J. Phys. Chem. 1992,96, 1455-1459
1455
resulted in the increasing intensity of the transverse acoustic modes. of this background is probably due to Raman scattering. A large value of the intensity for the transverse component can The only other material that exhibits elastic properties somewhat similar to 7-0, and cyclooctane I is succinonitrile. Ultrasonic then be expected in 7-0,due to its small value of C., The difference in the transverse intensities between 7-0,and cyclomeasurements in succinonitrile have indicated a high degree of octane I is also reflected in the different elastooptic coefficients elastic isotropy (A = 0.85) near the triple point with respect to as measured by PU (almost 3 times larger in yoz)and, in fact, sound propagation at gigahertz frequencies4 and a high value of by P l l - P12(4-5 times larger in 7-0,). 5.0 for the Cauchy ratio although the ratios of VL/VTare not as Theoretical values of the three elastooptic coefficients can be large for different symmetry directions (see Table VI). Dielectric obtained from a recently developed dipole-induced dipole theory"6 studies in succinonitrile have indicated very little change in the for the rare gas solids. For cyclooctane I, the calculated coefnature of molecular reorientation between the liquid and the plastic ficients are almost independent of temperature and are P I , = 0.37, phase.41 RT coupling is strong enough to give a resonance line P12= 0.34, and P" = 0.09. Except for PU, this is in good shape to the transverse acoustic mode in succinonitrile. A theagreement with the values determined in the present experiments oretical model describing the coupling between the reorientational (see Table V). The calculated values of the elastoopticcoefficients motion and the acoustic phonons is in excellent agreement with are P l l = 0.29, P12= 0.28, and P, = 0.04. The large for 7-0, the observed experimental data and correctly reproduces the difference between the values of P I 1and P I , in 7-0,as seen in ultrasonic values of the elastic constants of ~uccinonitrile.~~ A Table I11 is particularly evident and represents a very significant depolarized background was also present in the Brillouin spectra with respect to the rare gas solids. Again, a possible of succinonitrile whose origin was considered u n l ~ n o w n . ~ ~ ~ ~ discrepancy ~ explanation or mechanism may involve the peculiar structure and A distinguishing feature of the Brillouin spectra of yo2,which molecular rotational motion of yo2in that the molecules on the is different from cyclooctane (and succinonitrile), is the high faces of the cube (which are arranged in the form of long, mutually intensity of the transverse acoustic mode. The intensity ratio I L / I T orthogonal chains and are rotating about the (100) axes) are for cyclooctane varies from 0.02 to 0.07 at the triple point to capable of sustaining strong transverse or "softn longitudinal 0.07-0.23 at 234.2 K. This ratio is unusually high in 7-0, and acoustic vibrations independent of the rest of the solid (see also varies from 0.4 to 2.0 at the triple point to 0.5-2.9 near the phase ref 47). This effect (and hence the elastooptic coupling) would transition at 44.0 K. Very intense transverse components have be greater in yo, than in cyclooctanesince the molecular weight also been observed in the Brillouin spectra of KCN and NaCN ratio is 1:4 and is also consistent with isotropic nature of both single crystals," but only very close to the phase transition. The authors" noted that this intensity is proportional to P442/C44,45 systems. In conclusion, the Brillouin spectrum of 7-0, may be unique such that softening of C, as the phase transition was approached in that it exhibits almost exact isotropy (at the triple point), and the transverse components are slow and very intense. A tem(40) Bird, M. J.; Jackson, D. A.; Pentecost, H. T.A. In Proceedings of the perature dependence study and comparison with cyclooctane I 2nd International Conference on Light Scattering in Solids; Balkanski, M., Ed.: Flammarion: Paris. 1971. indicate that these features are associated with strong RT coupling (41) Williams, D. E.;Smyth, C. P. J . Am. Chem. SOC.1962, 84, 1808. effects in the Pm3n structure. (42) Courtens, E. J . Phys. (Paris) 1976, 37, L-21. Registry No. 02,7782-44-7; cyclooctane, 292-64-8. (43) Boyer, L.; Vacher, R.; Adam, M.; Cecchi, L. In Proceedings of the ~~~
~
~
2nd International Conference on Light Scattering in Solids; Balkanski, M., Ed.; Flammarion: Paris, 1971. (44) Wang, C. H.; Satija, S.K. J. Chem. Phys. 1977,67, 851. (45) Fabelinskii, I. L. Molecular Scattering of Light; Plenum: New York, 1968.
(46) Mazzacurati, V.; Signorelli, G.; R u m , G. Europhys. Lett. 1986, 2, 877. (47) Leon, J. Phys. Lett. A. 1991, 152, 178.
Polar Intermolecular Interactions Encoded in Partition Coefficients: An Indirect Estlmatlon of Hydrogen-Bond Parameters of Polyfunctional Solutes Nabil El Tayar, Bernard Testa,* and Pierre-Alain Carrupt Institut de Chimie Thgrapeutique, Ecole de Pharmacie, Universitt de Lausanne, BEP, CH- IO15 Luusanne, Switzerland (Received: August 15, 1991)
Lipophilicity (expressed as log P,the logarithm of partition coefficients) is known to be decomposable into a cavity/volume term V expressing mainly hydrophobic and dispersive solute-solvent interactions, and polar terms reflecting electrostatic solute-solvent interactions, e.g. log P = a V + b?r* + ca + do, where ?r*, a,and j3 are solvatochromic parameters, Le., the dipolarity/polarizability, H-bond donor acidity, and H-bond acceptor basicity, respectively. Here, we define a parameter A such that A = b?r* + ca + dj3 and show that A, (Le., A calculated from 1-octanol/water log P values) is correlated mainly with j3 (9= 0.867; n = 168), while Balk(Le., A calculated from alkane/water log Pvalues) is correlated mainly with a and j3 (r2 = 0.897; n = 104). Thus, and within the explored range of values, a fair estimate of the H-bond donor acidity and acceptor basicity of solutes can be obtained from their log PWtand log Palkvalues and calculated molecular volumes.
Introduction Lipophilicity, as expressed by the logarithm of partition coeffcients (log P), is a physicochemical property which describes a partitioning equilibrium of solute molecules between water and an immiscible organic solvent. It is of particular importance in drug design not only because it correlates with biological data but 'Address corrcspondencc to this author at the above address.
0022-3654/92/2096-1455$03.00/0
also because it encodes a wealth of structural information.l Since the pioneering work of C ~ l l a n d e rthere ~ - ~ has been a great deal of interest in relating partition coefficients to chemical structures. A first approach in this direction is to express partition coefficients (1) van de Waterbeemd, H.; Testa,B . Aduances in Drug Research; Testa, B., Ed.; Academic Press: London, 1987; Vol. 16, pp 87-225. (2) Collander, R.Acta Chem. Scand. 1950, 4 , 1085. (3) Collander, R.Acta Chem. Scand. 1951, 5, 774.
0 1992 American Chemical Society
14%
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
El Tayar et al.
TABLE Ik Partition Coefficients and Their Related Polar Parameters in 1-Octanol/Water a d ALlune/Water Systems,and Free Energy of
Hydration" logb name methane ethane n-propane n-butane n-pentane n-hexane n- heptane n-octane cyclopentane cyclohexane 2-propanone 2-butanone 2-pentanone 2-hexanone cyclopentanone cyclohexanone 2-heptanone acetaldehyde propanal butanal hexanal ethyl formate n-propyl formate methyl acetate ethyl acetate propyl acetate n-butyl acetate ethyl propanoate acetonitrile propionitrile formic acid acetic acid propanoic acid butanoic acid pentanoic acid hexanoic acid methanol ethanol propanol 2-propanol 1-butanol isobutyl alcohol 2-butanol ten-butyl alcohol 1-pentan01 2-methyl- 1-butanol isopentyl alcohol 2-pentanol 3-pentanol 1 hexanol 2-propen-1-01 cyclobutanol cyclopentanol cyclohexanol cycloheptanol ammonia methylamine ethylamine 1-propylamine 1-butylamine 2-propylamine 2-butylamine 1-pentylamine 1-hexylamine cyclopentylamine cyclohexylamine cycloheptylamine pyrrolidine piperidine N-methylmethylamine N-ethylethylamine N-propyl- 1-propylamine N-butyl- 1-butylamine N,N-dimethylmethylamine
-
log
poct
&ad
1.09 2.30 1.81 2.97 2.36 3.61 2.89 4.25 3.39 4.99 3.90 5.70 4.66 6.29 5.18 6.98 3.00 3.44 -0.24 -0.91 0.29 -0.25 0.91 0.43 1.38 0.87 0.81 1.98 -0.21 0.59 0.88 1.78 0.83 0.18 -0.26 0.73 0.29 1.24 0.90 1.82 1.67 1.21 -0.34 -1.48 0.10 -0.54 -1.60 -0.24 -2.80 0.30 -2.30 0.79 -0.96 1.39 -0.52 1.90 0.24 -0.70 -2.80 -0.25 -2.10 0.28 -1.52 0.13 -1.73 0.75 -0.77 0.76 -0.98 0.61 0.35 1.40 -0.40 1.29 1.16 0.08 1.19 1.21 2.03 0.45 0.17 -
-
1.23
-
-
-
-0.57 -0.13 -1.80 0.48 -1.00 0.91 -0.62 0.26 0.74 1.49 -
-
1.49
-
0.84 -0.38 0.58 1.67 2.83 0.16
-
-0.03 0.09 0.03 -0.05 -0.05 -0.10 0.08 0.03 -0.13 -0.27 -2.66 -2.74 -2.72 -2.75
-
'k.lkc
0.06 0.02 -0.06 -0.12 0.03 0.08 -0.01 0.01
-
-4.67 -4.73 -4.76 -4.91
-
-2.87 -2.73 -2.03 -1.84 -2.13 -2.38
-
-2.42 -2.44 -2.50 -2.61 -2.59 -2.64 -2.13 -2.25 -2.01 -2.31 -2.38 -2.50 -2.50 -2.59 -2.09 -2.25 -2.33 -2.48 -2.46 -2.45 -2.60 -2.85 -2.41 -2.52 -2.65 -2.62 -2.60 -2.39 -2.23 -2.64 -
-4.27 -4.42 -4.54 -4.43
-
-
-2.11 -2.27 -2.27 -2.39 -2.49 -2.62 -2.47 -2.52
-
0.10 -2.55 -2.55 -0.48 -2.80 1.53 -2.92 2.68 -2.97 -0.44 -2.63
-
-
-
-4.51
-
-4.25 -6.16 -6.37 -5.74 -6.01 -5.96 -5.36 -5.37 -5.51 -5.72 -5.46 -5.67 -
-
-5.80 -5.32
-
-5.67 -
-5.24 -5.16 -5.49
-
-
-4.81
-
-5.38 -4.79 -5.06 -4.64
AGoHb
2.00 1.83 1.95 2.08 2.34 2.49 2.62 2.90 1.20 1.23 -3.86 -3.64 -3.53 -3.30 -
-
-3.30 -3.51 -3.45 -3.18 -2.82 -2.65 -2.49 -3.32 -3.10 -2.86 -2.56 -2.80 -3.89 -3.85
-
-6.72 -6.49 -6.37
-
-5.12 -5.02 -4.83 -4.76 -4.72 -4.53 -4.58
-
-4.48
-
-4.43 -4.40 -4.36 -4.37 -5.04
-
-5.51 -5.49 -5.50 -4.57 -4.51 -4.40 -4.30
-
-4.10 -4.04
-
-5.49 -5.11 -4.29 -4.07 -3.67 -3.33 -3.24
name N.N-diethvlethvlamine N&"dipripyl- f-propylamine ethyl ether propyl ether isopropyl ether tetrahydrofuran formamide acetamide propanamide butanamide hexanamide N-methylformamide N-ethylformamide N-methylacetamide N-propylformamide N-ethylacetamide N-propylacetamide N,N-dimeth ylformamide N,N-dimethylacetamide N,N-diethylacetamide urea thiourea methylurea ethylurea propylurea butylurea Nfl-dimethylurea N,N-diethylurea N,N'-dimethylurea N,N'-diethylurea 1,2-ethanediol 1,2-propanediol 1,3-propanediol 2,3 butanediol 1,3-butanediol 1,4-butanediol 1,5-pentanediol 2,4-pentanediol 2,5-hexanediol 1,6-hexanediol 1,7-heptanediol 1,8-octanediol cis- 1,2-cyclohexanediol tram- 1,2-~yclohexanediol 1,2,3-propanetriol dimethoxymethane diethoxymethane 1,2-dimethoxyethane 1,2-diethoxyethane 1,4-dioxane morpholine benzene toluene ethylbenzene propylbenzene but ylbenzene 1,2-dimethylbenzene 1,3-dimethylbenzene 1,4-dimethylbenzene 1,3,5-trimethylbenzene
-
log
log
pmb
Pa,kc
bd
1.36 0.91 2.79 0.89 0.66 2.03 2.00 2.03 0.46 -0.10 -1.51 -5.10 -1.26 -4.68 -4.23 -0.21 -3.59 -2.63 -
-3.25 -3.21 -2.27 -2.34 -2.24 -2.13 -3.13 -3.48
-1.05 -
-3.90
-
-
-
-
-3.64
-
-
-1.01 -2.71 -0.77 -1.42 0.34 -2.11 -5.46 -1.02 -
-3.88 -4.24 -4.34 -4.15 -3.37
-0.74
-4.01
-
-
-
-0.49
-
-3.78
-1.36 -0.92 -1.04 -0.92
-4.76 -4.19
-3.63 -3.80 -3.92 -4.40
-
-
-
-
-
-
-
-4.37
-
-3.27 -
0.23 0.08 -1.76 -5.70 0.18 0.84 -0.21 0.66 -0.27 -0.86 -2.00 2.13 2.29 2.69 2.89 3.15 3.26 3.68 4.11 4.00 3.12 3.39 3.20 3.54 3.15 3.46 3.84 4.05 1,2,3,5-tetramethylbenzene 4.17 1,2,4,5-tetramethylbenzene 4.00 1,2,3,4-tetramethyIbenzene 4.11 4.56 pentamethylbenzene 5.11 hexamethylbenzene fluorobenzene 2.27 2.46 2.84 2.99 chlorobenzene 2.99 bromobenzene 3.12 3.25 3.33 iodobenzene 1.58 1.14 acetophenone 1.48 1.12 benzaldehyde nitrobenzene 1.85 1.55 2.11 2.15 methoxybenzene ethoxybenzene 2.51 2.77
-
-
-
-3.91
-5.42
-
-3.97 -4.06
-
-4.06 -7.93 -8.21 -8.47 -8.54 -9.01
-
-7.00 -6.42
-
-8.18
-
-8.35 -8.50
-
-9.38
-
-9.71 -
-
-
4.06
-
-4.91 -2.59 -3.14 -3.59 -3.93 -3.01 -3.83 -0.84 -0.92 -0.91 -0.98 -1.24 -0.94 -0.86 -0.91 -0.82 -1.07 -1.24 -1.13 -1.26 -1.29 -0.92 -0.71 -0.81 -0.83 -2.61 -2.23 -1.96 -1.79 -1.90
-10.32
AGoHb -3.02
-
-1.64 -1.16 -0.53 -3.47
-
-9.73
--
-7.67
-
-
-9.23 -2.94
-
-4.84 -3.53 -5.06 -7.19 -0.87 -0.89 -0.80 -0.53 -0.40 -0.90 -0.84 -0.81
-6.41 -2.13 -2.28 -2.43 -2.29
-
-2.30 -2.15 -2.23 -2.35
-
-
-
-
-
-2.21 -2.10 -2.27 -2.39 -4.71 -4.16 -3.85 -3.36 -3.33
-
-1.12 -1.46
-
-4.59 -4.03 4.13 -1.03
-
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1457
Polar Intermolecular Interactions
TABLE I1 (Continued) log Pab 3.18 2.16 2.64 3.97 2.20 2.24 2.46 2.41 2.64 2.55 2.45 2.45 2.74 2.66 2.66 2.51 2.35 2.43 1.72 2.19 3.42 3.28 3.33 2.75 0.90 2.16 2.28 3.31 4-methyl-NJ-dimethylaniline 2.61 2-methylaniline 1.35 3-methylaniline 1.41 4-methylaniline 1.40 2-chloroaniline 1.91 3-chloroaniline 1.99 4-chloroaniline 1.83 2- bromoaniline 2.11 3-bromoaniline 2.10 4-bromoaniline 2.05 2-fluoroaniline 1.26 3-fluoroaniline 1.30 name propanoxybenzene methyl benzoate ethyl benzoate benzyl benzoate propiophenone 2-chloronitrobenzene 3-chloronitrobenzene 4-chloronitrobenzene 3-bromonitrobenzene 4-bromonitrobenzene 3-methylnitrobenzene 4-methylnitrobenzene 2-methoxytoluene 3-methoxytoluene 4-methoxytoluene 3-chloroacetophenone 4-chloroacetophenone 4- bromoacetophenone 4-fluoroacetophenone 4-methylacetophenone 2-chlorotoluene 3-chlorotoluene 4-chlorotoluene 2-methyl methylbenzoate aniline N-ethylaniline N,N-dimethylaniline N,N-diethylaniline
log Palkc
-
Ld &e -1.81
AG0Hb
-2.30 -4.77 -2.40 -4.72 -2.88 2.02 -2.50 -4.42 -2.14 -1.92 -1.97 -1.99 -2.08 -1.97 -1.97 -1.67 -1.76 -1.76 2.00 -2.21 -4.47 1.85 -2.37 -4.62 -2.56 1.20 -2.66 -4.86 -2.58 -0.71 -0.85 -0.80 -2.29 0.03 -2.55 -4.94 -2.43 2.40 -2.28 -3.88 3.43 -2.41 -4.21 2.78 -2.53 -4.18 0.47 -2.66 -5.17 0.54 -2.60 -5.10 0.44 -2.61 -5.20 1.12 -2.06 -4.46 0.71 -1.98 -4.87 0.57 -2.14 -5.01 -2.1 1 -2.12 -2.17 -2.35 -2.30 1.40 2.13
-
-
name 4-fluoroaniline 2-nitroaniline 3-nitroaniline 4-nitroaniline 4-phenylaniline 4,4’-diaminobiphenyl pyridine 2-methylpyridine 3-methylpyridine 4-methylpyridine 2,ddimethylpyridine benzylamine benzamide acetanilide phenol 2-methylphenol 3-methylphenol 4-methylphenol 3-chlorophenol 4-chlorophenol 3-bromophenol 4- bromophenol 2-nitrophenol 3-nitrophenol 4-nitrophenol 4-cyanophenol 3-hydroxybenzaldehyde 4- hydroxybenzaldehyde benzoic acid 3-nitrobenzoic acid 4-nitrobenzoic acid 3-chlorobenzoic acid 4-chlorobenzoic acid 3-bromobenzoic acid 4-bromobenzoic acid phenylacetic acid benzyl alcohol phenylacetonitrile 1-phenyl-2-propanone phenyl acetate
log pab 1.15 1.85 1.37 1.39 2.84 1.34 0.65 1.11 1.20 1.22 1.68 1.09 0.64 1.16 1.49 1.95 1.96 1.94 2.49 2.45 2.63 2.59 1.79 2.00 1.91 1.60 1.38 1.35 1.87 1.83 1.89 2.68 2.65 2.86 2.87 1.46 1.10 1.56 1.44 1.49
log Palkc
-
Ld ii,lke
-2.46 0.31 -2.41 -0.46 -2.89 -1.09 -2.87 -3.13 -5.05 -0.31 -2.15 0.31 -2.35 0.27 -2.26 0.21 -2.24 0.67 -2.44 -0.21 -2.95 -2.28 -3.47 -1.70 -3.54 -0.82 -1.81 0.25 -1.91 -0.35 -1.90 -0.19 -1.92 -0.07 -1.32 -0.12 -1.36 -1.44 -0.20 -1.48 1.04 -2.32 -1.23 -2.11 -2.15 -2.20 -2.29 -2.27 -1.93 -2.58 -2.54 -2.61 -0.72 -2.12 -1.22 -2.95 -2.89 -1.81 -1.84 -1.88 -1.87 -1.07 -3.08 -0.62 -2.80 1.31 -2.62 0.98 -3.33 1.13 -2.97
-
-5.62 6.39 -7.02
-
-
-4.52 -4.68 -4.72 -4.78 -5.09 -5.88 -8.03 -8.14 -5.62 -5.21 -5.81 -5.65 -5.47 -5.52
-
-5.90 -4.71 -6.98 -7.90 -7.76 -7.51 -8.12 -6.33 -7.76
-
-7.32 -6.13 -4.52 -5.55 -5.04
-4.71 -4.64 -4.78 -4.94 -4.61
-
-6.63 -5.88
-
-6.15
-
-7.15 -9.65 -10.67 -10.19 -9.53 -10.49
-
-
-2.46
“ A dash means data not available. 1-Octanol/water partition cocffi~ients.’~cn-Heptane, n-hexane, or cyclohexane/water partition dInteractive polar parameter calculated from eq 8 and log Pa values as the distance on the ordinate from the line for n-alkanes. eInteractive polar parameter calculated from eq 9 and log p,Ik values as the distance on the ordinate from the line for n-alkanes. !Free energy of hydration at 25 0C.34
in terms of fragmental or atomic contributions and intramolecular interaction^.^' Although very useful for predicting and calculating log P values, these approaches are of limited value in unraveling the intermolecular interactions expressed in lipophilicity. Yet intermolecular interactions of the same basic nature are precisely those that govern drug recognition by and binding to biological sites of action- similarity that may explain at the fundamental level many of the lipophilicity-biological activity relationships that have been e s t a b l i ~ h e d . ~ ~ ~
Theoretical Background As repeatedly shown, partition coefficients encode two major structural contributions, namely a cavity or rolume-related term reflecting the energy needed to create a cavity in the solvent (Le., an endoergic term), and an exoergic interactive term which results from solute-solvent interactions such as dipole-dipole and hydrogen bonds.l*14 Particularly informative in this respect has (4) Rekker, R. F. I1 Farmaco Ed. Sci. 1979, 34, 346. (5) Hansch, C.; Leo, A. Substituent Constants for Correlation Analysis in Chemistry and Biology; Wiley: New York, 1979. (6) Broto, P.;Moreau, G.; Vandycke, C. Eur. J . Med. Chem. 1984, 19, 61. (7) Klopman, G.; Iroff. L. D. J. Compur. Chem. 1981, 2, 157. (8) Hansch, C.; Blaney, J. M. In Drug Design. Fact or Fantasy? Jolles, G., Wooldridge, K.R.H., Eds.; Academic Press: London, 1984; pp 185-208. (9) Testa, B.; Kier, L. B. Med. Res. Rea 1991, 11, 35. (10) Moriguchi, I.; Kanada, Y.; Komatsu, K. Chem. Pharm. Bull. 1976, 24, 1799. (11) Cramer 111, R. D.J. Am. Chem. Soc. 1980, 102, 1837. (12) Testa, B.; Seiler, P.Arzneim.-Forsch. 1981, 31, 1053.
been the contribution of Taft, Kamlet, Abraham, and wworkers who have developed a new set of parameters to assess quantitatively the H-bond donor acidity (a),the H-bond acceptor basicity (B), and the dipolarity/polarizability ( r * )of Using UV-visible spectral data, the magnitude of enhanced solvatochromic shifts resulting from H bonding was used to establish scales of H-bond donor acidity (a)and the H-bond acceptor basicity (8). The dipolarity/polarizability ( r * )scale was also derived from the solvatochromic effects on the electronic spectral transitions. For more detail, the reader is referred to the original work of Taft, Kamlet, and co-~orkers.’~-~* These, so-called solvatochromic parameters, have proven to be useful in evaluating and identifying the physical forces governing partitioning of uncharged solutes between biphasic solvent systems. For example, a solvatochromic analysis of 1-octanol/water partition coefficients yielded the following correlation18 log P,t = 5.15 (*0,16)Vw/100 - 1.29 (f0.16)~~ 3.60 (f0.18)8 0.45 (f0.12)
+
n = 103; 6 = 0.978;
s = 0.16
(1)
(13) Griinbauer, H. J. M.; Tomlinson, E. Int. J . Pharm. 1984, 21, 61. (14) Taft, R. W.; Abraham, M. H.; Doherty, R.M.: Kamlet, M. J. Nature 1985, 313, 384. (15) Kamlet, M. J.; Taft, R. W. J. Am. Chem. Soc. 1976, 98, 377. (161 Kamlet. M. J.: Abboud. J.-L. M.: Abraham. M. H.: Taft. R.W. J. Org. Chem. 1983, 48, 2877. (17) Kamlet, M. J.; Doherty, R. M.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R.W. J. Pharm. Sci. 1986, 75, 338. (18) Leahy, D. E. J. Pharm. Sci. 1986, 75, 629.
1458 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
El Tayar et al.
where Vw is the calculated van der Waals’ molecular volume of the solutes, n the number of compounds, 3 the squared correlation coefficient, and s the standard deviation of the regression. Values in parentheses are the 95% confidence limits. n-Heptane/water partition coefficients revealed another balance of intermolecular forces as previously reported by us:19 log Phcp= 6.78 (f0.69)Vw/100 - 1.02 (*0.39)~* 5.35 (f0.50)@- 3.54 (f0.30)a - 0.06 (4Z0.43)
n = 75; rz = 0.953; s = 0.36 (2) A noteworthy difference between the two equations is the absence of an a term in eq 1, and its significant contribution in eq 2. The successful factoring of lipophilicity into various intermolecular effects as exemplified by eqs 1 and 2 could find its way into QSAR (quantitative structureactivity relationships) studies when approaches will be found to determine solvatochromic parameters for any compound and particularly for drugs with various functional groups. In previous studies, we have shown that the or a) can be determined with H-bond donor acidity (log reasonable accuracy and precision from the water-dragging effect
e
(Afw)20-21 log KZ = 3.09 (f0.36) log Afw - 6.02 (k0.85)
0 0 0
4t 0
0e
0
slti I
-1
-4 -3
L
‘p
@
D
gf3 0
0
0
50
100
150
L
Figure 1. Relationship between 1-cctanol/water partition coefficients and van der Waals molecular volumes of various uncharged solutes. The filled circles refer to n-alkanes while the empty circles refer to polar solutes. The regression line was calculated by eq 8.
n = 20; 3 = 0.947; s = 0.26 (3) or from the A log Pa-@ parameter (i.e., log Pa minus log PheP):l9 A log P,t-hcp = 3.35 (f0.36)a + 0.37 (f0.15)
n = 75; rz = 0.837; s = 0.45 (4) The present work is a continuation and a generalization of an effort to estimate parameters accounting for polar intermolecular interactions from partition coefficients. As a prerequisite to such an approach, the reliability of calculated molecular volume will again be ascertained. Furthermore, it proved useful to define a parameter representing the sum of all polar interactions affecting partition coefficients, such that log P = cavity + polarity (5) Since volume parameters can account for the cavity term, we have chosen to designate this polar interactive parameter A for the prosaic reason that it resembles an upside-down V,I2i.e. log P = a V + bA (6) Results and Discussion Volume Parameters. For pure liquid solutes, the calculated van der Waals’ molecular volume ( Vw) was shown to be a reliable alternative to the bulk liquid molar volume.18*22 To establish that the same holds for partial molar volumes of solutes in water at infinite dilution (i.e., closer to biological conditions than bulk phase volumes), we have compiled the volume parameters shown in Table I (supplementary material). A good correlation exists between partial molar volumes in water (Vaso) and calculated van der Waals volume ( Vw): Vaqo = 1.51 (f0.05)Vw + 5.45 (f2.63)
n = 119; ? = 0.973; s = 4.04
(7) This equation clearly demonstrates that solutewater interactions have a seemingly constant effect on the effective volume occupied by the solute in aqueous solution and that the calculated van der Waals’ molecular volume can be used as a measure of the cavity term in linear solvation energy relationships as previously shown by Leahy18 and Taft et al.2zfor liquid solutes in the pure state. Calculation of the Interactive Polar Parameter A. The l-octanol/water and alkane/water partition coefficients of the solutes (19) El Tayar, N.; Tsai, R.-S.; Teata, B.; Carrupt, P.-A,;Leo, A. J . Pharm. Sci. 1991, 80, 590.
(20) Fan, W . ;El Tayar, N.; Testa, B.; Kier, L.B. J . Phys. Chem. 1990, 94, 4764. (21) Abraham, M. H.; Grellier, P. L.;Prior, D. V.; Duce, P. P.; Morris, J. J.; Taylor, P.J . Chem. SOC.,Perkin Trans. 2 1989, 699. (22) Taft, R.W.; Abraham, M.H.; Famini, G. R.; Doherty, R. M.; Abb u d , J.-L. M.; Kamlet, M. J. J . Pharm. Sei. 1985, 74, 807.
1
-5.
I 0
0
a 0
0
% O
,o
100
50
1 0
VW
Figure 2. Relationship between alkane/water partition coefficients and van der Waals molecular volumes of various uncharged solutes. The filled circles refer to n-alkanes while the empty circles refer to polar solutes. The regression line was calculated by eq 9.
in Table 1are listed in Table 11. The merging of n-heptanelwater, n-hexanelwater, and cyclohexane/water partition coefficients as log P- values is permissible since the three solvent systems differ only negligibly as far as partitioning is con~erned.~’.~~ A plot of log P,, versus Vw values (Figure 1) shows that the eight apolar solutes in the set (Le., the n-alkanes) fall on one line log P,, = 0.059 (f0.003)Vw + 0.107 (f0.161) n = 8; ? = 0.998; s = 0.073
(8)
and that all the other points (i.e., all polar solutes) fall below this line. The same behavior is seen for log Palkvalues (Figure 2), the relationship for the eight apolar solutes being log Palk = 0.069 (*O.O03)Vw + 1.05 (f0.15) n = 8; 9 = 0.998; s = 0.069 (9) Equations 8 and 9 thus define the value of the a coefficient in eq 6 within the explored property space; setting the value of the b coefficient as +1, A, and Aalkvalues can be calculated as the distance on the ordinate from the line for apolar solutes. These values, which are compiled in Table 11, are hypothesized at this stage to represent the sum of all polar interactions involving a solute in a given solvent/water system. Before examining how (23) Seiler, P. Eur. J . Med. Chem. 1974, 9, 473. (24) Leo, A,; Hansch, C. J . Org. Chem. 1971, 36, 1539.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1459
Polar Intermolecular Interactions solvatochromic parameter values can be obtained from the A parameters, we briefly investigate the nature of the latter. For uncharged polar solutes partitioning in an alkane/water system, polar interactions are essentially restricted to the aqueous phase. Hence AaIk should quantitate mainly solute-water polar interactions (orientation and inductive forces, H bonds). That this is indeed the case is verified by the good correlation between Aalkand the hydration free energy (AGOH) (Table 11): A G O H = 1.42 (f0.12)Aalk + 2.64 (f0.54)
n = 63; r2 = 0.906; s = 0.971 (10) This equation suggests that & values may be useful in estimating the hydration free energy of polyfunctional and even on permanently charged compounds when traditional methods are difficult to apply.25.26 In contrast to alkane/water systems, polar interactions in alkanol/water systems occur in both phases. Hence & should not correlate with AGOH, as indeed found (9= 0.49). Sohatochromic Analysis of A, and Aalk Equations 1 and 6 suggest that & must correlate with A* and j3,as is indeed found: A,, =i -0.636 (f0.124)~' - 3.90 (*0.20)j3 - 0.186 (f0.103)
n = 168; 9 = 0.918; s = 0.25
(11) Note that the squared correlation coefficient in eq 11 is not as good as that in eq 1. However, the two sets of data are not comparable since the present study is based on a set of solutes (Table I) of greater size and structural variety. The a parameter is nonsignificant and has been excluded from eq 11, While the T* term is significant, its contribution is modest (15% of the variance), A, being mainly related to 8: -4.17 (f0.25) j3 - 0.489 (f0.108) A,
n = 168; r? = 0.867; s = 0.32 (12) This equation is of particular interest, because it indicates that a fair estimate (87% of the variance) of the H-bond acceptor basicity of a solute can be obtained once its log P, is known and its molecular volume is calculated. As for Aalk, eqs 2 and 6 suggest a correlation with all three solvatochromic parameters: haIk -1.37 ( f 0 . 3 0 ) ~ *- 6.19 (f0.48)/3 - 3.42 ( f 0 . 3 5 ) ~-~ 0.626 (f0.234) n = 104; r? = 0.944; s = 0.46
(13)
(25) Kang, Y. K.; Ngmethy, G.; Scheraga, H. A. J. Phys. Chem. 1987, 91, 4105. (26) Ooi, T.; Oobatake, M.; Nlmethy, G.; Scheraga, H. A. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 3086.
While all three parameters have significant contributions, that of A* explains only 15% of the variance. Hence A , I ~= -6.81 (f0.62)O - 3.82 (f0.45)a - 1.16 (f0.27)
n = 104; r? = 0.897; s = 0.62 (14) This equation is again an interesting one since it indicates that a fair estimate (89.7% of the variance) of the total H-bonding capacity (aand 8) of a solute can be obtained from its log Palk and its calculated molecular volume. Conclusion The solvatochromic parameters of solutes are the most useful ones in physicochemistry, but their application to medicinal chemistry is singularly restricted by the difficulty of either determining them by the classical solvatochromic method2'qZ8or estimating them by the parameter estimation rules29for drugs bearing several functional groups. In the present study, we show that, within the explored range of values, the H-bond donor acidity (a)and acceptor basicity (8) can be reasonably well estimated for solutes whose log PWtand log Palkvalues are known and whose molecular volume has been calculated. Once CY and j3 have been estimated, the calculation of T* is straightforward (i.e., eqs 11 and 13). This indirect determination of the solvatochromic parameters may prove of value in molecular design by affording interpretable QSAR equations, and more generally in the physicochemical study of not-too-simple molecules.3b33 Acknowledgment. B.T., N.E.T., and P.A.C. are indebted to Swiss National Science Foundation for support. Supplementary Material Available: Table I, a compilation of van der Waals volumes, partial molar volumes, and solvatochromic parameters of various solutes (7 pages). Ordering information is given on any current masthead page. (27) Kamlet, M. J.; Taft, R. W. J . Am. Chem. SOC.1976, 98, 377. (28) Taft, R. W.; Kamlet, M. J. J . Chem. Soc., Perkin Trans. 2 1979, 1723. (29) Kamlet, M. J.; Doherty, R. M.; Abraham, M. H.; Marcus, Y.; Taft, R. W. J . Phys. Chem. 1988, 92, 5244. (30) Young, R. C.; Mitchell, R. C.; Brown, T. H.; Ganellin, R.; Griffith,
R.; Jones, M.; Rana, K. K.; Saunders, D.; Smith, I. R.; Sore, N. E.; Wilks, T. J. J . Med. Chem. 1988, 31, 656. (31) Abraham, M. H.; Duce, P. P.; Prior, D. V.; Barratt, D.G.; Morris, J. J.: Tavlor. P. J . Chem. SOC..Perkin Trans. 2 1989. 1355. (32) El Tayar, N.; Tsai, R.-5.; Carrupt, P.-A.; Tesk, B.;Hansch, C.; h, A. J . Pharm. Sci. 1991,80,744. (33) El Tayar, N.; Tsai, R.-S.; Testa, B.;Carrupt, P.-A. J . Chem. SOC., Perkin Trans..2, in press. (34) Cabani, S.;Gianni, P.; Mollica, V.; Lepori, L. J. Solution Chem. 1981, 10, 563. (35) Hansch, C.; Leo, A. The Pomona College Medicinal Chemistry Project, Pomona College, Claremont, CA 9171 1.
