J. Phys. Chem. B 2007, 111, 9853-9857
9853
QSPR Modeling of Solubility of Polyaromatic Hydrocarbons and Fullerene in 1-Octanol and n-Heptane Dana Martin, Uko Maran, Sulev Sild, and Mati Karelson* Department of Chemistry, UniVersity of Tartu, 2 Jakobi Street, Tartu 51014, Estonia ReceiVed: March 1, 2007; In Final Form: June 4, 2007
Solubility of polyaromatic hydrocarbons (PAH) and carbon nanostructures is important both from the technical and environmental points of view. In the present work, two general quantitative structure-property relationship (QSPR) models were developed, describing the solubility of PAH-s and fullerene (C60) in two different condensed media (1-octanol and n-heptane). Statistically good QSPR models were obtained by using forward selection techniques from large space of theoretical molecular descriptors. The physical meaning of the models is discussed and analyzed.
Introduction Solubility is one of the most important properties in many fields, from technical applications to bioavailability of compounds, toxicity, and environmental protection. Small PAH (having 2-3 condensed aromatic cycles) are known as useful technical compounds in plastics, dyes, and drugs fabrication. PAH are also byproducts in many combustion processes and have well-known toxicity and carcinogenic potential.1 Because of their technical importance and toxic behavior, their solubility in different solvents is of considerable interest. Polyaromatic hydrocarbons (PAH) have toxic impact on the environment when washed by ground and surface water from contaminated soils and for this reason PAH solubility in water is most frequently studied.2-5 PAH are intermediates in carbon nanostructures (fullerenes, carbon nanotubes) synthesis.6 Due to their extended π electronic system and the structure which consist of fused pentagons and hexagons, PAH and fullerenes have similar properties, and PAH property analysis is a useful tool in understanding properties of fullerenes.7-10 In this context, extended knowledge about PAH solubility in different solvents could give insight into the mechanism of solubility of different carbon nanostructures. Knowledge about the solubility of PAH and carbon nanostructures is also helpful in separation of nanostructures from byproducts resulting from the synthesis. Furthermore the prediction of solubility in different media is important for the prediction of optimum conditions for the fractional precipitation of nanostructures in different organic solvents during the purification process. It is well-known that the carbon nanostructures in their basic forms are very little soluble in water.11 At the same time, aqueous solubility of fullerenes has many potential uses in medical applications, and thus their solubility has been realized by functionalization of their external surface with hydrophilic functional groups12 The solubility can be modeled quantitatively for a series of solutes in a single solvent13-16 or for a series of solvents for a single solute.17 In the first case, the QSPR model expresses the solubility as a function of the solute descriptors. In the second case, the solubility is determined by the solvent descriptors. Both models are fundamentally important. Most PAH solubility studies until now have expressed the solubility of a single solute in a series of solvents or binary * Corresponding author phone:+3727375255; E-mail:
[email protected].
fax:+3727375264.
mixtures of solvents. The studies of PAH solubility rely on linear solvation energy relationship (LSER),18,19 mobile order theory (MOT),20 and QSPR.17 The LSER approach involved the multilinear regression (MLR) analysis of solubilities of individual solutes including anthracene,21 phenanthrene,21 fullerene C6022 in various solvents and binary mixtures of solvents. The MOT theory can predict mol fraction solubilities of solutes in nonelectrolyte solvents and has been applied to solubilities of solutes like anthracene,23 phenanthrene,21 pyrene,24 acenapthene,25 fluoranthene.23 The QSPR methodology has been used to model the solubility of 22 monocyclic and polycyclic aromatic hydrocarbons.17 Studies of nanostructures solubility in organic solvents using QSPR models have mainly concentrated on C60 fullerene26-29 with one exception of carbon nanotubes.30 To the best of our knowledge no QSPR or other predictive models have been reported on solubility of series of PAH and fullerene in the same solvent. The reason could be the difficulty of finding experimental solubility data in the same solvent for a series of PAH and fullerene. In the case of PAH with a small number of cycles (2-3 condensed aromatic cycles) like anthracene and phenanthrene, the solubility data are available in many organic solvents, because these compounds are widely used in organic synthesis. The PAH with a larger number of cycles (more than four condensed cycles) have scarce solubility data in organic solvents, because it is difficult to obtain these compounds in necessary amounts with a high degree of purity which is required for solubility studies. Their solubility in organic solvents is also less interesting from an industrial point of view because they are generally not precursors used in organic synthesis, and as a result, their solubility in organic solvents has been less studied than those of PAH with small number of rings. In this work, we have used QSPR methodology to study the solubility of a series of PAH and fullerene C60 in n-heptane and 1-octanol. These two solvents were selected due to the availability of reliable solubility data at the same temperature (25 °C). In addition, both solvents do have different physicochemical properties, one being nonpolar and the other having -OH group and average polarity. Data and Methodology. The solubility data of PAH was collected from the IUPAC-NIST Solubility Database31 that contains experimental data for PAH in nonaqueous solvents. It includes a large amount of solubility data for PAH with a small
10.1021/jp071679x CCC: $37.00 © 2007 American Chemical Society Published on Web 07/28/2007
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TABLE 1: The Solubility Data for PAH and C60 in n-Heptane
TABLE 2: The Solubility Data for PAH and C60 in 1-Octanola
polycycle name (abbreviation)
log S (exp)
log S (calc)
S (exp)
S (calc)
polycycle name (abbreviation)
log S (exp)
log S (calc)
S (exp)
S (calc)
anthracene (ATR) benzanthracene (BATR) benzo[a]pyrene (BP) biphenyl (BPH) benzo (ghi)perylene (BGP) buckminsterfullerene (BMF) chrysene (CH) coronene (CO) dibenz[a,h] anthracene (DBA) naphthacene (NPTHC) naphthalene (NPTH) perylene (PRL) phenanthrene (PHN) pyrene (PY) triphenylene (TPHNL)
-2.3979 -1.8752 -2.4685 0.2209 -2.9208 -4.0868 -2.3979 -3.3188 -3.4685 -3.7959 -0.2218 -3.4318 -1.5686 -1.9208 -2.2518
-1.9377 -2.7029 -2.9255 -0.1172 -2.7596 -3.9407 -2.6399 -3.5075 -3.4118 -3.8047 -0.1778 -2.7074 -1.5119 -1.7916 -1.9756
0.0040 0.0133 0.0034 1.6630 0.0012 8.190‚10-5 0.0040 0.0005 0.0003 0.0001 0.6000 0.0004 0.0270 0.0120 0.0056
0.0115 0.0020 0.0012 0.7634 0.0017 0.0001 0.0023 0.0003 0.0004 0.0001 0.6640 0.0020 0.0307 0.0161 0.0106
acenaphthene (ANP) anthracene (ATR) 2,3-benzofluorene (23BF) biphenyl (BPH) buckminsterfullerene (BMF) chrysene (CH) coronene (CO) dibenz[a,h] anthracene (DBA) fluoranthene (FA) fluorene (FL) naphthacene (NPTHC) naphthalene (NPTH) perylene (PRL) phenanthrene (PHN) pyrene (PY)
-0.5916 -1.9281 -1.8060 -0.1603 -4.1850
-0.4127 -1.4434 -1.8122 -0.1345 -4.0511
0.2560 0.0118 0.0156 0.6913 6.530‚10-5
0.3866 0.0360 0.0154 0.7336 8.89‚10-5
number of cycles in different organic solvents but less solubility data for PAH with a larger number of cycles. However, the solubility data of different PAH in the same solvent, measured at the same temperature are rather scarce. The available solubility data in n-heptane and 1-octanol are summarized in Table 1 and Table 2, involving 15 compounds in both solvents. Both tables contain solubility expressed in mol per liter (mol/ L) and experimentally measured at 25 °C, as found in the CHART 1: The Structure of PAH and C60 Molecules Used
-2.6990 -2.5775 0.0020 -3.4134 -3.4354 0.0004 -3.0278 -3.5515 0.0009
0.0026 0.0004 0.0003
-0.7630 -0.6815 -2.2757 -0.0182 -2.5166 -0.3966 -0.8542
0.1112 0.1113 0.0067 0.7567 0.0067 0.2774 0.1087
-0.9537 -0.9536 -2.1746 -0.1211 -2.1752 -0.5569 -0.9638
0.1725 0.2082 0.0053 0.9589 0.0030 0.4012 0.1398
a exp, experimentally determined solubility (mol/L); calc, calculated solubility (mol/L).
IUPAC-NIST database. For the modeling purposes the data has been used in logarithmic scale. After modeling the data was back converted to original scale. The molecular structures of polycycles (see Chart 1) were optimized at semiempirical level using AM1 parametrization32
QSPR Solubility Study of PAH and Fullerene
J. Phys. Chem. B, Vol. 111, No. 33, 2007 9855 into two equal groups with nearly equal dispersions of solubility values. Thereafter, new model coefficients were calculated for both groups, by using the descriptors of the original model, and each model obtained was used to predict the solubility values for the other group of compounds. The values obtained were merged, and R250 and the s250 were calculated for the correlation between all experimental and predicted solubility values. Results and Discussion
Figure 1. The plot of experimental vs calculated log of solubility in n-heptane (mol/L), (logS); For PAH names and structures see Table 1 and Chart 1.
with MOPAC version 6.01 program.33 The calculations were carried out for the isolated molecules, and a 0.01 kcal/Å gradient norm was used. The descriptors used in CODESSA34 software package were calculated by using the optimized molecular structures. The constitutional, topological and geometrical descriptors were calculated using the 3D geometry of the molecule. The quantum chemical descriptors were calculated using information extracted from MOPAC output files including orbital energies and coefficients (and their combinations), atomic and bond populations, various components of the energy partitioning scheme, polarizabilities up to second order and dipole moments. In total, 328 descriptors were calculated. No experimental data were used as descriptors. The QSPR models were derived with Heuristic and best multilinear regression (BMLR) descriptor forward selection approaches35 implemented in CODESSA program. During the first steps of model development the set of 328 descriptors was glanced (cleaned from insignificant descriptors (R2 < 0.1), highly intercorrelated descriptors (R2 > 0.99) and the descriptors with missing values) and 210 descriptors (see the Supporting Information) remained for the final model development.During the model development phase a number of QSPR models were developed for both data sets. Several criteria were considered for the selection of final models. Models were ranked by statistical parameters, including squared correlation coefficient (R2), leave-one-out cross validation coefficient (R2cv), square of standard error of multiple linear regression (s2), Fisher criterion (F), and number of descriptors in the QSPR model (n). The leave-one-out cross validation was also used as one of criteria’s for the selection of optimal number of descriptors in the final QSAR models. In the case of both datasets, the optimal number of descriptors in the model appeared to be three. While additional descriptors still improved the R2, the improvement to the R2cv was insignificant. Finally, the theoretical relevance of selected descriptors to solubility was evaluated. If some descriptor in the model did not have plausible physico-chemical relation to solubility, the model was rejected. In addition to leave-one-out cross validation the internal, leave50%-out, validation described by R250 and s50, was performed for all the proposed models. For the internal validation, the data were reordered with increasing solubility values, and divided
The QSPR models of solubility in n-heptane and 1-octanol have a good overall statistical quality. In both cases, the best models obtained are three-parameter correlations involving topological, charge related and quantum chemical descriptors. Solubility in n-Heptane. The QSPR model for the solubility in n-heptane is given with eq 1, and a plot of experimentally vs calculated logarithm of solubility is presented in Figure 1. The model involves three descriptors: Relative negative charge (Zefirov’s PC) (RNCG) (t test ) 9.4938), average structural information content (order 2) (2ASIC) (t test ) -4.2393), min exchange energy for a C-C bond (Emin ee (C-C)) (t test ) -2.5843).
log S ) 3.49((3.46) + 76.98((8.11)‚RNCG 9.56((2.25)‚2ASIC - 1.18((0.45)‚Emin ee (C-C) R2 ) 0.9047, Rcv2 ) 0.8378, s2 ) 0.1816, R502 ) 0.8232, s502 ) 0.3503, F ) 34.79, N ) 15, n ) 3 (1) According to the t test, the most significant descriptor in eq 1 is RNCG. This descriptor has been introduced by Jurs and coworkers36,37 and is defined as the charge of the most negative atom divided by the sum of negative charges. The partial charges were calculated using Zefirov’s electronegativity equalization scheme.38 The RNCG descriptor encodes features describing polar interactions between molecules and shows the relative influence of the most negatively charged atom on the overall charge of the molecule. According to eq 1, compounds with higher localization of negative charge have better solubility in n-heptane. The next descriptor involved in the QSPR solubility model for n-heptane is the topological descriptor 2ASIC. It reflects the size and compactness of the molecule. The regression coefficient of this descriptor is negative which indicates that the solubility in n-heptane decreases with increasing of the molecule size. The descriptor 2ASIC is based on Shannon information theory and like other molecular complexity indices makes the division of atoms into different classes depending on the size of coordination sphere taken into account near a given atom. This leads to the indices of different order k. The average value of structural information content (kSIC) has been defined by Basak39 by eq 2.
SIC ) kIC/log2n
k
(2)
The definition of kSIC relies on information content index (kIC) descriptor given by eq 3. k
k
IC ) -
ni
ni
log 2 ∑ n i)1 n
(3)
where, ni is the number of atoms in the ith class, n the total number of atoms in the molecule, and k represents the number
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Figure 2. The plot of experimental vs calculated log of solubility in 1-octanol (mol/L), (logS); For PAH names and structures see Table 1 and Chart 1.
of atomic layers accounted for in the coordination sphere around a given atom. The third descriptor involved in the solubility model for 40 n-heptane is the quantum-chemical descriptor Emin ee (C-C). The mathematical formulation of this descriptor is given by eq 4. It reflects the exchange energy between atomic pairs (A,B).
Eee(AB) )
∑ ∑
PµλPνσ 〈µλ|νσ〉
(4)
µ,ν∈A λ,R∈B
where Pµν, and Pλσ are density matrix elements and denote electron repulsion integrals on atomic basis {µνλσ}. Emin (C-C) influences the short-range contribution to the ee interaction energy between solute and solvent molecules. Compounds that have nonaromatic bonds in molecule (like ANP, FL, 23BF) have more negative Emin ee (C-C) values and better solubility in n-heptane. Solubility in 1-octanol. The solubility in 1-octanol is given by eq 5 and a plot of experimentally vs calculated logarithm of solubility is presented in Figure 2. The QSPR model includes the following descriptors: Information content of order 1 (1IC) (t test ) -10.8978), Emin ee (C-C) (t test ) -9.6761) and relative positive charged surface area (RPCS) (t test ) 5.7229).
log S ) 10.45((1.30) - 8.40‚10-2((7.71‚10-3)‚1IC 1.57((0.16)‚Emin ee (C-C) + 0.88((0.15)‚RPCS R2 ) 0.9637, Rcv2 ) 0.9346, s2 ) 0.0782, R502 ) 0.9554, s502 ) 0.1008, F ) 97.28, N ) 15, n ) 3 (5) The solubility of PAH decreases with the increase of the dimension of molecule and with its extension along one axis. As a general trend, those with less compact shape have higher 1IC values and are less soluble in 1-octanol. The negative value of the regression coefficient for 1IC topological descriptor indicates that the solubility decreases with increasing of 1IC value. The 1-octanol is more polar as compared to n-heptane due to the presence of OH group, and as a consequence the solubility of PAH is influenced by the respective charge redistribution which is characterized by RPCS descriptor. For this descriptor,
the partial charges were also calculated using Zefirov’s electronegativity equalization scheme.38 The RPCS descriptor is defined as the most positive surface area in a molecule.36 The QSPR term with this parameter has a positive value, which indicates that there is a direct relationship between the local polarity of a PAH and its solubility in 1-octanol. This can be explained by the fact that PAH with higher RPCS values are attracted by the -OH group of the solvent with partial negative charge and as a consequence are more soluble in 1-octanol. The quantum chemical descriptor Emin ee (C-C) has the same significance as in the case of solubility in n-heptane. As a general trend, the solubility in these two solvents decreases with increasing the size of the molecule (with the number of cycles in PAH). However there are several exceptions from this trend. Anthracene’s solubility in n-heptane is lower than that of benzanthracene, pyrene, and triphenylene against the fact that anthracene has only three cycles (and lower molecular weight), whereas benzanthracene, pyrene, and triphenylene have four cycles. Also, the solubility of naphthacene (four hexagons) in n-heptane is lower than that of benzo(ghi)perylene (six hexagons), coronene (seven hexagons), perylene (five hexagons), and dibenz(a,h)anthracene (five hexagons). The solubility of PAH in 1-octanol in relation with their molecular weight has a similar trend as the solubility in n-heptane. The solubility in 1-octanol decreases with increasing number of cycles (molecular weight), but there are also exceptions. Chrysene (four hexagons) has lower solubility than perylene (five hexagons) even if it has a lower molecular weight. This confirms the fact that solubility is a complex phenomenon which does not depend only on molecular weight of a molecule, but is very much influenced by specific interactions between solute and solvent. The model was validated with cross-validation (leave-oneout) analysis. In case of the 1-octanol the value of the cross validated correlation coefficient (R2cv ) 0.9346) and square correlation coefficient (R2 ) 0.9637) are in good agreement. In the case of n-heptane, a similar agreement is moderate but acceptable considering the dispersion of data. Further validation with leave-50%-out cross-validation proved the quality of the developed models. Tables 1 and 2 also provide correlation between experimental and calculated data expressed in the natural scale. Obviously, the statistical criteria (R2 ) 0.8524, s2 ) 0.0739 for n-heptane and R2 ) 0.9336, s2 ) 0.0081 for 1-octanol) in natural scale are not as good as the one obtained in the logarithmic scale. This is due to the fact that when transforming calculated data back to original scale the errors are exponentially multiplied and the correlation between experimental and calculated data in original scale worsens compared to that in the logarithmic scale. The QSPR models constructed for n-heptane and 1-octanol indicate that the solubility of PAH and C60 in nonpolar solvents like n-heptane and in average polar solvents like 1-octanol depends on the compound spatial structure (reflected by 2ASIC and 1IC topological descriptors), on electron distribution, reflected by electrostatic molecular descriptors (RNCG and RPCS) and on interaction energy between solute and solvent molecules (indirectly reflected by quantum chemical descriptor Emin ee (C-C)). Conclusions In conclusion, the solubility of PAH in nonpolar solvents (like n-heptane) and average polar solvents (like 1-octanol) is influenced by their dimension but also by the charges in
QSPR Solubility Study of PAH and Fullerene polycycles which can attract or reject the charges of the solvent. This is shown by the two QSPR models for solubility, where PAH and C60 are treated together. Significantly, the solubility of C60 is predicted correctly by the QSPR models for both n-heptane and 1-octanol, even when left out from the model treatment (cf. Figures 1 and 2). This encourages the further development of those models upon availability of new experimental data that could provide additional improvement of precision of solubility of carbon nanostructures. Acknowledgment. We thank EU 6th Framework Program project NANOQUANT (MRTN-CT-2003-506842) and Estonian Science Foundation (grant no. 5805) for the financial support. Supporting Information Available: Table with the set of 210 calculated descriptors. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Pagnout, C.; Rast, C.; Veber, A. M.; Poupin, P.; Ferard, J. F. Ecotoxicol. EnViron. Saf. 2006, 65, 151-158. (2) Karasek, P.; Planeta, J.; Roth, M. Ind. Eng. Chem. Res. 2006, 45, 4454-4460. (3) Karasek, P.; Planeta, J.; Roth, M. J. Chem. Eng. Data 2006, 51, 616-622. (4) Sverdrup, L. E.; Nielsen, T.; Krogh, P. H. EnViron. Sci. Technol. 2002, 36, 2429-2435. (5) Fetzer, J. C. Polycyclic Aromat. Compd. 2002, 22, 321-326. (6) Reilly, P. T. A.; Gieray, R. A.; Whitten, W. B.; Ramsey, J. M. J. Am. Chem. Soc. 2000, 122, 11596-11601. (7) Tasaki, K. J. Electrochem. Soc. 2006, 153, A941-A949. (8) Yu, J.; Sumathi, R.; Green, W. H. J. Am. Chem. Soc. 2004, 126, 12685-12700. (9) Dang, H.; Levitus, M.; Garcia-Garibay, M. A. J. Am. Chem. Soc. 2002, 124, 136-143. (10) Shanker, B.; Applequist, J. J. Phys.Chem. 1994, 98, 6486-6489. (11) Heymann, D. Lunar Planet. Sci. XXVII 1996, 542-543. (12) Sayes, C. M.; Fortner, J. D.; Guo, W.; Lyon, D.; Boyd, A. M.; Ausman, K. D.; Tao, Y. J.; Sitharaman, B.; Wilson, L. J.; Hughes, J. B.; West, J. L.; Colvin, V. L. Nano Lett. 2004, 4, 1881-1887. (13) Katritzky, A. R.; Maran, U.; Lobanov, V. S.; Karelson, M. J. Chem. Inf. Comput. Sci. 2000, 40, 1-18. (14) Katritzky, A. R.; Fara, D. C.; Petrukhin, R.; Tatham, D. B.; Maran, U.; Lomaka, A.; Karelson, M. Top. Curr. Med. Chem. 2002, 2, 13331356. (15) Katritzky, A. R.; Oliferenko, A. A.; Oliferenko, P. V.; Petrukhin, R.; Tatham, D. B.; Maran, U.; Lomaka, A.; Acree, W. E. J. Chem. Inf. Comput. Sci. 2003, 43, 1794-1805.
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