J. Phys. Chem. 1984,88, 6295-6302
6295
Environmental Interaction of Hydrogen Bonds Showing a Large Proton Polarizability. Molecular Processes and the Thermodynamics of Acid Dissociation Georg Zundel* and Johannes Fritsch Institute of Physical Chemistry, University of Munich, 0-8000 Miinchen 2, West Germany (Received: October 5, 1983; In Final Form: April 25, 1984)
The dissociation process of acids in solutions is discussed on the basis of a two-step equilibrium. In the first step the proton transfers in an AH-B + A--.H'B hydrogen bond. The second step consists of the transfer of the positive charge into a structurally symmetrical B+H-.B + B-.H+B hydrogen bond. It is shown that, for the adjustment of these equilibria, the interactions of these hydrogen bonds with their environments caused by large proton polarizabilities of these hydrogen bonds are of particular importance. The first step is described by In KPT= -(AHo' + AHIo)/RT+ (ASo" + ASIo)/R. AHo" which is usually positive is determined by the acidity of the hydrogen bond donor and by the basicity of hydrogen bond acceptor, whereas AHI" is determined by the interactions of the hydrogen bonds with their environments. AHIo is negative and relatively large; it is caused by the average dipole of the hydrogen bond interacting with the reaction field in the solvent and by specific interactions. This dipole of the hydrogen bond is usually for the most part an induced dipole since these hydrogen bonds show large proton polarizability. The term ASI' is also negative and relatively large due to the ordering of the environment. ASI" shifts the equilibrium to the left. But the influence of this term as well as the influence of AHoo is overcompensated by AHI' if dissociation occurs. With increasing polarity of the environment, the amount of the negative term AHI" increases, favoring the polar structure A-s-H'B. The second step, the transfer of the positive charge from this structure into B'H-B + B-.H+B hydrogen bonds, is promoted by the enthalpy caused by the strong interactions of these hydrogen bonds with their environmentsresulting from their large proton polarizability,which contributes in addition to the usual solvation enthalpies of cations and anions.
1. Introduction It was shown by Leuchs and Zunde11*2that AH-B (I) + A--.H+B (11) hydrogen bonds with large proton polarizability, formed between acid and water molecules, are of decisive importance for the molecular processes with dissociation of acids in aqueous solutions. If one considers acid-base pairs without environments, as shown in the following, transfer of the protons from the acid to the base molecules occurs only with combinations of very strong acids and very strong bases. Kul'bida and Schreiber3 have demonstrated by IR spectroscopy that in trifluoroacetic acid-trimethylamine complexes in the gas phase no protons transfer from the acid to the base molecules. Using N M R spectroscopy Golubev and D e n i ~ o vstudied ~ , ~ CF3COOH, HCl, and HBr with (CH3)315Nin the gas phase. They found that in the trifluoroacetic acid-trimethylamine and in the HC1-trimethylamine complexes, strong hydrogen bonds are formed but the protons do not transfer to the base. With the HBr-trimethylamine complex, however, they found that this complex is already fairly close to the ion pair in which the proton may transfer to the base. Schuster et aL6 have shown, however, by a rough estimation on the basis of the gas-phase acidities,' that, with combinations of ammonia and HCl, HBr, and HI, the proton may transfer to some extent to the ammonia molecule. An a b initio treatment with a reasonably extended basis set performed in the same groups (1) Leuchs, M.; Zundel, G. Can. J . Chem. 1980, 58, 31 1. (2) Leuchs, M.; Zundel, G. Can. J . Chem. 1982, 60, 2118. (3) Kul'bida, A. I.; Schreiber, V. M. J . Mol. Struct. 1978, 47, 32. (4) Golubev, N. S.; Denisov, G. S. Chem. Phys. (USSR) 1982, 5, 563. (5) Denisov, G. S . ; Golubev, N. S.J . Mol. Struct. 1981, 75, 31 1. (6) Schuster, P.; Wolschann, P.; Tortschanoff, K. "Molecular Biology, Biochemistry and Biophysics"; Springer: Heidelberg, 1977; Vol. 24, p 114. (7) In the experiment for the determination of the gas-phase acidities (Kebarle, P. Annu. Reu. Phys. Chem. 1977, 28, 445. Bartmess, J. E.; Scott, J. a,; McIver, R. T. J. Am. Chem. Soc. 1979, 101, 20) the proton is transferred during collisions without the formation of a long-lived complex. The collision partners are separated immediately after the proton transfer. A rough estimation is performed by taking into account the electrostatic attraction between these two particles. Thus from the difference in the proton affinities of the base and acid anion, the Coulombic interaction enthalpy in the ion pairs is subtracted.
0022-3654/84/2088-6295$01 SO10
has in the meantime shown that, with the HCl-NH3 pair, the proton is still localized at the acid side. A largely symmetrical double minimum is, however, found, with the HBr-CH3NH2paireg Extrapolating ab inito data of other systems, KollmanIo concluded that with the HI-NH3 pair the proton may transfer to the N H 3 molecule. Thus, in the gas phase the proton may transfer from the acid to the base only if pairs of very strong acids with strong bases are considered. If the systems are in the condensed phase, the environment induces transfer of the proton to the base, even in complexes between much weaker acids and bases. It is this environmentally induced transfer of the proton in acid-base (solvent) hydrogen bonds and the subsequent formation of homoconjugated hydrogen bonds with large proton polarizability formed by the excess proton wi-th solvent molecules which will be considered in the following.
2. Results and Discussion 2.1. Acid-Base (Solvent) Hydrogen Bonds and Molecular Processes with Dissociation. The first step of the dissociation process is the formation of acid-base (solvent) hydrogen bonds, for instance, acid-water hydrogen bonds.'T2 We shall consider first Km, the equilibrium constant for the transfer of a proton in this type of hydrogen bond AH...B + A- ...H+B I I1 The thermodynamic quantities determining KPTcan be split into two parts, one intrinsic part (AHo", Moo), given by the acidity of the hydrogen bond donor A H and by the basicity of the hydrogen bond acceptor B. AHo" and ASo" are the thermodynamic quantities which determine the proton transfer equilibrium I == I1 in a hydrogen bond present in a medium with 6 = 1. They can be obtained from studies of the equilibrium in solvents of various polarities and by extrapolation to e = 1. If the hydrogen bond is in a real medium the proton transfer is characterized by AHo (8) Brzic, A,; Karpfen, A,; Lischka, H.; Schuster, P., manuscript in preparation. (9) Karpfen, A,, private communication. (IO) Kollman, P., lecture at the VIth workshop "Horizons in Hydrogen Bonding", Leuven, 1982.
0 1984 American Chemical Society
6296 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
Zundel and Fritsch
and ASo.The interaction of the hydrogen bond with the medium is given by the differences MIo= AHo - AHoo and MIo= ASo - ASo’. Thus one obtains In KPT = -
AH,’
+ AH,’ RT
+ ASoo R+ MIo
Various experimental have shown that ASo for a proton transfer process in hydrogen bonds embedded in a liquid is always negative and amounts to -30 to -100 J/(mol K) [-8 to -25 cal/(mol K)]. On the basis of gas-phase experirnent~”~and theoretical treatments,+1° Moo is always positive for pairs of not too strong acids and bases. AHO, the sum of AHooand M I ofor proton transfer equilibria of hydrogen bonds with environments, were measured by UVI2-l6 and IRI5J7spectroscopy by various authors. With all these studies AHo values in the region -6 to -32 kJ/mol [-1.5 to -8 kcal/mol] were found. All these results taken together show that, in a hydrogen bond with an environment in which the proton may transfer, the influence of the terms ASoand AHooresults in the exclusive formation of the molecular form of the complex, Le., the structure AH-B. Thus, if the proton transfer equilibrium is shifted to the right, AH,’, the interaction enthalpy of such a hydrogen bond, must be negative and so large that it overcompensates the other terms. We shall discuss in the following, firstly, the influence of Soo on the proton transfer equilibrium in AH-eB A--.H+B bonds. This equilibrium is considered with systems in which both proton-limiting structures have noticeable weight due to the influence of M I oLe., , due to the environment. Secondly, we shall discuss the properties of the hydrogen bonds responsible for the fact that the AHI’ values become negative and relatively large. 2.1.1. The Influence of Moo. Figure 1 shows the percentage of proton transfer as a function of ApK, for a family of complexes with OH-oN F? O-.-H+N bonds.ls ApK, is the pK, of the protonated base minus the pK, of the acid. According to Huyskens and Z e e g e r s - H u y s k e n ~“families” ~ ~ ~ ~ ~ of systems are defined as follows: within a family, the chemical compounds possess the same donor and same acceptor groups. These compounds have, however, different pK, values due to different substituents, but these substituents show similar interaction properties with their environments. With such families of systems, the following relation is valid to a good a p p r o ~ i m a t i o n : ~ ~ ~ ~ ~ In KPT = EApKa - 6 where $, and 6 are constants. Good agreement with this relation is shown by the results for the family shown in Figure lb. With the family of systems shown in Figure 1, a and b, AHo’ is varied by the acidity of the hydrogen bond donor. Similar results are obtained if Moo is varied by the basicity of the hydrogen bond acceptor molecules. Analogous results were already obtained with different methods for a large number of families of system^.^'-^^ (11) Denisov, G. S.; Bureiko, S. F.; Golubev, N. S.; Tokhadze, K. G. “Molecular Interactions”, Ratajczak, H.; Orville-Thomas, W. J., Eds.; Wiley: New York, 1981; Vol. 11, p 107. (12) Baba, H.; Matsuyama, A.; Kokubun, H. Spectrochim. Acta, Part A 1969, 25, 1700. (13) Crooks, J. E.; Robinson, B. H. Faraday Symp. Chem. SOC.1975,10, 29. (14) Denisov, G. S.; Schreiber, V. M. Vestn. Leningr. Uniu. 1976, 4 , 61. (15) Schreiber, M.; Koll, A.; Sobczyk, L. Bull. Acad. Polon. Sci., Ser. Chim. 1978, 26, 651. (16) Koll, A.; Rospenk, M.; Sobczyk, L. J . Chem. SOC.,Faraday Trans. 1 1981, 77, 2309. (17) Rospenk, M.; Fritsch, J.; Zundel, G. J. Phys. Chem. 1984, 88, 321. (18) Albrecht, G.; Zundel, G. J. Chem. SOC.,Faraday Trans. 1 1984,80, 553. (19) Huyskens, P.; Zeegers-Huyskens, Th. J. Chim. Phys. 1964, 61, 81. (20) Zeegers-Huyskens, Th.; Huyskens, P. In “Molecular Interactions”, Ratajczak, H.; Orville-Thomas, W. J., Eds.; Wiley: New York, 1981; Vol. 11, p 1.
Figure 1. Octylamine with phenols (0.1 M/dm3 solutions in CCI,): (1) 4-chlorophenol; (2) 3-chlorophenol; (3) 3,4-dichlorophenol; (4) 3,5-dichlorophenol; (5) 2,4-dichlorophenol; (6) 2,3-dichlorophenol; (7) 2,3,4trichlorophenol; (8) 2,4,5-trichlorophenol; (9) 2,3,5-trichlorophenoI;(10) 2,4,6-trichlorophenoI; (1 1) pentachlorophenol. (a) Proton transfer as a function of the ApK,. (b) log KpT as a function of the ApK,. (Reproduced with permission from ref 18. Copyright 1983, The Chemical Society.)
All these results demonstrate very well the relation between AHoo and the acidity and basicity of the hydrogen bond donors and acceptors. Of particular interest is the behavior of acids in water. It was shown’s2that, in 1:l mixtures of strong acids and water AH-OHZ (I) + A-.-H+OHz (11), bonds with large proton polarizability are present. In the series H N 0 3 , C6H5SO3H,H2Se04,HC104, H2S04,and CF3S03Hthe weight of proton-limiting structure I1 increases. This sequence reflects the influence of the term AHo’. (21) Barrow, G. M. J . Am. Chem. SOC.1956, 78, 5802. (22) Johnson, S. L.; Rumon, K. A. J. Phys. Chem. 1965, 69, 74. (23) Sobczyk, L.; Pawelka, 2. J. Chem. Soc., Faraday Trans. 1 1974,70, 832. (24) Lindemann, R.; Zundel, G. J. Chem. SOC.,Faraday Trans. 2 1977, 73, 788. (25) Bohner, U.; Zundel, G., manuscripts in preparation. (26) Brycki, B.; Dega-Szafran, Z.; Szafran, M. Adv. Mol. Relaxation Interact. Processes 1980, 15, 7 1. (27) Brycki, B.; Dega-Szafran, Z.; Szafran, M. Pol. J . Chem. 1980, 54, 221. (28) Zundel, G.; Nagyrevi, A. J . Phys. Chem. 1978,82, 685. (29) Ratajczak, H.; Sobczyk, L. J . Chem. Phys. 1969, 50, 556. (30) Kristof, W.; Zundel, G. Biophys. Struct. Mech. 1980, 6, 209. (31) Kristof, W.; Zundel, G. Biopolymers 1982, 21, 25.
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 6297
Environmental Interaction of Hydrogen Bonds
a M, al
t a
d
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s
3
20 1
Ld!L
wave number cm"
lo ApK,
I
b
-0.6 -0.5 -0.4 4 3
v
-
/
.
.
.
.
.
.
0.1 0.2 0.3 a4 0.5 0.6
x [AI
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A PKa Figure 2. (a) Average dipole moment of phenol-triethylamine hydrogen bonds as function of ApK,. (Reproduced with permission from ref 29. Copyright 1969,American Institute of Physics.) (b) Calculated dipole moment of
5r c
0
H502+ as function of the displacement of the excess proton.
2.1.2. Properties of AH-B * A---H+B Hydrogen Bonds with Respect t o AHI'. With increasing proton transfer in these hydrogen bonds a large average dipole moment arises. It was shown in H u y s k e n ~ ' ,M ~ ~a i e ~ k i ' s ,and ~ ~ S o b ~ z y k ' s *groups ~ , ~ ~ that this dipole is 8-15 D if the polar proton-limiting structure I1 is realized (see Figure 2a). This hydrogen bond dipole is composed of two contributions. The first, intrinsic, one is the dipole moment of the hydrogen bond isolated from its environment. The second, 0 extrinsic, one, usually much larger, is induced by the interaction -4 -3 -2 -1 0 1 2 of the hydrogen bond with its environment. This interaction is KPT very significant due to the proton polarizability of such hydrogen b o r ~ d s . ~These ~ - ~ ~proton polarizabilities are caused by the proton Figure 3. (a) IR spectra: (-) acetic acid + imidazole; (---) acetic acid + n-propylamine; (-) acetic acid + 2methylpyrazine. (Reproduced with shift within the hydrogen bonds. They are about two orders of permission from ref 24. Copyright 1977,The Chemical Society.) (b) magnitude larger than usual electron polarizabilities if symmetrical proton vibrational potentials in hydrogen bonds are p r e ~ e n t . ~ ~ - ~ ' Absorptivity of the continuum at 1800 cm-I as a function of ApK,, with the same systems as in Figure 1. (Reproduced with permission from ref Caused by this large proton polarizability the proton vibrational 18. Copyright 1983,The Chemical Society.) (c) Absorptivity of the potential is very soft and is easily deformed by electrical fields. continuum at 1600 cm-' with 2,4,6-trichloropheno1 (0)and 2,3,5-triThis results, in the case of AH.0.B A--H+B bonds, in a shift T from ref 39). chlorophenol (0)systems as function of the In K ~ (taken in favor of the polar form and, thus, in a large increase in the average dipole moment. The proton polarizability is largest if interactions of hydrogen bonds with large proton polarizability a symmetrical double minimum potential would be realized. In with their environments. These interactions are both static and real systems, however, the symmetrical situation is not present, dynamic in (see section 2.1.3). since all hydrogen bonds are polarized more or less strongly due In Figure 3b the absorptivity of such continua (at a wavenumber to these large polarizabilities (see below). value at which no bands of donor and acceptor molecules disturb The proton polarizability of hydrogen bonds24,37,38 is indicated the evaluation) is plotted against ApK,, whereby each point by continua in the IR spectra, as shown by the solid line spectrum represents one acid-base In Figure 3c the abin Figure 3a. These infrared continua are caused by the strong sorptivity of the continua of two acid-base systems is shown, ~ _ _ _ _ ~ whereby ~ the proton transfer equilibrium is shifted by various solvents.3g The flat maximum in the intensity of the continuum (32) Nouwen, R.;Huyskens, P. J . Mol. Srruct. 1973, 16, 459. (33)Jadiyn, J.; Makcki, J. Actn Phys. Polon. 1972, A41, 594. as a function of ApK, or In KPT, respectively, observed in both (34)Sobczyk, L. In "The Hydrogen Bond-Recent Developments in cases, reflects the change of the average proton potential and the Theory and Experiments", Schuster, P.; Zundel, G.; Sandorfy, C., Eds.; North associated proton polarizability discussed above. The fact that Holland: Amsterdam, 1976;Vol. 111, pp 939-955. the maxima are strongly flattened illustrates that symmetrical (35)Weidemann, E. G.;Zundel, G. Z . Narurforsch. A 1970, 25, 627. (36) Janoschek, R.; Weidemann, E. G.; Pfeiffer, H.; Zundel, G. J . Am. vibrational potentials are not realized in any case, instead, the Chem. SOC.1972, 94, 2387. vibrational potentials are deformed due to the polarization, as (37) Zundel, G.In "The Hydrogen Bond-Recent Developmentsin Theory discussed. and Experiments", Schuster, P.; Zundel, G.; Sandorfy, C., Eds.; North Hol-
u '
~~
land: Amsterdam, 1976;Vol. 11, Chapter 15. (38)Hayd, A,; Weidemann, E. G.; Zundel, G. J . Chem. Phys. 1979, 70, 86.
(39) Fritsch, J.; Zundel, G. J . Phys. Chem. 1981, 85, 556
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Figure 4. In KpT with 2,4,6-trichlorophenol+ N-methylpiperidinesystems in various solvents as function of the Onsager parameter (e - 1)/(2s + 1) (taken from ref 39). The shape of the average proton potential is directly related to the enthalpy of the proton transfer process. If the acid-base hydrogen bonds are considered without an environment this potential has usually a deep well at the donor group and, especially if the pK, of the protonated acceptor is not too small, a second well usually at much higher energy (Moo > 0). The interaction with the environment lowers, however, this second well. The resulting increased proton polarizability favors this change of the average proton potential. The term MIo becomes larger caused by the increasing induced dipole moment resulting in a stronger interaction of the hydrogen bonds with their environments (see section 2.1.3). Thus, the term MIo is responsible for this change of the average potential. If the deeper well is at the acceptor group the term M I owhich is always
