4860
J . Phys. Chem. 1987, 91, 4860-4864
infer that the solvation processes of Cr(acac)3 in solutions are merely the replacement of CC14 molecules in OSC by chloroform molecules. Possible solvation of C ~ ( a c a c )with ~ carbon tetrachloride molecules should be considered,2balthough the solvation mechanism may differ with chloroform. Consequently, the I3C Ti data measured in the CCl,-Cr(a~ac)~system cannot be applied directly to the interpretation of the relative translational diffusion
between carbon tetrachloride and the chromium complex.2 The contribution of the existence of the OSC to spin relaxation rates of solvent nuclei should be considered. Both theoretical and experimental investigations along these lines are underway in our laboratory and the result will be published elsewhere. Registry No. CHCI,, 67-66-3: Cr(acac)3, 21679-31-2.
Hydrogen Bonds Originating from Charge- Induced Electronic Delocalization P. L. Huyskens,* M. C1. Haulait-Pirson, H. Collaer, and D. J. Pirson Department of Chemistry, University of Leuven, 3030 Heverlee, Belgium (Received: February 2, 1987)
A new type of hydrogen bond is described. Its formation requires two conditions: (1) the presence of a neat negative charge on the proton acceptor, and (2) the presence of an aromatic group susceptible of electronic delocalization in the proton donor near its A-H site. The negative charge induces a shift of the electrons of the A-H bond toward the aromatic ring and this
enhances strongly the proton donor character of this bond. The proximity of a counterion reduces the effect. Experimental evidence for the existence of this type of H bond is found in conductometricand IR spectroscopicresults for systems containing picrate or halogenide ions and phenyl-substituted guanidines or phenols as proton donors.
Introduction A fundamental question in the field of hydrogen bonding is that of the influence of the electric charge on one or on both partners of the hydrogen bond on its thermodynamic and spectral characteristics. In a previous work1 we pointed out that two factors can influence the energy of a cation-anion hydrogen bond: a purely electrostatic interaction resulting from the attraction between the two nominal charges, and a more covalent one resulting from charge transfer and the weakening of the A-H valence bond. As a consequence it happens that the stability constants of the H bonds a cation forms with anions are much larger than that of the bonds the cation forms with neutral ligands whereas on the contrary the shifts of the Y ~ stretching - ~ frequencies are much larger for the cation-ligand bonds. In the last case the purely electrostatic interaction is much weaker because it is only an ion-dipole attraction. In the present work, however, we will present a special kind of H bonds where the electric charge of the anion exerts a direct influence on the covalent and spectral characteristics of the bond. However, this effect is only observed when the other partner possesses an aromatic group susceptible of electronic delocalization. Under such circumstances the proximity of the negative charge of the anion provokes a displacement of the electrons that strengthens the proton donor ability of the A-H bond in the ligand. Evidence for the formation of such charge-induced delocalization (CID) hydrogen bonds can be drawn from both conductometric and spectroscopic data. Conductometric Evidences for the Formation of CID Hydrogen Bonds I . Differences in Ligand Effects between Alkyl- and Phenylsubstituted Guanidines on the Dissociation Constants of Their Picrate and Iodide Salts in Nitrobenzene. The effect of a ligand on the dissociation constant of an ionophore can be expressed by the following e q ~ a t i o n which ~ . ~ is a generalization of that of Gilkerson,
Kd - ( 1 + kl+L + kl+kzfL'...)( 1 + kl-L + kI-k,-L '...) _ (1 + K I L + K l K 2 L'...) Kdo
where Kd is the dissociation constant of the ionophore in the presence of the ligand, corrected for the change of the dielectric constant. K: is the dissociation constant in absence of the ligand. L is the concentration of the free ligand molecules in the solution. k , + and k2+ are the addition constants of the ligand on the first and the second active sites of the dissociated cations. k l - and k2are the addition constants on the anions. K , and K 2 are the complexation constants on the sites which are still available on the ion pairs. These constants can be obtained by plotting the ratio R = K d / K 2 determined by conductometric measurements against the concentration L of the ligand. Three types of curves are found. 1. I . R against L Gives a Straight Line Passing through 1 at Zero Concentration. This demonstrates that only the cation or only the anion is solvated by one ligand molecule and that the ion pair is not complexed. Equation 1 reduces to R =1
+ kl+L
or
1
+ kl-L
(2)
The constant ( k i f or k , - ) can be deduced from the slope of the straight line. 1.2. R us. L Exhibits a Downward Curvature. This indicates that the denominator of eq 1 differs from 1 and thus that the ion pairs are also solvated by the ligand. The experimental points often obey the following equation 1
R =
+ k , + L + kl+k2+L2 or 1 + K1L
1
+ k,-L + k,-k2-L2 1 + K,L
(3)
where K , is larger than k2+ or k2-. Such behavior is typical for the interaction between pyridines or amines and diethylammonium bromide, picrate or perchlorate in nitr~benzene,~ or for the complexation of triethylammonium bromide, nitrate, hydrogen sulfate, or iodide by benzoic acids6 or citric acid.' 1.3. R us. L Exhibits an Upward Curuature. Such behavior will be observed for instance if eq 3 holds but with K , zero or smaller than k2+. An example is the complexation of pyridinium picrates by some substituted pyridines.' However, an upward
(1)
(1) Huyskens, P. J . A m . Chem. SOC.1977, 99, 2578. (2) Macau, J.; Lamberts, L.; Huyskens, P. Bull. SOC.Chim. Fr. 1971,
2387. ( 3 ) Delcoigne, V.: Haulait, M . C. J . Solution Chem. 1976, 5 , 47
0022-3654/87/2091-4860.$01.50/0
(4) (a) Gilkerson, W. R. J . Chem. Phys. 1956, 25, 1199. (b) Gilkerson, W. R. J. Phys. Chem. 1976, 80,2488. (c) Gilkerson, W. R.; Ralph 111, E. J . Am. Chem. SOC.1967,89, 808. (5) Haulait, M. C.; Huyskens, P. J . Phys. Chem. 1975, 7 9 , 1812. (6) Pirson, D. J.; Huyskens, P. J . Solution Chem. 1974, 3, 5 0 3 . (7) Haulait-Pirson, M. C.; De Pauw, M. J . Phys. Chem. 1980, 84, 2492.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4861
Charge-Induced Delocalization Hydrogen Bonds
80 I
LO
I
IR
'7
R
I
30
/
/
20
/
LO
10
20
c Me'Gu i . M e L G j
I
I
0
1
I
I
010
0 05
015
0
Figure 1. Ratio R = Kd/Kd0 of the dissociation constants of diphenylguanidinium and tetramethylguanidinium picrate in nitrobenzeneat 25 OC vs. the concentration L of the corresponding neutral guanidine.
curvature is also found for systems where both the anion and the cation are complexed. In some cases R obeys the expression
+ kl+L)(l + kl-L)
R = (1
(4)
This is the case for ligands like methanol2 or imidazoles* which are typically amphiprotic. The derivatives of guanidine NH '>c=NH NH2
belong to the strongest bases of organic chemistry. The pK, of guanidine and of NjV',N,N'-tetramethylguanidine in water reaches 13.69 whereas that of the N,N'-diphenyl derivative is still 10.1,9 the order of magnitude of that of the aliphatic amines. In the previous works2g5we have never noticed any complexation of anions by the N-H groups of primary or secondary aliphatic amines. Therefore we did not expect to find measurable k,- values when neutral guanidine is added for instance to a guanidinium picrate or iodide. In fact, when tetramethylguanidine, Me4Gu, is added to tetramethylguanidinium picrate or iodide in nitrobenzene, plots of R vs. L give straight lines (Figures 1 and 2). These systems follow eq 2. Within the limits of experimental error the slopes of the lines of Figures 1 and 2 are equal (34.6 f 4 dm3 mol-' and 28.2 f 3 dm3 mol-'). These slopes are thus obviously due to the formation of homoconjugated cations of the type Me2N\
c,
7
=ti
+
H+-
Me2N
e
2
N =C
I
\NMe2
H
H
the constant kl+ being 32.5 f 5 dm3 mol-'. The linearity of the functions excludes any noticeable solvation of the remaining N-H sites of the homoconjugated cation. Solvation of the ion pairs seems also negligible because this would lead to differences between the iodide and picrate systems. For a similar reason these results show that hydrogen-bond formation between tetramethylguanidine and the anions can be neglected. The behavior of diphenylguanidine, Ph2Gu, which according to Kiselev et a1.I0 has the structure H\ N / H
I
H \ /C=N-Ph /N Ph
(8) Haulait-Pirson, M. C . Bull. Sor. Chim. Eelg. 1976, 85, 639. (9) Angyal, S . J.; Warburton, W. K. J . Chem. SOC.1951, 2492. (10) Kiselev, L. A.; Galushina, V.V.; Ryabova, A. N.; Shvetswashilovskaya, K. D.; Tibanov, P. V. Zh. Org. Khim. 1975, 11, 224.
0 05
I 010
L
I
015
Figure 2. Ratio R = Kd/Kdoof the dissociation constants of diphenylguanidinium and tetramethylguanidinium iodide in nitrobenzene at 25 O C vs. the concentration L of the corresponding neutral guanidine (the ordinate scale is twice as large as the Figure 1).
is completely different. As can be seen from Figures 1 and 2, the curves of R vs. L exhibit a marked upward curvature. On the other hand important differences between the picrate and iodide systems are observed. Both curves fit eq 4. Such fitting yields a pair of constants equal to 34 and 27 dm3 mol-' for the picrate system, and to 34 and 69 dm3 mol-] for the iodide system. As k l + has to be the same for both systems, it is obviously equal to 34 dm3 mol-I. The two other constants strongly differ from each other and it is therefore improbable that the upward curvature could be due to a k2+term in eq 3, which has to be the same for both systems. The values of 27 and 69 dm3 mol-] thus correspond clearly to the complexation constants k l - of the picrate and the iodide anions by diphenylguanidine.
The fact that these complexes are formed only with the phenyl derivatives of guanidine demonstrates that the aromatic rings play an essential role in the formation of this type of H bond. We may explain the phenomenon as resulting from the repulsion (under the influence of the negative charge of the anion) of electrons of the N-H group which acts as proton donor. This strongly enhances the proton donor character of this N-H group. The above results provide a first experimental indication for this CID effect. It is noteworthy that in the case of I-, ki-is larger than kl+. This means that the ability of diphenylguanidine to act as proton donor for I- is greater than its ability to act as proton acceptor for the diphenyl guanidinium ion. The origin of this paradox might be the absence of steric hindrance around the iodide ion. 2. Differences between 4-Nitrophenol and Benzoic Acids in Their Complexation Abilities with Anions and Ion Pairs in Nitrobenzene. The C-C bond that separates the aromatic ring of benzoic acid from the 0-H group markedly reduces the possibilities of electronic delocalization. Charge-induced delocalization is therefore expected to be less important in benzoic acid complexing anions than in phenols. As a matter of fact, as illustrated by Figure 3, for ionophores such as Et3NHCl, Et3NHBr, Et3NH2CIdissolved in nitrobenzene, the dependence of the ratio R = Kd/Kdoon the concentration of the ligand is completely different for phenols and for benzoic acids. The curves for 4-nitrophenol exhibit an upward curvature whereas the reverse is observed for benzoic acids. Both curves fit eq 3. However, for 4-nitrophenol the addition constant K of the ligand on the ion pair is smaller than the second addition constant k2-
4862 The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Huyskens et al.
H e p t 4 N i * Ph2Gu '
-
.
:
:
:
:
:
r
0
I
O
L l
0 005
0 IO
Figure 3. Ration R = K d / K 2 of the dissociation constants of triethylammonium bromide in nitrobenzene at 25 OC vs. the concentration L/ mol dm--'of 4-nitrophenol and 3-methylbenzoicacid. TABLE I: Addition Constants in dm3 mol-' of the Ligand on the First Site of the Free Anion, k on Its Second Site, k2-,and on the Ion Pair, K , in Nitrobenzene at 25 OC ligand ionophore k2K ki14000 21 12 4-nitrophenol" Et3NHtCI14 4 2200 4-nitrophenol" Et3NHtBr' 14 4 2200 4-nitrophenol" Et2NH2'Br138 4 I1 3-methylbenzoicacidb Et,NHtBr20 90 Et3NHtCI1180 benzoic acidb 155 4 12 benzoic acidb Et3NHtBr6 16 294 3-chlorobenzoic acidb Et,NHtBr215 3-chlorobenzoic acidb Et2NH2+Br8 50
,-,
"This work.
Reference 6.
l
l
I
l
1
LO
29
l
1
8G
130
l
50
Figure 4. Inverse of the difference (Woo- WLo)/ohm-' cm2CPmol-' of the overall Walden product of tetrabutylammonium picrate and tetraheptylammonium iodide in nitrobenzene at 25 O C vs. the reverse of the concentration of diphenylguanidine.
is practically complete. In the last case, as predicted by the Onsager relation,12one observes a linear relationship between the equivalent conductance ( K - K ~ ) /and F the square root of the concentration F of the ionophore. The overall Walden product P at infinite dilution, which corresponds to the sum of those of the cations and of the anions (possibly solvated), can be obtained from the intercept at the origin of the following function 10000(~- K ~ ) /=F W' - k ' i 2 F
(5)
7 being the viscosity and K the specific conductance of the solutions.
One observes that P systematically decreases when diphenylguanidine is added to solutions of Bu,NPi or Hept4NI. This decrease can be ascribed to the solvation of the ions. However, since the tetraalkylammonium cations cannot be solvated, this demonstrates that diphenylguanidine forms specific bonds with Pi- and I-. The Walden products wi- of the monosolvated anions must indeed be smaller than wo- of the nonsolvated ion as a consequence of the larger size. The diminution of the overall experimental Walden product from Wooin the absence of ligand to WLodepends on the proportion of the anions that become solvated. This proportion depends on the addition constant k l of the ligand to the anion, and on the concentration of the ligand. The quantitative relation can be written
on the free anion. The contrary occurs for benzoic acids. The kl-, k2-, and K constants obtained from the experimental R vs. L curves are listed in Table I. For both CI- and Br- ions, the values of k l - are an order of magnitude larger for 4-nitrophenol than for the benzoic acids, despite the fact that 4-nitrophenol is a much weaker acid in water (its pK, is 7.15 compared to respectively 4.27, 4.20, and 3.83 for 3-methy1, unsubstituted, and 3-chlorobenzoic acid). Moreover, the effect is clearly related to the electric charge of the anion. As a matter of fact the addition constants of these acids on a neutral proton acceptor, as for instance triethylamine in benzene solution, are an order of magnitude larger for the benzoic acids: these values are 3760 dm3 mol-] for unsubstituted benzoic acid and only 260 dm3mol-] for pnitrophenol." For this neutral base the magnitude of the stability constants of the H bonds follows thus the order predicted by the pK,'s of the ligands in water. The very large values of the phenol-anion addition ccnstants are thus related to (1) the neat electric charge of the proton acceptor, and (2) the possibilities of electronic delocalization of the proton donor. This effect still exists for the second addition constant k , of the ligands on the free anion, but is severely reduced for the addition of the phenol on the ion pair. This is obviously due to the proximity of the counter charge. As a consequence, for the complexes of phenols, K is smaller than kl- and the inverse order is found for the adducts of the benzoic acids. This explains the difference in the curves of Figure 3. 3. Decrease of the Apparent Walden Products of Tetrabutylammonium Picrate and Tetraheptylammonium Iodide in Nitrobenzene upon Addition oflliphenylguanidine. In contrast to the guanidinium salts considered above that only partly dissociate in nitrobenzene at concentrations of 10-5-10-4mol dm-3, the dissociation of the corresponding tetraalkylammonium salts
Spectroscopic Evidences for the Formation of CID Hydrogen Bonds The infrared spectrum of diphenylguanidine in CC14 shows two bands in the N-H stretching region, at 3505 and 3408 cm-I (Figure 5 ) . They correspond respectively to the antisymmetric and symmetric vibrations of the N H 2 group. When Hept,N+Iis added to the solution, the intensities of these bands decrease and new absorptions are observed at 3478 and 3300 cm-'. The first one can be ascribed to the free N H bond (having some character of uas motion) and the second one to the NH-I- bond.
( 1 1) Davis, M. M. Acid-Base Behavior in Aprotic Organic Solvents. Nat. Bur. Stand. Monograph 105; US.Department Commerce: Washington, DC, 1968. Davis. M. M.: Paabo, M. J . A m . Chem. Soc. 1960, 82, 5081
(12) Onsager, L. Phys. Z . 1927, 277. Fuoss, R. M.; Onsager, L.Proc. Natl. Acad. Sci. U.S.A. 1955, 41, 214, 1010; J . Phys. Chem. 1957, 6 1 , 6 6 8 . ( 1 3) Pirson, D. J.; Huyskens, P. J . Solution Chem. 1974, 3 , 5 1 5 .
1 --
Woo - WLo
1
1
wO-
-
wI-
wO-
-
1 ~
1
ki-L -
(6)
As can be seen from Figure 4, the experimental quantity at the left varies indeed linearly with the inverse of the concentration of the ligand. The intercepts yield a difference w0-- wl-of 19 ohm-' cm2 CPmol-' for the solvated and nonsolvated picrate and 15.8 ohm-' cm2 CP mol-l for the iodide. These differences are of the order of magnitude of those encountered in similar cases.I3 The slopes yield k,- values of respectively 23 and 70 dm3 mol-' for the picrate ion and iodide ion, in good agreement with the values obtained above in fully independent way.
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4863
Charge-Induced Delocalization Hydrogen Bonds
IlA
3550
3250
3350
3L50
c m-‘
Absorbance A (in arbitrary units) of diphenylguanidine in CC14 at 25 “C as a function of the wavenumber at various concentrations of tetraheptylammonium iodide: (1) 0 mol dm-’; (2) 0.005 mol d ~ n - (3) ~; 0.010 mol dm-’; (4) 0.040mol d d ; (5) 0.100 mol dw3. F i g u r e5.
IkA TABLE II: Dissociation Constants Kt/mol dm-3 of Ionophores in Pure Nitrobenzene at 25 OC and B Factor of the Denison-Ramsey Eauation
I
I
3L31
3L50
3350
3250
cm-’
Figure 6. Absorbance A (in arbitrary units) of triphenylguanidine in CC4at 25 OC as a function of the wavenumber at various concentrations of tetraheptylammonium iodide: (1) 0 mol dm-3; (2) 0.005 mol dm-3; (3) 0.010 mol d d ; (4) 0.060 mol dm-’.
The spectroscopic changes are not observed with neutral electron donors. If triethylamine or pyridine is added in the same concentration to the solution of diphenylguanidine, the shape and the position of the bands are only weakly perturbed. Similar observations can be made for triphenylguanidinium in CC14 (Figure 6 ) . The addition of Hept4N+I- reduces the intensity of the 3437and 3408-cm-’ bands that correspond to the two N-H vibrations. A large band with two maxima at 3475 and 3240 cm-’ can be assigned to the N-H.-I-(Hept,N+) vibrations. The parallelism in the decrease of the two bands a t 3475 and 3240 cm-’ on increasing the iodide concentration suggests that both N-H groups of triphenylguanidine are involved in a similar way in the formation of H bonds with I-. For aniline (Figure 7) the intensities of the antisymmetric N H stretching band a t 3482 cm-’ and the symmetric one at 3398 cm-’ decrease when an iodide is added to the solution. A new band appears at 3308 cm-’ which can be ascribed ,,This band is perturbed by a Fermi to the v ~ - ~ , ,vibration. resonance with 2 1 3 ~according ~ to Lafaix and JosienI4 and to Wolff and Mattias.IZ’ These examples demonstrate that N-H bonds connected with phenyl groups are able to form hydrogen bonds with iodide ions. This effect is related to the negative charge of the proton acceptor. In the spectroscopic examples above the effect is already reduced by the proximity of the counterion because in CC14 solution the ionophores are practically not dissociated. Conclusion The experimental data above show that the presence of a negative electric charge in a proton acceptor can strongly strengthen the hydrogen bonds it forms with proton donors. This occurs when the A-H group of the donor is connected with delocalization rings of electrons. The role of the latter is illustrated by the fact that conductometric measurements show no detectable (14) Lafaix, A.; Josien, M. L. J. Chim. Phys. 1965, 62, 684. (15) Wolff, H.; Mattias, D. J . Phys. Chem. 1973, 77, 2081.
ionophore Me4GuH+PiMe4GuH+IPhzGuH+PiPhzGuH+IEt3NH+CIEt,NH+BrEtzNH2+Br-
KAQ 5.45 x 10-3 6.03 x 10-3 3.25 X 9.37 x 10-5 1.34 X 10” 7.92 X 10” 8.16 X 10“
B
52
65 51 62 60 60 60
H-bond formation between picrate ions and butylamine or dib~tylamine.2~ Of course it is not excluded that some weak H-bond formation could be detected between anions and aliphatic N H groups, using spectroscopic methods. But, at any event, the presence of an aromatic ring changes the order of magnitude of the stability constants. This has led us to consider the latter bonds as a special kind of hydrogen bonding, related to the interactions between the negative charge of the anion and the delocalizable electrons of the donor. On the other hand, if the electronic delocalization influences the formation of the H bonds, in its turn, the H bond perturbs the delocalization. This phenomenon was studied recently by Clark and Cook.16 Experimental Section 1 . Dissociation Constants of Ionophores. For a given system some eight solutions of the ionophore are used, with concentrations F ranging from 1 to 25 X lo4 mol dm3. The specific conductance K is measured. For each system the relative dielectric constant t and the viscosity are also determined. From these data the dissociation constant Kd,the limiting equivalent conductance Ao, and the limiting overall Walden product W ,at zero concentration of the ionophore, are calculated according to a procedure previously described” and based on the Fuoss equation.l8 The dissociation constants Kdoobtained in this way in the absence of ligand are tabulated in Table 11. The dependence of Kdoon the dielectric constant can be described to a first approximation by a Denison-Ramsey e q ~ a t i o n : ’ ~
log Kdo/Kdo’ = B[e’-’
- e-’]
The B factors were calculated from the dissociation constants of the ionophores in nitrobenzene solutions containing respectively lo%, 20%, and 30% benzene. They are listed in Table 11. These (16) Clark, J. H.; Cork, D. G. J . Chem. Soc., Chem. Commun. 1984, 15, 1014. (17) Pawelka, Z . ; Haulait-Pirson, M. C. J . Phys. Chem. 1981, 85, 1052. (18) Fuoss, R.M. J . Am. Chem. SOC.1935, 57, 488. (19) Denison, J. T.; Ramsey, J. B. J . Am. Chem. SOC.1955, 77, 2615.
4864
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
B values allow to correct for the change of permittivity the experimental dissociation constants Kd of ionophores in solutions containing ligands. Conductance measurements were performed with a WayneKerr Universal Bridge B224 operating at a frequency of 1592 s-l, with a Philips DW 1902/01 cell. The cell was calibrated by determining the conductance of aqueous KC1 solutions in the concentration range 0.001-0.01 N, using the equation of Lind et a1.20 Viscosities were measured with the automatic Lauda viscosimeter. Dielectric constants were determined by means of a W.T.W. Dekameter operating at 2 MHz. All measurements were carried out at 25 f 0.01 "C. 2. Walden Products. The Walden products of the strongly dissociated ionophores Bu4N+Pi- and Hept4N+I- were determined by using some eight solutions with concentrations of the salts ranging from 0.6 to 14 X mol dm-3. The overall Walden products of these ionophores in absence of ligands in nitrobenzene in 25 O C are respectively 51.0 and 55.0 ohm-l cm2 CP mol-]. 3. Infrared Spectra. The spectra were taken with a Perkin Elmer 325 spectrophotometer with a slit of 1.07 cm-l at 3000 cm-'. 4. Solvent and Products. Nitrobenzene (Fluka purissimum) was distilled from activated alumina under reduced pressure. The (20) Lind, J. E.;Zwolenik, J. J.; Fuoss, R. M. J . Am. Chem. SOC.1959, 81, 1557.
Additions and Corrections residual conductivity K~ is lower than 3 X ohm-' cm-'. Tetramethylguanidine was a Merck product distilled under reduced pressure. Diphenylguanidinium, Fluka purissimum, was recrystallized from a methanol solution. Tetramethylguanidinium picrate and diphenylguanidinium picrate were prepared from picric acid and the bases, dissolved in benzene. The salts were purified by recrystallization respectively from methanol and benzene solutions. Tetrabutylammonium iodide (Eastman) was recrystallized from ethanol-ether solutions. Tetrabutylammonium picrate was prepared from picric acid and Merck tetrabutylammonium hydroxide. It was recrystallized from ethanol solutions. Triethylammonium chloride was a Fluka purissimum product recrystallized from benzene-methanol mixtures. Triethylammonium bromide, an Eastman Kodak product, was recrystallized from a methanol-butanol mixture. Diethylammonium bromide was obtained from diethylamine and HBr in aqueous solution. The solution was evaporated and the salt several times recrystallized from a dichloroethane-methanol mixture. 4-Nitrophenol, a Fluka purissimum product, was recrystallized from a water-methanol mixture. Acknowledgment. We thank Dr. Th. Zeegers-Huyskens who took and interpreted the infrared spectra. We thank the University of Leuven and the Belgian Instituut voor Wetenschappelijk Onderzoek in de Nijverheid en de Landbouw, for their financial support.
ADDITIONS AND CORRECTIONS 1986, Volume 90
David M. Wardlaw and R. A. Marcus*: Unimolecular Reaction Rate Theory for Transition States of Any Looseness. 3. Application to Methyl Radical Recombination.
+
Pages 5383-5393. The factor (23 1) should be deleted from eq 1.3. In eq IV.l, IV.3, and IV.4, the quantity g, should be in the numerator rather than in the denominator. In Table V, the heading for the fourth column should be NEJ(Rlt)uI/(2J+ l ) , with uI as defined in the text (p 5386). In Table IX, the headings for the second and third columns should be [ N Ef uMC]a//101* and [ N E Af (rAMC]u1/1018, respectively.
