The Journal of Physical Chemistry, Vol. 82, No. 2, 1978 245
Cornmunicatlons to the Editor
(8) J. 0. Hirschfelder, C. F. Curtiss, and R. 6. Bird, “Molecular Theory of Gases and Liquids”, Wiley, New York, N.Y., 1954.
trans (stag1
cis
u
trans (eclip)
H
I. E. Kleln B. S. Rabinovllch”
Department of Chemistry University of Washington Seattle, Washingon 98 195 Received August 1, 1977
H-0
0
0
H ‘
AH = 0.544 kcal mol.‘
AH = 0 kcal mol.’
Rotational Isomers of o-Cresol
troversy. Our MO calculations using the CND0/2 method have predicted the existence of three stable rotational isomers, one cis (most stable) and two trans of equal stability. Figure 1 gives the conformations of the three isomers. Trans (stag) and trans (eclip) have the H atom of the CH3 group lying in the plane, away from and toward the OH group, respectively. Table I compares the calculated and experimental values of isomerization energy (AH),the potential barrier height for the CH3 group (VCHs) and the OH group ( VOH), and torsional frequencies due to the OH group (v,) for the three rotational isomers of o-cresol assuming that the three OH torsional bands belong to three isomers. Allinger et a1.,6using the molecular mechanics method, found that three conformations are possible with the trans being more stable than the cis, which is not in accord with our findings. According to Carlson and Fateley, the band a t 297 cm-’ belongs to the trans (stag). If the band at 322 cm-l belongs to the cis isomer, the potential barrier height for the cis is higher than that for the trans isomer and the cis is more stable than the trans. Our MO calculations have predicted the same. It may be seen from Table I that there is good agreement between the calculated and observed torsional frequencies. However, that is misleading. Our calculations show that the energy difference between the trans (stag) and trans (eclip) is almost negligible and the CH3 group can be treated as a free rotor. If so, only one OH torsional band should be observed for the trans conformer. Our calculations obtained 280 and 274 cm-l for the trans (stag) and trans (eclip) respectively while the observed values are 297 and 266 cm-l. We feel therefore, that either 297 or 266 cm-I is the OH torsional frequency for the trans isomer. As the observed OD torsional frequency3 corresponds to 297 cm-’ of OH and the OH torsional frequencies for xylenols7can be very well predicted using 297 cm-l, we feel 297 cm-l is the proper choice for torsional frequency and 266 cm-’ is present due to some kind of splitting.s In reality, the potential energy for internal rotation is an inseparable function of both torsional angles, and 0022-3654/78/2082-0245$0l .OO/O
Figure 1. Three rotational isomers of o-cresol.
Flgure 2. Potential energy curves for (a) OH and (b) CH3 rotors.
observed transitions among internal rotational energy levels cannot be directly associated with any particular rotational configuration. Fortunately, the values of thermodynamic functions calculated from a partition function are not very sensitive to the values assigned to the individual energy levels, as long as the overall distribution of energies is approximately correct. Thus we can expect to calculate reasonably good thermodynamic functions of o-cresol by assuming a mixture of two or three rotational species in which the OH and CH3 rotations are independent. The available information on the potential energies for internal rotation, assuming no interaction between CH3 and OH groups, is summarized in Figure 2. The internal rotation energy levels of the OH group were calculated from the two types of potential functions:
v = 1/2Vz(1-
cos 28)
(5
(1)
=2
and
v = 1 / 2 v,(1- COS e ) +
- COS 20)
(2)
o = l
where d is the rotational angle and 6, the symmetry number. In case of cis-o-cresol the internal rotation energy levels of the CH3 group were calculated from the function
v = ~ / ~ v , ( ~ - c o s o~ =~ 3) (3) In trans-o-cresol, the CH3 group was assumed to be a free rotator with 6 = 3 when only one trans isomer was assumed to be present and 6 = 6 when both trans (stag) 0 1978 American Chemical Society
246
Communications to the Editor
The Journal of Physical Chemistry, Vol. 82, No. 2, 1978
TABLE I : Isomerization Energies, Potential Barrier Heights, and Torsional Frequencies for Three Rotational Isomers of o-Cresol
VCH,, cal mol-'
AH, cal mol-'
Cis Trans (stag) Trans (eclip)
Calcd
Expt"
Calcd
Expt
0 958 1044
0
2073
b
1:;
VOH, cal mol-' Calcd Expt" 4716 3279 3150
{fre:6 almost
4313 3769 2986
v r ( O H ) , cm-'
Calcd
Expt
338 280 274
322 297 266
rotor a
Obtained from torsional frequencies.
-2100 cal mol-' for o-xylene.
TABLE 11: Comparison of Calculated Entropies for Various Models with Experimental Entropies Potential energy function OH Parameters cal mol-'
Model Isomer
no.
Eq
1 2 3 4 5
Cis Trans (stag) Trans (eclip) Trans (stag t eclip) Cis t trans
6
Cis
V, = 4313 V, = 3769 V , = 2986 V , = 3769
1 1 1 1 2
v,= 544
Trans Experimental by third law
\
V, = 4041 -
Eq
CH, Parameters cal mol-'
So, cal K-' mol-'
298.15
400K
3
Free rotor, u = 6 Free rotor, u = 6 Free rotor, u = 3 V , = 2073
82.33 82.10 82.35 83.48 83.66
92.60 92.13 92.38 93.50 94.04
3
V , = 2073
84.27
94.47
3
V , = 2073
Free rotor. u = 3 84.80 t 0.7
TABLE 111: OH Torsional Frequencies of Xylenols (cm-' ) Calculated usinga Compound
Expt
Avtrans
Avcis
2,3-Xylenol 2,4-Xylenol 2,5-Xylenol 2,6-Xylenol 3,4-Xylenol 3,5-Xylenol
300 301 300 303 298 312
299 285 299 284
324 310 324 334 300b 314b
Avtrans + Avcis
309
vr used: phenol = 310; o-cresol (cis = 322, trans = 3,4- and 297), rn-cresol= 312;p-cresol= 298 cm-I. 3,5-xylenol have no trans and cis differentiation, a
and trans (eclip) were assumed to be present. The remaining contributions to the partition function were obtained by the usual procedure. The calculated entropies for several models for o-cresol a t 298.15 and 400 K are presented in Table I1 and are compared with the third law values reported by Andon et al.9 It is clear that model 6 with o-cresol as a mixture of two isomers obtained entropy values which have the best agreement with the experimental values a t both the temperatures. It is shown by Fateley et al.7 that for multisubstituted phenols, the OH torsional frequency can be predicted using Av, values (i.e,, the shift of the torsional frequency from its position in phenol) for various substituents. These authors observed only one torsional band due to the OH group for each xylenol. Their predicted values of OH torsional frequencies, using Av, values for trans-o-, m-, and p-cresol agreed well with the experimental values for 2,3-, 2,5-, 3,4-, and 3,5-xylenol, but not for 2,4- and 2,6-xylenol. We feel that this is due to the neglect of the cis conformer in o-cresol. When Av, for the cis-o-cresol is considered, better agreement between the predicted and the calculated values of OH torsional frequencies for 2,4- and 2,6-xylenol is obtained. The comparison is given in Table I11 and the results seem to favor the presence of cis-o-cresol as well as trans. 0022-3654/78/2082-0246$01 .OO/O
94.97
* 0.4
We conclude that there are strong interactions between the rotations of OH and CH3groups in cresols and xylenols in which these groups are in ortho positions. We cannot account for the observed spectroscopic and thermodynamic properties by neglecting such interactions. A model based on the presence of two isomers in equilibrium does give a good approximation to the experimental ideal gas entropy. We cannot explain the observation of only one band in the OD torsion of deuterated o-cresol.
References and Notes (1) J. H. S. Green, Chem. Ind. London, 1575 (1962). (2) J. H. S. Green, D. J. Harrison, and W. Kynaston, Spectrochim. Acta, Part A , 27, 2199 (1971). (3) G. L. Carlson and W. G. Fateley, J . Phys. Chem., 77, 1157 (1973). (4) S. A. Kudchadker, R. M. Hedges, and B. J. Zwoilnski, J. Mol. Struct.,
submitted for publication.
(5) S. A. Kudchadker,A. P. Kudchadker,R. C. Wilhoit, and B. J. Zwolinski, J . Phys. Chem. Ref. Data, submitted for publication. (6) N. L. Allinger, J. J. Maul, and M. J. Hickey, J . Org. Chem., 36,2747 (1971). (7) W. G. Fateley, G. L. Carlson, and F. F. Bentley, J . Phys. Chem., 79, 199 (1975). (8) D. R. Lide, private communication. (9) R. J. L. Andon, J. F. Counsell, E. 8. Lees, J. F. Martin, and C. J. Mash, Trans. Faraday SOC.,63,1115 (1967).
Thermodynamics Research Center Texas Engineering Experiment Sfation Texas A& M University College Station, Texas 77843
S. A. Kudchadker" R. C. Wllholt B. J. Zwollnskl
Received August 17, 1977
Triplet-Triplet Annihilation by Diffusive Encounter of Benzophenone Triplets in Benzene Solution Publication costs assisted by the U S . Army Research Office
-
Sir: Previously, we reported that triplet-triplet annihiS1 So) of benzophenone triplets lation (TI + TI proceeds with h2 = (1.1f 0.1) X 1O1O M-l s-l in benzene at 25 O C 1 which is very near the diffusion limit.2 This rate constant was obtained by curve matching the nonexpo-
+
C 3 1978 American Chemical Society
