J . Phys. Chem. 1985,89, 326-332
326
and slightly (b) a zwitterion as shown in eq 7. There is also a
CH3
‘Y
ci3
question about the nature of the proton-transferred species of MS, whether it is a tautomer or a z w i t t e r i ~ n . ’ ~It J ~seems that the species of MS has mainly a tautomer structure as well as the case of the triazines.
Summary (1) The excited-state and ground-state proton-transfer reactions of 6-(2-hydroxy-5-methylphenyl)-s-triazinescan be accounted for by the schematic energy-state diagram as shown in Figure 3. (2) The excited-state intramolecular proton transfer (k,) occurs from the excited singlet state of the intramolecularly hydrogenbonded enol form of the triazines (SI)to the excited singlet state of the keto form (SIt)with no potential barrier. The rate constant for the excited-state proton-transfer reaction km is very fast (>2 X 10” s-l, probably 2 X 10l2 s-I). The green emission at near 500 nm with the large Stokes shift (- 10 X lo3cm-I) arises from the SI’ state. (3) The rapid nonradiative decay kd competitive with km takes place with activation energies 1.15 (00),1 S S (ON), and 1.65
(NN) kcal mol-’. The kd process is due to internal conversion from the SI state associated with the out-of-plane bending vibration to the vibrationally excited So state. The kd process is negligibly small at 77 K. (4) The lifetimes q‘of the SI’state increase with decreasing temperature to give the constant values [5.0 (00)and 5.6 (ON) ns] at 77 K. For (NN), there is no temperature effect on 7; [5.7 ns (NN)]. (5) The transient absorption spectra with the absorption maxima 470 (00),490 (ON) and -494 (NN) nm are ascribed to the SI’ So’ electronic transitions. (6) The ground-state proton-transfer kmo from the S’, state (ground keto form) to the So state (ground enol form) of the starting material takes place relatively slowly ( lo3 s-l) at room temperature. The kpToprocess involves an activation energy in contrast to that of km. The potential barriers AERO are in the (NN) > 5.1 (ON) > 1.8 kcal mol-I (00).As a result, order the ground-state proton-transfer rate constants are in the order (00)> (ON) > (NN). (7) The strength of intramolecular hydrogen bonding in the starting materials is closely related to both excited-state and ground-state proton-transfer reactions, which is favorable to the former process k,, but not advantageous to the latter process km0. (8) The nature of the excited-state proton-transferred species SI’(or S,l) seems to be a resonance structure between a keto form (tautomer) and a zwitterion considering the electronic structures of triazines calculated by the usual S C F MO CI method. Registry No. 00,33950-62-8; ON, 52752-89-3; NN, 52752-90-6.
-
-
Cyclodextrin-Adamantanecarboxyiate Inclusion Complexes: Studies of the Variation in Cavity Size William C. Cromwell, Katarina Bystrom, and Maurice R. Eftink* Department of Chemistry, University of Mississippi, University, Mississippi 38677 (Received: September 17, 1984)
The standard free energy change, AGO, and standard enthalpy change, AHo, for the interaction of adamantanecarboxylate with three cyclodextrins (CDs) of var ing cavity size, a-CD (internal diameter = 5A), b-CD, (internal diameter = 6.9 A), and y C D (internal diameter = 8.5 ), have been studied to characterize structure/energetics relationships for complex formation. The 8-CD-adamantanecarboxylate interaction is thd most exergonic (AGO = -5.85 kcal/mol) and exothermic (AHo = -4.85 kcal/mol). The exothermic AHo can be interpreted as indicating that the binding forces for this complex include both the hydrophobic effect and a strong van der Waals interaction, due to the snug fit of adamantanecarboxylate into the &CD cavity. The binding of adamantanecarboxylate to a-CD, with its smaller cavity, and y-CD, with its larger cavity, is poorer (140-fold lower binding constant for a-CD). This highlights the importance of an optimum matching of the cavity size and ligand size in determining the strength of binding. Interestingly, the AHo for forming the y-CD complex is endothermic, suggesting that binding is driven primarily by the hydrophobic effect in this case. pH titration studies of the CD-adamantanecarboxylate complexes show that the neutral carboxylic acid form of the ligand binds better than does the carboxylate form. These studies also demonstrate the formation of a 2: 1 a-CD-adamantanecarboxylic acid complex, whereas 1:l complexes form with 8-CD and y-CD.
dl
Cyclodextrin (CD, also known as cycloamyloses) inciusion complexes have been very useful models for studying the nature of hydrophobic and van der Waals forces in aqueous solution.’-’ (1) M. L. Bender and M. Komiyama, “Cyclodextrin Chemistry”, Springer-Verlag, New York, 1978. (2) R. L. VanEtten, J. F. Sebastian, G. A. Clowes, and M. L. Bender, J . Am. Chem. Soc., 89, 3242-3253 (1967). (3) F. Cramer, W. Saenger, and H.-Ch. Spatz, J . Am. Chem. Soc., 89, 14-20 (1967). (4) W. Saenger in ‘Proceeding of the First International Symposium on Cvclodextrins”.J. Szeitli. Ed.. Reidel. New York. 1982. DD 141-150. (5) R. J. Bergeron,*D.’M.hllor, d. Gibeily, and W. xkoberts, Eioorg. Chem., 1,263-271 (1978).
0022-3654/85/2089-0326$01.50/0
CDs are torrus shaped molecules with an apolar cavity and show a certain degree of selectivity in binding ligand hosts. Thus they are a very good model for studying the molecular and thermodynamic bases for selectivity in protein-ligand interactions. Examples of this selectivity include the preferential binding of p-nitrophenolate as compared to p - n i t r o p h e n ~ l ~ *and ~ . ~the *~ (6) I. Tabushi, Y. Kiyosuke, T. Sugimoto, and K. Yamamura, J . Am. Chem. Soc., 100, 916-919 (1978). (7) R. Gelb, L. M. Schwartz, B. Cardelino, H. S. Fuhrman, R. F. Johnson, and D. A. Laufer, J . Am. Chem. Soc., 103, 1750-1757 (1981). (8) R. J. Bergeron, M. A. Channing, G. J. Gibeily, and D. M. Pillor, J . Am. Chem. Soc., 99, 5146-5151 (1977).
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 327
Cyclodextrin Inclusion Complexes
Scheme I1
Scheme I
ti+
H+
M
+
LH
-+ d
M
L-
M
preferential binding of alkyl carboxylic acids as compared to the analogous carboxylate^.^^^^'^ A very interesting inclusion complex that we have studied is that formed between adamantanecarboxylate and j3-CD (cycloheptaamyl~se).'~The association constant for this complex is quite large compared to other inclusion complexes and is of similar magnitude to many protein-ligand association constants. A study of the solvent dependence of the binding led us to conclude that about 70% of the -AGO for the formation of this complex is due to van der Waals interactions between the ligand and the apolar binding pocket, and about 30% of the -AGO is due to the hydrophobic effect. A curious observation was that the association constant of adamantanecarboxylate to a-CD (cyclohexaamylose) is about 100 times smaller than that for j3-CD. This suggests that there is a poorer fit between adamantanecarboxylate and the smaller cavity of a-CD. To further characterize the interaction between adamantanecarboxylate and CDs we have now performed thermodynamic studies of the binding of adamantanecarboxylate to a-, j3-, and y C D ( + 2 D is cyclooctaamylose). A comparative study of the binding of this ligand with the set of CDs should provide insight concerning the bases for specificity in inclusion complex formation. We have also studied the binding of both the carboxylate and carboxylic acid forms of the ligand to the CDs. Models for the Ligand-CD Interaction. In order to interpret the microcalorimetric and potentiometric binding data to be presented below, two binding schemes will be considered. Case I pertains to the exclusive formation of 1:l CD-ligand complexes, while case I1 pertains to the stepwise formation of both 1:l and 2:l CD-ligand complexes. The latter case is considered since there is much evidence for the formation of 2:l complexes with certain l i g a n d ~ ~ J ~ I *In~ 'both ~ . binding schemes coupling is included between ligand binding and the proton dissociation of the ligand. Case I. In thermodynamic Scheme I, L H represents the neutral adamantanecarboxylic acid, L- is the carboxylate, M is CD, K , and K l - are the respective association constants of these ligand forms, K, is the acid dissociation constant of adamantanecarboxylic acid, and K,' is the acid dissociation constant of the CD-ligand complex. In binding studies in which the concentration of ligand is fixed and the concentration of C D is varied, the saturation parameter for complex formation, v, will be given as (v is defined as the concentration of complexed ligand divided by the total concentration of ligand) (M-LH) v=
(LH)
+ (M-L-)
+ (L-) + (M-LH) + (M-L-) (M)K,[1 + K,'/(H+)I
v=
1 + K,/(H+)
+ (M)K,[1 + K l / ( H + ) I
(la)
+
LH d*
M
+
L-
and (L), is the total ligand concentration. In proton uptake binding studies, v is experimentally measured where H i s the difference in the fractional degree as v = An/", of protonation of the ligand in the ML complexes as compared to the fractional degree of protonation of the ligand in the absence of CD (Le., H is the maximum proton uptake, per mole of ligand, upon saturation of ligand with CD at a particular pH), and An is the proton uptake, per mole of ligand, upon mixing nonsaturating levels of C D with ligand. From Scheme I
Thus from experimentally determined An values, which equal VAN for this case, as a function of (M), a hyperbolic binding profile described by eq 3a is obtained. Likewise, a linear double reciprocal plot corresponding to eq 3b obtains for this case of 1:l complex formation. An =
(M)Kl[1 + K,'/(H+)lAN 1 + Ka/(H+) + (M)K1[1 + K,'/(H+)I
_1 An
1 + K,/(H+) (M)K,[l + K,'/(H+)]AN
1 + -AN
(3a) (3b)
For microcalorimetric studies, v is determined as Q/Qm, where
Q is the observed heat effect for the association reaction and Q, is the maximum heat effect at saturation. Plots of Q vs. (M) will be hyperbolic and double reciprocal plots will be linear, according to equations analogous to (3a) and (3b) in which Q,,, and Q are is substituted for Iw and An, respectively. The value of proportional to the apparent molar enthalpy change for the as= AHo,,,, where f is the flow sociation process, Le., Q,,,/flL], rate through the microcalorimeter. From analysis of either proton uptake or microcalorimetric data, one can obtain, for 1:l complex systems, both the maximum signal (ANor Q), and the apparent association constant, which is equal toK,[l + K,'/(H+)]/[l K,/(H+)]. At low pH (Le., pH C pK, or pK,') and high pH (Le., pH > pK,' or pK,) this apparent association constant will approach K1 and K1-, respectively. AN and Q ,,, will also be pH dependent; AN will approach zero at will approach f(L),AH0, and flow and high pH and (L),AjYoI- at low and high pH, respectively, where Moland AHol..are the standard enthalpy changes for the M L + ML ML- associations. and M + LCase II. In addition to the formation of 1:1 CD-ligand complexes, 2: 1 complexes may also be formed as described by Scheme I1 where, in addition to the terms defined above, K2and K2-are defined as the association constants for the binding of a second C D molecule to either MeLH or M-L-, respectively, and K," is the acid dissociation constant of the 2:l complex, M2.LH. In this case v is equal to
em,,
+
em,,
(lb)
In this relationship the free C D concentration, M , is determined as (M) = (M), - v(L),, where (M), is the total CD concentration (9) M. R. Eftink and J. C. Harrison, Bioorg. Chem., 10,388-398 (1981). (10) K. A. Conners and J. M. Lipari, J. Pharm. Sci., 65,379-383 (1976). (11) K. A. Conners, S.-F. Lin, and A. B. Wong, J . Pharm. Sci., 71, 217-222 (1982). (12) K. A. Conners in 'Proceedings of the First International Symposium on Cyclodextrins", J. Szejtli, Ed., Reidel, New York, 1982, pp 163-172. (13) J. C. Harrison and M. R. Eftink, Biopolymers, 21, 1153-1 166 (1982). (14) R. Gelb, L. M. Schwartz, and D. A. Laufer, Bloorg. Chem., 9, 450-461 (1980).
+
v=
(L-)
(M-LH) + (M,.LH) + (M*L-) + (MyL-) + (LH) + (M-LH) + (MyLH) + (M-L-) + (M2.L-) (4a)
Cromwell et al.
328 The Journal of Physical Chemistry, Vol. 89, No. 2, 1985
0.6 -
Q Qmox
where the first term in the numerator of eq 4b relates to the probability of the 1:l complex and the second term relates to the probability of the 2:l complex. The value of (M), the free C D concentration, is related to the total C D concentration, (M)o, by eq 5 , where (LH), the free concentration of the neutral adamantanecarboxylic acid ligand species, is related to the total ligand concentration, (L)o, by eq 6. (M)o = (MI + Kl(M)(LH)[l + Ka/(H+)I + 2(M)2(LH)K1K2[1 + Ka"/(H+)I (5) (LH) = (L)" . .1 + - (H+) Ka + Kl(M)[ 1 +
51
+ K1K2(M)'[
1+
$1
(6) In proton uptake binding studies, An will be equal to An = ANl
1 + - (H+) Ka
+ Kl(M)[ 1 +
+ KIKz(M)'[ 1 +
s]
$-AN2
+ KlK2(M)2[ 1 +
$1
(7) where ANl,the proton uptake signal due to 1:l complex formation, is given by eq 2 and AN2, the complete proton uptake due to 2: 1 CD-ligand complex formation, is given by
An equation similar to eq 7 describes microcalorimetric binding studies for this case, with Qmax,land Qmx,2,representing the heat signal for 1:l and 2:l complexation, being substituted for AN1 and AN2. (Note that Qmax,2is the total heat effect for binding two M molecules to one L; the stepwise heat effect for binding the second M is equal to QmZ - Qml.) These equations describe a complex dependence of An and Q on (M), including terms in (M)2. In this case direct plots of An or Q vs. (M) will have a sigmoidal character and double reciprocal plots of l/An or l / Q vs. 1/(M) will be upward curving. Thus a simple way to distinguish between case I and case I1 is by inspection of double reciprocal plots.
Materials and Methods Material. 1-Adamantanecarboxylicacid (99%) was obtained from Aldrich Chemical Co. a-CD, b-CD, and y-CD were obtained from Sigma Chemical Co. and were used without further purification. As previously reported for LU-CD,'~ we find the CDs to be hydrated, by weighing samples before and after drying in a vacuum oven. We find degrees of hydration of 9.5%, 14.1%, and 9.3% for a-, p-, and y-CD, respectively. This is consistent with stoichiometries of one water per glucose ring for a-CD and y-CD (i.e., a-CD.6Hz0 and y-CD-8Hz0). For p-CD, the stoichiometry appears to be /3-CD.9H20. Regardless, it is important to use a hydrated molecular weight for the preparation of C D solutions (unless the CDs are vacuum dryed before weighing). We have used the following apparent molecular weights; 1081.0, 1297.1, and 1449.3 for CY-CD,(3-CD, and y-CD, respectively. All other (15) R. I. Gelb, L. M. Schwartz, B. Cardelino, and D. A. Laufer, Anal. Biochem., 103, 362-368 (1980).
0.4 -
0.2 -
2
4
6
[CD],
0
x 103M
Figure 1. Microcalorimetric binding profiles of adamantanecarboxylate to a-CD at 25 "C at pH 4.08 and 8 . 5 . Q/Q,,,, is the ratio of the observed heat effect, Q, to the value at saturation, Qmx. Q,, is related to the AIP of binding as AH" = Q-/Aligand],, wherefis the flow rate of solution through the microcalorimeter cf = 8.0 pL/s in this experiment), and [ligand], is the total concentration of ligand (adamantanecarboxylate in this case) within the microcalorimetric cell. [CD], is the total concentration of a-CD within the microcalorimetriccell. See ref 9 for further details of these microcalorimetrictitration experiments. The solid lines are fits of equations analogous to eq 3a and 7 to the data at pH 8.5 and 4.08, respectively. At pH 8.5 the fit is according to case I with K = 1.4 X lo2 M-l and AH' = -3.22 kcal/mol (where the above K is an apparent pH dependent value equal to K, [ 1 + Kl/(H*)]/[ 1 + K,/(H+)] in eq 3a; at pH 8.5 this apparent K is approximately equal to KIJ, At pH 4.08 the fit is according to case I1 with K1 = K,.= 1.3 X lo2 M-I, K2. = 10 M-I, A H o , = -3.2 kcal/mol, and AHo2 = -12 kcal/mol.
reagents were obtained commercially and used without purification. The water used was distilled and deionized. Methods. An LKB flow microcalorimeter was used to determine Iigand-CD association constants and enthalpy changes. The procedure and the details of the analysis of these experiments are described el~ewhere.~ The pH of ligand and CD solutions used in these microcalorimetric experiments were matched to within EtO.01 pH units with a London PHM 64 pH meter. Corrections for the heat of dilution of reactants were generally found to be unnecessary due to the low concentrations employed. Microcalorimetric studies were performed in the following buffers: 0.01 M NaH2P04,0.02 M Na2HP04, pH 7.22 buffer; 0.01 M Na2HzP2O7,pH 8.5 buffer; 0.02 M Na acetate, pH 4.08 buffer. For studies in the latter buffer, adamantanecarboxylate and the CD were first dissolved in a sodium acetate solution above pH 7, and then HCl was added to bring the solutions down to pH 4.08. This procedure was necessary due to the poor solubility of adamantanecarboxylic acid. Potentiometric pH titrations of adamantanecarboxylic acid (a M solution in 0.1 M NaCI) were performed at 25 OC 1X with a Brinkman Metrohm E526 titrator and a 5-mL waterjacketed reaction vessel. The HCl titrant (generally 8.63 X M) was standardized with potassium biphthalate. Nitrogen was bubbled through the solutions for at least 10 min preceding each experiment and a stream of nitrogen was directed over the solution for the duration of the titrations. Titrations of adamantanecarboxylic acid were conducted in the absence and presence of M y-CD, or 1.0 X either 1.0 X lo-' M a-CD, 1.0 X M p-CD. The formation of adamantanecarboxylate complexes with a-, /3-, and y-CD was also studied potentiometrically at pH 4.5 by back-titrating to the initial pH following additions of C D to a 5.0-mL ligand solution (1.0 X M). In this manner the proton uptake, An (defined as the moles of proton absorbed/moles of total ligand), as a function of added C D can be determined. Data obtained in this manner were analyzed with the models presented in the previous section.
Results Microcalorimetric Studies. Mixing adamantanecarboxylate with a-CD and @-CDwas found to give an exothermic signal, while
The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 329
Cyclodextrin Inclusion Complexes
1.0
I
TABLE I: Thermodynamics Parameters for the Interaction between Cyclodextrins and Adamantanecarboxylate/Carboxylic Acid'
pH 4.08
p H 8.5
AGO,
PH
kcal / mol
4.08 7.22 8.50
-2.9 f O.lb -3.6 f 0.1' -3.22 f 0.07 -2.94 f 0.04
4.08 7.22 8.50
-7.45 0.15 -6.2 f 0.1 -5.85 f 0.04
4.08 7.22 8.50
(-5.9 f O.l)d -5.05 f 0.03 -4.81 f 0.05
Q Qm,,
0.5
2
8
6
4
*
[CD]f xlO'M1
calculated as [CDIf = [CD], - Q[L]o/Q,.,.
1.0
1
I/ Y
I
I
I
I
9
-3.2 f 0.1' -8.8 f 0.1' -3.10 f 0.04 -3.22 f 0.06
so 1
cal/(mol-deg) -1.0 -17.2 0.4 -0.3
f0 9 f 0.5' f 0.3 f 0.3
8-CD -7.53 f 0.02 -5.4 f 0.1 -4.85 f 0.02
-0.1 f 0.5 2.5 f 0.5 3.4 f 0.2
7-CD
Figure 2. Microcalorimetricbinding profile of adamantanecarboxylate to 8-CD at 25 "C, pH 4.08 and 8.5. [CDIfis the free CD concentration
I
AHo
kcal/mol CY-CD
-0.1 f 0.1 1.26 f 0.08 1.20 f 0.05
(22.0 f 0.5)d 21.2 f 0.3 20.2 f 0.3
'Values determined calorimetrically at 25 OC. Values are the averages of three determinations, in most cases. Error limits refer to the range of values determined. 1: 1 complex formation. Stepwise 2: 1 complex formation (Le,, MLH M M,LH). dAGo value calculated as sum of the AGO at pH 8.50 and -RT In KJK,'. This AGO, and the resulting ASo,thus reflect the binding of the carboxylic acid form of the ligand to y C D (Le., the K, equilibrium).
+
4.08 can be used to calculate an association constant for the carboxylic acid form of the ligand via the relationship K1 = K(,,,)[ 1 Ka/(H+)]/[l Ka'/(H+)]. Using values of pKa and pK,' determined below, Kl is calculated to be 3.3 X lo5 M-I. We note that there is large uncertainty in the determination of K(applat pH 4.08, since, due to the strong binding, j3-CDr becomes less than 10% of the total j3-CD concentration. Nevertheless, the protonated form of the ligand is found to bind 15-20 times stronger than the anionic form of the ligand. For y-CD, the apparent association constants are 3.3 X lo3 and 5.0 X lo3 M-I at pH 8.5 and 7.22. At pH 4.08 the AHo for ligand binding is so small that an association constant cannot be determined. From the pKa and pK,' values (see below) for this system, however, one can calculate values of 3.3 X lo3 and 2.4 X lo4 M-I for K,. and K1. In other words, the carboxylic acid form of the ligand binds about 7 times stronger to y than does the carboxylate form. For the binding of adamantanecarboxylate to a-CD, association constants of 1.4 X lo2 and 2.3 X lo2 M-' are found at pH 8.5 and 7.2. If one takes the former value as a measure of KI. for this system, then association constants for adamantanecarboxylate of 2 X lo4, 3 X lo3, and 1.4 X lo2 M-' are found for the host series /3-CD, y-CD, and a-CD. Thus there is a 140-fold variation in K,. as one goes from j3-CD to a-CD. These results indicate a preferential affinity of the ligand for a CD cavity large enough to allow maximum penetration, yet small enough to allow for effective cavity-ligand interaction. The AHo for the binding of adamantanecarboxylate to a-and p-CD is found to be exothermic (see Table I), in agreement with earlier reports.I3 The binding of adamantanecarboxylate to y-CD, on the other hand, is found to be characterized by a small, endothermic AHO and to be driven, instead, by a large, positive ASo of 20 cal/(mol deg). The binding of the carboxylic acid form of the ligand to both j3-CD and y-CD is found to be more exothermic, as shown in Table I, as compared to the carboxylate ligand form. For y-CD, this results in the AHo being essentially zero for the carboxylic acid form. Returning to the data for the binding of a-CD at pH 4.08, one sees a sigmoidal curvature in Figure 1 which indicates that, whereas a 1:1 a-CD-adamantanecarboxylate complex is the principal species formed at high pH, a significant amount of a 2:l complex forms at low pH between two a-CD and the neutral ligand, adamantanecarboxylic acid. Thus case I1 applies to this system with K2 being much greater than Kz.. Gelb and cow o r k e r ~ have ' ~ previously reported that a 2: 1 complex of a-CD and adamantanecarboxylic acid forms, based on their conductivity and pH potentiometric studies. Also, Comers et al."12 have
+
I
I
I
5
10
15
I
Figure 3. Microcalorimetricbinding profile of adamantanecarboxylate to y C D at 25 OC, pH 8.5. The fit is according to case I with K = 3.3 X 10' M-I and AHo = 1.20 kcal/mol. At pH 4.08 the microcalorimetric signal was too small to perform the binding study (Le., AHo 0 at low PHI. S=
mixing with y-CD was found to give an endothermic signal. In Figures 1-3 are shown binding profiles of adamantanecarboxylate to a-,j3-, and y-CD obtained by flow microcalorimetric experiments a t pH 4.08 and 8.5. Binding data (not shown) were also obtained at pH 7.22 to allow comparison with our previous report.I3 The data a t pH 7.22 and 8.5 were nearly identical. At the higher pH values the free ligand is more than 99% in the carboxylate form, whereas, a t pH 4.08, the free ligand is 87% protonated (see pK, value below). Thus the studies at pH 4.08 and 8.5 reflect primarily the interaction of the carboxylic acid and carboxylate forms of the ligand, respectively, with the CDs. (Due to solubility limitations of the carboxylic acid form, we were not able to perform calorimetric experiments at lower pH without loss of signal intensity.) The data are plotted as Q/Q,,,,, where Q is the observed heat effect for the association reaction and Qmx is the maximum heat effect at saturation, vs. the free C D concentration, CDf (see ref 9 for the procedure for calculating CDJ. The shape of the binding curves is consistent with the formation of 1:l CD-ligand complexes (see case I) in all instances except for the binding to a-CD at pH 4.08. The latter binding curve deviates form a hyperbola, as can be seen by comparison of the curves in Figure 1, and suggests the formation of a 2: 1 complex (case 11). The data for a-CD at pH 4.08 will be discussed below; first we will analyze the data for those systems in which only 1:l complexes appear to form. By analyzing such data with eq 3, the apparent association constant, standard free energy change, AGO, standard enthalpy change, W ,and standard entropy change, ASo,for the association reactions were determined, as listed in Table I. The apparent association constants of the ligand for j3-CD are the highest, being 1.9 X lo4, 3.3 X lo4, and 2.9 X lo5 M-' at pH 8.5, 7.22, and 4.08, respectively. The association constants at high pH are a good measure of the binding of the carboxylate form of the ligand to j3-CD. The apparent association constant at pH
+
Cromwell et al.
330 The Journal of Physical Chemistry, Vol.89, No. 2, 1985
An
8
7
5
6
4
PH Figure 4. pH titration of adamantanecarboxylate in the absence and presence of CDs at 25 "C. The following excess CD concentrations were M @-CDand 1.0 X M yCD. used: 1.0 X 10-1M a-CD; 1.0 X Solid lines are fits with pKa values of 4.9,6.6,6.2,and 5.7 for free adamantanecarboxvlate and the binarv comulexes with a-CD, a-CD, and y-CD, respectively. I
.
An
1 An
I
I
I
I
I
2
4
6
8
10
x1om3M-' x10~M-l o Figure 6. Proton uptake binding profiles of adamantanecarboxylate to 6-CD (0)and y-CD (0)at 25 "C, pH 4.5. A. Plot An vs. total CD concentration. Solid lines are fits of case I (eq 3) to the data with K = 3.9 X lo4 M-' for @-CDand K = 2.4 X lo3 M-' for y C D . (Note that these apparent K values are equal to K1[l + K,'/(H+)]/[l + K,/(H+)] in eq 3a.) B. Double reciprocal plots of I/An vs. I/[CDIf, where [CDIf is calculated as [CD], - An[L],,/AN. I/[CD]f
1 -
An
6 I
I
I
I
10
20
30
A0
1/[CDIf
x
1d2M-'
Figure 5. Proton uptake binding profiles of adamantanecarboxylate to a-CD at 25 "C, pH 4.5. A. Plot of An vs. total a-CD concentration. Solid line is a fit of case I1 (eq 7) to the data with K I = KI. = 1.5 X 10' M-I, K2 = 6.0X l o 2 M-I, K2. = 12 M-l, pK, = pK,' = 4.9,and AN, = 0.295 (note that ANI = 0 since K1 = K1.. Also note that AN2 is related to KC by eq 8 and that K," = KaK2./Kz. Since K , is independently known, the fit is actually a three parameter ( K , ,K2,and the ratio K2/K2.) fit.
reported that 2:1 complexes form with a number of other ligands. The analogous equation to eq 7, describing case 11, was fitted to the low pH binding data in Figure 1 for a-CD in order to determine the relevant thermodynamic parameters for the association process. Gelb and co-workersls have reported that K, is approximately equal to K,. for this system. Our proton uptake data (see below) are consistent with this finding and we assumed in our fit that K1 = K,. and used the value of K1. determined independently at high pH. Also, in order to be consistent with the data presented below for the maximum proton uptake (AN
value) and the observed pK, shift on a-CD binding, we assumed that K2/K2. = 50 (Le., note from eq 8 that AN2depends on K/ and K, and that if K1 = K1., then K,/K," = K2/K2.). The value of AHo, was selected to be approximately the same as that found for 1:l complex formation at high pH and K2 and AHo2were varied to obtain a fit. The fitting procedure involved selecting a value of (M) and calculating, via eq 5 and 6, the concentrations of (LH), (M)o, and, finally, Q, corresponding to this free concentration of (M). The solid line through the pH 4.08 data in Figure 1 is a fit of case I1 to the a-CD microcalorimetric binding data for K, = K,. = 1.3 X lo2 M-l, K2 = 5.0 X lo2 M-l, K2- = 10 M-I, AHo, = -3.2 kcal/mol, and W 2 = -12 kcal/mol. Note that AHo2 is the total enthalpy change for interaction of two a-CD with one ligand; the stepwise A H for binding the second a-CD to the M-LH complex is -8.8 kcal/mol. These enthalpy changes are in good agreement with van't Hoff values determined by Gelb et al. for the a-CD-adamantanecarboxylic acid interaction. Potentiometric Titration Studies. pH titrations of adamantanecarboxylate and its CD inclusion complexes are shown in Figure 4. Titrations were conducted from pH 8 to 3.5 employing the necessary levels of CD to ensure at least 90% saturation in each case. The apparent pK, of adamantanecarboxylic acid was found to shift upward from 4.9 for the free molecule to 6.6 for the a-CD complex, 6.2 for the p-CD complex, and 5.7 for the y C D complex. Due to the large ApK,'s observed, potentiometric measurements of ligand binding are possible by measuring the proton uptake as a function of the concentration of added CD. Figures 5 and 6 show binding curves and double reciprocal plots for these experiments at pH 4.5. As with the microcalorimetric studies, the proton uptake binding curves for B-CD and y-CD appear hyperbolic and the double reciprocal plots are linear. With a-CD, however, a sigmoidal character is seen in the proton uptake vs. [a-CD] curve, and the resulting double reciprocal plot is nonlinear. In each case the magnitude of the maximum proton uptake is consistent with the above pK, shifts. Also the position of the
The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 331
Cyclodextrin Inclusion Complexes binding profiles along the CD concentration axis is consistent with preferential binding in the order 0-CD > y-CD > a-CD. The proton uptake data with 8-CD allow us to definitively conclude that only a 1:l complex forms with this CD. Since the association constant is so large for this pair, the An vs. [@-CDl0titration curve in Figure 6a shows a sharp break at a @-CDconcentration of 1.0 X M. Since the total adamantanecarboxylic acid concentration is also 1.O X in this experiment, this indicates that saturation w u r s at a ratio of 8-CD to ligand of 1.O, or in other words, that the complex is exclusively 1:l. If a 2:l complex were to form in this case, it would have to show no additional proton uptake, an extremely unlikely situation. For y-CD, the near perfect linearity of the double reciprocal plot over a wide y-CD concentration range suggests that a 1:l complex forms exclusively in this case as well. The data for a-CD were again analyzed according to case I1 by fitting eq 7 to the data. Again we assumed Kl = Kl- and K2/K2= 50. The fit shown in Figure 5 was obtained with K l = K l . = 1.5 X lo2 M-I, K2 = 6.0 X lo2 M-I, and K2. = 12 M-’. The constants used to fit the proton uptake data are thus found to be very similar to those required for the fit of the microcalorimetric data at low pH.
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Discussion In our previous work with cyclodextrin inclusion comp1exesI3 we demonstrated that the interaction of adamantanecarboxylate with @-CDdisplays what can be called a ”nonclassical hydrophobic effect”.16 That is, the interaction is characterized by a large and negative standard enthalpy change and a near zero standard entropy change, even though one would expect, by consideration of the chemical nature of the ligand and the CD cavity, that the association would be hydrophobically driven. From studies of the solvent dependence of the thermodynamics of the @-CDadamantanecarboxylate interaction we concluded that there is a significant contribution from the classical hydrophobic effect (i.e., a positive AS contribution) but that this contribution is masked by a predominant binding force characterized by a negative AH and a negative AS. We speculated that this latter binding force may be a van der Waals interaction between the ligand and CD pocket, which is particularly strong in this case due to the deep penetration and snug fit between the reactants. The thermodynamic parameters (see Table I) for the binding of adamantanecarboxylate to a-CD suggests that both of these binding forces, the hydrophobic effect and van der Waals forces, again contribute, but to a lesser degree for both types. This is as expected since adamantanecarboxylate is too large to completely penetrate into the a-CD cavity.” With a smaller area of contact between the reactants one would expect both of the above binding forces to be diminished. Thus there should be a smaller-AH contribution from van der Waals contacts (leading to a smaller -AHo as compared to that for 0-CD) and a smaller AS contribution from the hydrophobic effect (leading to a less positive ASo as compared to that for @-CD,although the value of ASo for the complexes also depends on the degree of rotational restriction of adamantanecarboxylate and conformational restriction of the CD cavity that occurs upon binding). The thermodynamic parameters for the binding of adamantanecarboxylate to y C D , on the other hand, show a small endothermic AHo. Such values follow the pattern of the classical hydrophobic effect. The question then arises as to why the exothermic van der Waals interaction is apparently not seen in this case. This can be explained as being due to the comparatively large cavity of y C D . If the diameter of the cavity is 1-2 A larger than the diameter of the adamantyl group (see below) then the small, endothermic AW’can be attributable to the critical distance dependence of van der Waals forces and the fact that the ligand is able to “touch” only a small portion of the internal cavity wall (16) W. P. Jencks, ‘Catalysis in Chemistry and Enzymology”, McGrawHill, New York, 1969. (17) K. Komiyama and M. L. Bender, J . Am. Chem. Soc., 100,2259-2260 (1978).
at a time. Alternatively, there may be a partial collapse of the 7-CD structure around the adamantyl group to provide a snug fit, but this ”collapse” may contribute a positive AH effect that cancels any negative AH contribution gained by the improved van der Waals contacts. The rationalization of A W and ASovalues, while of interest for understanding the molecular details and driving forces invovled in complex formation, is necessarily somewhat speculative and it must be realized that other factors such as the displacement of high-energy water from within the C D cavity or structural to the AHo and changes of the C D m o l e c ~ l e ~may * ~ ~contribute ’~ ASofor ligand binding. However, a straightforward interpretation of the AGO for CD-adamantanecarboxylate complex formation is possible in terms of the match between the molecular size of the ligand and the size of the CD cavity. Regardless of the details of the balance between hydrophobic and van der Waals binding forces, we see that the stability of the Chdamantanecarboxylate complexes is in the order @-CD> y-CD > a-CD, with there being roughly a 140-fold difference in the association contants for @-CD and a-CD. Since the chemical nature of the reactants is the same in this series and all that varies is the size of the C D cavity, this trend clearly indicates that an optimum matching between the size of the ligand and the size of the CD cavity leads to optimum binding. The /3-CD cavity apparently has the optimum dimensions for interaction with adamantanecarboxylate. The adamantyl group is a spherical roup having a radius of about 7 A and a volume of about 180 X 3 . l g The diameter of the cavity of the three CDs has been estimated by different group^.'^^^^ Taking the average of these estimates, the diameter, d , and cavity volume, u, of the three CDs are as follows: a-CD, d = 5 A, u = 150 A3; 6-CD, d = 6.9 A, v = 270 A3;y-CD, d = 8.5 A, v = 400 A3.Since these volumes refer to a cylindrical cavity and the adamantyl group is spherical, comparisons of the volume of the ligand with that of the cavity is probably less useful than comparison of the diameters. We see that the adamantyl group should fit into the y C D cavity with room to spare, that the group should fit very snugly into the @-CDcavity, and that it should not be able to fully penetrate into a-CD. The latter observations have been made by use of space filling models by Komiyama and Bender.” Also, X-ray studies of a complex between adamantanol and a @-CD derivative show the ligand to be almost completely engulfed within the P-CD cavity.20 A clear relationship can thus be seen between the A G O for adamantanecarboxylate binding and the structural complimentarity of the C D cavity. The pH potentiometric studies performed on these complexes provide additional thermodynamic and stoichiometric information. The pK, of adamantanecarboxylate in the CD complexes was found to shift upward by 0.8 units for y C D to 1.7 units for a-CD, as compared to the free ligand. The direction of these pK, shifts is consistent with other reports involving C D complexes with carboxylic acidsI0 and indicates that the CD cavities have a preferential affinity for the neutral acid form of these ligand types. An explanation for this phenomenon is that the requirement for solvation of the charged carboxylate group by water may prohibit the adamantyl group (or other aliphatic side chain) from fully penetrating the CD cavity, whereas deeper penetration may be possible with the neutral carboxylic acid group. Not only may the ligand penetrate deeper into the cavity when the carboxylic acid group is neutral but this functional group may also form hydrogen bonds with hydroxyl groups on the rim of the CD cavity. Alternately, the ligand may preferentially bind carboxylic acid group first into the cavity” (assuming that insertion occurs into the secondary hydroxyl side of the CD cavity). There is evidence for this mode of binding for the protonated form of some carboxylic (18) W. Saenger, M. Noltemeyer, P. C. Manor, B. Hingerty, and B. Klar, Bioorg. Chem., 5, 187-195 (1976). (19) J. L. Dote and R. N. Schwartz, J. Phys. Chem., 85, 3756-3758 (1981). --, (20) J. J. Stezowski, M. Czugler, and E. Eckle in ‘Proceeding of the First International Symposium on Cyclodextrins”,J. Szejtli, Ed.,Reidel, New York, 1982, pp 151-161. \ -
332
J. Phys. Chem. 1985, 89, 332-335 H
0 H-0'
H Figure 7. Proposed structures for the 2:l a-CD-adamantanecarboxylic acid complex.
acids.21 Insertion of the charged carboxylate group of a ligand into a CD cavity is probably energetically prohibitive. The large ApK, of 1.7 units for the a-CD-adamantanecarboxylate complex, which seems to indicate a much higher affinity for the neutral form of the ligand, is actually misleading. As Gelb and c o - ~ o r k e r s have ' ~ shown, and as our data in Figures 1 and 5 corroborate, the large ApK, in this case appears to be due almost entirely to a preferentially binding of the neutral ligand in the 2: 1 a - C D complex, instead of preferential binding in the 1:l complex. That is, in terms of Scheme 11, the data are consistent with K1 being equal to Kl. and K2 being much greater than K2.. Thus 2:l complexes are formed with a-CD and such ternary complexes are preferentially formed with the neutral form of adamantanecarboxylic acid. The K,, K1., K2, and K2. values used to fit Figures 1 and 5 may not be unique but they do suggest a couple of interesting molecular interpretations. If K, is approximately equal to K1- there is no preferential binding of the carboxylic acid in the 1:l complex with a-CD. This suggests that the functional group of adamantanecarboxylate is directed away from the CY-CDcavity when its carboxylic acid group is both protonated and unprotonated. Also it is interesting that K2 > K1. In other systems in which 2:l a-CD inclusion complexes are formed K2 is less than K,.11,12If K2 > K, there must be positive cooperativity in binding the second a-CD to the complex. The enthalpy change for formation of a 2:l a-CD-adamantanecarboxylic acid complex has a rather large negative value of -12.0 kcal/mol. When one substracts the AHo value of -3.2 kcal/mol for forming the 1:l complex, the enthalpy change for the binding ~
of the second a-CD molecule to the 1:1 complex is calculated to be -8.8 kcal/mol. This large exothermic value suggests that the binding of the second CYCDinvolves a significant improvement in hydrogen bonding or van der Waals interactions. A possible explanation for the cooperative and exothermic binding of the second CY-CDis that hydrogen bonding occurs between the secondary hydroxyl groups of the two a-CD molecules in the ternary complex, as depicted by Figure 7. For adamantanecarboxylate complexes with 6-CD and y C D the data in Figure 6 indicate that the complexes are 1:1, at least in the concentration range studied (Breslow et a1.22have evidence for 1:2 /3-CD-adamantanecarboxylate complex formation at high concentrations of the latter species). This being the case the observed ApK,s of 1.3 and 0.8 units, for 0-CD and y C D , respectively, can be attributable to a preferential interaction with the protonated carboxylic acid form of the ligand. As mentioned above, this may be due to a deeper penetration of the neutral ligand into the cavities or to a carboxylic acid group first binding mode. It is particularly striking that neutral adamantanecarboxylic acid binds to p-CD with a very large association constant. From Scheme I, a K I .of 2.0 X lo4 M-I determined microcalorimetrically, and a ApK, of 1.3 units, one can calculate the association constant of adamantanecarboxylic acid to p-CD to be 4.0 X los M-I. The latter value is approximately equal to the value determined by a direct microcalorimetric binding study at pH 4.08 (after correcting the apparent binding constant at this pH to obtain K l ) . The stronger binding of p-CD to the neutral ligand is due entirely to a more negative enthalpy change for the association. This improved AHo could be consistent with either of the abovementioned possibilities that (a) deeper penetration and hydrogen bonding with the carboxylic acid group occurs for the neutral ligand or that (b) carboxylic acid first binding occurs.
Acknowledgment. This work was supported by research grants from the National Science Foundation (PCM 82-06073), and the donors of the Petroleum Research Fund, administered by the American Chemical Society, and by a fellowship (for K.B.) from the Swedish Natural Science Council. Registry No. a-CD, 10016-20-3; @-CD,7585-39-9; y-CD, 1746586-0; adamantanecarboxylate,65012-54-6; adamantanecarboxylic acid, 828-51-3.
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(21) R. J. Bergeron, M. A. Channing, and K. A. McGovern, J. Am. Chem. SOC.,100, 2878-2883 (1978).
(22) R. Breslow, M. F. Czarniecki, J. Emert, and H. Hamaguchi, J . Am. Chem. Soc., 102, 762-770 (1980).
Photoinduced Electron-Transfer Reactions between Optical Isomers Youkoh Kaizu, Takahiro Mori, and Hiroshi Kobayashi* Department of Chemistry, Tokyo Institute of Technology. 0-okayama, Meguro- ku, Tokyo 152, Japan (Received: June 5, 1984)
The luminescence quenching of (-)D-[Ru(bpy)s]2+(bpy: 2,2'-bipyridine) by (+)D-, rac-, and (-)D-[Co(edta)]- (edta: ethylene diaminetetraacetate) was studied in aqueous and also aqueous methanol media. The quenching rate constant k, in mixtures of methanol and water of (-)D-[Ru(bpy)3]2+found with (-)D-[Co(edta)]- was greater than the k, found with (+)D-[Co(edta)]and their mean value was obtained with the racemic mixture of [Co(edta)]-. A difference in the quenching constants observed between the optical isomers reveals that the electron transfer to the quencher in the luminescent excited state of [R~(bpy)~]*' can occur only in a contact ion pair but not in the solvent-separated ion pair.
Excited [ R ~ ( b p y ) ~(]*~[+R ~ ( b p y ) ~ ] ~in' ) solution is quenched by three possible processes: *[Ru(bpy)3I2++ Q == [Ru(bpy)312+ + Q*
(1)
0022-3654/85/2089-0332$0l.50/0
where Q denotes the quencher. In process 1, the excitation energy 0 1985 American Chemical Society
