3h sin 4a 4:195 sin 3h sin 5a 9:522 cos 6h cos a 1:875 cos 6h cos 2a 0:831 cos 6h cos 3a 0:656 cos 6h cos 4a
in cm 1
Figs. 2 and 3 represent the V h and V a potentials, respectively. Fig. 2 shows two lines corresponding to the gauche (continuous line) and trans (dashed line). In Fig. 3, we compare the ab initio PES with the one ®tted by Durig and Larsen [7] from the experimental FIR frequencies. Both curves coincide in the gauche well but dier around the trans minimum showing an unusual behaviour that cannot be explained as a computational error. We have con®rmed that the trans conformer is the unique second minimum. For eliminating the possibility of the existence of a trans±gauche minima, the energies of four geometries, corresponding to values of h lying between 0° and 30°, have been calculated. Our experience [19±22] shows that calculations and experiments are always in very good agreement if the employed ab initio methods are accurate enough. However, the calculations are
Fig. 3. The potential energy surface V a of TFE (±±) compared with the one ®tted from the bands assigned in Ref. [7] (- - -).
performed on isolated molecules and fail when the intermolecular forces are not negligible. In
26
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
accordance with the measurements of Marco and Orza [8] and Orza et al. [15], the TFE behaviour could be explained by the polymerization of some molecules or by the binding of TFE and water molecules in the experimental mixture, that can stabilize the trans conformer. These authors have studied the infrared spectrum shifts caused by the production of TFE complexes with dierent bases by formation of intermolecular FH hydrogen bonds [15]. It can be concluded that some bands observed in Ref. [7] have to be assigned to the dimer spectrum or to the TFE±H2 O spectrum and cannot be attributed to the isolated molecule. The kinetic parameters of the torsional Hamiltonian have been determined with the KNP.f program [28] from the optimized geometries. Table 2 shows the vibrational parameters B11 , B22 , B12 , and V 0 of the two conformers. The values for each conformation have been ®tted to completely symmetric periodic functions. For CF3 CH2 OH the resulting functions are: B11 h; a 1:1239
0:0013 cos 3a
0:0021 cos 4a
0:0002 cos 5a
0:0063
cos 6h
0:7931 cos a 0:5517
cos 2a
0:1259 cos 3a 0:0038 cos 5a
0:0029 cos 6a 0:0620 cos 3h cos a 0:0937 cos 3h cos 2a 0:0482 cos 3h cos 3a 0:0346 cos 3h cos 4a
0:0156 cos 3h
cos 5a 0:0052 cos 3h cos 6a 0:0734 sin 3h sin a
0:0848 sin 3h
sin 2a 0:0553 sin 3h sin 3a 0:0295 sin 3h sin 4a 0:0123 sin 3h sin 5a 0:0044 cos 6h cos a
0:0003 cos 6h cos 2a
0:0003 cos 6h cos 3a 0:0011 cos 6h cos 4a
in cm 1
0:5519 0:0201 cos 3h 0:0022 cos 6h 1:0473 cos a
0:0430 cos a
0:0244 cos 2a
0:0125 cos 3h
0:0183 cos 4a
B12 h; a
0:0155 cos 3h
0:0024 cos 6h
B22 h; a 21:7374
0:0165 cos 2a 0:0196 cos 3a 0:0049 cos 4a 0:0010 cos 5a 0:0005 cos 3h cos a
0:0011 cos 3h cos a
0:0052 cos 3h cos 2a
0:0048 cos 3h cos 2a
0:0052 cos 3h cos 3a
0:0002 cos 3h cos 3a
0:0025 cos 3h cos 4a
0:0006 cos 3h cos 4a
0:0017 cos 3h cos 5a
0:0003 cos 3h cos 5a
0:0005 cos 3h cos 6a
0:0017 sin 3h sin a
0:0059 sin 3h sin a
0:0057 sin 3h sin 2a
0:0111 sin 3h sin 2a
0:0008 sin 3h sin 3a
0:0031 sin 3h sin 3a
0:0005 sin 3h sin 4a
0:0025 sin 3h sin 4a
0:0001 sin 3h sin 5a
0:0011 sin 3h sin 5a
0:0003 cos 6h cos a
0:0009 cos 6h cos a
0:0006 cos 6h cos 2a
0:0006 cos 6h cos 2a
0:0003 cos 6h cos 3a
0:0003 cos 6h cos 3a 1
0:0002 cos 6h cos 4a in cm
0:0003 cos 6h cos 4a in cm 1
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
The independent terms of B11 (tri¯uoromethyl torsion) and B22 (hydroxyl torsion) are 1.1239 and 21.7374 cm 1 close to the ones employed by Durig and Larsen [7] (1.0465 and 20.6949 cm 1 ) for the ®tting of the potential energy surfaces. We omit the transcription of the pseudopotential function V 0 h; a, since its order of magnitude is 1 cm 1 . The relations between cartesian and internal coordinates are also omitted (see Ref. [28]). 5. Assignments The 1D and 2D non-degenerate energy levels Ai of CF3 CH2 OH are compared in Table 5. The 2D gauche energies of the isotopic varieties CF3 CH2 OD, CF3 CD2 OH and CF3 CD2 OD are shown in Table 6. They are labelled using the vibrational quantum numbers (v and v0 ) and the irreducible represent of TFE. The tunnelling eect
27
between the gauche conformers causes a splitting of each gauche level into two sub-components labelled as v and v ; v represents a trans-level. Two properties have been calculated for the labelling of the states: the expectation values of the 1D Hamiltonians on the 2D wave functions and the probability integrals in the potential surface wells (see Ref. [18]). The tri¯uoromethyl barriers produces a splitting of each sub-component into three microstates, one non-degenerate Ai and two degenerate Ei levels, although the Ai E energy dierence is negligible. As a result, nine microstates corresponding to the nine wells of the potential energy surfaces, appear. All levels shown in Table 5 are referred to the calculated vibrational ground state calculated with each model. In gauche-CF3 CH2 OH, the 2D zero vibrational (213.750 cm 1 ) splits into two subcomponents v v0 0 0 and v v0 0 0 at 0.000 and 0.179 cm 1 whereas the energy dierence calculated in 1D is 0.205 cm 1 (Table 5). For
Table 5 Comparison between the non-degenerate energy levels (cm 1 ) of CF3 CH2 OH, calculated in 1D and 2D v v0
a b
Symmetry
1D
2D
Experimental [7]
OH
CF3
0.000a 0.205
0.000b 0.000
0.000c 0.179
0.0 0.95
114.6 114.6 227.3 227.3
115.0 115.0 228.0 228.0
119.8 119.8 238.9 238.9
283.5 286.7 497.2 519.8 698.4 861.5
272.2 281.0
0.0c 112.4 222.9 101.5 293.1
0.0 104.6 206.0 284.2
gauche-TFEa 0 0 00
A1 A2
CF3 torsion 10 1 0 20 2 0
A2 A1 A2 A1
OH torsion 0 1 01 0 2 02 03 04
A1 A2 A1 A2 A1 A2
277.0 280.4 492.4 513.6 692.1 844.3
trans-TFEb 00 10 20 01 02
A1 A2 A1 A2 A1
0.0a 92.9 278.5
0.0b 105.2 209.9
Zero vibrational a 149:5 cm 1 ; b 55:6 cm 1 ; c 213:8 cm 1 . Zero vibrational a 730:1 cm 1 ; b 52:8 cm 1 ; c 792:1 cm 1 .
28
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Table 6 Calculated energy levels of isotopic varieties of gauche-TFE (in cm 1 ) v v0 0 0 0 0 0 0 0 0 1 1 2 2 3 3 4 4 5 5 1 1 2 2 1 1
0 0 1 1 2 2 3 3 0 0 0 0 0 0 0 0 0 0 1 1 1 1 2 2
Symmetry
CF3 CH2 OH
CF3 CH2 OD
CF3 CD2 OH
CF3 CD2 OD
A1 A2 A1 A2 A1 A2 A2 A1 A2 A1 A2 A1 A1 A2 A2 A1 A1 A2 A2 A1 A1 A2 A2 A1
0.0 0.2 283.5 286.7 497.2 519.8 679.9 698.4 115.0 115.0 228.0 228.0 339.0 339.0 447.6 447.6 554.0 554.0 397.5 399.0 509.5 509.6 608.2 628.2
0.0 0.0 217.1 217.3 408.3 409.8 566.5 556.5 111.4 111.4 220.9 220.9 328.5 328.5 433.8 433.8 537.0 537.0 327.6 327.5 436.4 436.3 518.9 517.5
0.0 0.2 283.0 286.1 497.3 519.2 681.6 696.2 106.4 106.4 211.1 211.0 314.0 314.0 415.0 415.0 514.1 514.1 388.2 390.1 491.4 492.6 600.5 620.4
0.0 0.0 216.1 216.2 406.4 408.0 565.1 554.6 103.7 103.6 205.6 205.6 305.9 305.9 404.5 404.5 501.2 501.2 318.9 318.9 420.0 419.9 508.9 508.5
CF3 CH2 OD, CF3 CD2 OH and CF3 CD2 OD, the splitting was found to be 0.005, 0.177 and 0.005 cm 1 , respectively. Experimentally, the FIR values are 0.95 cm 1 (CF3 CH2 OH), and 0.21, 1.0 and 0.19 cm 1 , for the three deuterated varieties [7]. Our calculated splittings agree with those observed by microwave spectroscopy that are 0.2 cm 1 for CF3 CH2 OH and 0.007 cm 1 for CF3 CH2 OD [9]. As V3 is three times higher than the hydroxyl barriers, it produces really a small splitting. It is imperceptible at the lowest energy levels. The trans ground state v v0 0 0 lies at 578.4 cm 1 over the gauche ground state (213.8 cm 1 ) (Table 5). As is evident, the assignment of the levels over the gauche±trans barrier (707.5 cm 1 ) to the trans or gauche conformations is not simple because the eigenfunctions cannot be localized in the wells. The probability integrals around the two minima are identical. For example, the OH torsional level at 679.9 cm 1 could be identi®ed with the ®rst excited trans OH level ( v v0 0 1, Table 5) or with an excited gauche
OH level ( v v0 0 3 , Table 6). The probability integrals around the two minima are identical. The ®rst labelling, that is the most believable, implies the calculated trans OH fundamental 0 0 ! 0 1 to lie at 101.5 cm 1 , far away from the experimental data of Ref. [7] (284.2 cm 1 ). This discrepancy relates to the dissimilarity between our calculated trans±gauche barrier of 26 cm 1 (707.5± 681.5 cm 1 ) and the one arising from the assignment of Ref. [7] (601 cm 1 ). In the case of ethanol [18], the OH torsional mode behaves as an independent mode, whereas the CH3 torsion is aected by the interactions, due to the conditions imposed during the geometry optimization (the number of optimized coordinates is dierent in the 1D and the 2D calculations). In TFE, the dierences between OH levels calculated in 1D and 2D are larger than the CF3 group ones. The OH levels (0 1 ) and (0 1 ) have been determined to be 283.5 and 286.7 cm 1 in 2D and to be 277.0 and 280.4 cm 1 in 1D. The CF3 levels (1 0 ) and (1 0 ) have been determined to be
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
115.0 and 115.0 cm 1 in 2D, and to be 114.6 cm 1 in 1D. The comparison of the gauche levels of dierent isotopic varieties clari®es the assignments (Table 6). We omit the transcription of the trans levels where the dierences between calculations and available experimental data are too large. As in ethanol, the deuteration of the ±CH2 ± group imparts the largest eects on the CF3 levels, which shows the dependencies of the ¯uoromethyl group torsion in other vibrations (Table 5). The two fundamentals shift to 103.6 and 103.7 cm 1 and to 216.1 and 216.2 cm 1 when the molecule is fully deuterated. They are found at 111.4 and 111.4 cm 1 , and 217.1 and 217.3 cm 1 , for CF3 CH2 OD. The corresponding experimental values, assigned by Durig et al. [7], are 112.9 cm 1 (CF3 torsion), 194.8 and 189.4 cm 1 (OH torsion). The prominent Q branches observed in the experimental spectra [7] correspond to Type-C bands. Their intensities depend on the variation of the out-of-plane dipole moment component. For this reason, the dipole moments along the C principal axis of the selected conformations, have been ®tted to symmetry adapted periodic series. The ``in plane'' la , and lb components transform
29
as the totally symmetric representation A1 and the ``out of plane'' lc transforms as the antisymmetric non-degenerate A2 . The analytic form of lc h; a is, lc h; a
0:01746 sin 3h 1:15222 sin a 0:04723 sin 2a
0:09102 sin 3a
0:00157 sin 4a 1:51072 sin 5a 0:00304 cos 3h sin a 0:00083 cos 3h sin 2a 0:00026 cos 3h sin 3a 0:00251 sin 3h cos 2a 0:00011 sin 3h cos 3a 0:00132 sin 3h cos 4a 0:00276 sin 3h cos 5a 0:00171 sin 3h cos 6a
in Debyes
Absolute intensities are adimensional properties determined with the oscillator strength equation [18±20]. Tables 7±9 show the frequencies and intensities of the most prominent ¯uoromethyl torsional bands, hydroxyl torsional bands and
Table 7 Tri¯uoromethyl torsional frequencies (in cm 1 ) and absolute intensities of CF3 CH2 OH and CF3 CH2 OD v v ! v0 v0
a
Symmetry
CF3 CH2 OH
CF3 CH2 OD a
Frequencies
Intensities 10 4
Experimental
Frequencies
Intensities 10 4
trans ! trans 00 ! 10 10 ! 20 20 ! 30
A1 ! A2 A2 ! A1 A1 ! A2
112.4 110.4 108.2
0.073 0.032 0.007
104.6 102.9 99.4
110.7 109.8
0.173 0.515
gauche ! gauche 00 ! 10 00 ! 10 10 ! 20 10 ! 20 20 ! 30 20 ! 30 30 ! 40 30 ! 40 40 ! 50 40 ! 50
A1 A2 A2 A1 A1 A2 A2 A1 A1 A2
115.0 114.9 113.0 112.9 110.9 110.9 108.7 108.7 106.4 106.4
0.009 0.002 0.008 0.003 0.005 0.003 0.003 0.002 0.002 0.002
119.8
111.4 111.3 109.5 109.5 107.6 107.6 105.3 105.3 103.3 103.3
± ± ± ± ± ± ± ± ± ±
! A2 ! A1 ! A1 ! A2 ! A2 ! A1 ! A1 ! A2 ! A2 ! A1
Experimental data are from Ref. [7].
119.1 118.2 116.2 115.0
Experimentala
112.9 112.2 109.9 107.8 106.3
30
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Table 8 Hydroxyl torsional frequencies (in cm 1 ) and absolute intensities of CF3 CH2 OH and CF3 CH2 OD v v ! v0 v0
Symmetry
gauche ! gauche 00 ! 01 A1 ! A2 E!E 00 ! 01 A2 ! A1 E!E 01 ! 02 A2 ! A1 E!E 01 ! 02 A1 ! A2 E!E trans ! trans 00 ! 01 A1 ! A2 E!E 01 ! 02 A2 ! A1 E!E
CF3 CH2 OH
CF3 CH2 OD 4
a
Frequencies
Intensities 10
Experimental
Frequencies
Intensities 10 4
Experimentala
286.7 286.7 283.3 283.3 210.5 210.5 236.3 236.3
21.73 21.73 23.16 23.16 4.03 4.03 2.08 2.28
284.2
217.3 217.3 217.1 217.1 192.7 192.7 191.1 191.1
14.24 14.24 14.27 14.27 5.11 5.11 5.40 5.40
194.3
101.5 101.5 191.6 191.6
1.78 1.78 3.01 3.01
281.0 >200 and <250
54.4 54.4
194.8
185
0.308 0.308
Table 9 Frequencies (in cm 1 ) and absolute intensities of the combination bands CF3 CH2 OH and CF3 CH2 OD v v ! v0 v0
10 10 01 01 11 11 11 11 20 20 a
! 11 ! 11 ! 11 ! 11 ! 21 ! 21 ! 12 ! 12 ! 21 ! 21
Symmetry
A1 A2 A1 A2 A1 A2 A1 A2 A1 A2
! A2 ! A1 ! A2 ! A1 ! A2 ! A1 ! A2 ! A1 ! A2 ! A1
CF3 CH2 OH
CF3 CH2 OD
Frequencies
Intensities 10 4
Experimentala
Frequencies
Intensities 10 4
Experimentala
282.5 284.1 114.0 112.3 110.5 112.0 209.2 230.7 281.6 281.6
12.33 12.13 0.03 0.04 0.04 0.02 1.76 1.54 6.70 6.48
'284
216.3 216.1 110.5 110.4 108.8 108.8 191.3 189.9 215.4 215.5
7.07 7.07 ± ± 0.03 0.03 2.79 2.28 4.39 4.39
'194
<200 and >250 '284
'185 '194
Experimental data are from Ref. [7]. Bold numbers correspond to our predictions.
combination bands. Some E bands are excluded from the tables because the intensities of the Ai and E components of each transition are identical. The experimental frequencies shown in the tables are from Ref. [7]. The calculations allow to predict approximate band positions where the experimental spectra shows protuberances. The dipole moment c-component depends strongly on the hydroxyl torsion and slightly on the ¯uoromethyl torsional coordinate. For this reason, it may be expected that the OH internal rotation transitions yield the largest intensities.
5.1. The CF3 CH2 OH spectrum In Fig. 4, the calculated and experimental far infrared spectra of CF3 CH2 OH, are compared. The water spectra is shown on the top of the ®gure. The region of the weak tri¯uoromethyl group transitions has been ampli®ed. As was expected, the most intense bands correspond to the OH torsional mode which produces the largest variation of the dipole moment. The gauche±gauche bands of the CF3 mode (Table 7) are of very low intensity and the frequencies are in
M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
Fig. 4. The calculated far-infrared spectrum of CF3 CH2 OH (C) compared with the experimental one (A) recorded in Ref. [7] with an eective resolution of 0.10 cm 1 . The experimental CF3 torsional bands can be observed on the B spectrum.
good agreement with the experimental data [7]. The calculated CF3 trans±trans bands (Table 7) lies among the gauche±gauche bands whereas the corresponding assigned frequencies are lower. The OH torsional fundamental frequencies 00 ! 01 and 00 ! 01 have been calculated to be 286.7 and 283.3 cm 1 con®rming the assignment of Durig and Larsen [7] to the pattern observed near 280 cm 1 (Table 9) and refuting the assertion of Xu et al. [9] who predicted the OH fundamental to lie at 364 cm 1 using the torsional splittings. However, the calculated intensities of the two gauche-transitions are almost identical (21:73 10 4 and 23:16 10 4 ), and contradict the assignment of Durig and Larsen [7] to the two bands of dierent intensity observed at 281.0 and 272.0 cm 1 . In addition, the calculations do not predict strong bands around 270 cm 1 .
31
On the basis of the calculated potential shape, it can be proposed a new interpretation for the band observed at 284.2 cm 1 , that was assigned to the OH trans fundamental in Ref. [7]. It has to be taken into account that the trans fundamental has been calculated far away at 101.5 cm 1 (679:9 792:2 213:8 cm 1 ). The two bands observed at 284.2 and 281.0 cm 1 shows similar intensities and they can be related to the two components of the gauche OH fundamental, 00 ! 01 and 00 ! 01 . Two combinations bands have been calculated near the OH gauche fundamentals. The calculated intensities of the transitions at 10 ! 11 and 10 ! 11 at 282.470 and 284.1 cm 1 are 12:33 10 4 and 12:13 10 4 . The calculations provide sets of strong bands near 210 cm 1 and near 230 cm 1 , where some experimental patterns were observed but were not assigned. For example, the OH ®rst sequence 01 ! 02 and 01 ! 02 have been calculated at 210.5 and 236.3 cm 1 and two combination bands have been found at 209.2 and 230.7 cm 1 . There intensities are 4:03 10 4 , 2:08 10 4 , 1:76 10 4 , and 1:54 10 4 , respectively. The remaining bands are of low intensity. Two strong transitions 20 ! 21 and 20 ! 21 are calculated to be around 281 cm 1 . 5.2. The CF3 CH2 OD spectrum The calculated frequencies of the gauche±CF3 transitions (Table 7) con®rm previous assignments [7]. The strongest bands correspond to the OD torsional mode. The frequencies of the 00 ! 01 and 00 ! 01 transitions have been determined to be 217.3 and 217.1 cm 1 and the intensities of the nondegenerate components 14:24 10 4 and 14:27 10 4 . As in the case of the OH isotopomer, the two components show similar strength for this reason, they can be reassigned to the bands observed at 194.3 and 194.8 cm 1 , that are of the same intensity. Durig and Larsen [7] have assigned these two transitions to the two bands observed at 194.8 and 189.4 cm 1 . Some strong transitions are predicted near 190 cm 1 and may be assigned to the bands observed
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M.L. Senent et al. / Chemical Physics 266 (2001) 19±32
near 185 cm 1 . The A transitions of 01 ! 02 and 01 ! 02 lie at 192.7 and 191.1 cm 1 and show intensities of 5:11 10 4 and 5:40 10 4 . The calculated intensities of the combination bands at 191.4 and 189.9 cm 1 are 2:79 10 4 and 2:28 10 4 , respectively. Two strong combination bands are calculated near 215 cm 1 in the region of the OH gauche fundamentals. In CF3 CH2 OD the pattern of strong intensity observed in the experimental spectra near 250 cm 1 has been assigned to a CF3 rocking mode that has been neglected in the calculations and can push the torsional band to the lower frequencies. This vibrational eect could explain why the differences between calculations and experiments are larger for the deuterated species. Acknowledgements This work has been supported by the ``Consejerõa de Educaci on y Cultura'' of the Castilla and Le on Community, Spain (BU07/97), and the ``Vicerectorado de Investigaci on y Relaciones Internacionales'' of the University of Burgos, Spain. M.L. Senent acknowledges Prof. J.M. Orza (C.S.I.C.) for all his useful help. References [1] H. Sticht, D. Willbold, P. R osch, J. Biochem. Struct. Dyn. 12 (1994) 019. [2] P.J. Krueger, H.D. Mettee, Can. J. Chem. 42 (1964) 340. [3] A.J. Barnes, H.E. Hallam, D. Jones, Proc. R. Soc. Lond. A 335 (1973) 97. [4] J. Travert, J.C. Lavalley, Spectrochim. Acta 32A (1975) 637. [5] M. Perttil a, Spectrochim. Acta 35A (1978) 585. [6] V.F. Kalansinsky, H.V. Anjaria, J. Phys. Chem. 84 (1980) 1940. [7] J.R. Durig, R.A. Larsen, J. Mol. Struct. 238 (1989) 195. [8] J. Marco, J.M. Orza, J. Mol. Struct. 267 (1992) 33. [9] Li.-H. Xu, G.T. Fraser, F.J. Lovas, R.D. Suenram, C.W. Gillies, H.E. Warner, J.Z. Gillies, J. Chem. Phys. 103 (1995) 9541.
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