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(4) (5) (6) (7) (8) (9) (10)
J. H. Lunsford and J. P. Jayne, J. Phys. Chem., 70, 3464 (1966). A. J. Tench and R. L. Nelson, J. Co//o@Interface Sci., 28, 364 (1968). J. H. Lunsford and J. P. Jayne, J. Pbys. Chem., 89, 2182 (1965). A. J. Tench and P. Holroyd, Chem. Commun., 471 (1968). G. R. Freeman, Actions Chim. Biol. Radiat., 14, 73 (1970). D. R. Smith and A. J. Tench, Can. J. Chem., 47, 1381 (1969). (a) M. C. R. Symons, Chem. SIX.Rev., 5,337 (1976). (b) See papers in "Metal-Ammonia Solutions", W. L. Jolly, Ed., Dowden, Hutchinson & Ross, New York, 1972. A. J. Tench and D. Giles, J. Chem. Soc., Faraday Trans. 7 , 68, 193 (1972). R. Catterall, W. T. Cronewett, R. J. England, and M. C. R. Symons, J. Cbem. SOC.A , 2396 (1971). R. Catterall, "Metal-Ammonia Solutions", J. J. Lagowski and M. J. Sienko, Eds., Butterworths, London, 1970, p 105. M. C. R. Symons, D. R. Smith, and P. Wardman, J. Chem. Soc., Chem. Commun., 71 (1978). P. Wardman and D. R. Smith, Can. J. Cbem., 49, 1869 (1971). P. Wardman and D. R. Smith, Can. J. Cbem., 49, 1860 (1971). A. J. Tench and R. L. Nelson, J . Chem. Phys., 44, 1714 (1966). J. E. Wertz, P. Auzins, R. A. Weeks, and R. H. Silsbee, Phys. Rev.,
(11) (12) (13) (14) (15) (16) (17) (18)
Andini et al. 107, 1535 (1957). (19) R. L. Nelson, J. W. Hale, B. J. Harrnsworth, and A. J. Tench, Trans. Faraday Soc., 84, 2521 (1968). (20) P. F. Meier, R. H. Hauge, and J. L. Margrave, J . Am. Chem. Soc., 100, 2108 (1978). (21) W. T. Cronewett and M. C. R. Symons, J . Chem. SOC.A , 2991 (1968). (22) K. Bar-Eli and T. R. Tuttle, J. Cbem. Phys., 40, 2508 (1964). (23) R. Catterall, I. Hurley, and M. C. R. Symons, J. Chem. Soc., Dalton Trans., 139 (1975). (24) J. M. Moskowitz, M. Boring, and J. H. Wood, J . Chem. Pbys., 62, 2254 (1975). (25) M. D. Newton, J. Phys. Chem., 79, 2795 (1975). (26) S.Golden, C. Guttman, and T. R. Tuttle, J . Am. Chem. Soc., 87, 135 (1965). (27) S.Ray, Chem. Pbys. Lett., 11, 573 (1971). (28) S.Golden and T. R. Tuttle, J . Phys. Chem., 82, 944 (1978). (29) D. Razem and W. H. Hamill, J. Pbys. Chem., 81, 1625 (1977); 82, 488 (1978). (30) K. S. Pitzer, J . Chem. Pbys., 29, 453 (1958). (31) J. R. Morton and K. F. Preston, J . Magn. Reson., 30, 577 (1978).
Collision Complexes. 2. An 'H Nuclear Magnetic Resonance Study of the Complex Caffeine-Benzene Salvatore Andlni, Luclano Ferrara, Plero A. Temussi, * Istituto Chimico, University of Naples, Naples, Italy
Francesco Lelj, Dipat?imento di Chimica, UniversitCi delle Calabria, Cosenza, Italy
and Teodorlco Tancredi L.M.I.B. del C.N.R., Arc0 Felice, Italy (Received November 20, 1978; Revised Manuscript Received February 26, 1979)
The collision complexes formed by caffeine and benzene in solutions of carbon tetrachloride were studied by means of NMR spectroscopy over a very wide benzene concentration range (up to a molality of 39.2). The ring current shifts of the resonances can only be interpreted on the basis of a mixture of 1:l and 1:2 complexes. Both graphical (projection maps) and fairly sophisticated automatic minimization procedures were employed for the first time to extract equilibrium parameters from this type of NMR data. The successful fit of our data suggests that other systems that also show unaccountable differences in formation constants measured from different nuclei of the some acceptor molecule may contain complexes with a molar ratio different from 1:l
Introduction Studies of collision complexes between purines and aromatic hydrocarbons have been prompted both by rather general physicochemical motivations, such as the need to understand the nature of weak intermolecular forces, and by specific biophysical interest in the role played by this type of complexes in carcinogenesis.'-' We have recently shown1 that, in favorable cases, NMR measurements can be crucial to discriminate among the forces responsible for the stabilization of the complexes. The decisive advantage presented by NMR spectroscopy over other solution techniques resides in the fairly precise structural information furnished in most instances. The resonances of the (acceptor) purine are usually shifted upfield by addition of the (donor) aromatic molecule, and these shifts may be interpreted8-10on the basis of the formation of a simple 1:l complex to yield a formation constant and as many limiting chemical shifts as there are shifted resonances in the purine spectrum. If we can measure a sufficient number of chemical shifts of the pure complex, i.e., those previously referred to as limiting shifts, it is possible to characterize its geometry completely. When both molecules forming the collision complex are 0022-365417912083-1766$0 1.OOlO
conformationally rigid the number of variables necessary to define the geometry of the system is six, but in many practical cases we may actually need a smaller number of corresponding chemical shifts. For instance, we need only five shifts in all cases in which we can make use of the cylindrical symmetry of the magnetic field of certain aromatic molecules or even four if we can also limit the distance of closest approach (of the two molecules) as dictated by the van der Waals radii of the outer at0ms.l Such was the case for the complex between benzene and tetramethyluric acid (TMU) in which the four measurable chemical shifts defined the geometry of the system almost comp1etely.l Here we present an extension of this approach to the complex formed by another purine, caffeine, with benzene. One obvious reason for this extension is that the structure of caffeine is much closer to those of the purinic bases of nucleic acids than that of TMU. Another reason is that in a previous NMR study2 of the system caffeine-benzene (in carbon tetrachloride solution) the interpretation of the data led the authors to conclusions different from ours on TMU-benzene. However, only one limiting chemical shift was actually measured for the complex caffeine-benzene, both because of the small ring 0 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
Caffeine-Benzene Collision Complexes
current shifts induced at 60 MHz and owing to the superposition of the resonances of benzene and of the C-H proton of caffeine. These limitations are circumvented in the present study by the use of a stronger magnetic field and of deuterated benzene.
Experimental Section Materials. Caffeine was purchased from Merck (Milano, Italy) and used without further purification. Spectrograde carbon tetrachloride was purchased from Fluka AG (Buchs, Switzerland); benzene-de (99.96%)was purchased from Wilmad Glass Co., Inc. (Buena, U.S.A.). Procedure. All solutions were prepared in such a way that the molar concentration of caffeine remained approximately constant (0.03 M) while the molality of benzene varied from 0.4 to nearly pure benzene. Even in the first solution the molar ratio benzene:caffeine is high enough to assure the applicability of the Benesi-Hildebrand equation," as modified by Hanna and Ashbaugh.8b lH NMR spectra were recorded on a Varian Associates XL-100 spectrometer at probe temperature (29 "C). Chemical shifts were taken with respect to internal cyclohexane (less than 0.5% in all cases) and are accurate to better than 0.2 Hz. Results The resonances of the spectrum of caffeine in carbon tetrachloride have been already assigned by Hanna and Sandoval.2 We have adopted their assignments without any change, also considering that they are consistent with literature data on analogous compounds.ll The numbering of the groups whose chemical shifts were used to monitor complex formation is actually for the atoms of the molecular skeleton, e.g., 1-CH3is the methyl group linked to nitrogen number 1 as illustrated in 1. Table I shows the
1707
TABLE I: Experimental Chemical Shifts for Solutions of Caffeine in Mixtures of CCl, and sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20
mlmol kg-'
S ,/Hz
S,/Hz
S,/Hz
S,/Hz
0.0 0.3783 0.4129 0.4834 0.5508 0.6551 0.6686 0.7729 0.7778 1.020 1.053 1.342 1.402 2.177 4.409 8.911 17.96 20.69 28.11 39.25
187.6 186.1 186.3 185.9 185.9 185.6 185.9 185.6 185.9 185.6 185.2 185.1 185.4 185.4 185.1 186.9 188.2 189.3 190.0 190.9
207.3 204.4 204.3 204.0 203.3 203.2 203.5 202.9 202.9 202.3 201.9 201.1 201.4 199.8 197.4 195.7 195.1 195.5 195.2 195.3
255.1 242.5 242.3 241.1 239.7 238.0 237.2 235.6 235.5 231.4 230.6 225.7 225.8 216.0 201.1 186.9 179.6 176.6 173.7 171.7
593.1 576.2 575.9 574.8 573.4 571.6 570.8 569.1 569.2 564.9 564.5 559.4 559.6 550.4 535.6 522.6 516.2 513.6 511.0 509.6
The concentration of caffeine is approximately 0.03 M throughout. The column headed m gives the molalities of C,D,. All chemical shifts are referred to internal cyclohexane.
0
0
I 1
assignments in neat CCll together with all the shifts induced by the ring current of benzene upon formation of the collision complex. The unusually wide concentration range employed for the donor is justified (inter alia) by the desire to identify as clearly as possible all regions of nonlinear behavior in plots of the reciprocal of the shift A0m-' vs. the reciprocal of donor concentration m-l. Many authors have in fact used the upfield shifts induced by aromatic molecules (referred to as donors) upon complexation with N-alkyl amides to estimate the equilibrium quotient and the shift of the pure complex.12 Provided it is possible to assume the presence in solution of only 1:l complexes, the NMR data can lead to an equation12similar to that of Benesi-Hildebrandsa
+ -1
QAcm Ac where & b d = Si- Si, is the observed difference in chemical shift between acceptor (Le., caffeine) protons in a solution with a donor (C6D6in our case) concentration m (Si)and the chemical shift of the same protons in a solution without donor (Si&. A, is the corresponding shift for the pure Aobsd
40
60
A
Figure 1. Plots of the experimental shlfts of groups 3, 7, and 8 of Caffeine, induced by increasing molalities of benzene. The dashed lines are indicative only.
CH3
1 = -1 1 -
2'0
complex and Q is the equilibrium quotient for association of the complex. Deviations from linearity in plots of A o ~ - l vs. m-l or in the analogous plots12 m(Aob?d vs. m and Aobsd/m vs. Aobsd are obviously an indication that this simplified treatment of the equilibria in solution is not satisfactory. Figure 1 shows that such is the case for our system since the nonlinearity of the plots relative to groups 3, 7, and 8 is indeed quite pronounced in the range of molality between 0.0 and 1.00, The appearence of the graph concerning the shifts of methyl-1, shown in Figure 2, is even more disconcerting since it is quite unusual to observe such a discontinuity in these plots. Actually, to the best of our knowledge, this is the first reported case of clear sign reversal in chemical shifts induced by complexation with aromatic molecules. Other data, including those for the system benzenecaffeine at 60 M H Z ,were ~ in general too uncertain owing to the very small absolute values of the shifts, comparable to the errors at the low fields employed. In our case, the shifts induced by benzene, albeit small, are definitively beyond experimental error. The behavior illustrated by the graph of Figure 2 can
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
1766
I t turns out that if we treat the data on the basis of a mixture of one 1:l complex plus one 1:2 complex we can account for all sorts of nonlinearities observed in the graphs, as expected, but we can also eliminate the anomaly of different formation constants, as measured for different parts of the molecule.
I
1
0
200
100
10P/m Flgure 2. Plots of the experimental shifts of methyl-1 of caffeine, induced by increasing molalities of benzene. The dashed lines are indicative only.
TABLE 11: Apparent Values of Association Quotient and Limiting Shifts Calculated from the Linear Portions of Figures 1 and 2 A,
Q
Andini et al.
l b
3a
la
2.67 3.32
12.56 0.78
89.26 0.35
88.24 0.44
a Calculated with solution shifts with m > 1.00. culated with solution shifts with m < 4.4.
Cal-
perhaps be rationalized on the basis of the presence of several complexes whose limiting chemical shifts can have different signs. This is tantamount to saying that we must postulate at least a 1:2 complex (together with the 1:l complex) since it h a been demonstrated12J3that mixtures of 1:l complexes behave in a way that is not distinguishable from that of a single 1:l complex. However, the data of Table I contain a further “anomaly”. If one ignores the relatively small initial portion of the concentration range where the nonlinear behavior is outstanding it is possible to extract apparent formation constants and limiting chemical shifts by formally interpreting the chemical shift data as those of typical 1:l complexes. Table I1 shows the results of this treatment of the experimental data; although the apparent errors derived from a least-squares fitting of the lines are small, the four formation constants are drastically different from one another far beyond probable errors. There are already several similar examples in the literature; i.e., there are similar observations of drastically different formation constants when measured from nuclei located in different parts of an acceptor m01ecule.l~No convincing explanation has been produced so far, although it is clear that the oversimplified model based on a single 1:l complex must be responsible, at least in part. In our case, as already illustrated, independent indications point to the presence of a 1:2 complex.
Methods The mathematical treatment of systems containing more than one complex leads to rather cumbersome equations from which it is not possible to extract equilibrium parameters directly. In the case of interest tQ us the equation that relates observed shifts to formation constants and limiting shifts of 1:l and 1:2 complexes, as derived by Dodson et al.,l’ reads mQl(A1O)i + m&2(Az0)i (1) (Aobsd)i = 1 + mQ1 + m2Q1Q2 where Q1 is the formation constant of the following equilibrium between caffeine (A) and benzene (D) A+D=AD ( A t ) i is the limiting constant of the ith group of caffeine, i.e., the shift in AD, Qz is the formation constant of AD2 AD+D+AD2 is the shift of group i in AD2,and m is the equilibrium concentration of benzene (considered coincident with the analytical benzene concentration). These authors have been able to treat a few actual systems by means of a computer program that refines the starting values of Q1, Q2, A t , and Azo (easily obtained by crude extrapolations) through a four dimensional mapping procedure. Such an approach is not quite satisfactory because it is time consuming and offers no clear way of estimating the errors. (It may also be questionable from the point of view of its capacity of refining bad starting values.) Instead, we have written computer programs that can refine even extremely crude (or rather we should say “even completely wrong”) starting values because these programs are based on a powerful minimization procedure (vide infra). However, before discussing these programs in more detail, as a simple alternative we wish to propose also the use of a graphical procedure that has already proved very useful in the field of ionic equilibria, Le., the procedure based on the so-called projection maps.16 The method, in its simplest form, was originally formulated by Sillen16who suggested the use of normalized functions to study chemical equilibria by graphical methods. The main feature consisted of the use, as independent variables, of dimensionless quotients instead of the free concentration of the reacting species. In the case of three-variable systems the number of independent variables can be reduced by considering sections of the three-dimensional surface. Each section gives a curve on a planar diagram; the family of these curves forms the projection map of the surface. In order to treat our system by this method let us introduce the normalized variable u = m2Q2
Equation 1 can now be rewritten as a function of u: mQIAlo+ uAzO/m (2) Aobsd = 1 + mQi + uQi A plot of the type log A vs. log u may now be used to estimate the best values of A: and Q2 consistent with an initial guess of Al0 and Q1. Figure 3 shows a plot of Aobsdvs. 2 log m together with
The Journal of Physical Chemistty, Vol. 83, No. 13, 1979
Caffeine-Benzene Collision Complexes
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TABLE 111: Equilibrium Parameters for a Mixture of 1:l and 1:2 Complexes CH,(1) CHd3) CH3(7) H(8) Automatic Minimization Procedure Q, = 3.7 i 1.3; Q, = 0.291 f 0.021 A,' 3.73f0.41 4.11+0.80 1 1 . l i 3 . 6 18.2k4.2 A,O -1.54 * 0.46 13.51 f 0.44 90.16 i 0.62 90.05 f 0.46 Projection Maps Procedure Q, = 3.8; Q, = 0.27 A,' 4.2 5.0 12.1 20.1 A z o -1.9 11.2 93.3 92.7
d
I
a family of A vs. log u curves corresponding to values of Qz differing from one another by 0.1 units, whereas Azo is held fixed at 93 Hz. It is easy to see that the position along the abscissa of the calculated curves varies substantially as a function of Q2. Once we have the right shape (as can be easily ascertained by superposing the experimental and calculated curves) the value of log Qz can be read directly as the translation along the abscissa that is needed for a complete superposition. The process evidently is iterative since we can now start from the determined values of Azo and Qz as constants and refine AIo and Q1by introducing the function u' = mQ1. By means of this procedure we obtained for our system the values reported in Table 111. The same table also gives the best values obtained by means of an automatic minimization procedure. Actually, in order to find a method that could handle this somewhat complex equilibrium system with reasonable computer time, we wrote two programs for an IBM 370 computer, based on two different, but equally powerful, minimization procedures. Both programs, however, use first derivatives of the function to be optimized in the search for the minimum. The first program was written using the well-known method of variable metric by Davidon, Fletcher, and Powell. The second one used the algorithm by Newton and Marquardtg and Leevenberg,20 as modified by Fletcher.21 This second program enables a more precise evaluation of the hessian matrix since it is based on a function that is already a sum of squares. It is also very convenient for a direct assessment of the errors of the parameters through the variance and covariance matrices. Both programs led essentially to the same minima, even
p
11.
0
I
I
I
,,:
1
2
3
4
log u Figure 3. Projection map employed to determine the value of O2from the shifts of methyl-7. The three curves differ by 0.1 unit of Q2.
starting from completely wrong parameters, but the second moved much fasterqzZ In our opinion procedures based on such powerful minimization methods ought to be preferred to the mapping proposed by Dodson et al. not only because of their speed but also for the superior accuracy in evaluating the errors and probably also for their reliability in the search for true minima. The fit is summarized in Table IV where the experimental chemical shifts are compared to values calculated using the parameters of Table 111. The agreement, however, is probably best assessed by a simple inspection of Figure 4; the continuous lines are indeed calculated curves based on the final equilibrium parameters of Table 111.
TABLE IV: Comparison of Experimental Shifts with Those Calculated through the Minimization Procedurea CHS1) sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a
CH3(3)
CH3(7)
H(8)
Aexpt
A calcd
Aexpt
A calcd
Aexpt
A calcd
Aexpt
A calcd
1.5 1.3 1.7 1.7 2.0 1.7 2.0 1.7 2.0 2.4 2.5 2.2 2.2 2.5 0.7 -0.6 - 1.7 - 2.4 - 3.3
1.6 1.7 1.8 1.9 2.1 2.1 2.2 2.2 2.2 2.3 2.3 2.2 2.0 1.1 0.0 -0.4 - 1.0 -1.3 - 1.5
2.9 3.0 3.3 4.0 4.1 3.8 4.4 4.4 5.0 5.4 6.2 5.9 7.5 9.9 11.6 12.2 11.8 12.1 12.0
2.8 3.0 3.4 3.7 4.1 4.1 4.5 4.5 5.3 5.4 6.1 6.2 7.4 9.3 10.8 11.4 11.8 12.3 12.5
12.6 12.8 14.0 15.4 17.1 17.9 19.5 19.6 23.7 24.5 29.4 29.3 39.1 54.0 68.2 75.6 78.5 81.4 83.4
11.3 12.2 13.9 15.4 17.6 17.8 19.9 20.0 24.2 24.8 29.1 29.9 38.7 53.9 67.4 75.0 78.1 81.5 83.8
16.9 17.2 18.3 19.7 21.5 22.3 24.0 23.9 28.2 28.6 33.7 33.5 42.7 57.5 70.5 76.9 79.5 82.1 83.5
14.4 15.4 17.3 19.0 21.5 21.8 24.0 24.1 28.6 29.2 33.6 34.5 43.2 57.4 69.5 76.7 79.2 82.0 84.0
The RMS, calculated on all points, is 0.59 Hz.
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The Journal of Physical Chemistry, Vol. 83,No. 13, 1979
& 0 7
~8 t l
m
0
+
Andlnl et el.
large Q’s (that ought to reflect a relatively close approach) and vice versa. In our opinion, the explanation of this paradox resides in the nonrigid nature of collision complexes. That is, addition of a second benzene molecule changes also the relative position of the first benzene molecule. If this is true the magnitude of the second limiting chemical shift must be ascribed more to the first benzene molecule (Le., to a virtual 1:l complex) than to the second one, at least as far as direct influence is concerned. In this respect only the first limiting chemical shift can be ascribed to a well-defined 1:l complex (AD), the one that tends to form initially when both donor and acceptor are rather dilute. As we add more donor the formation of AD2 becomes predominant and its geometry preserves no “memory” of the original AD molecule. Whether this view is accepted or not it is clear that all considerations of the interaction forces made in the previous work on this system2are of little value since they were based on the assumption that only a 1:l complex was formed. It must be said that it would have been very difficult indeed to detect a clear nonlinear behavior from the data at 60 MHz. Besides, we cannot compare the present system with that formed by TMU and benzene in chloroform since no 1:2 complex was detectable in that case and the analysis of the simple geometry of the 1:l complex allowed a fairly conclusive assessment of the interaction forces involved. Unfortunately in our case we do not have enough parameters to describe the geometry of the 1:2 complex and a comparison with the quoted system TMU-benzene will only be possible if we determine enough parameters, (perhaps from 13Cdata) or if, by changing the solvent, we can prevent formation of the 1:2 complex. Studies are in fact in progress in our laboratory along both lines.
Acknowledgment. It is a pleasure to thank Professor D. Ferri of the University of Naples who suggested the method of the projection maps and effectively helped us in applying it to our work.
References and Notes A. Donesi, L. Paolillo, and P. A. Temussi, J . Phys. Chem., 80, 279 (1976). M. W. Hanna and A. Sandoval, Biochim. Biophys. Acta, 155, 433 (1978). B. L. Van Duuren, Nature (London), 210, 622 (1966). 8. Pulmann, P. Claverle, and J. Caillet, Science, 147, 1305 (1965). A. M. Liquori, B. De Lerma, P. Ascoli, C. Botr6, and M. Trasciatti, J. Mol. Blol., 5, 521 (1962). P. De Santis, E. Giglio, A. M. Llquori, and A. Ripamonti, Nature (London), 191, 900 (1962). B. L. Van Duuren, J. Phys. Chem., 68, 2544 (1964). (a) H. A. Benes1 and J. H. HiMebrand, J. Am. Chem. Soc., 71, 2703 (1949); (b) M. W. Hanna and A. L. Ashbaugh, J . Phys. Chem., 88, 811 (1964). A. A. Sandoval and M. W. Hanna, J. Phys. Chem., 70, 1203 (1966). P. J. Trotter and M. W. Hanna, J. Am. Chem. Soc., 88,3724 (1966). D. Lichtenberg, F. Bergmann, and 2 . Neiman, J. Chem. Soc. C , 1939 (1971). R. Foster, “Organic Charge-Transfer Complexes”, Academic Press, New York, 1969. L. E. Orgel and R. S.Mulliken, J. Am. Chem. Soc., 79, 4839 (1957). M. I. Foreman, R. Foster, and D. R. Twiselton, Chem. Commufl., 1318 (1969). 0. Blederman and T. G. Spiro, Chem. Script., 1, 193 (1971). L. G. SIIIBn, Acta Chem. Scand., IO, 803 (1956). B. Dodson, R. Foster, and A. A. S. Bright, J. Chem. Soc. B, 1283 (197 1). R. Fletcher and M. J. D. Powell, Comput. J., 6, 163 (1963). D. A. Marquadt, J. Slam., 11, 431 (1963). K. Levenberg, 0.J . Appl. Math., 2, 164 (1944). R. Fletcher, Harweli Technical Report No. R6799 AERE (U.K.),1971. The listing of this program is available upon request from the authors.
