AM1 calculations on reactive oxygen species Part 3. Stereochemistry of hydroperoxide products obtained from oxidation of linoleic acid

THEO CHEM ELSEVIER

--~

Journal of Molecular Structure (Theochem) 424 (1998) 207-223

AM1 calculations on reactive oxygen species Part 3. Stereochemistry of hydroperoxide products obtained from oxidation of linoleic acid’ B. Vernon Cheney Pharmacia & Upjohn, Inc., Kalamazoo, MI 49007-4940, USA

Received 18 March 1997; accepted 26 March 1997

Abstract Autoxidation of linoleic acid leads to four major products: 9-hydroperoxy-lo-trans-12-cis-octadecadienoic (l), 9-hydroperoxy-lo-truns-12-trans-octadecadienoic (2), 13-hydroperoxy-9-c&I I-trans-octadecadienoic (3), 13-hydroperoxy-9-trans1I-truns-octadecadienoic (4) acids. The trans,cis:trans,trans product ratio (1 + 3:2 + 4) is dependent upon temperature, the concentration of linoleic acid undergoing peroxidation, and the presence of cosubstrates in the medium. To elucidate these effects, theoretical studies of linoleic acid peroxidation have been unde~~en using absolute reaction rate theory. As a test of the theoretical model, the estimated rate constants have been employed in computer simulations of the experimental reaction systems. Calculated temperature, concentration, and cosubstrate effects are found to be in good qualitative agreement with experiment. 0 1998 Elsevier Science B.V. &words:

AM 1 calculation;

Linoleic acid peroxidation;

Stereochemistry;

1. Introduction

Reaction mechanism;

hydroperoxides

Absolute reaction rate theory

1-4,

Peroxidation of linoleic acid (9-cis-12-cis-octadecadienoic acid) and its esters has been the subject of various experimental kinetic studies [l-3], and some investigations have been carried out on product stereochemistry [4-61. It has been established that the bisallylic site (Cl 1) is the preferred target for hydrogen abstraction, and that the oxidative process yields

‘Ninetables detailing the results of computations on oxidative reactions of benzene, 1,4-cyclohexadiene, cumene, and species involved in branching reacfions of the peroxy adduct to” 9,12octadecadienoic acid and 1,4-cyclohexadiene are available as Supplementary Material. This Material can be accessed via the THE~HEM HomePage at h~p://~.elsev~er.ni~~ate/the~hem

3

O2 H

RI

4

OzH

where R1 = (CH2)$OzH and R2 = (CH&CHx, as the dominant products accounting for == 97% of the total oxygen uptake. The traditional rationale for the

0166-1280/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved. PII SOl66-1280(97)00144-9

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kinetics of autoxidation assumes that the propagation stage consists of two rapid, irreversible reactions: (1) hydrogen abstraction by a peroxy radical to form the pentadienyl-type radical 5; (2) O2 addition at C9 or Cl3 of 5 to

5 regenerate the peroxy radical. Although these propagation reactions lead in a straightforward way to the trans,cis isomers 1 and 3, the existence of trans,trans isomers 2 and 4 is more difficult to explain. Porter and coworkers [5,6] have suggested that cis-trans isomerization occurs as a result of reversible oxygen addition, where they describe the separation of O2 from the lipid radical as @-scission. Difficulty in monitoring radical species prevents direct experimental proof of the fl-scission hypothesis, and the theoretical model [7,8] developed previously predicts that reversible peroxy-radical addition to the double bonds of the unsaturated acid is a more likely mechanism for isomerization. This work extends the earlier theoretical findings by addressing the experiments of Porter et al. that were designed to reveal factors affecting the stereochemistry of hydroperoxide products derived from linoleic acid. Parts 1 and 2 of this series describe a chemical model in which oxidative mechanisms have been investigated using AM1 CI calculations to explore the potential surfaces of the reactions, and a scaling procedure based on comparisons with empirical barriers has been employed to correct the distorted AM1 barriers. Rate constants have been determined from considerations of absolute reaction rate theory [9]. The use of the CHEMKIN II program [lo] to simulate actual experiments serves as a powerful tool to examine the validity of estimated rate constants. Although CHEMKIN II has been designed for gas-phase kinetics, it may be appropriately used in constant temperature studies with rate constants determined for condensed fluids. The findings of this chemical model serve to explain factors affecting the entropy and energy of activation that determine the course of lipid peroxidation reactions in the early stage of the process. Validation of the model

Structure (Theochem) 424 (1998) 207-223

is provided by comparison of the results of computer simulations with experimentally observed product yields. The capability of following radical populations and reactive intermediates that are unobserved experimentally is an advantage of the procedure. Since the chemical model is both predictive and amenable to experimental test, it should stimulate further investigation into the many unanswered questions conceming lipid-peroxidation kinetics and mechanisms. The kinetic model for formation of hydroperoxide, L02H, through oxidation of lipid, LH, follows the reaction sequence outlined below: Initiation

-X0;

ri

(1)

XO;+LH+XO,H+L

kl

(2)

Propagation

L+

0, -

LO;

k2

(3)

k3

LO;+LH+LO,H+L’

(4)

Radical control

2Lo; Z LOdL

k,, k-6

LO; + Yj ~ ‘YjO*L

(5)

k,j, k7j

(6)

In these expressions, XO;is a radical derived indirectly from decomposition of an initiator such as azobis-isobutyronitrile (AIBN); Yj is an unsaturated molecule, such as an octadecadienoic acid or 1,4cyclohexadiene; Ti is the rate of chain initiation; and k is a rate constant for an elementary reaction in the process. Under the assumption that the system attains a steady state in the concentration of free radicals, [LO;] and [L] are given by the following expressions: [Lo;]

=

ri +2k_e[LOdL]

+ Cj k_,j[‘Y,OzL]

“2

2k, (7) [L’] = ri + k3

[L;;&H1

(8)

2

In the derivation

of Eq. (7), terms

involving

the

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quotient k71k6 have been neglected since peroxyperoxy combination is a barrier-free process and peroxy addition to an unsaturated molecule must overcome a rather high barrier due to loss of conjugation. At the steady state, the rate of oxygen uptake in this model may be written as

(9) ri+2k..6[LO,L]+

+k

&k_,j[‘YjO2L]

“2

3 2k

[LHI

>

Since Y, is generally negligible compared with other terms in Eq. (9), Eqs. (7)-(9) reveal the importance of Eqs. (5) and (6) for radical control and maintaining the rate of oxygen uptake when the steady state is reached. Results obtained with this model qualitatively reproduced experimental observations regarding the nature of the hydroperoxide products and the relative rate of reaction at different sites in the lipid chain. The foregoing kinetic model differs from the

Table 1 Order-of-magnitude

values of factors contributing

Energy mode

to pre-exponential

Partition function factor

Translation and rotation b van der Waals vibration ’ 5

2L4

non - propagating

ati q2M

2LO; -

products

non - propagating

non-propagating

k4

(10)

products

products

ks kg’

(11) (12)

Although the reactions (10) and (11) exhibit small barriers and large rate constants, the extremely small concentration of L’ leads to minor accumulations of stable high-molecular weight dimers, peroxides, alcohols, and ketones in the early stages of oxidation. Tetroxide decomposition in the reverse reaction of Eq. (5) exhibits a much lower barrier than the fragmentation yielding non-propagating products. As a result, the reversible reactions in Eqs. (5) and (6) are much more important for control of the oxidative chain than the termination reactions in Eqs. (lo)-( 12).

terms of rate constants

Moiety or molecule M a L

(hdw

classical one [ 1 l] in that reversible radical-control reactions have been substituted for the termination step of the chain consisting of Eqs. (lo)-( 12).

L+ LO; -

4021 - dt=ri

209

X,B,C,D

02,OH

H>O.OzH

1 lO_‘T

102 lo-‘T

10”T’l? lo-‘T

106 10.‘T

_

10m2T

10-2T

IO-‘T

VO)

Internal rotation ’

q3rvl

(M f L) Internal rotation d

q4M

T

_

a The same value of the factor is used for all molecules or free radicals containing M as the major fragment. The entities represented in the second subcolumn are IBN (X), benzene (B), cumene (C), and 1,4-cyclohexadiene (D). b aM accounts for the effects of differences of other molecules from linoleic acid (L) in the translational and rotational partition functions. ’ The van der Waals modes in the transition-state complex are vibrations that evolve from the translational and rotational degrees of freedom of the smaller reactant, M. Two van der Waals vibrations, ~$1 and yS2, may be described as shifts or pendulum swings of M in directions orthogonal to the reaction coordinate. A torsional mode, vu, corresponds to rotation about the axis of the reaction coordinate, and two other torsional modes, yt2 and Y,~,may be specified approximately as rotations about axes perpendicular to each other and the reaction coordinate. In the transition-state complexes for O2 addition, vt3 does not exist since the center of gravity of the diatomic molecule lies on the axis of rotation. As significant contributions to the entropy of activation are found only for low-frequency modes, the exponent of qZM is given by 6 =N{ yVdw5 va}, where yt, is taken as 200 cm _’ in the temperature range 280 5 T % 320 K. d The contributions of most single bonds in linoleic acid essentially cancel in the rate expression. However, X is evaluated from the number of mid-chain single bonds that undergo a significant change in rotational freedom in the transition-state complex. If a C-C linkage gains single bond character through loss of conjugation when attack occurs at an unsaturated carbon, X is incremented by + I. On the other hand, each single bond that becomes fixed contributes - 1 to the value of X. For unimolecular decomposition, the values of 6* and a* are determined by internal rotations that are converted into van der Waals modes in the transition-state complex. In addition to the rotational motions, a low-frequency vibrational mode in M that is shifted above ~a in the transition-state complex increases 6’ by one.

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2. Methods As outlined in Part 2 [8] of this series, the bimolecular (Eq. (13)) and unimolecular (Eq. (14)) rate kb = 1.11 x lo%,&&-

kuL- 2.08 x iO1oAT

q%q::

(13)

exp

(14)

constants employed in the kinetic model were obtained from absolute reaction-rate theory. In these expressions, E’ is the reaction barrier, u is the net energy ( = 0.2 kcal mol-‘) required to desolvate the reaction sites in the two molecules, and the pre-exponential terms are derived from partition functions of the reactant(s) and transition-state complex. Definitions and values of the pre-exponential terms used in Eqs. (13) and (14) are given in Table 1. The units of the rate constants in this work are M-’ s-’ for kb and s-’ for k,. The numerical part of the pre-exponential term for factor contains a kb v = Qt(M’)Q,(M’)/ [Q,(M’)Q,(M’)] > 1, where Qt and Ql are specific partition functions for translation and rotation of the transition-state complex, Mt, and the larger reactant, M’. In the simple approximations employed for the partition functions in the previous study [8], the same value of n was employed for all reactions. However, comparison of the calculated and experimental values of k3 suggest that the value of n used previously is roughly an order of magnitude too large when lipid moieties are constituents of both reactants. To give more accurate quantitative results in this study, the pre-exponential factor of Eq. (13) has been reduced to one-tenth of the value used earlier. Furthermore, if the reaction involves one or two small molecules, n should be near unity. To provide this correction, the values of uM for M # L in Table 1 reflect a reduction in n by two orders of magnitude. This change affects the values of kl and k2 which do not play an important role in oxygen uptake at the steady state according to Eq. (9). Smce - d[O,]/dt m k3ki iI2 , reductions in the pre-exponential terms of the bimolecular rate constants diminish the rate of oxygen uptake to a smaller degree than would be expected from the effect on k3 alone. Although calculations with the new rate

constants on the systems studied previously give improved agreement with experimental rate studies, the findings with respect to the relative rates of oxidation at different sites in the lipid molecule remain unchanged. The AM 1 semi-empirical molecular orbital procedure [ 12,131 was employed to calculate approximate energy barriers, AH, # , and evaluate the normal-mode frequencies used to determine the exponents of the q factors. The procedures employed in calculations on benzene, cyclohexadiene, and cumene were the same as those used on model lipids in Part 2 [8]. Improved estimates of the activation energies were obtained by scaling the exaggerated AM1 = CI barriers using Eq. (15) Es=0.64AH;

+/3

(15)

where /3 is a parameter determined from the empirical activation energy and the calculated value of AHf’ for each gas-phase reaction employed as a calibration standard. In some cases, where empirical data are lacking, estimates of p have been made through comparisons with barriers found by ab initio quantum mechanical calculations using the Gaussian 94 program [ 141. Calculated rate constants were used as input for CHEMKIN II in various computational experiments designed to follow the time course of linoleic = acid and cosubstrate peroxidation. The rate of reaction between molecule M and radical R’ is given by d[Pr;yl=

k,,,[M][R]

(16)

where the apparent rate constant, kapp, depends on the degeneracy, n, of the site of attack in M. kapp= ‘%

(17)

The form of kapp for input to CHEMKIN I1 and for comparison with empirical rate expressions is kapp= A 'T" exp( - E’/RT)

(18)

where E’ = E’ + u if the reaction is bimolecular, and E’ = E ’ if it is unimolecular. All computational rate studies carried out on linoleic acid solutions were assumed to take place in a 1 1 vessel surrounded by a constant temperature bath. AIBN was used as initiator in the model experiments to avoid the additional calculations necessary to

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characterize reactions of the initiators employed by Porter et al. [5,6]. The system was considered to be well stirred, open to the atmosphere (po, = 152 tort-), and saturated with O2 throughout the experiment; i.e., any oxygen consumed in the reaction was immediately replenished from the large supply in the environment. To simulate this condition, the equilibrium between gas-phase and dissolved oxygen, O,(g) F! O*(o), was taken into consideration by treating OZ(g) as a pseudo species present in the reaction vessel at extremely high concentration relative to LH. The concentration of oxygen dissolved in the medium was found by means of Henry’s law.

3. Results Since AM1 molecular orbital calculations have already been performed on linoleic acid models, computations in this study focus on the reactivity of benzene, 1,4-cyclohexadiene, and cumene. In the calculations MeOi was employed as the model peroxy radical. Branching reactions in the oxidative chain involving the peroxy radical adduct, ‘LH02L, have also been investigated. Tables Sl-S3 (see WWW Supplementary Material) list the values of the AM1 reaction barriers, AHr’ , the empirical barriers, E’, the exponents, 6, derived from vibrational analysis of the transition-state complexes, and the parameters, /3, used in scaling the AM1 energies. Rate constants derived from the AM1 data using Eqs. (13) and (14) are provided as supplementary material in Tables S4-S9. Values of A’ in the tables also reflect the symmetry factor, n, employed in Eq. (17). Included in the compilation are rate constants for reactions of linoleic acid and its isomers, many of which differ from the previously reported [8] values as a consequence of adjusting parameter r] in the calculation of kb.

4. Discussion 4.1. Reactions cumene

of benzene, I,$-cyclohexadiene,

and

Of particular interest, in view of Eqs. (6) and (9), is the possibility that benzene (B) and the cosubstrates

211

act as radical-control traps through formation of peroxy adducts at unsaturated carbons. Hydrogen abstraction reactions were considered only at sp3 carbons of 1,Ccyclohexadiene (DH) and cumene (CH) since much higher barriers are expected to be found for sp2 sites. Furthermore, Cl’, the tertiary carbon in the cumene methylethyl substituent was taken to be the principle target of attack for H abstraction. Since Howard and Ingold [ 151 have suggested that hydrogen abstraction by 02 from the cyclohexadienyl radical is important in the autoxidation of 1,4cyclohexadiene, this reaction has been examined in addition to those involving peroxy radicals. Creation of cosubstrate peroxy radicals through O2 addition to the cyclohexadienyl (D’) and cumenyl (C) radicals was also investigated. Owing to loss of resonance in the aromatic ring, a high barrier was obtained for addition of a peroxy radical to benzene or cumene. In cumene, since methylethyl is an ortho-para directing group, the barriers to addition at C2 and C4 are lower than those at C 1 and C3. At every site, the barrier to adduct decomposition is considerably lower than the peroxyaddition barrier. The barrier for addition to 1,Ccyclohexadiene is found to be much lower than those for benzene and cumene. Furthermore, the cyclohexadiene adduct is significantly more stable than the adducts formed from peroxy attack on aromatic rings. The relative stability of the adducts indicates that 1,4-cyclohexadiene should be a much better peroxy-radical trap than benzene or cumene. Barriers to hydrogen abstraction from 1,4-cyclohexadiene and the bisallylic site in linoleic acid are similar in height. In both cases, the transition-state complex is stabilized by the development of resonance extending over five carbon atoms. Removal of hydrogen from Cl ’ of cumene yields a radical with the unpaired electron delocalized into the aromatic ring. The higher barrier for this reaction suggests that conjugation does not develop sufficiently to provide effective stabilization of the transition-state complex. As a result cumene is less susceptible to Habstraction than linoleic acid or 1,4-cyclohexadiene. It has been observed that benzene and hydrogen peroxide are the dominant products from oxidation of 1,4-cyclohexadiene [ 151. This implies that hydrogen abstraction is preferred to oxygen addition (k,, > k,) when oxygen attacks D’ as shown in Scheme 1. To

B. V. CheneylJournal oJ’Molecular Structure (Theochern) 424 (1998) 207-223

212

+

involving addition to C’ and D’, as well as the one involving H abstraction from D’. The peroxy-adduct, ‘DH02L, exhibits a low-frequency rocking mode of the ring methylene groups (~4 = 104 cm-‘) that is shifted above 200 cm-’ in the decomposition transition-state complex. This corresponds to a loss of vibrational freedom that occurs as conjugation develops in the’ C-C bond when the peroxy radical departs. Therefore, 6* is incremented by 1 in the preexponential term of k, for decomposition of ‘DHOzL.

HO/

kh f

I

DlO;

0;

4.2. Chain-branching radical adducts

reactions involving peroxy-

D30;

Scheme I. give a product distribution near the observed 9: 1 ratio of hydrogen peroxide to organic hydroperoxides, the required value of Ef for hydrogen abstraction is approximately 5 kcal mol-’ if the oxygen-addition barriers are of the magnitude ( = 8.5 kcal mol-‘) found from the scaled AM1 values. Since the drive toward the aromatic product could cause the H-abstraction barrier to be lower than that for OZ addition, this empirical estimate is used in the kinetic studies. As with other calculations on oxygen reactions, the huge error in the AM1 heat of formation for O2 leads to a highly exaggerated barrier for hydrogen abstraction from D’, and 6 is found to have a large negative value. Frequencies of the normal modes found in the vibrational analysis were examined to determine factors affecting the entropy of activation for the reactions under investigation. Only three van der Waals modes in the transition-state complex for addition of a peroxy radical to benzene are small compared with kT/hc and, therefore, contribute to the value of 6. As with other peroxy-radical reactions, the relative orientation of the molecules about the C.d.0 axis of attack is almost unrestricted since the magnitude of v,~ is near zero. On the other hand, shift vs2 and torsion v,~ (which, respectively, resemble C-C...0 and C-.,00 “bond angle” bends) are higher frequency modes with little effect on the temperature dependence of the pre-exponential term. In all bimolecular peroxyradical addition and H-abstraction reactions involving CH and DH, only vt2 exhibits a frequency greater than the cut-off value. This is also the case for O2 reactions

The total concentration of radical adducts, ‘LHOzL, is much larger than the overall peroxy radical concentration in simulated reactions using Eqs. (l)-(6) and the rate constants reported in Part 2 [S]. As a result, the possible reactions of the adduct in Scheme 2 that may compete with peroxy elimination must be considered to provide a more complete analysis of the system. Repetition of the addition sequence with 6 as the attacking peroxy radical to create O-O linked polymers is commonly observed in autoxidation of lor 2-alkenes [ 161. However, several workers [ 171 have found that long reaction times are required to proceed as far as dimer formation in the autoxidation of linoleic acid. High temperature, as well as long reaction time, is necessary to obtain an observable yield [18] of monoene epoxides from intramolecular substitution on ‘LHOIL with release of LO’. Generation of extended conjugation should drive H abstraction by O2 from Cl 1 of the 9- or 13-isomers of ‘LH02L, but the conjugated diene lipid peroxides formed in the reaction are observed as very minor products, and hydrogen peroxide has not been observed in the peroxidation of methyl linolenate [ 151. These observations strongly suggest that the rate constant, kd, for decomposition of the radical adduct in Scheme 2 must be significantly greater than the magnitude of k,, k,[OZ] and kh[02]. Unfortunately, experimental rate constants for these reactions have not been determined in the linoleic = acid system. In the absence of experimental information with which to calibrate results of AM1 calculations, ab initio calculations have been used when simple models of the system could be devised. However, the environment of the reaction center in ‘LHO ZL cannot be represented with

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of Molecular Structure (Theochem) 424 (1998) 207-223

+

0

A

LO.

R3

R4

i’

ke

IL P0

LH +‘02L

9

0

02

lLHO2L

-

b ka

kd

O+c R3

R4

6

+

HO;

Scheme2 a molecular fragment small enough to permit highlevel calculations. Therefore, estimates of k, and kh in Scheme 2 have been made by monitoring the yield of major and minor products using simulations with the CHEMKIN II program. The lowest values of the 02-‘LH02L addition and abstraction barriers that do

not seriously perturb the product yields in the system from those observed experimentally are 21.5 and 20.0 kcal mol-‘, respectively. Miyashita et al. [19] found that the dimer corresponding to H02LH02L maintained a relatively constant low concentration at reaction times from

6

/H

0 H

R3

+

*OH

’ 0

-

. > R3

10 Scheme 3

R4

9

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Although some limitation of the concentration of 13 is caused by further hydrogen abstraction to give the unstable benzene-peroxy radical adduct, ‘BOzR, the intramolecular decomposition pathway outlined in Scheme 3 does not exist for 11, and the buildup of the dihydroperoxy product 12 would be inevitable unless O2 addition to the hydroperoxy adduct is slow in comparison with the rate of decomposition of ‘DHO*R. To aid in the assessment of factors affecting these branching reactions, AM1 calculations have been carried out on model systems using 1-( 1-methyldioxyethyl)pent-3-cis-enyl radical (‘LH02L) as the model precursor to 6. It was found that a larger CI calculation is required to describe H abstraction by 02 than the Mopac 6.0 program is designed to handle. Results of the large AM1 = CI calculations on this system are adversely affected by orbital degeneracies and excessive correlation effects arising from the presence of several high-energy oxygen lone-pair orbitals and spectator ?Tbonds that are not directly involved in the reactions. Therefore, ‘LHOZL was truncated to the 3cis-butenyl radical (‘BdH) to remove degeneracies involving high-lying spectator orbitals isolated in the moieties that were eliminated. In the 1,4-cyclohexadiene system, the models for the peroxy-radical adduct, ‘DHOZL, and truncated adduct, 3-cyclohexenyl radical (‘DHH), were also used to find AM1 barriers to O2 addition and H abstraction, respectively. The values of /3 used in scaling these reactions

96 to 192 h, while trimers were not observed during this period. This suggests that 6 decomposes at a higher rate than it reacts with LH by H abstraction or addition. Since G2(MP2) calculations on a model system, O2 + ‘CH&H202H - ‘02CH&H202H, give the value of 36.9 kcal mol-’ for the heat of reaction, loss of molecular oxygen appears unlikely as the mode of decomposition for the stable /3-dioxyalkylperoxy radical. However, 6 may undergo intramolecular hydrogen abstraction followed by a series of decomposition reactions to give a ketone, two aldehydes, and a hydroxy radical in Scheme 3. In the linoleic = acid system, the ketone 8 is either 9oxo- 10,12-octadecadienoic acid or 13-0x0-9,1 loctadecadienoic acid, while the pair of aldehydes 9 and 10 depend upon which double bond is the site of fragmentation: A9 gives 9-oxo-nonanoic acid and 3nonenal, while Al 2 yields 12-oxo-9-dodecenoic acid and hexanal. The unsaturated aldehydes may also serve as reactants in this scheme to give malonaldehyde and a saturated aldehyde with the chain length shortened by 3 carbon atoms. All of these compounds have been observed as minor products of oxidation

WI. Consideration of the branching reactions involving the peroxy-adduct to 1,4-cyclohexadiene, ‘DHOZR, yields Scheme 4. Since R = H when DH is the only oxidizable substrate in the system, there would be substantial accumulation of the organic hydroperoxides 12 and 13 if k, and kh were both large.

ln “2

HO2

02R

0,R

DH b

ka /

ti

+ Do u -

-

12

11

+ 02 O2R

/

+ ‘02H d

Scheme 4

. -

+HOH2

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of Molecular Structure (Theochem) 424 (1998) 207-223

were determined from estimates of E’ which did not significantly alter production of the major hydroperoxide products, 1-4, or give excessive yields of very minor peroxide, aldehyde, and ketone products through the branching reactions. To obtain values of @for the O-O cleavage reactions, G2(MP2) calculations were performed on the reactants, products, and transition-state complexes of the following simple systems: ‘CH,O-OCH, ‘CH20-OH

-

CH,O +‘OCH,

CH,O +‘OH

(19) (20)

The ab initio calculations produced barriers of 3.9 and 3.6 kcal mol-’ for the cleavage reactions in Eqs. (19) and (20), respectively. Both reactions are virtually irreversible since the recombination barriers exceed 38 kcal mol-‘. Although the AM1 procedure and the model fragments depicting the environment of the reaction centers in LHOlL and’ DH02L are inadequate for quantitative purposes, the calculations provide qualitative insights into observed relative rates of similar reactions. For example, the calculations indicate that k, in Scheme 2 should be much smaller than k2 in accord with the slow production of peroxide dimers. There are two reasons for the difference: (1) the value of the AM1 barrier for O2 attack on ‘LHOZL is about 5 kcal mall’ higher than AHf’ for L’; (2) the preexponential factor in the rate constant is much smaller in the’ LHO?L reaction than the L’ since there is no increase in the rotational freedom of the lipid chain in the transition-state complex. Furthermore, kh in Scheme I is predicted to be much larger than its counterparts in Scheme 1 and Scheme 3 since the AM1 H-abstraction barriers for O2 attack on D’, ‘LHOIL, and ‘DH02L are 23.5, 35.8, and 40.5 kcal mol-‘, respectively. This order follows the expectation that increasing conjugation in the product drives the reaction. The large difference in barrier size also accounts for the observation that H02H is produced in the oxidation of 1,4-cyclohexadiene, but not unsaturated lipids [ 151. These qualitative features of the potential surfaces are preserved in the linear transformations used to produce quantitative estimates of E’. Exploration of the AM1 potential surface indicates that the reaction to form monoene epoxides in Scheme

215

2 proceeds by elimination of LO’ before the ring closes in a barrier-free reaction. AHf # for the concerted reaction is higher in energy by nearly 27 kcal mall’. As a consequence, the scale factor obtained previously [8] for cleavage of peroxide O-O bonds may be applied to this reaction, giving the estimate E+ = 35.6 kcal mol-‘. As E ’ is 17-21 kcal mall’ lower for heterolytic than homolytic cleavage, the value of kd in Scheme 2 is found to be much larger than k,. Elimination of relatively stable LOi restores the lipid double bond, while departure of LO’ leaves behind an extremely unstable biradical. This finding accounts for the slow formation of monoene epoxides in linoleic = acid peroxidation. Subsequent to elimination, LO’ readily abstracts hydrogen from linoleic acid isomers (E # I 3.8 kcal mol-‘) to give 9-hydroxy- lotram, 12-cisltrans-octadecadienoic or 13-hydroxy-9cisltrans- 11-trans-octadecadienoic acid. Analysis of the entropic factors affecting 02 attack on ‘LH02L and ‘DH02L reveals that 6 = 3, whether the reaction is addition or H abstraction. In both cases, the only van der Waals mode with a frequency high enough to preclude a contribution to the temperature effect on the pre-exponential term of kb is vt2. As with all O2 reactions that have been studied, there is little restriction on the orientation of the oxygen molecule about the reaction coordinate since vtl is near zero in the transition-state complex for both addition and H abstraction. In the case of H abstraction from ‘BdH, the C 1-C2 bond acquires significant double-bond character in the transition-state complex, and this suggests that the corresponding bond in the lipid chain of the ‘LH02L radical suffers a notable loss of rotational freedom as the reaction proceeds. This entropic effect is taken into account by setting X equal to - 1. The values of E # calculated for intramolecular H abstraction from models of 6 and 11 (R = L) are 16.8 and 19.3 kcal mall’, respectively. As R, = R2 = CH3 in the model of 6 (denoted ‘02BuHOzL in Table Sl), the same barrier is used for intramolecular H abstraction reactions in any long chain molecule where ‘02L attack on a double bond has been followed by O2 addition. Two modes, v2 and ~3, associated with vibrations in the eight-member ring of the transitionstate complex make a significant contribution to the temperature effect in the pre-exponential term of the rate constant. Fixing five torsional angles in the transition-state complex of the 6 - 7 reaction extracts

216

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a high entropic cost, since 6* is incremented by 1 and E* by 4. Nevertheless, the reaction is predicted to occur at a much higher rate than the loss of O2 from the stable /3-dioxyalkylperoxy radical. In the case of ‘02DH02L, 6* is increased by 4 as there is no rotational freedom in the ring bond. Steric problems are expected to hamper ‘02LH02L and ‘02DH02L in bimolecular hydrogen abstraction reactions; however, calculation of the abstraction barriers is not feasible owing to the complexity of the reactants, and such reactions have been ignored in this work. Following intramolecular H abstraction, decomposition of 7 (H02LHOzL’) is predicted to occur rapidly since none of the bond-cleavage barriers exceeds 6 kcal mol-’ . In the break up of H02DHOzL’, the barrier for C-C cleavage is 14.6 kcal mol-‘. Only two van der Waals modes, vtl and vsl, make an important contribution to the entropy of activation when 8 and 9 depart in the disintegration of H02LH02L’. Separation of ‘OH in the final step of Scheme 2 yields 6 = 1 since a single van der Waals shift falls below the cutoff frequency. These entropic factors are also found for the corresponding reactions in the breakup of H02DH02L’. Production of ‘OH in Scheme 3 necessitates the inclusion of further addition and H-abstraction

from vtl and vx, a mode associated with the reactant that is shifted below the 200 cm-’ cutoff in the transitionstate complex. Hydroxy addition to the 2-butene model of a chain containing a double bond produced no low-frequency van der Waals modes contributing to 6. Since the double bond retains its character in the reactant-like transition-state complex, no rotational freedom is introduced into the chain. When DH is under attack in the addition reaction; a significant entropic contribution is made by v3, a perturbed 1,4cyclohexadiene mode that exhibits a frequency above the cutoff in the isolated molecule. 4.3. Entropic factors in linoleic = acid reactions In this study, 2,5-heptadiene models have been used in the AM1 calculations to describe the reaction sites in linoleic acid. As a consequence, the nature of the chain extension on either side of the fragment remains undefined. Linoleic acid is denoted as L,,H; its isomers are designated as L,,H and L,,H, where [L,,H] includes the concentrations of both 9-trans, l%-cisand 9-&s, 12-trans-octadecadienoic acid. The notation employed to describe the radicals derived from these isomers is defined by the 2,5-heptadien-4-yl and (lmethyl-2,4_hexadienyl)peroxy radicals shown below: .

reactions in the kinetic processes of the system. The scaled barriers for hydrogen abstraction by a hydroxy radical are small ( 5 4.7 kcal mol-‘), but exceed those for addition to double bonds by at least 0.5 kcal mol-‘. The only van der Waals mode that contributes to 6 in the H-abstraction reaction involving linoleic acid or 1,4-cyclohexadiene is v,,. Two additional contributions to the temperature effect in the pre-exponential term are found with the isomers of linoleic acid exhibiting one or two trans double bonds; these arise

.

Since the chain extensions are not specified, L, represents both 9- and 12-trans isomers of the radical. As no differentiation is made between 02 addition at C9 and Cl3 in the lipid chain, both [L,,O;] and [L,,O;] consist of equal concentrations of the C9and C13-substituted isomers. Likewise, L,,02H represents the combination of 1 and 3, while L,,OzH represents 2 and 4. Under the assumption that local symmetry controls oxidative reactions, proper accounting for the production of isomeric radical

B. V. Chewy/Journal of Molecular Structure (Theochem) 424 (1998) 207-223

adducts differing only in the chain extensions is made through the factor 12 = 2 in Eq. (17). This is reflected in the value of A’ for radical-addition reactions involving linoleic acid and several of its derivatives. In all propagation and radical-control reactions, except peroxy-radical combination, the pre-exponential term of a reaction involving L,H or Li exhibits larger temperature effects than that of a reaction involving CH, DH, C’, or D’. The difference in the entropy of activation found in H abstraction is due to the fact that all van der Waals modes exhibit low frequencies when attack occurs at the bisallylic site of linoleic acid, while vt2 is a high-frequency mode when CH and DH are the targets. Enhancement of the entropy of activation in the addition reactions is caused by differences in the rotational degrees of freedom of the lipid chain in the reactant and transitionstate complex. For example, O2 addition to Lb leads to a large value of m in Eq. (18) because two conjugated bonds in the radical parent acquire single bond character in the transition-state complex, and X = 2 in such a case. This effect is lacking in O2 addition reactions involving alkyl radicals derived from the cosubstrate molecules for the following reasons: (1) the Cl ‘-Cl bond in C’ exhibits little double-bond character in either the reactant or transition-state complex; (2) the ring in D’ prevents rotation about the two bonds that lose conjugation. Peroxy addition to an unsaturated carbon in L,H produces an enhanced entropic effect due to loss of conjugation in the C=C bond under attack, and this is taken into account by setting h equal to 1. ring constraints prevent this contriHowever, bution when MO; adds to benzene, cumene, or 1,4cyclohexadiene. In this study, the hydroperoxy radical is assumed to experience the same energy barrier as an organic peroxy radical for a given reaction. Nevertheless, there are generally marked differences in the size of the rate constants owing to entropic factors reflected in the coefficient A’. There is a major difference between HO;; and LO; associated with loss of the reactant’s translational and rotational degrees of freedom in forming the transition-state complex for addition to double bonds, as evidenced by the value of aM in Eq. (13) and Table 1. Furthermore, the disparity in the magnitude of the van der Waals

217

contributions, q2M, in Eq. (14) yields a slower rate for loss of HO; than LOi from the radical adduct. 4.4. Model

kinetic

experiments

The case of 0.45 M linoleic acid in benzene solution was investigated to determine whether the model predicts an important role for ‘B02L as a peroxycontrol reservoir. Variation of reactant and product concentrations during the course of the simulation is portrayed in Fig. 1. The total concentration of lipid radicals, [L’], which is of the order 10ei8 M at the steady state, is not shown in the plot. The aggregate of peroxy-radical adducts constitutes the largest freeradical pool ([‘LH02L] = lo6 M) in the system, exceeding the concentration of LO; by more than a factor of three. Benzene does not play a role in radical control since the rate of peroxy addition to the

__

0

._

3600

7200

t @I

Fig. 1. Calculated time course of peroxidation initiated by 0.5 mM AIBN in a 0.45 M solution of linoleic acid in benzene at 300 K. The species followed in the reaction are: L,,H (a), L,,H (D), L,,H (A), L,,02H (O), L,,02H (A), ‘LH02L ( x ). LO; (0). LOIL (0) and ‘B02L (0). All isomers are included in the molecules denoted by LO;, ‘LHO*L, ‘B02L and LOIL. At the conclusion ofthe computational experiment, 6.5% of the linoleic acid was oxidized to hydroperoxide products.

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218

ofMolecular Structure (Theochem) 424 (1998) 207-223

aromatic ring is not competitive with hydrogen abstraction from linoleic acid, and this leads to an extremely small steady-state concentration of ‘BOIL. The evolution of the experiment portrayed in Fig. 1 is taken from the complete solution given by CHEMKIN II of the set of differential equations in the model. This solution is not based on the steadystate assumption used to analyze the system in terms of Eqs. (7)-(9). It is seen that radical concentrations continuously increase during the early stages of oxidation contrary to the steady-state approximation. Nevertheless, the approximation is reasonable since radical concentrations and their rate of change are several orders of magnitude smaller than those of the octadecadienoic acid isomers and hydroperoxide products following completion of the induction

1E-07

period. O2 is the only species that maintains a steady concentration ( 10e3 M) in the reaction medium. Repetition of the experiment with the inclusion of branching reactions led to an overall reduction of 0.2% in hydroperoxide production, and the final tc:tt ratio changed from 0.5 1 to 0.52. Accumulation of the more important minor products predicted by the model is illustrated in Fig. 2. At the end of the 2 h run, the minor species exhibit concentrations in the range of 0.l- 100 nM. Insignificant concentrations of water and hydrogen peroxide are also produced. As the focus of this study is the hydroperoxides produced in the initial stages of autoxidation, branching reactions are ignored in further simulations. Porter et al. [5] found identical hydroperoxide product ratios in monitoring oxidation of 1.8 M linoleic acid in benzene at intervals over a period from 0.5 to 8 h. Based on this result, they concluded that product distribution is independent of the extent of oxidation within a 2% total oxidation limit. Since Eq. (6) indicates that isomerization, like Habstraction, is dependent upon the peroxy-radical and linoleic = acid concentration, one might expect

lE-OS

10000.0

1000.0

100.0 1Eil13

.s

I

d ” z

f

10.0

lE-15 0

3600

7200

t k@

Fig. 2. Some minor products produced by the system of Fig. I when branching reactions were considered. The total yield of peroxide dimers (0), ketones (A), monoene epoxides (A), and diene alcohols (0) is represented in the graph since no effort was made to keep track of the individual isomers. Hexanal (B), 12-oxo-9-dodecadienoic acid, 3-nonenal, and Y-oxo-nonanoic acid are products obtained in the same yield with the assumptions used in the model. HZ0 (a) and HOzH (0) are the other species followed in the reaction. Malonaldehyde (not shown) exhibited a final concentration of 2.5 x 1O-2o M.

1.0

0.1 0%

1%

2%

3%

4%

5%

6%

7%

PercentOxidation

Fig. 3. Variation of tt:tc ratio, r, with the percent oxidatioqp, from the system consisting of 0.45 M linoleic acid in benzene at 300 K. Except for values of p very close to zero, the expression r=1.527pm’ +0.35 provides a satisfactory fit to the data points.

B. V. Cheney/Joumai

of Molecular Structure (Theochem) 424 (1998) 207-223

some relationship to exist between the tt:tc ratio, Y, and the extent of oxidation as measured by the percentage, p, of linoleic acid that has been converted to hydroperoxide products. Results from the 0.45 M linoleic acid system yield the plot shown in Fig. 3. The lag time in the isomerization reaction results in a preponderance of the tc isomer during the induction period of the oxidative chain reaction. On the other hand, when an equilibrium distribution of L,,H, L,,H, and L,,H is achieved, the hydroperoxide product ratio asymptotically approaches the thermodynamic limit favoring the more stable isomer, L,,02H. In the model system, the tc:tt ratio nears the thermodynamic limit in the region of 5% oxidation. Judging from the experimental observations, isomerization must occur more rapidly relative to oxidative chain propagation than it does in the simulation. Nevertheless, the model calculations suggest that the constant value of Yfound in the Porter experiment is the result of measurements made after the thermodynamic product ratio was achieved. Contrary to the conclusion drawn by Porter et al., the greatest changes in the product ratio take place in the very early stages of oxidation

0

1

2

3

4

LH Corm (M) Fig. 4. Hydroperoxide product ratio from oxidation of linoleic acid in benzene solution. The points correspond to measurements taken at the following times in each run: 14400 s at 280 K ( +), 2700 s at 300 K (U), and 261 s at 320 K (A). The extent of oxidation is less than 2.0% at each point.

219

Table 2 Values of the percent oxidation, p, in runs with different initial concentrations of linoleic acid, where the time of measurement, 1, was chosen to give ~(0.24 M) = 1.9% at each temperature.

T W)

280 300 320

t (s)

20400 3200 261

lL,,Wo (W 0.24

0.45

0.90

1.8

3.2

1.93 1.88 I .89

1.20 1.20 1.27

0.67 0.68 0.74

0.36 0.37 0.4 I

0.21 0.22 0.24

Porter and coworkers discovered a linear relationship between the tc:tt ratio and linoleic = acid concentration, where the slope of the line depends upon the temperature. To investigate the performance of the model, simulations of these experiments were carried out at T= 280,300, and 320 K with initial linoleic acid concentrations of 0.24, 0.45, 0.90, 1.8, and 3.2 M. In all simulations performed at 300 and 320 K, the initial concentration of AIBN was 0.5 mM. To reduce the time required to achieve a 2% yield of diene hydroperoxides at 280 K, [AIBN10 was increased to 5 mM. These calculations produced lines (Fig. 4) exhibiting the qualitative behavior of the experimental data, although the magnitude of Y is too high as a result of the apparent error in the calculated relative rates

04 0

1

2

3

4

LH Cone (M)

Fig. 5. Hydroperoxide product ratio from oxidation of linoleic acid in benzene solution, where measurements at each temperature ( l , 280 K; n, 300 K; A, 320 K) correspond to the times given in Table 2. The values ofp are all less than 2.0%.

B. V. Cheney/Joumal

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ofMolecular

of isomerization and hydroperoxide formation. Runs made with different initial concentrations of linoleic acid at a given temperature yield plots of r versus p identical to Fig. 2. This indicates that the dependence upon the parametric variables t and [L,,H], is eliminated in the relationship between r and p. Further analysis of the findings reveals an interesting dual behavior of linoleic acid as a good propagator of the oxidative chain through facile H abstraction at the bisallylic site and a good retardant of oxidation through reversible peroxy addition at the double bonds of the molecule. The competitive advantage of double-bond addition over H abstraction in vying for peroxy radicals causes a marked reduction in the extent of oxidation for a given reaction time as the initial concentration of linoleic acid is increased in the system. As shown in Table 2, this effect appears to be nearly independent of the temperature of the lE+OO

Structure (Theochem) 424 (I 998) 207-223

system. The Porter graph of the tc:tt ratio versus [L,,Hlo in Fig. 5, corresponding to the reaction times in Table 2, exhibits marked decreases in the slopes of the lines for the 280 and 300 K data points. This again demonstrates that r is not independent oft in the early stages of autoxidation. Experimental observations of linoleic = acid oxidation in the presence of the cumene and 1,4cyclohexadiene cosubstrates led Porter and coworkers [6] to conclude that the product ratio depends upon the overall hydrogen-atom donating ability of the solution. To determine the behavior of the present model, simulations of the reactions were run over a 2 h time span at 300 K in neat CH (Fig. 6) and 9.5 M DH (Fig. 7). As cumene is a rather poor hydrogenatom donor and resists formation of peroxy-aromatic adducts, there is essentially no difference between the total peroxy-radical concentration (MO; = 10m6M) portrayed in Fig. 6 and the LO;; concentration obtained from 0.24 M linoleic acid in benzene at

1E-01 lE-02 lE-03 lE-64 lE-05 lE-06

lE_M

.

lE-07 lE-06 lE-09 $

lE-10

e

lE-11

5

lE-12 lE-13 lE-14

e lE-06

o 0

1 E-15 1 E-16 lE-17 lE-16 lE-19

............

1 E-20 1 E-21 lE-22

........................... 0

3600

7200

.......................

t (8) lE-15

Fig. 6. Simulated course of peroxidation initiated by 0.5 mM AIBN in a 0.24 M solution of linoleic acid in cumene at 300 K. The species followed in the reaction are: L,,H (a), L,,H (W), L,,H (A), L,,OrH (Q L02H (A), ‘LH02L ( x L LO& ( + 1, MO; (O), ‘CHOsL (0) and Cl’OzH (0). All adduct isomers produced from attack of a lipid-peroxy radical on cumene are included in the species denoted as ‘CHO*L. MO; represents the collection of all peroxy radicals.

i 0

I 3600

7200

t w

Fig. 7. Calculated peroxidation reaction initiated by 0.5 mM AlBN in a solution consisting of 0.24 M linoleic acid, 0.29 M benzene, and 9.5 M 1,4_cyclohexadiene cosubstrate at 300 K. The species followed in the reaction are: L,,H (+), L,,H (W), L,,H (A), L,,OZH (0,

L,,OzH (A), HOzH (Oh DlOzH (O), D302H ( x ), MO; (0).

B. V. Cheney/Joumal

of Molecular Structure (Theochem) 424 (1998) 207223

300 K. On the other hand, peroxy radicals highly prefer addition to 1,4-cyclohexadiene over any Habstraction reaction. Since this causes a significant reduction in the total peroxy-radical concentration ([MO;] = 10e9 M), both oxidation and isomerization of linoleic acid are greatly retarded. The hydroperoxy radical is an important driver of the propagation step when DH is the cosubstrate, and the equilibrium constant for reversible HO; addition is three orders of magnitude greater than the one for LO;. As a result, the isomerization delay may be ascribed for the most part to reduced hydroperoxy-radical concentration through rapid formation and slow decomposition of ‘DH02H and ‘LH02H. The effect of 1,4-cyclohexadiene concentration on the tc:tt ratio exhibited by systems containing 0.24 M linoleic acid at 300 K is shown in Fig. 8. Porter and coworkers [6] found a nearly linear relationship, where Y= 27.3 ? 2 at 9.5 M DH. The decidedly nonlinear response and the large range of Y found in this study seems to be the result of the slow rate of isomerization relative to oxidation. The error most likely results from scaled AM1 reaction barriers for decomposition of peroxy-radical adducts that are about 1 kcal mall’ too high. However, since no report of reaction times for the experimental data points was

_“”

I

221

given, quantitative comparisons with experiment cannot be made. The effects of the cosubstrates on the tc:tt ratio over the full time span of the experiments in neat cumene and 9.5 M 1,4-cyclohexadiene are portrayed in Fig. 9. Since r(CH):r(B) = 1 over the 7200 s range, cumene and benzene prove to be equivalent in their effects on the product ratio. In contrast, r(DH):r(B) reaches a maximum of 211.4 at about 1890 s and declines thereafter to 96.0 at 7200 s. At this concentration of DH, the data reported by Porter et al. [6] yield r(DH):r(B) = 114 f 18 as the only point for comcorresponds to the parison, and this presumably calculated value of 197 found when the value of p in the system without cosubstrate is near 2%. The rapid variation of r(DH):r(B) indicates that very careful measurements would have to be made to obtain a precise value of the tc:tt ratio at a given reaction time in a system with a high concentration of 1,4-cyclohexadiene. The experimental data reported by Porter et al. [6] do exhibit much greater scatter for repetitive measurements at 4.0 and 9.5 M DH than at lower concentrations of the cosubstrate.

I

20-m O”“‘--“-““““‘---“---‘--“----“’ 0 0

2

4

6

10

DH Cone (M)

Fig. 8. Calculated tc:tt hydroperoxide product ratio derived from oxidation of 0.24 M linoleic acid in cyclohexadiene/benzene solution. Points were taken at 3420 s, wherep = 2.16% in the absence of cosubstrate.

3600

7200

t (a) Fig. 9. Variation with reaction time of the product ratio r(cosubstrate) relative to r(benzene). The symbols + and 0 denote r(DH):r(B) and r(CH):r(B), respectively. Values of r(cosubstrate) are taken from the runs portrayed in Figs. 6 and 7, and r(benzene) is obtained from a simulated oxidation reaction in a 0.24 M linoleic acid solution initiated by 0.5 mM AIBN at 300 K.

222

B. V. Cheney/Journal

of Molecular

Structure (Theochem) 424 (1998) 207-223

5. Conclusions The classical kinetic model of an oxidative chain reaction proceeding in a series of irreversible initiation, propagation, and termination steps cannot explain the existence of diene hydroperoxide products with isomerized double bonds relative to linoleic acid. Porter et al. have suggested that the difficulty may be resolved by considering reversibility of O2 addition to the lipid radical in the propagation stage. However, calculations based on scaled AM 1 reaction barriers do not support this hypothesis since a peroxy radical abstracts hydrogen from linoleic acid much more rapidly than it dissociates through 0 scission. In the early stages of autoxidation, isomerization of the linoleic = acid double bonds takes place through the mechanism of reversible peroxy-radical addition, which occurs prior to hydrogen abstraction. The simulations also indicate that double-bond addition and reversible tetroxide formation play an important role in peroxy-radical control. Furthermore, the calculations reveal that the traditional chain termination reactions yielding non-propagating products are unimportant for radical control. Since [‘LH02L] > [L’] at the steady state of the oxidation reaction, the consequences of 02 attack on the peroxy adduct have been considered in this investigation. The stable ‘02LHOZL radical appears to undergo intramolecular hydrogen abstraction in preference to the sterically hindered bimolecular reaction. The resultant H02LHOZL’ radical decomposes easily into four fragments: a 9- or 13oxo-octadecadienoic acid, two aldehydes from cleavage at the double-bond site, and a hydroxy radical. Hydrogen abstraction by O2 from Cl 1 of ‘LH02L yields a peroxide dimer and a hydroperoxy radical. Since products of these branching reactions are observed in very low yield following long incubation at moderate temperature, O2 attack on ‘LH02L must be slow in comparison with the rate of decomposition of the peroxy adduct. Empirical estimates of the 02-‘LHOsL reaction barriers were made by monitoring the relative yields of the major and minor products in simulations of autoxidation. There is some uncertainty in the size of the addition barriers since the actual yield of the minor products during the initial stages of reaction is unknown.

Simulations have been carried out to elucidate the effects of temperature, linoleic = acid concentration, and certain oxidative cosubstrates on the trans,cis:trans,trans ratio of diene hydroperoxide products. Comparisons have been made with the experimental results of Porter and coworkers. Although rather crude approximations based on AM1 calculations have been employed to estimate entropic and energetic contributions to the rate constants, the results of the simulations are in satisfactory qualitative accord with experimental findings. Contrary to the conclusion of Porter et al., the tc:tt ratio is found to vary strongly with the extent of oxidation in early stages of the reaction. Although Yandp depend on the reaction time and the initial concentration of linoleic acid, a relationship of the type r = a( T)p- ’ + b(T) appears to hold, where a(T) and b(T) are independent of t and [L,,Hlo. The reaction underlying all of the effects is reversible peroxyradical addition to double bonds. Increased trapping of peroxy radicals in the’LH02L reservoir accounts for the seemingly paradoxical finding that enlarging the initial linoleic acid concentration reduces the percentage yield of hydroperoxide products in a given reaction time. Since the rate of production of LO; in the propagation step is diminished, there is also an adverse effect on the rate of isomerization; hence, r increases with [L,,H],,. An enhanced tc:tt ratio develops for two reasons when 1,4-cyclohexadiene is in the system: (1) reduction of the total peroxy-radical concentration through formation of ‘DHOZM; (2) rapid formation and slow decomposition of ‘DHOZH relative to ’ DHOzL as a result of entropic differences in the reactions. Since peroxy radicals prefer hydrogen abstraction from LH and DH over addition to an aromatic ring, the presence of benzene or cumene has no direct effect on radical concentration or the tc:tt ratio.

References [I] (a) J.L. Bolland, Proc. R. Sot. London, Ser. A 186 (1946) 2 18; (b) J.L. Bolland, Q. Rev. London 3 (1949) 1. [2] (a) L. Bateman, L. Morris, Trans. Faraday Sot. 48 (1952) 1149; (b) L. Bateman, Q. Rev. London, 8 (1954) 147. [3] J.A. Howard, K.U. Ingold, Can. J. Chem. 45 (1967) 793. [4] H.W.-S. Chan, G. Levett, Lipids 12 (1977) 99.

B. V. Cheney/Journal

of Molecular Structure (Theochem) 424 (I 998) 207-223

[5] N.A. Porter, B.A. Weber, H. Weenen, J.A. Khan, J. Am. Chem. Sot. IO2 (1980) 5597. [6] N.A. Porter, L.S. Lehman, B.A. Weber, K.J. Smith, J. Am. Chem. Sot. 103 (1981) 6447. [7] B.V. Cheney, J. Mol. Struct. (Theochem) 364 (1996) 219. [8] B.V. Cheney, J. Mol. Struct. (Theochem) 364 (1996) 239. [9] A.A. Frost, R.G. Pearson, Kinetics and Mechanism, 2nd edn., Wiley, New York, 1961, pp. 77-102. [lo] R.J. Kee, F.M. Rupley, J.A. Miller, CHEMKIN II: A Fortran Package for the Analysis of Gas Phase Chemical Kinetics, Sandia National Laboratories, Livermore, CA, Rep. SAND 898009. [I l] (a) H.W.S. Chan, in: H.W.-S. Chan (Ed.), Autoxidation of Unsaturated Lipids, Academic Press, London, 1987, pp. l16. (b) H.W. Gardner, in: H.W.S. Chan (Ed.), Autoxidation of Unsaturated Lipids, Academic Press, London, 1987, pp. 51-93. [12] M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, .I. Am. Chem. Sot. 107 (1985) 3902. [ 131 J.J.P. Stewart, J. Computer-Aided Mol. Design 4 (1990) I. [14] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Peters-

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son, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, ES. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian 94, Revision C.3., Gaussian, Pittsburgh, PA, 995. J.A. Howard, K.U. Ingold, Can. J. Chem. 45 (1967) 785. F.R. Mayo, Act. Chem. Res. 1 (1968) 193. (a) S.S. Chang, F.A. Kummerow, J. Am. Oil Chem. Sot. 30 (1953) 403; (b) K. Miyashita, K. Fujimoto, T. Kaneda, Ag. Biol. Chem. 46 (1982) 2293. W.E. Neff. E.N. Frankel, D. Weisleder, Lipids 16 (1978) 415. K. Miyashita, K. Fujimoto, T. Kaneda, Ag. Biol. Chem. 46 (1982) 751. (a) E. Vioque, R.T. Holman, Arch. Biochem. Biophys. 99 (1962) 522; (b) W. Grosch, in: H.W.S. Chan (Ed.), Autoxidation of Unsaturated Lipids, Academic Press, London, 1987, pp. 95-139; (c) H. Tamura, and T. Shibamoto, Lipids 26 (1991) 170.