1254
(27) (28) (29) (30)
The Journal of Physical Chemistty, Vol. 82, No. 11, 1978 Extraction”, Vol. 6, J. A. Marinsky and Y. Marcus, Ed., Marcel Dekker, New York, N.Y., 1974, p 139. C. Hansch, J. H. Quinlan, and G. L. Lawrence, J. Org. Chem., 33, 347 (1968). C. Hansch and T. Fugita, J. Am. Chem. SOC.,88, 1616 (1964); T. Fugita, J. Iwasa, and C. Hansch, ibld., 86, 5175 (1964); J. Iwasa, T. Fugita, and C. Hansch, J . Med. Chem., 8 , 150 (1965). D.F. Evans, S. L. Wellington, J. A. Nadis, and E. L. Cussler, J. Soluibn Chem., 1, 499 (1972). R. M. Izatt, D. P. Nelson, J. H. Rytting, B. L. Haymore, and J. J. Christensen, J. Am. Chem. Soc., 93, 1619 (1971); J. J. Christensen, J. 0. Hill, and R. M. Izatt, Science, 174, 459 (1971); B. L. Haymore, MSc. Thesis, Brigham Young University, Provo, Utah, 1972; D. P. Nelson, MSc. Thesis, Brigham Young University, Provo, Utah, 1971.
H. P. Hopkins, D. V. Jahagirdar, and F. J. Windler (31) H. S. Harned and B. 8. Owen, “The Physical Chemistry of Electrolyte Solutions”, 3rd ed, Reinhold, New York, N.Y., 1958, pp 726, 727. (32) Reference 26, Chapter 6; A. P. Altshuller, J . Chem. Phys., 24, 642 (1956). (33) H. Brusset, L. Kaiser and J. Hocquel, Chim. Ind. Gen. Chim., 98, 1710 (1967); N. J. L. Megson, Trans. Faraday Soc., 34, 525 (1938). (34) P. Schuster, W. Jakubetz, and W. Marius, Top. Current Chem., 60, 1 (1975). (35) R. P. Taylor and I. D. Kuntz, Jr., J. Am. Chem. Soc.,94, 7963 (1972). (36) D. J. Turner, A. Beck, and R. M. Dlamond, J. Phys. Chem.,72, 2831 (1968); T. Kenjo, S. Brown, E. Held, and R. M. Diamond, ibid., 76, 1775 (1972). (37) Y. Marcus, N. Ben-Zwi, and I. Shlloh, J. Soiuibn Chem., 5 , 87 (1976).
Molecular Complexes in Solutions Containing Macrocyclic Polyethers and Iodine Harry P. Hopkins, Jr.,* D. V. Jahagirdar, and Frank Joseph Windler, I11 Department of Chemistry, Georgia State University, Atlanta, Georgia 30303 (Received January 18, 1978)
Spectroscopic studies have been performed in the UV-visible region on methylene chloride and cyclohexane solutions containing iodine and 12-crown-4,15-crown-5,and 18-crown-6. In cyclohexane these crown ethers form 1:l molecular complexes with iodine with correspondingequilibrium constants which are identical within experimental error, but are a factor of 2-3 times larger than the literature values for mono- and diethers. When methylene chloride is the solvent, the triiodide ion is an important species, in solutions containing iodine and 18-crown-6.
Crown ether chemistry began with the accidental discovery by Pedersen of one member of this class of Macrocyclic polyethers. During subsequent work,14 Pedersen gave these compounds their trivial “crown” nomenclature, synthesized many members of the family, and determined their properties and complexing abilities with several metal ions. The most unique attribute of this class of neutral molecules is their ability to form complexes with many metal cations;-l0 including all the alkali metal cations. The stability of these complexes appears to be related to the size of the cavity formed by the oxygen atoms in the ring. For many cations the magnitude of the interactions with crown ethers varies at least qualitatively with the diameter of the cavity, being a maximum when the cavity diameter matches the ionic diameter. The spectral studies reported here on iodine-crown ether solutions were performed to determine if cooperative effects could be observed in the formation of charge transfer complexes from crown ethers and iodine. The crown ethers included in the study are the now readily available 18-crown-6 ( 1,4,7,10,13,16-hexaoxacyclooctadecane), 15-crown-5 (1,4,7,10,13-pentaoxacyclopentane), and 12-crown-4 (1,4,7,10-tetraoxacyclodecane) which do not have benzo groups attached to the cyclic ether rings which might complicate the interpretation of the spectral data. These cyclic ethers contain only oxygen atoms as potential donor centers and have cavity diameters that range from 1.2 to 3.4 A, compared to a van der Waals diameterll for the iodine atom of 3.9 A. Spectral studies on solutions containing a particular crown ether and iodine were performed in the UV-visible region in cyclohexane and methylene chloride in order to provide thermodynamic data for the 1:l complexation process, which could then be compared to the literature data for the complexation of iodine with mono- and diethers. This comparison provides information regarding the possibility in the crown 0022-365417812082-1254$01 .OO/O
ether-iodine charge-transfer complexes of cooperative or simultaneous interaction of all the oxygens with the iodine molecule.
Experimental Section Baker reagent grade iodine was sublimed and stored in a desiccator over phosphorus pentoxide before use. Fisher spectral grade cyclohexane and methylene chloride were dried for a t least 48 h over molecular sieves and used as solvents in all measurements. The 18-crown-6 used in these experiments was kindly provided by Dr. Charles L. Liotta of the Georgia Institute of Technology. The 18-crown-6 was purified prior to use by recrystallization from acetonitrile and then evacuated for 48 h on a vacuum line to remove the acetonitrile. The 15-crown-5 used in these experiments was synthesized according to the procedures of Liotta et al.12 The identification of 15-crown-5and its purity was established by NMR and infrared spectroscopy. A sharp singlet (in benzene) was observed at 3.58 ppm (TMS standard) which is identical with the results of previous workers.12 The infrared spectra (CC14,0.1-mm NaCl cell) of 15-crown-5 exhibited the following spectral characteristics which are nearly identical with those reported in the literature? 2875, 1550, 1355, 1290, 1250, 1135, 982, and 940 cm-l. Infrared analysis showed water to be present in the isolated product. The water was removed by allowing a carbon tetrachloride solution of the 15-crown-5 to stir over molecular sieves for 24 h. Vacuum distillation (boiling range of 15-crown-5 a t 0.2 mmHg was 100-135 “C) of the dried carbon tetrachloride solution yielded dry 15-crown-5. The 12-crown-4 used in these experiments was synthesized according to the procedure of Liotta et a1.l’ The identification of 12-crown-4and its purity were established by NMR and infrared spectroscopy. A sharp singlet (in CHC1,) was observed at 3.65 ppm (TMS standard) which 0 1978 American
Chemical Society
The Journal of Physlcal Chemistry, Vol. 82, No. 11, 1978 1255
Macrocyclic Polyether-Iodine Molecular Complexes
is identical with the results of previous workers.12 Infrared spectroscopy (neat, NaCl plates) of 12-crown-4exhibited the following spectral characteristics which are nearly identical with the literature valued2 2900, 1465, 1365, 1295, 1260, 1135, 1102, and 920 cm-l. Infrared analysis showed water to be present in the isolated product. The water was removed by allowing a carbon tetrachloride solution of the 12-crown-4to stir over molecular sieves for 24 h. Vacuum distillation (boiling range of 12-crown-4 at 0.2 mmHg was 67-70 "C) of the dried carbon tetrachloride solution yielded dry 12-crown-4. The tetrabutylammonium triiodide used in this work was synthesized according to the procedure described by Popov.13 Description of Apparatus. Spectral measurements were made with a Beckman Acta V double beam spectrophotometer and a pair of matched quartz cells of 1.0-cm path length. The cell containing the solution was maintained at a set temperature to f0.05 OC by circulating water from a thermostated bath through a double walled cell insert. The temperature inside the cell compartment next to the quartz cuvet was monitored with a copper-constantan thermocouple. Description of Procedure. An appropriate quantity of iodine was weighed to five places directly into a 50-mL volumetric flask and made up to volume in a nitrogen purged drybox with dried cyclohexane at 20.0 "C. Iodine solution (3 mL) was placed in a quartz cell. Dry cyclohexane was used as a reference in a matched cell. The cells were placed in the spectrophotometer and the spectrum of the iodine solution was recorded in the region 1300045 000 cm-l. The iodine containing cell was returned to the drybox where an appropriate quantity of crown ether was added by weight (approximately 15 mg) to the iodine solution and the spectrum of this solution was recorded at each temperature. All concentrations were determined on a molar basis, ignoring the small change in volume due to the addition of the crown ether. The iodine concentration remained constant while the concentration of crown ether was increased on a stepwise basis. The equilibrium constants were determined from the absorbance values determined at 21 750 cm-l where a large increase occurred for each crown.
Results and Discussion Initially, spectral studies on 18-crown-6were attempted in methylene chloride with maxima found at 20 500,27400, and 33 900 cm-l (Figure 1). Although an isosbestic point can readily be located, the latter two bands are uncharacteristic of ether-iodine molecular complexes. It was thought that the new bands were due to triiodide ion as suggested by Lang14 in previous studies. Consequently a 1.85 X 10" M solution of tetrabutylammonium triiodide was scanned over the same spectral range shown in Figure 1. This spectrum exhibited very intense bands with maxima at 33 875 and 27 375 cm-l (Figure 1) which are virtually identical with the locations of two of the bands found in curves A-F. The new bands found in Figure 1 can be, therefore, assigned to the triiodide ion which is proposed to be formed by the reaction 51,
+ 2(18-crown-6)+. 21,- + 2(I,+.
*
.18-crown-6)
(1)
This reaction could be promoted by traces of water in the chlorinated solvent that solvate the ions, by the interaction of the 18-crown-6 with the 12+ion, and, or by the stabilization of the ions by the acidic hydrogens of methylene chloride. When spectral studies were performed in cyclohexane the two intense bands did not appear, but a shifting of the
ABS
35500
28000
20500
CM-' Figure 1. The uv-visible spectrum of methylene chloride solutions of iodine (9.35 X lo4 M) at 25 O C where the concentration at 18-crown-6 is (A) 0.0643, (B) 0.0931, (C) 0.1585, (D) 0.1870, (E) 0.2109, and (F) 0.2336 M. The bottom (unlabeled) curve is a methylene chloride solution of tetrabutylammonium triiodide (1.85 X M) at 25 O C .
iodine maximum to higher wavenumber values was observed with a well-defined isobestic point (Figure 2). A gradual increase in the baseline absorbance occurred in the ultraviolet region, but a well-defined maximum was not located in the region which could be assigned to the charge-transfer band. Spectra of this type were observed up to a ratio of 18-crown-6 to iodine of 251 upon the stepwise addition of 18-crown-6 to the iodine solution. It was concluded from this observation and the excellent fit of the data to a 1:l complexation model that only the 1:l 18-crown-6-iodine complex exist in these solutions over the temperature range employed. The maxima for the blue-shifted iodine band was located at 20 860 f 172 cm-l by deconvolutingthe spectra by a least-squares technique assuming that there exist only two Gaussian bands in the visible region. In studies on 15-crown-5- and 12-crown-4-iodine solutions, deviations from the well-defined isosbestic point were observed at ratios of 300:l and 140:1, respectively. With these solutions apparently a 1:l complex is the major species formed at the lower ratios where good fits for the data were obtained for the 1:l model. At higher ratios a 2:l crown ether-iodine complex is probably present, presumably in a sandwich type structure. In the case of 12-crown-4,this tendency to form species other than the 1:l complex at relatively low ratios limited the temperature range of the studies. At the lower ratios the spectral curves were qualitatively similar to those found for the 18crown-6-iodine solutions with the maxima for the blue shifted iodine band at 21 443 f 185 and 20820 f 149 cm-l for 15-crown-5 and 12-crown-4,respectively. In these studies the crown ethers were found to have essentially zero extinction coefficients in the region of
1256
The Journal of Physical Chemistry, Vol. 82, No. 7 1 , 1978
H. P. Hopkins, D. V. Jahagirdar, and F. J. Windler
TABLE I: Equilibrium Constants and Thermodynamic Values in Cyclohexane for 1 : l Adducts of Iodine and Crown Ethers Compclred t o Available Mono- and Diether Values in Similar Solventsa
18-Crown-6
15-Crown-5 12-Crown-4 Propylene oxideb Diethyl etherb Tetrahydrofuranb Te trahydropyranb 1,4-Dioxanec a
Kw L/mol
T:mP, C
Donor
All values are on a molar basis.
25.0 4.93 f 0.33 35.0 3.92 k 0.18 40.0 3.57 * 0.28 45.0 3.35 f 0.35 25.0 4.78 f 0.82 35.0 3.86 f 0.35 45.0 3.48 f 0.04 25.0 5.36 2 0.37 30.0 4.76 f 0.27 25 0.94 25 0.94 25 2.54 25 2.51 25 0.97 Reference 19. Reference 18.
ABS
A
28000
18000
23000
-AH,
kcal/mol
13000
CM-' Figure 2. The spectrum of a cyclohexane solution of iodine (1.06 X M) at 25 O C where the concentration of 18-crown-6 is (A) 0.0, (B) 0.0197, (C) 0.0295, (D) 0.0571, (E) 0.092, and (F) 0.155 M.
interest, so that the Rose and Drago method15for a 1:l complex could be employed where free iodine and the complex are the only absorbing species. With these assumptions, the rearrangement of the equilibrium and absorbance equations yields the Rose and Drago15 equation l/K,,= ( A - A ' ) / ( & - E % )C ', - C ', + C ~ ° C ~ o ( ( EEcl -z ) / ( A- A o ) (2) where K is the 1:l equilibrium constant; CAo and CBo are the initia iodine and crown ether concentrations; E , and EI, are the molar extinction coefficients for the complex and iodine; and A and Ao are the absorbances of the crown ether-iodine and pure iodine solutions, respectively. For each solution an initial guess for E, is made and the values of l/Keqcalculated for a series of E, values that cover a
3.28
2.97
%
i
0.27
0.53
-AS,
cal/mol 7.8
6.9
4.15 3.8 4.3 5.3 4.9 3.5
10.5 13.6 15.3 16.7 15.3 12.1
e,
I
L/mol cm 883 i 862 858i 825 i 1020 i 1010 * 920 f
34
* 28
800
f
870
f
37 60 67 55 8 47 43
large segment of l/Keqvalues. The resulting intersection of the lines defines the best fit of the data to a particular Kq and E, value. A well-defined intersection was obtained for all the crown ethers studied when the concentration M and the ratio of iodine (CAO)was in the range 1-3 X of crown ether to iodine did not exceed the previously noted values. From these results and the spectral curves exhibiting the isobestic points, it was concluded that the 1:l complex is the major species in the dilute solutions. In order to obtain an error estimate for the equilibrium constants and extinction coefficients, the values of these parameters were calculated from eq 2 for all possible pairs of data sets. In this way the average and standard deviation of the K,, values were evaluated. In all cases the saturation fraction, s, defined as the concentration of the complex divided by CAo was in the range 0.1-0.5. Deranlead6 has shown that s should be in the range 0.2-0.8 in order to obtain well-defined K, values and our data are in accord with this conclusion. %he K,, and E , values obtained from the absorbance and concentration data in the manner described above are tabulated in Table I. For 18-crown-6and 15-crown-5,the enthalpies of association were evaluated by means of a least-squares fit of In K,, vs. 1/T to give AH and the corresponding standard deviation (the small temperature dependence of the density of the solvent has been ignored). Since K,, values are reported at only two temperatures for 12-crown-4 because of the experimental difficulties mentioned, an error value is not available, but is probably of the same order of magnitude as that reported for the other crown ethers. However, the AH values reported here for the complexes should be considered only an estimate due to the limited amount of data. As can be seen from inspection of the data in Table I, the size of the crown ether ring does appear to affect appreciably the association constant. If a cooperative association of the end of the iodine molecule with all the oxygens of the crown occurs, the 18-crown-6 molecule would be expected to have the largest K, value. This is not the case, nor does any particular or%er to the data appear to exist based on the number of oxygens present or the size of the cavity formed by the crown ether oxygens. Following the lines of the argument presented by Mulliken,17 it is assumed when molecular complexes are formed with iodine that electron density is donated from the base (crown ether) to the bZouantibonding molecular orbital of iodine. Now, when the iodine molecule approaches the cavity of the crown ether end-on, it is conceivable that an interaction would occur between the lone pairs of electrons on the oxygens and the iodine molecular
Monte Carlo Free Energy Calculations on Dilute Solutions
orbital. For example, the appropriate set of lone pairs on each of the four oxygens in 12-crown-4 will form four molecular orbitals in which the lone pairs of electrons can be distributed. The net overlap between the three highest in energy 12-crown-4 molecular orbitals and the blou molecular orbital of iodine is seen to be zero from symmetry requirements when iodine approaches the cavity end-on, A net overlap will occur in this situation for the totally symmetric lowest energy molecular orbital, but because of energy considerations will not be an important term of the stabilization energy. Consequently, from simple molecular orbital arguments cooperative interactions are predicted to be less favorable than a simple interaction with a single oxygen in the 12-crown-4-iodine molecular complex. The arguments in the case of 18crown-6 and 15-crown-5 are similar, however, there will be a small nonzero net overlap for the 15-crown-5 molecular complex. These conclusions, derived from simple molecular orbital considerations, that a cooperativeinteraction is not favored in the crown ether-iodine molecular complexes, are in accord with our data. It is also instructive to compare the crown-ether data with the available mono- and diether equilibrium constants listed in Table I. Changing the structure of the ether from linear to cyclic raises the Kegfrom 0.94 for diethyl ether to 2.54 for tetrahydrofuran or tetrahydropyran. However, 1,4-dioxane has a K , = 0.97 which is lower by nearly a factor of 5 than that w%ich is predicted on a statistical basis from the data for tetrahydropyran, i.e., there are two basic sites in l,4-dioxane. Garito and Waylandls conclude from this observation that the presence of the second oxygen reduces the basicity of the oxygen atom in the 1,Cdioxane relative to tetrahydropyran. Accepting their conclusion, it is seen that 18-crown-6, 15-crown-5, and 12-crown-4 are expected to have K value of about 3, 512, and 2 times that of 1,Cdioxane. ??he Kq values found for these crowns are close in magnitude to this prediction but are not of the order expected. In fact all the thermodynamic values for the molecular complexes are virtually identical within
The Journal of Physical Chemistry, Vol. 82, No. 11, 1978 1257
experimental error, thus indicating that the relative basicity of these compounds toward iodine is the same although larger than any other ethers yet studied. This is due to a decrease in the entropy of complexation rather than an increase in AH. In fact the enthalpies of complexation, AH, for the crown ethers studied here are nearly the same as those found for propylene oxide, 1,4dioxane, and diethyl ether and smaller by 1-2 kcal/mol than the AH values listed for tetrahydrofuran and tetrahydropyran. The AH given for 1,4-dioxane is within experimental error the same as those found for the 18crown-6 and 15-crown-5,but the A S for 1,4-dioxanediffers from the A S values for the crown ethers by nearly a factor of 2. Since there is not evidence to suggest a cooperative bonding of iodine to all the oxygens in the crown ether, the more positive entropy of complexation found for the crown ethers is probably due to the larger number of complexation sites present in the crown ethers than in 1,4-dioxane. References and Notes (1) C. J. Pederson, J. Am. Cbem. Soc., 89, 2945 (1967). (2) C. J. Pederson, J. Am. Cbem. Soc., 89, 7017 (1967). (3) C. J. Pederson, Fed. Proc., Fed. Am. Soc. Expl. Biol., 27 1305 (1968). (4) C. J. Pederson, J. Am. Cbem. Soc., 92, 386 (1970). (5) C. J. Pederson, J. Am. Cbem. Soc., 92, 391 (1970). (6) C. J. Pederson, J. Org. Chem., 38, 1690 (1971). (7) C. J. Pederson, J. Am. Cbem. Soc., 89, 2495, 7017 (1967). (8) C. J. Pederson, J. Am. Cbem. Soc., 92, 386 (1970). (9) C. J. Pederson and H. J. Freusdorff, Agnew. Cbem., Int. Ed. Engl., 84, 16 (1972). (10) J. J. Christensen, J. 0. Hill, and R. M. Izatt, Science, 29, 439 (1971). (11) A. Bondi, J . Pbys. Chem., 88, 441 (1964). (12) F. L. Cook, T. C. Caruso, M. P. Byrne, C. W. Bowers, D. H. Speck, and C. L. Liotta, Tetrahedron Lett., No. 48, 4029-4032 (1974). (13) R. E. Buckles, J. P. Yuk, and A. I. Popov, J . Am. Cbem. Soc., 74, 4379 (1952). (14) R. P. Lang, J . Pbys. Cbem., 78, 1657 (1974). (15) N. J. Rose and R. S. Drago, J. Am. Cbem. Soc., 81, 6138 (1959). (16) D. A. Deranleau, J. Am. Cbem. Soc., 91, 4044 (1969). (17) R. S. Mulliken, J. Am. Cbem. Soc., 74, 811 (1952). (18) A. F. Garito and B. B. Wayland, J. Pbys. Cbem., 71, 4062 (1967). (19) M. Brandon, M. Tarnres, and S. Searles, J . Am. Cbem. Soc., 82, 2129 (1960).
Monte Carlo Free Energy Calculations on Dilute Solutions in the Isothermal-Isobaric Ensemble' John C. Owicki" and Harold A. Scheraga*2b Department of Cbemistty, Cornell University, Itbaca, New York 14853 (Received September 22, 1077)
A method is presented for the theoretical calculation of differences in free energy between dilute solutions in which the size of the repulsive core of the solute in one solution differs from that in the other. The effectiveness of this Monte Carlo algorithm is due primarily to the use of umbrella sampling to increase the efficiency of the calculation of ensemble averages related to the differences in free energy. A sample calculation (in the isothermal-isobaric ensemble) of free energies of solvation of hard-sphere solutes in the Lennard-Jones fluid is presented. The calculation also gives the distribution of cavity sizes in the solvent, a function of interest in scaled particle theory. The limitations of the technique, and extensions to calculations on less restricted classes of solutes, are discussed.
I. Introduction Monte Carlo (MC) and molecular dynamics (MD) computer simulations have been used successfully to calculate ensemble- or time-averaged properties in a variety of model liquid system^.^ The importance of such calculations is twofold. First, given an intermolecular PO0022-3654/78/2082-1257$01 .OO/O
tential energy function which is sufficiently close to that of a real liquid, it is possible to compute quantities that are not presently accessible by experimental or other theoretical methods. Second, and just as important, the numerical computer techniques can provide essentially exact results for a given model potential; this furnishes a 0 1978 American Chemical Society
