Ind. Eng. Chem. Res. 1999, 38, 4081-4091
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GENERAL RESEARCH Prediction of Octanol-Water Partition Coefficients Using a Group Contribution Solvation Model Shiang-Tai Lin and Stanley I. Sandler* Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
Using our recently derived group contribution solvation (GCS) model, we have developed a predictive model for the octanol-water partition coefficient (KOW), the GCSKOW model. In this model KOW is calculated from two molecular structure parameters, which take into account the size and shape effects, and one energy parameter that determines the attractive interactions between the solute and the solvent. On the basis of quantum mechanical studies, we found that for organic solutes with a single strong functional group, all these parameters can be obtained in a group contribution manner. Consequently, we present a database here for various functional group contributions in this new, easy-to-use model. The root-mean-square deviation of the predicted log KOW from the GCSKOW model for 226 solutes is found to be 0.14 (which corresponds to 38% in KOW), which is considerably less than those from the methods of Hansch and Leo (0.18 in log KOW or 51%), KOW-UNIFAC (0.21 or 62%), and LSER (0.23 or 71%). Introduction At ambient temperature and pressure, water and 1-octanol are partially miscible, forming an octanol-rich phase (72.5 mol % 1-octanol), designated as OR here, and a water-rich phase (99.99 mol % water), indicated by the superscript WR. The octanol-water partition coefficient of a solute i, KOW,i, is defined as the equilibrium ratio of concentrations of this solute between the two liquid phases when a very small amount is added to an equilibrated water and 1-octanol mixture, that is,
KOW,i )
COR i CWR i
(1)
This coefficient is a measure of the hydrophobicity of the solute. A hydrophobic chemical preferentially partitions into the octanol-rich phase, resulting in a large value of KOW, while a hydrophilic chemical will have a small KOW value. Therefore, this parameter is used to describe the hydrophobic interaction in the well-known quantitative structure-activity relationships (QSARs),1,2 which has been extensively applied to predict the biological activity of bioactive compounds and the toxicity of chemicals3,4 and to design new drugs.5,6 Also, 1-octanol is a good surrogate for the lipids in aquatic and animal biota, and the organic matter in soils and sediments because of the chemical similarity between 1-octanol and most lipids; that is, both have a long hydrophobic hydrocarbon chain and a hydrophilic end group. On the basis of this, Mackay7 and co-workers8 developed a fugacity model to predict the distribution of long-lived organic chemicals in the environment using * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: 302-831-2945. Fax: 302-831-4466.
information on KOW. Moreover, values of KOW have been found to correlate bioaccumulation phenomena in the food chain. For example, Thomann9 used a simple steady-state model and found that biomagnification (or accumulation up the food chain) occurs when KOW is greater than about 105. Experimental methods have been developed to measure octanol-water partition coefficients (see, e.g., Sangster10 for a review of experimental methods), and data for more than 18000 organic chemicals have been gathered.11 However, because of experimental difficulties, especially of measuring the extremely low concentrations of a hydrophobic solute in the water-rich phase for chemicals with large KOW values, there can be considerable uncertainty in the data, indeed, sometimes uncertainties of orders of magnitude. Also, since there are many chemicals for which KOW has not been measured, there is substantial interest in methods for its prediction. This is especially true for very hydrophobic species that are not very biodegradable and are of concern for both toxicity and bioaccumulation. In addition, thousands of new compounds are synthesized each month in combinatorial chemistry, especially for drug discovery and design. Therefore, an accurate predictive model for the octanol-water partition coefficient based on molecular structure would be very useful. Current predictive models for the octanol-water partition coefficient are in two categories: the linear solvation energy relationships (LSERs)12 method and group contribution methods. In the LSER, the logarithm of KOW is estimated from the sum of contributions of repulsive (cavity formation), nonspecific attractive (dipolarity/polarizability), and specific attractive (hydrogen bond) interactions between the solute and the octanolwater liquid pair.13,14 The repulsive contribution is determined from the molar volume of the solute, and
10.1021/ie990391u CCC: $18.00 © 1999 American Chemical Society Published on Web 09/08/1999
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Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999
the attractive contributions are calculated using three solvatochromic parameters, which can be determined from the ultraviolet spectrum of the π f π* electronic transition.15 Several researchers have studied the replacement of the solvatochromic parameters with other descriptors, the values of which were obtained from quantum mechanical calculations.16-18 Group contribution models (see Sangster10 for a brief introduction and comparison of various group contribution models) assume that each functional group contributes a fixed amount to the logarithm of KOW independent of other groups in the solute. A refinement of this assumption is to add correction factors when two strong functional groups are in close proximity. A good example of this type is the method of Hansch and Leo,4,19 where 1000 fragments and up to five bond types for each connection have been defined. Despite the success of these models, they are basically empirical and have little theoretical foundation. Recently, Wienke and Gmehling20 applied the UNIFAC model21 with a new set of group interaction parameters to predict the octanol-water partition coefficients and obtained a comparable accuracy to those of the LSER and the method of Hansch and Leo. In this work, we introduce the use of the group contribution solvation (GCS) model, recently developed by Lin and Sandler,22 to predict KOW. In our earlier work on the GCS model, the interaction energy between the solute and the solvent was calculated from computational quantum mechanics. An analysis of the results of such calculations showed that the interaction energies obtained can be decomposed into contributions from the functional groups. This observation helped us reduce the original approach to an easy-to-use group contribution method, obviating the need for quantum chemistry calculations, and to develop a new group contribution solvation model for KOW (GCSKOW). The GCSKOW model possesses features of both the LSER and group contribution models: the octanol-water partition coefficients are determined from solvation free energies calculated in a group contribution manner that does not require quantum chemistry calculations. As will be demonstrated here, GCSKOW is a simple, accurate, and theoretically based model to predict the octanol-water partition coefficient. Theory Octanol-Water Partition Coefficient. The typical amount of solute added to the octanol-water mixture is small (usually less than 10-3 M), so that KOW can be written in terms of the ratio of the infinite dilution activity coefficients of solute i in the water-rich and the octanol-rich phases
KOW,i )
COR i CWR i
)
OR COR tot ‚xi WR CWR tot ‚xi
)
WR,∞ COR tot γi OR,∞ CWR tot γi
) 0.148
γWR,∞ i γOR,∞ i (2)
where Ctot is the total molar concentration of each phase (8.229 mol/L for the octanol-rich phase, 55.679 mol/L for the water-rich phase). Also, in eq 2 we have used WR,∞ ) the liquid-liquid equilibrium relationship xWR i ‚γi OR OR,∞ WR,∞ W,∞ and the approximation γi ) γi , since the xi ‚γi water-rich phase is essentially pure water. Experimentally, it is easier to measure γ∞ of a chemical in pure 1-octanol rather than in the water-
Table 1. Experimental Data Used in Determining the Constants a and b in Eq 3 name
formula
1,2-dichloroethane dichloromethane 1,1-dichloroethane 1,1,2-trichloroethane chloroform 1,1,1-trichloroethane tetrachloromethane trichloroethene pentane hexane heptane octane cyclohexane ethanol benzene toluene nitromethane acetonitrile propionitrile acetone 2-butanone methyl acetate
CH2ClCH2Cl CH2Cl2 CH3CHCl2 CH2ClCHCl2 CHCl3 CH3CCl3 CCl4 CHClCCl2 C5H12 C6H14 C7H16 C8H18 C6H12 C2H5OH C6H6 CH3C6H5 CH3NO2 CH3CN C2H5CN CH3COCH3 C2H5COCH3 CH3COOC2H5
O,∞ a log10 γW,∞ log10 KOW 1 /γ1
2.39 2.22 2.73 2.89 2.92 3.47 3.78 3.51 4.58 5.15 5.79 6.45 4.56 0.54 3.06 3.67 0.57 0.17 0.76 0.44 1.09 1.45
1.48b 1.25c 1.79b 1.89d 1.90c 2.49b 2.64c 2.42d 3.39b 4.11c 4.66c 5.18c 3.44b -0.31b 2.15b 2.73b -0.34c -0.34d 0.16b -0.24b 0.26b 0.73b
a γW,∞ values were taken from ref 38. γO,∞ values were taken 1 1 from ref 39 and 40. b Suzuki and Kudo.36 c Isnard and Lambert.37 d Sangster.10
saturated 1-octanol. Tse and Sandler23 found the following empirical correlation between KOW and the ratio of infinite dilution activity coefficients in pure water and pure 1-octanol
log10 KOW,i ) b + a log10
γW,∞ i γO,∞ i
(3)
where a and b are constants and found to be 0.91 and -0.65 from fitting to 12 halogenated compounds. Wehave re-examined this correlation with other types of compounds and found a similar set of values, a ) 0.91 and b ) -0.68, using the 22 species listed in Table 1 (the correlation coefficient R2 is 0.997). Both eqs 2 and 3 will be examined for calculating octanol-water partition coefficients here. Following the analysis of Ben-Naim,24 the solvation process can be considered to be the transfer of one molecule from a fixed position in an ideal gas phase to a fixed position in the fluid phase at constant temperature and pressure. He derived the following expression for the infinite dilution activity coefficient from solvation energies
ln γj,∞ i )
Fj 1 /sol /sol - ∆Gi/i ) + ln (∆Gi/j RT Fi
(4)
/sol is the solvation free energy of transferwhere ∆Gi/j ring one molecule of species i from the ideal gas phase to the solvent j (j could be a pure solvent, such as water, or a mixed solvent such as water-saturated 1-octanol). The notation used is that the superscript * denotes that the molecules are in a fixed orientation, and Fi is the number density of i (for pure water, FW ) 3.35 × 1025 L-1; for water-saturated 1-octanol, FOR ) 4.95 × 1024 L-1). To proceed with the calculation, the solvation free energy is decomposed into a cavity formation contribution, that is, the free energy required to form a cavity for the solute in the solvent, and a charging free energy contribution, that is, the work needed to turn on the
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 4083
interactions between the solute and the solvent after the solute is placed in the cavity /sol /cav /chg ∆Gi/j ) ∆Gi/j + ∆Gi/j
(5)
Combining eqs 2, 4, and 5, the octanol-water partition coefficient is found to be proportional to the solvation free energy difference between the water-rich and the octanol-rich phases or, equivalently, the free energy oftransfer between the two phases
log10 KOW,i ) )
1 /sol /sol - ∆Gi/OR ) (∆Gi/W 2.303RT 1 /cav /cav [(∆Gi/W - ∆Gi/OR )+ 2.303RT /chg /chg )] (6) (∆Gi/W - ∆Gi/OR
Equation 6 is in agreement with the assumption of the LSER that log KOW is linearly proportional to the repulsive and attractive interactions between the chemical species and the water-octanol solutions. Lin and Sandler22 started from eq 4 and developed a group contribution solvation (GCS) model to determine the infinite dilution activity coefficient in a binary mixture from solvation free energy calculations. In their method, modern computational chemistry was used to calculate the charging free energy, and the combinatorial part of the UNIQUAC model25,26 was used for the cavity formation contribution, resulting in j,∞ ln γj,∞ i ) ln γi (comb) + qi(τi - τj) + 1 /chg /chg (∆Gi/j - ∆Gi/i ) (7a) RT
where γj,∞ i is the infinite dilution activity coefficient of solute i in solvent j. Also
ln
γj,∞ i (comb)
ri z qirj ) ln + qi ln + rj 2 qjri ri z ri qj - q i + 1 (7b) 2 rj rj
(
) ( )
is the combinatorial part in the UNIQUAC model; ri and qi are the normalized van der Waals volume and surface area of species i; z is the coordination number, usually taken to be 10. The second term on the right-hand side of eq 7a is a result of the interactions between solvent molecules. The energy parameter τi that appears is determined from the results of quantum mechanical solvation calculations using the following relation /chg ∆Gi/i ) qi(τi - 1 + ln τi) RT
log10 KOW,i ) b +
(8)
The contribution of this term to eq 7a is usually insignificant due to the small values of τi (approximately 10-3 for hexane and 10-5 for water). The original GCS model only applies to the infinite dilution activity coefficient of a solute in a single solvent; therefore, eq 3 must be used. With this model, the ratio of activity coefficients in both pure water and pure 1-octanol can be determined, and then the octanolwater partition coefficient can be predicted from
[
γW,∞ (comb) a i ln O,∞ + 2.303 γi (comb)
qi(τO - τW) +
]
1 /chg /chg (∆Gi/W - ∆Gi/O ) (9) RT
Quantum Chemistry Basis of the Group Contribution Solvation Model. The parameters needed for predicting the octanol-water partition coefficient using eq 9 are of two types: molecular structure parameters (r and q) and energy parameters (∆G*chg and τ). All these parameters can be determined directly from quantum chemical calculations. [Readers not familiar with quantum mechanical nomenclature can refer to textbooks such as that by Szabo and Ostlund.27] The quantum chemistry package GAMESS (General Atomic and Molecular Electronic Structure System)28 was used for molecular calculations. An outline of the calculation procedure of the model parameters follows. 1. Molecular Structure Parameters. The calculation of the structure parameters was done by, first, performing a quantum mechanical geometry optimization for the solute in a vacuum using the Hartree-Fock (HF) method with the DZPsp(df) basis set [double zeta basis set with polarization functions (DZP)29,30 plus one set of diffuse and polarization functions with exponents of one-third of the most diffuse DZP set]. The volume and surface area of the solute were then calculated using the van der Waals radius for each atom. Finally, the volume parameter r and the surface area parameter q were determined from normalizing the van der Waals volume and surface area of the solute by the corresponding values of a standard segment (15.17 cm3/mol and 2.5 × 109 cm2/mol), that is,
ri ) qi )
van der Waals volume of speices i 15.17 cm3/mol
van der Waals surface area of species i 2.5 × 109 cm2/mol
However, the parameter values r ) 0.92 and q ) 1.40 were used for water, as in the UNIQUAC model. 2. Energy Parameters. The polarizable continuum model (PCM)31,32 was used to compute the charging free energy. In the PCM, the solvent is considered to be a dielectric medium with no internal structure. The solute molecule is embedded in this homogeneous dielectric solvent and its shape is described by fused spheres centered on the solute nuclei, the radii of which are the van der Waals radii multiplied by a group scale factor, R, listed in Table 2. (The procedure for determining the value of R for each functional group can be found in ref 22). The need for group scale factors is based on the fact that the dielectric behavior of the first solvation layer around a molecule is not the same as that of the bulk fluid and will also be different around different groups.22 The interaction between the solute and the solvent is then determined by solving the Schro¨dinger equation for the solute in an electric field imposed by the dielectric solvent. The PCM takes into account the electrostatic and induction contributions to the charging free energy, and the newly implemented method of Amovilli and Mennucci33 is used for the dispersion and repulsion contributions. The charging free energy was calculated at the same DZPsp(df) level with the optimized solute geometry in step 1. The values of the
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Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999
Table 2. Group Scale Factor r for Functional Groups in Water and 1-Octanola functional group
R value in water
R value in 1-octanol
CH3, CH2, CH, C cyclic CH2 ACHb OH CN NO2 CdO OCdO Cl(CCl4) Cl(CnH2n+1CCl3) Cl(CnH2n+1CHCl2) Cl(CnH2n+1CH2Cl)
1.42 1.35 1.33 0.88 1.10 1.12 0.88 0.85 1.26 1.23 1.20 1.17
1.14 1.14 1.22 1.15 1.38 1.33 1.32 1.31 1.16 1.20 1.24 1.28
a Examples. C H CN in water: R ) 1.42 for each atom in the 2 5 groups CH3 and CH2, R ) 1.10 for each atom in the CN group. CH3CHCl2 in water: R ) 1.42 for all C and H atoms, R ) 1.20 for the two Cl atoms. b ACH represents the CH group in an aromatic ring.
physical properties of the solvent (dielectric constant, ionization potential, refractive index, and density) were taken from the CRC Handbook of Chemistry and Physics.34 The parameters τW and τO are determined from eq 8 using the quantum mechanical calculation for the charging free energy. They were found to be very small and had a negligible effect on the prediction of the octanol-water partition coefficients. Nevertheless, τW ) 8.14 × 10-6 and τO ) 3.37 × 10-4 were used in our calculations. The predictions of the octanol-water partition coefficients for 28 linear and 12 nonlinear solutes from eq 9 are presented in Table 3 and Figure 1. The values of a and b were taken to be 0.91 and -0.68. The predictions are in good agreement with experimental data with the overall root-mean-square (RMS) deviation on log KOW being only 0.15 (or an average deviation of 41% in KOW).
tions from other groups in linear species, such as CH3, OH, CN, Cl, NO2, and so forth, could then be determined. With this information, we then determined the contributions of CH and C which appear in nonlinear molecules. These functional groups also gave approximately the same contribution to the octanol-water partition coefficient independent of the molecular species in which they appeared. Using this procedure, we are able to establish a group contribution method for both the molecular structure and the energy parameters based on results of the previous quantum mechanical calculations. However, we found that slightly better results were obtained with much less computational effort if the energy parameters were directly fitted to measured octanol-water partition coefficient data. In this way, assuming that the group contribution method for the charging free energy in pure solvents is also valid for solvent mixtures, we could directly use eq 2 to predict KOW and eliminate the two empirical constants a and b in the approximate correlation of eq 3. Furthermore, many more functional groups could be rapidly considered without the need for timeconsuming computational chemistry calculations. However, it was first necessary to extend the original GCS model to multicomponent solvent mixtures (see Appendix I). The result is where the superscript and
[
xjqjτj
N
q1 τ1 -
∑ N j)2 ∑ xkqkτkj k)2
+
(
/chg ∆Gl/mix
-
RT
)
∆G/chg l/l RT
(10)
subscript mix indicates that the solvent is a mixture and τkj is the binary energy parameter in the UNIQUAC model. Substituting eq 10 into eq 2, we obtain
Development of the GCSKOW Model That Does Not Require Quantum Chemistry Calculations From a detailed analysis of the structure and energy parameters obtained from quantum mechanical calculations, we found that, for the molecules considered, each functional group contributes a fixed amount to the total value of each molecular parameter. By subtracting the contribution of ethane (2 methyl groups) from other alkane species and dividing this value by the number of methylene groups the alkane contains, we found that the contribution from a methylene group was approximately the same in all alkanes. For example, the /chg /chg - ∆Gi/O from a contributions to r, q, and ∆Gi/W methylene group in butane were 0.668, 0.523, and 0.773, respectively, and in octane these values were 0.665, 0.523, 0.743. Moreover, when we subtracted the contribution of methanol (1 methyl group and 1 hydroxy group) from other alcohols and divided the remainder by the number of methylene groups that the alcohol contains, we obtained similar values for the methylene parameters to those found with the alkanes (e.g. the /chg /chg - ∆Gi/O for a methylcontributions to r, q, and ∆Gi/W ene group in butanol were 0.662, 0.522, 0.732). This observation suggests that the methylene group makes the same contribution to the three parameters, regardless of the molecule in which it is contained. Knowing the contributions of a methylene group, the contribu-
]
ln γmix,∞ ) ln γmix,∞ (comb) + 1 1
log10 KOW,i ) log10 0.1478 + log10
) -0.83 +
[
qi
{
γW,∞ i γOR,∞ i
γW,∞ (comb) 1 i ln OR,∞ + 2.303 γi (comb)
xOR W qWτW
OR xOR W qW + xO qOτOW
+
xOR O qOτO OR xOR O qWτWO + xO qO
]
- τW +
}
1 /chg /chg (∆Gi/W - ∆Gi/OR ) RT
(11)
where xOR is the mole fraction of species j in the j OR octanol-rich phase (xOR W ) 0.275, xO ) 0.725); τOW and τWO can be determined from the two infinite dilution activity coefficients of the water-octanol binary mixture and are found to be 1.13 and 0.67, respectively. Both structure and energy parameters can now be easily determined from adding the contribution of each group contained in the molecule Ni
ri )
∑ Rk
k)1
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 4085 Table 3. Computational Chemistry Results for the Structure and Energy Parameters and the Prediction of log KOW from Eq 9 structure parameter name
formula
r
methane ethane propane butane pentane hexane heptane methanol ethanol propanol butanol benzene nitromethane nitroethane nitropropane acetonitrile propionitrile acetone 2-butanone methyl acetate ethyl acetate chloropropane chlorobutane dichloromethane 1,1-dichloroethane chloroform 1,1,1-trichloroethane tretrachloromethane
CH4 C2H6 C3H8 C4H10 C5H12 C6H14 C7H16 CH3OH C2H5OH C3H7OH C4H9OH C6H6 CH3NO2 C2H5NO2 C3H7NO2 CH3CN C2H5CN CH3COCH3 C2H5COCH3 CH3COOCH3 CH3COOC2H5 C3H7Cl C4H9Cl CH2Cl2 CH3CHCl2 CHCl3 CH3CCl3 CCl4
1.117 1.777 2.446 3.113 3.776 4.419 5.101 1.437 2.088 2.752 3.424 3.289 2.002 2.648 3.306 1.840 2.507 2.528 3.181 2.845 3.504 3.079 3.741 2.387 3.044 3.015 3.667 3.634
cyclopentane cyclohexane isobutane neopentane 2-propanol isobutanol 2-butanol tert-butyl alcohol isopentane neopentane 3-pentanone 2-chloropropane
C5H10 C6H12 C4H10 C5H12 C3H8O C4H10O C4H10O C4H10O C5H12OH C5H12OH C5H10O C3H7Cl
3.362 3.996 3.103 3.765 2.760 3.421 3.423 3.421 4.091 4.069 3.848 3.085
energy parameter ∆G/chg 1/W
∆G/chg 1/O
∆∆G*chg a
log KOWcalc
log KOWexpt
Linear Compounds 1.151 -3.025 1.681 -4.544 2.204 -5.820 2.728 -6.984 3.250 -8.218 3.765 -9.473 4.295 -10.593 1.416 -11.918 1.936 -13.366 2.460 -14.543 2.981 -16.113 2.617 -10.460 1.854 -14.204 2.355 -15.251 2.874 -16.369 1.692 -12.031 2.215 -13.084 2.260 -14.171 2.765 -15.119 2.499 -14.936 3.023 -16.195 2.656 -9.959 3.182 -11.121 2.068 -9.082 2.570 -10.365 2.494 -10.096 2.972 -10.862 2.892 -10.096
-4.909 -7.547 -9.591 -11.534 -13.533 -15.458 -17.310 -10.991 -13.354 -15.305 -17.382 -13.260 -14.225 -15.891 -17.568 -11.382 -13.334 -13.986 -15.671 -14.998 -17.248 -13.104 -15.026 -11.178 -12.988 -12.910 -14.047 -13.965
1.884 3.004 3.770 4.550 5.315 5.985 6.717 -0.927 -0.013 0.762 1.270 2.800 0.022 0.640 1.199 -0.650 0.251 -0.185 0.552 0.062 1.053 3.145 3.904 2.097 2.623 2.814 3.185 3.869
1.07 1.84 2.39 2.96 3.50 3.98 4.52 -0.81 -0.17 0.39 0.78 2.10 -0.13 0.33 0.74 -0.55 0.09 -0.23 0.31 -0.03 0.66 2.07 2.61 1.38 1.79 1.98 2.31 2.82
1.09d 1.81b 2.36b 2.89b 3.39b 4.11c 4.66c -0.77b -0.31b 0.25b 0.88b 2.15b -0.34c 0.18c 0.87c -0.34d 0.16b -0.24b 0.26b 0.18b 0.73b 2.04b 2.64b 1.25c 1.79b 1.90c 2.49b 2.64c
Nonlinear Compounds 2.771 -8.593 3.208 -9.681 2.708 -6.840 3.190 -7.874 2.450 -14.547 2.952 -14.342 2.961 -14.788 2.942 -15.044 3.457 -16.785 3.420 -14.772 3.274 -15.783 2.643 -9.880
-13.136 -14.556 -11.102 -12.637 -14.844 -16.255 -16.268 -15.966 -18.760 -16.940 -17.427 -12.922
4.543 4.875 4.262 4.764 0.297 1.914 1.480 0.922 1.975 2.169 1.644 3.041
3.15 3.48 2.77 3.20 0.10 1.24 0.94 0.59 1.34 1.50 1.10 2.02
3.00b 3.44b 2.76b 3.11b 0.05b 0.76b 0.61b 0.35b 1.42b 1.36c 0.99c 1.90b
q
RMS a
∆∆G*chg )
0.15 ∆G/chg 1/W
-
∆G/chg 1/O
(kcal/mol). b Suzuki and Kudo.36
c
Isnard and Lambert.37
d
Sangster.10 Ni
/chg ∆Gi/W
-
/chg ∆Gi/OR
)
(W - OR) ∑ ∆∆G/chg k
k)1
where Ni is the number of functional groups contained (W - OR) are the in species i; Rk, Qk, and ∆∆G/chg k volume, surface area, and charging free energy contributions of functional group k, as listed in Table 4. The values of Rk and Qk were established using the proce(W - OR) values dure described above, and ∆∆G/chg k were determined from minimizing the RMS deviation between the measured and predicted octanol-water partition coefficients using eq 11. Results and Discussion Figure 1. Comparison of predictions between molecular calculation and experimental data. Ni
qi )
∑ Qk
k)1
(12)
Predictions from the GCSKOW model for 133 linear and 93 nonlinear monofunctional compounds are shown in Figure 2. (Some example calculations are provided in Appendix II. A computer program is also available upon request.) Here, species containing only one strong functional group in addition to alkyl groups (CH3, CH2, CH, and C) are considered as monofunctional com-
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Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 Table 5. Comparison of the Prediction of the Octanol-Water Partition Coefficient between Different Models GCSKOW Hansch and Leo KOW-UNIFAC
Figure 2. Octanol-water partition coefficients for 133 linear and 93 nonlinear monofunctional compounds from the GCSKOW model. Table 4. Functional Group Volume and Surface Area Parameters, R and Q, and the Functional Group Contribution of the Charging Free Energy Difference ∆∆G*chg(W - OR) (kcal/mol) main group
subgroup
CH2
CH3-CH2-
R
Q
∆∆G*chg(W - OR)
0.887 0.665 0.497
0.840 0.523 0.235
1.459 0.649 -0.393
0.213
0.000
-1.261
cyclic-CH2
-CH2-
0.665 0.497
0.523 0.235
0.724 -0.182
OH COOH CHO
-OH -COOH CH2O -CHO -COHCOO-COO-O-NO2 -CN -NH2
0.532 1.307 1.230 0.984 0.716 1.362 1.062 0.401 1.086 0.954 0.742 0.553
0.572 1.176 1.230 0.892 0.527 1.046 0.821 0.327 0.986 0.852 0.748 0.401
-1.907 -1.273 0.967 -1.058 -2.767 -1.526 -2.311 -2.649 -1.264 -1.607 -1.869 -3.197
0.341
0.000
-4.228
CdO OCdO CH2OCH2 NO2 CN NH2
CONH2 C6H6
-CONH2 -ACH-
1.467 0.537 0.316
1.284 0.431 0.114
-2.641 0.499 -0.469
CdC
-CHCH2 -CHCH-
1.359 1.135 1.135
1.210 0.895 0.895
1.372 0.607 0.649
C:::C Cl
-CCH -CC-CCl3
1.129 0.908 2.780 2.157
1.008 0.690 2.131 1.730
0.181 -0.615 1.782 1.095
F Br I
-Cl -F -Br -I
0.861 0.376 1.114 1.491
0.771 0.458 0.935 1.129
0.106 -0.160 0.360 0.848
pounds. Linear compounds are species in the homologous series CnH2n+1X, where X represents H for alkanes, OH for alcohols, COOH for acids, CHO for aldehydes, CH2COCH3 for ketones, HCOO and CH3COO for esters, NO2 for nitro compounds, CN for nitriles, CONH2 for amides, C6H5 for phenyl compounds, CHCH2 for alkenes, CCH for alkynes, and Cl, CHCl2, CCl3, F, Br, and
LSER
AADa RMSb data points
0.10 0.13 133
Linear Compounds 0.11 0.17 133
AAD RMS data points
0.12 0.15 93
Nonlinear Compounds 0.13 0.19 93
0.17 0.23 78
0.16 0.23 41
AAD RMS data points
0.10 0.14 226
Overall 0.12 0.18 226
0.15 0.21 175
0.16 0.23 112
0.13 0.18 97
0.16 0.23 71
a AAD ) absolute average deviation. b RMS ) root-mean-square deviation.
I for halogenated alkanes, and esters [(CnH2n+1)2O] and amines [CnH2n+1NH2, (CnH2n+1)2NH, (CnH2n+1)3N]. Nonlinear compounds are cyclic alkanes [CnH2n] and species containing CH, C, cyclic CH, or more than two ACH groups in a aromatic ring, that is, branched, secondary, or tertiary species, such as tert-butyl alcohol, diisopropyl ether, cyclohexanone, isobutyl acetate, hexamethylbenzene, and so forth. The predictions from the GCSKOW model for both linear and nonlinear compounds agree very well with experimental data, as expected on the basis of our previous quantum mechanical solvation calculations. A comparison between different models is presented in Table 5. The method of Hansch and Leo, as put into computer form by the Biobyte Corp.,35 is used as an example of the group contribution method. The model of Kamlet et al.14 is an example of the LSER method. The predictions from the KOW-UNIFAC model20 are also provided as an example of another group contribution method. All the models, including the GCSKOW model, are slightly less accurate for KOW predictions for nonlinear compounds than for linear compounds. However, for both linear and nonlinear molecules the performance of the GCSKOW model is somewhat better than those of all of the other models. It should be noted that fewer compounds could be considered with the KOW-UNIFAC and LSER models because some of the required parameters are not available. The root-meansquare (RMS) deviation of log KOW from the GCSKOW model, 0.14, is considerably less than those from the method of Hansch and Leo, 0.18, KOW-UNIFAC, 0.21, and LSER, 0.23, corresponding to errors of 38%, 51%, 62%, and 71% in KOW, respectively. It is noteworthy that the data for the 133 linear and 93 nonlinear compounds were all the experimental data for monofunctional compounds that were available in the literature10,14,35-37 and were not a “selected” set chosen to reduce the error of any one model. The only literature data that were not included were for the compounds dodecane, dodecanoic acid, and tert-butyl bromide, where all four methods studied resulted in a large overestimate of KOW, about a factor of 10 or one log unit, as shown in Table 6. The measured data35 for these systems may be less reliable, since larger uncertainties are associated with large KOW values. The success of the GCSKOW model is impressive, especially when one realizes that fewer parameters are needed. For example, GCSKOW uses only three parameters for tert-butylamine (i.e. the three ∆∆G*chg(W - OR) values for CH3, C, and NH2) while the method of Hansch and
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 4087 Table 6. Compounds with Deviations in log KOW Greater than 1 Logarithm Unit Hansch KOWGCSKOW and Leo UNIFAC LSER experiment dodecane dodecanoic acid tert-butyl bromide a
7.11 5.19 2.37
7.04 5.10 2.53
7.40 5.87 2.77
6.85 5.22 N/Aa
6.1 4.2 1.15
Parameters for calculation were not available.
Leo requires six parameters (i.e. primary amine, aliphatic isolating carbons, hydrogens on isolating carbons, branch chain, nonhalogen polar group branch, and bond chain) and both models predict the log KOW to be 0.57, which is 0.17 unit higher than the measured value. An important feature of the approach we propose here is its theoretical basis. The method of Hansch of Leo uses empirically defined groups and correction factors that must be obtained from fitting to experimental data. LSER captures the essential idea that the octanolwater partition coefficient is the free energy of transfer of the solute from the water-rich phase to the octanolrich phase, as shown in eq 6. However, the linear sum of the contributions from the three solvatochromic parameters is empirical in nature. The UNIFAC model reduces the calculation of KOW to that of interaction energies between functional groups. These interaction energies are very approximate because they have to account for both orientation and proximity effects. Unlike those methods, the GCSKOW model uses a parameter whose meaning is clear, the charging energy of a solute in the solution, which can in principle be obtained from first principle quantum chemistry calculations, as we did when first starting this work. Although current solvation calculations are limited to pure solvents, this should change as the field develops. Using the model parameters of Table 4 obtained from fitting monofunctional solutes, we may elucidate some limitations of the group contribution methods. Table 7 gives the deviations of the GSCKOW predictions of log KOW values for solutes containing two strong end groups separated by n methylene groups, that is, X(CH2)nY. Two things can be immediately observed: the GCSKOW model always underpredicts the octanol-water partition coefficient when two strong end groups are in close proximity, and predictions become more accurate as the number of methylene groups separating the end groups increases. This is, in fact, an example of a proximity effect which is not properly accounted for in any simple group contribution method. The failure here is because in the GCS model a scale factor is used for each type of functional group in the charging free energy calculation to account for the nonhomogeneity of the solvent in the proximity of the functional group. Thus, this scale factor accounts for the differing distribution of solvent molecules around each functional group. That the distribution of solvent molecules should be the same around the same type of functional group in every molecule results in the additivity of the charging free energy and leads to the group contribution method of the GCSKOW model. However, the proximity of another strong group will alter the electron cloud around both groups, changing their interactions with the solvents. Therefore, the failure of group contribution methods in these cases can be expected. As two strong functional groups within a molecule become further separated by methylene groups, the interference of one functional group on the solvent distribution around the other diminishes and group
contribution methods become more accurate. This explains the decrease of the error in Table 7 as we go across the columns. Notice also that the prediction for a molecule containing two strong groups immediately connected to each other is especially poor, but the deviation from experiment drops significantly as the first methylene group is placed between them. The negative deviations of all these solutes are probably due to the cancellation of the dipole moments from the end groups, and thus, these solutes become less water soluble. In the analysis here the parameters for strong functional groups were determined using solutes containing only that functional group and alkyl groups. As a consequence, the charging free energies ∆∆G*chg(W - OR) reported here are strictly valid only for nonalkyl groups when they are connected to alkyl groups. For the same reason, when using the KOW-UNIFAC model, one must distinguish between, for example, aromatic hydroxyl and aliphatic hydroxyl groups. Such proximity effects can be corrected for by using quantum chemistry calculations at different levels. The predictions for CN(CH2)nCN, Cl(CH2)nCl, and CN(CH2)nCl from eq 9 are shown in Table 8 together with a comparison of predictions from the GCSKOW model. The use of quantum mechanical solvation calculations reduces the errors down to its RMS (0.15) when n > 2. The failure for solutes with n < 2 results from the deficiency of treating the solvent as a continuum. In these cases the proximity effects are so large that the group scale factors given in Table 2 can no longer be used, and it is necessary to explicitly consider the solvent molecules for these solutes. Conclusion As a result of its wide applications in biological, pharmaceutical, and environmental studies, the octanol-water partition coefficient has been the focus of much research and more than 10 methods have been proposed to correlate or predict its value. Many of these are empirical, multiparameter models providing limited insight and resulting in predictions for new compounds that may be unreliable. The theoretically based GCSKOW model presented here is an easy-to-use and yet accurate group contribution method for the octanolwater partition coefficient that contains only three parameters: molecular volume, surface area, and charging free energy, that is, the work required to turn on the attractive interaction between the solute and the solvent. Each of these parameters possesses a clear physical meaning and can be determined from quantum chemical methods or, as we show here, from a simple group contribution method. The basis for the group contribution method is the insights we obtained from detailed quantum mechanical calculations. Further, since the model parameters have well-defined physical meanings, such detailed calculations can be used with the formalism presented here when the group contribution method fails, as when proximity effects are important. Acknowledgment The authors would like to thank the National Science Foundation (Grant CTS-9521406) and the Department of Energy (Grant DE-FG02-85ER13436) for financial support of this research. We also thank the BioByte Corp. and Professor J. Gmehling of Universitaet Old-
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Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999
Table 7. Deviations of log KOW for X(CH2)nY Type Compounds from the GCSKOW Model deviationa for X
n)0
Y
-OH -COOH CH3COCH3COOCH3O-CN -NH2 C6H5CH2CHClBrI-
-OH -COOH CH3COCH3COOCH3O-CN -NH2 C6H5CH2CHClBrI-
C6H5C6H5C6H5C6H5C6H5C6H5C6H5C6H5C6H5C6H5C6H5C6H5C6H5C6H5C6H5-OH -OH -OH -CN -CN -COOH CH2CH-
-OH -COOH -CHO CH3COCH3COOCH3O-NO2 -CN -NH2 -CONH2 CH2CHClFBrI-NH2 ClFCH2CHClClBr-
a
Deviation ) log
KOWcalc
- log
n)1
-0.80 -1.91 -0.79 -1.69 -1.54
-0.70 -1.20 -2.64 -0.46 -0.22
-0.06 -0.17 -0.78 -0.91 -0.30
-1.30 -1.16 -0.60 -0.82 -0.40 -1.35 -1.14 -1.07 -0.70 -0.90 -0.29 -1.14 -0.84 -0.99 -0.74
-0.40 -0.17 -0.38 -0.15 -0.34 -0.63 -0.50 -0.54 -0.36 -0.18 -0.04 -0.39
-0.27 -1.24 -0.79 -0.16
-0.47 KOWexpt.
X
Y
-CN -CN -Cl
-Cl
-CN -Cl
n log KOWcalc 1 2 3 1 2 3 1 2 3
-1.90 -1.13 -0.87 0.82 1.31 1.89 -0.40 0.24 0.58
n)4
-0.58 -0.26
-0.26 -0.10
-0.40
-0.28
-0.10
-0.26 -0.12
-0.13
0.03
0.09
-0.06 0.13
-0.60 -0.15 -0.88 -0.30 -0.17 -0.15 -0.11
-0.13 -0.04 -0.08
-0.08
-0.03
-0.44 -0.45
n)5
n)6
0.02
-0.47 -0.34 0.04 -0.12 -0.12
-0.80 -0.51 -0.13 -0.65
n)3
X*Y -0.13 -0.07
-0.14
-0.21 0.07 -0.13 0.20 -0.46 -0.54 -0.08
-0.36
-0.29
Blanks in this table are a result of the lack of experimental data.
Table 8. Predictions of Multifunctional Solutes X(CH2)nY from Eq 9 and GCSKOW eq 9
n)2 X)Y -0.79 -0.49 -0.71 -0.66 -0.76 -0.52 -0.04 -0.18 -0.04 -0.47 -0.46 -0.18
GCSKOW dev
log KOWcalc
dev
log KOWexpt
-1.40 -0.14 -0.15 -0.43 -0.17 -0.11 -0.85 0.06 0.02
-2.04 -1.51 -0.98 0.47 1.00 1.53 -0.79 -0.26 0.27
-1.54 -0.52 -0.26 -0.78 -0.47 -0.47 -1.24 -0.44 -0.29
-0.50 -0.99 -0.72 1.25 1.48 2.00 0.45 0.18 0.56
enburg for providing us with their computer programs for the log KOW calculations with their models. Nomenclature a ) correlation constant in eq 3 b ) correlation constant in eq 3 C ) molar concentration, mol/L G ) Gibbs free energy per mole of molecules, J/molecule K ) partition coefficient N ) number of functional groups contained in a molecule q ) normalized van der Waals surface area Q ) group surface area contribution r ) normalized van der Waals volume R ) gas constant; also group volume contribution T ) temperature, K x ) mole fraction z ) coordination number
Greek Letters R ) group scale factor γ ) activity coefficient F ) number density, molecules/L Subscripts tot ) total molar concentration mix ) a mixture solvent Superscripts ∞ ) infinite dilution * ) the solute molecule is fixed at a certain position cav ) cavity formation chg ) charging W ) water WR ) water-rich phase O ) octanol OR ) octanol-rich phase sol ) solvation τ ) energy parameter in the UNIQUAC or GCS model
Appendix I. Group Contribution Solvation Model for Multicomponent Mixtures The infinite dilution activity coefficient of species 1 in a multicomponent mixture from UNIQUAC is
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 4089
[
ln γmix,∞ ) ln γmix,∞ (comb) + 1 1 N
N
θjτ1j
θjτj1) - ∑ ∑ N j)2 j)2 θkτkj ∑ k)2
q1 1 - ln(
]
/cav ∆G1/mix
(A1)
-
RT
/cav ∆G ˆ 1/1
RT
+ ln
Fmix
) ln γmix,∞ (comb) + 1
[
F1
where
r1
(comb) ) ln ln γmix,∞ 1
+
q1 ln
2
( ) ∑x r q1 j)2 j j r1
N
r1
+ l1 -
xjqj ∑ j)2
N
N
xjrj ∑ j)2
xjlj ∑ j)2
(A2)
/cav ∆G1/mix
-
RT
/cav ∆G1/1
RT
+ ln
Fmix
/sol ∆G1/1
-
RT
RT
+ ln
/sol ∆G1/1
-
RT
RT
+ ln
Fmix
[
F1
N
N
θjτ1j
θjτj1) - ∑ ∑ N j)2 j)2 ∑ θkτkj k)2
q1 1 - ln(
(A3)
(
τ1j ) exp -
RT
) ( ) ( )
τj1 ) exp and
/cav ∆G1/mix
RT
-
) exp
RT uj1 - u11 RT
/cav ∆G ˆ 1/1
RT
ujj
[
+ ln
Fmix F01 N
[
]
]
) ln γmix,∞ (comb) + ln γmix,∞ 1 1 N
q1 τ 1 -
xjqjτj
∑ N j)2 xkqkτkj ∑ k)2
+
(
/chg ∆G1/mix
-
RT
)
/chg ∆G1/1
RT
(A9)
(A4)
First, we calculate the molecular structure parameters for 1-octanol (one CH3 group, seven CH2 groups, and one OH group) and water from eq 12:
rO ) RCH3 + 7(RCH2) + ROH ) 0.887 + 7(0.665) + 0.532 ) 6.074 qO ) QCH3 + 7(QCH2) + QOH ) 0.840 + 7(0.523) + 0.572 ) 5.073 rW ) 0.92 and qW ) 1.40
) τj,
Then the combinatorial contribution to the infinite dilution activity is determined from eq A2
) exp(0) ) 1, ) ln
γmix,∞ (comb) 1 N
θjτj
θj) - ∑ ∑ N j)2 j)2 θkτkj ∑ k)2
q1 1 - ln(
]
(A8)
Appendix II. Some Examples of Using the GCSKOW Model
Next, we turn off the interactions between molecule 1 and all other species. Therefore,
u1j - ujj
∑ N j)2 ∑ xkqkτkj k)2
Finally, by subtracting eq A8 from eq A3, we obtain the final result
Fmix F1
) ln γmix,∞ (comb) + 1
xjqjτj
N
q 1 τ1 -
To derive the expression for a multicomponent system, we first combine eqs A1 and A3 /sol ∆G1/mix
(A7)
) ln γmix,∞ (comb) + 1
[
F1
where θi ) area fraction of species i ) xjqj and lj ) z/2(rj - qj) - (rj - 1). This activity coefficient can also be determined from solvation free energy calculations
) ln γmix,∞ 1
(A6)
/cav Subtracting eq A7 from eq A6 to eliminate the ∆G ˆ 1/1 term gives
N xiqi/∑j)1
/sol ∆G1/mix
]
/cav /cav ∆G ˆ 1/1 ∆G1/1 ) q1(1 - τ1) RT RT
xjrj N
z
∑ N j)2 ∑ xkqkτkj k)2
Now, consider the case in which all species are component 1 and obtain
N
∑ j)2
xjqjτj
N
q1 1 -
]
+
(A5)
where the ˆ accent indicates that the charges on the solvent molecules are switched off.22 N N Since ∑j)1 θj ) θ1 + ∑j)2 θj ) 1 at infinite dilution of species 1, eq A5 simplifies to
ln
(comb) γW,∞ i γOR,∞ (comb) i
) ln
OR xOR W rW + xO rO + rW
OR rW(xOR W qW + xO qO) z + qi ln 2 q (xORr + xORr )
(
W
W
W
O
O
)
z z q + xOR q - 1 1 - (xOR O qO) 2 W 2 O W + ri rW xORr + xORr W
W
O
O
) 1.622 - 2.781qi + 2.374ri OR where z ) 10, xOR W ) 0.275, and xO ) 0.725 are used.
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Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999
Finally, taking τW ) 8.14 × 10-6, τO ) 3.37 × 10-4, τOW ) 1.13, τWO ) 0.67, and T ) 298.15 K, then eq 11 simplifies to
log10 KOW,i ) -0.126 - 1.208qi + 1.031ri + /chg /chg - ∆Gi/OR ∆Gi/W (B1) 1.364
Therefore, the octanol-water partition coefficient of solute i can be easily determined once the structure and energy parameters are calculated from their group contributions listed in Table 4. Following are two examples: Butylbenzene (bb): five ACH groups, one AC group, three CH2 groups, and one CH3 group. The molecular structure and energy parameters of butylbenzene are calculated using eq 12
rbb ) 5(RACH) + RAC + 3(RCH2) + RCH3 ) 5(0.537) + 0.316 + 3(0.665) + 0.887 ) 5.866 qbb ) 5(QACH) + QAC + 3(QCH2) + QCH3 ) 5(0.431) + 0.114 + 3(0.523) + 0.840 ) 4.678 /chg /chg /chg ∆Gbb/W - ∆Gbb/OR ) 5(∆∆G/chg ACH) + ∆∆GAC + /chg /chg ) + ∆∆GCH 3(∆∆GCH 2 3
) 5(0.499) - 0.469 + 3(0.649) + 1.459 ) 5.432 The octanol-water partition coefficient of butylbenzene is then obtained by substituting these values into eq B1
log10 KOW,bb ) -0.126 - 1.208(4.678) + 1.031(5.866) +
5.432 ) 4.25 1.364
compared to the measured value 4.26. 2. Cyclohexylamine (ch): five cyclic-CH2 groups, one cyclic-CH group, and one NH2 group.
rch ) 5(Rc-CH2) + Rc-CH + RNH2 ) 5(0.665) + 0.497 + 0.742 ) 4.564 qch ) 5(Qc-CH2) + Qc-CH + QNH2 ) 5(0.523) + 0.235 + 0.748 ) 3.598 /chg /chg /chg ∆G/chg ch/W - ∆Gch/OR ) 5(∆∆Gc-CH2) + ∆∆Gc-CH + /chg ) 5(0.724) - 0.182 - 1.869 ) 1.569 ∆∆GNH 2
Substituting these values into eq B1, we have
log10 KOW,ch ) -0.126 - 1.208(3.598) + 1.031(4.564) +
1.569 ) 1.3 1.364
The experimental value is 1.49. Literature Cited (1) Hansch, C.; Fujita, T. A Method for the Correlation of Biological Activity and Chemical Structure. J. Am. Chem. Soc. 1984, 86, 1616. (2) Leo, A.; Hansch, C.; Elkins, D. Partition Coefficients and Their Uses. Chem. Rev. 1971, 71, 525.
(3) Hansch, C.; Kim, D.; Leo, A.; Novellino, E.; Silipo, C.; Vittoria, A. Toward a Quantitative Comparative Toxicology of Organic Compounds. Crit. Rev. Toxicol. 1989, 19, 185. (4) Hansch, C.; Leo, A. Exploring QSAR: Fundamentals and Applications in Chemistry and Biology; American Chemical Society: Washington, DC, 1995. (5) Martin, Y. C. Quantitative Drug Design; Marcel Dekker Inc.: New York, 1978. (6) Franke, R. Theoretical Drug Design Methods; Akademie Verlag: Berlin, 1984. (7) Mackay, D. Multimedia Environmental Models; the fugacity approach; Lewis: Chelsea, MA, 1991. (8) Mackay, D.; Shiu, W. Y.; Ma, K. C. Illustrated Handbook of Physical-Chemical Properties and Environmental Fate for Organic Chemicals; Lewis: Chelsea, MA, 1992-1995. (9) Thomann, R. V. Boiaccumulation Model of Organic Chemical Distribution in Aquatic Food Chains. Environ. Sci. Technol. 1989, 23, 699. (10) Sangster, J. Octanol-Water Partition Coefficients: Fundamentals and Physical Chemistry; Wiley and Sons: New York, 1997. (11) Sangster, J. LOGKOWsa Databank of Evaluated OctanolWater Partition Coefficients; Sangster Research Laboratories: Montreal, 1993. (12) Taft, R. W.; Abboud, J.-L. M.; Kamlet, M. J.; Abraham, M. H. Linear Solvation Energy Relations. J. Solution Chem. 1985, 14 (3), 153. (13) Leahy, D. E. Intrinsic Molecular Volume as a Measure of the Cavity Term in Linear Solvation Energy Relationships: Octanol-Water Partition Coefficients and Aqueous Solubilities. J. Pharm. Sci. 1986, 75, 629. (14) Kamlet, M. J.; Doherty, R. M.; Abraham, M. H.; Marcus, Y.; Taft, R. W. Linear Solvation Energy Relationships. 46. An Improved Equation for Correlation and Prediction of Octanol/ Water Partition Coefficients of Organic Nonelectrolytes (Including Strong Hydrogen Bond Donor Solutes). J. Phys. Chem. 1988, 92, 5244. (15) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. Linear Solvation Energy Relationships. 23. A Comprehensive Collection of the Solvatochromic Parameters, π*, R, and β, and Some Methods for simplifying the Generalized Solvatochromic Equation. J. Org. Chem. 1983, 48, 2877. (16) Famini, G. R.; Wilson, L. Y. Using Theoretical Descriptors in Quantitative Structure Activity Relationships: Application to Partition Properties of Alkyl (1-Phenylsulfonyl) CycloalkaneCarboxylates. Chemosphere 1997, 35 (10), 2417. (17) Haeberlein, M.; Brinck, T. Prediction of Water-Octanol Partition Coefficients Using Theoretical Descriptors from the Molecular Surface Area and the Electrostatic Potential. J. Chem. Soc., Perkin Trans. 2 1997, 289. (18) Eusfeld, W.; Maurer, G. Study on the Correlation and Prediction of Octanol/Water Partition Coefficients by Quantum Chemical Calculations. J. Phys. Chem. B 1999, 103, 5716. (19) Leo, A. Calculating Log P(oct) from Structures. Chem. Rev. 1993, 93, 1281. (20) Wienke, G.; Gmehling, J. Prediction of Octanol-Water Partition Coefficients, Henry Coefficients and Water Solubilities Using UNIFAC. Toxicol. Environ. Chem. 1998, 65, 57. (21) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. GroupContribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21 (6), 1086. (22) Lin, S.-T.; Sandler, S. I. Predictions of Infinite Dilution Activity Coefficients from Ab Initio Solvation Calculation. Submitted for publication to the AIChE J. 1999. (23) Tse, G.; Sandler, S. I. Determination of Infinite Dilution Activity Coefficients and 1-Octanol/Water Partition Coefficients of Volatile Organic Pollutants. J. Chem. Eng. Data 1994, 39, 354. (24) Ben-Naim, A. Solvation Thermodynamics; Plenum Press: New York, 1987. (25) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21 (1), 116. (26) Maurer, G.; Prausnitz, J. M. On the Derivation and Extension of the UNIQUAC. Fluid Phase Equilib. 1978, 2, 91. (27) Szabo, A.; Ostlund, N. S. Modern Quantum Chemistrys Introduction to Advanced Electronic Structure Theory; McGrawHill: New York, 1989.
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(36) Suzuki, T.; Kudo, Y. Automatic LogP Estimation Based on Combined Additive Modeling Methods. J. Comput.-Aided Mol. Des. 1990, 4, 155. (37) Isnard, P.; Lambert, S. Aqueous Solubility and n-Octanol/ Water Partition Coefficient Correlations. Chemosphere 1989, 18, 1837. (38) Kojima, K.; Zhang, S.; Hiaki, T. Measuring Methods of Infinite Dilution Activity Coefficients and a Database for Systems Including Water. Fluid Phase Equilib. 1997, 131, 145. (39) Hait, M. J.; Liotta, C. L.; Eckert, C. A.; Bergmann, D. L.; Karachewski, A. M.; Dallas, A. J.; Eikens, D. I.; Li, J. J.; Carr, P. W.; Poe, R. B.; Rutan, S. C. Space Predictor for Infinite Dilution Activity Coefficients. Ind. Eng. Chem. Res. 1993, 32, 2905. (40) Tiegs, D.; Gmehling, J.; Medina, A.; Soares, M.; Bastos, J.; Alessi, P.; Kicic, I. Activity Coefficients at Infinite Dilution; Chemistry Data Series Vol. IX, parts 1 and 2; DECHEMA: FR Germany, 1986.
Received for review June 4, 1999 Revised manuscript received July 29, 1999 Accepted July 30, 1999 IE990391U
