oxidation mechanism of δ-hydroxyisoprene alkoxy radicals: hydrogen abstraction versus 1,5 h-shift

Oxidation mechanism of d-hydroxyisoprene alkoxyradicals: hydrogen abstraction versus 1,5 H-shift

Jun Zhao a, Renyi Zhang a,*, Simon W. North b

a Department of Atmospheric Sciences, Texas A&M University, College Station, TX 77843, USAb Department of Chemistry, Texas A&M University, College Station, TX 77843, USA

Received 22 October 2002; in final form 5 December 2002

Abstract

The competing pathways of H-abstraction by oxygen molecules and 1,5 H-shift of the d-alkoxy radicals with the Z-configuration arising from OH-initiated reactions of isoprene have been investigated using density functional theory

(DFT) and ab initio molecular orbital calculations. The activation and reaction energies of the alkoxy radical reactions

were obtained with B3LYP, CCSD(T), and MPW1K and various basis sets. Kinetic calculations employing variational

RRKM/ME formalism and separate statistical ensemble (SSE) theory show that a significant fraction of the chemically

excited alkoxy radicals undergo prompt 1,5 H-shift. The results also reveal that 1,5 H-shift of thermalized d-alkoxyradicals dominates over H-abstraction by O2.

� 2003 Elsevier Science B.V. All rights reserved.

1. Introduction

Atmospheric oxidation of isoprene is mainlyinitiated by attack from the hydroxyl radical OH,

the dominant tropospheric removal pathway for

isoprene [1]. The reaction between isoprene and

OH occurs by OH addition to the �C@C� bonds,forming thermodynamically favored hydroxyalkyl

radicals,

OH� þ C5H8 ! C5H8OH� ð1Þ

Under atmospheric conditions, the hydroxyalkyl

radicals react with oxygen molecules to form the

hydroxyalkyl peroxy radicals [2–5],

C5H8OH� þO2 ! C5H8OHO

�

2 ð2Þ

Addition of O2 occurs only at the carbons b to theOH position for the OH–isoprene adducts of in-

ternal OH addition, but takes places at two centers

(b or d to the OH position) for the OH–isopreneadducts of terminal OH addition, leading to the

formation of b- and d-hydroxyperoxy radicals.Subsequent reactions of the hydroxyperoxy radicals

with NO yield b- and d-hydroxyalkoxy radicals,

C5H8OHO�

2 þNO! C5H8OHO� þNO2 ð3Þ

Alternatively, a small fraction of the peroxy radi-

cals react with NO to form organic nitrates [6].

Under atmospheric conditions, the hydroxyalkoxy

radicals undergo decomposition, isomerization,

or reaction with O2. Fig. 1 shows a mechanistic

Chemical Physics Letters 369 (2003) 204–213

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* Corresponding author. Fax: +1-979-862-4466.

E-mail address: [email protected] (R. Zhang).

0009-2614/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0009-2614(02)02006-7

mail to: [email protected]

diagram for the competing pathways of H-ab-straction by O2 and H-migration of the two d–alk-oxy radicals with the Z-configuration.

The alkoxy radicals are important intermediates

in the isoprene oxidation reactions [7]. On the

basis of product distributions of the OH–isoprene

reaction system in the environmental smog cham-

ber experiments, several mechanisms of the alkoxy

radical degradation pathways have been postu-lated [8–12]. For example, it has been suggested

that the alkoxy radicals formed by terminal OH

addition undergo C–C bond fission to form methyl

vinyl ketone (MVK) and methacrolein (MACR),

along with �CH2OH [8–11]. The �CH2OH radical

subsequently reacts with O2 to form formaldehyde

and HO2. The alkoxy radicals formed by internal

OH addition also decompose to form formalde-hyde and respective radicals; the radical products

further react with O2 to produce MVK or MACR.

The previous studies also suggest that later

two radicals may undergo cyclization to produce

3-methyl furan [8,10,11]. Two theoretical studies

have investigated the C–C fission pathways of the

hydroxy-isoprene alkoxy radicals and provided

insight into the fate of the alkoxy radicals [13,14].On the basis of ab initio calculations, it is con-

cluded that the activation barrier to C–C bond

cleavage between the a and b carbons is relatively

small, indicating that the unimolecular dissocia-

tion of the b-hydroxyalkoxy radical representstheir dominant fate. Since the b-alkoxy radicalsundergo primarily decomposition, the likelihood

of formation of 3-methyl furan from cyclization of

the b-alkoxy radicals can be eliminated. As sug-gested by Atkinson et al. [8], an alternative route

to 3-methyl furan formation is via H-migration of

the d-alkoxy radical A to form a dihydroxy radicalspecies A2 followed by reaction with O2 and cy-

clization (Fig. 1). Very recently, Dibble [15] has

investigated isomerization of the E/V configura-

tions of the d-alkoxy radicals arising from the

OH–isoprene reactions.Currently, there remains considerable uncer-

tainty concerning the fate of the alkoxy radicals

formed during the isoprene oxidation. The hy-

droxyisoprene alkoxy radicals have not been

detected analytically. The reaction of the hy-

droxyisoprene alkoxy radicals with O2 has not

been assessed theoretically or experimentally.

Furthermore, there exist some discrepancies withrespect to the activation barriers of the hydroxy-

isoprene alkoxy radical reactions predicted by the

quantum chemical methods [13,14].

In this study, we investigate the competition

between H-migration by O2 and 1,5 H-shift of the

d-alkoxy radicals with the Z-configuration formedfrom OH-initiated reactions of isoprene. We ex-

amine effects of electron correlation and basis seton the reaction and activation energies of the two

reaction pathways of the d-alkoxy radicals. Inaddition, the kinetics of the alkoxy radical reac-

tions is assessed using the variational RRKM/ME

formalism and transition state theory (TST).

2. Theoretical method

The theoretical computations were performed

on an SGI Origin 3800 supercomputer using the

GAUSSIANAUSSIAN 98 software package. All radicals were

treated with the unrestricted Hartree–Fock (UHF)

formulation. Geometry optimization was executed

using Becke�s three parameter hybrid method em-ploying the LYP correction function (B3LYP) inconjunction with the split valence polarized basis

set 6-31G(d, p). The DFT structures were then

Fig. 1. Mechanistic diagram for H-abstraction and 1,5 H-shift

reactions of the d-hydroxyisoprene alkoxy radicals.

J. Zhao et al. / Chemical Physics Letters 369 (2003) 204–213 205

employed in single-point energy calculations using

frozen core second-order Møller–Plesset pertur-

bation theory (MP2) and coupled-cluster theory

with single and double excitations including per-

turbative corrections for the triple excitations

(CCSD(T)) with various basis sets. Harmonic vi-brational frequency calculations were made using

B3LYP/6-31G(d, p). Recently we have evaluated

the level of ab initio theory that applies to complex

organic radical species, on the basis of computa-

tional efficiency and accuracy [16]. A procedure

involving determination of a correction factor as-

sociated with basis set effects evaluated at the MP2

level and subsequent correction to the energy cal-culated at a higher level of electron correlation

with a moderate size basis set has been developed

for accurate energy description [16]. This method

has been validated for several isoprene reactions

initiated by OH, Cl, NO3, and O3 [16–19]. In this

work, we have corrected the CCSD(T)/6-31G(d)

energies with the basis set correction method,

corresponding to the CCSD(T)/6-31G(d) +CFmethod. Additional energy calculations were car-

ried out using CCSD(T)/6-311G(d, p).

In addition, we have employed the MPW1K

functional described previously by Truhlar and co-

workers [20]. This approach has been evaluated for

a series of H-abstraction reactions [20].

3. Results and discussion

3.1. Hydrogen abstraction

No theoretical or experimental studies have

been reported on O2 hydrogen abstraction of the

alkoxy radicals formed from the OH-initiated re-

actions of isoprene. For the smaller methoxy rad-icals, a previous theoretical study suggested the

formation of methyl trioxy radicals as intermedi-

ates, which possess lower activation barriers than

direct H-abstraction [21]. However, a more recent

theoretical employing the multireference configu-

rational ab initio method predicted that the direct

H transfer pathway occurs with an Arrhenius ac-

tivation energy of only 2.8 kcal mol�1, yielding arate constant in good agreement with the experi-

mental value [22].

We considered in the present study only the

direct hydrogen abstract mechanism. Fig. 2 depicts

the geometries of the products and transition

states of H-abstraction of the two d-alkoxy radi-cals. The evaluation of the vibrational frequencies

confirmed that the product geometries representminima on the potential energy surfaces. Transi-

tion states search of the H-abstraction of the

alkoxy radicals was performed by using TS key-

word in geometry optimization at the B3LYP/

6-31G(d, p) level of theory. The H–C bond length

was successively increased relative to the equilib-

rium structures of the corresponding alkoxy radi-

cal. Once an initial geometry optimization reachedconvergence, a frequency calculation was per-

formed to identify whether this optimized geometry

represented a first-order saddle point. A transition

state was verified by finding only one imaginary

component in the calculated vibrational frequen-

cies. The vibrational modes along the reaction

coordinates were examined to confirm that these

modes represented the trend along the intendedreaction coordinate. For the H-migration of the

alkoxy radicals, the reaction coordinates are along

the dissociating C–H bond and the newly formed

O–H bond. At the B3LYP/6-31G(d, p) level of

theory, we performed additional calculations using

the intrinsic reaction coordinate (IRC) method,

showing that each TS uniquely connects the reac-

tant to the product. In the transition states, thedistances of breaking the C–H bond are 1.22 �AA forA and 1.21 �AA for B, and the distances of formingthe new O–H bond are 1.54 �AA for A and 1.55 �AA forB. Also as shown in Fig. 2, there exists intermo-

lecular hydrogen bond for species A1 and B1 as

well as for their corresponding transition states.

The lengths of hydrogen bond are 1.85 and 1.89 �AAfor A1 and B1 and 1.88 and 1.97 �AA for TSA1 andTSB1, respectively. The geometries of the H-ab-

straction products and transition states of alkoxy

radicals A and B obtained with MPW1K/

6-31G(d, p) generally resemble those obtained with

B3LYP/6-31G(d, p). At the MPW1K/6-31G(d, p)

level of theory, the lengths of hydrogen bond are

1.86 and 1.91 �AA for A1 and B1 and 1.94 ad 1.93 �AAfor TSA1 and TSB1, respectively.Table 1 summarizes the total energies of all spe-

cies considered in this work. The activation energies

206 J. Zhao et al. / Chemical Physics Letters 369 (2003) 204–213

for H-abstraction of the alkoxy radicals A and Bobtained with the various methods are listed in

Table 2. The activation barriers obtained with

B3LYP/6-31G(d, p) are 1.83 and 1.23 kcalmol�1 for

A1 and B1, respectively. The activation energies of

the H-abstraction reactions obtained using

CCSD(T)/6-31(d) are considerably higher than

those predicted by B3LYP/6-31G(d, p), by 7 to 10kcal mol�1. Inclusion of the basis set correction

factor slightly reduces the CCSD(T) values. The

MPW1K/6-31G(d, p) method also produces higher

activation energies than those derived from the

B3LYP method. The barriers calculated with

CCSD(T)/6-31G(d) +CFandMPW1K/6-31G(d, p)

Fig. 2. Optimized geometries of H-abstraction products and their transition states of the d-hydroxyisoprene alkoxy radicals at theB3LYP/6-31G(d, p) level of theory.

Table 1

Total energies (in hartrees) of the products and transition states for H-abstraction and 1,5 H-shift of the d-hydroxyisoprene alkoxyradicals

Species B3LYP/ CCSD(T)/ MPW1K/

6-31G(d, p) 6-31G(d) 6-311G(d, p) 6-31G(d, p)

A1 )345.772965 )344.763633 )344.979336 )345.658568A2 )346.34870 )345.313797 )345.545178 )346.241354B1 )345.768321 )344.760505 )344.976012 )345.653902B2 )346.350900 )345.315680 )345.547178 )346.24379TSA1 )496.618981 )495.218588 )496.434108TSA2 )346.29664 )345.259149 )345.488626 )346.1835TSB1 )496.620522 )495.224568 )496.434108TSB2 )346.297882 )345.260015 )345.489255 )346.184664


are similar, with a difference of less than 2 kcalmol�1. The zero-point correction reaction energies

are presented in Table 3. The reaction energies ob-

tained with B3LYP/6-31G(d, p) and CCSD(T)/

6-31G(d) +CF are similar, with a difference of less

than 1.3 kcal mol�1. At the CCSD(T)/6-31G(d) +

CF level of theory, hydrogen abstraction of the

alkoxy radicals A and B occurs with the exother-

micity of 32.6 and 31.2 kcal mol�1, respectively.Additional, we also obtained the reaction energies

using CCSD(T)/6-311G(d, p), which are in agree-

ment with the CCSD(T)/6-31G(d) +CF values.

Fig. 3 shows the potential energy surfaces (PES) for

the H-abstraction reaction of the d-hydroxyiso-prene alkoxy radicals.

3.2. H-Shift

Fig. 4 shows the structures of the products and

transition states of the 1,5 H-shift reaction of the

d-alkoxy radicals A and B. H-migration of the

d-alkoxy radicals A and B leads to the formationof the dihydroxy radical species A2 and B2. It is

apparent from Fig. 4 that hydrogen bonding plays

a role in stabilizing the radical products. Thelengths of hydrogen bond (OH–O bond) are 1.69

and 1.70 �AA for A2 and B2 at the B3LYP/

6-31G(d, p) level of theory, respectively. The dis-tances of breaking the C–H bond are 1.22 �AA for

A2 and B2, and the distances for forming the new

O–H bond are 1.34 �AA for A2 and 1.36 �AA for

B2. The geometries of 1,5 H-shift products and

transition states for alkoxy radicals A and B ob-

tained with MPW1K/6-31G(d, p) are generally

similar to those obtained by B3LYP/6-31G(d, p).

Table 2 also contains the activation energies of1,5 H-shift for the alkoxy radicals A and B pre-

dicted by the various methods. In general, the ac-

tivation barriers obtained with B3LYP/6-31G(d, p)

are smaller than those derived from the other

methods. 1,5 H-shift of the two alkoxy radicals

occurs with the activation barriers of 2.3 and

0.9 kcal mol�1 according to B3LYP/6-31G(d, p).

The activation barriers predicted by CCSD(T)/6-31G(d) +CF are 6.3 and 5.4 kcal mol�1. In

addition, we calculated the H-migration barriers

using CCSD(T)/6-311G(d, p). The barriers calcu-

lated with CCSD(T)/6-311G(d, p) and CCSD(T)/

6-31G(d) +CF are identical for reaction A2 (6.3

kcal mol�1) and differ by 0.5 kcal mol�1 for reac-

tion B2. The MPW1K functional predicts slightly

lower activation energies than those predicted byCCSD(T)/6-31G(d) +CF, with the largest differ-

ence of 1.6 kcal mol�1. The recent work by Dibble

Table 3

Zero-point corrected reaction energies (kcal mol�1) for H-abstraction and 1,5 H-shift of the d-hydroxyisoprene alkoxy radicals

Rxn B3LYP/ CCSD(T)/ MPW1K/

6-31G(d, p) 6-31G(d) 6-311G(d, p) 6-31G(d)+CF 6-31G(d, p)

A1 32.06 30.42 33.02 32.61 28.72

A2 26.65 21.29 24.16 25.46 27.14

B1 29.98 29.26 31.70 31.24 26.71

B2 28.51 22.91 25.80 27.07 29.26

Table 2

Zero-point corrected activation energies (kcal mol�1) for H-abstraction and 1,5 H-shift of the d-hydroxyisoprene alkoxy radicals

Rxn B3LYP/ CCSD(T)/ MPW1K/

6-31G(d, p) 6-31G(d) 6-311G(d, p) 6-31G(d)+CF 6-31G(d, p)

A1 1.83 11.54 10.69 10.17

A2 2.28 9.27 6.29 6.29 5.33

B1 1.23 8.19 7.98 9.67

B2 0.90 8.16 4.91 5.42 3.86


Fig. 3. Schematic energy diagram for the reactions of H-abstraction and 1,5 H-shift of the d-hydroxyisoprene alkoxy radicals atCCSD(T)/6-31G(d) + CF level of theory.

Fig. 4. Optimized geometries of 1,5 H-shift products and their transition states of the d-hydroxyisoprene alkoxy radicals at theB3LYP/6-31G(d, p) level of theory.


[15] also determined the activation energies of 1,5

H-shift for alkoxy radicals A and B using the

B3LYP and MPW1K: the activation barriers of

6.6 for A2 and 6.5 kcal mol�1 for B2 were reported

at the MPW1K/6-31G(d, p) level of theory, which

are slightly higher than our values. The reactionenergies of 1,5 H-shift of the alkoxy radicals A and

B are presented in Table 3. The reaction energies

of 1,5 H-shift of the alkoxy radicals are consistent

according to the various levels of theory. The PES

of the 1,5 H-shift reactions of radicals A and B is

also illustrated in Fig. 3.

3.3. Kinetic calculations

The entrance channel of the RO2–NO reaction

(3) is exoergic, leading to a vibrationally excited d-alkoxy radicals A* and B*, which subsequently

reacts via unimolecular reactions or collision sta-

bilization. The excited A* and B* undergo two

possible prompt unimolecular reactions, 1,5 H-

shift to form A2 and B2 or C–C bond decompo-sition to form a carbonyl and radical product.

There are three plausible reaction pathways for the

thermalized A and B, decomposition, isomerize to

form A2 and B2, or bimolecular reaction with O2to form A1 and B1. Since the C–C bond decom-

position barriers are significantly higher than 1,5

H-shift for the two d-alkoxy radicals [13,14], wehave neglected this reaction pathway in the kineticconsideration.

We performed calculations to assess the fate of

the chemically excited alkoxy radicals A* and B*

using the steady-state master equation (ME) for-malism in conjunction with the RRKM method.

The reaction of the isoprene hydroxyperoxy radi-

cals with NO (3) initially forms a vibrationally

excited peroxynitrite intermediate [6]. Our recent

theoretical study shows that the entrance channel

of the NO–RO2 reaction to form nitrite proceeds

via a barrierless pathway and that a Morse po-

tential including the centrifugal barrier can be used

to variationally locate the transition states for NO

addition to the hydroxyperoxy radical as a func-

tion of energy. Similarly, we found that dissocia-

tion of ROONO to RO and NO2 also occurs

through a barrierless process [6]. Hence both ni-

trite formation and dissociation can be treatedusing vRRKM theory. In the present work, the

entrance and exit channels of the peroxynitrites

were treated similarly as in our previous work [6].

The steady state distribution of the excited per-

oxynitrite, modified by considering stabilization,

was obtained from the vRRKM/ME approach. In

our previous study, we found that there is insig-

nificant formation of thermalized nitrite underambient conditions, since at all energies above the

entrance channel for reaction (3) the dissociation

rates of the nitrites are larger than their collision

rates and on average only 1–4 kcal mol�1 of nitrite

internal energy is lost to collisions [6]. We treated

prompt 1,5 H-shift of the alkoxy radicals A and B

by using a second RRKM/ME approach. The

energy distributions of the excited alkoxy radicalswere calculated according to the separate statisti-

cal ensemble (SSE) theory, by assuming a statis-

tical distribution of the available internal energy

over the vibrational degrees of freedom of each of

the two fragments and over the degrees of freedom

of their relative motions [23]. For the dissociation

of the peroxy nitrite radical (ROONO) to form the

alkoxy radical (RO), i.e., ROONO! ROþNO2,the probability (PEtot

ROi) of occupying a given vibra-

tional (rotational) level i of the RO radical with

internal energy ERO is given by [23],

where Etot is the total disposable energy which ispartitioned over RO, NO2 and over the degrees of

freedom of their relative motion (the degrees of

freedom of relative motion of RO and NO2 are 6).

NROiðEROÞ; NNO2ðENO2Þ, and Nrel:motðEtot � ERO�ENO2Þ are the density of state of the i th energy

level for RO, the density of state of NO2, and the

density of state of relative motion, respectively.For the relative motion, Nrel:motðEÞ varies with E2

PEtotROi

ðEROÞ ¼NROiðEROÞ

R Etot�ERO0

½NNO2ðENO2ÞNrel:mot:ðEtot � ERO � ENO2Þ�dENO2R Etot0

fðP

i NROiðEROÞÞR Etot�ERO0

½NNO2ðENO2ÞNrel:mot:ðEtot � ERO � ENO2Þ�dENO2gdERO; ð4Þ


since we treated the relative motion as unhindered

motion which NðEÞ varies with its degrees of

freedom r as Eðr=2Þ�1.

Exact state counts and vibration density ofstates of all relevant species were evaluated by

using the Beyer–Swinehart algorithm [24]. The

vibrational frequencies were modified along the

reaction coordinate according to an exponential

switching model [25]. The RRKM/ME calcula-

tions employed an exponential model for collision

energy transfer using an average energy of 500

cm�1. For the alkoxy radicals A and B, a Lennard-

Jones collision frequency of ZLJ ¼ 1:3� 1010 s�1 at298 K and 760 Torr was estimated using the values

of r ¼ 6:07 �AA and e ¼ 486:3 K. All vibrations weretreated as harmonic. We found that explicit

treatment of the internal rotors as hindered rotors

did not significantly alter the results. Calculations

were performed at fixed total angular momentum

and subsequently Boltzmann averaged.

The RRKM isomerization rates for 1,5 H-shiftof alkoxy radicals A and B as a function of energy

are shown in Fig. 5. Also plotted in the figure is the

energy population of the excited alkoxy radicals

calculated according to the SSE theory. For the

kinetic calculations shown in Fig. 5, we employed

the energetics for the 1,5 H-shift reaction obtained

at the CCSD(T)/6-31G(d)þCF level of theory.

Fig. 5 reveals that a significant amount of thealkoxy radicals are distributed above the activa-

tion barriers for the 1,5 H-shift reaction, indicating

that prompt H-migration plays an important role

in determining the kinetics of the excited alkoxy

radicals. Table 4 summarizes the ratios of prompt

1,5 H-shift and stabilization of the d-alkoxy radi-cals. It is apparent from the table that prompt 1,5

H-shift of the alkoxy radicals dominates overstabilization, even at 1 atm. Using the CCSD(T)/

6-31G(d)þCF calculated energetics, the stabil-

ization ratios are 0.42 for A and 0.21 for B at 760,

and decease to 0.06 for A and 0.03 for B at 7.6

Fig. 5. RRKM rates for 1,5 H-shift of the alkoxy radicals A

and B as a function of microcanonical energy. For comparison,

the collision rate is 1:3� 1010 s�1 at 760 Torr and 298 K. Alsoshown is the energy distribution of the excited alkoxy radicals

A* and B* calculated according to the SSE theory.

Table 4

Prompt 1,5 H-shift and stabilization ratios of the d-hydroxyisoprene alkoxy radicals at various pressures

A B

Pressure (Torr) 7.6 76 760 7.6 76 760

I Prompt 1.00 1.00 1.00 1.00 1.00 1.00

Stabilization 0.00 0.00 0.00 0.00 0.00 0.00

II Prompt 0.94 0.85 0.58 0.97 0.94 0.79

Stabilization 0.06 0.15 0.42 0.03 0.06 0.21

III Prompt 0.98 0.95 0.83 1.00 0.99 0.97

Stabilization 0.02 0.05 0.17 0.00 0.01 0.03

I: Barrier heights and frequencies from B3LYP/6-31G(d, p). II: Barrier heights from CCSD(T)/6-31G(d)+CF and frequencies from

B3LYP/6-31G(d, p). III: Barrier heights and frequencies from MPW1K/6-31G(d, p).


Torr. The RRKM/ME calculations are sensitive to

the predicted activation barriers; the results em-

ploying the energetics predicted by B3LYP/

6-31G(d, p) and MPW1K/6-31G(d, p) both show

negligible stabilization of the alkoxy radicals at all

pressures.We also calculated the high-pressure limit rate

constants for the alkoxy radicals using classic

transition state theory (TST) [26]. The calculated

high-pressure limit rate constants for H-abstrac-

tion and 1,5 H-shift reactions of the alkoxy radi-

cals are listed in Table 5. 1,5 H-shift of thermalized

alkoxy radicals A and B occurs with the rate

constants of 2:1� 108 and 2:1� 109 s�1 at theCCSD(T)/6-31G(d) level of theory, respectively.

The recent work by Dibble [15] reports the rate

constants of 8:5� 107 and 1:0� 108 s�1 for 1,5H-shift of alkoxy radicals A and B at 298 K and

1 atm of air, respectively, on the basis of the acti-

vation energies predicted by the MPW1K func-

tional. Our calculated high-pressure limit rate

constants of 1,5 H-shift for alkoxy radicals A andB are hence consistent with those reported by

Dibble. Table 4 also indicates that the bimolecular

rate constants of H-abstraction by O2 for the

alkoxy radicals are strongly dependent on the

quantum chemical methods. At the B3LYP/

6-31G(d, p) level of theory, the calculated bimo-

lecular rate constants are 3:4� 10�15 and 7:7 �10�15 cm3 molecule�1 s�1 for A1 and B1, respec-tively, while the rate constants predicted by

CCSD(T)/6-31G(d)+CF andMPW1K/6-31G(d, p)

are significantly smaller. Note the bimolecular

rate constants predicted by using the B3LYP/

6-31G(d, p) method are similar to those previously

suggested for the hydroxyalkoxy radicals [7]. Even

if the lower activation barriers predicted by the

B3LYP method are considered (i.e., about 1.8 kcal

mol�1 for A1 and 2.3 kcal mol�1 for A2), the es-

timated first-order rate constants for the H-ab-

straction are 1:7� 104 s�1 for A1 and 3:8� 104 s�1for B1, significantly smaller than their corre-sponding rate constants for the 1,5 H-shift reac-

tion. Consequently, if thermalized, the d-alkoxyradicals are anticipated to undergo predominantly

the 1,5 H-shift reaction to form the dihydroxy

radical intermediates. As previously suggested

[8], the consecutive reactions of the dihydroxy

radical intermediates with O2 form hydroxycar-

bonyls which have been qualitatively observed[27]. Further cyclization of the hydroxycarbonyls

provides a mechanism for the formation of

3-methyl furan [8].

4. Conclusions

We have presented a theoretical study of H-ab-straction by O2 and 1,5 H-shift for the d-alkoxyradicals with the Z-configuration from the OH-

initiated reactions of isoprene. The effects of elec-

tron correlation and basis set on the reaction and

activation energies of the alkoxy radical reactions

have been evaluated. The results allow for a direct

assessment of the relative important of the two

competing reaction pathways. The calculationsusing RRKM/ME formalism in conjunction with

the SSE theory show the dominance of prompt 1.5

H-shift over stabilization for the chemically excited

d-alkoxy radicals, indicating that a significant

fraction of the d-alkoxy radicals undergo prompt1,5 H-shift to form the dihydroxy radical interme-

diates. The results also indicate that the fate of

stabilized d-alkoxy radicals is dominated by theunimolecular 1,5 H-shift reaction over bimolecular

H-abstraction reaction by oxygen molecules.

Acknowledgements

The work was supported by the Robert A.

Welch Foundation (A-1417) and the NationalScience Foundation (CHE – 0204705). Additional

support for the computation part of this research

Table 5

High-pressure limit rate constants of H-abstraction and 1,5

H-shift reactions of the d-hydroxyisoprene alkoxy radicals

Rxn B3LYP/

6-31G(d, p)

CCSD(T)/

6-31G(d) + CF

A1a 3:42� 10�15 2:46� 10�21A2b 1:21� 1012 2:15� 108B1a 7:67� 10�15 1:38� 10�20B2b 1:77� 1012 2:13� 109a In cm3 molecule�1 s�1.b In s�1.


was provided by the Texas A&M University Su-

percomputing Facilities. The authors are grateful

to Jiho Park and Dan Zhang for assistance with

kinetic calculations reported in this work and to

Ted Dibble for sending a preprints and helpful

discussions, and acknowledge the use of the Lab-oratory for Molecular Simulations at Texas A&M.

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oxidation mechanism of δ-hydroxyisoprene alkoxy radicals: hydrogen abstraction versus 1,5 h-shift

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