1683
J . Phys. Chem. 1990, 94, 1683-1686 is accompanied by formation of the stable neutral species CuH(IF). Close examination of the cross section for this process shows that it has a second feature which begins at -0.3 eV (Figure 2c). This feature could be the result of formation of a different structure for the C 2 H 3 0 +ion, either CH2=COH+ or the cyclic species, both of which should be formed in endothermic reactions. Of the three metal ions studied here, Cu+ is the only one which reacts with ethylene oxide to form M C H 2 0 + (reaction 16). The cross section for this product, however, is very small since it competes directly with formation of the thermodynamically favored CuCH2+. In the Co and Ni systems, this product may not be observed simply because there are many more competing channels.
Summary The reactions of Co+, Ni+, and Cu+ with c-C3H6and c-C2H40 are studied by using guided ion beam mass spectrometry. Revised bond energies are found for Do(Co+-CH2) and Do(Ni+-CH2) and a new value for Do(Cu+-CH2)is reported. These are listed in Table VI. It is shown that these values are more reliable than those determined previously and that they are in better agreement with the periodic trends correlation of ref 2. Further, these values lead to a more comprehensive periodic trends analysis detailed elsewhere.30
In addition to the bond energies for MCH2+, we also evaluate values for Do(M-H), where M = Co, Ni, and Cu; Do(M+-O) and Do(M-0) where M = Co and Ni; as well as lower limits to both Do(M+-C2H4) and Do(M+-C2Hz) for all three metal ions. These are included in Table VI. The bond energies derived here for the MH species agree well with the results of another recent study2*and are used to revise our suggested values for Do(M-H). Likewise, the MO+ bond energies for M = Co and Ni are in good agreement with values derived from the reaction of M+ with 02.33 The reaction mechanism for the interaction of metal ions with these cyclic compounds is discussed in some detail. An alternative to the commonly assumed mechanism is suggested which can also explain several minor reactions observed in these studies. This mechanism also provides an explanation for the observation of an activation barrier in excess of the reaction endothermicity for formation of CuCH2+ from cyclopropane. Acknowledgment. This work was funded by the National Science Foundation, Grant No. CHE-8796289. Registry No. Cot, 16610-75-6; Ni+, 14903-34-5;Cut, 17493-86-6; COCH~',76792-07-9; COCZH~', 124687-61-2; COC~H~', 124687-59-8; CoH', 12378-09-5;COO', 60131-09-1; NiCH2', 87453-14-3; NiC2H2+, 124687-62-3;NiC2H4+, 124687-60-1;NiOt, 60131-11-5; CuCH2+, 117130-08-2; CUCZH~',45326-64-5;CIIC~H~', 67729-41-3; CUCH~O', 124687-63-4; cyclopropane, 75-19-4;ethylene oxide, 75-21-8.
Relative Partition Coefficients for Organic Solutes from Fluid Simulations William L. Jorgensen,* James M. Briggs, and M. Leonor Contrerast Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: June 16, 1989)
A procedure is noted for obtaining the difference in partition coefficients (log P) for two solutes between two solvents. Fluid simulations are required in which one solute is mutated to the other in both solvents, and the changes in free energies of solvation are computed. The method is illustrated for eight pairs of organic solutes partitioning between water and chloroform. Monte Carlo statistical mechanics simulations are used with statistical perturbation theory to calculate the requisite free energy changes. The results are compared with experimental log P data and relative free energies of hydration. For the present solute pairs, the differences in partition coefficients are dominated by the differences in hydration. Such computations are useful for providing estimates of the effects of substituent changes on partitioning behavior and for further testing of intermolecular potential functions. The paper also contains previously unreported potential function parameters for acetic acid, methyl acetate, acetone, and pyrimidine and a summary of thermodynamics results for the corresponding pure liquids.
The distribution of an organic solute between water and nonpolar media is an important parameter for structure-activity analyses in pharmacological research.l" Many procedures have now been devised to estimate the logarithm of the partition coefficient (log P) for a solute between water and several solvents, especially l - ~ c t a n o l . ~ These -~ methods mostly feature additive schemes with atom and group increments or correlations involving solvent-accessible surface areas. The associated parameters have been selected to give the best fit to experimental log P data. In the present paper, a more fundamental, theoretical approach to computing differences in partition coefficients is explored based on fluid simultaneous at the atomic level. If one considers the thermodynamic cycle below for two solutes, A - B
solvent 1: AG,w
solvent 2:
J
A G W )
JAG
m
1 and 2 in terms of the free energies of transfer. From the cycle, eq 3 is obtained which yields eq 4. The last expression associates AGt(B) - AGt(A) = AGz(AB) - AGI(AB) (3) A log P = log PB - log PA = (AG,(AB) - AG,(AB))/2,3RT (4) the difference in log P's with the difference in free energies for mutating A to B in the two solvents. If contributions from internal degrees of freedom are ignored, AG, and AGZ are just the difference in free energies of solvation for A and B. For example, if solvent 1 is water and solvent 2 is a nonpolar solvent, a positive A log P implies that the change from A to B results in greater affinity for the nonpolar solvent. This comes about by the change in solvation free energies for A going to B being less favorable in water than in the nonpolar solvent (AGI > AG2). Fortunately for the present purposes, AC, and AG2 are available from Monte Carlo or molecular dynamics simulations in which
A - 0
AG(AB)
AGt(A) = -2.3RT log P A AGt(B) = -2.3RT log Ps
( 1 ) Leo, A.; Hansch, C.; Elkins, D. Chem. Reu. 1971,71,
(1)
(2) A and B, in two solvents, log P for the solutes is defined in eq 'Permanent address: Chemistry Department, University of Santiago de Chile, Santiago-2, Chile.
525.
(2) Hansch, C.; Leo, A. Substituenr Constants for Correlation Analysis in Chemistry and Biology; Wiley: New York, 1979. ( 3 ) Partition Coefficient;Determination and Estimation; Dunn, W. J., 111, Block J. S., Pearlman, R. S.,Eds.; Pergamon: New York, 1986. (4) Dum, W. J., Ill; Koehler, M.G.; Grigoras, S. J . Med. Chem. 1987, 30, 1121. ( 5 ) Klopman, G.;Namboodiri, K.; Schochet, M. J . Comput. Chem. 1985, 6, 28.
0022-3654/90/2094- 1683$02.50/0 0 1990 American Chemical Society
1684 The Journal
ef Physical
Chemistry, Vol. 94, No. 4, 1990
A is mutated to B in the solvent^.^,^ Computations of this type
have now been used in a range of applications,8aincluding some preliminary results for relative partition coefficients8 It may be noted that absolute log P s could also be computed by directly calculating the free energy of transfer. This would require taking the difference in absolute free energies of solvation for the solute which could be obtained from simulations in which the solute is made to vanish in the two solvent^.^^^^ However, the computational requirements would be much greater than for the calculation of A log P for solutes of similar size and the results would be prone to greater imprecision. lnterconversions of eight solute pairs have been considered in this initial study, methanol to ethylamine, methanethiol and ethane, acetic acid to acetamide, acetone and methyl acetate, and pyrazine to pyrimidine and pyridine. The selected solvents are water and chloroform. These choices were made for the variety of functional groups in the solutes as well as for the availability of experimental data and potential function parameters. Besides assessing the viability of this approach to estimating A log P, the present calculations provide some insight into the variations from the AG1 and AG2 components in eq 4 and additional tests of the potential functions. Computational Elements
Fluid Simulations. The free energy changes for mutating one solute to another were computed in the same manner as previously de~cribed.~,"Briefly, Monte Carlo simulations were carried out in the isothermal-isobaric ensemble at 25 "C and 1 atm for systems typically consisting of the solute plus 216 or 265 solvent molecules in a cubic cell with periodic boundary conditions. All atoms in the solute and solvent molecules were explicitly represented except for CH, groups which were treated as united atoms centered on the carbon. The free energy changes, ACl and AC2, were obtained via a series of 3-5 separate simulations with statistical perturbation theory.I2 Thus, solute A was gradually converted to B along the series by using a coupling parameter, A, which represents the linear admixture of A and B as A goes from 0 (A) to 1 (B). The 3-5 simulations yielded 6-10 incremental free energy changes by perturbing to both smaller and larger A in each simulation, which is known as double-wide sampling7 The incremental values are provided by eq 5 which equates GI - CJ = -kBT In (exp(-(H, - H , ) / b T ) ) , (5) the free energy change for perturbing from A, to A, with an average over the energy difference between the systems at AJ and A,, HI - HJ.12 The average is obtained by configurational sampling for the system at A:, Each simulation entailed an equilibration period for 5 X lo5 to 1 X IO6 configurations starting from equilibrated boxes of solvent, followed by averaging for 2 X lo6 configurations. Little drift in the averages was found during the last 1 X lo6 configurations, consistent with prior experience.'JI Also, the results for the acetic acid to methyl acetate conversion in water were found to be the same with the use of 8 or 10 increments. Other details are that Metropolis and preferential sampling were employed, and the ranges for attempted translations and rotations of the solute and solvent molecules were adjusted to give a ca. 40% acceptance rate for new configuration^.^," The intermolecular interactions were spherically truncated at 8.5 A in water and 12 A in chloroform based roughly on the center-of-mass separations with quadratic feathering over the last 0.5 A. The Monte Carlo simulations were executed on Sun 4 and Gould 32/8750 computers with the BOSS program that has been developed in our laboratory. (6) Tembe, B. L.; McCammon. J . A. Comput. Chem. 1984, 8, 281. (7) Jorgensen, W. L.; Ravimohan, C. J . Chem. Phys. 1985, 83, 3050. (8) (a) Jorgensen, W. L. Acc. Chem. Res. 1989,22, 184. (b) Essex, J. W.; Reynolds, C. A.; Richards, W. G. J . Chem. Soc., Chem. Commun. 1989, 1152. (9) Cieplak, P.; Kollman, P. A. J . Am. Chem. SOC.1988, 110, 3734. (10) Jorgensen, W. L.; Blake, J. F.; Buckner, J. K. Chem. Phys. 1989, 129, 193. ( 1 I ) Jorgensen, W. L.; Briggs, J. M. J . Am. Chem.Soc. 1989, I l l , 4190. (12) Zwanzig, R. W. J . Chem. Phys. 1954, 22, 1420.
Jorgensen et al. Intermolecular Potential Functions. The intermolecular interactions were described in the standard Coulomb plus Lennard-Jones format (eq 6). The interactions occur between all AEab = x C ( q i q j e 2 / r i j+ AV/rijl2- C../r.6) JJ U i
(6)
J
intermolecular pairs of interaction sites which are located on the atoms. However, the TIP4P model has been used for water which has a fourth site located 0.15 A from the oxygen on the bisector of the HOH angIe.l3 The charges and Lennard-Jones parameters have been selected to yield correct thermodynamic and structural results for pure liquids and reasonable interaction energies and geometries for gas-phase c ~ m p l e x e s . ' ~ The parameters for water,13 methanol,I5 methylamine," methanethiol,16 ethane,17 and acetamideI8 have been reported previously. Though the parameters for chloroform, pyridine, and pyrazine have been used in two communication^,'^^^^ more complete characterization is provided here. In addition, the parameters for acetic acid, methyl acetate, acetone, and pyrimidine are reported for the first time. A summary is given in Table I. It should be noted that the A's and Cs in eq 6 are related to the d s and 6's in Table I by Aii = 4tiui12and Cii = 49~:. Furthermore, the adopted combining rules are Aij = (AiiAj,)l/2and Cij = (CiiCjj)'/2. A summary of key thermodynamic results from these potential functions is presented for the corresponding pure liquids in Table 11. The results were obtained from Monte Carlo simulations using well-established procedure^.'^-^^ The sample sizes were 128-267 molecules in cubic cells with periodic boundary conditions. The main point from Table I1 is that the potential functions yield liquid densities and heats of vaporization with average deviations of 1-2% from experimental values. The geometries of the individual molecules have been taken from gas-phase experimental results in all cases.1*18,21,22It should be noted that these geometries and the charges in Table I yield reasonable dipole moments for the isolated molecules, as summarized in Table 111. As discussed previously, the simple partial charge model often requires somewhat enhanced dipole moments to produce correct liquid proper tie^."^'^^'^^^^ In all the calculations, the bond lengths and bond angles have been kept fixed. Torsional motion was included in the simulations of the pure liquids about the C-N bond in acetamide and the C-0 bond in acetic acid and methyl acetate, the only possible cases. For these systems, a two-term Fourier series (eq 7) suffices to describe the torsional V ( 0 ) = (Vl/2)(1 - cos 0) (V2/2)(1 -cos 2 0 ) ( 7 )
+
potential. For primary amides, the rotational barrier is ca. 20 kcal/mol, so VI and V2 are taken as 0.0 and 20.0 kcal/mol for acetamide.18 For acetic acid and methyl acetate, theoretical and experimental estimates of the E / Z energy differences are 5-9 kcal/mol with a barrier of 9-13 k c a l / m 0 1 . ~ ~It~was ~ ~ decided to set Vl = 5.0 and V2 = 6.2 kcal/mol for both molecules which fits the MM2 results for acetic acid.22 This gives an E / Z energy difference of 5.0 kcal/mol and a barrier of 8.9 kcal/mol. In practice, at 25 OC only the torsional wells for the Z conformers are sampled. Furthermore, for the A log P calculations, torsional motion was not included, and acetic acid and methyl acetate were fixed in the Z forms at 0 = 0 ' . It seems unlikely that there would (13) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J . Chem. Phys. 1983, 79, 926. Jorgensen, W. L.; Madura, J. D.Mol. Phys. 1985, 56, 1381. (14) Jorgensen, W. L.; Tirado-Rives, J. Am. Chem. SOC.1988, 110, 1657. (15) Jorgensen, W. L. J . Phys. Chem. 1986. 90, 1276. (16) Jorgensen, W. L. J . Phys. Chem. 1986, 90, 6379. (17) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J . Am. Chem. SOC. 1984, 106, 6638. (18) Jorgensen, W. L.; Swenson, C. J. J. Am. Chem. SOC.1985,107,569. (19) Jorgensen, W. L.; Boudon, S.; Nguyen, T. B. J . Am. Chem. Soc. 1989, 1 1 1 , 755. (20) Jorgensen, W. L. J . Am. Chem. SOC.1989, 1 1 1 , 3770. (21) (a) Harmony, M. D.; Laurie, V. W.; Kuczkowski, R. L.; Schwendeman, R. H.; Ramsay, D. A.; Lovas, F. J.; Lafferty, W. J.; Maki, A. G. J. Phys. Chem. ReJ Data 1979,8, 619. (b) Cradock, S . ; Liescheski, P. B.; Rankin, D.W . H.; Robertson. H. E. J . Am. Chem. SOC.1988, 110, 2158. (22) Allinger, N. L.; Chang, S . H.-M. Tetrahedron 1977, 33, 1561. (23) Wiberg, K. B.; Laidig, K. E. J . Am. Chem. SOC.1987, 109, 5935.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990
Partition Coefficients for Organic Solutes TABLE I: OPLS Potential Function Parameters for Organic Molecules and Water site a, e a. A c, kcal/mol CH,CH, 0.0 3.775 0.207 CHI CH,NH2 0.207 0.200 3.775 CH3 0.170 -0.900 3.250 N 0.0 0.350 0.0 H
CHSOH CH3 0 H
0.265 -0.700 0.435
CH,
0.180 -0.450 0.270
3.775 3.070 0.0
0.207 0.170 0.0
CH$H S
H
3.775 3.550 0.0
0.207 0.250 0.0
CH3 COCH3 CH3 C 0
0.062 0.300 -0.424
3.910 3.750 2.960
0.160 0.105 0.210
CH3CONHZ CH, C 0
N H
0.0 0.500 -0.500 -0.850 0.425
3.910 3.750 2.960 3.250 0.0
0.160 0.105 0.210 0.170 0.0
CH,COOH CH, C O(=C) 0
H
0.080 0.550 -0.500 -0.580 0.450
3.910 3.750 2.960 3.000 0.0
0.160 0.105 0.210 0.170 0.0
CH,COOCH, CH,(-C) C O(=C) 0
C H3 (-0)
0.050 0.550 -0.450 -0.400 0.250
3.910 3.750 2.960 3.000 3.800
0.160 0.105 0.210 0.170 0.170
Pyridine N C3H C4H
-0.490 0.230 -0.030 0.090
N CH
-0.490 0.245
N
C2H C4H C5H
-0.490 0.410 0.245 0.080
CH CI
0.420 -0.140
0
0.0 0.520 -1.040
C2H
3.250 3.750 3.750 3.750
0.170 0.1 IO 0.1 10 0.1 10
Pyrazine 3.250 3.750
0.170 0.110
Pyrimidine 3.250 3.750 3.750 3.750
0.170 0.110 0.1 IO 0.1 IO
CHCI,
H M'
3.800 3.470
H2O
3.15365 0.0 0.0
0.080 0.300 0.1550 0.0 0.0
" M is a point on the bisector of the HOH angle, 0.15 A from the oxygen toward the hydrogens.
be significantly different contributions to AG, and AG2 in eq 4 from the internal degrees of freedom.
Results and Discussion The principal thermodynamic results from the present calculations a r e shown in Table IV along with the available experimental data on differences in free energies of hydration and A log P for chloroform/water. The reported statistical uncertainties
1685
TABLE 11: Densities and Heats of Vaporization for the Liquids' liquid T , OC p(calc) p(exptl) AHJcalc) AHJexptl) 3.52b -88.63 0.545 0.546b 3.52 CH,CH, 6.17d 6.13 -6.3 0.701 0.694' CH,NH2 8.94' 0.787c 9.05 25.0 0.759 CH3OH 5.878 5.83 0.88g 5.96 0.866 CH3SH 7.40' 7.41 0.762 0.784h 25.0 CHpCOCH, 15.65 0.997 0.999 85.0 CH3CONH2 12.77 12.49' 1.042 1.044' 25.0 CH3COOH 100.0
0.961
0.958"
11.70
1 1.30"
7.91 7.57p 0.904 0.927O CH+2OOCHg 25.0 9.61' 9.59 0.962 0.9784 25.0 pyridine 10.65 1.036 1.03l5 61.0 pyrazine 11.95* 1.139' 11.36 1.060 25.0 pyrimidine 7.48 7.430 I .473" 1.480 25.0 CHCI, 10.51* 1.002 10.64 0.997w 25.0 H20 Densities are in g/cm3 and heats of vaporization are in kcal/mol. bRossini, F. D.; Pitzer, K. S.;Arnett, R. C.; Braun, R. M.; Pimentel, G. C. Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds; American Petroleum Institute Research Project 44; Carnegie Press: Pittsburgh, 1953. Egloff, G. Physical Constants of Hydrocarbons, ASTM Technical Publication no. 109A; American Society for Testing and Materials: Philadelphia, 1963. 'Felsing, W. A.; Thomas, A. R. Ind. Eng. Chem. 1929, 21, 1269. dAston, J. G.; Siller, C. W.; Messerly, G. H. J. Am. Chem. SOC. 1937, 59, 1743. CWilhoit,R. C.; Zwolinski, B. J. J . Phys. Chem. ReJ Data, Suppl. I 1973, 2. fBerthoud, A,; Brum, R. J . Chim. Phys. Phys.-Chim. Eiol. 1924, 21, 143. ERussell, H., Jr.; Osborne, D. W.; Yost, D. M. J . Am. Chem. SOC.1942,64, 165. TRC Thermodynamic Tables: Non-Hydrocarbons; Table 23-2-1-(1.1130)-a; Texas A&M University System: College Station, TX, 1965; p A-5370. 'Smith, 9. D.; Srivastava, R. Thermodynamic Daia for Pure Compounds. Part A: Hydrocarbons and Ketones: Elsevier: Amsterdam, 1986; p 622. J Weast, R. C., Ed. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1988. 'Riddick, J. A.; Bunger, W. 9.;Sakano, T. K. Organic Solvents; Wiley: New York, 1986. 'Guthrie, J. P. J . Am. Chem. SOC.1974, 96, 3608. "Hales, J. L.; Gundry, H. A.; Ellender, J. H. J . Chem. Thermodyn. 1983, 15, 211. "Armitage, J. W.; Gray, P. Trans. Faraday SOC.1962, 58, 1746. OChadwell, H. M. J . Am. Chem. SOC. 1926, 48, 1912. PGatta, G. D.; Stradella, L.; Venturello, P. J . Solution Chem. 1981, 10, 209. qMurthy, N. M.; Subrahmanyam, S. V. Ind. J . Chem. 1980, 19A, 724. 'Spencer, J. N.; Holmboe, E. S.; Kirshenbaum, M. R.; Barton, S. W.; Smith, K. A.; Wolbach, W. S.; Powell, J. F.; Chorazy, C. Can. J . Chem. 1982, 60, 1183. Windholz, M.; Budavari, S.; Blumetti, R. F.; Otterbein, E. S., Eds. The Merck Index; Merck & Co., Inc.: Rahway, NJ, 1983; No. 7859. 'Nabavian, M.; Sabbah, R.; Chastel, R.; Laffitte, M. J . Chim. Phys. Phys.-Chim. Biol. 1977, 74, 115. "Sanni, S. A.; Hutchison, P. J . Chem. Eng. Data 1973, 18, 317 "Majer, V.; Svab, L.; Svoboda, V. J . Chem. Thermodyn. 1980, 12, 843. WKell,G. S. J . Chem. Eng. Data 1975, 20, 97. *Dorsey, N. E. Properties of Ordinary Water Substance; Reinhold: New York, 1940; pp 258, 574, 616.
TABLE 111: Calculated and Exwrimental Diwle Moments molecule r(calc), D r(expt1): D 0 CH3CH3 0 1.57 1.31 CH3NH2 1.70 2.22 CH90H 1.52 2.22 CH3SH 2.96 2.88 CH3COCHj 4.34 3.76 CH3CONH2 1.74 1.51 CH3COOH 1.72 1.44 CH,COOCH, 2.16 2.19 pyridine 0 0 pyrazine 2.83 2.33b pyrimidine 1.01 1.07 CHC13 2.18 1.85 H20 Weast, R. C., Ed. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1988; p E52-54. bMcClellan, A. C. Tables of Experimental Dipole Moments; Rahara Enterprises: El Cerrito, 1974; Vol 11.
for the computed values are f 1u and were obtained from separate averages over blocks of 1 X los to 2 X lo5 configurations. For the relative free energies of hydration, experimental data are available for the two series involving methanol and acetic acid.
1686 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990
Jorgensen et al.
TABLE I V Differences in Free Energies of Solvation (kcal/mol) and in the Logarithms of the Cbloroform/Water Partition Coefficients calc AG(A-+B) exptl AG(A-B)’ log Ps - log PA B H,O CHClt H,O calc exptlb A 1.3 f 0.1 0.30 f 0.03 CHjOH CHpNH, 0.5 0.7 f 0.1 0.2 to 0.8 3.1 f 0.1 0.02 f 0.02 3.8 2.3 f 0.1 CHjOH CHjSH 0.84 f 0.04 6.8 f 0.2 6.9 4.4 f 0.1 CHlCH, CH30H -4.0 f 0.2 -1.20 f 0.05 -3.0 -2.1 f 0.2 -0.2 to -1.3 CHjCOOH CH,CONH, 0.18 f 0.05 2.9 2.7 f 0.2 1.4 to 2.4 3.9 f 0.2 CHjCOOH CHjCOCHj 5.0 f 0.2 2.4 to 2.9 -0.49 f 0.09 3.4 4.0 f 0.2 CHjCOOCH3 CHjCOOH -0.3 f 0.2 -0.1 f 0.1 -0.14 f 0.05 pyrazine pyrimidine 0.34 f 0.04 1.5 f 0.1 2.4 f 0.1 pyrazine pyridine Reference 24.
Reference 30 and 31.
Overall, the average error for the six interconversions is 0.9 kcal/mol. The computed ordering of the free energies of hydration is also correct for the two series, Le., C H 3 0 H < C H 3 N H 2< CH3SH < CH3CH3 and CH3CONH2 < CH3COOH < (CH3)&O < CH,COOCH,. However, the computed range for the second series of 9.0 kcal/mol is significantly greater than the experimental spread of 6.4 kcal/mol. While acetamide is computed to be too hydrophilic relative to acetic acid, acetone and methyl acetate are too hydrophobic. There is some uncertainty in the experimental data; however, it is probably not greater than ca. f0.2k c a l / ~ n o I . ~Thus, ~ J ~ fine tuning of the potential functions is still possible to perfect simultaneously the pure liquid and aqueous solution results. Among the nitrogen heterocycles considered here, the free energy of hydration from the gas phase has been reported only for p y r i d i ~ ~ eThe . ~ result ~ ~ ~ ~of -4.7 kcal/mol, using molar concentration units for both phases, can be combined with the results in Table IV to yield predicted AGhyd’Sof -7.1 kcal/mol for pyrazine and -7.4 kcal/mol for pyrimidine. However, experimental data are available for 2-methylpyridine” and 2-methyIpyra~ine.~~ The difference of 0.9 kcal/mol is less than the present prediction of 2.4 kcal/mol for the parent compounds. Some reservation about the accuracy of the experimental difference can be expressed since it comes from two different sources. Furthermore, one source finds a difference of 0.30 kcal/mol between 2-methypyridine and 2e t h ~ l p y r i d i n e ,while ~ ~ the other obtains 0.05 kcal/mol for 2methylpyrazine vs 2 - e t h y l p y r a ~ i n e .The ~ ~ small difference predicted here favoring the hydration of pyrimidine over pyrazine seems reasonable. The numbers and types of hydrogen-bonding loci are the same; however, pyrimidine has a significant dipole moment (Table 111). The computed differences in free energies of solvation for the eight pairs of solutes in chloroform are comparatively small. Clearly, the replacement of the solute-water hydrogen bonding with weaker dipole-dipole interactions is responsible for the leveling effect. The weaker interactions in the nonaqueous medium also lead to smaller statistical fluctuations in the simulations and higher precision for the calculated free energy changes. The range of the differences in free energies of solvation spans only 2 kcal/mol in chloroform as compared to 11 kcal/mol in water. The individual differences do have the same sign in both solvents except for the acetic acid/methyl acetate pair. In the absence of strong hydrogen bonding, the molecule with the larger dipole moment could be expected to be more favorably solvated.29 This is only borne out by about half of the results in chloroform; the pyrazine/pyridine pair provides a striking exception that points out the importance of local electrostatic interactions or higher multipole moments. The largest changes (5-6 kcal/mol) in the two series are for the most hydrophobic solutes, ethane and methyl Pearson, R. G . J. Am. Chem. SOC.1986, 108, 6109. Abraham, M. H.J. Chem. SOC.,Forodoy Trans. I 1984, 80, 153. Hine, J.; Mookerjee, P. K. J. Org. Chem. 1975, 40, 292. Andon, R. J. L.; Cox, J. D.; Herington, E. F. G . J . Chem. Soc. 1954,
3188. (28) Buttery, R. G.; Bomben, J. L.; Guadagni, D. G.; Ling, L. C. J. Agric. Food Chem. 1971, 19, 1045. (29) (a) Abraham, R. J.; Bretschneider, E. In Internal Rorarion in Molecules; Orville-Thomas, W. J.; Ed.; Wiley: London, 1974;Chapter 13. (b) Onsager, L. J. Am. Chem. SOC.1936, 58, 1486.
acetate, while changes in still 3-4 kcal/mol are found for the pairs with methanethiol and acetone. In comparison to the reference compounds, methanol and acetic acid, these solutes experience significantly diminished hydrogen bonding in water. Unfortunately, experimental data do not appear to have been reported for free energies of solvation in chloroform. Combination of the computed results for AG(AB) in water and chloroform leads to the calculated A log P values in Table IV via eq 4. Positive values of A log P indicate that the change from A to B results in increased affinity for the chloroform solution over water. Experimental data are available for comparison in four of the eight ~ a s e s . ~ O There * ~ ~ is often some spread in alternative experimental log P values, so the experimental A log P‘s are shown as ranges in Table IV. For example, six measurements for log P of acetic acid cover from -1.2 to -1.7 and results of -1.9, -2.0, and -2.5 have been reported for acetamide.%J1 Consequently, the range shown in Table IV is -0.2 to -1.3. The qualitative accord between theory and experiment for A log P is fine; there are no errors in sign, and the four absolute values are in the correct order. However, the computed range of values for the acetic acid series is too broad. This can be traced back to the overly large spread in calculated relative free energies of hydration discussed above. It is important to note that the sign and magnitude of the calculated A log P’s closely parallel the relative free energies of hydration (AC,(AB) = AAG,,). In fact, A log P = 0.64AAGhyd 0.22 with a standard deviation of 0.33 and a correlation coefficient of 0.990. This reflects the limited variation in the free energies of solvation in chloroform and emphasizes the dominance of the free energies of hydration in determining the partitioning behavior. For the nitrogen heterocycles, a log P of 1.43 has been measured for pyridine in c h l o r ~ f o r m / w a t e r . ~ ~Combination with the calculated A log P values in Table IV then yields log P estimates of -0.1 f 0.1 for pyrazine and -0.2 f 0.1 for pyrimidine. Analogously, the experimental results of -1.3 f 0.1 for the log P of methano130can be merged with the computed A log P‘s to assign log P values of 1.0 f 0.1 to methanethiol and 3.1 f 0.1 to ethane. These predictions stand for future experimental tests. Overall, the present methology provides a flexible and fundamental approach to estimating changes in log P that accompany structural modifications. The initial results appear promising, and no dramatic flaws have been revealed in the OPLS potential functions that describe the intermolecular interactions in solution. Nevertheless, expansion of the united-atom CH, groups to an all-atom model, particularly for the aromatic rings,33 explicit treatment of polarization effects, and the inclusion of internal degrees of freedom are all areas for possible refinement of these calculations.
+
Acknowledgment. Gratitude is expressed to Toan B. Nguyen and James F. Blake for computational assistance and to the National Science Foundation for support of this research. Registry NO. CH3COCH3.67-64-1; CH$OOH, 64-19-7; CH3COOCH3, 79-20-9; CHCIj, 67-66-3; pyrimidine, 289-95-2. (30) Leo, A. Pomona College Medicinal Chemistry Dora Bose; Pomona College: Claremont, 1988. (31) Radzicka, A,; Wolfenden, R. Biochemistry 1988, 27, 1664. (32) Golumbic, C.; Orchin, M.J. Am. Chem. SOC.1950, 72, 4145. (33) Jorgensen, W. L.; Severance, D. L., to be published.
