J . Phys. Chem. 1987, 91, 1996-2004
1996
the place of a varying barrier height.
Conclusions In this work the direct time-dependent solution of the diffusion equation for the Kramers barrier-crossing problem in more than one dimension has been obtained for the first time by a novel numerical procedure. At low viscosities, motion along the reaction coordinate is faster than along the perpendicular direction, and reaction proceeds over the barrier. At high viscosities, however, motion along the perpendicular direction is faster, and most of the relative flux bypasses the central barrier through regions where the crest line is lower. The result is that the high-viscosity rate is larger than anticipated, leading to the fractional viscosity dependence, eq l , with 0 < a I l . One must add, however, that if the surface is modified so that the trend in the variation of the barrier along the perpendicular coordinate is reversed, the above-mentioned effect would be reversed, leading to a > 1. Such values for the exponent have not yet been found experimentally. It is possible that these effects would be amplified for the real stilbene, which has two phenyl rings which can rotate. To check this point, a three-dimensional calculation should be performed. The model predicts that, for stilbene, one should also observe some phenyl-ring dynamics following the excitation pulse. There are indeed some experimental indications that this is the If so, this effect should be more pronounced at the higher viscosities.
For lower barrier heights, the change in the barrier along the perpendicular coordinate is smaller, so that the viscosity dependence becomes more Kramers-like. Whereas deviations from Kramers in the non-Markovian theories occur for sharp barriers, here they are more pronounced for higher barriers. Both explanations are in qualitative agreement with experiment, since a barrier curvature is usually correlated with its height. It is interesting to ask whether part of the solvent-dependent barrier height observed in photochemical isomerization in solut i o may ~ ~be due ~ ~to ~a dynamical rather than a static effect. This is inherent in the present model, where the average barrier height decreases with increasing viscosity, due to the shift of the mainstream flux away from the C$= 0 reaction coordinate. At the present stage of our knowledge, the model presented here can suggest only a qualitative explanation to the photochemical isomerization experiments. Fuller knowledge of the potential energy surfaces and diffusion coefficients involved, as well as experimental work that would probe the perpendicular-coordinate dynamics, would submit the model to more stringent tests. Acknowledgment. The authors thank Dr. H. Tal-Ezer for helpful discussions and suggestions. We thank Profs. G. R. Fleming, J. T. Hynes, K. Schulten, and V. Sundstrom for correspondence. R.K. is supported by the Binational Science Foundation. The Fritz Haber Research Center is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munich, F.R.G.
Linear Solvation Energy Relationships. 41. Important Differences between Aqueous Solubility Relationships for Aliphatic and Aromatic Solutes Mortimer J. Kamlet, Ruth M. Doherty,* Michael H. Abraham, Peter W. Carr, Robert F. Doherty, and Robert W. Taft Naval Surface Weapons Center, White Oak Laboratory, Silver Spring, Maryland 20910; Department of Chemistry, University of Surrey, Guildford, Surrey GU2 5XH, United Kingdom; Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455; U. S. Department of Agriculture, Agricultural Research Service, Beltsville, Maryland 20705; and Department of Chemistry, University of California, Irvine, California 9271 7 (Received: October 21, 1986)
Aqueous solubility relationships of aromatic and aliphatic solutes differ from one another in two important regards: (a) Solubilities of aliphatic solutes do and those of aromatic solutes do not show important dependences on solute dipolariand (b) dependences on the solute hydrogen bond acceptor ty/polarizability (as measured by the solvatochromicparameter, t*), basicity parameter, 8, are about one-fourth smaller for aromatic than for aliphatic solutes. Solubilities of 70 liquid and solid aromatic solutes containing up to three fused rings are well correlated by the equation: log S, = 0.57 - 5.58Vl/100 + 3.858 - 0.01 1O(mp - 25); r = 0.9917, sd = 0.216. VI is the computer calculated intrinsic (van der Waals) molar volume. Liquid aliphatic solutes follow a rather different relationship: log S , = 0.05 - 5.85V1/199+ 1.09n* + 5.238; n = 115, r = 0.9944, sd = 0.153. The differences between aliphatic and aromatic solutes may be due, in part, to "vertical stacking" in aromatic liquids.
In earlier papers we have shown that solubility properties, SP, of organic nonelectrolytes are well correlated by equatio_nsthat include linear combinations of an endoergic cavity term ( mV/ 1 OO),
an exoergic dipolar term ( S A * ) , and one or several exoergic hydrogen-bonding terms (bp and aa),eq 1. P i n eq 1 is the solute S P = SPo
+ mP/100 +
SA*,
+ bp, + a a ,
(1)
molar volume, taken here as its molecular weight divided by liquid density at 20 OC,'and A*, a,and 8 are the solvatochromic parameters that measure solute dipolarity/polarizability, HBA basicity, and HBD acidity (HBA = hydrogen bond acceptor, HBD = hydrogen bond d o n ~ r ) . ~The - ~ subscript m indicates that, for *Address correspondence to this author at the Naval Surface Weapons Center.
0022-3654/87/2091-1996$01 S O / O
compounds which are capable of self-association, the parameters apply to solutes in their non-self-associated ("monomer") forms.6 For non-self-associating solutes, A* = t*m, 8 = 8,. (1) We have used V/lOO so that the parameter measuring the cavity term should cover roughly the same range as the other independent variables, which makes easier the evaluation of the relative contributions of the various terms to the solubility property studied. (2) Kamlet, M. J.; Taft, R. W. Acta Chem. Scand. 1985, 39B, 61 1. (3) Taft, R. W.; Abboud, J.-L. M.; Kamlet, M. J.; Abraham, M. H. J . Solution Chem. 1985, 14, 153. (4) Kamlet, M. J.; Abboud, J.-L. M.; Taft, R. W. Prog. Phys. Org. Chem. 1981, 13, 485. ( 5 ) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. J . Org. Chem. 1983, 48, 2871. ( 6 ) Abboud, J.-L. M.; Sraidi, L.; Guiheneuf, G.; Kamlet, M. J.; Taft, R. W. J . Org. Chem. 1985, 50, 2870.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987 1997
Linear Solvation Energy Relationships The first successful correlation of a solubility property by eq 1 involved octanol/water partition coefficients, K, of 47 aliphatic non-HBD solutes (for which aa = 0.00);’ the correlation was given by log KO, = 0.24 2.66V/100 - 0.96?r* - 3.388 (2a)
+
n = 47, r = 0.991, sd = 0.18 Equation 2a was later shownx to apply well to weak HBD solutes (a, not significantly greater than a, of octanol) if we adopted T * , = 0.40 for all alkanols (from a **/dipole moment correlat i ~ n )and , ~ &,, = 0.40 for methanol,I0 0.45 for all other primary alkanols, 0.51 for all secondary alkanols, and 0.57 for all tertiary alkanols. Stronger HBD solutes can be included in eq 2a if we include also a term in Aa,, the difference in a , between the stronger HBD solute and octanol.” Carbocyclic aromatic solutes (but not pyridines)I2 were also shown* to conform to eq 2 if we adopted the following rather simple set of “ground rules” for which we there appeared to be adequate justification: (a) 0.10 was added to V/lOO of alicyclic and aromatic compound^;'^ (b) assuming minimal polarizability contributions to octanol/water partition, we used the (T* dS) f o r m a l i ~ md, ~= -0.40, 6 = 0.00 for nonpolychlorinated aliphatic solutes, 0.50 for polychlorinated aliphatics, and 1.OO for aromatic solutes; and (c) assuming that effects of hydrogen bonding at multiple sites are additive, we used C@ for multifunctional solutes. With these “ground rules”, the correlation for 39 carbocyclic aromatic solutes was given by eq 2b, and that for the combined set of 102 aliphatic and aromatic non-hydrogen bonding, HBA, and weak HBD solutes (including the alkanols) was given by eq 2c. It is seen that agreement between eq 2a, b, and c is excellent,
+
log KO, = 0.09
+ 2.70V/100
- 0.74** - 3.398
(2b)
results being S,/K,, values recently reported for a number of homologous series by Abraham.I6 For 115 liquid aliphatic non-hydrogen bonding, HBA, and weak HBD alkanol solutes (data assembled in Table I), the revised multiple linear regression is now given by eq 3 (which agrees quite well with the earlier correlation equation).I5 log SiL1: log ( S g / K g w = ) (0.69 f 0.07) (3.44 f O.O4)V/lOO (0.43 f 0.06)~*,
+
+ (5.15 * 0.06)@, (3)
n = 115, r = 0.9962, sd = 0.126’’ Correlations with “Intrinsic” Molar Volumes. In order that we might later extend the aqueous solubility equations to include solid solutes, for which estimation of P (the volume they would occupy if they were liquid at 20 “C) can be quite difficult, we have also carried out a correlation for the 115 aliphatic solute data set using “intrinsic” (van der Waals) molar volumes, VI, to measure the cavity term. Leahy has recently shownlXthat with the same log KO, data set as gave eq 2c, use of VI/ 100 in place of P/ 100 gave a correlation with better statistical goodness than eq 2c (n = 103, r = 0.991, sd = 0.16), and Leahy and c o - w ~ r k e r s have ’~ reported that VI in place of Pgives “cleaner” dissections into the various contributing terms in several correlations of HPLC capacity factors by eq 1. The VI values used in the new correlations (included in Table I) are those reported by Leahy and co-worker~’~J~ and do not differ markedly from van der Waals (molar) volumes calculated by fragment additivity methods, such as that of BondLzo The new correlation for the aliphatic solutes is given by eq 4; experimental log SiL log ( S g / K g w = ) (0.05 f 0.08) (5.85 f O.lO)VI/lOO + (1.09 f 0.07)~*,
+ (5.23 f 0.07)&
n = 39, r = 0.983, sd = 0.14 log KO,
0.20
+ 2.74V/100
- 0.92n*
- 3.398
(4)
(2~)
n = 102, r = 0.989, sd = 0.17 and that no major obstacle needed to be overcome to accomodate aliphatic and carbocyclic aromatic solutes to the same correlation (although there was still an unresolved problem involving the pyridine derivatives) .I2 Solubilities of Liquid Aliphatic Solutes in Water. More re~ e n t l y ’ we ~ ~have ’ ~ reported that solubilities in water at 25 OC, S,, of liquid aliphatic solutes, and the nearly equivalent quantities, S,/K,,, are also well correlated by a linear solvation energy relationship of the form of eq 1. Kgw is the solute gas/water partition coeffiLient at 25 “ C and S, is the solute molar concentration in its own saturated vapor at 25 OC (S,= P,,,/24.5). We have since expanded the data base slightly, the newly included (7) Kamlet, M. J.; Abraham, M. H.; Doherty, R. M.; Taft, R. W. J. Am. Chem. SOC.1984, 106, 464. (8) Taft, R. W.; Abraham, M. H.; Famini, G. R.; Doherty, R. M.; Abboud, J.-L. M.; Kamlet, M. J. J. Pharm. Sci. 1985, 74, 807. (9) Taft, R. W.; Abboud, J.-L. M.; Kamlet, M. J. J. Am. Chem. SOC.1981, 103, 1080.
(10) We now prefer a p, value of 0.42 for methanol. (1 1) Thus, for a representative data set of 29 aliphatic and aromatic solutes, including l l strong HBD solutes with A a , = 0.1 1-0.82, and 6 alkanol solutes with Aa, = 0, we obtain the following correlation: log K, = 0.09 n
+ 2.73 r/ 100 - 0 . 7 9 ~ ’-~3.608, + 1.4OAam = 29, r = 0.9943, sd = 0.16
(12) To accommodate pyridine derivatives to the correlation equation, we needed to subtract 0.17 from p, or add a further 0.30 to V/lOO. We could find no justification for any such correction. (13) The 0.10 increment to v/lOO of carbocyclic aromatic solutes, on the other hand, is readily justified by the differing V/v relationships for ;he aromatic and aliphatic solutes and may derive from the same effect as causes S, of aromatics and aliphatics to show different dependences on log S , (vide infra). (14) Taft, R. W.; Abraham, M. H.;Doherty, R. M.; Kamlet, M. J. Nature (London) 1985, 313, 384. (15) Kamlet, M. J.; Doherty, R. M.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. J . Pharm. Sci., in press.
n = 115, r = 0.9944,
sd = 0.153
and calculated log S, values are compared in Table I. It is seen that, unlike Leahy’s KO, and HPLC correlation^,^^^'^ the log S, fit with VI/lOO is slightly poorer than that with V/lOO. This is more than offset, however, by the fact that, as will later be demonstrated abundantly, adding a term in (mp - 25) will allow eq 4 to be used for estimation of aqueous solubilities of solid solutes. An important aspect of eq 3 and 4 is that, as has evidently been overlooked by most other workers who have attempted correlations of aqueous solubilities with other properties, they can be applied through the S,/K,, term to solutes like acetone, methanol, and dimethyl sulfoxide, which are miscible with water in all proportions. Further, that eq 3 and 4 apply equally well to directly determined solubilities, and to SiLvalues derived from gas/water partition coefficients at very much lower concentrations, implies that most of the not totally miscible solutes fitted to these equations obey Henry’s law reasonably well up to saturation, Le., no evidence of dimerization of the alphatic solutes at higher concentrations. It is also significant that we appear to have achieved equations that are at or near the level of exhaustive fit (where the reliability of the calculations equals or surpasses the reliability of the measurements) without equation of state corrections or explicit relationships for activity coefficients or fugacity coefficients. It should be noted that the coefficients of the independent variables in eq 3 and 4 have the expected signs, reflecting an endoergic dependence of aqueous solubility on solute molar volume, and exoergic dependences on solute dipolarity/polarizability and (16) Abraham, M. H. J . Chem. SOC.,Faraday Trans. 1 1984, 80, 153. Abraham, M. H.J . A m . Chem. SOC.1982, 104, 2085. (17) For the 77 nonhydroxylic solutes, the correlation is given by log S, = 0.67 - 3.430/100 + 0.44~’+ 5.128. Thus, eq 3 meets the important criterion for an LSER that correlation equations should be similar for subsets of the data. (18) Leahy, D. E. J . Pharm. Sci., submitted for publication. (19) Leahy, D. E.; Carr, P. W.; Pearlman, R. S.; Taft, R. W.; Kamlet, M. J. Chromafogruphia,submitted for publication. (20) Bondi, A. J. Phys. Chem. 1964, 68, 441.
1998
The Journal of Physical Chemistry, Vol. 91, No. 7 , 1987
Kamlet et a].
TABLE I: Aqueous Solubilities at 25 OC of Non-HBD and Weak HBD Aliphatic Nonelectrolytes no. 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76
solute
-logs, 1.56 2.09 2.61 3.12 2.28 1.43 1.94 2.45 2.45 2.49 3.91 1.54 2.48 3.18 2.61 2.71 2.98 3.26 3.45 2.34 3.73 2.31 2.72 3.21 3.68 4.14 1.48 1.88 1.94 2.30 2.79 3.04 3.54 2.33 2.70 2.76 3.25 3.70 3.09 3.59 1.19 1.59 2.25 2.78 3.29 3.79 2.23 1.98 1.64 2.37 2.15 2.43 3.47 1.83 3.52 3.10 2.10 3.66 2.32 3.61 1.91 1.93 1.24 1.78 2.25 2.73 3.21 3.68 4.14 1.05 3.24 2.06 2.40 3.00 4.16 4.66
V/IOO 1.152 1.305 1.465 1.626 1.180 1.164 1.319 1.476 1.390 1.372 1.696 1.038 1.359 1.694 0.704 0.536 0.7 15 0.890 1.060 0.883 1.231 0.895 1.065 1.235 1.408 1.563 0.616 0.803 0.794 0.978 1.150 1.316 1.487 0.963 1.146 1.137 1.298 1.455 1.322 1.494 0.719 0.882 1.044 1.209 1.373 1.532 0.968 0.805 0.624 0.787 0.996 0.897 1.052 0.772 1.204 0.865 1.411 0.774 0.521 1.136 0.734 1.037 0.660 0.824 0.987 1.155 1.321 1.486 1.651 0.860 0.978 0.91 1 1.077 0.871 0.924 0.710
V*/IOO 0.553 0.648 0.745 0.842 0.598 0.553 0.648 0.745 0.709 0.729 0.923 0.505 0.699 0.893 0.369 0.348 0.445 0.542 0.639 0.480 0.674 0.477 0.574 0.670 0.767 (0.867) 0.325 0.424 0.424 0.521 0.622 0.7 16 0.813 0.524 0.622 0.622 (0.722) (0.820) (0.7 16) (0.8 16) 0.352 0.450 0.548 0.645 (0.745) (0.843) 0.514 0.427 0.336 0.442 0.519 0.492 0.617 0.406 0.700 0.528 0.699 0.444 0.271 0.619 0.380 0.535 0.335 0.433 0.535 (0.633) 0.729 (0.827) (0.925) 0.433 0.522 0.455 0.553 0.467 0.543 0.455
T* 5
-0.08 -0.04 -0.02 0.01 0 (-0.06) (-0.02) (0.00) 0.14 (0.25) (0.25) 0.27 0.26 0.24 0.70 0.85 (0.80) (0.78) (0.76) (0.63) (0.61) 0.67 (0.65) (0.63) (0.61) (0.59) 0.62 0.61 0.60 0.55 (0.53) (0.51)e (0.49) (0.55) (0.53) (0.53) (0.51) (0.49) (0.51) (0.49) 0.47 (0.39) (0.37) (0.35) (0.33) (0.31) 0.29 0.58 0.82 0.81 0.49 0.53 0.95 0.44 0.62 0.75 0.26 0.88 0.75 0.76 0.7 1 (0.25) (0.32) (0.31) (0.31) (0.30) (0.30) (0.29) (0.29) 0.16 0.76 0.58 0.51 (0.68) 0.88
.oo
1
p"
0 0' 0 0
0 0 0 0 0.71 0.70 (0.70) 0.47 0.46 0.46 0.31' 0.25 (0.25) (0.25) (0.25) 0.41 (0.41) 0.48 (0.48) (0.48) (0.48) (0.48) 0.37 0.36 0.42 0.45 (0.45) (0.45) (0.45) 0.45 (0.45) (0.45) (0.45) (0.45) (0.45) (0.45) 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 (0.05) 0.47 0.69 0.31' 0.53 0.48 (0.70) (0.70) (0.69) (0.69) (0.69) (0.69) (0.69) (0.69) 0.65 0.52 0.55 0.54 0.31' 0.76 0.76
log S, or 1% (Sg/Kgd -3.27 -3.97 -4.53 -5.24 -3.18' -3.16 -3.74 -4.30 -0.26 -0.54 -1.44 -0.13 -1.44 -2.71 0.33 0.20 -0.29 -0.80 -1.46 -0.15 -1.30 0.49 -0.18 -0.78 -1.43 -2.03d 0.44
-0.01 0.46 -0.05 -0.74 -1.36 -1 .so -0.14 -0.68 -0.6Sd -1.36d -1.87d -1.25d -1.75d -1.05 -1.53 -2.14 -2.73 -3.29d -4.00d -2.22 -1.12 -0.65 -1.05 -2.00 -1.95 -1 .75 -1.19 -2.61 -1.67 -1.70 1.86 0.53 0.01 0.88 1.03 2.06d 1.52 0.96 0.27 -0.25 -0.90d -1 .46d 1.32 0.56 0.48 -0.1 1 -0.33 2.1 1 2.55
calcd,b eq 4 -3.27 -3.78* -4.33* -4.86** -3.45* -3.25 -3.76 -4.3 1 -0.23 -0.28* -1.41 -0.15 -1.35 -2.39** 0.28 0.25 -0.37 -0.96 -1.55 0.08* -1.08* 0.50 -0.09 -0.69 -1.26* -1.86* 0.76** 0.12 0.42 -0.04 -0.65 -1.23 -1.82 -0.06 -0.65 -0.65 -1.26 -1.87 -1.23 -1.83 -0.97 -1.63 -2.23 -2.82 -3.42 -4.03 -2.13 -1.29* -0.50* -1.13 -1.93 -1.73* -2.00* -1.32 -2.84* -1.96* -1.30** 2.02* 0.91** 0.03 l.ll* 0.86* 2.10 1.47 0.87 0.27 -0.28 -0.85 -1.42 1.09*
0.55 0.90** 0.20**
-0.32 1.81* 2.46
Linear Solvation Energy Relationships
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
1999
TABLE I (continued) no.
77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
102 103 IO4 105 106
107 108 109 110 111 112 113 114 115
solute
-log S, 1.38
V/lOO 0.566
V,/100 0.283
(0.67)
(0.42)
"*m
Om
2.17 2.50 2.97 3.44 3.18 3.93 3.75 3.90 4.41 3.95 3.95 3.85 3.69 4.92 4.12 5.35 2.62 3.02 3.50 3.35 3.87 3.58 (3.4) (3.4) (3.4) 4.27 4.34 (4.4) (4.1) 4.48 2.67 3.05 3.36 3.12 3.76 (3.8) 4.31 4.41
0.405 0.584 0.748 0.915 0.920 1.082 1.076 1.089 1.256 1.237 1.257 1.234 1.227 1.414 1.394 1.575 0.765 0.917 1.096 1.073 1.252 1.244 1.230 1.265 1.240 1.419 1.413 1.420 1.428 1.585 0.940 1.089 1.232 1.233 1.43 1 1.412 1.599 1.572
0.205 0.305 0.402 0.499 0.499 0.593 0.593 0.593 0.690 0.690 0.690 0.690 0.690 0.789 0.789 0.882 0.401 0.500 0.595 0.595 0.690 0.690 0.690 0.687 0.690 0.785 0.785 0.785 0.785 0.885 0.498 0.593 0.690 0.692 0.786 0.786 0.882 0.882
0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40
7r*a
p"
0.42 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.51 0.51 0.51 0.51 0.51 0.51 0.5 1 0.51 0.51 0.5 1 0.51 0.51 0.51 0.51 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.47
log S, or log (WLJ 1.19 1.56 1.10 0.62 -0.01 0.06 -0.61 -0.48 -0.5 1 -1.24 -1.11 -1.14 -1.04 -1.17 1.83 -1.52 -2.35 0.83 0.39 -0.24 -0.21 -0.82 -0.74 -0.81 -0.71 -0.64 -1.55 -1.44 -1.40 -1.38 -2.09 0.63 0.09 -0.39 -0.41 -1.09 -1.00 -1.72 -1.60
calcd,b eq 4 1.32 1.48 1.06 0.49
-0.08 -0.08 -0.63 -0.63 -0.63 -1.19 -1.19 -1.19 -1.19* -1.19 -1.77 -1.77* -2.32 0.81 0.23* -0.33 -0.33 -0.88 -0.88 -0.88 -0.86 -0.88* -1.44 -1.44 -1.44 -1.44 -2.02 0.56 0.00 -0.57* -0.58 -1.13 -1.13 -1.69 -1.69
'Values in parentheses are estimated either from corresponding values for closely related compounds or from a set of parameter estimation rules which we shall publish in a forthcoming paper. b A single asterisk denotes difference of more than one standard deviation, a double asterisk denotes difference of more than two SD. 'After changing the value back and forth several times between 0.30 and 0.37, we have now settled on this value for nitriles. dData of Abraham,I6 not included in earlier paper.I5 CObtainedby parameter estimation rules; differs from earlier value of 0.46. /As discussed earlier,* we use @ = 0.10 for chloroaliphatic solutes, but continue to use p = 0.00 for chloroaliphatic solvents.
HBA basicity. Also, as with KO,and all other solubility roperties that we have studied, the leading factors influencing St' are seen to be the cavity term and the opposing hydrogen bond term involving water as the HB donor and the solute as the HB acceptor. Many workers have discussed the important dependence of aqueous solubility on a cavity term proportional to the molar volume of the or its molecular volume or surface area,21b but we believe that our present and earlier c ~ r r e l a t i o n s ' ~repJ~ resent the first quantitative demonstration and evaluation of the comparable importance of the hydrogen bonding term. Thus, for the more bulky solute molecules and the weaker HBA bases, mV/lOO'is the leading term in eq 3 and 4, whereas for smaller molecules which are stronger HBA bases, bp is the leading term. (We have shown earlier15 how the forerunner of eq 3 allowed the dissection of free energies of solution in water into contributing terms.) The changes in the coefficients of the independent variables between eq 3 and 4 are of some interest. It is seen that there is only a minor change in the coefficient of @, but an important increase in the coefficient of K*. This is because, as is intuitively expected, and as has been pointed out by Leahy and co-work(21) (a) Polak, J.; Lu, B. C.-Y. Can. J . Chem. 1973, 51, 4018. (b) Pearlman, R. S. "Molecular Surface Areas and Volumes and Their Use in Structure/Activity Relationships" In Physical Chemical Properties of Drugs: Marcel Dekker: New York, 1980; pp 321-347.
ers,18*19 Pcorrelates strongly with a linear combination of VI and K*.
Results and Discussion Nonconformance of Aromatic Solutes to Aqueous Solubility Equation Derived for Aliphatic Solutes. The situation is far less clear-cut when we consider the aqueous solubilities of the aromatic solutes. Unlike octanol/water partition, where correlation equations derived separately for the aromatic and aliphatic solutes (eq 2a and 2b) agreed reasonably closely with oqe another, agreement between experimental solubilities of aromatic solutes and values calculated through eq 3 or 4 is quite poor. Solubility results at 25 "C (S, or S,/K,,) for 31 aromatic solutes are assembled in Table 11, together with values of V/lOO, V I /100, K*, p, log solubilities calculated through the aliphatic solutes correlation equation, and A log S, (exptl minus calcd, eq 3). The data are mainly those assembled by Hine and Mookerjee,22a n d by Valvani, Yalkowsky, and R ~ s e m a nwith , ~ ~ additional results from seven other ~ o u r c e s . *We ~ ~have ~ not included (22) Hine, J.; Mookerjee, P. J. J . Org. Chem. 1975,40, 292. (23) Valvani, S. C.;Yalkowsky, S. H.; Roseman, T. J. J . Pharm. Sci. 1981, 70, 502. (24) Miller, M. M.; Wasik, S. P.; Huang, G. L.; Shiu, W. Y . ;Mackay, D. Enuironm. Sci. Technol. 1985,19, 522. (25) Amett, E. M.; Chawla, B. J . Am. Chem. Soc. 1979, 101, 7141. (26) McGowan, J. C.; Atkinson, P. N.; Ruddle, L. H. J . Appl. Chem. 1966,16, 99.
2000
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
Kamlet et al.
TABLE 11: Correlation of Aqueous Solubilities of Liquid Aromatic Solutes
no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
solute nitrobenzene 3-nitrotoluene benzaldehyde acetophenone benzene toluene o-xylene m-xylene p-xylene ethylbenzene n-propylbenzene isopropylbenzene mesitylene n-butylbenzene tert-butylbenzene fert-amylbenzene fluorobenzene chlorobenzene bromobenzene iodobenzene o-dichlorobenzene methyl benzoate ethyl benzoate n-propylbenzoate anisole N,N-dimethylaniline benzonitrile pyridine 3-meth ylpyridine dimethyl phthalate diethyl phthalate
-logs, 4.82 4.97 4.18 4.70 2.29 2.8 1 3.44 3.35 3.32 3.29 3.73 3.60 3.82 4.23 3.92 4.28 2.40 3.18 3.65 4.27 4.01 4.62 4.77 5.06 3.64 4.37 4.34 2.97 3.51 6.73
V/lOO 1.129 1.285 1.119 1.269 0.989 1.139 1.306 1.328 1.333 1.324 1.494 1.495 1.489 1.661 1.649 (1.83) 1.039 1.118 1.150 1.215 1.227 1.356 1.539 1.705 1.186 1.367 1.130 0.905 1.074 1.736 2.089
V,/100b 0.631 0.731 0.606 0.690 0.49 1 0.591 0.671 0.671 0.671 0.671 0.768 0.768 0.768 0.868 0.868 0.968 0.520 0.581 0.624 0.671 0.670 0.736 0.836 0.936 0.630 0.752 0.590 0.470 0.570 0.953 1.153
7r*o
p”
1.01 (0.97) 0.92 0.90 0.59 (0.55) (0.51) (0.51) (0.51) (0.53) (0.51) (0.51) (0.47) (0.49) (0.49) (0.47) 0.62 0.71 0.79 0.81 0.80 (0.76) 0.74 (0.72) 0.73 0.75’ 0.90 0.87 0.84 (0.82) (0.80)
0.30 (0.31) 0.44 0.49 0.10 0.11 (0.12) (0.12) (0.12) (0.12) (0.12) (0.12) (0.13) (0.12) (0.12) (0.12) 0.07 0.07 0.06 (0.05) (0.03) 0.39 0.41 (0.41) 0.22 0.33 0.37 0.64 0.67 (0.78)‘ (0.82)e
exptl -1.80 -2.44 -1.21 -1.34 -1.64 -2.25 -2.78 -2.76 -2.73 -2.84 -3.34 -3.38 -3.24 -3.94 -3.60 -4.15 -1.79 -2.44 -2.58 -2.87 -3.01 -1.81 -2.22 -2.67 -1.85 -2.04 -1.65 0.47 0.04 -1.69 -2.57
calcd, eq 3 -1.21 -1.72 -0.49 0.76 -1.94 -2.42 -2.97 -3.04 -3.06 -3.01 -3.60 -3.60 -3.54 -4.16 -4.15 -4.78 -2.26 -2.49 -2.60 -2.86 -2.95 -1.64 -2.14 -2.75 -1.94 -1.93 -0.90 1.25 0.81 -0.91 -1.93
difff -0.59 -0.72 -0.72 -0.58 +0.30 +0.17 +O. 19 +0.28 +0.33 +0.17 +0.26 +0.22 +0.30 +0.22 +0.55 +0.63 +0.47 +0.05 +0.02 -0.01 -0.06 -0.17 -0.08 +0.08 +0.09 -0.1 1 -0.75 -0.78 -0.77 -0.78 -0.64
calcd, eq 10 -1.79 -2.31 -1.11 -1.38 -1.78 -2.30 -2.7 1 -2.71 -2.71 -2.71 -3.25 -3.25 -3.21 -3.80 -3.80 -4.36 -2.06 -2.40 -2.67 -2.98 -3.05 -2.03 -2.51 -3.07 -2.09 -2.35 -1.29 -0.42 -0.03 -1.73 -2.70
diffcsd -0.01 -0.13 -0. I O +0.04 +0.14 +0.05 -0.07 -0.05 -0.03 -0.13 -0.09 -0.13 -0.03 -0.14 +0.20 +0.21 +0.27* -0.04 +0.09 +0.11 +0.05 +0.22* +0.29* +0.30* +0.24* +0.31* -0.36* -0.05 +0.07 +0.04 +0.13
ref 22 22 22 22 22 22 22 22 22 22 22 22 23 22 22 22 22 22 22 23 22 23 23 27 26 28 29 22, 25 22, 25 30 30
“Values in parentheses are estimated from corresponding values for closely related compounds or by a set of parameter estimation rules which we shall publish in a forthcoming paper. *0.10 is added to V/lOO of aromatic compounds. CExperimental minus calculated. d A single asterisk denotes difference of more than one standard deviation. ‘Taken as twice the value for the corresponding benzoic acid ester. Hydrogen bonding effects are assumed to be additive. /Estimated from dipole moment; differs from earlier estimated value.
a log S,”” value of -2.08 reported by Valvani and c o - ~ o r k e r s ~ ~ for phenetole, which was inconsistent with the result for anisole, and which was too high by 0.5-0.6 log unit compared with the correlations discussed below. Results for dimethyl and diethyl phthalate are included, with the assumption being made that hydrogen-bonding effects at the multiple sites are additive (i.e., values are twice those of the corresponding benzoic acid esters). We have used “ground rule” (a) above, Le., added 0.10 to V/loO of the aromatic compounds but, assuming maximal polarizability contributions to solubility in water, we have taken d to be zero in the (T* d6) formalism (as distinct from the situation for log KO,,where polarizability contributions were considered to contribute equally to solute-solvent interactions in both phases, hence cancelling o ~ t ; ~taking , ~ ’ d = -0.40 would not materially affect the conclusions). It may be seen in Table I1 that the differences between experimental log solubilities of the aromatic solutes and values calculated through the aliphatic solute correlation equation range from +0.63 for t-amylbenzene to -0.78 for pyridine. The average difference for the 3 1 data points is =t0.37 log unit, compared with a standard deviation of 0.14 for the aliphatic solutes. Nor is the scatter of the residuals random. The A log S, (eq 3) values are generally positive for benzene and the alkylbenzenes, and grow
x3p
o.6100 0.4
O
-
0.2
2
-0.21
m
+
(27) Hafkenscheid, T.L.; Tomlinson, E. Int. J . Pharm. 1983, 17, 1. (28) Chiou, C. T.; Schmedding, D. W. Enuiron. Sci. Techno/. 1982, 16, 4.
(29) Marcus, Y. Introduction to Liquid State Chemistry; Wiley: New York, 1977. (30) Deno, N. C.; Burkheimer, H. E. J . Chem. Eng. Data 1960,5 , 1 . ( 3 1 ) Since we are dealing here only with aromatic compounds, these ‘ground rules” do not influence the goodness of fit to eq 5 or 6, but only influence the intercepts. They are meaningful, however, when we compare log S, of the aromatics with the correlation equation derived for the aliphatics.
0
-0.41
-0.6
1 0.6
0.8
I
I
1.0
1.2
1.4
1.6
(rr*+PI Figure 1. Differences between aqueous solubilities of aromatic solutes and solubilities calculated through the aliphatic solute correlation equation plotted against (7r* 6).
+
increasingly negative with increasing solute dipolarity and HBA basicity. A plot of A log S, (eq 3) against (a*+ p) in Figure 1 shows the progression to be regular and, indeed, roughly linear. Correlation Equation for Liquid Aromatic Solutes. The trend which is observed in Figure 1 suggested that there might be systematic differences between aliphatic and aromatic solutes
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987 2001
Linear Solvation Energy Relationships insofar as their responses of aqueous solubility to solute A* and
p are concerned. For this reason we carried out a separate correlation of the data in Table I1 according to eq 1. The multiple linear regression is given by log S,ARE log ( S g / K g w= ) (1.44 f 0.27) (3.17 f 0.13)V/lOO - (0.81 f 0 . 2 6 ) ~ * (4.05 f 0.15)p (5)
+
n = 31, r = 0.9899, sd = 0.150 On the basis of our earlier experiences in the correlation of solubility properties by eq 1, eq 5 is unusual in a number of important regards. (i) Unlike the log KO, correlations, eq 5 for the aromatics differs significantly from the corresponding eq 3 for the aliphatic solutes insofar as the intercept and the coefficients of A* and p are concerned. (ii) Indeed the coefficient of a* seemingly has the “wrong” sign, suggesting an endoergic rather than an exoergic dependence of aqueous solubility on solutesolvent dipolar interactions. (iii) Unlike the log KO, correlations, where the pyridine derivatives did not fit using the established “ground rules”, the pyridine derivatives fit eq 5 to within 0.10 log unit. Despite these anomalies, however, the statistical goodness of fit was highly satisfactory, and the standard deviation of the correlation compared quite favorably with the usual reproducibility among laboratories of aqueous solubility measurements. One of the above anomalies was ameliorated, but not completely resolved, when we carried out the correlation for the 31 liquid aromatic solutes using Vl/lOO instead of F‘/lOO to measure the cavity term. The LSER is given by log S,ARN log (Sg/Kgw) = (0.37 f 0.26) (5.30 f O . ~ ~ ) V I / ~ O O (0.08 f 0 . 2 5 ) ~ * (3.85 f 0.19)p (6) n = 31, r = 0.9873, sd = 0.169
+
+
The coefficient of a* has the “proper” sign in eq 6, but is not statistically significant according to Student’s t-test, and there is no deterioration in statistical goodness of fit when the term is omitted as in log s , A R log (Sg/Kgw) = (0.44 f 0.15) - (5.33 f 0.21)VI/lOO
+ (3.89 f 0.14)p
(7)
n = 31, r = 0.9873, sd = 0.166 The following may be noted in eq 6 and 7. (1) First, foremost, and most necessary to explain, whereas the equation for log SiL contains an important term in r * ,the dependence of log StRon A* is not statistically significant. (2) The dependence of aqueous solubility on solute p values is about 1/3 higher for the aliphatic than for the aromatic solutes. (3) Although slightly poorer than in the F‘ equation (eq 5), the standard deviation of eq 7 still compares favorably with the usual reproducibility of the measurements. As will be discussed in detail below, we believe that ( l ) , and possible (2), above, derive from the fact that aIiphatic and aromatic solutes differ in the magnitudes of the solute-solute dipolarity/ polarizability interactions that need to be overcome in separating the single solute molecule from the bulk liquid solute before depositing it in the solvent cavity. It should be recognized that, if these differences between aqueous solubility relationships of aliphatic and aromatic solutes are real, they have important implications on solubility studies of organic compounds in any and all solvents. Correlation Equations for Liquid and Solid Aromatic Solutes. The absence of a dipolarity/polarizability term in eq 7 is a fortunate circumstance, which makes very much easier the correlation and prediction of the aqueous solubilities of solid aromatic solutes. This is because A* values of solid compounds are much more difficult to measure or estimate than VI and /3 values, and elimination of the term in A* allows an equation that is much more convenient to work with. To arrive at such an equation requires that we introduce an additional term that accounts for the endoergic process of conversion of the solute from solid to supercooled liquid at 25 OC.
Using an entropy of fusion approximation, and following a quite elegant line of reasoning, Yalkowsky and Valvani,, have shown that “supercooled liquid” solubilities can be estimated from aqueous solubilities of solids by adding O.Ol(mp - 25) to log S,, the term in parentheses being zero for compounds melting below 25 “C. Accordingly, combining our findings with those of Yalkowsky and Valvani, our preferred preliminary equation for the prediction of aqueous solubilities of liquid ana‘ solid aromatic solutes is given by log
StR= 0.44 - 5.33Vl/100 + 3.89 - O.Ol(mp - 25)
(8)
An excellent way to test an LSER like that given by eq 8 is to ascertain whether an independent data set, covering a different range of the property studied, yields similar intercept and coefficients of the independent variables. Accordingly, we have assembled in Table I11 aqueous solubility data for 39 mainly solid mono- and polycyclic aromatic compounds containing up to three fused rings, together with solvatochromic parameters required for the correlations. Parameter Estimation Rules for Solid Solutes. Before proceeding with the correlations, however, we need to set forth the “parameter estimation rules”, which we have used to arrive at values of VI/ 100 and p of the solid compounds when these were not otherwise available. The rules for estimation of p are consistent with earlier published parameter values5 and were arrived at mainly by back-calculations from octanol/water partition coefficients and from correlations of HPLC capacity factors involving large numbers of solutes, stationary phases, and mobile phases (as will be discussed in future papers). From the group increments to VI recommended by Leahy,’8,’9the VI numbers arrived at generally agree to within 2 cm3/mol with values obtained by multiplying molecular volumes reported by Pearlman, Yalkowsky, and Banerjee,, by Avogadro’s number. The parameter estimation rules, which we have applied successfully to prediction of aqueous solubilities and octanol/water partition coefficients of polycyclic aromatic compounds containing up to six fused rings (as will be discussed in future papers), are as follows: (a) For replacement of aromatic H by CH3, or introduction of CH, in side chain, add 9.8 to VI (an exception is toluene xylene, see Table 11); add 0.01 to p for each CH,, but only once for methyl ethyl in side chain. (b) For replacement of aromatic H by C1, add 9.0 to VI; subtract 0.04 from p. (c) For replacement of aromatic H by Br, add 13.3 to VI; subtract 0.04 from 0. (d) For replacement of aromatic H by NO,, add 14.0 to VI; add 0.20 to p for first NO,, 0.25 for second in meta or para position (e.g., p = 0.35 for nitronaphthalene, 0.60 for dinitronaphthalene). (e) For addition of fused ring (e.g., naphthalene anthracene) add 6.55 per additional C H to VI; add 0.05 to p for ring fused to carbocyclic ring but nil for ring fused to nitrogen-containing benzo(f)quinoline, but ring (e.g., add 0.05 to p for quinoline not for quinoline acridine). Aqueous Solubility Correlations for Solid Aromatic Solutes. The correlation for the 39 mainly solid aromatic solutes in Table I11 is given by eq 9; the correlation for the combined data sets in Tables I1 and 111 is given by eq 10. Experimental solubilities are compared with values calculated through eq 10 in Tables I1 and 111. A plot of the data is shown in Figure 2.
-
-
-
-
log
-
StR= (0.54 f 0.30) - (5.60 ic 0.34)k‘1/100 +
(3.68 f 0.20)p - (0.0103 f O.O008)(mp- 25) (9) n = 39, r = 0.9870, sd = 0.238
log SiR= (0.57 f 0.15) - (5.58 f 0 . 1 9 ) ~ 1 / 1 0 0+ (3.85 f 0.12)p - (0.0110 f O.O006)(mp- 2 5 ) (10) n = 70, r = 0.9917, sd = 0.216 (32) Yalkowsky, S . H.; Valvani, S. C. J . Pharm. Sci. 1980, 69, 602. (33) Pearlman, R. S.; Yalkowsky, S. H.; Banerjee, S. J . Phys. Chem. Ref. Data 1984, 13, 5 5 5 .
2002 The Journal of Physical Chemistry, Vol. 91, No. 7, 1987
Kamlet et al.
TABLE 111: Correlation of Aqueous Solubilities of Solid Aromatic Solutes
solute
no.
32 33 34 35 36 37 38 39 40 41 42 43 44
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
1,3,5-C,H;BrJ 1,2,4,5-C6H2Br4 CIoHs (naphthalene) 2-CioH7CHj I-CloH7CH3 1,3-CioHdCH3)2 134-CioH6(CH3)2 1r5-CioH6(CH3)2 2,3-Cio%(CH& 2,6-C10H6(CH3)2 1-CIoH7CH,CH, 1,4,5-CioH~(CH3)3 l-CIoH7CI 2-CIoH7CI
quinoline isoquinoline 3-methylisoquinoline anthracene 2-methylanthracene 9-methylanthracene 9, IO-dimethylanthracene phenanthrene 1-methylphenanthrene benzov)quinoline
V,/lOO
P
0.771 0.721 0.729 0.867 0.965 0.67 1 0.761 0.761 0.851 0.851 0.851 0.94 1 1.031 0.757 0.890 0.890 1.023 0.753 0.851 0.851 0.949 0.949 0.949 0.949 0.949 0.949 1.047 0.843 0.843 0.734 0.734 0.832 1.015 1.113 1.113 1.21 1 1.015 1.113 0.996
0.55 0.26 0.31 0.14 0.15 0.03 0 0 0 0 0 0 0 0.02 0 0 0 0.15 0.16 0.16 0.17 0.17 0.17 0.17 0.17 0.16 0.18 0.11 0.11 0.64 0.64 0.65 0.20 0.21 0.21 0.22 0.20 0.21 0.69
( m p - 25) 157 65 35 60 29 28 28 38 22 29 115 61 205 62 19 97 157 55 IO 0 0 0
56 80 83 0 39 0 36 0 2 43 191 184 57 158 76 84 69
logs, -3.33 -2.85 -2.39 -4.58 -3.99 -3.45’ -3.96’ -4.546 -4.47’ -4.83‘ -5.26’ -5.57‘ -7.776 -4.07 -4.50 -5.60 -6.98 -3.576 -3.75 -3.70 -4.29 -4.14 -4.68 -4.72 -4.89 -4.16 -4.90 -3.86 -4.14 -1.30 -1.45 -2.19 -6.40b -6.75‘ -5.87 -6.57 -5.15 -5.85 -3.36
calcd, eq I O
diff“
-3.34 -3.16 -2.68 -4.38 -4.55 -3.36 -3.98 -4.09 -4.41 -4.49 -5.44 -5.35 -7.44 -4.25 -4.60 -5.46 -6.86 -3.65 -3.67 -3.56 -4.06 -4.06 -4.68 -4.95 -4.98 -4.10 -5.00 -3.70 -4.10 -1.06 -1.08 -2.04 -6.42 -6.85 -5.45 -7.07 -5.15 -5.75 -2.93
+O.Ol +0.31* +0.29* -0.20 +0.56** -0.09 +0.02 -0.45** -0.06 -0.34* +O. 18 -0.22 -0.33* +0.18 +0.10 +0.14 -0.12 +0.08 -0.08 -0.14 -0.23 -0.08 0.00 +0.23 +0.09 -0.06 +0.10 -0.16 -0.04 -0.24* -0.37* -0.15 +0.02 +0.10 -0.42* +0.50** 0.00 -0.10 -0.43*
ref 27 27 27 27 27 32, 24 32, 24 32, 24 32, 24 32, 24 32, 24 32, 24 32, 24 32 32 32 32 32, 24 32 32 32 32 32 32 32 32 32 39 39 33 33 33 32, 33 32, 33 32 32 32 32 32
OA single asterisk denotes difference of more than one standard deviation, a double asterisk denotes a difference of more than two standard deviations. bThese are averages of the values in the two references cited.
1
BENZENE DERIVATIVES
-7.01
. I
I
PYRIDINE AND BENZOPYRIDINE DERIVATIVES
P
.’7 o
r = 0.9917 = 0.216
sd
I
0
-1.0
1
-2.0 log S,
I
-3.0
,
-4.0
,
-5.0
I
I
-6.0
-7.0
I
(CALC’D, eq. 151
Figure 2. Aqueous solubilities of aromatic solutes plotted against values calculated through eq 15.
The following may be seen in eq 9 and 10: (a) The intercept and the coefficients of V,/100 and p agree quite well with one another and with eq 8. (b) The coefficients of /3 ( b values) differ significantly and reproducibly from the b value for the aliphatic solutes (eq 4). (c) The coefficient of (mp - 25), arrived at by
multiple linear regression analysis, agrees remarkably well with Yalkowsky and Valvani’s theoretical estimate32from entropies of fusion. (d) The standard deviations of the correlation equations compare favorably with the usual reproducibility of the measurements between laboratories. (For example, the log S, value of -3.45 for compound 37 of Table I11 is an average of experimental values of -3.21 and -3.68; the value of -3.96 for 38 is an average of -3.76 and -4.17;and the value of -5.26 for 42 is an average of -5.56 and -4.95.) (e) Depending on molecular size, melting point, and HBA basicity, any one of the three terms is liable to be the dominant factor influencing solubility. We shall show in a future paper that the correlation equation does not change appreciably when the data set is expanded to include more than 50 additional polychlorinated biphenyls and polycyclic aromatic hydrocarbons of environmental interest, containing up to six fused rings. We shall also offer evidence that we have reached the “level of exhaustive fit” in the prediction of aqueous solubilities of monofunctional liquid and solid aliphatic and aromatic solutes, Le., the condition where nonagreement between experimental and calculated values casts more doubt on the measurement than the calculation. Why Different Aqueous Solubility Relationships for Aliphatic and Aromatic Solutes? All of the above derives from our finding that aqueous solubility relationships for aliphatic and aromatic solutes differ in two important regards: (a) Aqueous solubilities of aromatics do and those of aromatics do not show statistically significant dependences on solute dipolarity/polarizability (as measured by **). (b) Dependences on solute HBA basicity are ca. 25% smaller for aromatic than for aliphatic solutes. Although the evidence for these effects seems overhwelming and incon-
Linear Solvation Energy Relationships trovertible, the reasons are not completely clear. We have mentioned earlier15 that, conceptually, eq 1, when applied to solubilities, should include an additional endoergic term that relates to the process of separating a single solute molecule from the bulk liquid solute before depositing it in the solvent cavity. It is very likely that such a term would depend strongly on solutesolute dipolarity/polarizability interactions, which would be expected to covary strongly with x * . If this were the case, the terms in ?r* in eq 3-6, which we had earlier represented as measures of solute-solvent dipolarity/polarizability interactions, should in fact be regarded as differences between exoergic effects on solubilities of solutesolvent interactions and endoergic effects of solute-solute interactions. On this basis the differences in the coefficients of A* in eq 3 and 4 vs. eq 5 and 6 could derive from systematic differences between strengths of solutesolute interactions in aromatic compared with aliphatic solutes. Such an explanation would also resolve the seeming anomaly, commented on earlier,15 that the dependence on solute ?r* values is greater for octanol/water partition than for aqueous solubility (compare eq 2a and 3). A number of workers have recognized the possibility that interactions involving aromatic solutes are qualitatively different from those with aliphatics. It is known34that the crystal structures of numerous compounds containing *-electron systems involve vertical stacking in a way that is impossible for aliphatic molecules. Information on aromatic molecules in the liquid state or in solution is limited, but it is known that purine and 6-methylpurine associate in water by vertical stacking due to electrostatic interaction between the *-electron c l o u d ~ .Significantly, ~~ such association of the purines does not take place in the nonaqueous solvents Me2S0 and DMF. On the other hand, very careful vapor pressure measurements have show@ that benzene itself associates to such a small extent in aqueous solution that the solubility would be affected by only 0.005 log unit. As concerns interactions in the pure liquid state, it has been s ~ g g e s t e d ~ ’on * ~the * basis of a variety of experimental data that liquid benzene exists as a locally ordered, somewhat structured medium. Indeed, the Hildebrand solubility parameter of aromatic compounds is always higher than that of the model compounds (aH = 9.15 for benzene and 8.19 for cyclohexane, or 8.91 for toluene and 7.82 for methylcyclohexane). The effects on aqueous solubility of “association” in the pure liquid and in aqueous solution are not the same. If the pure liquid is more associated or structured, it will be more difficult to break the structure, and the aqueous solubility of the liquid will be less than expected. But, if the compound exists in aqueous solution as unassociated and associated species, the total (observed) solubility will be larger than calculated for the unassociated form. Any combination of association in the aromatic liquid and in solution could make it more difficult to predict even whether the observed solubility should be greater or smaller than calculated on the assumption of no association (as in the correlation equation for aliphatic solutes). The point we stress, however, is that there does seem to be strong evidence of interactions in the pure aromatic liquids and in aqueous solutions of aromatic compounds that do not exist with corresponding aliphatic molecules. Hence, it has been necessary to set up different LSERs for aqueous solubilities of aliphatic and aromatic compounds. Attempts To Include a Term Measuring Solute-Solute Interactions. We considered that all problems would be resolved if we could include in the correlations statistically significant terms that measured the endoergic process of disrupting solute-solute interactions to extract the single solute molecule, and if these terms were significantly different for aliphatic and aromatic solutes. The (34) Boegens, J. C. A.; Herbstein, F. H. J . Phys. Chem. 1965,69, 2160. (35) Chan, S. I.; Schweizer, M. P.; Ts’o, P. 0.P.; Helmkamp, G. K. J. Am. Chem. SOC.1964.86, 4182. (36) Tucker, E.E.;Lane, E.H.; Christian, S. D. J . Solution Chem. 1981, 10, 1.
(37) Narten, A. H. J . Chem. Phys. 1968, 48, 1630. (38) Schmidt, R. L.; Goldstein, J. H. J . Chem. Phys. 1969, 50, 1494. (39) Mackay, D.; Shiu, W. Y . J . Phys. Chem. Ref. Dura 1981, 10, 1175.
The Journal of Physical Chemistry, Vol. 91, No. 7, 1987 2003 parameters considered were ijH2,the square of the solute Hildebrand solubility parameter, and log S,, a measure of the solute vapor pressure (S, = P,,,/24.5). Values of the Hildebrand solubility parameter are known for 16 of the liquid aromatic compounds in Table 11, and, when we included the additional term, there was, indeed, a seemingly significant improvement in statistical goodness of fit. The four parameter correlation was given by log
StR= (-0.03
+
f 0.26) (0.91 f 0.25)6H2/100 (5.48 f 0.21)V1/100 - (0.41 f 0 . 2 2 ) ~ * (3.68 f 0.17)p (1 1)
+
n = 16, r = 0.9953, sd = 0.103 It is seen, however, that despite the excellent fit, the correlation equation makes no chemical sense. The term in 6H2,expected to be endoergic, is exoergic; the term in T * , expected to be exoergic, is endoergic. It is obvious that the solutesolute and solutesolvent interactions are not properly sorted out between aH2 and ?r*. The results seemingly made more chemical sense when we used log S, as the additional term. The correlation equation for the 31 liquid aromatic solutes of Table I1 was then given by log s
tR
log (S,/Kgw)= (0.42 f 0.32) (0.36 f 0.10) log S, (3.31 f 0.33)~1/100+ (1.23 f 0 . 4 0 ) ~ *+ (3.95 f 0.17)p (12) n = 31, r = 0.9912, sd = 0.143
+
Here, in addition to an improved goodness of fit relative to eq 6, the coefficients of the independent variables all have the “proper” signs. Aqueous solubility does, indeed, decrease with decreasing solute vapor pressure and increase with increasing solute dipolarity/polariza bility . Problems arose, however, when we carried out the correlation with the same parameters for the aliphatic solutes. The multiple linear regression equation for the 115 aliphatic solutes of Table I is given by eq 13; the correlation for the 77 nonhydroxylic compounds is given by eq 14. It is seen that, although eq 13 and
= log (S,/K,)
= (0.13 f 0.07) - (0.10 f 0.03) log S, (6.30 f 0.15)V1/100 + (0.91 f 0 . 0 8 ) ~ *+ (5.16 f 0.07)p (13) n = 115, r = 0.9951, sd = 0.144
log S t L
log (S,/Kgw)= (0.15 f 0.11) - (0.12 f 0.05) log S, (6.39 f 0.28)V1/100 (0.89 f 0.14)a* (5.12 f 0.08)p (14) n = 76, r = 0.9953, sd = 0.161
log S t L
N
+
+
14 agree quite well with one another, they both have the “wrong” sign of the coefficients of log S,,suggesting that solubility increases with decreasing solute vapor pressure. On this basis, the unresolved problem remains that, certainly in eq 13 and 14, and probably in eq 12, solute-solute and solute-solute interactions are not properly sorted out between the terms in log S, and T * . From the above we are reluctantly forced to conclude that solutesolute and solutewater dipolarity/polarizability interactions covary so strongly that they cannot properly be apportioned between the A* parameter and any of the obvious measures of solute cohesive energy. Hence, in evaluating the factors influencing aqueous solubilities, it will need to be understood that the dipolarity/polarizability term measures a combination of effects, and that this combination may be different for aliphatic and aromatic solutes. We have not addressed the question of why the difference in the coefficients of p for aliphatic and aromatic solutes, and why the pyridine solutes do not fit the log KO, equation (eq 2b and 2c), but fit the log StRequations quite well. Again, we can suggest
J. Phys. Chem. 1987, 91, 2004-2005
2004
that this may be because of self-association of the aromatic solutes in water (which was shown to be insignificant for benzene, as mentioned above, but which may be more important for the more dipolar aromatic solutes). However, this would require that there be significant differences between S, values, determined for dipolar aromatic solutes in saturated aqueous solutions, and S,/ Kw values, determined in dilute solutions (Le., nonconformance with Henry’s law), and such differences have not, to our knowledge, been demonstrated. Correlations of Vapor Pressure with Solute Molar Volume and Dipolarity. That including a term in log S, leads to differences of 1.15 in the coefficient of a* and 1.99 in the coefficient of V I /100 between eq 6 and 12, while maintaining good statistical fit in both equations, suggests that log S, for aromatic solutes must be highly correlated with a linear combination of VI and a* (as seems intuitively reasonable). This is indeed the case; the correlation of log S, vs. V,/lOO and a* for 30 aromatic solutes of Table I1 (excluding diethyl phthalate) gives r = 0.972, sd = 0.24. The corresponding correlation for 5 1 nonchlorinated, nonself-associating aliphatic compounds of Table I (excluding alcohols and primary and secondary amines) gives r = 0.883, sd = 0.38. A slightly better correlation for the aromatics, and a significantly better one for the aliphatics, are obtained when VI/lOO and (a*)2are taken as the independent variables. The correlations, which we will discuss in greater detail in a future paper, are given by
log S,(aromatics) = (1.05 f 0.20) - (5.36
* 0.23)‘v~/100- (2.39 f 0 . 1 4 ) ( ~ * ) ~ (15)
n = 30, r = 0.9801, sd = 0.184 log S,(aliphatics) = (1.22 f 0.16) - (4.94 f 0.22)V1/100 - (3.20 f 0 . 1 4 ) ( ~ * ) ~ (16)
n = 51, r = 0.9674, sd = 0.205 The correlation for the combined data sets is given by eq 16, which is seen to have a somewhat higher standard deviation than eq 14 or 15. We conclude that, although not as evident as with aqueous log S,(combined) = (1.17 f 0.12) - (5.03 f 0.17)1/,/100 - (2.99 f 0 . 1 1 ) ( ~ * ) ~ (17)
n = 81, r = 0.973, sd = 0.237 solubilities, vapor pressure comprises yet another property that depends on solute cohesive energy, where better correlations with solute parameters are obtained when aliphatic and aromatic solutes are treated separately.
COMMENTS Comment on the Fujimoto-Schurr Analysls of Steady-State Fluorescence Polarlzation of DNA/Dye Complexes Sir: Fujimoto and Schurr’ discuss the possibilities and limitations of extracting information about internal DNA mobility from the steady-state fluorescence polarization anisotropy (FPA) of intercalated dyes. The authors derive an expression for the steady-state FPA of the elastic continuum DNA model and present a detailed analysis of the uncertainties obtained in the parameters when these are evaluated from steady-state FPA measurements. In a previous study2 we used the steady-state FPA of two excitation transitions in various dyes to obtain information about anisotropic “twisting” and “out-of-plane” motions. We found that twisting DNA motions dominate the FPA in all cases. In addition, we noted that the observed out-of-plane mobility was strongly dependent on the assumed binding site geometry; Le, we observed some out-of-plane mobility when we assumed a binding site geometry where the dye plane intercalates perpendicular to the helix axis, but no out-of-plane motions when we assumed a tilted binding site as described by Hogan et aL3 The study also contained a detailed discussion about uncertainties in estimated parameters and the limitations of the applied model. In particular, we noted that the extent of “out-of-plane” mobility (in a perpendicular site) strongly depended on the value of the ARF parameter used to account for subnanosecond librational motions of the dye within the intercalative pocket. In our opinion, the correct value of the ARF was obtained by Magde et aL4 using a jitter-free streak ( 1 ) Fujimoto, B. S.; Schurr, J. M. J. Phys. Chem., in this issue. (2) Hard, T.; Kearns, D.R. J. Phys. Chem. 1986, 90, 3437-3444. (3) Hogan, M.; Dattagupta, N.; Crothers, D. M. Biochemisfry 1979, 18,
281-88. (4) Magde, D.; Zappala, M.; Knox, W. H.; Nordlund, T. M. J . Phys. Chem. 1983, 87, 3286-3288.
camera to reach the subnanosecond region. Fujimoto and Schurr, in their analysis, emphasize the “tilted” binding site geometry. Like us, they do not find any evidence for “out-of-plane” motions in this case. The authors find that a “perpendicular” binding site geometry leads to the same results, when ARF values S0.9 are used, although these results are not included in the paper. Still, we think that out-of-plane motions of DNA bases and intercalated dyes, that are too slow to be reflected in the initial rapid decrease of the time-resolved FPA, could account for the low limiting dichroism observed by Hogan et al. Therefore, we suspect that the A R F factors employed by Fujimoto and Schurr, which are lower than what is observed in time-resolved subnanosecond experiments: may have diminished, or eliminated, the possible contribution of out-of-plane motions to the observed depolarization. Thus, it would be very interesting to see whether analysis of the present steady-state FPA data using the Schurr model with larger A R F values would permit slow out-of-plane motions of a dye bound in a “perpendicular” mode.
Department of Chemistry, B-014 University of California. San Diego La Jolla, California 92093
Torleif Hard David R. Kearns*
Received: December 19, 1986
Is Quantum Monte Carlo Competitive? Lithium Hydride Test Case Sir: In this Comment we point out that quantum Monte Carlo (QMC) with fixed nodes can be computationally competitive with large-scale state-of-the-art techniques. We show this with lithium hydride at an internuclear separation of 3.015 bohr as a test case.
0022-365418712091-2004$01.50/0 0 1987 American Chemical Society
