Theoretical calculations of the torsional spectra of ortho-, meta-, and para-fluorophenols

Journal of Molecular Structure (Theochem), 149 (1987) 127-137 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

THEORETICAL CALCULATIONS OF THE TORSIONAL OR THO- , ME TA- , AND PARA- FLUOROPHENOLS*

YVES G. SMEYERS

SPECTRA OF

and A. HERNANDEZ-LAGUNA

Znstituto de Estructura de la Materia, C.S.Z.C. Serrano, 119, 28006 Madrid (Spain) (Received 24 February 1986)

ABSTRACT The influence of the tilt of the CO bond on the torsional far-infrared (FIR) spectra of ortho-, meta-, and para-fluorophenols is analyzed using two different approaches: The symmetric rigid rotor approximation and the asymmetric rotor approximation, each of them both with and without tilt. In all the calculations, the CNDO/B method was used to determine the minimum energy tilts, as well as the potential-energy functions for the internal rotation of the hydroxyl moiety. Different tilt values were found, and employed in the calculations, for the cis- and trans-isomers of the ortho- and meta-derivatives. An improvement of the calculated transition energies was found with increasing complication of the model, when compared with the known experimental data. The importance of the tilt, a proper selection of the rotation axis, and the possible deformation of the phenylene ring, for the FIR torsional spectra of these fluorophenol compounds are discussed. INTRODUCTION

The far-infrared spectra (FIR), corresponding to the internal rotation of the methyl moiety in toluene, and the torsion of the hydroxyl group in phenol and m-fluorophenol, have been calculated theoretically using the symmetrical rotor approach [l, 21. The FIR spectrum of toluene has not been measured. The theoretical values obtained for phenol and m-fluorophenol were in reasonable agreement with experimental data. In these calculations the hydroxyl group was first considered to be a symmetrical rotor. In addition, the C-O bond and the rotation axis were both supposed to coincide with the symmetry axis of the phenyl group. There is experimental evidence, however, to show that the C-OH bond is somewhat tilted [3-6]. In a second approach, the FIR spectrum of phenol was computed by assuming the asymmetry of the rotor, as well as a tilt of the C-OH bond [7]. An appreciable improvement of the frequencies was found with increasing complexity of the model, when compared with experimental data. In the present work, we extend these approaches to the torsional spectra of ortho-, meta-, and para-fluorophenols. No reliable FIR spectra of the ortho- and para- derivatives are available, but that of meta-fluorophenol in the gas phase is well known [ 81. An improvement in the FIR spectrum values of this compound is found with these new approaches over those of previous calculations [ 11. *Dedicated to Professor Gerhard Herzberg. 0166-1280/87/$03.50

0 1987 Elsevier Science Publishers B.V.

128 THEORY

The torsional spectrum calculations for mono-fluorophenols were carried out in the rigid rotor and Born-Oppenheimer approximations, neglecting the interaction with the other vibrational modes. Only the CC0 angle was optimized for all the conformations considered. Neglecting the coupling with the overall rotations, the classical torsional Hamiltonian function of a planar asymmetric rotor, linked to a planar frame, may be written as: Jc =C(r(W2 + V(d)

(1)

where & is a torsional parameter depending in a complicated way on the torsional angle 0, and V(O) is the potential-energy function. As is well known, the j+ parameter may be expanded into a trigonometric series [ 9] : pT(d) = ,..i; + &’

cos 6 + pjyz) sin2 6 + . . .

(2)

where &., pq), p(r2’, etc., are functions of the components of the moments of inertia of both the frame and the rotor. Expressions for these parameters can be found in [ 91. In order to write down the correct quantum mechanical Hamiltonian operator, the kinetic term of eqn. (1) must be symmetrized: (3) After introducing (2) and (3) in (l), it is easily found that:

[+I$

K = f

c0s

ke f

- fk c0s ke]

+ v(e)

(4)

k=O

where

(5) B2 +&)

+ 3,&’

f2

=

I.@)

In the same way, the potential-energy function may be expanded in terms of trigonometric functions of the torsional angle: v(e) = f k=O

(A; cos k0 + Ai sin kd)

(6)

129

Since the frame and the rotor of the molecules under study possess a symmetry plane, the potential-energy function expansion will not contain any sine functions [lo]. So, after including the fk corrections, which are indeed very small, into the coefficients of the potential, the Hamiltonian operator may be written as: X =

c [-13k;cos kt’ -$+A$

cos kt9-j

k=O.l,..

Generally, the expansions appearing in eqn. (7) converge rapidly, and only a few terms of each of them need to be considered. In the case of a symmetric rotor, the kinetic contribution terms are reduced to the rotational constant B,,, the value of which is given by the classical formula [ 111 : p;(e)

= 330 = +i/21,

(9)

where 1, is the reduced moment of inertia of the rotor. In order to solve Schriidinger’s equation, corresponding to the Hamiltonian operator (7), the torsional wave-functions are developed on the basis of the free rotor solutions [2, 111 : \ki=

1

[C& cos kf3 -I-Cfk sin k0 ]

(9)

k=O

The coefficients of these expansions are determined variationally. As is well known, eqn. (7) has different symmetry solutions which may be classified according to the irreducible representations of the “nonrigid” symmetry group of the molecule. In the case of para-F-phenol, which belongs to the symmetry group G 4, isomorphous with the CzV group, these solutions may be ordered in the representations Al and AZ, or B1 and Bz , according to the parity of thenumber k in eqn. (9). In the same way, they can be arranged in the representations A 1 and B1 or A2 and &, according to the parity of the trigonometric functions appearing in eqn. (8). In the case of ortho- and netu-F-phenols of lower symmetry (C,), the solutions can be classified as the representations Al or AZ, according to the parity of the trigonometric functions. The absolute FIR intensity of a transition between two levels Ei+ ef is closely given, in the rigid frame scheme, by the expression [ 21: Iif=

,&(Ej-Ef)(Ci-Cf)

~i’~~~2

(10)

where Ci and Cf are the populations of the initial and final states respectively, *i and 9,, the corresponding wavefunctions, solutions of (9); R is the radius of rotation, e is the elemental electron charge, and ~(0) the dipole-moment vector, expressed as a function of the rotation angle, 6. Again, the two components of the dipole moment can be expanded into a trigonometric series. Because of their vectorial nature, they may be classified into the representa-

130

tions B1 or Bz in the case of par-u-F-phenol, and AI or A2 for ortho- and meta-F-phenols [ 71, Taking into account the symmetry of the initial and final states, as well as that of the components of p(e), the following selection rules may be easily deduced [ 71 for pam-F-phenol: Al +Bl ++B1 A2

Al ++B2 A2 +B2

(11)

Because no variation of the dipole moment along the rotation axis is considered, the transitions A1 * Al ,A2 * A*, B1 0 B1 and Bz * Bz are forbidden. In contrast, all the transitions are allowed from the point of view of symmetry for ortho- and me&-fluorophenols. It must be remarked that, in the scheme of the theory of the asymmetric double well of potential energy, the lowest solutions are strongly localized alternatively in one of the minima of the double well [ 11. Besides, the transitions between states localized in different minima of the well, i.e., occuring by tunnelling through the energy barrier, are practically forbidden [l]. This result means that, in fact, two different chemical species exist during a certain time. The species are the planar “cis” and “trans” ortho- or me&-F-phenol rotational isomers, the configurations of which correspond to the two minima of the energy double well. The lifetime of these two species will depend on the height,and thickness of the energy barrier, because of the tunnel effect, and also on temperature, since transitions may occur inside the branches of the well up to the top of the barrier [ 11. As a result, the following selection rules are obtained for the lowest levels of ortho- or me&-F-phenols: cis ff cis

trans 4-btrans

(12)

From the rotational energies 4 the populations C, of expression (9) are determined as a function of temperature. CALCULATIONS

Conformational calculations The conformational calculations were carried out by the well known CND0/2 procedure with standard parametrization, since this method was found to yield reliable results for the rotational barrier of phenol [I, 2, 7, 121 , as well as for the tilt of this molecule [7]. In these calculations the phenylene radical was considered as a regular hexagon with internulcear distances C-C = 1.394 A and C-H = 1.084 8, and bond angles LCCC = LCCH = 120”. The structural parameters of the hydroxyl group were C-O = 1.36 a, O-H = 0.985 A and LCOH = 111.87”. Finally, those of the fluorine substituent were C-F = 1.354 8, and LCCF = 120”. In a first step, the deviation angles, Ar (tilt), between the CO bond and the rotation axis are determined in the planar conformation of the paru-F-

131

phenol, and of the cis and trans ortho- and meta-F-phenol molecules. The rotation axis is assumed to coincide with the Cz symmetry axis of the phenyl group [7]. For this purpose, calculations were performed for values of AT from -6” to +6” in the plane of the molecule, at both sides of the rotation axis. The negative values of the tile correspond to structures in which the OH bond crosses the rotation axis. Figure 1, the corresponding potential-energy curves, are given as a function of the tilt angle, for the cis and trans isomers of ortho-F-phenol. It is seen that the cis isomer presents a minimum at -2”, and the tram isomer at -3”. The cis conformation is found to be slightly more stable, as was to be expected. A similar result was found for meta-F-phenol. In contrast, the more symmetric para-F-phenol molecule presents two equivalent minima at -3”. These values for the tilt of the CO bond were in reasonable agreement with the theoretical value encountered for phenol [7, 13, 141, as well as with experimental data [ 3-61. In a second step, the potential-energy functions for the hindered rotation

L -6

-4

-2

I

I

I

I

2

4

6

8

r (7

Fig. 1. Potential-energy curves for the tilt of the C-O bond of ortho-fluorophenol, tained in the planar cis (0) and tram (A) configurations, by the CNDO/B procedure.

ob-

132

of the hydroxyl moiety around the Cz symmetry axis of the phenyl group were determined for the three mono-F-phenol molecules, for the three tilt angle values: 0”, -2” and -3’. The total energy value was computed every 22.5”, for conformations from 0” to 90”, and from 0” to HO”, for thepara-, ortho- and meta-compounds, respectively, taking the planar cis conformation as the origin of the rotations. The variations of the dipole-moment components were also obtained. The expansion coefficients of the potential-energy functions (6), fitted by a leastsquare procedure, are given in Table 1. It is seen that the expansions converge well, especially when AT # 0, so that only six terms were retained. Notice that the expansions for the para derivative contain only terms with even lz values, which is in accordance with [lo] . The fk corrections were not introduced in these expansions because their influence on the results was shown to be insignificant in the case of phenol [ 71. Calculations of the spectrum Schrodinger’s equation for the hindered internal rotation, corresponding to operator (7), was solved in the symmetric and asymmetric rotor approximations for the three fluorphenols considered and for the three tilt angle values, i.e., using the potential-energy functions of Table 1. For this purpose, the program described in [2] was employed, but modified for taking into account the contributions of the higher kinetic terms. The intensity calculation, according to eqn. (lo), was included in the same program. As we are mainly interested in the transitions between the most populated levels, i.e., the lowest ones, the expansion of the wave function (9) was limited to 16 cosine functions (including the constant term) and 15 sine functions. The rotational parameters of the expansion (7) employed in these compuTABLE 1 Expansion coefficients (cal mol-‘) obtained with the CNDO/B approximation for the potential-energy functions for the internal rotation of the hydroxyl moiety, with different tilt values, AT, of different fluorophenols Molecule

-40

-4,

A,

-4,

A,

-4,

o-F-phenol m-F-phenol p-F-phenol

2320.4 1790.8 1490.7

-654.6 -88.0 -

-1518.2 -1613.1 -1397.4

-38.6 1.2 -

-101.9 -88.2 -90.6

-3.1 0.1 -

4.0 2.6 2.7

-2

o-F-phenol m-F-phenol p-F-phenol

2198.3 1794.9 1542.3

-553.9 -44.6 -

-1537.0 -1675.6 -1464.5

-22.4 0.3 -

-80.9 -73.1 -75.8

-1.4 0.0 -

2.7 1.9 2.0

-3

o-F-phenol m-F-phenol p-F-phenol

2114.2 1758.8 1545.9

-506.7 -17.4 -

-1518.8 -1674.8 -1465.8

-15.9 0.9 -

-71.0 -65.7 -68.4

-0.8 0.0 -

1.0 0.0 1.7

A7

0

4 --

133 TABLE 2 Rotational constants (Cal mol-‘) obtained with different tilt values in the symmetric and asymmetric (A) rigid planar rotor approximations for different molecules Molecule

S

A

&I

6,

B,

B2

4

(8’)

&

0

o-F-phenol m-F-phenol p-F-phenol

57.57 57.60 57.83

59.31 59.30 59.36

-0.71 0.03 -

0.81 0.51 0.19

-0.00 0.00 -

0.038 0.016 0.003

82

o-F-phenol m-F-phenol p-F-phenol

62.95 62.98 63.21

63.05 63.07 63.29

-0.12 0.07 -

0.04 0.03 0.09

0.00 0.00 -

0.000 0.000 0.000

93

o-F-phenol m-F-phenol p-F-phenol

63.53 63.55 63.78

63.58 63.61 63.85

0.21 -0.09 -

0.03 0.02 0.06

0.00 0.00 -

0.000 0.000 0.000

tations were determined in a previous calculation. These are given in Table 2, where it is seen that the expansions converge well, especially when A7 % -3”, i.e., when the center of gravity of the hydroxyl moiety coincides approximately with the rotation axis [7]. They were limited, therefore, to h G 4, in the case of the asymmetric rotor; otherwise, only one term was necessary (8). In the same way, only one term was employed in the expansions of the dipole-moment components. RESULTS

AND DISCUSSION

The calculated torsional FIR spectra found for the three mono-fluorophenol compounds are considered below. These spectra possess the typical doublet structure corresponding to a double potential-energy well. Since the experimental FIR spectrum of me&-F-phenol is well known, we will discuss its theoretical calculation more extensively. Table 3 shows the six most intense transition energies encountered for this molecule by using four different approaches: the symmetric (S) and asymmetric (A) rigid rotor approximations, with and without tilt of the CO bond. They correspond to the transitions between the lowest torsional levels, cis or tram, according to the selection rules (eqn. 12). The nature, cis or tram, of the torsional states was determined by inspection of the localization of the wave function in the double well. In addition, in the results where the tilt is considered, the values of AT = -2” and -3” are used for the cis and tram “isomers”, respectively, so that some interaction is introduced between the torsion and the bending mode of the COH angle in the plane of the molecule. In the same Table the experimental values for the transitions, are given, as well as the calculated and measured intensities at 50” C [8] .

134 TABLE 3 FIR torsional spectrum of mete-fluorophenol (transition energies in cm-‘), and intensities), calculated with different approximations, (8) rigid symmetric rotor, and (A) asymmetric rotor approximation (AT is the tilt used in the calculations)

AT (“1

Experimentalb

-2

Transition energy

Intensities (%)

318 311 288 281 256 248

100 100 75 62 32 30

or -3a

Transition energies

Transition energies

S

A

S

A

303.2 298.7 267.3 261.3 225.6 219.0

308.3 303.7 270.1 264.8 226.8 220.8

316.3 314.1 279.0 277.1 240.1 232.2

316.6 314.1 279.2 277.1 240.1 232.2

aA = -2” and -3” intensities X 10.

Sym.

IntensitiesC A

c-*c

0.120 0.110 0.050 0.046 0.013 0.015

T+T

c+c T-+T T-T c-+c

for the (C) cis and (T) tram isomers, respectively. bRef. 8. =Absolute

As was to be expected, the asymmetric rotor approach gives a better fit for the experimental data when AT = 0. The introduction of the tilt of the C-O bond in the calculations furnishes a second improvement, but the results are similar for the symmetric and asymmetric approaches. It seems interesting to point out that in the deformed structure the oxygen and hydrogen atoms rotate approximately around their center of mass, which is situated at -2.2”. The agreement of the theoretical results with experimental data decreases with increasing excitation of the levels involved in the transition. This fact may be attributed to the failure of the rigid-rotor approximation, i.e., to the interaction of the torsion with other vibrational modes. In this sense, it must be remarked that the use of different tilt values for the cis and truns “isomers” significantly improves the results, especially in the cases of transitions between the higher excited levels in which a shift of 5 cm-’ towards the experimental values is observed. If we consider now the splitting values between the doublets found in the case of meta-F-phenol, it is seen that they are too small when compared with the experimental ones. This result means that the energy difference between the two branches of the potential-energy well is too small [l] . This incorrect shape of the potential-energy function may have two explanations: (1) the CNDO/B procedure is not good enough for describing the interactions between the rotor and the frame; (2) the rotation axis does not coincide any more with the Cz symmetry axis of the phenyl group, or, more explicitly, the phenylene group loses its hexagonal symmetry. We believe that the second hypothesis is probably the correct one. The CNDO/B procedure indeed gives the correct splitting values for phenol [ 71. In addition, as it will be seen, the splitting error appears to be larger for ortho-F-phenol, in which more distortion of the phenylene group may be expected [ 141.

135

The absolute intensities obtained for these six transitions of the meta-Fphenol are also in good agreement with the experimental data, taking into account that the experimental values correspond to the heights of the peaks [8] . An estimation of the areas of the bands seems to be impossible. Table 4 gives the six most intense transition energies, calculated in the same way for ortho- and para-F-phenols in the asymmetric rotor approximation with tilt of the CO bond. They correspond to transitions between the lowest torsional level, cis or tram, according to the selection rules (12) in the case of o&o-F-phenol; and Al and &, or B1 and AZ, according to (11) in the case of Par-u-F-phenol. It is seen that the ortho-F-phenol FIR spectrum virtually loses its doublet structure, because of a crossing of the cis and truns levels. This feature is due to the larger energy difference between the two branches of the potentialenergy well. The calculated spectrum agrees relatively well with the experimental one, which presents three bands of decreasing intensities at 379, 342 and 319 cm-’ [ 151. However, the second and third bands have been assigned in ref. 15 to the tram and cis isomers, which is probably incorrect. The splitting between the first doublet, i.e., between the cis-cis and tram--tram transitions is again, too small at 41 cm-‘, when compared with the experimental one (60 cm-‘). The calculated frequencies are also too low. Both defects may again be attributed to a distorsion of the phenylene ring, and to an incorrect selection of the rotation axis. Returning to Table 4, it is seen that pum-F-phenol possesses an FIR spectrum which is very similar to that of phenol, but at slightly lower frequencies. Unfortunately the experimental spectrum is not well known. Only one band at 280 cm-’ measured in cyclohexane is given in the literature [ 161. It seems interesting to point out that the torsional spectrum of ortho-F-phenol measured in the same solvent shows a shift of 10-15 cm-’ relative to that in the TABLE 4 FIB torsional spectra of ortho- and para-fluorophenols (transition energies, in cm-‘, and intensities) calculated in the asymmetric approximation (AT is the tilt used in the calculations) Para-fluorophenol

Ortho-fluorophenol A~=-2’or-3’~

AT=+?

Transition energies

Absolute intensities X 10

Sym.

323.3 285.9 282.5

0.194 0.079 0.037

C+C C-C

244.5

0.027

239.1 180.8

0.017

aA,

= -2”

0.006

T+T C-*C T-T T-+T

Transition energies

Absolute intensities

295.4 295.2 257.6 254.1 223.9 195.3

0.104 0.104 0.047 0.046 0.018 0.015

and -3” for the (C) cis and (T) tmns isomers, respectively.

X

10

Sym.

B, A, 4, B, B, -4,

--+A, +B, +S, -‘A, +A, -+B,

136

gas phase [ 151. Thus, the calculated value for the most intense transition of para-F-phenol, 295 cm-‘, seems to agree fairly well with the experimental one. CONCLUSIONS

In this paper the far-infrared spectra corresponding to the torsion of the hydroxyl moiety in the monofluorophenol molecules have been calculated by two different approaches: The symmetric and asymmetric rotor approximations, each of them both with and without tilt of the CO bond. The minimum-energy tilt values of the CO bond in the planar conformations of the molecules were calculated by the CND0/2 method. Different tilt values were found for the cis and trans structures of the ortho- and metuderivatives, and used in calculations of the spectra. The inclusion of the tilts in these calculations significantly improves the frequency distribution as compared with the known experimental data, especially in the symmetric approximation. In particular, the use of different tilt values for the cls and trans isomers provides an improvement of 5 cm-’ in the transition energies between the higher levels of me&-F-phenol. In the case of the ortho- and, especially, the metu-derivatives the calculated spectra (transition energies and intensities) agree relatively well with the known experimental data. The reasons for the main deviations of the theoretical calculations must lie in the use of a non-deformed phenyl ring and of an incorrect roation axis. Calculations are in progress in this laboratory to solve this difficulty. In the case of the para derivative, the present calculations seem to offer a good approach for the FIR spectrum. REFERENCES 1 Y. G. Smeyers, Folia Chim. Theor. Lat., 5 ( 1977) 27. 2 Y. G. Smeyers, A. Hernandez-Laguna and P. Galera-Gomez, An. &trim., 76 (1980) 67. 3 H. Forest and B. P. Dayley, J. Chem. Phys., 45 (1966) 1736. 4 H. D. Bist, J. C. D. Brand and D. R. Williams, J. Mol. Spectrosc., 24 (1967) 402. 5 J. V. Knopp and C. R. Quade, J. Chem. Phys., 48 (1968) 3317. C. R. Quade, J. Chem. Phys., 48 (1968) 5490. 6 T. Pederson, N. W. Larsen and L. Nygaard, J. Mol. Struct., 4 (1969) 59. 7 Y. G. Smeyers and A. Hernlndez-Laguna, Int. J. Quantum Chem., 22 (1982) 681. 8 A. S. Manocha, G. L. Carlson and W. G. Fateley, J. Phys. Chem., 77 (1973) 2094. 9 C. R. Quade and C. C. Lin, J. Chem. Phys., 38 (1963) 540. C. R. Quade, J. Chem. Phys., 47 (1967) 1073. J. V. Knopp and C. R. Quade, J. Chem. Phys., 48 (1968) 3317. 10 J. Maruani, A. Hernandez-Laguna and Y. G. Smeyers, J. Chem. Phys., 63 (1975) 4515. 11 J. D. Lewis, T. B. MaIIoy, T. H. Chao and J. Laane, J. Mol. Struct., 12 (1972) 427. 12 C. Sieiro, P. Gonzalez-Diaz and Y. G. Smeyers, J. Mol. Struct., 24 (1975) 345. 13 G. Bertholon, C. Decoret, M. Perk, J. Royer, A. Thozet and B. Tinland, Int. J. QuanA. Thozet, G. Bertholon, C. Decoret and tum Chem., 19 (1981) 1167. M. Perk, J. Royer. J. Mol. Struct., 70 (1981) 87. 14 H. Konschin, Low-Frequency Raman Spectroscopic and STO-3G Molecular Orbital

137 Investigations of some Hydroxyand Methoxy-substituted Benzenes, Ph.D. Thesis, University of Helsinki, 1985, and references therein. 15 G. L. Carlson, W. G. Fateley, A. S. Manocha and F. F. Bentley, J. Phys. Chem., 76 (1972) 1553. 16 W. G. Fateley, G. L. Carlson and F. F. Bentley, J. Phys. Chem., 79 (1975) 199.