1940
TAKAYUKI FUENO,TAIKYUE REE AND HENRYEYRING
would hence tend to be stable a t slightly lower pressures than the South African garnet.$ Mr. A. J. DeLai of our laboratory has recently studied the high pressure, high temperature behavior of Gore Mountain garnet. Essentially his method was to place powdered garnet in a nickel capsule and heat it to a predetermined temperature a t a selected pressure. After about 5 minutes of heating the sample was chilled, the pressure was reduced, and the material in the capsule was examined under the microscope. 111this way it was possible to determine whether the garnet had melted or decomposed. This garnet was found to melt and decompose in uucuo a t 1185'. If the pressure is less than 26,000 atmospheres, this garnet cannot be melted without decomposition. The principal products of decomposition were enstatite and glass. A t pressures above 26,000 atmospheres the solid and molten garnet can exist together, and the melting temperature increases with pressure. If the molten garnet a t high pressure is cooled slowly from say 2000°, solid garnet forms from it. However, if the melt is quenched from too high a temperature a t high pressure, enstatite and glass are formed even though the pressure is high enough for garnet to be stable. This suggests that some semblance of the solid garnet structure may exist in liquid garnet a t high pressures. It appears that well-developed crystals of garnet are rarely included in diamond; most of the garnet inclusions are irregular in shape. This would imply that the garnet was molten or nearly molten as the diamond formed around it.
Vol. 63
I n any event, the diamonds which contain garnet inclusions probably did not form a t temperatures higher than about 2000°, or they would contain enstatite instead of garnet. Enstatite is a relatively rare inclusion in diamond. And because the garnet inclusions mostly appear to have been molten, the diamond often evidently formed at temperatures above about 1300'. Now we have two high pressure minerals, garnet and diamond, one encased in the other. It is very unlikely that both were formed metastably, that is, a t pressures below which either was stable. At least the garnet must have been stable. This implies that the diamonds containing garnet formed a t pressures of a t least 25,000 atmospheres. If in addition the diamond formed at a pressure where it was stable, then the lowest pressure possible would be about 55,000 atmospheres. Such a pressure would exist a t a depth of about 150 km. beneath the surface of the earth. Thus, it now seems even more likely that diamonds have been formed a t considerable depths in the earth, and we are quite fortunate to have any of them at the surface. The problems of the origin of natural diamonds are by no means completely solved. But you can see that we are making some progress toward understanding them. It is very likely that within a few years the diamond will prove to be a very valuable geological indicator from which we will be able to deduce much about the physical and chemical conditions which have existed and now exist in the deeper layers of the earth.
QUANTUM-MECHANICAL STUDIES ON OXIDATION POTENTIALS AND ANTIOXIDIZING ACTION O F PHENOLIC COMPOUNDS BY TAKAYUKI FUENO, TAIKYUE REE AND HENRYEYRING Department o j Chemistry, University of Utah, Salt Lake City, Utah Received June 6,1969
Available data on osidation potentials of phenolic compounds (including polyphenols) are found to be linearly related to the highest occupied molecular orbital energies for r-electrons, which are calculated on the basis of the LCAO MO (linear combination of atomic orbital molecular-orbital) theory. The oxidation potentials of nearly 180 monophenols, including some never synthesized, are predicted from the calculated values for the orbital energies. The antioxidizing action of phenolic compounds for radical chain reactions is examined theoretically, and the proposal is made that the rate-determining step for the inhibition involves an electron transfer from the phenols t o the radicals. The charge-transfer stabilization energies of the transition states proposed for the primary reactions between a radical and some phenols and the degrees of charge transfer in these transition complexes are calculated by perturbation theory, assuming r-electronic interaction between the two reaction centers as the perturbation. These calculated values prove to be closely related to the antioxidizing efficiencies of the phenolic compounds.
I. Introduction It has long been known that phenolic compounds are useful inhibitors for autoxidation of organic substances, and a large technical literature exists concerned with various kinds of inhibited autoxidation systems. Although these inhibitors are generally believed to affect the chain propagation step of the autoxidation processes by a reaction in which the inhibitior is oxidized, the mechanism. of the initial step of the inhibition is still unsettled.' (1) C. Walling, "Free Radicals in Solution," John Wiley and Sons, Inc., New York, N. Y.,1957, pp. 430-436.
Bolland and ten Have2 considered that the initial step is the abstraction of a phenolic hydrogen to yield a phenoxy (or semiquinone) radical and subsequently demonstrated that the antioxidizing efficiency of phenols parallels the oxidationreduction potential. Recently, however, Hammoizd, et U Z . , ~ - ~ have suggested, on the basis of (2) J. L. Bolland and P. ten Have, Disc. Faraday Soc., 2, 252 (1948). (3) C. E.Boozer and G. S. Hammond, J . A m . Chem. Soc., 76, 3861 (1954). (4) C. E. Boozer, G. 8. Hemmond, C. E. Hamilton and J. N. Sen, ibid., 77,3233 (1955).
Nov., 1959
QUANTUM-MECHANICAL STUDIES OF OXIDATION POTENTIALS OF PHENOLS
1941
several lines of evidence, that the inhibition molecular orbital (HOMO) energy of phenols reaction involves complex formation between an would be responsible for determining the potentials of their irreversible oxidations. inhibitor and a radical. I n order to examine the expected relationship for I n the present paper, the known oxidation potentials of phenols are interpreted from the monophenols theoretically, we apply the firstmolecular orbital (MO) theory of the linear order perturbation theory. Let Ejo be the ,energy combination of atomic orbitals (LCAO), and the of a a-electron in the jth molecular orbital, ' k j , relation between antioxidizing efficiencies and of the reference hydrocarbon anion15which has the oxidation potentials7 of phenols is discussed on this same arrangement of atomic pn-orbitals and the basis. Furthermore, a possible model is proposed same number of a-electrons as a phenol. Then, for the transition state of the inhibition process, replacement of the side chain (-CHZ-) of the anion and the stability of this transition state is quantita- by an OH-group will change the value of EjO tively dealt with by perturbation theory. into Ej. The first-order perturbation theory 11. Oxidation Potentials of Phenolic Compounds gives Ej = Ejo + f qjHf+j d r (2) 1. Dependence of Oxidation Potential of Monophenols upon their n-Conjugating Nature.-The where H' is the perturbation term of the oneprimary step in the oxidation of phenolic compounds electron Hamiltonian for the phenol with respect in neutral media consists in the removal of one to that of the corresponding reference hydrocarbon hydrogen atom from the phenolic oxygen. With anion. Now in the LCAO approximation respect to the mechanism, then, there is no differq j = C Cjr+r (3) ence between the oxidation of monophenols and the r compounds of the hydroquinone type, except that the oxidation products of monophenols by the Cjr being the linear combination coefficient of removal of hydrogen atoms are usually much less atomic orbital 4r in the jth molecular orbital. stable than those of the hydroquinone type. Putting eq. 3 into eq. 2, we obtain Fieser7 developed a method for measuring the Ej = Ejo C Cj,Cj, f +,H'+,dr (4) r s potentials with a reasonable degree of accuracy even for such unstable oxidation-reduction sys- I n eq. 4, the most important integral will be the tems. It consisted in measuring the potentials of a coulomb term of the oxygen (X) whose atomic solution of some stable oxidation-reduction system orbital is designated by +x. Since the HOMO'S in the presence of phenols and thereby determining of the reference hydrocarbons are all non-bonding, the minimum potential a t which the velocity of the HOMO energy, E h o , of phenols is, thus, approxthe reaction between a given phenol and the ref- imated by erence oxidant reaches a limiting small value. E h o = 01 (CnX)'kXP (5) The potential was referred to as the '"critical where a and /3 are coulomb integral of a carbon oxidation potential." Furthermore, Fieser demonstrated experimentally that the critical oxida- atom and resonance integral of a carbon-carbon tion potential Vc bears a definite relationship to double bond, respectively, C n x is the coefficient of QX in the noli-bonding molecular orbital (NBthe normal oxidation potential Vothrough MO),l8and kx is a coulombic parameter for oxygen F'o - V , = 0.136 v. for monophenols defined asf +xH'$xdr/@. and (1) For about 200 phenols, including some never V O - V , = 0.068 v. for hydroquinones synthesized, the values of ( C n x ) ' were calculated by Careful examination of the above reactions will the NBMO method.16 Plots of the values of lead to the possibility that the potential-deter- ( C n x ) ' of several existing phenols against the mining step involves one electron transfer from available data for Vc give a straight line, as seen in phenols to the reference oxidant, followed by Fig. 1. Since /3 is a negative quantity and kx proton migration. Under an essentially identical a positive the HOMO becomes more stable assumption, several workers8-14 have shown that as the value of ( C n x ) ' increases. Thus, the linear the reduction potentials of conjugated compounds relationship between ( C n x ) ' and V , in Fig. 1 subare linearly related to their lowest vacant molecular stantiates the expectation that, the less stable the orbital (LVMO) energies calculated by quantum- HOMO of phenols, the more easily are they oximechanical principles. Thus, it is to be expected dized. It will be worthwhile to note that the that the relative height of the highest occupied above qualitative conclusion does not depend upon ( 5 ) G. S. Hammond, C. E. Boozer, C. E. Hamilton and J. N. Sen, the empirical parameters a,0and kx. J. A m . Chem. Soc., 7 7 , 3238 (1955). The straight line in Fig. 1 is expressed as (6) C. E. Boozer, G. S. Hamniond. C . E. Haillilton and C. Peterson,
+
+
ibid., 77, 3380 (1955). ( 7 ) L. F. Fieser, ibid., 52, 5204 (1930). ( 8 ) A. Maccoll, Nature, 168, 178 (1940). (9) A. Pullman, B. Pullman and G . Berthier, B u l l . aoc. c h i n . France, 17, 591 (1950). (10) G. J. Hoijtink and J. van Schooten, Rec. trau. chim., 71, 1089 (1952). (11) G. J. Hoijtink and J. van Schooten, ibid., 72, 691 (1053). (12) G . J. Hoijtink and J . van Schooten, ibid., 72, 903 (1952). (13) G. J. Hoijtink, ibid., 74, 1525 (1955). (14) T. Fueno, K. Morokuma and J. Furukawa, J . Chem. Soc. J a p a n , Pure Chem. Section, 79, 116 (1958).
V,
=
2 . 8 0 7 ( C , ~ )-~ 0.450
(6)
with a correlation coefficient, r = 0.977. By using eq. 6 and the values of (Cnx), z the critical oxidation potentials, ITo, can be predicted for (15) For example, the reference hydrocarbon anion for phenol is benzyl anion (C6HsCHz-). (16) H. C. Longuet-Higgins, J . Chem. P h y s . , 18, 275 (1950). (17) The parameter kx is a measure of the electronegativity of X compared with carbon atom and is plus in sign when X is more electronegative than the carbon.
1.2
Biphenyl
=-bP P0
1,2-Benzanthracene
I.o
1’ 2’ 3’ 3 4’
0.0
4 5 6 7 8 9 10
0
6
>’
.5161 (1.036) .5161 (1.038)
7(yJy
1.1
-+‘
Vol. 63
TAKAYUKI FUENO, TAIKYUE REE AND HENRYEYRING
1942
10
6
0.6
4
0.7
0.6
0.6
0.38
0.48
0.40
0.60
0.88
0.60
( C n d a = (he-a)/ k,B,
.4949 .4900 .5326 .4579 .4083 .4083 .3984 .4949 .4804 .4083 .3403 .3141
0.930 0.916 1.036 0.826 ,687 .687 ,659 .930 .989 .687 .496 .423
.4638 .4444 .4571 .5246 .5161 .4638
.843 .788 .824 1.014 .990 .843
.4138 .3636 ,5714
.703 ,562 1.145
,4741 .4103 .4476 .5378 .5039 .4741
0.872 .693 ,797 1.051 0.955 0.872
.5294 .5000
1.027 0.945
Fig. 1.-Linear relationship between critical oxidation potentials of monophenols and the HOMO energies.
various possible monophenols. I n Table I the predicted values of V , for nearly 180 possible monophenols belonging to 23 different parent alternant hydrocarbons (the number of unsaturated six-membered rings ranging from 3 to 5) are summarized. Inspection of Table I shows that the effect of the nature of the hydrocarbon skeletons upon V c of the corresponding phenols will be comparatively of less consequence than that of the position of terminal carbon where the hydroxyl group is linked to hydrocarbons. With several familiar
A
Pyrene
TABLE I5 POTENTIALS Vo PREDICTION OF THE CRITICALOXIDATION OF
MONOPHENOLS Position of t h e carbon atom bearing OHgroup
Parent hydrocarbon
...
Benzene 8
Naphthalene
6
039
0.5714
(1.089)
l(a) 2(p)
.4500 (0.797) .5294 (1.017)
1 92
.3810 (0.602) .4706 ( .820) .2857 .343
1 2 3 4 9
.4630 ( .848) .5435 (1.057) .5102 (1.013) .4902 0.918 .4464 ( .789)
4
6
7
10
8
8
Naphthacene
1 22 35 6
6
Pentacene
4
.3333 .4167 .2083
.477 .711 .126
1
.2975 .376 .3711 .583 .OOO .1636 .1379 -0.072
1 2 3
.3165 .4016 .4975 .4785 .4149 ,3521 .3831
03330 8
oc’
Phenanthrene
Vo, v.
1
6
Anthracene
(Cnx)P
6
4
Pentaphene A
I /
0.429 .668 .937 .884 .706 .529 .616
Nov., 1959
QUANTUM-MECHANICAL STUDIESOF OXIDATION POTENTIALS OF PHENOLS TABLE I (Continued) Position of the carbon atom bearing OHgroup
Parent hydrocarbon
Picene
1,2,3,4Dibenzanthracene 9‘
10
.4881 .4983 .5311 .4601 .4235 .4198 .3902 .3404
.911 ,940 1.033 0.833 .730 .719 .636 ,497
Perylene
1
.3432
.504
1,2,3,4-Dibenzphennnthrene
1’ 2‘ 3’ 4‘
.4851 .5297 .5212 .4925 .4962 .5052 .5341 .4712 .4558 .5117 .5241 ,4465 .4188 .4876
.903 1.028 1.004 0.923 .934 .959 1.040 0.864 .820 .977 1.012 0.794 .717 .910
.4761 .506U .5348 .4531 .4694 .5137 .5265 .4692 .4225 .4592 ,4447 .4531 .4270 .4774
.877 .961 1.042 0.813 .859 ,985 1.019 0.830 .727 .830 ,789 ,813 .740
.3916 .4ao2 ,4764 .3941 .4481 .5084 .5105 .4498 .3025 ,3087 .4261
.640 ,889 .878 ,647 .799 .968 .974 .804 .390 ,737 ,408
.4672 .4246
.852 .733 .651
V.
8 9 10 11 12
.4880 .4709 .5159 .4475 .3682 .3839 .2432 .2301 ,3491 .4402 .4332 ,3537 .2382 .2647
.911 .863 :989 .797 .575 .619 .224 .187 .521 .777 .757 .534 .210 .284
1’ 2’ 3’ 4’ 1 2 3 6 7 8 9 10 11 12
.3878 .4859 .4708 .3980 ,4291 .3634 .2937 .3184 .4821 ,3829 .4368 .5284 .4959 .4618
.630 .905 .863 ,658 .745 .561 .365 .435 .894 .616 .767 1.024 0.933 .837
1’ 2‘ 3’ 4‘ 5 6 9
.5000 .5200 .5200 ,5000 .4194 .5008 .3611
,945 1.001 1.001 0.945 .718 .945 .555
*
3
10
4
6’ 7’ 6 7
8 9 10
1,2,5,6-Dibenzphenanthrene
.4932 .4932 .5373 .4557 .409 1 .4235 .3636
.925 .925 1.049 0.820 ,689 .730 .562
1’ 2’ 3‘ 4’ 5‘ 7’
10 8
7 8 9 10
9
2,3,5,6-Dibenzphenanthrene
1‘ 2’ 3‘ 4’ 3 4 9
1’ 2‘
vo.
.889 ,949 1.056 0.803 .692 .841 .786
1’ 2’ 3’ 4’ 3 4 5 6
4,5-Benzchrysene
(Cnx)’
.4801 .5015 .5399 .4495 .4102 .4630 .4436
1 2 3 4 5 6 13
1,2-Benznaphthacene
1,2,7,8-Dibenzanthracene
1943
1’ 2‘ 3’ 4’
;;j 8;
.tay ; \7
2’
7’
9
1’
1
10
8 9 10
.3954
.881
‘FAKAYUKIFUENO, TAIKYI JE REEAND HENRY EYRING
1944
TABLE I (Continued) Position of the carbon atom bearing OHgroup
Parent hydrocarbon
3,4,5,6-Dibenzphenanthrene
1’
(Cnx)*
VO. V.
,4555 .5314 ,5090 .4734 ,4568 ,4311 .4617
1,033 01.970 ,870 .823 ,751 .837
.4959 ,5193 .4143 .5576 .3993
,933 ,999 ,704 1 .lo6 0 ,662
.4500
.804 .744 1.027 0.594 ,552
.820
21/\i9 i io 1,2-Benzpyrene
1/
305 4
3,CBenzpyrene
1‘ 2’ 3’ 4’
.4286
.5294 ,3750 ,3600 ,4500 .2500
2oi,j 5
67 8 9 10 a The values of V , in parentheses are data determined by Fieser.7 7
3’
4’
6
6
,804
.243
,3750 ,594 .594 ,3333 .477 .5625 1.120 .3214 0.443 the experimental
phenols, the importance of the latter effect was qualitatively interpreted by Fieser7 in terms of an a-naphthol and a 0-naphthol type: the phenols with the oxidizable group in the unreactive 0position to a second benzene ring differ relatively little in potential from each other and are subjected to oxidation with more difficulty than are the CYnaphthol types. This trend seems to remain valid for a larger number of phenols as shown in Table I, where the phenols with predicted values of V , larger than 1 volt are of the /3-naphthol type almost without exception. 2. Oxidation Potentials of Polyphenols.-In order to make the above-mentioned linear relation more conclusive, it is further necessary to examine whether the relation would also hold for polyphenols. Thus, the relative heights of the HOMO levels, Zho, for polyphenols as well as monophenols, Xh& are calculated being defined as E h o = a as the roots of the simple LCAO MO secular equations (neglecting overlap integrals). The electronegativity parameter, kx, for the oxygen is tentatively assigned the value unity. I n Table 11, the calculated values of xho are compared with the critical oxidation potentials
+
(18) J. E. Conant, Chem. Reus., 8 , 1 (1926). (19) L. F. Fieaer, J . A m . Chem. SOC.,Sa, 4915 (1930).
Vol. 63
Va and the normal oxidation potentials, VO. All the data for Vo are obtained by correcting Fieser’s data7 for V , using the relationship (l), except as otherwise noted. Comparison of xh0)s should be made with the Vo”srather than with the VC’ssince only the Vo’scan be related to the free energy changes between oxidants and reductants for both the polyphenols and the monophenols. The relationship between V Oand IL’ho is graphically represented in Fig. 2, where a single straight line is seen to fit the plots for polyphenols as well as those for monophenols. Thus, it is concluded that the potential-determining step for the oxidation of phenolic compounds is a n electron transfer from the compounds to the relevant oxidants. Strictly speaking, however, some factors other than the n-electronic energy difference, AET, e.g., the differences in r-electronic energy, in entropy term and in solvation energy between reductants (phenols) and oxidants (molecular cations of the phenols) should also be taken into account. Nevertheless, the linear relationship in Fig. 2 shows that these other factors are of less significance than the ?r-electronic energy. This argument will be represented by the simple equation AF
AH =
c + A&
Fvo
(7)
where AF and AH refer, respectively, to the changes in Gibbs’ free energy and in heat content accompanying the oxidation process, and C and F denote the constant energy term (corresponding to the change in a-bond energy and solvation energy) and Faraday’s constant, respectively. Since AET is nothing else than the absolute value of the HOMO energy, a Xho& of a phenol, eq. 7 can be transformed into VO (c - ZhoP (8) where the three constants, C, a and 0,are expressed in units of electron volts. Now, statistical treatment of the data listed in Table I1 gives the linear equation
+
CY)
Vo
= 2.0822h0
+ 0.245
(9)
with a correlation coefficient T = 0.963. Comparison of eq. 8 and 9 gives /3 = -2.082 e.v. in reasonable agreement with -2.23 e.v.12and -2.27 e.v.I4 obtained from the linear relations between polarographic reduction potentials and LVMO energies for conjugated hydrocarbons and substituted stilbenes, respectively. It is to be expected that the calculated value of Xho would also be a measure of ionization potential of phenolic compounds. However, we have not yet enough accumulated data to check this point. 111. Phenolic Compounds as Antioxidant for Radical Chain Reactions 1. Relationship between Antioxidizing Power of Phenols and their Oxidation Potential.-Some comparisons20-22of the effectiveness of various phenols as inhibitors in different oxidation systems are available. These comparisons have been made on the basis of the length of the induction period (20) C. D. Lowry, G. Egloff, J. C. Morrell and C. G. Dryer, Ind. Eng. Chem., a6, 804 (1933). (21) H. El. Olaott, J . A m . Chem. Soc., 66, 2492 (1934). (22) K. K. Jeu and H.N. Ayes, ibid., 66, 575 (1933).
Nov., 1959
QUANTUM-MECHANICAL STUDIESOF OXIDATION POTENTIALS OF PHENOLS
1945
TABLE I1 COMPARISON OF OXIDATION POTENTIALS OF PHENOLIC COMPOUNDS WITH THEIR HOMO ENERQIES Serial n0.a
Phenol
Symmetry of HOhlOC
VO ,
Vo,b V.
Xho
V.
1.089 1,225 0.5043 S 1 Phenol 0.797 0.933 .3642 ... 2 a-N aphthol 1.017 1.153 .4307 ... 3 6-Naphthol 0.848 0.984 .3760 ... 4 l-Phenanthrol 1.057 1.193 .4595 ... 5 2-Phenanthrol 1.013 1.149 .4072 ... 6 3-Phenanthrol 0.798 0.934 .3596 ... 7 9-Phenanthrol .602 .738 .2785 ... 8 l-Anthrol .a20 ,956 .3250 ... 9 2-Anthrol 1.036 1.172 .4275 S 10 p-Hydroxybip henyl 1.038 1.174 .4374 ... 11 o-Hydroxybiphen yl 1.043 1.179 ,4450 A 12 Resorcinol ... 0 . 715b ,2541 SXA, 13* Hydroquinone 0.747 .810d ,2624 S 14* Catechol ,609 .67Bd ,1912 S 15* Pyrogallol ... .482d ,1334 A 16* 1,4-Naphthohydroquinone ... ,564" ,1468 ... 17* 1,2-Dihydroxynaphthalene .753 ,889 ,3190 ... 18 1,3-Dihydroxynaphthalene .673 .741 .2079 S 19* 1,5-Dihydroxynaphthalene .812 .948 ,3393 S 20 2,3-Dihydroxynaphthalene ,690 .758 ,2880 S 21* 2,6-Dihydroxynaphthalene 1.007 1.143 ,3964 A 22 2,7-Dihydroxynaphthalene 1.010 1.146 .4019 ... 23 2,6-Dihydroxyphenanthrene 0.832 0.900 .3157 8 24* 3,6-Dihydroxyphenanthrene .882 ,9541 .3111 SxAs 25 * p , p '-Dihydroxybiphenyl ,786 .854/ .2541 SxAs 26 * p , p '-Dihydroxystilbene The asterisk indicates that the phenol is of hydroquinone type. b Taken from ref. 7. c The symmetry of the HOMO function with respect to a relevant axis of :ymmetry is represented, where ap ropriate, by the symbol S (symmetric) or A (antisymmetric). For hydroquinone, p , p -dihydroxybiphenyl and p,p'-dihyfroxystibene, the line connecting two phenolic oxygena is chosen as the z-axis. d Taken from ref, 2. e Estimated from the normal oxidation-reduction potential (0.506 volt) for 1,2-naphthoquinone in 0.2 N HCl.'* (In the same medium, the potentials for 1,4-naphthoquinone and quinone are, respectively, 0.426 and 0.656 volt, which are smaller than the Vo'sby 0.056 and 0.059 volt, respectively. Taken from ref. 19. Thus, VOfor 1,2-dihydroxynaphthaleneis to be estimated as 0.506 0.058 = 0.564 volt.) (1
+
which precedes the autoxidation of initiator-free organic substances. However, these data are not necessarily adequate for theoretical consideration since the rate of chain initiation is by no means constant in the course of the induction period. Bolland and ten Have2 made a kinetic analysis of the peroxide-initiated oxidation of ethyl linoleate in the presence of phenols (ROH) by measuring the diminution in oxidation rates due to the inhibitory action of phenols. From the results of the analysis, they established a table of dimensionless values representing relative antioxidizing efficiencies, K , of phenols, taking hydroquinone as the standard, with a value of unity (see Table 111). Furthermore, they found that the value of log K increased linearly with diminishing normal oxidation potential (i.e., increasing oxidizability) . According to these workers, this quantitative dependence of antioxidant efficiency on the oxidizability of the phenols is interpreted by assuming that the chain termination reaction involves the transfer of a hydrogen atom from the antioxidant to the propagating radical (R'OO.), uix.
AH(RP-H)
=
AHu(R0-H)
+ AHr(R0-H)
(11)
where AH,(ROH) and AH,(RO-H) represent the respective changes in the energies of u- and of Telectrons accompanying the dissociation. Then, AH,(RO-H) remains substantially constant over zt series of phenolic compounds, because of the localized nature of u-electrons in chemical bonds. The relative efficiency may, therefore, be related to the difference in the total a-electronic energy between phenols (ROH) and the correspondiiig phenoxy radicals (Roe). If we assume that the energy level of each occupied molecular orbital in RO. remains identical with that of the' corresponding orbital in ROH, then AHr(R0-H)
= AEn =
-Eho = -(a
+
Xhd)
(12)
because the HOMO of RO. is occupied by one Telectron whereas that of ROH is doubly occupied. The linear dependence of log K upon Xho is, thus, to be expected, provided the entropy of activation remains constant for the different phenols. I n Fig. 3, the value of log K for several phenols, which were investigated by Bolland and ten Have, are plotted against Xho, where it is seen that the ROH + R'OO. +RO. + R'OOH (10) expected linear relationship between the two and, thus, the efficiency can be controlled entirely quantities is actually substantiated. The linear by the heat of reaction of the dissociation: ROH + dependence of log K upon V ois comprehensible if RO. +*H. one compares eq. 8 and 12. Now, let us assume that the heat of the homolytic The above interpretation of the different antioxidissociation, aH(R0-H), of ROH is divided into didng efficiencies of phenols is, however, rather two parts, viz. tentative; the transition state of the termination
1946
TAKAYUKI FUENO,TAIKYUE REE AND HENRYEYRING
Vol. 63
dissociation between the heteroatoms and hydrogen is not a rate-determining step. As the possible evidence for this, they mentioned that N-deuterated N-methylaniline3 and diphenylamine6 show identical kinetics to those of the undeuterated substances and that N,Ndimethylaniline and N,N, N’,N‘-tetramethyl-p-phenylenediamineare fairly potent inhibitors despite the absence of a labile N-H function in their structures.6 On the basis of these observations, they suggested that the inhibition reaction involves the rate-determining step
1.3
1.2
1.1
1.0
0.9
c 0
+ Inhibitor
R’OO. 0.6
in which the complex is assumed to be a loose acomplex.6 Recently, an ionic mechanism of termination of the chains by amines was proposed by P e d e r ~ e n , ~ ~ who formulated it as
3 0.7
0.6 I7
/
R’00.
0 Monophenol
0.5
0 Polyphenol
0.4 0.I
0.2
03
0.4
0.5
0.6
= ( Et,,,- a ) / B . Fig. 2.-Linear relationship between normal oxidation potentials of phenolic compounds and the HOMO energies. The numbers in Figs. 2, 3 and 5 indicate the phenols shown in Table 11. xho
I
2 ,
I
!\
I + :N-+ I
(R’O0:)-
I + (.N-)+
+ HOR
[R’OO**.O-R]
H (transition complex) [R’OO.- +Of-R] H or (R‘OO: )-(HOR)
I
I
I
I
0.2
0.3
0.4
0.5
XhO’
(Ello- 0 ) / / 3 .
Fig. 3.-Relationship between antioxidizing efficiencies of some phenolic compounds and the HOMO energies.
reaction should be taken into consideration. This point will be discussed in a later section. 2. Re-examination of the Antioxidation Mechanism of Phenols.-As already described, Bolland and ten Have2 concluded that the antioxidizing action of phenols is associated with the abstraction by the propagating radical of hydrogen atom attached to the phenolic oxygen. On the other hand, Hammond, et al.,a-e have drawn the conclusion that this is not generallv the case. Thev made extensive studies-on the” antioxidizing aczions of phenols and amines toward the autoxidations of cumene and t e t r a h and found that the bond
(14)
I
where the detachment of a mobile hydrogen from the amino group is not involved. The above survey of the chain termination mechanism shows that current considerations suggest a polar (or ionic) interaction in the primary step of the reaction between the propagating radicals and the inhibitors. However, no consideration has been made of the transition state of this reaction by previous investigators. As already mentioned, the antioxidizing power of different phenols is closely related to their oxidizability, ie., the ease with which they are ionized to give the corresponding molecular cation. Thus, we assume that the rate-determining step of the termination would involve charge transfer betwee,n the attacking radical and the phenolic oxygen -6 +s R’OO.
0.1
(13)
Complex
(15) +
and that the a-conjugation between ROH and R’OO. in the transition state would be responsible for the charge transfer; the stabilization energy of the transition complex directly contributes to the determination of the different antioxidizing efficiencies of phenolic compounds. IV. Charge Transfer Between Phenols and Radicals 1. Perturbation Theory of Charge Transfer in the Transition Complexes.-The problem is confined to calculating, by perturbation theory, (1) the increase in total a-electron energy of the united system arising from the combination of a phenol and, for simplicity, a single atom radical and (2) the increase in r-electronic charge on the radical due to a-conjugation between the components in the transition complex. The r-electronic interaction between the radical (S) and the oxygen (23) c. J. Pedersen, Ind. Ens. Chem., 48, 1881 (1956).
(Em)occ,, then o n will continue to be larger than the Pm's for occupied levels because, in eq. 21 and 22, the perturbation terms should be small compared with the Em's. Thus, the number of electrons occupying the MO, Ym', is either 0 or 2 while that in 2,' is 1. Therefore, the increase in electron density, Aqs, on S in the transition complex is given by
where
occ
unocc
m
m
C and
c denote the summations over all
occupied and unoccupied levels, respectively. Introducing the conventional relations E, =
CY
+ z,p;
F. =
01
+ ap
(25)
into eq. 23 and 24, thus, gives
1
-1
(26)
and
(24) M. J. 8. Dewar, J . Am. Chem. Soc., 74, 3341 (1952).
2. Calculation of the
AE and Aps Values.-
1948
TAKAYUKI FUENO, TAIKYUE REE AND HENRYEYRING
TABLE I11 DEPENDENCE OF THE ANTIOXIDIZING EFFICIENCIES OF PHENOLS UPON Serial no.
Phenol
Ka
A.ps
THE
STABILITY OF AEb
THE
Vol. 63 TRANSITION STATE 9x
fx
16 15
1,4-Naphthohy droquinone 40 0.5863 1.8262 1.323 1.9490 Pyrogallol (central OH) 3.0 .4747 1.8548 1.374 1,9141 Pyrogallol (side OH) ,4335 1.5870 1.8961 1.347 13 Hydroquinone 1.00 .3161 1,4438 1,8415 1,336 14 Catechol 0.63 ,3132 I . 4590 1.8342 1.331 2 a-Naphthol .56 ,1872 1,3184 I.8098 1.272 3 &Naphthol .077 .I549 I . 2603 1,8141 1,295 12 Resorcinol .016 .I307 1.1963 1.8765 1.307 1 Phenol .O l O C ,1153 I.1374 1.8200 I . 301 a Taken from ref. 2, unless otherwise noted. I n units of y2/Pi2 c Estimated from the comparative data for resorcinol and phenol as inhibitors of the thermal oxidation of sodium sulfite.
-
For several phenols investigated by Bolland and signs of the A q d s it is also concluded that the ten Have, all the molecular orbital energies Xm electron transfer takes place in the direction from and the coefficients C m r are calculated by the simple phenols to radicals. LCAO MO method, assuming the electronegativity I n pyrogallol both the Aqs and the A E are larger parameter kx for the phenolic oxygen as 1. By for the complex, in which the charge transfer is putting these calculated results into eq. 27, assumed to take place through the central oxygen, the values of A E for different phenols are obtain- than for the one associated with one of the side able in units of -y2//3, provided the value for a oxygens. The primary attack of the radical on is given. I n calculating A E , a is tentatively set pyrogallol is, therefore, considered to occur prefequal to 0, ie., the electronegativity of the atom erentially on the central oxygen in agreement with (S) bearing an odd electron in the attacking radical Bolland and ten Have’s supposition.2 is assumed equal to that of carbon. The obtained Table 111 also includes the n-electron density values are compared with the data on relative qx and the free valence fx for the oxygen atom in antioxidizing efficiencies K , of the phenols in Table separated phenols, which were calculated fromz6 111,where it is seen that the larger the stabilization occ energy, the larger is the antioxidizing efficiency. 4x = 2 (CrnXI2 (29) Figure 5 gives plots of log K against A E . Alm though the points are somewhat scattered, there and does seem t o be a roughly linear relationship occ between log K and A E ; the line is given by the fx = 4 3 - 2 CmxCrnr, (30) equation m log K = 3.60AE
- 5.52
(28)
with the correlation coefficient, r = 0.911. From the slope of this line, -y2//3 is evaluated as 5.2 kcal./mole. I n a foregoing section @ is found to be -2.08 e.v. (ie., -48.0 kcal./mole). Hence, we find that y = -16 kcal./mole. The value for ( ~ / / 3 ) , ~ which is necessary in calculating the AQS by eq. 26, is thus found to have the value (y//3)2 = (1/3)’ = 0.11. The values of the Aqs for the above phenols are calculated by eq. 26, using the known values for the Zm’S, the CmX’S and (y//3).2 The results are listed in Table 111, where it is seen that the Aqs increases with increasing magnitude of A E . Since it is possible to regard the magnitude of the Aqs as a measure of the degree of charge transfer in the transition complex, it can be concluded that, the larger the degree of charge transfer, the more stable is the transition complex. From the positive
respectively, where rl refers to the carbon atom bearing a hydroxyl group. Comparison of these two quantities with K shows that neither of them is an index of antioxidizing efficiency of phenols. The absence of parallelism between qx and Aqs implies that the electrostatic force between the reaction centers is of little significance for the charge transfer from phenols to radicals; the more important factor is the ability of aromatic nuclei for r-conjugation with the radical through the oxygen atom as a reaction center. Acknowledgment.-The authors wish to express their appreciation to the Office of Ordnance Research, United States Army, for their support of the present work under Contract No. DA-04-495Ord-959 with the University of Utah. (25) For example, see R. U. Brown, Quart. Reus., 6, 68 (1852), or else B. Pullman and A. Pullman, “Lea Theories Electroniques de la Chimie Organigue,” Masson et Cie., Paris, 1952, p. 184.
