J. Chem. SOC., Faraday Trans. I, 1982,78, 1223-1236 Solvent Effects in the Electron Spin Resonance Spectra of Semiquinones B Y DOLORES M. HOLTON~ AND DAVID MURPHY* Department of Chemistry, Bedford College, Regent's Park, London NW 1 4NS Received 1st June, 1981 Solvent effects on the e.s.r. spectra of semiquinones in mixtures of H,O + hexamethylphosphoramide (HMPA), H,O +dimethylsulphoxide (DMSO), H20 + dimethylformamide (DMF), H,O + EtOH and EtOH + HMPA are reported and related to solvent basicity and radical structure. In many instances quantitative studies were possible and it is demonstrated that true thermodynamic equilibria are being studied. The significance of the measured equilibrium constants is discussed and an interpretation in terms of preferential solvation by the aprotic solvent is rejected in favour of one in which solvent-solvent and solvent-radical interactions operate simultaneously.In H20 + HMPA mixtures, for instance, competition between the radical and HMPA for water molecules is envisaged, the overall result being measured by e.s.r. This suggestion is compatible with the observed linear dependence of the coupling constants on [HMPA]/[H,O] and on measures of solvent polarity such as dielectric constant and the Kosower Z value. In a previous publication' it has been shown that a simple theoretical model due to Gendell et aL2 is applicable to the equilibrium between the two forms of a semiquinone present in a mixed solvent system: S, + RS, RS, + S, (1) where RS, is the radical solvated by solvent S, and RS, is the radical solvated by solvent S,.The equilibrium constant ( K ) for eqn (1) is given by Exchange between the two forms was always fast in the systems studied, so that K can be expressed in terms of a coupling constant, a, where a has the values a, in solvent S, and a, in solvent S,: Values for K are obtained either from sijpoid plots of a against log([S,]/[S,]) or, in more favourable cases, from one of the linear plots Ia-a,l-l against [S,]/[S,] and la- a,/-, against fS,]/[S,]. In the present paper the range of semiquinones for which thermodynamic data can be obtained is extended and the method is applied to systems other than S, = H,O, S, = HMPA. t Present address: University Chemical Laboratory, Lensfield Road, Cambridge CB2 1 EW. 1223TABLE 1 .-E.s.R.PARAMETERS (a f 0.031 10- T) AND EQUILIBRIUM CONSTANTS FOR SEMIQUINONES IN THE H20 + HMPA SYSTEM (i) substituents in 0- 4 ,"o; P ? w I m m 0- solvent a, a3 a5 '6 K P parameter used cd n I I I I I I 2-CH3 I 2-OCH3 1 2,5-But2 I A 2,6-But, I :20 :,0 [ZO i,O i20 :MPA [MPA [MPA [MPA [MPA B 2,6-(OCH3), HZ0 HMPA 2.38 2.38 2.45 2.45 aCHs = 2.10 1.73 a C H s = 1.77 2.05 aOCHs = 0.82 0.52 aOCHs = 0.47 1.16 2.08 2.33 1.31 2.25 aoCHs = 0.80 1.47 aOCHs = 0.50 1.92 aCHa = 2.10 1.87 aCHs = 1.85 2.22 2.38 2.45 2.60 2.73 3.60 3.48 1.31 2.25 1.47 1.92 1.87 2.22 2-38) 1.40b 2.45 2*39} 0.3Y 0.929 2.43 0-67c Om9"32 1.94 2.31 1 { 0.68d 0.993 2-08 } 0.07b 2.33 { 0.8W 1.16c 0-999} 0.996 aoCHs = 0.80 I 0-58c 0.68d 0.975} 0.995 0*986 } aOCHs = 0.50 0.38' '1 O.ad 0.980(ii) substituents in 0- Q5 4 K ra parameter used C H2O D 3-CH3 H2O E 3-OCH3 HZO F 4-CH3 H2O G 4,5-(OCH3), H2O H 4,5-OCH20 H2O HMPA HMPA HMPA HMPA HMPA HMPA HMPA 3,4,6-(OCH3), H20 0.75 1.56 aCH3 = 0.63 aoCH3 = 0.65 aOCH3 = 0.47 0.07 1 .oo - 0.32 0.33 -0.33 0.50 uCHs = 1.06 aoCH3 = 0.00 a o C H 3 = 0.00 3.69 3.34 2.85 2.83 1.25 1.90 acH3 = 4.89 uCHs = 3.85 uOCH3 = 1-05 aoCH3 = 0.85 ( I C H 1 = 4.22 uCHa = 2.39 aoCH3 = 0.90 u o C H 3 = 0.50 3.69 3.34 4.13 3.54 4.76 3.78 3.89 3.55 aOCH3 = 1.05 aOCH3 = 0.85 a C H 2 = 4.22 4CH2 = 2.39 1.15 2.13 0.75 1.56 0.28 1.06 0.46 0.98 } { K3:: 1.69 } { ;:z } { ::::: - 0.59 -0-32} 0.33 0.80" 0.22" 0.23d Oe50 ' 0.30" -0.33 0.998 0.997 1 0.989 0-990 1 0.994 0-994 1 0.993 0.983 0.990 0.996 0.972 0.995 a, + Q, +a, Q5 a 3 aCH3 2Q3,6 aCHz 2a3.5 a3 +a, + a, + a, p parameter used solvent a29 a 3 a57 a 8 as7 Q7 K 3.20 0.66 0.66 0.13" 0.965 2a,,, @ 0: H20 HMPA 3.33 0.24 0.65 } 0- a Correlation coefficient from linear regression analysis. Equilibrium constants from plots: Q against log ([S,]/[S,]>; la-ull-l against [Sll/[S21; 10- against ks2]/s~].1226 0.5- 50.0- 2 -2 I -0.5- E.S.R. SPECTRA OF SEMIQUINONES EXPERIMENTAL MATERIALS 1,4-dihydro~y-2,6-dimethoxybenzene,~ 1,2-dihydroxy-4,5-methylenedi~xybenzene~ and 1,2- dihydroxy-3,4,6-trimethoxybenzenes were prepared as in the cited literature.Other precursors and solvents were commerical materials. All compounds used were purified by the usual methods and had physical constants which agreed well with those of the literature. E.S.R. SPECTRA Mixtures of the two solvents were made up by weight fraction.The radicals were generated in the usual way by autoxidation,s using KOBut (solid) as the base. E.s.r. spectra were run, using a static system, on a Varian E4 spectrometer. RESULTS THE H,O+HMPA SYSTEM Table 1 contains equilibrium constants obtained in H,O + HMPA. The straight lines which best fitted the data were found by linear regression, the correlation coefficient, r, giving the quality of the ‘fit’. Where no value of r is given the magnitude of the changes incurred on altering the solvent was too small to allow meaningful equilibrium constants to be obtained from the linear plots; instead an approximate value was determined from the appropriate sigmoid curve. Wherever possible the parameter undergoing the largest change from water to HMPA was employed in calculating K.For methyl- and methoxy-substituted radicals, significant differences in the values of K were found if a splitting due to an alkyl proton rather than a ring proton was used in the calculation. Compare, for example, values given in table 1 for radicals (B) or (F) when different coupling constants are employed. In constrast, the total width and the parameter 2u3,, for 1,2-benzoserniquinone (C) yield the same value, as do uCHp and 2u3,6 for 4,5-methylenedioxy- 1,2-benzosemiquinone (H). At present no explanation for this behaviour may be advanced. The variation of a coupling constant over the entire range from pure water to pure HMPA reveals certain features which might have been overlooked had only the extreme values been available.It is known, for instance, that a, in radical (E) is negative when the radical is generated in water; this is confirmed by SCF calculations and I 1 I I I I -2.0 -1.0 0.0 1.0 2 .o 3.0 log (IH201 /[HMPAl) FIG. 1 .-Variation in a, for 3-methoxy-1 ,Zbenzosemiquinone (E) with solvent composition.D. M. HOLTON AND D. MURPHY 1227 - 2 x 1 0 - 4 ~ fd) FIG. 2.-Spectra of 4,5-methylenedioxy-l ,Zbenzosemiquinone (H) in H,O + HMPA. (a) Pure water, u ~ , ~ = (-)0.33 x lo-’ T; (b) [H,O]/[HMPA] = 19.33, u ~ , ~ = (-) 0.17 x lo-’ T; (c) [H,O]/[HMPA] = 6.51, a3,@ = 0.0; (d) pure HMPA, a3,,, = 0.50 x lo-* T. empirical graphical procedures. By observing the smooth change in a, with solvent composition (fig. 1) it is apparent that it changes sign. The same phenomenon is observed for radicals (G) and (H); some spectra for (H) are presented in fig.2. Note that five of the seven ‘best’ radicals in table 1, as suggested by the values of t, are o-semiquinones [radicals (C)-(F), (H)], the remaining two being 2,6-di-t-butyl- and 2-methoxy-p-benzosemiquinone. Omitting the last radical, in which the changes in coupling constants are too small in other solvents, these six radicals were selected for further study. EQUILIBRIUM CONSTANTS IN OTHER SOLVENT SYSTEMS Having verified that it leads to reasonably consistent equilibrium constants in H20+HMPA (table l), the treatment was extended to H20+DMS0, H,O+DMF, EtOH+HMPA and EtOH+H,O. Initially, a change in the aprotic solvent was studied : tables 2 and 3 contain equilibrium constants determined in the H20 + DMSO and H20 + DMF systems, respectively. In general, the linear regression [with the exception of radical (C)] is less satisfactory than in H20 + HMPA, but is nonetheless acceptable.Table 4 lists equilibrium constants obtained in the EtOH + HMPA system. Serious practical difficulties were encountered in this system due to the formation of secondary and dimeric radical species; these produced spurious lines in the e.s.r. spectra of the required radicals towards the ethanol end of the solvent range. Owing to the smaller variations in the coupling constants in EtOH + H20 compared with protic + aprotic mixtures, coupled with the difficulties inherent in obtaining ‘clean’ spectra in ethanol, it was not possible to construct linear plots for the majority of radicals in table 5.L h) h) 00 TABLE 2.-EQUILIBRIUM CONSTANTS IN H2O + DMSO (i) radical solvent a3 a4 a5 a, K r parameter used 0- 0- 1.31 2.01 H2O DMSO (ii) substituents in 0- &O- solvent a3 a4 a5 a, K r parameter used C D 3-CH3 E 3-OCH3 F 4-CH3 2a3,s 0.75 3.69 3.69 0.75 0.57“ 1.39 3.45 3.45 1.39 1 {0.57d 1000 DMSO aCH3 = 0.63 2.85 4.13 0.28} { C):M;i DMSO aCH3 = 1.00 2.80 3.70 1.00 0.993 DMSO aoCHs = 0.60 1.60 4.00 0.18 DMSO H@ H2O H2O H2O 0.997 } total width aoCH3 = 0.65 1.25 4.76 -0.59) 0.63d 0.992 a, 0.07 ~ C H ~ = 4.89 3.89 0.98 0.24“ 0.956) total width 0.80 aCH3 = 4.08 3.62 1.51 1 {0.26d 0.954 U d U 2: 0 a-d As in table 1.TABLE 3.-EQUILIBFUUM CONSTANTS IN H 2 0 + DMF ~ (i) radical solvent a3 a4 a5 ' 6 K r parameter used 1.31 2.12 2.12 le31 ) I 0- P (ii) substituents in ic: X 0 r c3 0 2, * 21 '6 K r parameter used solvent a3 a4 a5 0.75 3.69 3.69 0.75 0.54c 0.991) 2u3,6 U 3.48 1.28 { 0.45d 0.999 P C H2O DMF 1.28 3.48 DMF uCH3 = 1.06 2.90 3.66 0.98 } { 0.48d 0.998 z d P X D 3-CH, H20 uCH3 = 0.63 2.85 4.13 0.28 0.58c 0*998} total width 1 .07c cd E 3-OCH3 H2O DMF uoCH3 uOCH3 = 0.65 0.60 1.25 1.75 4.76 4.00 -(I:):} [0.91d 0.72c (I:;:} 4 " 0.41d ::;;:} H2O 3.89 0.98} 0.97c 0.978 a3 0.07 uCH3 = 4.89 3.65 1.60 F 4-CH.3 DMF 0.89 uCH3 = 4.01 -0.33 uCHz = 4.22 uCHe = 4.22 -0.33) { 0:71: uCH~ 0.43 uCHZ = 2.52 uCHz = 2.52 0.43 178 2u3,6 H 4,5-OCHzO H2O DMF a-d As in table 1.TABLE ~.---~QUILIBRIUM CONSTANTS IN EtOH -t HMPA (i) radical solvent a3 a4 a5 a6 K T parameter used 0- EtOH 1.21 2.25 0- ~~ (ii) substitutents in 0- a4 a5 a6 K r parameter used C EtOH D 3-CH3 EtOH HMPA HMPA F 4-CH, EtOH H 4,5-OCH,O EtOH HMPA HMPA 0.93 3.59 3.59 0.932 { WIi 1.56 3.34 3.34 1.56 aCHs = 0.80 2.80 4.07 0.44 0.87' uCHs = 1.06 2.83 3.54 1.06) (0.53" 0.59' aoCHJ = 0.65 1.30 4.59 -::I} 10.49" aoCHs = 0.47 1.90 3.78 0.67' 0.65" 0.33 aCHs = 4.47 3.70 1.10 0.78' 1.00 aCHs = 3.85 3.55 1.69 1 { 0.72" -0.08 aCHl = 3.64 3.64 -0.08 0.65' 0.50 aCHI = 2.39 2.39 0.50) (0.66" m m a-d As in table 1.TABLE 5.-EQUILIBRIUM CONSTANTS IN EtOH 4- H,O (i) radical solvent a3 a4 '6 '6 K r parameter used 1.31 1.21 le31 1.21 } 0.2b 2a3.5 0- (ii) substituents in 0- a4 a5 K r parameter used C H2O 0.75 3.69 3.69 0.36c 0.994) 2a3,6 EtOH 0.93 3.59 3.59 "0;: 1 \0.34d 0.998 D 3-CH3 H2O E 3-OCH3 H@ F 4-CH3 H2O H 4,5-OCH20 H2O EtOH EtOH EtOH EtOH aCHs = 0.63 aCHa = 0.80 aoCHs = 0.65 aoCHs = 0.65 0.07 0.33 - 0.33 - 0.08 2.85 4.13 2.80 4.07 1.25 4.76 1.30 4.59 aCHs = 4.89 3.89 aCHs = 4.47 3.70 aCHr = 4.22 aCHI = 4.22 aCHI = 3.64 a C H t = 3.64 0.44 - 0.40 1.10 - 0.08 0.45b 0.54b 0.30b 0.2Y { 0.21d 0.996 0.999 total width total width total width 2aCHo a-d As in table 1.1232 E.S.R. SPECTRA OF SEMIQUINONES TABLE 6.-CORRELATION OF COUPLING CONSTANTS OF RADICALS (A), (c) AND (F) WITH SOME SOLVENT POLARITY PARAMETERSa solvent 1. HMPA 29.6 2. acetone 20.70 3. DMF 37.0 4. DMSO 46.48 5. sulpholane, 43.3 TMSO, 6. ethanol 24.55 7. methanol 32.7 8. fomamide 11 1.0 9. water 78.39 10. 2-methyl-propan-2-01, 12.47 1 1. ethanediol 37.7 12. propan-2-01 19.92 13.butan-1-01 17.5 1 14. propan-1-01 20.33 t-BuOH 62.8 65.5 68.4 71.1 77.5 79.6 83.6 83.3 94.6 71.3 75.1 76.3 77.7 78.3 40.9 42.2 43.8 45.0 44.0 51.9 55.5 56.6 63.1 43.9 56.3 48.6 50.2 50.7 4.50 3.75 4.24 4.02 3.60 2.42 2.35 2.95 2.62 2.36 2.35 3.58 2.40 2.48 3.12 2.56 2.78 2.48 - 1.88 1.84 1.96 1.50 1.80 1.77 1.91 - - 1 .oo 0.89 0.80 0.60 - 0.33 0.3 1 0.38 0.07 a E , Z/kcal mol-l and ET(30)/kcal rno1-l are taken from ref. (7). Values of 2a3, &, 2a,, and a3 in T. CORRELATION OF COUPLING CONSTANTS WITH SOME MEASURES OF SOLVENT POLARITY In table 6 the hyperfine splitting constants of three representative semiquinones (A), (C) and (F) are presented, together with some physical properties’ of the solvents in which the spectra were determined. Overall, the correlation between the coupling constants and E , the dielectric constant, is poor; this has been found for other radicals by previous workers.However, for the solvents H,O, DMF, DMSO and HMPA, which are of particular interest in the present study, the correlation between a and E is 0.995,0.951 and 0.990 for radicals (A), (C) and (F), respectively. The success of this correlation suggests that the coupling constants of a given radical in any of these solvent systems are a linear function of the dielectric constant. This was tested on data for radical (C) in H20 + EtOH and H20 + DMSO mixtures. Over the entire concentration range from water to ethanol, there is a straight-line relationship between 2a,,, and E (r = 0.998). This is also true of H,O + DMSO solutions from pure DMSO to [DMSO]/[H,O] = 2.0 ( r = 0.993).When the Kosower 2 value8 is used as the measure of solvent polarity, the correlation is generally good and is better than that found with E . Values of r for radicals (A), (C) and (F), respectively, in the solvents water, DMF, DMSO and HMPA are 0.999, 0.976 and 0.998. For radical (A) that between the Dimroth-Reichardt polarity parameter E , (30)9 and a is 0.998. The excellent correlation suggests that the e.s.r. studies are measuring similar effects to those measured by the 2 value of the solvent. The effect of changing solvent polarity within the series of mixtures used for a ‘run’ was investigated for radical (C). From pure ethanol to [H,O]/[EtOH] = 2.0, the hyperfine splitting is a linear function of 2 (r = 0.989), while in H,O+DMSO theD.M. HOLTON AND D. MURPHY 1233 correlation ( r = 0.999) is from pure water to pure DMSO. 2 values are not currently available for other protic + aprotic mixtures. Correlations between e.s.r. parameters and 2 values have been noted for other radicals in pure solvents but their success appears to depend on the nature of the radical and the type of solvent studied. For p-benzosemiquinone,lO for example, a('") and a(170) are linearly related to the 2 values of solvents such as water, ethanol and DMSO, whereas only a poor correlation is observed for 2,6-dimethyl-p-ben~osemiquinone.~~~ l2 Here the major additional factor isconsidered to be steric. In the present study, aH for the 2,6-di-t-butyl-substituted radical (A), although a smooth function of 2, is not linearly related to it.It is likely that the steric explanation applies in this case also. DISCUSSION RADICAL-SOLVENT INTERACTIONS In the course of this investigation, the solvent dependence of radicals in the solvents water, ethanol, DMSO, DMF and HMPA has been studied qualitatively and, in favourable cases, quantitatively. In the aprotic solvent HMPA differences from the water hyperfine splitting constants are at a maximum for all radicals. Water is a good anion solvator by virture of its hydrogen-bonding ability, whereas in HMPA anion solvation is mainly via ion-dipole and ion-induced-dipole forces. Due to steric hindrance around the phosphorus atom anions are practically unsolvated in HMPA. With the other aprotic solvents, changes from the water values are smaller, presumably as interactions can occur to some extent between the anion and DMSO or DMF.The results demonstrate that the anions are only weakly solvated in aprotic solvents, but the protic solvents employed form hydrogen bonds to the basic sites of sufficient strength to perturb the semiquinones in a readily detectible way. l3 These perturbations are manifested as changes in coupling constants with solvent. APPLICATION OF THE GENDELL, FREED AND FRAENKEL MODEL TO SEMIQUINONES I N MIXED SOLVENTS Tables 1-5 demonstrate conclusively that the simple model2 applies to the equilibrium involving semiquinones in mixed solvents [eqn (l)]. Data from all five solvent systems investigated comply with this equation and graphs are of the form predicted by the theory for each case investigated.The consistency of the model is supported by the good agreement between equilibrium constants obtained using different plots: a against log([S2]/[Sl]), la - q1-l against [S,]/[S,] and la - a21-l against [S,]/[S]. Therefore, a single equilibrium is being measured throughout the range. Table 1 shows that the method is sensitive enough to differentiate between differently substituted semiquinones. For example, for radical (C), K has been obtained from two different linear plots and the values differ by 0.06, which is within experimental error. The difference between K for radical (C) in H20+HMPA and that for any of the other radicals is, in general, greater than the experimental error and the values of K are reproducible. In the case of radicals (G) and (H), the equilibrium constants are distinct although the substituents have similar effects on the spin density of a radical.Different 2,6-sulrstituents also lead to separate equilibrium constants (see table 1). MAGNITUDE OF THE EQUILIBRIUM CONSTANTS Tables 1-5 show that, with the particular exception of 2,6-disubstituted-p- semiquinones, which are asymmetrically solvated, equilibrium constants are generally less than unity. Comparing values obtained using the same parameters, K for1234 E.S.R. SPECTRA OF SEMIQUINONES H,O + HMPA is usually quite different from that for other aqueous + aprotic solvent systems. This is particularly marked for radicals (A) and (C), where equilibrium constants for H,O+DMF/DMSO are similar. In DMF and DMSO, of course, the radicals are not 'free' as they are in HMPA.The observed order of equilibrium constants changes with the nature of the radical : (A), (E), (F) K(H,O + HMPA) < K(H,O + DMSO) < K(H,O + DMF) K(H,O+HMPA) < K(H,O+DMSO) x K(H,O+DMF) K(H,O + HMPA) x K(H,O + DMSO) < K(H,O + DMF) (C) (D) K is, therefore, a function of the substitution pattern as well as the solvent combination. The immediate implications of equilibrium constants less than unity are rather surprising. In the original model,, K = 10 defines a situation in which the complex with solvent S, is considerably stronger than that with S, [eqn (2)]. A value of unity corresponds to unselective solvation, such as has been found for nitrobenzene anions.14 For the H,O + HMPA system, for example, K < 1 could be taken [eqn (4)] R..*HMPA+H,O~R"-H,O+HMPA K < 1 (4) as preferential solvation of the semiquinone radical by HMPA, but in view of the previous discussion this is an unacceptable conclusion.Moreover, values in H,O + HMPA are lower than those in H,O + DMF/DMSO, implying that solvation by HMPA is greater than that by DMSO or DMF, which is again unacceptable. Also, results from EtOH+H,O suggest [eqn (S)] that hydrogen bonding to the radical is stronger for ethanol than water: R. * .EtOH +H,O R. * .H,O + EtOH K < 1. ( 5 ) This is inferred, also, when values for H,O+HMPA and EtOH+HMPA are compared as K(Et0H + HMPA) is greater than K(H,O + HMPA). Equilibrium constants less than unity lead to positive AG* values, i.e. the reaction is unspontaneous. It is likely, therefore, that some other effect is operative in this system additional to that represented by eqn (1).SOLVENT-SOLVENT INTERACTIONS The results from the trihydroxybenzenes and n.m.r. studies are strong evidence that the additional effect overlooked in eqn (1) is an interaction between the two solvents. E.s.r. results from trihydroxybenzenes in H,O + HMPA showed the solvent structure to change in a definite manner, so that radical dianions cannot persist at high HMPA concentrations.l N.m.r. studies1*15 confirmed that this change was due to the formation of the relatively stable complex HMPA * 2H,O. Similarly, strong solvent- solvent interactions and complex formation were found for H,O + DMF, H,O + DMSO, EtOH + DMF, EtOH + DMSO and EtOH + HMPA.This would explain why the equilibrium constants found by e.s.r. are positive: there is actually competition for water molecules between the radical and HMPA and it is the result of this competition which is being measured by e.s.r. This conclusion is supported by studies on other types of radical. For the reaction : HMPA. * *H-OH+PhNOi-+HMPA+PhNOi-. * -H-OH K = 0.9, indicating that the concentration of hydrogen-bonded HMPA is greater than that for the hydrogen-bonded ion,lg an expected result as HMPA forms relatively strong hydrogen bonds.,' Equilibrium constants less than unity for t-butylnitroxide in mixed aqueous solvents1* were interpreted in terms of preferential solvation byD. M. HOLTON AND D. MURPHY 1235 organic solvents such as dioxan and alcohols.However, using di-t-butylnitroxide as a probelS this concept was shown to be totally misleading. Interaction with aprotic solvents is dipolar in nature. As the concentration of this type of solvent is increased, hydrogen bonds to the radical are lost due to the strong affinity of the basic solvent for hydrogen bonds, rather than to increased radical-aprotic-solvent interactions. Thus both radical-solvent and solvent-solvent interactions must be considered. The reliance of a on [H,O]/[HMPA] might appear to suggest that the equilibrium between the two radical forms is effectively independent of any interaction between the solvents, i.e. that eqn (1) stands. In the ideal case of zero solvent-solvent interactions such a relationship is expected. However, the positive AG* values deny this. Rather, there appear to be two simple situations for a semiquinone: either it is hydrogen bonded or it is not.The effects on spin density distribution within the radical would be expected to depend most critically on the strength of the primary hydrogen bond, that to the radical; thus it would be insignificant whether the radical were hydrogen bonded to a water molecule or to the HMPA * 2H20 complex, and la - all-1 could still be a linear function of [H,O]/[HMPA]. The structure of HMPA-2H20 is probably the same as that suggested for H20 + DMSO interactions:20 .* The first water molecule is bonded to the oxygen atom of the aprotic solvent (lo solvation), whereas the second water molecule is attached to the first by secondary solvation (2O), as shown above.Although it is often assumed that 1' solvation is complete before the onset of 2 O solvation, i.r. studies on tetra-alkylammonium halides21 have established that this is incorrect. The structure proposed for HMPA-2H20 has the capacity to form further hydrogen bonds. Depending on the relative concentrations, these can be either to the radical or to other water molecules. Thus the measured coupling constants are averages resulting from exchange between hydrogen-bonded radicals, either bonded to water or to HMPA - 2H20, and radicals solvated through dipolar interactions with HMPA. However, further details are not obtainable from the present results. This explanation is compatible with the finding that the coupling constants correlate simultaneously with E and 2, one a bulk, macroscopic property of the solvent and the second a measure of interactions at the molecular level.If the present picture of hydrogen bonding to the radical by HMPA-2H20 or water itself is accepted, the observed correlations are consistent : a must depend on the nature of the lo bond, i.e. on what is happening at the radical and therefore on 2, and also on the interactions throughout the solvent as a whole and therefore on E. Whatever the physical significance of the equilibrium constants it is clear from the linear relationships that unique values are being measured. Thermodynamic consid- erations confirm this. THERMODYNAMIC CONSIDERATIONS If the measured K values are true thermodynamic equilibrium constants, then AG* values calculated from them must be additive.Therefore, if two equilibrium constants are known, a third can be calculated and compared with the experimentally observed value. Constants for radicals in H 2 0 + EtOH were obtained in this manner (table 7).1236 E.S.R. SPECTRA OF SEMIQUINONES TABLE 7.-hEDICTED EQUILIBRIUM CONSTANTS FOR RADICALS IN HZO 4- EtOH K(H,O + HMPA) K(Et0H + HMPA) K(Et0H + H,O) K(Et0H + H,O) radical experimental experimental experimental calculated source of K experimental (C) 0.29 0.84 0.35 0.36 h,,, against log{[SJ/[S,]} (D) 0.19 0.71 0.45" 0.27 a, against log{[S,]/[S,]} (E) 0.40 0.60 0.54" 0.67 a6 against log{[SJ/[S,]} (F) 0.13 0.56 0.30 0.23 total width against log{[S,]/[S,]} (H) 0.16 0.63 0.25 0.22 aCHI against log {[S,]/[S,]) " K(H,O + EtOH) from total spectral width against log{[S,]/[S,]] plot. The limiting factor to accuracy in these calculations is the H20 + EtOH experiment. Values in this system are probably only correct to f0.2 due to the small changes involved and the fact that K can only be determined from the less reliable a against log ( [ S , ] / [ S , ] } plot; for other systems K is estimated to be correct to f 0.1.For con- sistency, only values obtained from log plots have been'used and, where possible, the same parameter has been employed in the calculation of K. In all cases the agreement between predicted and experimental values of K is good and, in fact, disparities are only greater than 0.1 when values obtained from different plots have had to be compared [radicals (D) and (E)].This supports the suggestion that a single, true equilibrium is being observed in the e.s.r. studies, that between hydrogen-bonded and non-hydrogen- bonded radicals. D. M. H. thanks the S.R.C. for a research grant. W. T. Dixon, D. M. Holton and D. Murphy, J. Chem. 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