3046
J. Phys. Chem. 1985, 89, 3046-3049
In view of the identical resonance structures of SI2and S22,one can readily verify the unitarity relation lS,212+ IS22I2 = 1
Substituting the appropriate expressions Tu given above, one obtains the final expression for the inelastic matrix element S , 2 :
SI2= -2iPa1/2Qa1/2exp(i)(/3 - 0) X cos 0 sin ( a - p + 0) + ub cos (0+ Xb) sin (a + Xb) cos 0 + ub exp(i)(g + x b - e) cos (0 + Xb) (A.5) where
I
[
a =
ff,
+ 6, - a2 - 8 2 - xa
For weak diabatic coupling (see Figure 6) 0 is readily identified as the diabatic bound state in a diabatic potential obtained by continuing W2(R) W3(R) at Rb, whereas for strong diabatic coupling, p is the phase integral for the corresponding adiabatic
bound state in the adiabatic potential W3(R). Since ub = P b - l - 1 = exp(2atb) - 1 where t b is the LandauZener factor IV231z/(vhAF23) (V23 = diabatic perturbation at Rb, M 2 3 = difference in slope of the diabatic potentials at R b (see Figure 6)), we have the two limits: u b
= 0 when V23 = 0 and
u b
-
co
when
V23
-
m
(25)
In the first limit (weak diabatic coupling), SI2reduces to the two-channel inelastic transition matrix element -2iPa'/2Q,1/2 sin ( a + p 0) which corresponds to the anticipated expression of a transition factor Pa1/2Q:/2 multiplied by a Franck-Condon factor sin ( a - /3 + e). Indeed from (A.6), one has
+
a -p
+ 0 = a , + 6, - a3 - 62 - Xa
-
(A.7)
For weak diabatic coupling at R,, a/4,2$ and one can identify from Figure 6 the expression A.7 as the overlap between the two continuum wave functions appropriate to the diabatic channels 1 and 2. Finally in the limit of strong diabatic coupling at Rb, we note becomes independent of U,, except for energies from (AS) that S12 where (8 4- Xb) = ( n 1/2)a corresponding to the presence of adiabatic resonances in the potential W3(R). Similarly, the condition 0 = (m + 1/2)a indicates the presence of quasi-diabatic resonances. Both resonances make SI2sensitive to the adiabaticity parameter U,.
+
Partition Coefficients of Aliphatic Ethers-Molecular
Surface Area Approach
Noriaki Funasaki,* Sakae Hada, and Saburo Neya Kyoto Pharmaceutical University. Misasagi, Yamashina- ku, Kyoto 607, Japan (Received: January 25, 1985)
The octanol-water partition coefficient P and cavity surface area S are determined for six uniconformation ethers and five multiconformation ethers and analyzed in terms of the molecular conformations of these ethers in water. For these uniconformation ethers which include two acyclic branched ethers and four cyclic ethers, the log P vs. S plots show a very good linearity; e.g., that trans-2,5-dimethyltetrahydrofuranis more hydrophobic than the cis isomer is explained quantitatively by the difference in S between these stereoisomers. The log P vs. S relation thus determined is used to estimate the molecular conformations of multiconformation ethers; diethyl ether has the all-trans conformation, diisobutyl ether is a mixture of some or all of four conformers, and dibutyl ether has some gauche interactions in the C-C bond on average. This estimation for diethyl ether is consistent with vibrational spectral data. The vicinal proton-proton coupling constant for the CH2-CH fragment of diisobutyl ether in CDC13 solution conforms to the estimation from the S and P data. The relations of log P with the molar volume and the molecular connectivity index depend on the type of the alkyl chain, linear, branched, or cyclic. The logarithm of the capacity factor, log [(t - t o ) / t o ] , in HPLC shows a good linearity with S, suggesting that the S approach is useful for estimation of the retention time t. Although empirical rules for estimation of P proposed for quantitative structure-activity relationships of drugs neglected the effect of the stereostructure on P, the present results provide the data for correction due to this effect.
Introduction Hydrophobicity plays an important role in a wide variety of phenomena, such as solubility in water, oil-water partition equilibrium, biological activity, and chromatographic separation. The solubilities of alkanes in water show a good linearity with the molar volumes of the alkanes and this linearity depends on types of alkanes, such as linear, branched, and cyclic alkanes.' However, this dependence on type vanishes when the solubilities are plotted against molecular surface areas of the alkanes.2 Hermann developed a computer pogram for determining a molecular surface area and considered the effects of the molecular conformations of alkanes on the area2 This surface area approach was used for the correlation with the solubilities of monofunctional (1) McAuliffe, C. J . Phys. Chem. 1966, 70, 1267. (2) Hermann, R . B. J. Phys. Chem. 1972, 76, 2754.
0022-3654/85/2089-3046$01.50/0
compounds in water, but only the surface areas of these solutes in the most extended conformations were ~ o n s i d e r e d . ~ The effects of alkyl chains on the partition coefficient were explained with another surface area approach, where a relative surface area was determined by counting the number of packed spheres around a Corey-Pauling-Koltun (CPK) model of a solute! This number of the packed spheres can be converted to an absolute surface area, and this area was shown to be linear with computed surface area.5 These surface area approaches applied for intramolecular hydrophobic association of double alkyl chain com(3) Amidon, G.L.; Yalkowsky, S.H.; Anik, S . T.; Valvani, S.C. J . Phys. Chem. 1975, 79, 2239. (4) Harris, M. J.; Higuchi, T.; Rytting, J. H. J . Phys. Chem. 1973, 77,
2694.
( 5 ) Funasaki, N.; Hada, S.; Neya, S.; Machida, K. J . Colloid Interface Sci., in press.
0 1985 American Chemical Society
Aliphatic Ethers
pounds in water on the basis of octanol-water partition coefficient data.6 While we investigate the correlation of biological activity with the chemical structure for double alkyl chain drugs, we notice that ethers are more hydrophobic than those expected from other double chain compounds. Molecular surface areas depend on the molecular conformations. Nevertheless, except for alkanes,2 the hydrophobicity-surface area relationship has not yet been considered taking into account the molecular conformation. Therefore, we measure the partition coefficients of six aliphatic ethers which have only one conformation and show that a linear log P vs. S relation holds true for these uniconformation ethers. By using this relationship, we may estimate the molecular conformations of multiconformation ethers. The conformation estimated will be compared with spectroscopic data. Chromatographic data are also correlated with surface areas of solutes. Experimental Section Materials. Most ethers and 1-octanol were obtained from Tokyo Kasei Organic Chemicals or Nakarai Chemicals. These materials were gas chromatographically (GC) 99% pure or more. 2,5-Dimethyltetrahydrofuran was purchased from Aldrich Chemical Co. This sample is a mixture of 44.3% cis and 55.7% trans as determined by GC. The ion-exchanged water was twice distilled before use. Determination of Partition Coefficients. A solute was dissolved in I-octanol previously saturated with water. This octanol solution was added into water previously saturated with octanol and shaken for 1 or 2 h in an incubator. This mixture was allowed to stand for 1 or 2 h before separation of two layers. In most cases, the concentration of the solute in the octanol phase was determined by GC. The partition coefficient of a solute was determined at four or five concentrations and was independent of the concentrations. Relative errors in the partition coefficient values are within 7%. Determination of Cavity Surface Area. A CPK model of the solute is constructed; Styrofoam balls representing water molecules (radius 1.0 A) are glued onto the model and packed as tightly as possible. The Styrofoam balls are counted, and the number is multiplied by 3.99 to convert to absolute cavity surface area S . This factor was evaluated by using spherical solutes.6 The S value for a molecule in water is defined as the area of the surface traced out by the center of a water molecule rolling over the van der Waals surface of the solute molecule.2 For a solute the reported S value is the average of four or five values. Chromatography. The quantitative analysis of ethers was made by gas-liquid G C (Shimadzu G C 3BT). The retention time t was measured under the following conditions: a Silicone DC 550 column (Nishio Kogyo), an oven temperature of 50 OC, and a He gas pressure of 3 kg/cm2. The peak area was calculated with a Shimadzu Chromatopack C-R1 B analyzer. High-pressure liquid chromatography (HPLC) was made with a Shimadzu LC 3A chromatograph under the following conditions: a Zorbax ODS (octadecyl silane) column, a methanol-water mixture (80:20 and 60:40 v/v), a flow rate of 0.5 mL/min, refractive index (Shimadzu RID-2A) for detection, and a column temperature of 45 OC. ' H a n d 13CNMR. The proton N M R spectrum (at 80 MHz) of diisobutyl ether in CDC13and proton noise completely decoupled carbon-13 N M R spectrum of diisobutyl ether in C6D6 were recorded on a Varian CFT 20 spectrometer a t room temperature. Me4Si was used as internal standard. Density. The density for a few ethers was measured with an Anton Paar DMA 60/602 digital density meter at 25.00 f 0.002 OC.
Results Uniconformation Ethers. The P values of 11 aliphatic ethers for the octanol-water system are shown in Table I. The values for diethyl ether (l), dipropyl ether (3), and ethyl butyl ether (4)
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 3047 TABLE I: Logarithm of Partition Coefficient, S , Molar Volume, Chromatomaohic Data. and Connectivitv Index for Ahhatic Ethers ~~
log P
ether 1 2 3 4 5 6 7 8 9 10 11
0.83' 0.94 2.03e 2.03' 1.52 3.21 2.78 0.22 0.64 1.22 1.34
s, A2/
molecule 188 191 235 235 215 284 g
164 180 203 209
u,'mL/ mol 104.8 118.8 137.7 137.2 142.3 170.4 174.4h 81.1' 98.2 120.81 120.81
0.07 d 0.67
d 0.49 1.23 1.31 -0.14 0.13 0.27 0.30
0.42 d 1.11 d 0.76 1.85 1.48 1.01 1.28 1.22 1.26
X 2.414 2.561 3.414 3.414 3.126 4.414 4.126 2.500 3.000 3.288 3.288
" Data from: "Organic Solvents. Physical Properties and Methods of Purification", 3rd ed., Weissberger, A,, Ed.; Wiley-Interscence: New York, 1970. bEluted by 60% methanol. cData from: Collander, R. Acta Chem. Scand. 1949, 3, 717. dNot determined. eTaken from ref 7. (Data from: Hansch, C.; Anderson, S . J . Org. Chem. 1967, 32, 2583. gData are shown in Table 11. *This work. 'Data at 20 OC. 'This work, for a sample (mixture of 10 and 11) supplied by Aldrich. TABLE II: S Values and Calculated Vicinal Proton-Proton Coupling Constants of the CHICH Fragment for Diisobutyl Ether in Four Conformations conformer S. A2/moIecuIe Jru.ru. H Z A 275 ( J E + Jt)/2 8.7" B 267 (Jg + J J / 2 8.7" C 263 (3Jg + Jd/4 5.9" D 259 JE 3.1" ~~
~
~
"Calculated by using values of JE = 3.1 H z and Jt = 14.3 Hz.
Figure 1. Logarithm of the octanol-water partition coefficients plotted against cavity surface areas for aliphatic ethers: 0, linear; A,& acyclic branched; m, cyclic ethers; hollow symbols, multiconformation; filled symbols, uniconformation. The numeral attached to each data point identifies one of the ethers shown in text.
are taken from the literature.' All P values shown in Table I except for these three ethers were determined in this work. Dibutyl ether ( 6 ) ,diisobutyl ether (7), 1,3, and 4, are multiconformation compounds. If we assume that only gauche and trans are stable conformations, methyl tert-butyl ether (2), diisopropyl ether (S), tetrahydrofuran (8), tetrahydropyran (9), cis-2,5-dimethyltetrahydrofuran (lo), and trans-2,5-dimethyltetrahydrofuran(11) are uniconformation compounds. The S value of a solute depends on the molecular conformation. The S values for the multiconformation ethers in Table I are those in the case where the main chain is in the all-trans conformation. The presence of one gauche conformation in the main chain leads to a reduction of about 4 A2/molecule in S.5 The S values for diisobutyl ether in four conformations are shown in Table 11.
(6) Funasaki, N.; Hada, S.; Neya, S.; Machida, K. J. Phys. Chem. 1984, 88, 5786.
( 7 ) Leo, A,; Hansch, C.; Elkins, D. Chem. Reu. 1971, 71, 525.
Funasaki et al.
3048 The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 H
TABLE 111: Correlation Parameters"in the Equation, log P = a x - @ S,b A=/ x type
mL/mol branched cyclic
u,
linear
molecule
(data) (n = 6)
(n = 4)
0.0252 3.893 0.9993 0.018
0.0363 2.964 0.9999 0.012
a /3 r u
Q r = Correlation
(n = 3) 0.0335 3.110 0.9927 0.114
coefficient and
H
X
acyclic
cyclic
(n = 4) (n = 7) (n = 4) 0.0269 1.196 1.357 2.105 1.979 3.241 0.9950 0.9973 0.9658 0.052 0.062 0.135 0
H
H
(A)
= standard deviation.
Uniconformer.
3.
Figure 3. Four possible conformations for diisobutyl ether.
10-
O
roo
60% &OH
150 v (mLlmole)
Figure 2. Logarithm of the partition coefficients plotted against the molar volumes for aliphatic ethers: 0, linear; A, acyclic branched; 0, cyclic ethers.
In Figure 1 the logarithm of P is plotted against S, where the line is drawn by using a least-squares method for six uniconformation ether data in Table I. As shown in Table 111, the correlation coefficient r is very close to unity. For uniconformation alkanes, a similar slope in the log (solubility in water) vs. S relation is ~ b t a i n e d . ~ . ~ log P = a s - p (1) For aqueous solubilities of alkanes, the correlations with the molar volume u and connectivity index x were investigated.',* A molecule may be regarded as a graph, the atom forming the vertices and the bonds the edges of this graph. The simple connectivity value 6i of a vertex i is the number of other vertices to which it is joined. The connectivity index x is defined by n
x = s=C(si6,)y2 1
(2)
where s identifies a subgraph (an edge) and 6i and 6, are the connectivity values at each end of an edge in the graphe9 As shown in Table 111, the log P vs. u relation depends on linear, branched, or cyclic ethers and the log P vs. x relation depends on cyclic or acyclic ethers. Figure 2 shows the log P vs. u plots for the ethers. The same dependences on type have been reported for aqueous solubilities of alkanes.'-8 The ethers 10 and 11 are stereoisomers. The S approach explains why the trans isomer is more hydrophobic than the cis isomer. On the other hand, the u and x approaches cannot explain why the correlation with u or x depends on the type and steric position of the alkyl chain. Thus S is the best of the three parameters for correlation with log P . Multiconformation Ethers. The correlation of log P with S determined by using uniconformation ether data may be used as the calibration line for multiconformation ethers. In Figure 1 the S values for these ethers in all-trans conformations are shown except diisobutyl ether. Diethyl ether 1 is the shortest ether of them. As Figure 1 shows, the plot of 1 falls on the calibration (8) Edward, J. T. Can. J . Chem. 1982, 60, 2753. (9) Kier, L. B.; Hall, L. H.; Murray, W. J.; Randic, 1975, 64, 1971.
M. J . Pharm. Sci
150
200
2 50
s (A~/mclecule) Figure 4. Logarithm of the HPLC capacity factors plotted against cavity surface areas for aliphatic ethers. Two sets of HPLC data for 60% methanol and 80% methanol are shown. line, suggesting that 1 is in the all-trans conformation. This estimation of the molecular conformation from P and S is in agreement with vibrational spectral data since these data show that 1 takes the all-trans conformation in the vapor phase, in the liquid phase, and in CS2 and CC14 solutions.I0 Therefore, we assume that the torsional angle around the CC-OC bond is 180° for all ethers. Isomers 3 and 4 have the same P and S values and both are on the calibration line in Figure 1. As Figure 1 shows, the S value for 6 in the all-trans conformation is larger than that expected from the calibration line. This means that 6 has some gauche interactions in the alkyl chains on average, suggesting that 6 is an equilibrium mixture of some conformers. As Figure 3 shows, 7 can take four conformations, A, B, C, and D. These four S values are shown in Figure 1, but none of them fall on the calibration line. Therefore, 7 seems to be a mixture of some or all of these four conformers. Chromatographic Data. To investigate the predictability of the retention time t from the S value of a solute and the necessity of the presence of water as solvent (mobile phase), we measured t values of ethers in HPLC and gas-liquid GC. When r,, denotes the retention time of an unretained peak, the capacity factor, ( t - t o ) / t o ,is proportional to the partition coefficient of the solute between the stationary and mobile phases." We determined the t values in HPLC by using 60% and 80% MeOH in H,O as solvent, where a mixture of the ethers in 60% or 80% MeOH was injected and then eluted with the same solvent. Further increases in MeOH content led to overlap of the peaks of ethers, whereas increases in water content led to difficulties in detection of some ethers because of the decreased solubility (10) Wieser, H.; Laidlaw, W. B.; Krueger, P. J.; Fuhrer, H.Spectrochim. Acta, Part A 1968, 24A, 1055. (11) Snyder, L. R.; Kirkland, J. J. 'Introduction to Modern Liquid Chromatography"; Wiley: New York, 1974; Chapter 2.
The Journal of Physical Chemistry, Vol. 89,No. 14, 1985 3049
Aliphatic Ethers TABLE I V Proton (6") and Carbon (&) Chemical Shifts and Vicinal Proton-Proton Coupling Constants for Diisobutyl Ether group
bo
CH2
3.15 1.85 0.895
CH
CH3
J",,, Hz
6Cb
6.6 6.5
78.16 28.97 19.57
'Expressed downfield from internal Me& in CDCb bExpressed downfield from internal Me@ in C6D6.
of ethers and broadening of peaks due to increased P values of ethers. Therefore, we could not determine accurate and reproducible t values outside 60% and 80% MeOH. Only 60% MeOH data are shown in Table I. Figure 4 shows two sets of plots of log [ ( t - to)/to]against S . Nearly linear relations hold in both sets, except for 7,independently of the type of the alkyl chain. Spherical ethers, such as 5, 7 , 8 , and 9, deviate upward as compared with other rodlike ethers. This may be due to the difference in adsorptivity to porous Zorbax ODS particles. The relation of HPLC log [ ( t - to)/to]with u shows the same dependence on type as shown in Figure 2. The gas-liquid GC retention time data for ethers are also included in Table I. N o GC log [ ( t - to)/to]data show good correlations with S, u, and x. The S approach serves to estimate the HPLC t value for systems containing water as solvent. NMR Data. To obtain information on the molecular conformation, we recorded 'H and 13CN M R spectra for diisobutyl ether. Assignments of IH and I3C peaks were made by comparison with the chemical shifts, the peak areas, and spin-spin splittings of Vicinal proton-proton coupling analogous compound^.^^*'^ constants were determined from the doublets of the CHI and CH3 groups due to coupling with the C H proton. Only three peaks were observed in the completely proton noise decoupled 13CN M R spectrum. These N M R data are shown in Table IV. Vicinal proton-proton coupling constants depend on the steric position of two protone. For diisobutyl ether, four conformations are expected, as shown in Figure 3. The vicinal coupling constants for the CH2CH fragment are expected as shown in the third column of Table 11. The exact vicinal constants for the gauche (g) and trans (t) positions are not reported for the present system. Therefore, we assumed values of Jg = 3.1 H z and Jt = 14.3 H z rather arbitrarily.12 The vicinal constants calculated from these values are shown in the last column. None of these JVifvalues are in agreement with the observed value, 6.6 Hz. From this result, therefore, it is concluded that diisobutyl ether is present as an equilibrium mixture of some or all of the four conformers in CDC1, solution. The populations of these conformers may be different in water from those in CDCl,. The populations of conformers with smaller S values are expected to be higher in water than those in CDCl,, because of hydrophobic interactions? Only three peaks (12) Oki, M.; Iwamura, H.; Nishida, T. "Solutions Manual for NMR Spectra"; Nankodo: Tokyo, 1968. (1 3) Stothers, J. B.'Carbon-13 NMR Spectroscopy"; Academic Press: New York, 1972; Chapter 5 .
are observed in the completely proton noise decoupled 13Cspectrum for diisobutyl ether in C6D6. This may be due to rapid exchange among the four conformers.
Discussion A large body of P values for the octanol-water system are reported to correlate biological activities of drugs with P . The log P value of a molecule may be estimated from the sum of log P values of the fragments which constitute the m o l e c ~ l e .In ~~~~ these approaches for estimation of log P,several correction factors are introduced empirically and the conformational effects are not well taken into account. For instance a branching correction of -0.2 is used for log P.7 According to the S approach, we do not need such a correction. The effect of cyclization on P is another example showing the merit of the S approach. The effect of the stereostructure on P for 10 and 11 is also explained by the S approach without any additional factor. This stereostructural effect should be included in other approaches as a correction factor. The S approach is also useful for predicting t values in HPLC. The HPLC t value depends on adsorptivity of the solute to adsorbent in addition to its tendency of escaping from solvent water. The latter factor is dependent on S, but the former may be influenced also by the size and shape of the solute. Another problem is the dependence of S on the radius of solvent. We used S for water, but S for a MeOH-H20 mixture as solvent may be a better parameter. Both the merit and demerit of the S approach originate from the conformational dependence of S . For multiconformation compounds we cannot determine the correct S value without knowledge of their molecular conformations. The u and x approaches do not require such information for predicting P and t . From the P value measured, however, we may be able to estimate the molecular conformations of the multiconformation compounds. Such possibilities were demonstrated for the ethers 1, 3, 4, 6 , and 7. In this case we must be deliberate in applying this method for the large ethers, 3, 4, 6,and 7, which fall outside the calibration line determined by uniconformation ethers (2, 5, and 8-11). A minor error in the calibration line can cause an inaccuracy for S values estimated for these multiconformation ethers. Therefore, accuracy in prediction of the molecular conformation decreases with increases in S over the range assured by uniconformation compounds. In general, spectroscopic methods are used to determine the molecular conformation. However, these methods are inapplicable for hydrophobic substances in water, such as dibutyl ether.12y13J5 For such cases the present S approach is useful for estimation of molecular conformations.
-
Registry No. 1, 60-29-7; 2, 1634-04-4; 3, 111-43-3; 4, 628-81-9; 5, 108-20-3; 6, 142-96-1; 7,628-55-7; 8, 109-99-9; 9, 142-68-7; 10, 214441-4; 11, 2390-94-5; 1-octanol, 11 1-87-5. (14) Rekker, R. F.; de Kort, H. M. Eur. J . Med. Chem. 1974, 1 4 , 4 7 9 . (15) Eliel, E. L.; Allinger, N. L.; Angyl, S . J.; Morrison, G. A. "Conformational Analysis"; Interscience: New York, 1965.
