J. Phys. Chem. 1988, 92, 4139-4142
4739
Free Energies of Hydration of Solute Molecules. 4. Revised Treatment of the Hydration Shell Model Young Kee Kang,? Kenneth D. Gibson, George NCmethy, and Harold A. Scheraga* Baker Laboratory of Chemistry, Cornel1 University, Ithaca. New York 14853-1301 (Received: December 21, 1987)
A recently published model for the free energy of hydration of conformationallyflexible solute molecules (Kang, Y. K.; NBmethy, G.; Scheraga, H. A. J . Phys. Chem. 1987, 91, 4104, 4109, 41181 has been improved by introduction of an exact method for the calculation of the volume of the hydration shells and by improved selection of the numerical parameters to describe the free energy of hydration of constituent atoms of the solute molecule.
Introduction The conformation and the thermodynamic properties of solute molecules in aqueous solution depend on the free energy of hydration, Le., on the interaction of the atoms of the solute with the surrounding solvent medium. The hydration shell model is an efficient way of introducing hydration into conformational energy computations of small organic molecules, peptides, and proteins.14 In a recent series of papers, we presented a new formulation of the hydration shell m0de1.~-~Improvements of the model over earlier forms included the exact computation of double and triple overlap volumes of spheres, a simplification of the representation of group interactions with the hydration shell, the use of recent experimental data on the free energies of hydration of simple solutes to obtain parameters of the model, and the explicit consideration of the conformational flexibility of the s o l u t e ~ .The ~ model was tested by computing the free energies of hydration of 130 uncharged and 14 charged organic molecules (not counting 31 other molecules that were used to derive the parameters of the The present article describes several improvements of the hydration shell model that relate to the computation of the hydration volume and to the evaluation of the numerical parameters. These corrections were necessary because the recent formulation of the models-' still contained some shortcomings. The first of these corrections improves the calculation of the volume of the hydration shells, which previously involved some approximations. Although the contribution of double and triple overlap volumes of spheres to the solvent-accessible volume has been calculated e x a ~ t l y ,no ~ *correction ~ was made earlier5v8for quadruple and higher overlap volumes. A procedure is now available for the exact computation of the volume of any fused hard-sphere molecule: this procedure has been used here to obtain exact values of the volumes of hydration. As a second correction, the choice of the parameters that describe the free energy of hydration of polar hydrogen atoms in O H and N H groups of polyfunctional molecules has been improved. Previously, the same numerical parameters had been assigned to all polar hydrogen atoms.6 A close inspection of experimental thermodynamic data for hydration, as well as a comparison with the hydrogen bond strengths for 0-H--0 and N-H--0 hydrogen suggested that a more self-consistent formulation is possible if different parameters are assigned to the hydrogen atoms in OH and N H groups. This change required a modification of this parameter for nitrogen atoms as well, for the sake of consistency. Third, the reparametrization required a revision of the numerical value of the dielectric constant of the hydration shell, t h , that is used in the computation of the polarization interactions between polar atoms (0,N , hydroxyl, and amine H) in polyfunctional molecules.6 'On leave from the Department of Chemistry, Chungbuk National University, Cheongju, Chungbuk 310, Korea. *Towhom correspondence and requests for reprints should be addressed.
0022-3654/88/2092-4139$01.50/0
The modifications of the previous procedure and of the numerical parameters are summarized here. They result in better agreement between experimental and computed free energies of hydration, as shown below.
Procedure General Description. The procedures have been described in detail earlier,w and only some of the salient points are summarized here. The free energy of conformation i in solution is given by AG,c') = A@') + AGh(i) (1) where
is the conformational energy, and k
is the free energy of hydration of the solute molecule in conformation i, expressed as the sum of the free energies of hydration of all its constituent atoms or groups k . vwa,k(i) is the water-accessible volume of group k in a given conformation i of the compound, and is the free energy density of hydration of group k. In polyfunctional molecules, a correction is added to account for the polarization of the hydration shell around polar groups by the presence of neighboring polar groups.6 The free energy of hydration of a compound is obtained as a Boltzmann weighted average over all conformation^.^^^ Computation of Solvent-Accessible Volumes. As before?*8the molecule is treated as the union of a number of van der Waals spheres representing atoms or groups of atoms, each of which is surrounded by a uniform hydration shell. Connectivity, as expressed by chemical bonds, and interatomic interactions within the molecule will cause one van der Waals sphere to penetrate the hydration shell of another, thereby removing solvent from that shell. The solvent-accessible volume of each hydration sphere is the volume of that part of its shell that is not occupied by any other sphere. Let the molecule be made up of N van der Waals spheres Si (1 I i I N), and let Hk be the sphere consisting of the van der Waals sphere Sk together with its hydration shell. Let (1) Gibson, K. D.; Scheraga, H. A. Proc. Narl. Acad. Sci. CJ.S.A . 1967, 58, 420. (2) Hopfinger, A. J. Macromolecules 1971, 4 , 731. (3) Hodes, Z. I.; Ntmethy, G.; Scheraga, H. A. Biopolymers 1979, 28, 1565. (4) Paterson, Y.; Nbmethy, G.; Scheraga, H. A. Ann. N.Y. Acad. Sci. 1981, 367, 132. (5) Kang, Y . K.; Ntmethy, G.; Scheraga, H. A. J . Phys. Chem. 1987,92, 4105. Erratum, Ibid. 1988, 92, 1382. ( 6 ) Kang, Y. K.; NEmethy, G.; Scheraga, H. A. J . Phys. Chem. 1987,92, 4109. Erratum, Ibid. 1987, 91, 6568. (7) Kang, Y. K.; Nbmethy, G.; Scheraga, H. A. J . Phys. Chem. 1987,92, 41 18. (8) Gibson, K. D.; Scheraga, H. A. J . Phys. Chem. 1987, 92, 4121. Erratum, Ibid., 6326. (9) Gibson, K. D.; Scheraga, H. A. Mol. Phys. 1987,62, 1247. (10) Momany, F. A.; McGuire, R. F.; Burgess, A. W.; Scheraga, H. A. J . Phys. Chem. 1975, 79, 2361. (11) Nbmethy, G.; Pottle, M. S.; Scheraga, H. A. J. Phys. Chem. 1983, 87, 1883. (12) Sippl, M. J.; NEmethy, G.; Scheraga, H. A. J . Phys. Chem. 1984.88, 6231.
0 1988 American Chemical Society
4740 The Journal of Physical Chemistry, Vol. 92, No. 16, 1988
Kang et al.
TABLE I: Hydration Shell Parameters
atom or group hydroxyl, amine H polyfunctional hydroxyl H polyfunctional amine, amide H protonated amine H thiol H aliphatic CH3 aliphatic CH, aliphatic CH aliphatic C alicyclic CHI alicyclic CH alicyclic C aromatic CH aromatic C bridged aromatic C of fused rings aromatic C bonded to 0 carbonyl, carboxylic or amide C primary amine N protonated primary amine N secondary amine N protonated secondary amine N tertiary amine N protonated tertiary amine N alicyclic amine N aromatic N protonated aromatic N amide N ether or hydroxyl 0 ester or carboxylic 0 carbonyl 0 ester, amide or carboxylic carbonyl 0 carboxylate 0 thiol or sulfide S S bonded to aromatic carbon
R,,"
A
Rh.
A
hb
kcali(m01.A~) -1.057 X -3.352 X 10-3d3e -8.296 X -3.244 X 6.065 X lo-'
1.415 1.415 1.415 1.415 1.415
4.17 4.17 4.17
2.125 2.225 2.375
5.35
1.577 X
5.35 5.35 5.35
3.533 x -4.151 X -1.488 X 4.469 X -6.783 X -1.488 X -2.734 X -1.991 X -1.396 X 6.298 X -1.488 X -1.877 X -1.034 X -9.958 X -1.182 X -1.549 X -1.268 X -9.068 X -9.409 X -1.143 X -1.200 x -9.450 X -5.334 x -1.218 X -5.334 x -9.287 X -6.737 X -3.766 X
2.06 2.225
2.375 2.06 2.10 1.85 1.85 1.85 1.87 1.755 1.755
1.755 1.755 1.755 1.755 1.755 1.755 1.755 1.755
1.62 1.62 1.56 1.56 1.56 2.075 2.075
4.17 4.17
5.35 5.35 5.35 5.35 5.35 5.35 5.35 5.35
5.05 5.05 5.05 5.05 5.05 5.05 5.05 5.05 5.05 5.05 4.95 4.95 4.95 4.95 4.95 5.37 5.37
10-4
lo4 lo-' lo-'
lo-' lo-' 10-3d lo-'
10-3 lo-, 10-3 lo-,
ref comDdc 2-propano1, 1-propanol 2-methox yethanol 2-methox yethanamine
ethyl-, diethyl- and triethylammonium ethanethiol ethane propane isobutane neopentane cyclopropane methylcyclopentane
f
benzene toluene naphthalene phenol
f
n-propylamine ethylammonium diethylamine diethylammonium triethylamine triethylammonium azetidine 2-methylpyridine pyridinium acetamide diethyl ether and methyl n-propyl ether n-propyl acetate 2-pentanone
g
propionate diethyl sulfide methyl phenyl sulfide
"The van der Waals radii R, and hydration radii Rh are identical with those used bThe precision of Agh corresponds to three significant figures. A fourth digit is included to reduce rounding errors. Used in determining adjustable parameters. dNewly determined parameter. All CThepolar hydrogen atoms in carboxylic acids and amides also were assigned the same respective others are identical with those derived parameters. /Assumed to be the same as for the aliphatic C. gAssumed to be the same as the ether 0 of esters.
M denote the whole molecule, and & f k the union of all the van der Waals spheres except sk. Then N
M =
us;= Sk u
= Sk
+ M k - Sk n Mk
(3)
1=1
If Mk(h)is a pseudomolecule made up from the hydrated sphere Hk and all the remaining van der Waals spheres Si( i # k), then h'fk(h) = Hk M k = Hk + M k - Hk n M k (4)
u
The solvent-accessiblepart of the hydration shell of the kth sphere, Ak, is the difference between the whole shell and the part of the shell that intersects all other spheres Si( i # k). Thus Ak = Hk - Sk - (Hk - sk) n Mk = Hk - Sk - Hk n M k + Sk n M k ( 5 ) Comparing eq 5 with eq 3 and 4 A k -- M (k " - M (6) Thus, the solvent-accessible volume of the kth hydration sphere is the difference between the volumes of the pseudomolecule MLh) and the original molecule M . Since each of these is a fused hard-sphere molecule, its volume can be computed exactly by a procedure described e l ~ e w h e r e . ~ Computation of the Free Energy of Hydration. The procedures for the computation of the free energy of hydration follow those described The experimental free energies of hydration were the same as those used They were taken from ref 13 and references therein. Hydration Shell Parameters. The van der Waals radii, R,, and the hydration shell radii, R,, are identical with those used bef~re.~ The . ~ free energy density of hydration for each atom or (13) Cabani, S.; Gianni, P.; Mollica, V.; Lepori, L. J . Solution Chem. 1981, 10, 563.
group k, &h,k has been obtained by fitting the computed free energy of hydration of only one compound per atom or group k (listed in the last column of Table I) to the experimental free energy, as before. Dielectric Constant of the Hydration Shell. The polarization correction term, used only for polyfunctional molecules, contains one adjustable parameter, viz., the dielectric constant q, of the hydration shell. Its numerical value has been redetermined by fitting the free energy of hydration of I ,2-dimethoxyethane to its experimental value, by using the revised hydration shell parameters. The best fit is obtained for t h = 2.39 (compared to the value of 2.78, obtained previously6). For the present purpose, polar functional groups, such as hydroxyl, carbonyl, amine, and thiol, are considered as monofunctional, and no polarization correction was applied within each functional group. The amide group, on the other hand, was considered as bifunctional, consisting of the two monofunctional groups CO and N H , because rotation can occur about the C-N bond. Hence, the correction term was applied to the amide group.
Results and Discussion The modifications described above have resulted in changes of the free energy density parameter Agh,kfor the following atoms only, as shown in Table I: hydrogen attached to 0 and N, nitrogen, bridged aromatic carbon of fused rings, and sulfur bonded to aromatic carbon. For some of these atoms, the numerical value of Agh,kwas altered significantly (cf. Table I of ref 6), but these changes were accompanied by corresponding changes of Vwa,k, so that the product of the two quantities, viz., the free energy of solution of group k , is affected little by the revision of the parameters. On the whole, a better fit of the data has been obtained with the revised parameters. The calculated and experimental free
Free Energies of Hydration of Solute Molecules
The Journal of Physical Chemistry, Vol. 92, No. 16, 1988 4741
TABLE 11: Comparison of Calculated and Experimental Free Energies of Hydration (kcal/mol) for Nonionic Organic Molecules" mokculeb naphthalene* a-methylnaphthalene 1,3-dimethylnaphthalene 1,4-dimethyInaphthalene 2,3-dimethylnaphthalene 2,6-dimethylnaphthalene fluorene anthracene phenanthrene pyrene methylamine eth ylamine n-propylamine* n-butylamine n-pent ylamine n-hexylamine trimethylamine triethylamine* aziridine axtidine* pyrrolidine piperidine N-methylpyrrolidine N-meth ylpiperidine 3-methylindole methyl phenyl sulfide* benzenethiol dimethoxymethane 1,2-dimethoxyethanee 1,l-diethoxyethane 1,2-diethoxyethane 1,3-dioxolane 1,4-dioxane 2-methoxyethanol*i 2-ethoxyethanol 2-propoxyethanol 2-butoxyethanol ethylene glycol glycerol 1,2-ethanediamine piperazine N-methylpiperazine N,N'-dimeth ylpiperazine 2-methylpyrazine 2-eth ylpyrazine 2-methoxyethanamine*g 3-methoxy-1-propanamine morpholine 4-meth ylmorpholine acetic acid" propionic acid butyric acid acetamide*** propionamide n-propylguanidine 4-methylimidazole
calcd -2.39 -2.34 -2.24 -2.25 -2.31 -2.30 -3.38 -3.79 -3.84 -4.84 -5.23 -4.61 -4.39 -4.22 -4.04 -3.88 -4.29 -3.02 -6.12 -5.56 -5.19 -4.73 -4.59 -4.10 -6.59 -2.73 -2.33 -3.58 -4.84 -2.08 -4.32 -4.90 -5.21 -6.77-6.49 -6.17 -5.99 -8.59 -12.22 -8.46 -9.23 -9.05 -8.76 -7.92 -7.46 -6.55 -6.82 -7.29 -7.24 -7.28 -6.79 -6.52 -9.71 -9.22 -10.93 -10.41
exptlC -2.39 -2.37 -2.47 -2.82 -2.78 -2.63 -3.44 -4.23 -3.95 -4.46 -4.56 -4.50 -4.39 -4.30 -4.10 -4.03 -3.24 -3.02 -5.41 -5.56 -5.48 -5.11 -3.98 -3.89 -5.91 -2.73 -2.55 -2.93 -4.84 -3.27 -3.53 -4.10 -5.06 -6.77 -6.61 -6.42 -6.27 -7.66 -9.22 -7.60 -7.38 -7.78 -7.58 -5.52 -5.46 -6.55 -6.93 -7.18 -6.34 -6.70 -6.48 -6.36 -9.71 -9.41 -10.92 -10.25
Ad
0.00 0.03 0.23 0.57 0.47 0.33 0.06 0.44 0.11 -0.38 -0.67 -0.11 0.00 0.08 0.06 0.15 -1.05 0.00 -0.71 0.00 0.29 0.38 -0.61 -0.21 -0.68 0.00 0.22 -0.65 0.00 1.19 -0.79 -0.80 -0.15 0.00 0.12 0.25 0.28 -0.93 -3.00 -0.86 -1.85 -1.27 -1.18 -2.40 -2.00 0.00 0.11 -0.1 1 -0.90 -0.58 -0.31 -0.16 0.00 0.19 -0.01 -0.16
Only those molecules are listed for which the revision resulted in a change of the calculated free energy. For other molecules, see ref 6 and 7. The free energy of hydration refers to the isothermal transfer of the molecule from the ideal 1 M gas state to the hypothetical ideal 1 M aqueous solution at 25 O C . bThe starred molecules were used to obtain the numerical values of Agh. CExperimentalvalues are taken from ref 13 and references therein. d A = calcd - exptl. CMoleculeused to obtain the dielectric constant within the hydration shell, eh = 2.39. 'Molecule used to obtain Agh of the hydroxy hydrogen atom of polyfunctional molecules. EMolecule used to obtain Agh of the amine hydrogen atom of polyfunctional molecules: *The hydrogen atoms in carboxylic acids and amides are considered as polyfunctional hydrogen atoms.
energies of hydration are listed in Tables I1 and I11 for those compounds for which the calculated values have been revised here. The average absolute difference and the standard deviation (AAD a n d SD, respectively, defined in eq 12 and 1 3 of ref 6) are listed in Table IV for each class of compounds and for the entire sets.
TABLE III: Comparison of Calculated and Experimental Free Energies of Hydration (kcal/mol) for Charged Amines" ionb methylammonium ethylammonium* n-propylammonium isopropylammonium n-butylammonium tert-butylammonium dimet hylammonium diethylammonium* di-n-propylammonium pyrrolidinium piperidinium trimethylammonium triethylammonium* 1-methylpyrrolidinium pyridinium'
calcd -72.60 -68.42 -66.42 -64.49 -65.79 -61.73 -67.12 -58.89 -54.41 -62.52 -59.09 -59.96 -50.19 -55.59 -56.1 1
exDtlC -7 1.3 -68.4 -66.7 -65.5 -66.2 -63.1 -63.9 -58.9 -57.7 -61.6 -60.0 -56.6 -50.2 -54.6 -56.1
Ad
~-
-1.3 0.0 0.3 1.o 0.4 1.4 -3.2 0.0 3.3 -0.9 0.9 -3.4 0.0 -1.0 0.0
"dSee corresponding footnotes in Table 11.
TABLE I V Comparison of Calculated and Experimental Free Energies of Hydration for Various Classes of Organic Molecules av absolute difference, std dev, molecules" kcal/mol kcal/mol
no. of
class of compounds uncharged molecules aliphatic hydrocarbons aromatic hydrocarbons* ethers monohydric alcohols ketones esters carboxylic acids amines and amidesb sulfides and thiols* polyfunctional molecules of N and 0 atomsb all uncharged moleculesb~e charged molecules carboxylates protonated aminesb all charged moleculesbSd
10 15 11 22 10 13 3 22 3 21
0.05 0.22 0.70 0.36 0.33 0.20 0.35 0.36 0.35 0.90
0.02 0.08 0.26 0.09 0.19 0.10 0.23 0.10 0.21 0.25
130
0.43
0.06
2 12 14
1.5 1.5 1.5
1.2 0.5 0.5
"Used for testing. Not counting the molecules used to determine the parameters. *Redetermined in the present work. All other data were taken from ref 6 and 7. 'The previously obtained values6 of the AAD and of the SD for all uncharged compounds were 0.46 and 0.07 kcal/ mol, respectively. dThe previously obtained values' of the AAD and of the SD for all charged compounds were 1.7 and 0.6 kcal/mol, respectively.
The changes in the AAD and the SD are small for most classes. The largest improvement occurred for the polyfunctional compounds, for which the AAD changed from 1.16 to 0.90 kcal/mol and the SD changed from 0.34 to 0.25 kcal/mol, as well as for the protonated amines, with a change of the AAD from 1.7 to 1.5 kcal/mol and of the SD from 0.6 to 0.5 kcal/mol (cf. Table XI of ref 6 and Table I11 of ref 7, respectively). Considering individual compounds, most of the newly computed free energies agree closely, to within 0.1-0.2 kcal/mol, with those computed earlier. Significant improvements between calculated and experimental free energies were obtained for the polyhydric alcohols and amines, as well as for some protonated secondary and tertiary amines, while worse agreement was found for piperazine derivatives. The assignment of parameters to the nitrogen atoms in guanidine and its derivatives has been changed in this revision. Earlier: different parameters had been assigned to the three nitrogen atoms, but now they were all treated as amide N atoms. As a result, a very large improvement occurred for n-propylguanidine, viz., the difference between the calculated and observed free energy of hydration decreased from 1.25 kcal/mol in the earlier calculation6 to -0.01 kcal/mol. The difference decreased from -0.36 to -0.16 kcal/mol in 4-methylimidazole as well. These results are important, because the two compounds serve as models for
J . Phys. Chem. 1988, 92, 4142-4145
4142 t h e arginyl a n d histidyl side chains in peptides.
Acknowledgment. This work was supported by research grants from the National Science Foundation (DMB84-018 1 I ) , t h e National Institute of General Medical Sciences (GM-14312), and t h e N a t i o n a l Institute on Aging (AG-00322) of the National Institutes of Health, U. S. Public Health Service. Support w a s also received from the National Foundation for Cancer Research and from Hoffmann-La Roche. Y.K.K. thanks the Korea Science and Engineering Foundation for support. Registry No. Naphthalene, 91-20-3; a-methylnaphthalene, 90-12-0; 1,3-dimethylnaphthalene,575-4 1-7; 1,4-dimethyInaphthalene,57 1-58-4; 2,3-dimethylnaphthalene,58 1-40-8; 2,6-dimethylnaphthalene,58 1-42-0; fluorene, 86-73-7; anthracene, 120-12-7; phenanthrene, 85-01-8; pyrene, 129-00-0; methylamine, 74-89-5; ethylamine, 75-04-7; n-propylamine, 107-10-8; n-butylamine, 109-73-9; n-pentylamine, 110-58-7; n-hexylamine, 111-26-2; trimethylamine, 75-50-3; triethylamine, 121-44-8; aziridine, 15 1-56-4; azetidine, 503-29-7; pyrrolidine, 123-75-1; piperidine, 110-89-4; N-methylpyrrolidine, 120-94-5; N-methylpiperidine, 626-67-5;
3-methylindole, 83-34-1; methyl phenyl sulfide, 100-68-5; benzenethiol, 108-98-5; dimethoxymethane, 109-87-5; 1.2-dimethoxyethane, 110-71-4; 1,l-diethoxyethane, 105-57-7; 1,2-diethoxyethane, 629-14-1; 1,3-dioxolane, 646-06-0; 1,4-dioxane, 123-91-1; 2-methoxyethanol, 109-86-4; 2-ethoxyethanol, 1 10-80-5; 2-propoxyethanol, 2807-30-9; 2-butoxyethanol, 111-76-2; ethylene glycol, 107-21-1; glycerol, 56-81-5; 1,2ethanediamine, 107-15-3; piperazine, 110-85-0; N-methylpiperazine, 109-01-3; N,N-dimethylpiperazine, 106-58-1; 2-methylpyrazine, 10908-0; 2-ethylpyrazine, 13925-00-3; 2-methoxyethanamine, 109-85-3; 3-methoxy-l-propanamine, 5332-73-0; morpholine, 110-91-8; 4methylmorpholine, 109-02-4; acetic acid, 64- 19-7; propionic acid, 7909-4; butyric acid, 107-92-6; acetamide, 60-35-5; propionamide, 79-05-0; n-propylguanidine, 462-25-9; 4-methylimidazole, 822-36-6; methylammonium, 17000-00-9; ethylammonium, 16999-99-8; n-propylammonium, 17033-39-5; isopropylammonium, 16999-98-7; n-butylammonium, 16999-97-6; tert-butylammonium, 22534- 19-6; dimethylammonium, 17000-0 1-0; diethylammonium, 19497-23-5; di-n-propylammonium, 29384-47-2; pyrrolidinium, 55526-39-1; piperidinium, 17523-59-0; trimethylammonium, 16962-53-1; triethylammonium, 17440-81-2; 1-methylpyrrolidinium, 67433-74-3; pyridinium, 16969-45-2.
Thermochemistry of Charge-Transfer Complexes. 1. Enthalpy of Formation of Charge-Transfer Complexes of Molecular Iodine with Chlorinated Benzene Derivatives Rad Morales, George C. Diaz, and Jeffrey A. Joens* Department of Chemistry, Florida International University, Miami, Florida 331 99 (Received: January 22, 1988; In Final Form: March 10, 1988)
A new approximate procedure for the determination of the enthalpy of formation and formation constant of a weakly bound charge-transfer complex has been developed. T h e method uses absorption measurements on the charge-transfer complex to determine the enthalpy of formation in the limit of low solute concentrations, where ideal solution behavior occurs. Values for the formation constant for a complex can also be obtained. The method is used to determine the enthalpy of formation for 1:1 charge-transfer complexes of iodine with benzene and chlorinated benzene derivatives. T h e enthalpy of formation for the donor-iodine complexes is found t o depend in a systematic manner on the number of chlorine atoms attached to the benzene ring but is independent of the positions of the chlorine atoms on the ring.
Introduction Beginning with the first investigations of the benzene-iodine system by Benesi and Hildebrand,1*2there has been considerable interest in t h e spectral and thermochemical properties of charge-transfer Such complexes have important applications in studies of organic r e a ~ t i v i t y . ~ - 'They ~ are also of interest because of the information they provide concerning weak interactions between molecule^.^^-^^ Spectroscopic methods have been most commonly used i n studies of the equilibrium and thermochemistry of charge-transfer complexes. The Benesi-Hildebrand,2 Scott," Rose-Drago?l and related equations have been developed for the analysis of experimental data from UV-visible spectroscopic data. However, there are seveal problems associated with t h e use of these equations, particularly for weakly bound charge-transfer complexes. A c c u r a t e values for the formation constant of a charge-transfer complex can only be obtained when t h e concentration of t h e complex can be made approximately equal t o t h e free concentration of the most dilute component in solution.4-6J2J3 For weakly bound charge-transfer complexes it is often impossible t o collect data under these conditions. Even for cases when such studies c a n be done, t h e r e are additional difficulties associated with nonideal solution behavior, particularly a t high solute concentrations, and the possibility of formation of complexes with different stoichiometries.6J6 Since thermochemical d a t a is usually obtained f r o m the variation of the formation constant for t h e charge-transfer complex with temperature, errors in t h e deter-
* Author to whom correspondence should be addressed.
mination of t h e formation constant will give rise to errors in the
thermochemical results as well. T h e present paper presents a new method for t h e analysis of spectral data on charge-transfer complexes. This method makes it possible to determine values of the enthalpy of formation of (1) Benesi, H. A.; Hildebrand, J. H. J . Am. Chem. SOC.1948, 70,2382. (2) Benesi, H. A.; Hildebrand, J. H. J . Am. Chem. SOC.1949, 71, 2703. (3) Andrews, L. J.; Keefer, M. Molecular Complexes in Organic Chemistry; Holden-Day: San Francisco, 1964. (4) Brieglieb, G. Electronen Donator Acceptor Komplexe; Springer-Verlag: Berlin, 1964. (5) Foster, R. Organic Charge Transfer Complexes; Academic: New York, 1969. ( 6 ) Mulliken, R. S.; Person, W. B. Molecular Complexes; Wiley: New York, 1969. (7) Foster, R. Molecular Complexes; Paul Elek London, 1973. (8) Tamres, M.; Strong, R. In Molecular Associations; Foster, R., Ed.; Academic: New York, 1979; Vol. 2, Chapter 5. (9) Kochi, J. Organic Mechanism and Catalysis; Academic: New York, 1978; Part 3. (10) Lewis, F. D. Acc. Chem. Res. 1979, 12, 152. (11) Fukuzumi, S.;Kochi, J. K. J . Phys. Chem. 1980, 84, 2246. (12) Fukuzumi, S.; Kochi, J. K. J . Am. Chem. SOC.1981, 103, 7240. (13) Fukuzumi, S.;Kochi, J. K. J . Am. Chem. SOC.1982, 104, 7599. (14) Fox, M. A.; Younathan, J.; Fryxell, G. E. J . Org. Chem. 1983, 48, 3109. (15) McHale, J.; Banerjee, A,; Simons, J. J . Chem. Phys. 1978.69, 1406. (16) Foster, R. J . Phys. Chem. 1980, 84, 2135. (17) Kroeger, M. K.; Drago, R. S.J . Am. Chem. SOC.1981, 103, 3250. (18) Stevens, B. J . Phys. Chem. 1984, 88, 702. (19) Snyder, R.; Testa, A. C. J . Phys. Chem. 1984, 88, 5948. (20) Scott, R. L. Red. Trau. Chim. 1956, 75, 787. (21) Rose, N.; Drago, R. S.J. Am. Chem. SOC.1959, 81, 6138. (22) Person, W. B. J. Am. Chem. SOC.1965.87, 167. 1969, 91, 4044. (23) Deranleau, D. A. J . Am. Chem. SOC.
0022-365418812092-4742$01 SO10 0 1988 American Chemical Society
