Semiempirical Molecular Orbital Calculations - American Chemical

and runways, we report semiempirical molecular orbital calculations of hexadecane-water partition coefficients (log Ph-w). The evaluation of hexadecan...
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Energy & Fuels 1997, 11, 647-655

647

Partition Coefficients of Fuel System Icing Inhibitors: Semiempirical Molecular Orbital Calculations Steven Trohalaki* and Ruth Pachter Materials Directorate, Wright Laboratory, Wright-Patterson Air Force Base, Ohio 45433-7702 Received September 26, 1996. Revised Manuscript Received February 7, 1997X

In our continuing efforts to design nontoxic and biodegradable fuel system icing inhibitor (FSII) compounds with improved fuel solubility and antiicing ability, and nontoxic deicers for aircraft and runways, we report semiempirical molecular orbital calculations of hexadecane-water partition coefficients (log Ph-w). The evaluation of hexadecane-water partition coefficients for a series of isomers by an empirical method yields only a single number, whereas our application of solvent models within a molecular orbital approach to methyl- and acetyl-substituted D-glucopyranose results in a range of log Ph-w values. Furthermore, these values are lowered when the conformational response of the FSII to the solvent is included. The extent of this effect depends on the solvation model used and is more pronounced for acetyl-substituted glucopyranoses than for methyl-substituted derivatives. Four methyl substituents in any substitution pattern are required for preferential partitioning into fuel whereas only specific tetraacetylglucopyranose isomerss1,2,3,4-R-D-tetraacetylglucopyranose, 1,2,3,6-R-D-tetraacetylglucopyranose, 1,2,4,6-R-Dtetraacetylglucopyranose, 1,2,4,6-β-D-tetraacetylglucopyranose, 1,3,4,6-R-D-tetraacetylglucopyranose, and 1,3,4,6-β-D-tetraacetylglucopyranoseswill do so.

Introduction Diethylene glycol monomethyl ether (DiEGME), at a concentration of about 0.1%, is currently being added to US Air Force and Navy jet fuels (fuel system icing inhibitor (FSII)) to prevent ice formation from trace amounts of water. This substance is under scrutiny by the US Environmental Protection Agency due to its human toxicity. Ethylene glycol monomethyl ether, which has an even higher toxicity than DiEGME, has been recently replaced. It is postulated that these FSIIs extract water from the fuel and prevent formation of ice crystals by lowering the freezing point of water. DiEGME partitions between the water “bottoms” that form in storage tanks from condensation or from leaking of ambient water. However, when this water is drained, it contains sufficient DiEGME to be disposed of as hazardous waste, which is a costly operation.1 Military and civilian airports also employ large quantities of similar, toxic (glycol-based) runway and wing deicers. Current deicers may soon be regulated as hazardous chemicals because of their toxicity to aquatic organisms,2 thus requiring the construction of extremely expensive containment systems.3 Such systems are inherently inefficient because Type-II deicers,4 composed of ethylene glycol and a thickening agent, prevent ice formation by coating the aircraft wing with a gellike protective layer that flows off only after application of sufficient shear stress experienced during takeoff. For example, flow-off of deicer has been recently blamed for a 3-4 min downpour of “green rain” in San Francisco.5

Alternative nontoxic and biodegradable FSIIs and deicing compounds, e.g., natural product candidates, are therefore being developed. Carbohydrates have recently been suggested6 as nontoxic antiicing candidates, where improved fuel solubility can be obtained by increasing the carbon number and enhanced antiicing ability by increasing the polarity, with any concomitant toxicity minimized. In particular, a series of methyl- and acetylsubstituted glucopyranoses, as summarized in Figure 1, have been proposed.6 It is the purpose of this study to investigate the partition coefficients for FSIIs by using computational techniques to predict these indicators and thus gain an understanding of preferential partitioning. The glucopyranose molecular systems we studied (cf. Figure 1) are in the D-form and substituted in the 1-position, i.e., glucopyranosides. All possible isomers of disubstituted, trisubstituted, and tetrasubstituted glucopyranoside isomers were considered as well as unsubstituted glucopyranose, 1-monosubstituted glucopyranose, and pentasubstituted glucopyranoses (acetyl only). In addition, the R and β anomers of each substituted compound were studied, resulting in a total of 60 compounds being investigated. Partition coefficients serve as QSAR (quantitative structure-activity relationship) predictors for toxicity and other biological activities7 and are also important indicators of antiicing ability. Typically, the octanolwater partition coefficient is calculated empirically by using the fragment approach7 or similarly by a technique where atomic contributions are derived from those of fragments8 (coded in the program HINT! 9). Although

Abstract published in Advance ACS Abstracts, April 1, 1997. (1) Steward, E. Wright Laboratory, personal communication. (2) Hartwell, S. I.; Jordahl, D. M.; May, E. B. Environ. Toxicol. Chem. 1995, 14, 1375. (3) O’Connor, R.; Douglas, K. New Scientist 1993, 137, 22. (4) Ross, J. F.; Connolly, J. T. J. Aircraft 1993, 30, 10.

(5) Davidson, K. San Francisco Examiner 1994, March 15, A3. (6) Mushrush, G. Fuel Sci. Technol. Int., in press. (7) Hansch, C.; Leo, A. J. Exploring QSAR; American Chemical Society: Washington, DC, 1995. (8) Abraham, D. J.; Leo, A. J. Proteins: Struct., Funct., Genet. 1987, 2, 130.

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Energy & Fuels, Vol. 11, No. 3, 1997

Trohalaki and Pachter energies of solvation ∆G0S defined as 0 0 ∆G0S ) G(sol) + G(g)

(1)

0 G(sol) is the free energy of the solvated solute and G0(g) is the free energy in the gas phase, both in the standard state, namely, at a temperature of 298 K and a concentration of 1 mol/L.15-18 ∆G0S can be expressed as a sum of contributions:

15-18

0 ∆G0S ) EEN(sol) + EEN(g) + GP + GCDS

Figure 1. R and β anomers of D-glucopyranose, and derivatives with methyl and acetyl substitutions.

these methods allow for efficient calculation of log P, differences due to structural isomers are not accounted for, and these calculations are also largely limited to the octanol-water solvent system. Incorporation of solvent models within a molecular orbital (MO) approach enables the calculation of partition coefficients for nonpolar solvent-water systems from the difference between the free energies of solvation. Structural isomers are then implicitly differentiated and the effect of conformational response to solvent can be examined. In this paper we report the log of n-hexadecanewater partition coefficients (log Ph-w) calculated using the solvent models encoded in AMSOL,10 as well as the log of octanol-water partition coefficients calculated empirically. Note that n-hexadecane has a dielectric constant of 2.06 at 298 K,11 which is nearly identical to that of current jet-fuel formulations.12 Also, solvation free energies in n-hexadecane are experimentally indistinguishable from those of isooctane, indicating that n-hexadecane can, to a significant extent, be used to model nonpolar, large-alkane solvents.13 The insight we gain into the differences in partitioning for the groups of isomers under study is essential when designing better-performing FSIIs. Methods and Computational Details Empirical Calculations. The log of octanol-water partition coefficients (log Po-w) were calculated empirically using the program HINT!, where the fragment constants of Hansch and Leo7 employed in the program CLOG-P (Pomona MedChem)7 are reduced to atomic contributions. Values of log Po-w for small molecules calculated with HINT! and CLOG-P have been shown previously to agree to within 0.1 log units.14 Solvation Models. The solvation models employed in AMSOL10 (versions 4.5 and 5.0) were used to calculate the free (9) Kellog, G. E.; Semus, S. F.; Abraham, D. J. Comput. Aided Mol. Des. 1991, 5, 545. (10) Cramer, C. J.; Hawkins, G. D.; Lynch, G. C.; Giesen, D. J.; Rossi, I.; Storer, J. W.; Truhlar, D. G.; Liotard, A. A. QCPE 606, AMSOLversion 5.0; based in part on AMPAC-version 2.1 by Liotard, D. A.; Healy, E. F.; Ruiz, J. M.; Dewar, M. J. S., and the EF routines by Jensen, F. (11) CRC Handbook of Chemistry and Physics, 71st ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1990-1991. (12) Handbook of Aviation Fuel Properties; Coordinating Research Council: Atlanta, GA, 1983. (13) Gieson, D. J.; Storer, J. W.; Cramer, C. J.; Truhlar, D. G. J. Am. Chem. Soc. 1995, 117, 1057. (14) HINT! User Guide and Reference Manual, eduSoft, Ashland VA.

(2)

where EEN(sol) and EEN(g) are the sums of the solute electronic kinetic and electronic nuclear Coulomb energies in solution (sol) and in the gas phase (g), respectively; GP is the free energy of the electric polarization, which includes both the solutesolvent interaction energy and solvent reorganization energy; 0 and GCDS is the remaining solvent free energy, which correlates with the solvent-accessible surface area. Terms accounting for the change in internal vibrational and electronic free energy upon solvation are expected to be small and are therefore neglected. The methods encoded in AMSOL10 are based on a semiempirical MO theory utilizing the NDDO (neglect of diatomic differential overlap) approximation,19 using AM1 (Austin method 1)20 as the electronic Hamiltonian for the solute (models utilizing the PM3 (parametrization method 3)21 Hamiltonian are also available), with two terms added to the Fock operator to account for solvation effects. The first term is based on a generalized Born approximation that accounts for electric polarization of the solvent with a continuum dielectric and for the effect of this polarization on the solute charge distribution. The second term accounts for the free energy of cavity formation, dispersion effects, and hydrophobic/hydrophilic first-hydration shell effects, and is proportional to the solvent-accessible surface area. The proportionality constants (surface tensions) are semiempirical. Parametrizations are available for water and alkane solvents. Three solvation models for water were used in this work. (1) AM1-SM2.1,22 referred to as SM2, yields results similar to AM1-SM2, which is an improvement of the original general parameter set, AM1-SM1.16 For a representative set of 147 neutral compounds, the rms error for AM1-SM2.1 is 0.8 kcal/ mol vs 1.5 kcal/mol for AM1-SM2. The AM1-SM2.1 model uses an improved integration scheme for the radial quadrature of the dielectric screening calculation as compared to AM1-SM1 and AM1-SM2. (2) The AM1-SM4-[HCO]SRP-(sugar)23 model was developed for glucose and other sugars; it is a “specific range parameter” (SRP) model for H, C, and O, with parametrization for hydrocarbons, ethers, and aldehydes. The rms error for a representative set of 47 compounds is 0.9 kcal/mol. Our application of AM1-SM4-[HCO]SRP-(sugar), referred to as SRP, to acetyl-substituted glucopyranoses represents an attempt to extend the model to a new class of compounds. (3) The third model is based on SRP except that it employs cutoffs of the Gaussian functions (COGs) used in calculating the generalized Born terms for O-O and N-H electrostatic interactions. COGs were used in the development of the AM1(15) Cramer, C. J.; Truhlar, D. G. J. Am. Chem. Soc. 1991, 113, 8305, 9901. (16) Cramer, C. J.; Truhlar, D. G. Science 1992, 256, 213. (17) Cramer, C. J.; Truhlar, D. G. J. Comput. Chem. 1992, 13, 1089. (18) Cramer, C. J.; Truhlar, D. G. J. Comput. Aided Mol. Des. 1992, 6, 629. (19) Pople, J. A.; Beveridge, D. L. Approximate Molecular Orbital Theory; McGraw-Hill: New York, 1970. (20) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902. (21) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209, 221; 1991, 12, 320. (22) Liotard, D. A.; Hawkins, G. D.; Lynch, G. C.; Truhlar, D. G.; Cramer, C. J. Comput. Chem. 1995, 16, 422. (23) Barrows, S. E.; Dulles, F. J.; Cramer, C. J.; French, A. D.; Truhlar, D. G. Carbohydr. Res. 1995, 276, 219.

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Energy & Fuels, Vol. 11, No. 3, 1997 649

SM1 and AM1-SM2 models. We designate this model as AM1SM4-[HCO]SRP-(sugar)-C, which shall be referred to as SRPC. Another difference between the AM1-SM2 and the two SRP water models involves the calculation of the generalized Born contribution; the AM1-SM2 model uses partial atomic charges based on the Mulliken analysis24 of the solute AM1 wavefunction optimized in aqueous solution while the SRP and SRP-C models use a CM1 (charge model 1)25 mapping of the Mulliken analysis, which yields partial charges of ab initio quality. Free energies of solvation in hexadecane were calculated from the SM4-hexadecane model,26 which also uses CM1 for the generalized Born terms. All free energies of solvation in hexadecane, and therefore all log Ph-w values were calculated using the SM4-hexadecane model, which yields an rms error for ∆G0S of 0.4 kcal/mol for 153 molecules representing many chemical classifications. Procedure. For each of the 60 compounds (Figure 1), only the lowest-energy gas-phase and solution-phase conformations were used to calculate ∆G0S. This approximation improves the tractability of the problem (e.g., 1458 potential conformers for a single chair form of glucopyranose) and is based on the observation that solvation “flattens” the free energy surface; six glucopyranose conformers are within 1 kcal/mol of the lowest minimum.27 Preliminary geometry optimizations were performed with the PCFF force field,28-30 as implemented by Discover (version 2.9531). Employing either MOPAC9332 or AMPAC 4.533 (identical results were previously obtained by the two programs for test cases), the AM1 Hamiltonian17 and the eigenvector following method34-36 were used to optimize all PCFF-minimized structures in the gas phase to a gradient norm (the scalar of thevector of derivatives of the energy with respect to the geometric variables) of less than 0.1 kcal/Å. Minima were confirmed by the absence of imaginary frequencies and only conformations with the lowest EEN were used for subsequent solvation calculations. The log of the hexadecane-water partition coefficient (log Ph-w) is calculated from

log Ph-w )

∆G0w - ∆G0h 2.303RT

(3)

where ∆G0w and ∆G0h are the free energies of solvation of the solute in water and in hexadecane, respectively, R is the gas constant, and T is the absolute temperature, 298 K. Computer Resources. Gas-phase optimizations were performed on a Silicon Graphics Power Series 4D/420 equipped with two 30 MHz processors (one processor per optimization) and typically required up to 3 h. SM2 optimizations of the acetyl-substituted compounds were performed on a SparcCenter 2000 equipped with 12 40 MHz processors (only one processor was used per calculation) and required an average of 3.9 h for monoacetyl compounds, 10.2 h for diacetyl compounds, 13.1 h for triacetyl compounds, 24.3 hours for (24) Mulliken, R. S. J. Chem. Phys. 1933, 1, 56. (25) Storer, J. W.; Giesen, D. J.; Cramer, C. J.; Truhlar, D. G. J. Comput. Aided Mol. Des. 1995, 9, 87. (26) Giesen, D. J.; Storer, J. W.; Cramer, C. J.; Truhlar, D. G. J. Am. Chem. Soc. 1995, 117, 1057. (27) Cramer, C. J.; Truhlar, D. G. J. Am. Chem. Soc. 1993, 115, 5745. (28) Hwang, M. J.; Stockfisch, T. P.; Hagler, A. T. J. Am. Chem. Soc. 1994, 116, 2515. (29) Sun, H., Mumby, S. J., Maple, J. R., Hagler, A. T. J. Am. Chem. Soc. 1994, 116, 2978. (30) Sun, H. J. Comput. Chem. 1994, 15, 752. (31) Discover; Molecular Simulations, Inc., 9685 Scranton Road, San Diego, CA. (32) MOPAC 93; Fujitsu Limited, Tokyo, Japan, 1993. (33) AMPAC 4.5; Semichem, 12715 W. 66th Terrace, Shawnee, KS, 66216, 1993. (34) Simons, J.; Banerjee, A.; Adams, N.; Shepard, R. J. Phys. Chem. 1985, 89, 52. (35) Baker, J. J. Comput. Chem. 1986, 7, 385. (36) Culot, P.; Dive, G.; Nguyen, V. H.; Ghuysen, J. M. Theor. Chim. Acta 1992, 82, 189.

Figure 2. log Po-w values for unsubstituted and methyl- and acetyl-substituted glucopyranose calculated empirically using HINT !. Lines are drawn according to least-squares fits to the data with slopes of 0.69 for methyl and 0.84 for acetyl derivatives. tetraacetyl, and 37.5 h for pentaacetyl compounds to complete. Most SM4-hexadecane, SRP, and SRP-C optimizations were performed on a Cray Y-MP. SM4-hexadecane optimizations required an average of 5.0 h for diacetyl compounds, 5.8 h for triacetyl compounds, and 8.3 h for tetraacetyl compounds. SRP optimizations required an average of 15.6 h for disubstituted compounds, 29.1 h for trisubstituted compounds, and 46.9 h for tetrasubstituted compounds. Because SRP-C optimizations were started with the SRP-optimized geometries, SRP-C calculation times are not reported here but are expected to be identical to those for SRP when started from the same geometry. SRP optimizations of the pentaacetyl were performed on the Sun Sparcserver and required an average of 106.0 h. Optimizations of the methyl-substituted compounds were performed on a variety of Silicon Graphics and Sun computers. Timings of the acetyl compounds can serve as an upper limit for the methyl compounds because they have two fewer atoms per substituent than the acetyl compounds. Single-point solvation calculations using optimal gas-phase geometries required times on the order of minutes for the Sun and SGI computers used and for all compounds.

Results and Discussion Values of log Po-w for methyl- and acetyl-substituted glucopyranose derivatives calculated empirically using HINT! are shown as a function of the number of substituents in Figure 2. For a given number of substituents of a given type, similar log Po-w values were obtained for all structural isomers, with a linear increase with the number of substituents, as expected, where the increase per substituent is larger for acetyl than for methyl substituents, namely, 0.84 vs 0.69, respectively. Free energies of solvation and log Ph-w values for methyl- and acetyl-substituted glucopyranose compounds using the SM2, SRP, and SRP-C models for water and the SM4-hexadecane model for hexadecane are presented in Tables 1 and 2, respectively: for a given solvation model, free energies were obtained at two levels of approximation. First, single-point solvation calculations were performed with optimized gas-phase molecular geometries, i.e., only the electronic relaxation due to the solvent was accounted for (table sections labeled (a)). Both electronic and geometric responses to the solvent were accounted for in the second set of calculations (table sections labeled (b)), where molecular geometries were reoptimized in solution to a gradient norm of less than 0.1 (version 4.5) or to a default convergence criterion (version 5.0) that ensures that all forces on the molecules are small by requiring the largest component of the gradient to be less than 0.45

650 Energy & Fuels, Vol. 11, No. 3, 1997

Trohalaki and Pachter

Table 1. Free Energy of Solvation (kcal/mol) and log Ph-w for Unsubstituted and Methyl-Substituted Glucopyranose Using Optimal (a) Gas-Phase and (b) Solution-Phase Molecular Geometries subst sites none none 1 1 1,2 1,2 1,3 1,3 1,4 1,4 1,6 1,6 1,2,3 1,2,3 1,2,4 1,2,4 1,2,6 1,2,6 1,3,4 1,3,4 1,3,6 1,3,6 1,4,6 1,4,6 1,2,3,4 1,2,3,4 1,2,3,6 1,2,3,6 1,2,4,6 1,2,4,6 1,3,4,6 1,3,4,6 none none 1 1 1,2 1,2 1,3 1,3 1,4 1,4 1,6 1,6 1,2,3 1,2,3 1,2,4 1,2,4 1,2,6 1,2,6 1,3,4 1,3,4 1,3,6 1,3,6 1,4,6 1,4,6 1,2,3,4 1,2,3,4 1,2,3,6 1,2,3,6 1,2,4,6 1,2,4,6 1,3,4,6 1,3,4,6

anomer R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β

∆Ghex

∆Gw(SM2)

-6.0 -5.9 -8.8 -7.3 -7.3 -7.3 -6.7 -7.8 -6.6 -7.1 -10.0 -8.0 -7.5 -8.2 -7.4 -7.9 -8.3 -8.5 -7.1 -7.5 -8.2 -8.7 -6.4 -8.5 -7.7 -8.0 -8.3 -9.4 -8.1 -8.7 -7.9 -8.6

-17.9 -17.8 -16.7 -15.0 -11.2 -11.5 -11.1 -11.7 -11.7 -12.4 -13.8 -11.6 -7.9 -8.4 -8.5 -9.0 -8.6 -8.8 -8.7 -9.3 -8.6 -9.1 -11.7 -9.2 -5.7 -6.0 -4.8 -5.5 -5.3 -5.9 -5.3 -6.9

-6.3 -6.0 -9.6 -7.4 -7.4 -7.3 -7.7 -7.9 -6.7 -7.2 -10.2 -8.2 -8.3 -8.3 -8.1 -8.0 -8.4 -8.6 -7.2 -7.7 -8.2 -8.9 -7.2 -8.6 -7.8 -8.1 -9.1 -9.5 -8.8 -8.8 -10.5 -8.7

-18.1 -18.0 -16.9 -15.2 -11.4 -11.6 -12.4 -11.9 -11.9 -12.5 -13.9 -11.7 -8.2 -8.7 -8.6 -9.2 -8.8 -9.0 -9.7 -9.4 -8.8 -9.4 -11.9 -9.6 -5.9 -6.4 -5.0 -5.7 -5.4 -6.1 -5.5 -6.5

∆Gw(SRP-C)

log P(SM2)

log P(SRP)

log P(SRP-C)

-17.5 -16.7 -14.8 -14.5 -9.8 -10.3 -8.0 -11.0 -8.4 -10.2 -12.9 -12.3 -6.0 -7.4 -5.6 -6.8 -8.6 -9.1 -6.1 -7.8 -8.6 -10.6 -8.2 -8.9 -3.4 -4.3 -4.5 -6.1 -4.1 -5.4 -4.0 -6.0

-8.7 -8.8 -5.8 -5.7 -2.9 -3.1 -3.2 -2.9 -3.8 -3.9 -2.8 -2.6 -0.3 -0.2 -0.8 -0.9 -0.3 -0.2 -1.2 -1.3 -0.3 -0.3 -3.9 -0.5 1.5 1.4 2.6 2.9 2.1 2.0 1.9 1.7

-10.4 -10.5 -5.6 -6.8 -3.0 -3.8 -2.4 -3.9 -2.7 -3.9 -3.5 -4.7 -0.3 -1.0 -0.2 -0.8 -1.5 -1.9 -0.7 -1.7 -1.4 -2.8 -2.7 -1.8 1.7 1.2 1.4 0.9 1.5 0.9 1.4 0.5

-8.4 -7.9 -4.4 -5.3 -1.8 -2.2 -1.0 -2.4 -1.3 -2.3 -2.1 -3.1 1.1 0.5 1.3 0.7 -0.3 -0.5 0.8 -0.2 -0.3 -1.4 -1.3 -0.3 3.1 2.7 2.8 2.4 2.9 2.4 2.8 1.9

(b) Solution Phase -22.7 -20.4 -22.2 -19.4 -19.6 -18.2 -18.7 -16.7 -13.1 -11.6 -14.1 -12.0 -14.3 -12.9 -15.3 -13.3 -14.1 -12.7 -14.3 -12.3 -17.4 -16.0 -16.1 -14.1 -9.9 -8.5 -10.6 -8.6 -10.3 -8.9 -10.3 -8.3 -11.2 -9.8 -12.2 -10.3 -10.4 -8.8 -11.5 -9.5 -11.1 -9.7 -13.7 -11.9 -13.2 -12.5 -12.4 -10.4 -6.4 -5.6 -7.2 -5.2 -7.6 -6.2 -8.6 -6.7 -7.4 -6.0 -8.2 -7.8 -7.6 -6.2 -8.7 -6.8

-8.7 -8.8 -5.3 -5.7 -2.9 -3.1 -3.5 -3.0 -3.8 -3.9 -2.8 -2.6 0.1 -0.3 -0.4 -0.9 -0.3 -0.3 -1.8 -1.3 -0.4 -0.4 -3.5 -0.7 1.4 1.2 3.0 2.8 2.5 2.0 3.6 1.6

-12.1 -11.9 -7.4 -8.3 -4.1 -4.9 -4.9 -5.5 -5.4 -5.2 -5.3 -5.8 -1.1 -1.7 -1.6 -1.7 -2.1 -2.7 -2.3 -2.8 -2.1 -3.6 -4.4 -2.8 1.1 0.6 1.1 0.6 1.0 0.5 2.1 0.0

-10.3 -9.8 -6.3 -6.8 -3.1 -3.4 -3.9 -4.0 -4.4 -3.7 -4.3 -4.4 -0.1 -0.3 -0.6 -0.3 -1.0 -1.3 -1.1 -1.4 -1.1 -2.2 -3.9 -1.3 1.6 2.1 2.1 2.1 2.1 0.7 3.2 1.4

∆Gw(SRP) (a) Gas Phase -20.3 -20.1 -16.4 -16.6 -11.4 -12.4 -9.9 -13.1 -10.3 -12.4 -14.8 -14.4 -7.9 -9.5 -7.6 -8.9 -10.2 -11.1 -8.0 -9.9 -10.2 -12.6 -10.1 -11.0 -5.3 -6.4 -6.4 -8.2 -6.1 -7.5 -6.0 -8.1

kcal/reduced units. This criterion was chosen since it results in nearly identical values to those where energies are converged to within 0.005 kcal and small deviations in geometry.37 It was previously shown that (37) Hawkins, G. D.; Lynch, G. C.; Giesen, D. J.; Rossi, I. J.; Storer, W.; Liotard, D. A.; Cramer, C. J.; Truhlar, D. G. QCPE Bull. 1996, 16, 11.

when using AM1-SM2 the geometric relaxation of glucopyranose accounted for only 0.1-0.2 kcal/mol of solvation free energy in addition to that due to electronic relaxation. Methyl Glucopyranosides. The free energies of solvation and log Ph-w values in Table 1a, which were obtained from optimal gas-phase conformations, are

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Energy & Fuels, Vol. 11, No. 3, 1997 651

Table 2. Free Energy of Solvation (kcal/mol) and log Ph-w for Acetyl-Substituted Glucopyranose Using Optimal (a) Gas-Phase and (b) Solution-Phase Molecular Geometries subst sites

anomer

∆Ghex

∆Gw(SM2)

1 1 1,2 1,2 1,3 1,3 1,4 1,4 1,6 1,6 1,2,3 1,2,3 1,2,4 1,2,4 1,2,6 1,2,6 1,3,4 1,3,4 1,3,6 1,3,6 1,4,6 1,4,6 1,2,3,4 1,2,3,4 1,2,3,6 1,2,3,6 1,2,4,6 1,2,4,6 1,3,4,6 1,3,4,6 1,2,3,4,6 1,2,3,4,6

R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β

-7.5 -8.7 -8.0 -7.6 -8.5 -9.1 -7.7 -8.7 -8.0 -8.2 -9.2 -9.6 -9.7 -10.2 -9.6 -10.3 -9.7 -10.2 -9.4 -11.2 -9.7 -10.6 -10.9 -11.0 -11.5 -11.6 -11.4 -12.0 -11.5 -11.9 -12.6 -12.7

-16.3 -17.5 -14.5 -13.6 -14.4 -15.0 -13.6 -14.6 -12.9 -13.7 -12.2 -12.0 -12.7 -13.0 -12.0 -12.2 -12.4 -12.9 -11.6 -14.3 -11.7 -13.2 -11.6 -11.5 -11.8 -11.0 -11.8 -12.4 -11.7 -12.0 -9.9 -11.4

1 1 1,2 1,2 1,3 1,3 1,4 1,4 1,6 1,6 1,2,3 1,2,3 1,2,4 1,2,4 1,2,6 1,2,6 1,3,4 1,3,4 1,3,6 1,3,6 1,4,6 1,4,6 1,2,3,4 1,2,3,4 1,2,3,6 1,2,3,6 1,2,4,6 1,2,4,6 1,3,4,6 1,3,4,6 1,2,3,4,6 1,2,3,4,6

R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β R β

-7.6 -8.9 -8.3 -7.8 8.7 -9.2 -8.0 -8.9 -8.2 -10.3 -9.5 -9.8 -10.0 -10.4 -9.8 -10.5 -9.9 -10.4 -9.6 -11.5 -10.0 -10.9 -11.2 -11.3 -11.8 -11.9 -11.6 -12.3 -11.8 -12.3 -13.1 -13.3

-16.3 -17.7 -14.8 -14.1 -14.6 -15.2 -13.9 -14.8 -13.2 -18.3 -12.6 -12.4 -13.6 -12.5 -12.4 -12.5 -12.8 -13.2 -12.1 -14.7 -12.5 -13.6 -12.1 -12.6 -12.2 -11.4 -12.2 -12.9 -12.0 -12.4 -10.7 -11.6

∆Gw(SRP-C)

log P(SM2)

log P(SRP)

log P(SRP-C)

-14.9 -18.1 -10.7 -8.9 -12.1 -13.0 -10.3 -11.9 -10.0 -11.3 -8.4 -9.2 -9.9 -10.4 -9.0 -9.5 -10.2 -10.9 -8.2 -13.1 -9.6 -11.6 -8.6 -8.7 -9.0 -9.0 -9.2 -9.9 -8.9 -9.8 -8.4 -8.7

-6.5 -6.4 -4.8 -4.4 -4.4 -4.4 -4.3 -4.4 -3.6 -4.0 -2.2 -1.8 -2.2 -2.1 -1.8 -1.4 -2.0 -2.0 -1.6 -2.3 -1.5 -1.9 -0.5 -0.3 -0.2 0.5 -0.3 -0.3 -0.1 -0.1 2.0 0.9

-8.5 -9.8 -6.4 -5.4 -7.0 -7.3 -6.5 -6.8 -6.1 -6.7 -5.3 -5.6 -6.0 -6.1 -5.5 -5.3 -6.3 -6.4 -5.1 -8.0 -6.1 -8.4 -5.7 -5.6 -5.7 -5.5 -6.3 -6.4 -5.6 -6.0 -5.8 -6.5

-5.5 -6.9 -2.0 -1.0 -2.6 -2.9 -1.9 -2.4 -1.5 -2.3 0.6 0.3 -0.1 -0.2 0.4 0.6 -0.4 -0.5 0.9 -1.4 0.1 -0.7 1.7 1.7 1.8 2.0 1.6 1.5 1.9 1.5 3.1 3.0

(b) Solution Phase -23.9 -20.1 -24.4 -20.5 -20.5 -14.7 -19.4 -13.7 -20.7 -14.9 -22.0 -16.1 -24.1 -16.0 -21.2 -15.3 -23.9 -18.0 -26.5 -18.0 -20.5 -12.7 -19.7 -11.8 -19.8 -12.1 -20.3 -12.3 -18.7 -11.0 -19.4 -10.5 -20.0 -12.2 -21.1 -13.2 -20.4 -12.4 -27.4 -18.8 -23.0 -15.1 -22.6 -14.7 -19.3 -9.7 -21.4 -11.6 -21.2 -11.2 -23.1 -13.1 -21.9 -11.4 -22.7 -11.9 -20.5 -10.5 -21.7 -11.7 -21.5 -10.3 -22.9 -10.3

-6.4 -6.5 -4.8 -4.6 -4.4 -4.4 -4.4 -4.3 -3.7 -5.9 -2.2 -1.9 -2.7 -1.6 -1.9 -1.5 -2.1 -2.0 -1.8 -2.4 -1.9 -1.9 -0.7 -0.9 -0.3 0.4 -0.4 -0.4 -0.1 -0.1 1.8 1.3

-11.9 -11.4 -9.0 -8.52 -8.9 -9.4 -11.8 -9.0 -11.5 -11.9 -8.0 -7.2 -7.3 -7.2 -6.6 -6.5 -7.4 -7.9 -7.9 -11.7 -9.6 -8.6 -6.0 -7.4 -6.9 -8.3 -7.5 -7.6 -6.3 -6.9 -6.2 -7.1

-9.2 -8.5 -4.8 -4.3 -4.5 -5.0 -5.9 -4.7 -7.2 -5.6 -2.3 -1.4 -1.6 -1.4 -0.9 0.0 -1.6 -2.1 -2.1 -5.4 -3.7 -2.8 1.1 -0.2 0.5 -0.9 0.2 0.3 1.0 0.5 2.0 2.2

∆Gw(SRP) (a) Gas Phase -19.0 -22.0 -16.7 -14.9 -18.1 -19.0 -16.5 -17.9 -16.3 -17.3 -16.4 -17.2 -17.9 -18.5 -17.0 -17.6 -18.2 -18.9 -16.3 -22.0 -18.1 -22.0 -18.6 -18.7 -19.3 -19.1 -19.9 -20.7 -19.1 -20.0 -20.6 -21.5

summarized as a function of the number of methyl substituents in Figure 3, a and b, respectively. For a given number of methyl substituents, i.e., a group of structural isomers, calculated ∆G0S values fall within ranges of up to 5 kcal/mol (except for monosubstituted compounds calculated using SRP) that exceed the rms errors previously established for the solvation models.

Similarly, log Ph-w values exhibit a range as large as 3.7 kcal/mol. All three aqueous solvation models predict that ∆G0w and log Ph-w generally increase with the number of methyl substituents; slopes of the linear correlations are similar for all three water models. In general, predicted ∆G0w and log Ph-w values for a given compound decrease depending on the model being

652 Energy & Fuels, Vol. 11, No. 3, 1997

Figure 3. (a, top) Free energies of solvation for methylsubstituted glucopyranose from optimal gas-phase conformations. The solvation free energies in water correspond to the left-hand ordinate and the solvation free energies in hexadecane to the right-hand ordinate. Lines were drawn according to least-squares fits to the data with slopes of 3.2 for SM2, 3.2 for SRP, 3.1 for SRP-C, and -0.4 for hexadecane. The correlation coefficients for the SM2, SRP, and SRP-C fits are all 0.9 while for hexadecane it is 0.5. (b, bottom) The log Ph-w values for methyl-substituted glucopyranose from optimal gasphase conformations. Lines were drawn according to leastsquares fits to the data with slopes of 2.6 for SM2, 2.7 for SRP, and 2.6 for SRP-C. The correlation coefficient for all three correlations is 1.0. 0 0 0 applied as ∆Gw(SRP-C) > ∆Gw(SM2) > ∆Gw(SRP) . Varia0 tions in ∆Gh among isomers are also evident in Figure 3a, where ∆G0h decreases only slightly as the number of methyls is increased. The slope of the linear fit to the data shows that this decrease is almost an order of magnitude smaller than the increase observed for ∆G0w. These general features are also noted in Figure 4, a and b, where the ∆G0S and log Ph-w values obtained from optimal solution-phase conformations (Table 1b) are plotted as a function of the number of methyl substituents. Once again, the variation in ∆G0S (except for monosubstituted compounds calculated using SRP) exceeds the rms error found for each solvation model. The range of log Ph-w values for tri- and tetrasubstituted isomers is larger than for the optimal gas phase conformations in Figure 3b. The slopes of the linear correlations of ∆G0w and log Ph-w as functions of the number of methyl groups for the three aqueous models are less similar than those observed in Figure 3a,b. The decrease in ∆G0h with the number of methyls is somewhat larger than that shown in Figure 3a. The effect of the conformational response to solvent is depicted in Figure 5, where changes in ∆G0S (difference in values in Table 1a and the corresponding values in Table 1b; a negative value indicates a lowering in

Trohalaki and Pachter

Figure 4. (a, top) Free energies of solvation for methylsubstituted glucopyranose from optimal solution-phase conformations. The solvation free energies in water correspond to the left-hand ordinate and the solvation free energies in hexadecane to the right-hand ordinate. Lines were drawn according to least-squares fits to the data with slopes of 3.1 for SM2, 3.7 for SRP, 3.5 for SRP-C, and -0.5 for hexadecane. The correlation coefficients for SM2, SRP, and SRP-C fits are all g0.96 while for hexadecane it is 0.54. (b, bottom) The log Ph-w values for methyl-substituted glucopyranose from optimal solution-phase conformations. Lines were drawn according to least-squares fits to the data with slopes of 2.67 for SM2, 3.07 for SRP, and 2.91 and SRP-C. The correlation coefficient for all three fits is 1.0.

Figure 5. Average effect on ∆G0S of the conformational response of methyl-substituted glucopyranose.

∆G0S) averaged for each group of isomers are plotted as a function of the number of methyl substituents. The 0 decrease in ∆G0h and in ∆Gw(SM2) due to geometrical relaxation in solvent is less than 1 kcal/mol for all methyl glucopyranoses. The decrease for ∆G0w calcu0 lated using the SRP and SRP-C models (∆Gw(SRP) and 0 ∆Gw(SRP-C)) roughly parallel each other; for unsubstituted, monosubstituted, and disubstituted compounds, the lowering (2-3 kcal/mol) in ∆G0w decreases approximately linearly as the number of methyl groups increases from two to four. Since the decrease in

Partition Coefficients of Fuel System Icing Inhibitors

∆G0h is almost independent of the number of methyl substituents, the corresponding average lowering of log Po-w, when plotted as a function of the number of substituents, parallels that indicated for free energies of solvation. The predicted log Ph-w values calculated using the SRP and SRP-C models decrease appreciably when geometrical response is accounted for. When SM2 is used, however, the effect of the conformational response to solvent is small or negligible. rms deviations of corresponding heavy atoms of superimposed gasphase and solution-phase conformations are small, ranging from 0.02 to 0.4 Å. Hexadecane-phase conformations invariably deviate less from gas-phase conformations than do aqueous-phase conformations. Arrangements of heavy atoms, however, give an incomplete picture of the intramolecular hydrogenbonding patterns in these molecules. Hydrogen bonds between adjacent donors and acceptors are evident in the gas-phase conformations except for the 1,3,6- and 1,3,4,6-substituted compounds, which lack adjacent donors and acceptors. One would expect intuitively that the hydrogen-bonding pattern would remain intact when in the hexadecane phase but vanish in the aqueous phase to facilitate hydrogen bonding to water. We find that the optimal hexadecane conformations do indeed display essentially the same basic hydrogenbonding patterns as the optimal gas-phase conformations. However, this is also true to a large extent for the SM2-optimized conformations. In the conformations optimized with SRP and SRP-C, the intramolecular hydrogen-bonding patterns are either greatly altered or completely absent. The difference in the number of hydrogen bonds in the hexadecane-phase and aqueousphase conformations does not by itself explain the variance in log Ph-w seen among isomers, although it must, of course, make a contribution. Acetyl Glucopyranosides. Results for ∆G0S and log Ph-w from optimal gas-phase conformations as a function of the number of acetyl substituents are shown in Figure 6, a and b, respectively, and from optimal solution-phase conformations in Figure 7, a and b, respectively. These values are qualitatively similar to those observed for the methyl-substituted glucopyranoses, with the exception that the SRP model does not predict clearly an increase in ∆G0w as a function of the number of acetyl groups. In Figure 6a, the SRP model predicts a small increase in ∆G0w from zero to three acetyl substituents and then a decrease from two to five. The slope of a linear fit to this decrease is about the same magnitude as the increase seen in the two other aqueous models. This complex behavior is absent when the conformational response to solvent is included; 0 is almost independent of Figure 7a shows that ∆Gw(SRP) the number of acetyl substituents. As in the case for the methyl-substituted compounds, calculated ∆G0S values for most groups of structural isomers fall within ranges that exceed the rms errors noted for the solvation models. Also, the range of ∆G0S and of log Ph-w values for almost all groups of isomers is larger when calculated from solution-phase conformations. The similarity of the linear correlations 0 with the number of acetyls in of ∆G0h and ∆Gw(SM2) Figures 6a and 7a indicate that the effect due to conformational response to solvent is small, which is reflected in the similarity of linear correlations of log

Energy & Fuels, Vol. 11, No. 3, 1997 653

Figure 6. (a, top) Free energies of solvation for acetylsubstituted glucopyranose from optimal gas-phase conformations. Lines were drawn according to least-squares fits to the data with slopes of 1.5 for SM2, 1.7 for SRP-C, and -1.4 for hexadecane. The correlation coefficients are 0.9, 0.8, and 1.0, respectively. A smooth curve was drawn through the SRP data. (b, bottom) The log Ph-w values for acetyl-substituted glucopyranose from optimal gas-phase conformations. Lines were drawn according to least-squares fits to the data with slopes of 2.08 for SM2, 0.8 for SRP, and 2.3 for SRP-C. The correlation coefficients are 1.0, 0.7, and 1.0, respectively.

Ph-w with the number of acetyls in Figures 6b and 7b when SM2 is employed. Average values calculated using SM2, as represented by the linear correlations in Figures 6b and 7b, also show a small effect due to the conformational response to solvent. The increase in ∆G0w with the number of acetyl groups predicted by the SM2 and SRP-C models, as given by the slopes in Figures 5a and 6a, are about half of those indicated for the methyl-substituted compounds (Figures 3a and 4a). In contrast, ∆G0h decreases with the number of acetyl substituents about 3-fold less than the decrease observed in Figures 2a and 3a for the methyl-substituted compounds. The increase in log Ph-w (using SM2 and SRP-C) with the number of acetyl groups is only about 85% of that with the methyls. Figure 8 shows the conformational response effect on ∆G0S of acetyl compounds to solvent. The average 0 change in ∆G0h and in ∆Gw(SM2) due to geometrical relaxation in solvent is less than 1 kcal/mol for all acetyl glucopyranoses, which is similar to the indication for the methyl derivatives (Figure 5). The ∆G0w decreases calculated using the SRP and SRP-C models are similar and much larger than those shown in Figure 5. The 0 0 and in ∆Gw(SRP-C) due to average lowering in ∆Gw(SRP) conformational relaxation, which is largest for disubstituted compounds (ca. 5 kcal/mol), is not a linear function of the number of substituents as noted for the methyl compounds. The corresponding average lowering of log Ph-w as a function of the number of substit-

654 Energy & Fuels, Vol. 11, No. 3, 1997

Figure 7. (a, top) Free energies of solvation for acetylsubstituted glucopyranose from optimal solution-phase conformations. Lines were drawn according to least-squares fits to the data with slopes of 1.5 for SM2, 0.4 for SRP, 2.3 for SRP-C, and -1.4 for hexadecane. The correlation coefficients are 0.9, 0.2, 0.9, and 0.9, respectively. (b, bottom) The log Ph-w values for acetyl-substituted glucopyranose from optimal solution-phase conformations. Lines were drawn according to least-squares fits to the data with slopes of 2.1 for SM2, 1.3 for SRP, and 2.7 for SRP-C. The correlation coefficients are 1.0, 0.8, and 1.0, respectively.

Figure 8. Average effect on ∆G0S of conformational response of acetyl-substituted glucopyranose.

uents parallels that seen for ∆G0S, thus being independent of the number of acetyls. The lowering of the log Ph-w values due to the conformational response to water is appreciable when SRP or SRP-C is employed but negligible when SM2 is used. As expected from the large lowering of ∆G0w due to the geometrical relaxation for acetyl compounds, the rms deviations of corresponding heavy atoms of superimposed gas-phase and solution-phase conformations are larger than those observed for methyl compounds, ranging from 0.02 to 1 Å. Hexadecane-phase conformations invariably deviate less from gas-phase conformations than do the aqueousphase conformations.

Trohalaki and Pachter

As in the methyl-substituted glucopyranoses, the hydrogen bonds between adjacent donors and acceptors evident in the gas-phase conformations remain essentially intact in the optimal hexadecane-phase conformations and also, to a large extent, in the SM2optimized aqueous-phase conformations. In the conformations optimized with SRP and SRP-C, the intramolecular hydrogen-bonding patterns are either greatly altered or completely absent. As seen with the methyl compounds, the variance in log Ph-w for a group of isomers is not due soley to the difference in the number of hydrogen bonds in the hexadecane-phase and aqueous-phase conformations. Since methyl-substituted glucopyranoses contain functionalities included in the parametrization of SRP and acetyl-substituted glucopyranoses have ester groups, which were not included in the parametrization set, it can be inferred from the qualitative agreement between SM2 and SRP for methyl compounds and the disagreement between these models when applied to acetyl compounds that SRP cannot be extended to acetylsubstituted glucopyranose. The qualitative agreement between SM2, SRP, and SRP-C for methyl compounds and between SM2 and SRP-C for acetyl compounds indicates that the inclusion of COGs corrects the shortcomings of SRP as applied to compounds containing ester functionalities. It is important to use consistently the same model when comparing log Ph-w values for a set of molecules since the variance in log Ph-w among isomers is of the same order as the difference in log Ph-w computed for the same molecule with different models. Conclusions The range of log Ph-w values calculated with MO methods for a group of structural isomers compared to the single value obtained from sums of empirical atomic contributions illustrate the abundance of information that is unavailable when relying solely on empirical log P methods. HINT! predicts log Po-w to increase by 0.69 for each additional methyl substituent and by 0.84 for each additional acetyl substituent on D-glucopyranose regardless of position. Since the empirical and MO methods model different solvent systems, results from the two methods cannot be compared. All three quantum mechanical aqueous solvation models based on MO theory which we employed predict that on average, ∆G0w and log Ph-w increase linearly with the number of methyl substitutions on D-glucopyranose. Both SM2 and SRP-C models predict that ∆G0w increases with the number of acetyl substituents but only about half as quickly as with the number of methyl groups. The free energy of solvation in hexadecane is predicted to decrease slightly with the number of methyl substituentssan order of magnitude smaller than the increase observed for ∆G0w. For acetyl-substituted compounds, however, the magnitude of the decrease is about the same as that noted for the increase for ∆G0w with the number of acetyls and about 3 times the decrease observed with the number of methyls. Although it is difficult to rank models without the benefit of comparison with experiment, SRP and SRP-C appear to better reflect reality than SM2 because they predict optimal aqueous-phase conformations consistent

Partition Coefficients of Fuel System Icing Inhibitors

with solute-water hydrogen bonding whereas SM2 does not. However, when making a quick assessment of general trends in log Ph-w from single-point calculations of gas-phase conformations, SM2 is equally adequate. We note that inclusion of COGs is required to extend the application of SRP to compounds containing ester groups. Future models should be applicable to all classes of compounds without modification. The extent of the effect of conformational relaxation in response to solvent, in addition to the electronic response, depends on the solvent and the solvation model applied. The inclusion of conformational relaxation increases the range of ∆G0S and log Ph-w values for almost all groups of isomers. The conformational response to hexadecane is small, as expected, resulting in a ∆G0h lowering of less than 1 kcal/mol, almost independent of the number of substituents. The SM2 magnitude of the conformational response to water is the same as that shown for hexadecane. In contrast, both the SRP and SRP-C models predict a substantial lowering in ∆G0S, which is larger for acetyl glucopyranosides than for methyl derivatives. Predicted ∆G0w and log Ph-w values for a given compound generally decrease when considering only the electronic response to solvent, depending on the model applied: SRP-C > SM2 > SRP. When geometrical relaxation is included, values decrease according to SM2

Energy & Fuels, Vol. 11, No. 3, 1997 655

> SRP-C > SRP, except for the tetra- and pentaacetyl compounds whose values decrease as SRP-C > SM2 > SRP. Assuming that the inclusion of conformational response to solvent yields more accurate log Ph-w values, all models predict that preferential partition into fuel requires at least four methyl substituents. With the exception of the SM2 prediction that 1,3,4,6-tetramethyl-β-D-glucopyranoside will partition equally between water and fuel, all models predict that all tetramethyl compounds will preferentially partition into fuel. The SM2 model predicts that only one of the tetraacetyl isomers, 1,2,3,6-tetraacetyl-β-D-glucopyranoside, will preferentially partition into fuel whereas the SRP-C model predicts that all but two of them, 1,2,3,4-tetraacetyl-β-D-glucopyranoside and 1,2,3,6-tetraacetyl-β-D-glucopyranoside, will. Both models predict such partitioning for pentaacetyl glucopyranosides. Acknowledgment. The authors acknowledge a productive collaboration with Dr. George Mushrush of George Mason University and the Naval Research Laboratory, who proposed the alternate FSIIs investigated in this study. We also thank Drs. Chris Cramer and Don Truhlar, and Mr. Dave Giesen, for their kind assistance with AMSOL. EF960166E