2740
J. Phys. Chem. 1900, 84, 2740-2751
(11) ZumwaR, L. R.; Badger, R. M. J. Am. Chem. Soc. 1940, 62,305. (12) Tien-Sung, L.; Flshman, E. Spectrochlm. Acta, Part A 1967, 23, 491. (13) Nouwen, R.; Huyskens, P. J. Mol. Struct. 1973, 16, 459. (14) Baraton, M. I., Thesis, Umoges, 1979, (15) See, for Instance: Schuster, P. Int. J. Quantum Chem. 1860, 3, 851. Morokuma, K. J. Chem. Phys. 1971, 55, 1236. DeiBene, J. E. J. Chem. Phys. 1975, 62, 1314. (16) Obvsson, I.; JBnsson, P. In "The !4ydrogen Bond, Recent Developments In Theory and Experlment"; Schuster, P.; Zundel, G.; sm&fy, c., Ed North Hdlend PuMishkrg Co.: Amsterdam, 1975; p 395.
(17) Labane, M. C.; Volgt, D.; Qaiellats, F. Btd. Soc. W n . Fr. 1987,3328. Chernlk, C. L.; Pedley, J. B.; Sklnner, H. A. J . Chem. Soc. 1956, 1402. Mortimer, C. T. Fure Appl. Chem. 1961, 2 , 71. (18) Wagner, E. L. J. Am. Chem. Soc. 1063, 65, 161. (19) chopsn,F.; Kauhnam, 0 A&, M A 1970, 28,2113. The bond order was calculated aqcordlng to the f m l a of Cor@, W. J . Chem. phys. 1964, 14, 305. (20) As pohted out by Denisw @bate communlcatlon), the complexes In the immediate vlchtty of the hfiectkn poht of the &/AH,,cuye and w t k h are characterized by very Smal O-0 Interdlstamm, could make an excepbkn. This would not affect the analytkal form of the correlatbn (eq 20).
.-
Dipole Moments and Complexation Enthalpies of 1-Methyl- and 1,P-Dimethylimldazole with Various Phenols in Benzene Solution. Angle between the Moment of the Bases and the Hydrogen Bond P. L. Huyskens,' W. Cleuren, M. Rant, and M. A. Vuybieke Depertment of Cbmktry, and w u t l n g Center, UnlversnY of Lewen, Ceh9sUJnenlaanZOOF, 3030 Heverlee, Belgkrm (Recetvd: Arrgust 13, 1979; In F h l F m : Apr# 7 1, 1980)
The dipole moments Pab, the complexation enthalpies and complexation constants, Kabof 32 complexes of 1-methyl-and 1,2-dimethylimidazoleswith various phenols were determined at 298.2 K in benzene solution. The dipole momenta of the bases were found to be respectively 3.71 f 0.02 and 3.72 f 0.01 D. The dipole incrementa Afii* are calculated from the dipole momenta and from the known ea angles the dipole moment of the acid forms with the direction of the bond, using arbitrary values of e,, the angle between the dipole moment of the base and the direction of the bond. These dipole increments are then plotted against the enthalpies of the bonds, together with the data of other systems for which eb is known. The most probable value of eb for the complexes of the imidazoles are those for which the best correlation can be obtained. This is the case when e b is taken to equal 38 f 10'. This result is in agreement with theoretical expectations and with the magnitudes of the Kerr constants. It demonstrates that complexation occurs on the lone pair of electrons of the imino nitrogen atom of the imidazoles. An expression is proposed which allows the calculation within 0.34 D of the dipole increment A p of any O-H-.Nhydrogen-bonded complex in benzene solution from the enthalpy of the bond.
Introduction In a previous paper' we proposed a method for the evaluation of some geometrical characteristics of hydrogen-bonded complexes in solution. This method is based on the assumption that the increment of dipole moment Aji brought about by the formation of the bond has nearly its direction and that its magnitude is related to the enthalpy of the bond, -AHb Furthermore, it is assumed that on account of the identity of the charges which undergo the most important displacements upon H-bond formation the relation between Ap and A H h is the same for all the complexes of a given type of hydrogen bond in a given solvent. For O-H--O bonds it was shown that this method effectively leads t~ angles which are not only in agreement with the theoretical calculations but also correspond with the mean values found by the diffraction methods in the crystalline complexes. The value of 4 can be drawn for a complex of moment &b between an acid of moment pa and a base of moment &, from the equation A p = (Pab2 - :p sin2 8, - pb2 sin2 ob 2c($Lbsin sin d b ( C 0 s #))1/2 - pa cos ea - pb cos eb (1)
e,
0, is the angle between the direction of the moment pa and 00223654/80/2084-2748$01,00/0
that of the hydrogen bond. db is the angle between the moment fib and the hydrogen bond. 4 describes the rotation around the hydrogen bond of one partner with respect to the other. In most 0-H-0 complexes it can be expected on the basis of molecular models that some angles # are excluded because of steric hindrance between the atoms of the partners and that thus (cos 4) must be negative. This is in effect found by the method we proposed. However, in many O-H-mNcomplexes, the study of molecular models does not predict the occurrence of such hindrances and (cos 4) can be a priori taken to equal zero. Furthermore, for some bases as trialkylamine or pyridines the angle must be zero for reasons of symmetry. When these bases are complexed with phenols (for which the values of 0, are known within a few degrees) the dipole incrementa Api can thus be deduced without ambiguity from the experimental values of pat,, pa,and pb. These A p values can be plotted against A H h and this gives a curve with a sigmoidal shape (Figure 3). If now we had used uncorrect values for 6b in the cdculation of A p from eq 1 this would lead to errors which would trigger a larger spreading of the points around the mean curve which passes through them. For other bases, as the imidazoles, eb is a priori unknown and can arbitrarily be choosen for the computation of A&. 0 1980 American Chemical Society
Complexation Enthalpies of Substituted Imidazoles
However, a better choice of the angle would lead to a narrowing of the "road" passing through the points in a diagram. From a practical point of view this narrowing can be studied by determining the standard deviation q of the points relative to the mean curve. This can easily be done if one possesses an analytical expression for this curve. As shown in the previous work,l the following equation with five adaptable parameters can be used (among others):
The coefficients A , B , C , A', and B1 are adapted so as to minimize the standard deviation q. This minimal standard deviation increases when a less correct choice is made for Ob in the computation of the Ak's using eq 1. An increase of this minimal standard deviation by changing the angle becomes significant when it surpasses the uncertainty due to the accidental errors on pab and In this work we apply this method to estimate the values of the angles Oh in the complexes of 1-methyl- and 1,2dimethylimidazole. Owing to the low solubilities of the polar complexes and of the imidazoles themselves, it was necessary to use a solvent other than cyclohexane. In this work we determined the complexation enthalpies -A&,, the stability constants Kab, and the dipole moments pab of some 30 complexes of 1-methyl- and 1,2-dimethylimidazole with several phenols in benzene solution at 298 K. According to the method described in the previous work each determination of the dipole moment of the complex involves a new determination of the dipole moment of the base. From these data, the dipole increments Apl*are calculated by using eq 1and taking different arbitrary values of Ob The various Apl* sets are correlated, together with those of other 0-H-N complexes for which Ob is known, with the enthalpy of the hydrogen bond. The most correct values of the angles Ob are those for which the best correlation can be found.
Experimental Results Methods of determination and the apparatus were described in the previous paper.' Aldrich l-methylimidazole (99%)and 1,2-dimethylimidazole (98%)were purified by distillation in vacuo on LiAIHI. Benzene of analytical grade was dried on molecular sieves 4A. The values of the complexation enthalpies A&, and of the complexation constants Kab are available as supplementary material for the 32 systems studied in this work together with the literature data for complexes between trialkylamines or pyridines and phenols. The dipole moment of the base pb, that of the complex p&,, and that of the acid taken in the same solvent are also tabulated in the supplementary material. In Table I we tabulated selected values as examples. Discussion A . Enthalpies of Hydrogen Bonds in Benzene Solution. The formation of a hydrogen bond in benzene solution is generally accompanied by a smaller change of the enthalpy than in cyclohexane because it necessitates the breaking of the bonds which the acid, and on occasion also the base, form with the more active solvent. On the other hand, the dipole increment may also be reduced because the charges are already displaced to a given extent in the uncomplexed acid molecules. As a matter of fact pa is generally somewhat higher in benzene than in cyclohexane. It would be
The Journal of phvsical Chemistry, Vola84, No. 21, 1980 2749
TABLE I: Complexation Constants Kab/dm3mol-', Complexation Enthalpies -AHab/kJ mol-', Bond Enthalpies -AHh/kJ mol-', Dipole Moment of the Base pb/D, Dipole Moment of the Acid pa/D, Dipole Moment of the Complex r&/D of Complexes of 1,2-Dimethylimidazoles in Benzene at 298 K substituent no. phenol Kab -AH& -A& pb pa p& 17 32.5 3.73 1.50 5.44 305 32.5 18 4-Me 234 31.2 31.3 3.72 1.57 5.33 19 4-tert-Bu 237 31.2 31.2 3.73 1.62 5.27 20 4-F 560 32.1 32.1 3.72 2.12 6.20 21 4 4 1 670 33.4 33.4 3.71 2.19 6.38 22 4-Br 860 32.5 32.5 3.73 2.25 6.40 23 4-1 620 32.4 32.4 3.71 2.13 6.31 24 3,5-C11 580 34.8 34.8 3.73 2.18 6.56 25 4-CN 1400 35.0 35.0 3.73 4.68 8.50 26 3,4,6-C13 860 36.7 35.7 3.71 3.13 7.39 27 4-N01 1100 36.7 36.7 3.71 4.83 8.71 29 C1, 1750 40.6 44.6 3.72 1.93 8.94 31 2,6-C11-4-N01 3400 55.3 71.3 3.71 3.32 13.50 32 2,4,6-(N03), 2150 84.9 103.9 3.71 1.51 13.60
possible to reduce the enthalpies to the values which would be found in cyclohexane, using for instance the procedure proposed by Drago et al.2 However, then, the dipole increments would be reduced. We therefore preferred to use for the &/AH correlation the direct experimental values in benzene. Moreover, the effect of the change of solvent on the Apt AH correlation will be cancelled to some extent, acting in the similar way on Ap and AH. As in cyclohexane, the difficulty remains, namely, that of estimating the enthalpy effect needed to break the intramolecular hydrogen bonds in ortho-substituted phenols which is necessary in order to find the true value of the enthalpies of the hydrogen bonds formed by these phenols and the nitrogen bases. This intramolecular enthalpy effect AHbephtn (which corresponds to the enthalpy of the intramolecular bond times the fraction of phenol molecules which exhibit intramolecular binding) is smaller in benzene than in cyclohexane. In the previous work the value of AHbtraxineawas determined from the comparison of of the complexes of phenols with ortho substituents and the values of the complexes of phenols without ortho substituents but with the same pKa value. Unfortunately in the present m e , most of the 0-Ha-N complexes with ortho substituents belong to the class where proton transfer is no longer negligible and where the A&,/ApK, relation changes. It is therefore necessary to restrict these comparisons to those complexes for which ApK, remains very close to the ApK, range of the complexes of phenols without ortho substituents, this is, for the imidazoles below ApK, = 3. I t appears that between ApK, = 0 and ApK, = 3 the complexation enthalpies of the imidazoles with phenols without ortho substituents obey the relation -AH,b/kJ mol-' = 35.6 + 2.39ApKa (3) with a coefficient of determination of 0.90. In Table 11we give for the complexes withortho substituents below ApK, = 3, the difference between the calculated value according to eq 3 and the experimental one. This corresponds to the value of AHheaxbea. I t appears that for the two phenols -AHhea is approximately 14 kJ mol-' lower in benzene than in cyclohexane. We assumed in a first approximation that this difference remains the same for the other phenols. This leads to a value of 6 kJ mol-' for -AHbtraxbtraof 2,6-dichloro-4-
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The Journal of Physical Chemistry, Vol. 84, No. 21, 1980
Huyskens et ai.
TABLE 11: Enthalpies of Intramolecular Bonds in Benzene -AHi,t"ripI kJ molin ben- in cycloacid complexed by ApK, zene hexane pentachlorophenol l-methyl1.78 3.2 18 imidazole pentachlorophenol 1,2-dimethyl- 2.81 4.3 18 imidazole 2,4-dinitrophenol l-methyl2.97 12.6 27 imidazole
,oo
1
AH,/
k J mole-'
Flgwe 2. Orientation of the mment C(b in 1-methylimidazde, 10
r
A PKa
- A H h / k J mole'
c n
I
I
50
I
I
I
I
I
I
I
100
Fbwe 3. Dipole Increments Ap,' D calcutated with = 30' for the lmidazdes from eq 1 against enthalpies -AH,IkJ mor' of the bonds (0).Dipole increments Ap, of triethylamine and pyrldine complexes against enthalpies -AH,& moT1of the bonds (0). Dipole increments Ap, of trtethyhnhe and pyridhe complexes agaht enthepies -AH,,/kJ md-1 of the bonds (0).
studied here (7.04 and 8.07) are substantially larger than that of pyridine (5.17). The nearly planar character of these imidazoles implies that the dipole moments lie in the plane of the ring. C. Value of the Angle in the Complexes of 1-Methyland 1,2-Dimethylirnidazole. For the complexes of the imidazoles the only unknown quantity in the right member of eq 1is the angle Ob. In effect the angle 0, for the phenols can be estimated within a few degrees ftom the additivity of the group moments. (cos 4 ) is zero, as stated in the Introduction. For the complexes of triethylamine and of the symmetrical pyridines db necessarily equals zero and all the quantities of eq 5 are known. With a given arbitrary value of db the Api*'s are computed from the experimental moments for the 32 complexes of the imidazoles. Together with the known A p ( s of the complexes of triethylamine or pyridine, they are plotted against the enthalpies -AHh of the bonds. A sigmoidal curve is always obtained. An example is given in Figure 3. For this curve we use the analytical form of eq 2 and compute by nonlinear regression the coefficients A , E, C, A', and B1 which minimize the standard deviation ui. The coefficients and the standard deviations obtained for several values of ob (imidazoles) are tabulated in Table
Complexation Enthalpies of Substituted Imidazoles
The Journal of phvsicsl Chemtstry, Vol. 84, No. 27, 1980 2751
TABLE 111: Optimized ParametersAID J - * mol,BID J-' mol, C/D J-' mol,and Standard Deviations (I l/D for Various e b Angles Chosen for the Imidazoles eb,
dee 8 18 28 38 48 58 68
A 0.0032 0.0074 0.0074 0.0074 0.0074 0.0168 0.0188
B C A, 4.87 0.039 -7.51 4.64 0.045 -7.70 4.64 0.045 -7.70 4.640.045 -7.70 -4.64 0.045 -7.70 4.64 0.042 -9.50 3.95 0.048 -16.44
B. 0.170 0.172 0.172 0.172 0.172 0.207 0.341
ui
0.45 0.42 0.38 0.34 0.39 0.43 0.53
III. The minimal standard deviation is the lowest around 8, = 3 8 O where ita value is 0.34 D. Taking the experimental errors into account, it can be stated that the correlation bekomes significantly worse when the standard deviation is 0.04 D higher. One can thus conclude that db is smaller than 48O and larger than 28'. This fully excludes a complexation on the amino nitrogen atom because the corresponding orbital surely makes an angle of more than 5 5 O with the plane of the ring. This also excludes the r electrons of the ring as basic site for the hydrogen bonds, because in such a case db would be equal to 9oo. The basic site involved in the complexes considered here is thus clearly the lone pair of electrons of the imino nitrogen atom, which has approximately the direction of the bisectrix of the C4-N3-C2angle. It is worthwhile to note that, according to the contributions of the various structures in imidazole, calculated by Martinez-Carrera, an angle of 24' would be computed between p b and the bisectrice of the C4-N3-C2angle. This is not far remoted from the value of 38O we find with this method. On the other hand, Bolotnikov et alS6determined the Kerr constants and dipole moments of 1-methyl- and 2methylimidazole in dioxan solution. They find a strong difference between the Kerr constants of the two isomers (10l2 mK2 being respectively 318 and 115) whereas the dipole momenta and the molar refractions are nearly the same. According to our results concerning the orientation of fib in the plane of the five-membered ring (which must be similar for both isomers), the difference between the two Kerr constants can be explained by the fact that the direction of the first principal axis of the polarizabilities, oriented approximately along the longest dimension of the molecule, makes only a small angle with p b in l-methylimidazole whereas this angle is of the order of 5 5 O for 2-methylimidazole.
From Table 11it also appears that the parameters A , B, C, A I ,and B1 undergo only small changes when db varies. D. Quantitative Correlation between the Dipole Increment and the Enthulpy of the Bond in 0-H-N Complexes in Benzene Solution. As in the previous work, the method leads to values of db which correspond with the expectations. The assumption of a single A p / AH relation for all the 0-Ha-N complexes in benzene can thus be considered as a good approximation. The equation used for the calculation of q for the angle db(imidazole) = 38O was of the form Ap = O.o074[-AHh] + (4.41 + 0.045[-~h])e-7.70eo.172[-AH~l 1 + e-7.70e0.172[-AHHhJ
(4) Although it must be emphasized that, within given limits, other coefficients can be used, leading to a standard deviation which is not significantly different and that the curve drawn in Figure 1could also be described by another function, eq 4 can be used to estimate the value of Ap from the experimental bond enthalpy within 0.34 D for all the O-H-eN complexes in benzene solution. Acknowledgment. The authors are indebted to the Instituut voor Wetenschappelijk Ondenoek in de Nijverheid en de Landbouw, the Katholieke Universiteit te Leuven, and the Belgian Government (convention no. 76.811.11.4) for their financial support. Supplementary Material Available: Complexation enthalpies and complexation constants of 32 complexes of 1-methylimidazole or 1,2-dimethylimidau>lewith substituted phenols in benzene at 298 K. Complexation enthalpies and complexation constants of trialkylamines and pyridines in toluene. Dipole momenta of the complexes and of the bases. Enthalpies of the hydrogen bonds and dipole incrementa calculated with two values of (Tables IA, IB,and IIB,6 pages). Ordering information is available on any current masthead page.
References and Notes (1) Huyakens, P.; eleven, W.; Van BrabanNbVaerts,H.; Vuytstehe, M. A. J. Phys. chem. Preceding artkle h thte issue. (2) Drag0 R. S.; Nazarl, M. S.; Vogel, Q. C. J. Am. Chem. SOC. 1072, 94, 90. (3) McClelian, A. L. "Tablesof Experimental Dipole Moments"; Rahara Enterprises: El Cerrito,, 1974, Vd. 2. (4) Martinez-Canera Acte Crystelkgr. 1066, 20, 783-89. (5) Boktnkov, V. S.; uffntseva, T. V.; Bulgarevttch, S. B.; Shelnher,V. N.; Oslpov, 0. A.: Gamovskl, A. D. Zh. Ckg. K h h . 1076, 12, 418-421.
