J. Phys. Chem. 1995, 99, 12081-12083
12081
Representation of c60 Solubilities in Terms of Computed Molecular Surface Electrostatic Potentials and Areas Jane S. Murray,* Sergei G. GagarinJ and Peter Politzer Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 Received: April 6, 1995; In Final Form: May 17, 1995@
We show that the solubilities of Cm in a variety of organic solvents can be represented analytically in terms of surface areas and statistically based quantities obtained from the electrostatic potentials calculated on the solvent molecular surfaces. This relationship, plus the surface potential computed for Cm itself, confirms that solubility is promoted by large solvent molecules and by moderately attractive interactions that are relatively balanced between positive and negative regions on the solute and solvent molecular surfaces.
Introduction There has been considerable interest in recent years in the preparation, reactions and properties of Ca (buckminsterf~llerene).'-~This is an allotropic form of carbon that was originally discovered in soot condensed from evaporated graphite.2 Its structure is cage-shaped with carbon atoms at the 60 vertices of a truncated icosahedron, such that its connectivity pattern resembles a soccer ball. One property of both fundamental and practical interest is the solubility of Cm in various organic solvents. This has now been measured by several
involving noncovalent interactions that do not involve any significant degree of charge transfer. The fist term on the righthand side of eq 1 gives the contribution of the nuclei and is positive; the second term reflects the distribution of the electrons and is negative. The sign of V(r) at any particular point depends upon which term is dominant there. atlo?and Y are defined in terms of V(r) plotted on a square grid generated on the 0.001 au molecular surface (eqs 2 q d 3). m
i= 1
researcher^.^.^ In several recent papers, we have shown that the solubilities of different solutes in a given solvent can be related to computed statistical quantities obtained from the electrostatic potentials calculated on the surfaces of the solute molecule^.'^-'^ In this work we explore the reverse situation, the solubility of a single solute, c60, in a variety of solvents, and focus on the computed molecular surface properties of the solvents.
Y
2 2 = a+2a-2/[a,,, I
(3)
HF/STO-3G* optimized geometries have been computed with GAUSSIAN 8815 for the 22 solvent molecules in Table 1. These structures were used to obtain the HF/STO-SG* electrostatic potentials V(r) (eq 1) on molecular surfaces defined, following Bader et al.I6as the 0.001 au contour of the electronic density @(r).From these surface potentials, we have calculated two statistically-based quantities, a,,? and v , that reflect the variability and degree of balance of the electrostatic potential on the surface (eqs 2 and 3). This approach has been used successfully in representing analytically a number of liquid and solution phase properties involving molecular interactions.'0,'l.'3.14,17 Our experience has been that the same trends are obtained when larger basis sets are u ~ e d . ' ~ , ' ~ The electrostatic potential is defined rigorously by eq 1. ZA is the charge on nucleus A, located at RA. V(r) is a real physical
Vf(ri) and V-(ri) are the positive and negative values of V(r) on the surface, and VS+ and VS- are their averages: VS+ = ( l / m ) c z , V+(ri)and Vs- = (lln)&lV-(rj). The surface area is obtained by converting the numbers of points on the surface to i 4 2 . We interpret a,,,? as a measure of electrostatic interaction tendency; it is a sum of the variances of the positive and negative regions of the surface V(r) and is particularly sensitive to the positive and negative extrema.'0-'' Y is a measure of the electrostatic balance, which reaches a maximum value of 0.250 when and a-2 are We have found that the product vq,? is especially important in representing properties related to how well a molecule interacts electrostatically with others of its own Values of vu,,? for organic molecules range from less than 1 (kcal/ mol)2 for saturated hydrocarbons to 62.5 (kcal/mol)2 for formamide. Those with high values of v (near 0.250) and relatively large a,,? are expected to have strong attractions for molecules of their own kind. We have used the SAS statistical analysis22 package to explore possible relationships between measured Cm solubility and the various computed quantities of the solvents. Many combinations of the latter, including products aned powers, were tested.
property, well established as a guide to molecular interactive behavior.20.2' It is particularly well suited to studies of properties
Results and Discussion
Methods and Procedure
* To whom correspondence should be addressed.
'
Present address: Institute of Fossil Fuels, 117912, GSP-1, Leninsky Prospect 29, Moscow, Russia. @Abstractpublished in Advance ACS Abstracts, August 1, 1995.
0022-365419512099-1208 1$09.0010
Table 1 lists the solubility of Cm in 22 solvent^,^ along with their computed molecular surface quantities: area, a+2,u - ~ , a,,?,and Y . The solvents are listed in order of increasing Cm solubility.
0 1995 American Chemical Society
12082 J. Phys. Chem., Vol. 99, No. 32, 1995
Letters
TABLE 1: Solubility of Ca in Various Solvents and Computed Molecular Properties of SolvenWb C a solubility, predicted, eq 4, surface mole fraction ( x lo4) log(so1 x lo4) log(so1 x 104) area (A) u + (kcaVmol)z ~
mo1ecu1e
0.000 0.000 0.001 0.001 0.008 0.059 0.073 0.22 0.27 0.40 0.7 1 0.78 1.1 2.1 4.0 4.8 8.4 9.9 15 53 68 97
methanol acetonitrile ethanol acetone n-pentane cyclohexane n- hexane chloroform' dichloromethane' carbon tetrachloride benzonitrile fluorobenzene nitrobenzene benzene toluene bromobenzene anisole chlorobenzene 1,2,4-trichlorobenzene 1,2-dichlorobenzene 1-methylnaphthalene' 1-chloronaphthalene'
-7.578 -5.243 -3.057 -2.847 -1.127 - 1.292 -0,724 -0.835 -0.448 -1.145 -0.567 0.341 0.730 -0.269 0.105 0.815 1.194 0.833 1.336 1.552 1.338 2.008
-3.000 -3.000 -2.097 - 1.229 -1.137 -0.658 -0.569 -0.398 -0.149 -0.108 0.041 0.322 0.602 0.68 1 0.924 0.996 1.176 1.724 1.833 1.987
64.7 75.9 87.1 99.4 139.7 136.8 159.6 107.6 91.1 120.3 135.6 117.7 142.8 115.3 136.0 137.0 144.2 132.2 160.5 146.3 184.8 181.1
49.6 23.6 45.1 15.9 2.8 2.5 2.7 53.5 46.3 28.8 18.4 12.0 16.9 7.1 6.8 13.4 15.9 14.4 18.0 22.4 7.7 13.3
(kcaVmol)* ut,,? (kcaVmol)* 181.5 167.8 182.4 159.8 0.9 0.7 0.9 7.4 13.8 2.5 176.9 32.9 105.2 9.2 11.1 18.8 61.3 22.9 12.5 23.2 9.4 15.5
231.0 191.4 227.5 175.7 3.6 3.2 3.6 60.9 60.1 31.3 195.3 45.0 121.9 16.3 17.9 32.2 77.2 37.4 30.5 45.6 17.1 28.8
Y
0.169 0.108 0.159 0.082 0.194 0.171 0.188 0.107 0.177 0.073 0.085 0.195 0.120 0.246 0.236 0.243 0.164 0.236 0.242 0.250 0.248 0.249
a Solubilities are taken from ref 9. Computed moperties are taken from refs 14 and 17, unless otherwise indicated. Computed properties for . . this molecule were calculated in the present work.
3
,
I
,
I
I
2
I
0
3' t
-4
-4
g I
I
I
4
I
I
1
-3
-2
-1
0
1
2
3
I
experimentally.measured log (sol x 10000)
Figure 1. Relationship between solubilities predicted with eq 4 and experimentally determined values, in mole fractions.
For the solvents in Table 1, the Cm solubilities (in mole fractions) range over 5 orders of magnitude, being very low for small, highly polar molecules and very high for the methyl and the chloronaphthalene derivatives. For these solvents, excluding methanol and acetonitrile which have reported zero solubilities, we find a good three-parameter relationship between log(so1 x lo4) and the computed molecular quantities, given in eq 4, where a = 28.98, /3 = 1.278, y = 1.533 x and E =
2.716. The effectiveness of eq 4 in reproducing the experimental solubilities is shown in Figure 1. The linear correlation coefficient is 0.954 and the standard deviation is 0.475. Equation 4 predicts log(so1 x lo4) for methanol and for acetonitrile to be about -8 and -5, respectively. When these values are put into the data set, the linear correlation coefficient for a relationship with the same form as eq 4, but for all 22 molecules, increases to 0.983. For this new relationship, a,/3, y , and E are 28.12, 1.250, 1.563 x and 2.691.
Equation 4 shows that solubility is enhanced by the solvent molecules having large surface areas. The role of their surface electrostatic potentials, as measured by a,,?, is more complex; according to eq 4, solubility varies both directly with ole?, through the term involving (vulo?)112, and inversely, because of the negative contribution of area)^". The latter term is needed to represent the virtual insolubility of c60 in the first four solvents: methanol, acetonitrile, ethanol, and acetone. These molecules are the only ones to combine very high values of ulo?,due primarily to u - ~with , relatively small surface areas. Evidently Cm is unable to compete with the strong attractive interactions between these molecules, presumably hydrogen bonding, which can apparently occur even more effectively because the small areas lessen the chances for unfavorable relative orientations. For the remaining solvents in Table 1, Cm solubility is favored by intermediate values of ulo? which involve a high degree of balance between the positive and negative contributions. This explains the need for the term It also suggests that the key to Cm solubility in these compounds is solute-solvent interaction through both positive and negative surface regions. To verify this, we computed ole? and v at the HF/STO-SG*// HF/STO-3G* level for Cm. We obtained oto12 = 15.8 (kcal/ and v = 0.250. In these respects, therefore, C ~ is O comparable to aromatic hydrocarbons (e.g., benzene, toluene, 1-methylnaphthalene). These results support the conclusion that the solubility of c60 in most of the solvents in Table 1 involves a moderately attractive interaction that is fairly balanced between positive and negative regions on the solute and solvent molecular surfaces.
Acknowledgment. We thank Dr. Jorge M. Seminario for providing an HF/STO-3G* optimized geometry for Cm. References and Notes ( 1) Kroto, H. W.; Heath, J. R.; OBrien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (2) Kratschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Nature 1990, 347, 354. (3) Iqbal, Z.; Baughman, R. H.; Ramakrishna, B. L.; Khare, S.; Murthy, N. S.; Bomemann, H. J.; Moms, D. E.Science 1991, 254, 826.
Letters (4) Zhu, Q.;Zhou, 0.; Coustel, N.; Vaughan, G. B. M.; McCauley, J. P. Jr; Romanov, W. J.; Fischer, J. E.; Smith, A. B. 111Science 1991, 254, 545. ( 5 ) Greaney, M. A.; Gorun, S. M. J. Phys. Chem. 1991, 95, 7142. (6) Olah, G. A.; Bucsi, I.; Lambert, C.; Aaniszfeld, R.; Trivedi, N. J.; Sensharma, D. K.; Surya Prakash, G. K. J. Am. Chem. Soc. 1991, 113, 9385. (7) Allemand, P. M.; Koch, A,; Wudl, F.; Rubin, Y.; Diedrich, F.; Alvarez, M. M.; Anz, S. J.; Whetten, R. L. J. Am. Chem. SOC. 1991, 113, 1050. (8) Sivaraman, N.; Dhamodaran, R.; Kaliappan, I.; Srinivasan, T. G.; Vasudeva Rao, P. R.; Mathews, C. K. J. Org. Chem. 1992, 57, 6077. (9) Ruoff, R. S.; Tse, D. S.; Malhotra, R.; Lorents, D. C. J. Phys. Chem. 1993, 97, 3379. (IO) Politzer, P.; Lane, P.; Murray, J. S.; Brinck, T. J. Phys. Chem. 1992, 96, 7938. (11) Politzer, P.; Murray, J. S.; Lane, P.; Brinck, T. J. Phys. Chem. 1993, 97, 729. (12) Brinck, T.; Murray, J. S.; Politzer, P. J. Org. Chem. 1993,58,7070. (13) Murray, J. S.; Brinck, T.; Politzer, P. J. Phys. Chem. 1993, 97, 13807. (14) Murray, J. S.; Brinck, T.; Lane, P.; Paulsen, K.; Politzer, P. J. Mol. Struct. (THEOCHEMJ 1994, 307, 55.
J. Phys. Chem., Vol. 99, No. 32, 1995 12083 (15) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, I.;Martin, R.; Kahn,L. R.; Stewart, J. J. P.; Nuder, E. M.; Topiol, S.; Pople, J. A. GAUSSIAN 88; Gaussian Inc.: Pittsburgh, PA, 1988. (16) Bader, R. F. W.; Carroll, M. T.; Cheeseman, J. R.; Chang, C. J. Am. Chem. SOC. 1987, 109, 7968. (17) Murray, J. S.; Lane, P.; Brinck, T.; Paulsen, K.; Grice, M. E.; Politzer, P. J. Phys. Chem. 1993, 97, 9369. (18) Hagelin, H.; Murray, J. S.; Brinck, T.; Berthelot, M.; Politzer, P. Can. J. Chem. 1995, 73, 483. (19) Murray, J. S.; Lane, P.; Politzer, P. Mol. Phys. 1995, 85, 1. (20) Chemical Applications of Atomic and Molecular Electrostatic Potentials; Politzer, P., Truhlar, D. G., Eds.; Plenum Press: New York, 1981. (21) Politzer, P.; Murray, J. S. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers: New York, 1991; Vol. 2, Chapter 7. (22) SAS; SAS Institute Inc.: Cary, NC, 27511.
JP9509830
