Experimental and theoretical studies of gas phase NO3 and OH radical reactions with formaldehyde, acetaldehyde and their isotopomers

Article abstract of DOI:10.1039/b211234p

Formaldehyde and acetaldehyde are among the most abundant carbonyls in the atmosphere. The vapor phase reactions of formaldehyde, formaldehyde-d₂, ¹³C-formaldehyde, acetaldehyde, acetaldehyde-1-d₁, acetaldehyde-2,2,2-d₃, and acetaldehyde-d₄ with NO₃ and OH radicals were studied at 298 K and 1013 mbar using long-path FTIR detection. The OH and NO₃ radicals reacted with formaldehyde and acetaldehyde entirely through H_ald-abstraction. The acetaldehyde with OH proceeded via two pathways - CH₃CHO + OH → CH₃CO + H₂O and CH₃CHO + OH → CH₃ + CO + H₂O - with a branching ratio of ≈ 9:1 at 298 K. In the acetaldehyde reaction with NO₃, the latter reaction path was not important in atmospheric conditions. Theoretical calculations results apparently reproduced all essential features of the experimental kinetic data for the parent compounds. Theoretical analysis of the kinetics of CH₃CHO + OH indicated a complex and a temperature dependent reaction mechanism with significant dominance of the formation of the adduct at low temperatures. However, the observed kinetic isotope effects for reactions of NO₃ were much smaller than those calculated by conventional transition state theory. This was also attributed to the formation of pre-reactions adducts.

Full text of DOI:10.1039/b211234p

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Experimental and theoretical studies of gas phase NO and OH
3
radical reactions with formaldehyde, acetaldehyde and their
isotopomersy
a
Barbara D’Anna, Vebjørn Bakken, Jon Are Beukes, Claus J. Nielsen,*
a
a
a
b
Katarzyna Brudnik and Jerzy T. Jodkowski
b
a
Department of Chemistry, University of Oslo, P. O. Box 1033 Blindern, N-0315,
Oslo, Norway. E-mail: claus.nielsen@kjemi.uio.no
Department of Physical Chemistry, Medical University of Wroclaw, pl. Nankiera 1,
b
5
0-140, Wroclaw, Poland
Received 13th November 2002, Accepted 5th March 2003
First published as an Advance Article on the web 25th March 2003
1
3
The vapour phase reactions of formaldehyde, formaldehyde-d
2
,
C-formaldehyde, acetaldehyde, acetaldehyde-
and OH radicals were studied at 298 ꢀ 2 K and
013 ꢀ 10 mbar using long-path FTIR detection. The values of the kinetic isotope effects at 298 K, as
1
1
1 3 4 3
-d , acetaldehyde-2,2,2-d , and acetaldehyde-d with NO
determined by the relative rate method, were: kNO +HCHO/kNO +DCDO ¼ 2.97 ꢀ 0.14, kNO +HCHO
/
3
3
3
k
k
k
NO +H13CHO ¼ 0.97 ꢀ 0.02, kOH+HCHO/kOH+DCDO ¼ 1.62 ꢀ 0.08, and kOH+H13CHO/kOH+DCDO ¼/ 1.64 ꢀ 0.12,
3
OH+HCHO/kOH+H13CHO ¼ 0.97 ꢀ 0.11, kNO +CH CHO/kNO +CD CHO ¼ 1.19 ꢀ 0.11, kNO +CH CHO
3
3
3
3
3
3
NO +CD CDO ¼ 2.51 ꢀ 0.09, kOH+CH CHO/kOH+CH CDO ¼ 1.42 ꢀ 0.10, kOH+CH CHO/kOH+CD CHO
¼
3
3
3
3
3
3
1
.13 ꢀ 0.04, and kOH+CH CHO/kOH+CD CDO ¼ 1.65 ꢀ 0.08. Quoted errors represent 3s from the statistical
3
3
analyses. These errors do not include possible systematic errors.
The reactions of NO and OH radicals with formaldehyde and acetaldehyde were studied by quantum
3
chemical methods on the MP2 and CCSD(T) levels of theory using the aug-cc-pVDZ and aug-cc-pVTZ basis
sets which include diffuse functions. The calculations indicate the existence of weak adducts in which the
radicals are bonded to the aldehydic oxygen. Transition states of the reactions X + HCHO ! products, and
X + CH
3
CHO ! products (X ¼ OH, NO
3
) were located. Energy level diagrams for reactants, intermediates
and products in the OH reactions are presented and discussed in relation to the observed product distribution.
Reaction rate coefficients and kinetic isotope effects calculated from different models of the reaction rate theory
are compared to experimental data.
wavelengths below 360 and 345 nm, respectively, and the reac-
tion with OH radicals. Reactions with Cl and Br atoms are
Introduction
5
important in the marine boundary layer, and the night-time
Formaldehyde (HCHO) and acetaldehyde (CH
3
CHO) are
among the most abundant carbonyls in the atmosphere. Both
have natural sources: vegetation emissions, biomass fires and
microbiological processes. They are also primary pollutants,
produced by partial oxidation of hydrocarbon fuels, and sec-
ondary pollutants produced by oxidation of volatile organic
compounds in the troposphere. On a global scale the most
important source of formaldehyde is the photochemical oxida-
loss processes are due to reaction with NO radicals and the
3
6
possible dry and wet deposition.
The kinetics of the OH reactions with HCHO and CH CHO
1
3
7
,8
have been extensively studied and critically evaluated. In
contrast, there are only three kinetic studies published, focus-
9
–11
ing on the NO3 reaction with HCHO,
and five on the
For all the aliphatic alde-
1
0,12–15
NO reaction with CH CHO.
3
3
tion of methane (CH ) although the photochemical oxidation
4
hydes studied so far, including HCHO and CH CHO, the OH
3
reactions show a negative activation energy while the NO
of non-methane hydrocarbons (NMHC) can dominate the
HCHO formation in regions of high NMHC emissions.
Ambient levels are in the order of a few tens of pptv in clean
3
2
8
reactions show a positive activation energy. Data for the
OH reaction with two formaldehyde isotopomers, HCDO
1
6
3
,4
13
and H CHO, have been published, and two other studies
17
background conditions,
polluted areas (1–20 ppb HCHO). The major daytime loss
but may reach tens of ppbv in
1
which include kinetic isotope effects in the NO (ref. 15) and
3
processes of HCHO and CH CHO are the photolysis at
3
OH (ref. 18) radical reactions with acetaldehyde have recently
appeared.
Results from quantum chemical studies of the OH reactions
y Electronic supplementary information (ESI) available: program
package FACSIMILE for simulation of the complex set of reactions
and the kinetics of the reactor system. Kinetic data from the acetalde-
hyde studies, the spectral ranges and the compounds included in the
subtraction procedures, and a full report of the statistical analyses.
Calculated energies of the reactants, intermediate stationary points
of the potential energy surface, and the products. Calculated vibra-
tional wavenumbers of the reactants and transition states. See
http://www.rsc.org/suppdata/cp/b2/b211234p/
1
9–23
with HCHO and CH CHO have been presented.
Both
CASSCF and MP2 calculations suggest that the barrier
3
23
2
0
to OH addition to the carbon atom in the HCHO is ca. 30
ꢁ1
kJ mol
reaction.
higher than the barrier to the Hald-abstraction
The larger aliphatic aldehydes show reactivity towards
OH and NO3 radicals which deviates from commonly used
1
790
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805
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DOI: 10.1039/b211234p

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structure activity relations and, strikingly, reaction rate coeffi-
cients that fall close to the correlation line for addition reac-
tions in a linear free energy plot showing log(kNO3) vs.
is valid:
ꢁ½
ꢂ
ꢁ
ꢂ
Aꢄ
kA
½Bꢄ0
½Bꢄt
0
ln
¼ k : ln
ð1Þ
2
4,25
½Aꢄ
t
B
log(kOH).
current understanding of the mechanisms of the OH and
NO radical reactions with aldehydes in general through
The aim of the present work is to improve the
where [A] , [A] , [B] and [B] denote the concentrations of the
0
t
0
t
3
compounds A and B at times zero and t, respectively. A plot of
ln{[A] /[A] } vs. ln{[B] /[B] } will give the relative reaction rate
experimental and theoretical investigations of the kinetics
and of the kinetic isotope effects.
0
t
0
t
coefficient krel ¼ k
A
/k
B
as the slope. The ratio between the
concentrations of the compounds was found by spectral sub-
traction using the spectra of the pure starting compounds,
spectra of other compounds identified in the reaction mixture
and a sloping background. Data from independent experi-
ments were analysed jointly according to eqn. (1) using
a weighted least squares procedure including uncertainties
in both reactant concentrations and allowing a zero-point
Experimental and data analysis
The experiments were performed in synthetic air (AGA plus;
CO and NO < 100 ppb, C H < 1 ppm) at 298 ꢀ 2 K and
x
n
m
1
013 ꢀ 10 mbar in a 250 L electropolished stainless steel reac-
tor equipped with a White type multiple reflection mirror sys-
tem of 120 m optical path length for on-line FTIR detection.
Infrared spectra were recorded with a Bruker IFS 88 employ-
ing a nominal resolution of 0.5 cm , Harp–Genzel apodiza-
tion and co-adding 100 scans (registration ca. 60 s). The
28
offset.
ꢁ1
Quantum chemical computations
NO
of N O . In the NO experiments a variable amount of cyclo-
3
radicals were generated in situ by thermal dissociation
Ab initio calculations were carried out using the Gaussian 98
2
5
3
2
9
hexane was added to the smog chamber to act as an OH
radical scavenger. The hydroxyl radicals were generated by
photolysis of different organic nitrites (methyl nitrite, 2-pro-
pyl-nitrite–2PN, and 2-propyl-nitrite-1,1,1,3,3,3-d –2PN-d )
employing Philips TLD-08 fluorescence lamps (lmax ꢂ 370
nm) mounted in a quartz tube and inserted into the reaction
chamber; the lamps were turned off during the registration of
the spectra.
suite of programs. The standard geometry optimisation con-
sisted of an (unrestricted) Hartree–Fock calculation followed
by a second order Møller–Plesset correlation energy correc-
tion, MP2, in which the inner shells were excluded from the
correlation calculation (Frozen Core, FC). The medium-size
basis set cc-pVDZ, which includes polarisation functions,
was utilised to probe the potential surface and to get reason-
able geometries for the most relevant minima and transition
states. Subsequent geometry optimisation and calculation of
harmonic frequencies was carried out using the augmented
cc-pVDZ basis set, which includes diffuse basis functions,
and in the cases of adducts or complexes the basis set superpo-
sition error (BSSE) was assessed by the counterpoise (CP) cor-
6
6
N
2
O
5
was synthesised by mixing a gas stream of NO
ꢃ
2
with
excess O , and trapping the product at ꢁ78 C. N O was pur-
3
2
5
ified by vacuum distillation prior to its use. Methyl nitrite, 2-
propyl-nitrite and 2-propyl-nitrite-1,1,1,3,3,3-d were prepared
from the alcohols following the procedure reported for butyl
6
2
6
30
nitrite; 2-propanol-1,1,1,3,3,3-d
procedures from acetone-d
ether.
6
was prepared by standard
by reduction with LiAlH in dry
rection. The final geometry optimisation was carried out at
the MP2 level using the aug-cc-pVTZ basis set, and the single
point energies were obtained by subsequent coupled cluster
calculations, including singles, doubles, and approximate triple
excitations, CCSD(T). For open-shell molecular systems the
UHF SCF wave functions can be contaminated by higher
states. In some cases such spin contamination may significantly
alter the energy. We have, however, consequently neglected
this and cite the EUMP2 and ECCSD(T) energies in the text.
For the stable molecules, for which it was possible to calcu-
late the harmonic vibrational frequencies with both aug-cc-
pVDZ and aug-cc-pVTZ, the two sets of frequencies were
found to be virtually identical. In all cases the vibrational fre-
quencies (and zero-point energies, EZPE) were therefore esti-
mated from the MP2/aug-cc-pVDZ calculations. In general,
the harmonic C–H and O–H stretching frequencies are calcu-
lated to be 5% too high in this approximation when compared
to the experimental data. As these vibrations have the domi-
nating contribution to the zero-point energy we have conse-
quently scaled the vibrational frequencies by an empirical
factor of 0.95. The effect of this scaling amounts, at most, to
6
4
All organics employed had a stated purity of 98% or better
and were used without further purification: formaldehyde (para-
2
formaldehyde, NMD), formaldehyde-d (99.8 atom% D, CDN
1
3
13
Isotopes), C formaldehyde (99 atom% C, ISOTEC Inc.),
acetaldehyde (Fluka, puriss); acetaldehyde-1-d (98 atom%
D, CDN Isotopes), 2,2,2-acetaldehyde-d (98.8 atom% D,
1
3
CDN Isotopes); acetaldehyde-d4 (99.6 atom% D, CDN
Isotopes) and cyclohexane (Merck, Uvasol). Typical volume
fractions were 1–3 ppm for the aldehydes and 5–20 ppm for
3 6 2 5
CH ONO, 2PN, 2PN-d , N O and cyclohexane. The chemi-
cal and photochemical stability of the aldehydes in the reaction
chamber was investigated separately; the compounds showed
lifetimes in the order of days, and wall-loss and direct photo-
lysis could thus be neglected in the data analyses.
The deuterated acetaldehydes showed a strong tendency to
form trimers in the liquid phase (acid catalysed). The trimer–
monomer equilibrium is strongly shifted towards the mono-
meric form in the vapour phase, but it takes hours for a
2
7
ꢁ1
complete conversion from trimer to monomer to take place.
2 kJ mol in the enthalpies of reaction.
Before each series of relative rate experiments a blind test with
only the oxidant precursor was carried out to ensure that for-
maldehyde or acetaldehyde were not produced by oxidation of
impurities either present in the synthetic air or adsorbed on the
cell walls.
The kinetic studies were carried out by the relative rate
method, that is by considering two simultaneous bimolecular
reactions with the rate coefficients kA and kB :
In addition to geometry optimisations of minima and saddle
points, the potential energy surfaces were investigated further
by performing relaxed potential energy scans from these sta-
tionary points to validate that the determined transition states
connected the correct reactant and product configurations.
Some of the systems were too large to allow CCSD(T)/aug-
cc-pVTZ or even CCSD(T)/aug-cc-pVDZ calculations to be
carried out with our current hardware and software resources.
For these systems the spectator part of the molecule was
described by the cc-pVDZ basis, while the active part of the
system was described by the aug-cc-pVDZ basis. We are aware
that the cc-pVDZ basis set, also when augmented with diffuse
functions, is too small to capture more than half of the electron
correlation energy, and that CCSD(T) calculations with this
kA
A þ Radical ꢀꢀꢀ! Products
kB
B þ Radical ꢀꢀꢀ! Products
Assuming that there are no other loss processes than the
two above bimolecular reactions, then the following relation
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805
1791

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basis set are considered as ‘‘unbalanced’’. However, keeping
the current hardware and software limitations in mind, this
method probably gives the best overall estimate of the differ-
ences between the energy levels of the reacting systems. Addi-
tional calculations of the thermochemistry were carried out
formaldehyde mainly through H-abstraction, and (ii) as the
amount of formic acid formed from the degradation of ca. 1
ppm of HCHO is at most 10 ppb, less than 1% of the reaction
3
is through the addition route (Ia). Thus, for NO the product
distribution is in perfect agreement with the reaction enthal-
pies. For OH the present results agree with previous studies
3
1
employing the Gaussian-2 (G2) theory, and the complete
basis set model chemisty, CBS-QB3.
3
2
17,34,35
of this reaction, and the ‘‘lack’’ of HCOOH formation
must be due to a kinetic limitation.
The formation of formic acid in some of the experiments can
be explained by the reaction due to the HO
tioned above, the initial step in the oxidation of formaldehyde
will eventually lead to the formation of HO radicals
2
radical. As men-
Results and discussion
Product study
2
M
ðHCO þ O2 ! CO þ HO2; H þ O2 ꢀꢀꢀ! HO2Þ, which may
A priori, the HCHO reactions with NO and OH radicals may
3
take three routes:
enter a reversible equilibrium (II) to form a formaldehyde
adduct.
The most important occurring in our reactor introduces an
additional route for the loss of formaldehyde and the details
are given below:
3
6–41
This adduct can react irreversibly in several ways.
X þ HCHO ! H þ XCHO
ðIaÞ
ðIbÞ
ðIcÞ
!
!
HX þ CHO
36,38
HX þ H þ CO
_
_
_
HCHO þ HO2 0 HOO CH2 O0 OO CH2 OH
ðIIÞ
ðIIIaÞ
ðIIIbÞ
Under atmospheric conditions reactions (Ib) and (Ic) will
immediately be followed by reaction of H or HCO with O2
leading to CO and HO , and both routes therefore result in
_
HO-CH2-OO þ HO2 ! HO-CH2-OOH þ O2
! HCOOH þ H2O þ O2
2
the same final products. Route (Ia) may be termed as an addi-
tion–elimination reaction (or for short: addition reaction),
while routes (Ib) and (Ic) are H-abstraction reactions. The
_
2
HO-CH2-OO ! HO-CH2-OH þ HCOOH þ O2
ðIVaÞ
ðIVbÞ
! 2 HO-CH - O_ þ O
2
2
3
3
reaction enthalpies derived from enthalpies of formation
and from quantum chemical calculations (see later) are sum-
marised in Table 1. For the NO reaction, the addition route
Ia) is endothermic; it is exothermic for OH but, at room tem-
_
_
HO CH2 O þ O2 ! HCOOH þ HO2
ðVÞ
3
Of the oxidation products formed in reactions (III) to (V) only
formic acid is thermally stable and it can thus be used as an
(
perature, it occurs significantly more slowly than the abstrac-
tion route because of a kinetic limitation (see below).
The observed products of the OH radical reaction with
indicator of the additional formaldehyde loss due to HO
DO2 .
2
/
3
In principle, the NO and OH radicals may react in similar
2
HCHO were CO and H O. In two of the experiments, where
ways with acetaldehyde as with formaldehyde and, in addition,
also by hydrogen abstraction from the methyl group. The
following five routes may be envisaged:
the starting concentrations of HCHO and 2PN were ca. 5
and 10 ppm, respectively, traces of formic acid, HCOOH, were
observed (<0.1 ppm after the reaction of ca. 1 ppm HCHO). In
all the other experiments the amount of formic acid formed
was below our detection limit in this reaction mixture (ca. 10
X þ CH3CHO ! CH3CXO þ H
ðVIaÞ
ðVIbÞ
ðVIcÞ
ðVIdÞ
ðVIeÞ
!
!
CH3 þ XCHO
CH3CO þ HX
ppb). The only products identified from the NO
tion with HCHO were CO and HNO . As in the OH experi-
3
radical reac-
3
ments small amounts of HCOOH (0.06–0.1 ppm) were found
when the initial concentration of HCHO was more than ca.
! CH3 þ HX þ CO
!
CH2CHO þ HX
4
ppm but, again, with lower starting concentrations of HCHO
Routes (VIa) and (VIb) occur via the decomposition of the
adduct CH CXHO and they will be termed as addition reac-
tions, while the other three routes give rise to H-abstraction
reactions. As seen from the experimental reaction enthalpies
in Table 1, all five routes are exothermic in the case of OH
radical reaction.
the amount of formic acid formed was below the detection
limit. The reaction of OH with formic acid is an order of mag-
3
3
3
nitude slower than its reaction with formaldehyde. There is
no information available on the NO reaction with formic
acid, but in all likelihood the situation is probably the
same. We therefore conclude that: (i) OH and NO react with
3
3
ꢁ1
Table 1 Enthalpies of reaction at 298 K (kJ mol ) for the reactions of NO
3
and OH radicals with formaldehyde and acetaldehyde
OH
NO
3
b
b
Calc.
Calc.
a
a
Reaction
Exp.
DZ
TZ
G2
CBS-QB3 Exp.
DZ
TZ
G2
CBS-QB3
HCHO + X ! HC(O)X + H
CHO + HX
CO + H + HX
(Ia)
(Ib)
(Ic)
15.4
n.c. ꢁ4.8
19.0
ꢁ91.5 ꢀ 2.2 ꢁ74.7 ꢁ82.1
ꢁ129.4 ꢀ 2.1 ꢁ118.4 ꢁ122.7 ꢁ127.4 ꢁ125.8
ꢁ65.1 ꢀ 2.1 ꢁ64.3 ꢁ58.6 ꢁ68.5 ꢁ60.6
ꢁ91.6 ꢁ89.3
ꢁ57.1 ꢀ 1.4 ꢁ60.9 ꢁ65.3 ꢁ74.1 ꢁ51.2
7.3 ꢀ 1.4 ꢁ6.8
ꢁ1.2 ꢁ15.2
n.c. n.c.
n.c. ꢁ21.1
14.0
35.7
3.1
CH
CH
CH
CH
CH
3
3
3
3
2
CHO + X ! CH
3
C(O)X + H (VIa)
(VIb)
n.c.
0.0
ꢁ87.6 ꢀ 2.2 ꢁ72.3
n.c. ꢁ89.3 ꢁ87.3
+ HC(O)X
ꢁ105.2 ꢀ 2.2 ꢁ90.0 ꢁ98.9 ꢁ107.9 ꢁ105.2
ꢁ125.3 ꢀ 2.5 ꢁ113.7 ꢁ117.2 ꢁ123.7 ꢁ122.9
CO + HX
+ CO + HX
CHO + HX
(VIc) ꢁ53.0 ꢀ 1.9 ꢁ56.3 ꢁ61.0 ꢁ70.4 ꢁ48.3
(VId) ꢁ7.1 ꢀ 1.5 ꢁ22.2 ꢁ18.0 ꢁ31.5 ꢁ1.9
(VIe) ꢁ30.4 ꢀ 9.3 ꢁ21.7 ꢁ25.4 ꢁ41.6 ꢁ25.2
ꢁ79.5 ꢀ 2.2 ꢁ78.5 ꢁ74.2
ꢁ102.7 ꢀ 9.4 ꢁ79.2 ꢁ81.7
ꢁ84.8 ꢁ76.4
ꢁ94.9 ꢁ99.8
a
b
Derived from the available experimental enthalpies of formation with error limits listed in ref. 33. Results from ab initio calculations. DZ:
CCSD(T)/aug-cc-pVDZ//MP2(FC)/aug-cc-pVDZ; TZ: CCSD(T)/aug-cc-pVTZ//MP2(FC)/aug-cc-pVTZ. G2: Gaussian 2 model chemistry,
see ref. 31. CBS-QB3: complete basis set extrapolation model chemistry, see ref. 32.
1
792
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805

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which are all exothermic. The results from ab initio calcula-
tions (see below) suggest that the addition route is endothermic
or at most thermoneutral. We have recently presented our
3
results from product studies of the NO reaction with acetalde-
hyde, and concluded that more than 95% of the reaction pro-
ceeds through the H-abstraction route (VIc), that is through
abstraction of the aldehydic hydrogen.
1
5
Kinetics
2 2
As mentioned, HO and/or DO are formed during the reac-
tions. This can give rise to a misinterpretation of the kinetic
data because the kinetic isotope effect in the hydroperoxy radi-
cal addition reaction with formaldehyde is expected to be
small. In two of the ten in total OH reaction experiments with
HCHO/DCDO mixtures, traces of formic acid were observed
(<0.1 ppm). The derived kinetic isotope effect in these experi-
Fig. 1 Volume fraction profiles for HCHO and CO as a function of
the CH CHO volume fraction during reaction with OH radicals. Initial
conditions: CH CHO, 5 ppm; 2PN, 2 ppm.
ments was also slightly lower than in the other experiments.
These data sets were therefore not included in the final analy-
3
3
sis. Besides the addition reactions to formaldehyde, DO
2
will
also form OD radicals (DO + NO ! OD + NO ). Model cal-
2
2
culations (see below) were therefore carried out to ensure that
the initial reactant concentrations were such that the contribu-
In the product studies of the OH radical reaction with
CH CHO, 2PN-d was used as the OH precursor. We
observed the formation of HCHO and CO in small amounts,
ca. 10% of the total reacted acetaldehyde, while peroxyacetyl-
nitrate (PAN) apparently was the only other product. Fig. 1
shows the concentration profiles of HCHO and CO vs. reacted
CH CHO. It can be seen that the profiles are typical of the
3
primary products at the start of the experiment (note that
ca. 25 ppb HCHO was present from the start), but that after
3
6
2 2
tions from the HO /DO addition reactions and the subse-
quent OD abstraction reactions contributed less than 2% of
the total degradation of HCHO and DCDO.
In the NO
formed may also react with NO
3 2 2
reaction experiments the HO /DO radicals
3
to give OH/OD radicals
(
faster with formaldehyde than NO
HO + NO ! OH + NO + O ). The OH radical reacts much
3
2
3
2
2
does, and it can therefore
give rise to erroneous relative rates. Again, model calculations
were carried out to select suitable initial reactant concentra-
tions to avoid such erroneous rates. In addition, cyclohexane
was sometimes added to the reaction mixture in excess to
monitor and quench the OH radicals formed in the NO3
experiments. However, it was actually easier and more
convenient to work with low reactant concentrations (see
below) than it was to analyse reaction mixtures with a high
cyclohexane content.
The program package FACSIMILE was employed to
simulate the complex set of reactions and the kinetics of the
reactor system. In total, 73 thermal and 7 photolytic reactions
were considered in the simulations of the experiments of for-
ca. 0.7 ppm of CH
formed as secondary products. Unfortunately, the experimen-
tal set-up did not allow a quantitative determination of CO
during this study, and we are therefore not able to distinguish
between the products formed through routes (VId) and (VIe),
with those originating from the acetyl radical in channel (VIc).
There were no traces of formic acid (<20 ppb) or acetic acid
3
CHO had reacted, CO and HCHO are also
2
(
<25 ppb) in any of the experiments, which suggests upper
limits to routes (VIa) and (VIb) of 2.5 and 2%, respectively.
The major reaction route therefore appears to be (VIc)
4
6
where the formation of acetyl radicals was followed by O
addition to form CH C(O)O which then enters an equilibrium
with NO to form PAN. Tyndall et al. identified ketene as a
minor product from the CH CO + O reaction. However, the
2
3
2
4
2
2
3
maldehyde with OH and NO radicals. The model is available
3
2
as electronic supplementary information. y The relevant ther-
reported yield of ketene is very small. Furthermore, it is
decreasing with increasing pressure (1% at 1 torr, 0.3% at 20
torr). The methyl radicals formed in (VIb) or (VId) will rapidly
mal reactions and their rate coefficients were selected from
the NIST database or taken from the evaluations of
4
7
3
3,48
Atkinson et al.
2 2
react with O leading to HO radicals and then eventually
The model calculations show that the amount of formalde-
hyde reacting via equilibrium (II) is almost negligible when
the initial concentrations of the reactants in the experiments
are below 5–6 ppm, in total, for formaldehyde, 5–6 ppm
˙
to HCHO. Finally, the formyl methyl radical, CH CH=O,
formed in (VIe) is in resonance with the ethenyloxy radical,
2
4
3
_
CH =CH–O, which, however, is energetically unfavourable.
2
2 2
A kinetic and product study of the CH CHO + O reaction
2
2 5 3
PN, and 10–20 ppm N O . Moreover, in the NO experi-
concludes with a ca. 15% glyoxal yield while the remaining
4
4
ments, the contribution to formaldehyde degradation from
the reaction with the OH radicals was less than 1% of the
carbon ends up in HCHO or CO. In the OH experiments the
product spectra show no indications of the characteristic bands
ꢁ
1
NO
3
initiated degradation.
around 2835 and 1732 cm from glyoxal (CHO–CHO). How-
ever, glyoxal reacts quite quickly with OH, k
Two different OH sources were used in the OH/formalde-
hyde studies: 2PN and 2PN-d
¼
OH+CHO–CHO
ꢁ11
3
cm molecule
ꢁ1 ꢁ1 45
6
6
. Photolysis of 2PN-d by
1
.1 ꢅ 10
s
, resulting primarily in CO
formation, and it could very well evade detection.
370 nm radiation leads to the formation of OH radicals in the
following sequence:
In summary, the experiments indicate that route (VIc) is the
dominant pathway at room temperature for the OH radical
reaction with acetaldehyde. The observed product distribution
indicates upper limits to the addition route of 2.5% through
_
CD3CHðONOÞCD3 þ hn ! CD3CHðOÞCD3 þ NO ðVIIÞ
_
_
CD3CHðOÞCD3 þ O2 ! CD3CðOÞCD3 þ HO2
ðVIIIÞ
ðIXÞ
(
VIa) and 2% through (VIb). Considering the lack of evidence
_
_
HO2 þ NO ! OH þ NO2
of the subsequent degradation of the acetyl radical, we assign
an upper limit of 10% in total to reaction through the two
other H-abstraction routes (VId) and (VIe).
Although the yield of reaction (VIII) is very close to 100% (see
below) any dissociation of the oxo radical into acetyl and CD3
radicals, or CH radicals in the case of 2PN, would contribute
For NO
3
0
298
there is only experimental data available to calcu-
3
late D H for the H-abstraction routes (VIc), (VId) and (VIe),
to the measured HCHO/DCDO ratio during the reaction. The
r
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1793

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13
Fig. 3 Decays of HCHO, H CHO and DCDO during reaction with
NO radicals. Different symbols indicate independent experiments. (A)
plot of ln{[HCHO] /[HCHO] } vs. ln{[DCDO] /[DCDO] } 44 points
from 3 experiments were fitted to krel ¼ 2.97 ꢀ 0.14; (B) plot of
Fig. 2 Infrared spectra of a reaction mixture containing HCHO,
DCDO and 2PN recorded after 1 min., 10 min., and 20 min. of irradia-
tion by TDL-08 fluorescence lamps.
3
0
t
0
t
13
13
0 t 0 t
ln{[HCHO] /[HCHO] } vs. ln{[H CHO] /[H CHO] } 20 points from
4
experiments were fitted to krel ¼ 0.97 ꢀ 0.02. The uncertainties
reactivity of HCHO and DCDO towards OH is orders of mag-
49
ascribed to each data point are based on an estimated uncertainty in
the subtraction procedure amounting to 2% of the initial concentration
of the compound in question.
3
nitude higher than that of acetone and deutero acetone,
3
and the reactive degradation of the latter two compounds in
the chamber should therefore not influence the measurements
severely. To ensure that the choice of the OH precursor did
not influence the experimental results for formaldehyde we car-
ried out experiments with four different isotope combinations:
HCHO/DCDO using 2PN as the OH precursor, HCHO/
ꢁ
at 2906 cm , and the
2
1
a growing n
Q-branch of the n20 (b
is on the shoulder of the decreasing 2PN band at 2987 cm
The kinetic results for formaldehyde are shown in Fig. 3 and
4, for the NO and OH studies, respectively, while the analo-
gous data from the acetaldehyde studies, the spectral ranges
and the compounds included in the subtraction procedures,
and a full report of the statistical analyses are available as elec-
tronic supplementary information.y The derived relative rates,
with 3s statistical errors, are given in Tables 2 and 3 together
+ n
(B
) band of NO
1
3
1
ꢁ1
2
) band of acetone at 2971 cm which
ꢁ
1
.
1
3
6 6
DCDO using 2PN-d , HCHO/H CHO using 2PN-d , and
1
3
H CHO/DCDO using 2PN. There was no systematic differ-
ences among the results from the HCHO/DCDO studies with
3
2
6
PN or 2PN-d , indicating that reactivity of the propane-
2
-oxo radical is close to 100% via route reaction (VIII). The
results also show that the reactivity of OH is slower with its
precursors, 2PN and 2PN-d , than with formaldehyde.
6
1
5,18
As an example of the experimental data obtained in this
work Fig. 2 shows parts of the FTIR spectra from a study
of the OH reaction with a HCHO/DCDO mixture using
with previously published data of kinetic isotope effects.
Forcing the regression lines through the origin has little or
no influence on the derived slopes—the changes in the slopes
being smaller than their estimated statistical uncertainties.
Morris and Niki measured the reactions of OH with
HCHO and HCDO using a discharge-flow time-of-flight mass
spectrometric set-up. They did not measure any significant dif-
2
PN as the OH precursor. The figure illustrates quite clearly
the different reactivity of HCHO and DCDO towards OH
radicals. The HCHO n (a ) parallel band at 2780 and the n
b1) perpendicular band at 2874 cm are reduced in intensity
by ca. 50% during the photolysis, while at the same time the
1
6
1
1
4
ꢁ
1
(
1
7
ference in reactivity of the two isotopomers. Niki et al. also
measured the OH reaction with H CHO relative to ethene.
ꢁ1
13
DCDO n (a ) parallel band at 2056 cm is only reduced by
1
1
ca. 30%. The n
cm is difficult to distinguish as it is overlapped by the grow-
4
(b
1
) perpendicular band of DCDO at 2160
Unfortunately, their result does not give accurate information
on the kinetic isotope effect. The present data for the OH-
formaldehyde system are, as mentioned, the results from four
different isotope combinations, and the data show internal
consistency.
ꢁ1
ꢁ
1
ing CO band around 2143 cm . One also notices that the
ꢁ
1
parallel band at ca. 2224 cm due to the n mode in N O is
3
2
present as trace component in the purified air. One sees also
1
794 Phys. Chem. Chem. Phys., 2003, 5, 1790–1805

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fluorescence experiments. As can be seen from Table 3, their
data are systematically lower than the present results.
Quantum chemical study–electronic structure calculations
Initially, calculations on the OH/HCHO reaction system were
done at the B3LYP/cc-pVDZ level, and some of these results
2
2
have been presented elsewhere. However, the DFT calcula-
tions with the B3LYP functional gave no barrier to the reac-
tion NO
3
+ HCHO ! HNO
3
+ CHO. A similar result was
2
7
previously experienced for the Cl + HCHO reaction, and
comparing with both the experimental and the MP2 results,
this is clearly not a correct description of the chemical reaction.
The electronic structure of the NO
lenge to both experimentalists and theoreticians. It is not pos-
sible to calculate the energy of the NO radical correctly at the
3
radical presents a chal-
3
MP2 level of theory due to symmetry breaking—nor is it pos-
sible at present to calculate its electronic structure correctly
using any other standard size extensive method also applicable
5
0
to larger systems. It should also be noted that the calculated
MP2 harmonic frequencies of vibration for NO deviate sub-
3
5
1
stantially from the experimental values. We have therefore
used the experimental frequencies of vibration for NO3 in
the calculation of the reaction enthalpies.
Table 1 summarises the experimental and calculated enthal-
pies of reaction for reactions (I) and (VI). Table 1 demon-
strates an impressive agreement between the experimental
data and the results of the CBS-QB3 calculations. The G2
results are also in excellent agreement with the experimental
data for the OH reactions. However, for the NO
the calculated reaction enthalpies are in general ca. 20 kJ
3
reactions
ꢁ
1
mol too exothermic. As mentioned above, this is linked to
the difficulties of describing the electronic structure of the
3
NO radical correctly. There appears to be a systematic differ-
ence between the experimental and theoretical results from the
CCSD(T)/aug-cc-pVXZ calculations. The only deviation
being the OH + CH
is due mainly to spin contamination in the UHF wave function
of the latter radical. For the NO reactions, the theoretical
3
2 2
CHO ! H O + CH CHO reaction, which
3
ꢁ1
reaction enthalpies are generally ca. 10 kJ mol more exother-
mic than the experimental values. Again, this is linked to the
3
difficulties in describing the NO radical.
OH + HCHO. As Table 1 shows, the three reaction routes
are exothermic. Fig. 5 shows the relevant energy levels,
ECCSD(T) + EZPE , of the system calculated at the CCSD(T)/
aug-cc-pVDZ//MP2/aug-cc-pVDZ level. For the sake of
brevity, we have not included the calculated energies of the
reactants, the intermediate stationary points of the potential
energy surface, and the products, but these results are available
as electronic supplementary information.y Effort was concen-
trated on the reaction pathway (Ib), OH + HCHO ! H
2
O +
HCO. To be discussed later, both the OH and the NO radicals
3
form pre- and post-reaction adducts with the substrate, and
Fig. 6 shows the OH–HCHO structures of the these stationary
points together with that of the transition state. The figure also
includes the more interesting bond distances and the imaginary
frequency corresponding to the negative eigenvalue of the Hes-
sian matrix. The energies, resulting from different levels of cal-
culation, for the separated reactants, adducts, transition states,
and separated products in pathway (Ib) are given in Table 4
together with results from CCSD(T)/6-311++G** calcula-
1
3
Fig. 4 Decays of HCHO, H CHO and DCDO during reaction with
OH radicals. Different symbols indicate independent experiments. (A)
Plot of ln{[HCHO]
0 t 0 t
/[HCHO] } vs.ln{[DCDO] /[DCDO] } 45 points
from 8 experiments were fitted to krel ¼ 1.61 ꢀ 0.09; (B) plot of
1
3
13
ln{[H CHO]
0 t 0 t
/[H CHO] } vs. ln{[DCDO] /[DCDO] } 14 points
from 2 experiments were fitted to krel ¼ 1.64 ꢀ 0.12; (C) plot of
13
13
0 t 0 t
ln{[HCHO] /[HCHO] } vs. ln{[H CHO] /[H CHO] } 20 points from
2
experiments were fitted to krel ¼ 0.97 ꢀ 0.11. The uncertainties
ascribed to each data point are based on an estimated uncertainty in
the subtraction procedure amounting to 2% of the initial concentration
of the compound in question.
2
3
30
tions previously published. The counterpoise correction
to the energies of the pre- and post-reaction adducts was ca.
ꢁ
1
3 kJ mol regardless of the basis set. That is, the CP cor-
ꢁ
rected energy of the pre-reaction adduct, including the zero
ꢁ
1
The results from the acetaldehyde studies show clear pri-
mary and secondary isotope effects for both the NO and
OH reactions. Taylor et al. derived kinetic isotope effects at
98, 400, 600, and 750 K from laser-photolysis laser-induced-
point energy, is ca. ꢁ11 kJ mol relative to that of the reac-
tants. Structures calculated at the MP2-level with the different
basis sets were practically identical and there were only slight
changes in the relative energies of the stationary points of
3
1
8
2
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805
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Table 2 Experimental and calculated kinetic isotope effects for the reactions of NO
represent 3s from the statistical analyses
3
and OH radicals with formaldehydes at 298 K. Quoted errors
1
3
13
HCHO/H CHO
HCHO/DCDO
Exp.
H
CHO/DCDO
HCHO/DCHO
Exp.
a
k
A
/k
B
Calc.
Exp.
Calc.
1.93
Exp.
Calc.
Calc.
1.39
NO
OH
3
2.97 ꢀ 0.14
1.62 ꢀ 0.08
b
See text. From ref. 16.
5.62
1.93
0.97 ꢀ 0.02
0.97 ꢀ 0.11
1.07
1.00
b
1.64 ꢀ 0.12
ꢂ1
a
the OH/HCHO reaction system. However, this is probably
partly due to the cancellation of errors. We note that the struc-
tures obtained with G2 and CBS-QB3 model chemistries differ
considerably in the pivotal distances from the ones obtained by
the MP2 method. Further, the imaginary frequency at the
transition state, obtained by the CBS-QB3 model chemistries
In the reaction route (VIc), OH + CH
CH CO, the OH radicals form pre- and post-reaction adducts
3
CHO ! H
2
O +
3
with the substrate that are similar to the ones formed in the
HCHO reaction and Fig. 8 shows the structures of the sta-
tionary points of the potential energy surface. The energies
resulting from different levels of calculation, for the separated
reactants, adducts, transition states, and separated products
in pathway (VIc) are given in Table 4. The energy of the
ꢁ
1
is only 183 cm compared to the MP2 value of 1532.
As can be seen from Fig. 5 and Table 4, the barrier to Hald
abstraction is calculated to be negative relative to the reactants
-
pre-reaction adduct, ECCSD(T) + EZPE ꢁ ECP , is ca. ꢁ15 kJ
ꢁ1
ꢁ1
energy, ECCSD(T) + EZPE ¼ ꢁ5.8 kJ mol , with the aug-cc-
mol relative to that of the reactants. The OH/CH CHO
3
ꢁ
1
pVDZ basis set and ꢁ5.9 kJ mol with the aug-cc-pVTZ basis
system is too large to allow CCSD(T) calculations with the
aug-cc-pVTZ basis set. To a certain extent we therefore have
to rely on the results from the OH/HCHO system, which
indicate only minor differences between the relative energies
obtained with the two basis sets. As can be seen from Table 4,
the relative MP2 energies are almost identical with the two
basis sets. The same is true for the relative CCSD(T) ener-
gies in the cases where they can be calculated, and this gives
us some confidence in the relative energies of the OH/
set. Also the CBS-QB3 model chemistry predicts a negative
ꢁ
1
barrier of ꢁ3.5 kJ mol . The similar CCSD(T) calculation
with the 6-311++G** basis set, however, gave a small positive
barrier of 0.5 kJ mol
ꢁ
1 23
.
Previous calculations of the barrier
to Hald-abstraction on various levels of approximations pre-
ꢁ1 19–21
,
dicted barriers in the region 5–24 kJ mol
which is
clearly inconsistent with the experimental results showing a
negative activation energy. As to the relative importance of
two routes in the Hald-abstraction reaction, route (Ib) con-
forms with the minimum energy path leading from the transi-
3
CH CHO system calculated with the smaller basis set. The
calculated energies of the reactants, the intermediate station-
ary points, and of the products are available as electronic
supplementary information.y
tion state via an adduct to the products, HCO + H
any barrier, whereas route (Ic) involves a barrier of ca. 70 kJ
2
O, without
ꢁ1
mol to the elimination of the hydrogen atom, Fig. 5. Unfor-
tunately, the experimental data alone does not allow us to
quantify the branching ratio between routes (Ib) and (Ic).
The barrier to the addition of OH to the carbonyl carbon
The barrier to Hald-abstraction is calculated to be negative
relative to the reactants energy as in formaldehyde. The value
ꢁ
1
obtained with the aug-cc-pVDZ basis, is ꢁ14.2 kJ mol
23
,
which is ca. 8 kJ mol lower than in formaldehyde—the same
ꢁ
1
ꢁ
1
was calculated to be 27.8 kJ mol using the aug-cc-pVDZ
basis set. The structure of the transition state (and the imagin-
ary frequency) is included in Fig. 6. Roughly half of the barrier
to the reaction is due to the increased zero point energy of the
transition state. Previous studies report barriers from ca. 34 to
change as obtained with the 6-311++G** basis. We notice
that the CBS-QB3 model chemistry predicts a barrier of
ꢁ1
ꢁ15.5 kJ mol . As in the OH/HCHO system, the minimum
energy path from the transition state to Hald-abstraction is
3 2
via a water adduct to the reactants, CH CO + H O, without
ꢁ
1
20,23
4
3 kJ mol depending on the method of calculation,
while
the CBS-QB3 model chemistry gives a value of only 13.3 kJ
any barrier. The alternative route (VId) involves a barrier of
ꢁ
1
ca. 70 kJ mol for the formation of CH
is in excellent agreement with the experimental value of ca. 65
3 2
+ CO + H O, which
ꢁ1
mol to this barrier. In any case, the barrier to the OH addi-
tion reaction with formaldehyde is so high that pathway (Ia) to
the formation of HCOOH has little importance at atmospheric
conditions (see below).
ꢁ
1 52
kJ mol
.
On the one hand, the transition state with respect
ꢁ
1
to the C–C bond breakage is ca. 50 kJ mol below the energy
of the reactants. Alternatively, it is probable that the excess
reaction energy is channelled into the loose bond to water than
into C–C bond breakage. That is, from the theoretical results
we expect route (VIc) to dominate over (VId). A recent study
3
OH + CH CHO. All five routes are exothermic, and the
relevant energy diagram, resulting from CCSD(T)/aug-cc-
pVDZ//MP2/aug-cc-pVDZ calculations, is shown in Fig. 7.
5
3
by Jagiella et al. concludes that the decomposition of
3
Table 3 Experimental and calculated kinetic isotope effects for the reactions of NO and OH radicals with acetaldehydes at 298 K. Quoted errors
represent 3s from the statistical analyses
CH
3
CHO/CH
3
CDO
CH CHO/CD
3
3
CHO
CH
3
CHO/CD
3
CDO
a
k /k
A B
Exp.
Calc.
Exp.
Calc.
Exp.
Calc.
b
NO
OH
3
2.39 ꢀ 0.07
1.42 ꢀ 0.10
4.78
1.40–1.48
1.19 ꢀ 0.11
1.13 ꢀ 0.04
1.41
1.05–1.17
2.51 ꢀ 0.09
5.73
1.50–1.68
d
d
d
1.65 ꢀ 0.08
c
c
c
c
c
1
1
1
0
.31 (298 K)
.05 (400 K)
.01 (600 K)
.98 (750 K)
1.21 (298 K)
1.19 (400 K)
1.23 (600 K)
1.17 (750 K)
c
c
c
a
b
See text. From ref. 15. From ref. 18. In the range of 300–1000 K.
c
d
1
796
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805

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and route (VIe) may therefore be of some importance under
atmospheric conditions (see below).
Using the aug-cc-pVDZ basis set the barrier of OH addition
to the carbonyl carbon, being the first step in routes (VIa) and
(
VIb), is calculated to have the same magnitude as in formal-
ꢁ
1
dehyde, 30.9 kJ mol ; the transition state structure is included
in Fig. 8. The addition pathway is therefore of little impor-
tance under atmospheric conditions, see later.
NO + HCHO. There is only one exothermic reaction
3
among the possible pathways. Like the OH radical, NO also
3
forms a weak pre-reaction adduct with HCHO and HNO a
3
weak post-reaction adduct with HCO. These are shown in
Fig. 9 together with the structure of the transition state to
H
3
ald-abstraction. It is not feasible to explore the NO /HCHO
Fig. 5 Energy levels, ECCSD(T) + EZPE , of the OH + HCHO reaction
system calculated at the CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-
pVDZ level.
reaction system by CCSD(T) calculations employing the larger
aug-cc-pVTZ basis set. As Table 5 shows, the relative energies
of the adducts and of the transition state in route (Ib) are over-
estimated. For example, the barrier to Hald-abstraction is
calculated to be 26.2 kJ mol with the aug-cc-pVDZ basis.
Note that the additional correlation energy captured by the
CCSD(T) calculations lowers the transition state energy from
ca. 120 to ca. 30 kJ mol . Obviously, a larger basis set is
required to obtain a more correct description of the system.
However, systems larger than NO /HCHO cannot even be cal-
3
culated at the CCSD(T) employing the aug-cc-pVDZ basis set.
ꢁ
1
CH
However, they produced the acetyl radicals by reaction of
CH CHO with Br atoms, and the reaction CH
CHO + Br !
CH + CO + HBr is actually endothermic.
Fig. 7 shows that the minimum energy path to Hmethyl
abstraction is also via pre- and post-reaction adducts. The bar-
3
CO at 298 K and 1 bar of synthetic air is essentially zero.
3
3
2
7
ꢁ1
3
-
ꢁ
1
rier to Hmethyl-abstraction is calculated as only 12.1 kJ mol
using the aug-cc-pVDZ basis set; the transition state structure
is included in Fig. 8. The CBS-QB3 model chemistry suggests
that the barrier is 7.1 kJ mol . In any case, the calculations
indicate that the barrier to Hmethyl-abstraction is not very high
We therefore decided to describe the reacting systems by an
active part and a spectator part. In this way we hoped to have
a chance of observing the system trends. In the transition state
of the NO /HCHO system the central N atom in NO and the
ꢁ
1
3
3
anchor O atom in HCHO can be considered as spectator
atoms. That is, they are described by the smaller cc-pVDZ
basis set (without diffuse functions), while the other atoms
are described by the aug-cc-pVDZ basis. The total number
of basis functions is thereby reduced by ca. 10% (from 156
to 138). As Table 5 shows, there is little difference between
the results obtained with the aug-cc-pVDZ and the ‘‘active-
spectator’’ basis sets. In view of the apparent insufficiency of
the basis set (limited by hardware/software) and the inherent
problems related to the description of NO
be regarded as qualitative.
3
, the results should
NO
exothermic. The energy level diagram of the NO
reactions is therefore not as interesting as that of the OH +
CH CHO reactions, and we have concentrated the study to
the reaction pathway (VIc), NO + CH CHO ! HNO +
3
+ CH
3
CHO. Only the H-abstraction reactions are
3
+ CH CHO
3
3
3
3
3
3
CH CO, and to the transition state of pathway (VIe)—the
Hmethyl-abstraction. NO forms pre- and post-reaction adducts
3
with the substrate similar to the ones formed with HCHO;
only the transition state structure is, however, included in
Fig. 9. The energies, resulting from different levels of calcula-
tion, for the separated reactants, adducts, transition states,
minima and separated products in pathway (VIc) are found
in Table 5. The MP2 frequency calculations and the CCSD(T)
energy calculations were carried out with an active/spectator
basis set as introduced above. In the Hald-abstraction reaction
only the aldehydic carbon and hydrogen, and the oxygen
atoms in NO were described as ‘‘active’’, the remaining atoms
3
were described as ‘‘spectators’’ (without diffuse functions).
This reduces the number of basis functions by ca. 20% (from
1
out. As mentioned above for the NO /HCHO system, the
97 to 158), thereby enabling the calculations to be carried
3
numbers presented for NO
be regarded as qualitative. The barrier to H -abstraction is
calculated as ca. 12.7 kJ mol , which is ca. 9 kJ mol lower
than in HCHO and this represents about the same change in
barrier height as was calculated for the OH reactions.
3 3
/CH CHO reaction system should
Fig. 6 MP2/aug-cc-pVDZ structures of stationary points in the
ald
OH + HCHO ! HCO + H
2
O reaction: (A) the pre-reaction adduct,
ADD1; (B) the transition state of Hald-abstraction; (C) the post-reac-
tion adduct; (D) the transition state of the OH addition reaction,
ꢁ1
ꢁ1
OH + HCHO ! HCOOH + H
2
O.
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Table 4 Electronic and zero-point energies of stationary points in the reactions: OH + RCHO ! H
2
O + RCO (R ¼ H, CH
3
)
a
a
a
E
OH+RCHO
DEpre-adduct
/kJ mol
DETS
/kJ mol
DEpost-adduct
/kJ mol
DEH O+RCO
/kJ mol
2
ꢁ
1
ꢁ1
ꢁ1
ꢁ1
Level of computation
/Hartree
OH + HCHO
b
MP2(FC)/aug-cc-pVDZ
MP2(FC)/6-311++G**
MP2(FC)/aug-cc-pVTZ
CCSD(T)/6-311++G**//
MP2(FC)/6-311++G**
CCSD(T)/aug-cc-pVDZ//
MP2(FC)/aug-cc-pVDZ
CCSD(T)/aug-cc-pVTZ//
MP2(FC)/aug-cc-pVTZ
ꢁ189.784449 (0.035315)
ꢁ21.9 (7.8)
ꢁ19.7 (7.6)
ꢁ23.4
19.6 (ꢁ2.9)
24.3 (ꢁ3.7)
18.3
ꢁ152.7 (2.2)
ꢁ151.4 (3.7)
ꢁ155.9
ꢁ140.5 (ꢁ2.3)
ꢁ137.9 (ꢁ2.0)
ꢁ144.2 (ꢁ2.3)
ꢁ117.0
c
ꢁ189.821680 (0.035684)
ꢁ189.942748 (0.035477)
ꢁ189.863306
ꢁ21.2
4.2
ꢁ130.5
ꢁ189.829255
ꢁ189.988496
ꢁ22.0
ꢁ21.7
ꢁ2.9
ꢁ3.0
ꢁ130.0
ꢁ133.8
ꢁ117.4
ꢁ121.7
3
OH + CH CHO
MP2(FC)/aug-cc-pVDZ
MP2(FC)/6-311++G**
MP2(FC)/aug-cc-pVTZ
CCSD(T)/6-311++G**//
MP2(FC)/6-311++G**
CCSD(T)/aug-cc-pVDZ//
MP2(FC)/aug-cc-pVDZ
CCSD(T)/aug-cc-pVTZ//
MP2(FC)/aug-cc-pVTZ
ꢁ228.983891 (0.064142)
ꢁ229.029567 (0.064780)
ꢁ229.180668
ꢁ25.4 (7.4)
ꢁ23.7 (7.2)
ꢁ25.3
11.8 (ꢁ4.7)
16.8 (ꢁ4.7)
11.6
ꢁ153.6 (7.0)
ꢁ149.8 (7.0)
ꢁ157.1
ꢁ136.9 (1.3)
ꢁ135.0 (ꢁ3.6)
ꢁ141.4
ꢁ229.088705
ꢁ24.8
ꢁ2.4
ꢁ130.8
ꢁ116.6
ꢁ229.046817
ꢁ229.243995
ꢁ25.5
ꢁ9.5
ꢁ132.7
ꢁ116.4
ꢁ121.0
a
b
See Fig. 6 and 8. FC, frozen core. Zero-point energies, EZPE , in parentheses. 6-311++G** calculations from ref. 23.
c
The minimum energy path from the transition state to
Hald-abstraction is via a nitric acid adduct to the reactants,
CH CO + HNO , without any barrier. As with the OH/
CH CHO system the alternative route (VId) involves a barrier
likely that the excess energy of reaction will be directed into
the loose bond to nitric acid than into C–C bond breakage.
We note that no formation of CO and HCHO was observed
3
3
1
5
in the NO reaction with CH CHO.
3
3
3
ꢁ
1
of ca. 70 kJ mol to the formation of CH
The difference between the two systems is that the transition
3
+ CO + HNO
3
.
The barrier to Hmethyl-abstraction was initially calculated
with the cc-pVDZ basis set, and a value of ca. 15 kJ mol
ꢁ1
ꢁ1
15
state towards C–C bond breakage is now only ca. 10 kJ mol
below the energy of the reactants. It is therefore much more
higher than that of Hald-abstraction was recently reported.
We have now extended these calculations using the active/
spectator basis set description. In this case the methyl group
Fig. 8 MP2/aug-cc-pVDZ structures of the OH + CH
CH CO + H O reaction: (A) the pre-reaction adduct, ADD1; (B)
3
CHO !
3
2
the pre-reaction adduct, ADD2; (C) the transition state to Hald-abstrac-
tion; (D) the post-reaction adduct; (E) the transition state of the OH
Fig. 7 Energy levels, ECCSD(T) + EZPE , of the OH + CH
tion system calculated at the CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-
pVDZ level.
3
CHO reac-
addition reaction, OH + CH
transition state to the Hmethyl-abstraction reaction, OH + CH
CH CHO + H O.
3
CHO ! CH
3
COOH + H
2
O; (F) the
3
CHO !
2
2
1
798
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805

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summarised in Table 6, are not very different from those pre-
viously reported: the barrier to H
-abstraction is calcu-
methyl
ꢁ1
ꢁ1
lated as 29.3 kJ mol
barrier to Hald-abstraction.
As mentioned before, it is not possible to calculate the
energy of the NO radical correctly at the MP2 level. It is
therefore pointless to compare the saddle point energies (Table
, 6 and Fig. 9) to that of the reactants in this approximation.
However, as the NO radical engages in the hydrogen abstrac-
or 16.6 kJ mol
higher than the
3
5
3
tion the initial D3h symmetry is lifted, and we therefore assume
that the transition state described is reasonably correct at the
UMP2 level although the basis set is somewhat too small,
and that the relative energy between the two saddle points is
also calculated with the right magnitude. The conclusion from
the theoretical calculations is clear: the NO reaction with acet-
3
aldehyde proceeds entirely through aldehydic H-abstraction at
atmospheric conditions.
Calculation of reaction rate coefficients
In the first approximation the reaction rate coefficients were
calculated from the generalised transition state theory:
5
6
ꢅ
ꢃ
ꢄ
ꢃ
ꢄꢆ
kBT QTS
TS
TS
R
elec
R
E
elec
þ E0 ꢁ E þ E0
kTST ¼
exp ꢁ
ð2Þ
h
QR
kBT
where k
B
is Boltzmann’s constant, h is Planck constant, Eelec is
the vibrational zero-point energy.
and Q are, respectively, the internal partition function at
the electronic energy and E
Q
0
TS
R
the generalised transition state, and the reactants partition
function per unit volume. These functions, in turn, are
approximated as products of electronic, rotational, vibra-
tional, and translational partition functions. The translation
and rotation partition functions were treated classically; the
vibration partition functions were calculated in the harmonic
oscillator approximation using the results from quantum
mechanics. The methyl torsion in the acetaldehyde systems
was treated as with the other modes since the effects of hin-
dered rotation will almost completely cancel in eqn. (2). Other
low-lying or torsion-like vibrations were also treated as harmo-
nic oscillators. For the sake of brevity, Fig. 5, 7 and 8 include
the imaginary wavenumber of the reaction co-ordinate as
Fig. 9 MP2/aug-cc-pVDZ structures of the NO
HCO + HNO reaction: (A) the pre-reaction adduct, (B) the
transition state, (C) the post-reaction adduct; (D) the transition state
in the NO + CH CO + HNO reaction; (E) the trans-
CHO ! CH
ition state in the Hmethyl-abstraction reaction, NO + CH
CHO !
CH CO + HNO
3
+ HCHO !
3
3
3
3
3
3
3
2
3
.
and the oxygen atoms of NO are considered active (aug-cc-
3
pVDZ basis) and the remaining atoms as spectators (cc-pVDZ
basis). This reduces the number of basis function from 197 to
166, which makes it possible to carry out CCSD(T) calculation
with the current software. The results from these calculations,
Table 5 Electronic and zero-point energies of stationary points in the reactions: NO
3
+ RCHO ! HNO
3
+ RCO (R ¼ H, CH
3
)
a
a
a
E
NO3 + RCHO
DEpre-adduct
/kJ mol
DETS
/kJ mol
DEpost-adduct
/kJ mol
DEHNO + RCO
/kJ mol
3
ꢁ
1
ꢁ1
ꢁ1
ꢁ1
Level of computation
/Hartree
NO
3
+ HCHO
b
MP2(FC)/aug-cc-pVDZ
ꢁ393.849951 (0.045012)
ꢁ393.832213 (0.045167)
ꢁ394.168845
75.3 (ꢁ8.2)
120.2 (ꢁ3.4)
116.3 (ꢁ3.8)
114.6
ꢁ51.6 (ꢁ9.4)
ꢁ31.5 (ꢁ14.5)
MP2(FC)/active-spectator
MP2(FC)/aug-cc-pVTZ
CCSD(T)/aug-cc-pVDZ//
MP2(FC)/aug-cc-pVDZ
CCSD(T)/active-spectator//
MP2(FC)/active-spectator
CCSD(T)/aug-cc-pVTZ//
MP2(FC)/aug-cc-pVTZ
73.3
0.1
ꢁ57.2
ꢁ82.0
ꢁ37.2
ꢁ62.4
ꢁ393.888827
29.6
ꢁ393.860202
ꢁ394.212069
25.2
ꢁ66.8
3 3
NO + CH CHO
MP2(FC)/aug-cc-pVDZ
MP2(FC)/active-spectator
MP2(FC)/aug-cc-pVTZ
CCSD(T)/aug-cc-pVDZ//
MP2(FC)/aug-cc-pVDZ
CCSD(T)/active-spectator//
MP2(FC)/active-spectator
CCSD(T)/aug-cc-pVTZ//
MP2(FC)/aug-cc-pVTZ
ꢁ433.049392 (0.073839)
ꢁ433.025776 (0.074288)
ꢁ433.406765
73.7
110.6
107.8 (ꢁ4.1)
ꢁ57.5
ꢁ27.9 (ꢁ10.8)
ꢁ34.4
ꢁ61.4
ꢁ433.106390
ꢁ432.984708
ꢁ433.467568
16.8
ꢁ66.2
a
b
See Fig. 9. FC, frozen core. For definition of ‘‘active-spectator’’ basis set, see text. Zero-point energies, EZPE , in parentheses.
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805
1799

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Table 6 Electronic and zero-point energies of the reaction: NO
3
+ CH
3
CHO ! HNO
3
+ CH
2
CHO
a
ꢁ1
ꢁ1
Level of computation
ENO3 + CH3CHO/Hartree
DETS /kJ mol
DEHNO + CH CHO/kJ mol
3 2
b c
MP2(FC)/cc-pVDZ
ꢁ432.948499 (0.074542)
ꢁ433.023640 (0.074098)
ꢁ433.049392 (0.073839)
ꢁ433.406765
118.7 (ꢁ23.4)
120.9 (ꢁ23.8)
124.8
37.9 (ꢁ11.2)
34.4 (ꢁ11.1)
34.5 (ꢁ10.6)
28.1
MP2(FC)/active-spectator
MP2(FC)/aug-cc-pVDZ
MP2(FC)/aug-cc-pVTZ
125.9
57.5
53.1
c
CCSD(T)/cc-pVDZ// MP2(FC)/cc-pVDZ
ꢁ432.999097
ꢁ23.6
CCSD(T)/active-spectator//MP2(FC)/active-spectator
CCSD(T)/aug-cc-pVDZ//MP2(FC)/aug-cc-pVDZ
CCSD(T)/aug-cc-pVTZ//MP2(FC)/aug-cc-pVTZ
ꢁ433.079182
ꢁ25.9
ꢁ26.2
ꢁ30.0
ꢁ433.106390
ꢁ433.467568
a
b
c
See Fig. 9. FC, frozen core. For definition of ‘‘active-spectator’’ basis set, see text. Zero-point energies, EZPE , in parentheses. From ref. 15.
A
B
where Q and Q are the partition functions of the reactants,
calculated from the Hessian matrix. The calculated vibrational
wavenumbers of the reactants and transition states are avail-
able as electronic supplementary informationy.
with the center of mass partition function factored out of the
A
B
product Q Q , and included in z together with the partition
functions of those inactive degrees of freedom which are not
considered by the sums of the states under the integral.
The derived rate coefficients for the reactions are based on
the results from the CCSD(T)//MP2 calculations using the
aug-cc-pVDZ basis set for the OH reactions and the active/
spectator basis set for the NO3 reactions. They differ from
the observations by an order of magnitude—the OH reactions
W
TS1(E,J,K) and WAD1(E,J,K) denote the sum of states at
energy less than or equal to E, and the angular momentum
quantum numbers J and K for the transition state and the acti-
vated complex for the unimolecular dissociation of the adduct.
being calculated as too fast, the NO reactions being calculated
3
as too slow. We assume that for the NO
3
reaction, this is pri-
V
0
is the threshold energy for reaction at the angular momen-
marily caused by errors in the calculated electronic energies of
the transition states and reactants, and so we have simply
adjusted the electronic energy differences to fit the observed
rate coefficients at 298 K. The OH reactions, in which the tran-
sition states are of lower energy than those of the reactants,
require a more sophisticated treatment.
tum J ¼ 0. If V denotes the potential energy of transition
i
state/activated complex, and U
at (J,K) (prolate symmetric rotor assumed) then the upper
i
(J,K) is its rotational energy
m
limit J for a given energy E is given by the following condi-
tions:
JmðEÞ ¼ minfJig
ð5Þ
The computational results indicate that there exists weak,
but stable adducts between OH and aldehydes in which the
hydrogen atom of the OH radical is bonded to the oxygen
atom of the carbonyl group. We have previously reported simi-
lar adduct formations by F, Cl and Br, and tentatively attrib-
uted the failure of transition state theory to reproduce the
observed kinetic isotope effects of the Cl and Br reactions with
i
where J
satisfies the inequality
i
(i ¼ AD1, TS1) is the highest integer number which
Vi þ UiðJi;0Þ ꢇ E
For fixed values of E and J, the upper limit of K, K is deter-
ð6Þ
m
2
7
mined by
formaldehyde and acetaldehyde to adduct formation. A sim-
ple estimate of the lifetime of the adducts shows that they are
K ðE; JÞ ¼ minfK g
m
i
ð7Þ
i
not in thermal equilibrium. The equilibrium constant K
X
, cal-
culated from the partitioning functions of the adduct and the
3
with K given by the conditions:
i
ꢁ23
ꢁ1
reactants, is roughly 6 ꢅ 10 cm molecule at 298 K for
the OH/HCHO system. A typical lifetime for the adduct, given
the potential of the OH/HCHO system, is then 10 –10 s,
Vi þ UiðJ;KiÞ ꢇ E and Ki ꢇ J:
The computational effort is then related to the calculation of
ð8Þ
ꢁ
13
ꢁ12
6
1
depending upon the efficiency of the formation reaction. That
is, a first approximation of the adduct lifetime suggests it to be
shorter than the time between collisions at atmospheric condi-
tions and that thermal equilibrium will not be established. The
stability of the adducts, however, will vary between the indivi-
dual isotopomers according to their zero-point energy. Mozur-
the sum of the states, W(E,J,K). Jodkowski et al. have devel-
oped an effective computational procedure based on the micro-
canonical version of the statistical adiabatic channel model
6
4
(
SACM). This calculation procedure depends on the level
at which the angular momentum conservation is considered,
and it is discussed in details in refs. 61 and 62.
In the case where the formed adduct is stabilized by colli-
sions, the kinetics of its formation in the intermediate second-
and third-order range is determined by the high-pressure
5
7
58–60
kevich and Benson, Chen et al.
and more recently
have developed theoretical models for
6
1–63
Jodkowski et al.
the description of kinetics of a bimolecular reaction which
proceeds via an intermediate adduct/complex
(kadd,1) and the low-pressure (kadd,0) limiting rate coefficients.
The overall expression for the pressure dependent rate coeffi-
cient (kadd) applicable in all pressure regimes, is given by the
reduced fall-off equation in the form:
A þ B . C ! D
ð3Þ
A general expression taking into account the rotational
energy was derived from RRKM theory. In the case where
the intermediate C is so short-lived (or the pressure is suffi-
ciently low) that it does not undergo any collisions, the rate co-
efficient k* for the formation of product(s), D, can be written as
kadd;0=kadd;1
kadd=kadd;1 ¼
F
ð9Þ
1
þ kadd;0=kadd;1
where the broadening factor, F, determines the shape of the
fall-off curve, and can be evaluated in terms of the empirical
expressions derived by Troe and co-workers.
enables a shorthand representation of the kinetic data and
allows one to describe the behaviour of the reaction systems
in the fall-off range.
6
5–67
1
Z
eqn. (9)
Jm Km
X X
z
kꢆ ¼
dE
WAD1ðE; J; KÞ
hQ QB
A
J¼0 K¼0
V0
WTS1ðE; J; KÞ
The high-pressure limiting rate coefficient, k , for the
add,1
association reaction was derived using one of the versions of
ꢅ
expðꢁE=RTÞ ð4Þ
WAD1ðE; J; KÞ þ WTS1ðE; J; KÞ
1
800
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805

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the statistical adiabatic channel model–the maximum free
energy method of Quack and Troe. In this approach k
good agreement with those obtained experimentally and can
be considered as the ‘best’ compromised values of the scat-
6
8
add,1
ꢁ12
is a function of two empirical parameters: a ‘‘looseness’’ para-
meter a and the Morse parameter b. The value of the para-
meter b is usually derived from the force constant of the
breaking bond and the dissociation energy of the adduct.
The looseness parameter a is often used as a fitting parameter
to get satisfactory agreement between the calculated and
experimental rate coefficients. The ‘‘standard’’ choice of a cor-
responds to a ratio of a/b ꢈ 0.5 according to the results of a
tered experimental results. Our value of k* ¼ 8.5 ꢅ 10
3
cm molecules
ꢁ1 ꢁ1
s
at 300 K is only slightly lower than the
ꢁ
12
3
cm molecules s . A
ꢁ1 ꢁ1 33
recommended value of 9.2 ꢅ 10
n
least squares fit of the expression k(T ) ¼ A ꢅ (T/300) ꢅ
exp(B/T ) to the calculated rate coefficient k* in the 200 to
ꢁ
12
1.9
1600 K region gives 3.9 ꢅ 10 ꢅ (T/300) ꢅ exp(230/T ),
Fig. 10 (solid curve). This is close to the recommended expres-
sion, resulting from a least squares fit to the experimental data,
6
9
7
comparative study by Cobos and Troe showing that the
also included in Fig. 10 (dotted curve).
’
of k for many of the reactions studied is obtained for the
best’ agreement between theoretical and experimental values
The rate coefficient, k* calculated from eqn. (4) describes
the rate of formation of the post-reaction adduct under the
assumption that the pre-reaction adduct (AD1) is not stabi-
lized by collisions, and that it rapidly undergoes subsequent
processes. However, if the pressure is sufficiently high to enable
an efficient collision stabilization of AD1, the kinetics of its
formation should be considered in more detail. Thus, the
importance of the adduct formation in the reaction mechanism
is revealed by comparing k* to the rate coefficient, kadd , which
describes the formation of the adduct AD1.
1
ratio a/b ¼ 0.46 ꢀ 0.09.
The low-pressure limiting rate coefficient (kadd,0) for the
adduct formation is given by
SC
add;0
kadd;0 ¼ bck
ð10Þ
with the collision efficiency, b
coefficient, k
ized expression derived by Troe. The collision efficiency fac-
c
, and the strong collision rate
, which was analyzed in terms of the factor-
SC
add;0
7
0
The high-pressure limiting rate coefficient kadd,1 gives an
upper limit to the rate coefficient for the formation of AD1
and also represents an upper limit to the overall rate coefficient
tor, b
c
, is estimated from a comparison of the calculated value,
(corresponding to b
SC
k
¼ 1), with kadd,0 . On the other
add;0
c
hand, b is related to the average energy transferred per colli-
c
describing the decay of reactants. The calculated k
are
add,1
sion, hDEi and the energy dependence factor for the density of
distinctly higher than the corresponding k*, calculated for
the same choice of the internal parameters, a and b. The
states, F by the relationship
E
ꢁ
11
3
cm molecules
ꢁ1 ꢁ1
s at
b
< DE >
FEkBT
high-pressure value of 9.0 ꢅ 10
¼
ꢁ
ð11Þ
1
=2
3
00 K is almost one order of magnitude higher than the
experimental results.
1
ꢁ bc
which essentially describes the temperature dependence of b
because of the apparently negligible temperature dependence
of hDEi.
c
The low-pressure limiting rate coefficient, kadd,0 , was evalu-
ated in terms of the factorized Troe’s expression. The Lennard-
Jones parameters, i.e. the collision diameter, s, and the
well-depth, e, are not available for the adduct, and were esti-
mated by comparison with the analogous molecular systems.
OH + HCHO. The kinetics was studied from 228 to 1600 K
by several methods and the data has been evaluated criti-
˚
The values of s ¼ 4.5 A and e/k ¼ 500 K were used in our
B
calculations. These parameters represent the most uncertain
molecular data of the adduct. However, varying their values
by 20% leads to changes in the collision frequency, ZLJ , by less
7
cally. The results of the rate coefficient calculations are com-
,8
ꢁ
1
pared to the literature data in the plot, k(T ) vs. T , in Fig. 10.
The description of unimolecular processes requires a choice
of the internal method parameters, a and b. The values of
01
c
than 3%. The strong collision values, Fcent ¼ b , depend on
the pressure of the bath-gas, and were calculated at the typical
experimental conditions corresponding to the pressure of
helium of 1 bar. Results from these calculations are shown
˚
ꢁ1
˚
ꢁ1
a ¼ 1.96 A and b ¼ 4.26 A (corresponding to the recom-
mended ratio of a/b ¼ 0.46) were used in our calculations of
k* from eqn. (4) with the threshold energy V ¼ 0, and the
01
0
as the dashed curve in Fig. 10. The values of Fcent ¼ bc corre-
pre-reaction adduct and TS for the H-abstraction labelled as
AD1 and TS1, respectively. The derived values of k* are in
c
spond to the collision efficiency b equal to one, and thus
represent upper limits to kadd,0 and kadd . As can be seen from
SC
add;0
Fig. 10, k
has a strong negative dependency on the tem-
(pHe ¼ 1 bar) of
SC
add;0
at 200 K decreases to
perature. The calculated value of k
ꢁ
ꢁ
11
3
cm molecules
ꢁ1 ꢁ1
2
7
.5 ꢅ 10
s
12
ꢁ12
ꢁ13
3 ꢁ1 ꢁ1
cm molecules s
.2 ꢅ 10 , 1.7 ꢅ 10
and 3.1 ꢅ 10
at 300, 500 and 1000 K, respectively. Values of the rate coeffi-
cient, kadd , are expected to be one order of magnitude lower
0
c
1
than Fcent ¼ b derived at the same bath-gas pressure.
According to the negative temperature dependence of the rate
coefficient, formation of the adduct, AD1, may significantly
contribute to the overall rate coefficient only at temperatures
below 250 K. Thus, the rate coefficient k* should be a realistic
approximation to the overall rate coefficient in the temperature
range studied.
The barrier to the addition reaction, leading to HCOOH,
1
ꢁ
was, as mentioned before, calculated to be 27.8 kJ mol
.
Further, the pre-exponential factor in kaddition is ca. 8 times
smaller than that of the Hald-abstraction reaction. The theore-
tical branching ratio, abstraction : addition, is therefore essen-
tially one. This would have been of little difference if the
pre-exponential factor had been an order of magnitude larger
and the barrier height half as much: the addition reaction is of
absolutely no importance under atmospheric conditions. Not
even at combustion temperatures of 1500 K will the addition
process be of importance.
Fig. 10 Observed and calculated rate coefficients of the reaction
OH + HCHO ! products. Data taken from reviews in refs. 7 and 8,
dotted curve: recommended rate expression from ref. 7; full curve:
the rate coefficient, k*, as calculated from eqn.(4); dashed curve: the
strong collision rate coefficient to adduct formation, k
SC
add;0
.
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805
1801

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2
3
ꢁ11
3
In a recent study Alvarez-Idaboy et al. described two of
the internal motions in the transition state as free internal
rotors in order to be able to calculate the rate coefficient at
and the Hald-abstraction rate coefficient to 1.44 ꢅ 10
cm
. However, the calculated pre-exponential fac-
tor in the rate coefficient for Hmethyl-abstraction is only
ꢁ
1
ꢁ1
s
molecule
ꢁ
13
3
ꢁ1 ꢁ1
2
98 K. Of the three out-of-plane modes of the transition state,
2.8 ꢅ 10
cm molecule s at 298 K. Describing the
Fig. 6, only the O ¼ C(H)ꢉ ꢉ ꢉO–H torsional deformation may
qualify as a free rotor. However, the barrier to rotation is of
medium height and located at a saddle point of order 2,
methyl torsional mode as a free internal rotor will actually
not increase the pre-exponential factor and describing the
C–Hꢉ ꢉ ꢉO–H torsional mode of the transition state as a free
internal rotor, of which it is not, will only increase the pre-
exponential by a factor of roughly 3 at 298 K. Tunnelling
might be important though, and if one assumes an Eckart
ꢁ
1
V(p)–V(0) ¼ 4.6 kJ mol . Alvarez-Idaboy et al. also sug-
gested that the Hald-abstraction proceeds in two steps:
5
4,55
ꢁ1
ꢁ1
R CHO þ OH 0 R CHO ꢉ ꢉ ꢉ HO
R-CHO ꢉ ꢉ ꢉ HO ! RCO þ H2O
with a fast equilibrium between the reactants and the pre-reac-
tion adduct, and an equilibrium distribution of the adducts.
They then included a tunnelling correction to increase the
pre-exponential factor in the rate coefficient (see later). They
did, however, not consider adjusting their calculated barrier
height of +0.5 kJ mol . Extending their model to the 200–
600 K temperature range results in curve, which is much
too flat, for the rate coefficient when compared to the experi-
mental data. Thus, the modified transition state model for
the OH reaction with formaldehyde suggested Alvarez-Idaboy
ðXÞ
ðXIÞ
potential,
kJ mol ) this results in a correction factor of ca. 10 at 298
(io ¼ 2150 cm , E
a
¼ 12 kJ mol , E
r
¼ ꢁ80
ꢁ1
K. If the (modified) pre-exponential factors are correct, then
ꢁ
1
the adjusted barrier heights are ꢁ5.1 and 1.4 kJ mol for
the H - and H -abstraction reactions, respectively. If the
methyl
ald
C–Hꢉ ꢉ ꢉO–H torsional mode in addition is described as a free
internal rotor, the adjusted barrier to the H -abstraction
methyl
ꢁ
1
reaction increases its value from 1.4 to 4 kJ mol . The experi-
mental kinetic data does not therefore warrant a distinction
between the two mechanisms, as suggested by Taylor et al.
ꢁ
1
1
8
1
ꢁ
1
A reaction barrier of only 1.4 (or even 4) kJ mol
to
Hmethyl-abstraction, however, appears unreasonably low when
ꢁ
1
compared to the experimental value of 8.5 kJ mol
in
2
3
33
et al. is therefore not in agreement with the experimental
results.
ethane. We therefore conclude that Hmethyl-abstraction and
the subsequent dissociation of the formyl methyl radical is
not the origin of the CO and HCHO formation in the
OH + CH CHO reaction. We are therefore left with the alter-
3
OH + CH CHO. The reaction was studied from 244 to 750
3
native dissociation of the acetyl radical, pathway (VId), as the
source to the observed CO and HCHO formation.
The profile of the potential energy surface of the
7
,8
K and the data have been evaluated critically. The theoreti-
cal results based on the Hald-abstraction reaction alone are
compared to the experimental data in Fig. 11. Included in
Fig. 11 is data extracted from Fig. 1 in a recent paper by
CH CHO + OH reaction system predicts a distinct dominance
3
of the Hald-abstaction route and the mechanism of the Hald
-
1
8
Taylor et al., who attributed the curvature of the Arrhenius
plot to the dominance of two different reaction mechanisms,
each dependent on the temperature.
abstraction seems to be similar to that of the HCHO + OH
reaction system. The theoretical analysis of the rate coefficients
calculated for HCHO + OH shows that formation of the pre-
reaction adduct only plays an important role in description
of the Hald-abstraction at temperatures below 250 K. How-
In the product study of the OH + CH CHO reaction both
3
CO and HCHO were observed as primary products in an
amount corresponding to ca. 10% of the reacted CH CHO.
3
ever, the rate coefficient measured for the CH CHO + OH
3
reaction shows some peculiarities. Considering only one
There are two pathways leading to CO and HCHO as primary
products: (i) the dissociation of the acetyl radical, pathway
VId), and (ii) the dissociation of the formyl methyl radical
formed by Hmethyl-abstraction in pathway (VIe). If the initial
HCHO and CO formation in the reaction stems from pathway
hydrogen atom, Hald , one may to a first approximation expect
the rate coefficient for the Hald-abstraction to be half of that of
the HCHO + OH reaction system. However, the rate coeffi-
cient measured at low temperatures is significantly higher than
that for HCHO + OH. In addition, the experimental rate coef-
ficient shows a distinct negative dependence on temperature
over a wide range of temperatures. Similarity between the
molecular and thermochemical properties of the structures
(
(
abstraction at 298 K. This would then fix the rate coefficient
VIe) alone, then 10% of the reaction is through Hmethyl
-
ꢁ12
3
ꢁ1 ꢁ1
for the Hmethyl-abstraction to 1.6 ꢅ 10 cm molecule s ,
which is ca. 10 times faster than the OH reaction with ethane,
3
3
important to the Hald-abstraction in the CH CHO/HCHO +
3
OH reaction systems, suggests a more complex reaction
mechanism for CH CHO + OH.
3
The rate coefficient, k*, derived from eqn. (4) with V
0
¼ 0
˚
ꢁ1
˚
ꢁ1
and a/b ¼ 1.96 A /4.27 A ¼ 0.46, is included in Fig. 11
as the short-dashed curve. The indices AD1 and TS1 are
related to the pre-reaction adduct and TS for the Hald-abstrac-
tion, respectively. The derived values of k* follows the
ꢁ
12
1.5
expression k*(T) ¼ 1.4 ꢅ 10 ꢅ (T/300) ꢅ exp(295/T ) and
ꢁ
12
ꢁ11
3
cm
increase from 3.8 ꢅ 10
at 300 K to 1.2 ꢅ 10
ꢁ1
s at 1000 K. As expected, the room temperature
ꢁ
1
molecules
value of k* is more than 2 times lower than that obtained for
the HCHO + OH reaction system. The predicted values of k*
clearly underestimate the reaction rate at low temperatures
but are approaching the experimental values at temperatures
above 700 K.
As mentioned before, the ab initio investigation of the poten-
tial energy surface shows the existence of an additional adduct
denoted by AD2, Fig. 7, in which the oxygen of the OH radical
is pointed towards the methyl group. Formation of AD2 may
be considered as the first elementary step of the reaction
pathway that leads to final products of the Hmet-abstraction.
The other possible pathway from AD2 is related to the
Fig. 11 Observed and calculated rate coefficients of the reaction
OH + CH
CHO ! products. Data taken from reviews in refs. 7 and
(S) and from ref. 18 (X). Short-dashed curve: rate coefficient, k*, cal-
culated from eqn. (4). Dotted curve: the low-pressure rate coefficient,
add,0 ; long-dashed curve: the rate coefficient to Hald-abstraction via
3
8
k
adduct formation, kadd , see text; full curve: the rate coefficient
k* + kadd , see text.
1
802
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805

View Article Online
isomerization to AD1. The energy barrier in this process is
only ca. 2 kJ mol , hence, a significant part of the AD2
adducts may undergo this isomerization. In this way, the initial
ꢁ
1
3
attack of OH on the methyl group of CH CHO may also result
in the formation of the Hald-abstraction product.
The formation of AD2 is expected to be a dominating pro-
cess in the decay of reactants at low temperatures, and a strong
negative temperature dependency of the overall rate coefficient
can be explained in terms of this extra adduct. Further support
for the proposed reaction mechanism may come from the cal-
culations of the rate coefficient kadd for the formation of the
adduct AD2. There are two major factors governing the mag-
nitude of kadd : the limiting rate coefficients kadd,1 and kadd,0
.
The calculated limiting high-pressure rate coefficients, kadd,1
˚
ꢁ1
˚
ꢁ1
(
describes the formation of AD2 cover the range from 1.1 to
.2 ꢅ 10
assuming a ¼ 1.97 A and b ¼ 4.28 A , a/b ¼ 0.46), which
ꢁ10
3
cm molecules s , are significantly higher than
ꢁ1 ꢁ1
2
the experimental data. Values of the Lennard-Jones para-
Fig. 12 Observed and calculated rate coefficients of the reaction
NO + CH CHO ! products. Data taken from refs. 12 and 15.
˚
meters of s ¼ 5.5 A and e/k ¼ 500 K were adopted in the
3
3
calculations of the limiting rate low-pressure rate coefficient,
kadd,0 . Under the assumption that the average energy trans-
ferred by collision, <DE > , is temperature independent, the
theoretical fall-off curves were constructed and fitted to experi-
ments at the given temperature and pressure of a bath-gas.
Evaluation of the broadening factor, F, was standard; it
on Hald-abstraction alone, are compared to the observations
in Fig. 12. To obtain agreement with the recommended rate
ꢁ
15
3
cm molecule
ꢁ1 ꢁ1 33
coefficient at 298 K, 2.7 ꢅ 10
s
culated barrier of 11.7 kJ mol was reduced to 7.1 kJ mol
,
the cal-
.
ꢁ
1
ꢁ1
0
c
:14
As can be seen from Fig. 12, there is a slight curvature in the
theoretical Arrhenius plot and the curve is well described by
has been expressed by Fcent and N, with Fcent ¼ b
and
N ¼ 0.75–1.27 log F . Assuming a bath-gas pressure of 1
cent
ꢁ13
the expression k(T ) ¼ 3.03 ꢅ 10 ꢅ (T/300) ꢅ exp(ꢁ1480/
bar of helium, the best fit to experimental data was obtained
ꢁ
1
T ) in the range 200–600 K. The barrier to Hmethyl-abstraction
is calculated to be ca. 15 kJ mol higher than the barrier to
for ꢁ<DE > ¼ 200 cm . Results from calculations of kadd
He
ꢁ1
are included in Fig. 11 as the long-dashed curve. The calcu-
lated kadd has a strong negative temperature dependency.
Thus, formation of AD2 is a dominating elementary process
at lower temperatures. According to the high values of the lim-
iting rate coefficient, kadd,1 , the fall-off behaviour of kadd can
H
ald-abstraction. Reducing this difference by 50% still leaves
the rate to Hmethyl-abstraction three orders of magnitude lower
than that of Hald-abstraction.
be neglected at temperatures higher than 350 K; k
(shown
add,0
Kinetic isotope effects
in Fig. 11 as the dotted curve) becomes very close to kadd
.
It is worth noticing that the sum of k* + kadd , denoted in
Fig. 11 by the solid curve, shows correspondence to the results
of experiments over a wide temperature range. This supports
the conclusion that the reaction mechanism is temperature
dependent, with dominant formation of AD2 at the lowest
temperatures studied. The agreement between the experimental
and theoretical results is very good, especially if one takes into
account possible uncertainties in the calculated molecular
parameters, computational simplifications (rigid rotor/harmo-
nic oscillator) and additional complications of the reaction
mechanism, e.g. the equilibrium between AD1 and AD2.
The barrier to the addition reaction, leading to either
The kinetic isotope effect, KIEa,b , is defined as the ratio
between the reaction rate coefficients of isotopomers a and b
with the same reactant. An isotopic substitution changes the
contribution to the rate coefficient from three terms, which
are related to the translational, rotational and vibrational
degrees of freedom. The two first are independent of the tem-
perature. Second, there is a contribution from the exponential
term caused by changes in the vibrational zero-point energies
upon isotopic substitution.
The translational term depends only upon the reduced
masses of the isotopomer reactants and transition states, and
will be close to unity. The rotational term depends only upon
the rotational constants of reactants and transition states, and
the vibrational term is essentially dominated by the low-lying
vibrational modes. The calculated kinetic isotope effects are
compared to the observations in Tables 2 and 3.
ꢁ
1
HCOOH or CH
and the pre-exponential factor in kaddition turns out to be ca.
0 times smaller than that of the Hald-abstraction reaction.
3
COOH, was calculated as 31.6 kJ mol ,
2
The theoretical branching ratio, abstraction : addition, is there-
fore one. Again, this would have been of little difference if the
pre-exponential factor had been two orders of magnitude lar-
ger and the barrier height half as much: the addition reaction
is of absolutely no importance under atmospheric conditions.
The observed kinetic isotope effect in the HCHO/OH reac-
tion upon perdeuteration, KIEHH,DD , is 1.62—the calculations
based on the rate coefficient, k*, predict 1.93 at 300 K, with
lowering to 1.38 at 1000 K. The calculated value of 1.39 for
the reaction of HCDO isotopomer is also a realistic estimation
1
3
of KIEHH,HD at room temperature. An influence of the C-
substitution on the calculated rate coefficient is too small to
appear on the second decimal digit of the KIE’s factor. The
experimental estimates are then well reproduced by the values
predicted theoretically.
NO
perature.
reaction rate coefficient at 298 K, 5.2 ꢅ 10
3
+ HCHO. The kinetics was studied only at room tem-
9
–11
To reproduce the (recommended) experimental
ꢁ
15
3
ꢁ1
cm molecule
the barrier to the reaction was reduced from the calcu-
ꢁ
1 33
s
,
ꢁ
1
lated value of 21.4 kJ mol (active-spectator basis set) to
ꢁ1
Theoretical analysis of KIE in the CH
system is more complex. The reaction rate is described by
the sum of the rate coefficients, k* + kass . The second one, kass
depends on the nature and pressure of a bath-gas, M, as well as
on the average energy transferred per collision, <DE > M
CHO/OH reaction
3
1
the range 200 to 320 K, and may conveniently be approxi-
4.6 kJ mol . The derived Arrhenius plot is nearly linear in
ꢁ
13
,
mated by k(T ) ¼ 5.19 ꢅ 10 ꢅ exp(ꢁ2023/T ).
.
NO
temperature dependence of the NO + CH CHO reaction cov-
3
+ CH
3
CHO. There are two consistent studies of the
Thus, the rate coefficients can be compared only at the same
pressure conditions, and under the assumption that <DE > He
does not change in the reactions of different isotopomers.
3
3
1
2,15
ering the range 260–380 K.
The theoretical results, based
Phys. Chem. Chem. Phys., 2003, 5, 1790–1805
1803

View Article Online
Fortunately, the association pathway plays an important role in
the reaction mechanism only at low temperatures. At tempera-
tures higher than 350 K, the pressure dependence of the
overall rate coefficient can be omitted due to a dominant
contribution from k*. Therefore, our analysis of KIE was
based on the derived values of k* in reactions of the differ-
ent isotopomers. Calculated in this way, the values of KIE
depend slightly on the temperature. Derived in the tempera-
ture range of 300–1000 K, the values of the KIE of 1.50–
dependent reaction mechanism with significant dominance of
the formation of the adduct at low temperatures. However,
the observed kinetic isotope effects for reactions of NO are
3
much smaller than those calculated by conventional transition
state theory. This is also attributed to the formation of
pre-reaction adducts.
Acknowledgements
1
.68, 1.40–1.48 and 1.05–1.17 are in excellent agreement with
those measured as 1.65 ꢀ 0.08, 1.42 ꢀ 0.10 and 1.13 ꢀ 0.04
This work is part of the project ‘‘Carbonyls in Tropospheric
Oxidation Mechanisms’’ (CATOME) and has received sup-
port from the CEC Environment and Climate program
through contract ENV4-CT97-0416. BDA acknowledges
financial support from The Research Council of Norway
through grant no. 123289/410. Part of the numerical calcula-
tion was carried out in the Wroclaw Center of Networking
and Supercomputing.
for k(CH
OH)/k(CH
3
CHO + OH)/k(CD CDO + OH), k(CH
3
3
CHO +
3
CDO + OH), and k(CH CHO + OH)/k(CD
3
3
CHO + OH), respectively.
The calculated values of KIEHH,DD in reactions of NO with
3
3
HCHO/CH CHO are distinctly overestimated (with the factor
of 2) compared to those obtained experimentally. For an
explanation of this fact, one has to focus attention on the cal-
culations of the rate coefficients. The rate coefficients in the
3
reactions of NO were derived using the conventional transi-
tion state theory. Therefore, an insight into the details of the
calculations of the rate coefficients, kTST and k* may be useful
for our analysis. In the TST calculation, kTST is determined by
the properties of the transition state. Contrary to that, k* is
evaluated from the molecular parameters of both the transition
state and the molecular complex. However, if the transition
state is located distinctly below the reactants energy, the micro-
canonical branching ratio in eqn. (4) becomes close to unity.
Thus, the values of k* calculated for reactions of OH radicals
depend rather on the molecular properties of the adduct than
on the transition state. This suggests that the fault of calcu-
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