Theoretical study of the reaction mechanism and kinetics
of low-molecular-weight atmospheric aldehydes (C1-C4)
with NO2
Yuemeng Ji a, Yanpeng Gao a, b, Guiying Li a, Taicheng Ana, ∗
a
State Key Laboratory of Organic Geochemistry and Guangdong Key Laboratory of
Environmental Resources Utilization and Protection, Guangzhou Institute of Geochemistry,
Chinese Academy of Sciences, Guangzhou 510640, China;
b
Graduate School of Chinese Academy of Sciences, Beijing 100049, China.
Abstract
Accurate description of atmospheric reactions of a series of low-molecular-weight
(LMW) aldehydes (C1-C4) with NO2 has been modeled using a direct dynamic approach. The
profiles of the potential energy surface were constructed at the BMC-CCSD//MPWB1K/6311G(d,p) level of theory, and two different pathways have been found: H-abstraction and
NO2-addition. The modeling results found that the contribution of NO2-addition reaction
pathway to the total rate constant is very small and thus this kind of pathway is insignificant
in atmospheric conditions. The predicted H-abstraction products are mainly reactive acyl
radical and nitrous acid (HONO) which is very mutagenic and carcinogenic pollutant as well
as the precursor of acid deposition. The rate constants of both pathways were also deduced by
using canonical variational transition state theory incorporating with the small-curvature
tunneling correction within 200–360 and 360–2000 K. Theoretical overall rate constants are
in good agreement with the available experimental values, whose increase in the order of
kformaldehyde < kacetaldehyde < kpropanal < kbutanal, implying that relative long-chain LMW aldehydes
∗
Corresponding author: Tel: +86-20-85291501; Fax: +86-20-85290706; E-mail address: [email protected] (T.C. An)
are more reactive toward NO2 than those short-chain LMW aldehydes in the atmospheric
condition. At 298 K, the total rate constants of LMW aldehydes (C1-C4) with NO2 are
obtained as 1.65 × 10-25, 1.43 × 10-24, 3.39 × 10-24 and 1.83 × 10-23 cm3 molecule-1 s-1,
respectively.
Keyword:
Low-molecule-weight
aldehydes;
NO2; Atmospheric chemical reaction;
Theoretical calculation model; Rate constant.
1. Introduction
Photochemical pollution has become an important air quality issue in China due to
increased emissions of volatile organic compounds (VOCs) and nitrogen oxides (NOx) driven
by the rapid economic growth (Liu et al., 2010). Aldehydes, an important class of VOCs, are
directly discharged into the troposphere from biogenic and anthropogenic sources (Zhang et
al., 2006b), and have received scientific and regulatory attention due to their potential adverse
health effects on humans as well as their important role in atmospheric photochemical
reactions (Grosjean, 1982; Hoekman, 1992; Nondek et al., 1992; Zhou et al., 1990). On the
other hand, NO2 is not only an important constituent of the natural unpolluted atmosphere, but
also one of the major pollutants from anthropogenic sources such as motor vehicles (Power et
al., 2011), power plants (Jurkat et al., 2011) and combustion process (Zhang et al., 2006a).
Thus, the ubiquitously presence of aldehydes and NO2 in the common atmospheric
environment could lead to a complex series of chemical transformation which can result in
such effects on the formation of photooxidants, acid deposition and secondary particulate
matter (Atkinson, 2000), as well as the photochemical smog formation (Zhou et al., 1990).
Therefore, to investigate the reactions of aldehydes with NO2 will facilitate the understanding
of photochemical and geochemical processes affecting organic matter in the atmospheric
environments.
Among many atmospheric aldehydes, the low-molecular-weight (LMW) aldehydes (C1–
C4) were often selected as the model of the atmospheric reaction of aldehydes due to their
higher concentrations and reactivity in urban atmospheres (Tanner et al., 1984; Zhou et al.,
1990). In early literatures, considerable experimental investigations have been devoted to the
experimental kinetics of formaldehyde (He et al., 1989; Lin et al., 1990; Pollard et al., 1949)
and acetaldehyde (Christie et al., 1967; Davis et al., 1972; Mcdowell et al., 1950; Pedler et al.,
1957) with NO2. For formaldehyde, a linear Arrhenius plot with the rate constants within a
temperature range of 393 to 476 K was reported by He et al. (1989). The rate constants are
higher than those of Pollard et al. (1949) by a factor of 5. As for acetaldehyde, the rate
constants measured by four experimental groups (Christie et al., 1967; Davis et al., 1972;
Mcdowell et al., 1950; Pedler et al., 1957) are not consistent well with each other. But there is
no reported on propanal and much limited information is reported relative to butanal based on
the experiments (Jaffe et al., 1974). The author summarized that the kinetics and mechanisms
of butanal with NO2 are all similar to three LMW aldehydes (up to propanal) based on
previously experimental results (Jaffe et al., 1974). Therefore, the questions will arise: are the
mechanisms of the reaction of propanal with NO2 similar to the other LMW aldehydes? Are
the rate constants and mechanisms of the reactions of LMW aldehydes (C1–C4) with NO2
really the same? However, there is still no experimentally confirmed conclusion drawn on this
point because of different experimental methods and instruments employed. Therefore, the
detailed theoretical study may be promising alternatives for these questions. However, there is
only one study relative to theoretical predicting the reaction of formaldehyde with NO2 (Xu et
al., 2003), and the theoretical studies for other aldehydes are never attempted. Thus, to
ascertain the environmental impact and to facilitate future experimental studies, further
systematic theoretical investigation is urgently required to illustrate the detail dynamical
mechanisms of the reactions of LMW aldehydes (C1–C4) with NO2.
Herein, a direct dynamic approach (Hu et al., 1996; Truhlar et al., 1996) was employed
to present the systematic study on the atmospheric reactions of LMW aldehydes (C1–C4)
with NO2. The rate constants are calculated using variational transition state theory (VTST)
(Truhlar et al., 1980; Truhlar et al., 1985) within a low temperature range of 200–360 K to
simulate the atmospheric temperatures from the surface of Earth to the tropopause (Ji et al.,
2008) and within a high temperature range of 360–2000 K to simulate combustion
temperatures in some extreme conditions. Our aims and objectives are as follows: (i) to
establish a model of the mechanism of the reactions of LMW aldehydes (C1–C4) with NO2
and to predict the reaction law of different aldehydes; (ii) to show the detailed kinetic model
comparing the measured rate constants with available experimental data; and (iii) to provide a
multi-coefficient correction methods (MCCMs) with the aim of finding a convinced and
widely applicable method to model the atmospheric chemical reactions of aldehydes with
NO2.
2. Methods
Quantum chemical calculations were performed with Gaussian 03 suite of programs
(Frisch et al., 2003). The MPWB1K method is a recent popular hybrid density functional
theory (DFT) model with performance for thermochemstry, hydrogen bonding and kinetics
(Zhao et al., 2004). The geometrical parameters of the stationary points were calculated at the
MPWB1K level with the standard 6-311G(d,p) basis set [DFT(MPWB1K)/6-311G(d,p)]. For
simplicity, hereinafter it is denoted by MPWB1K/6-311G(d,p) level. The vibrational analysis
was calculated at the same level of theory to characterize the stationary nature of various
structures, which a minimum state possess all real frequencies, whereas a transition state
possess one and only one imaginary frequency. The frequency calculations also provided the
thermodynamic quantities such as the zero point energy (ZPE) correction for potential energy
and the thermal correction for reaction enthalpy at a temperature of 298 K. The minimumenergy path (MEP) was constructed with the intrinsic reaction coordinate (IRC) theory to
confirm that the transition state (TS) really connect with minima along the reaction path.
To obtain more reliable profiles of the potential energy surface (PES), a multi-coefficient
correlation method based on coupled cluster theory with single and double excitations (BMCCCSD) was applied (Lynch et al., 2005) via the equation defined in Supporting Information.
In order to justify the performance of the BMC-CCSD method for energies, a higher energies
calculation CCSD(T)/6-311+G(3df,2p) [coupled cluster approach with single and double
substitutions including a perturbative estimate of connected triples substitutions with the
flexible 6-311+G(3df,2p) basis set], was compared. The dual-level potential profile along the
reaction path was further refined with the interpolated single-point energy (ISPE) method
(Chuang et al., 1999), in which a few extra single-point calculations are needed to correct the
lower-level reaction path. Herewith, the dual-level dynamics approach was denoted as X//Y,
where a single-point energy calculation at level X is carried out for the geometry optimized at
a lower level Y.
By means of the Polyrate 9.1 program (Corchado et al., 2002), the rate constants were
calculated using canonical variational transition state theory (CVT) (Garrett et al., 1979;
Gonzalezlafont et al., 1991) plus the small curvature tunneling correction (SCT) (Liu et al.,
1993). In this program, as an example of direct dynamic approach, the variational transition
state theory with interpolated single-point energies (VTST-ISPE) (Chuang et al., 1999) was
selected for all kinetics calculations.
3. Results and discussion
3.1. Reaction Mechanism
All the possible channels of the reactions of different LMW aldehydes (C1–C4) with
NO2 have been modeled and illustrated in Figs. 1–4. In summary, two different kind reaction
pathways exist, H-abstraction and addition of NO2 to aldehydes. Thus, before going further, it
will be useful to establish a nomenclature for each mechanism. We will use the following
notation where R stands for reaction: (see together with Figs. 1–4) H-abstraction: there exists
three kinds of H-abstraction channels, i.e., syn-H-abstraction by O atom of NO2 from
carbonyl group position or alkyl group position (syn-RO-abs1/2–4), anti-H-abstraction by O
atom of NO2 from carbonyl group position or alkyl group position (anti-RO-abs1/2–4), and Habstraction by N atom of NO2 from carbonyl group position or alkyl group position (RNabs1/2–4).
NO2-addition: three distinct channels are also feasible. That is, syn-NO2-addition
(syn-RO-add) and anti-NO2-addition (anti-RO-add) by O atom of NO2, and NO2-addition (RN-add)
by N atom of NO2.
As shown in Fig. 1, on the basis of the energy barriers for NO2-addition and Habstraction in the case of formaldehyde, it is clear why the NO2-addition pathway is not
favored in this reaction because the energy difference between the TSs of above two channels
is about 7 kcal/mol. Herein, the energies are calculated relative to the corresponding reactants
including ZPE corrections. ΔE energy is defined as the potential barrier (ΔE = ETS – Ereactants),
while ΔEP energy is defined as the reaction energy (ΔEP = Eproducts – Ereactants) in this
manuscript. For the H-abstraction channels of the reaction of formaldehyde with NO2, the ΔE
of the anti-RO-abs1 channel is 29.24 kcal/mol, which is higher than those of other two channels
(syn-RO-abs1 and RN-abs1) by nearly 7–8 kcal/mol, indicating that the anti-RO-abs1 channel will
be negligible. As can be seen from Fig. 2, for the reaction of acetaldehyde with NO2, the ΔE
of the syn-RO-abs2, anti-RO-abs1, anti-RO-abs2, RN-abs2, syn-RO-add, anti-RO-add and RN-add channels
are 28.92, 27.23, 34.67, 29.84, 28.99, 38.07, and 29.91 kcal/mol, respectively, which are
about 9–18 kcal/mol higher than those of the syn-RO-abs1 and RN-abs1 channels, indicating that
two latter channels are expected to be the dominated reaction pathways. The similar
conclusions can be drawn from the reactions of propanal/butanal with NO2 that the syn-ROabs1
and RN-abs1 channels are also the dominated reaction pathways (Figs. 3–4). Thus, in this
section, the reaction of different LMW aldehydes (C1–C4) with NO2 will mainly focus on the
channels of syn-RO-abs1 and RN-abs1, respectively, and other channels may be ignored due to
high potential energies.
The structures of four LMW aldehydes along with the TS involved in reactions are also
presented in Figs. 1–4. As shown in figures, the elongations of the forming bonds in the four
syn-TSO-abs1s are all greater than those of the breaking bonds, indicating that the four syn-TSOabs1s
are reactant-like. On the contrary, the four TSN-abs1s are product-like (detailed discussion
in Supporting Information). And there is a complex (denoted as CPN-abs) located at the exit of
this channel, which the C–H bond distance is 2.40 Å, while the other bond lengths are very
close to those of the products. The harmonic vibrational frequencies of the above stationary
points are also listed in Table S1, in order to confirm the optimized geometry corresponding
to a local minimum that has no imaginary frequency or to a saddle point that has only one
imaginary frequency.
The profiles of PES obtained using the BMC-CCSD//MPWB1K method are given in Fig.
S1a–1d. For comparison, other five methods, that is, BMC-CCSD//B3LYP, BMCCCSD//QCISD, CCSD(T)//MPWB1K, CCSD(T)//B3LYP, and CCSD(T)//QCISD methods
are performed and also given in Table S2. As concluded from the discussion in Supporting
Information, the BMC-CCSD//MPWB1K method not only is a more suitable method than
others to predict the energies, but also a good compromise of the computational accuracy and
the computational expensive. Seen from Fig. S1a, for the reaction of formaldehyde with NO2,
the ΔE of channel RN-abs1 is only 0.56 kcal/mol higher than that of channel syn-RO-abs1, while
the ΔEP of the former system is 17.54 kcal/mol, which is higher than that of the latter nearly 8
kcal/mol. From Fig. S1b–d, other aldehydes perform the similar behavior. The ΔE differences
between two channels (syn-RO-abs1 and RN-abs1) are 1.32, 1.50 and 1.44 kcal/mol for
acetaldehyde, propanal and butanal, respectively, and the ΔEP differences are all about 7
kcal/mol. Thus, it can be concluded that, for the reaction of LMW aldehydes (C1–C4) with
NO2, whether thermodynamically or kinetically, the syn-RO-abs1 channel seems to be the
major pathway, and the other channel of RN-abs1 is minor pathway. For the four RN-abs1
channels, the stabilization energy of CPN-abs1s are all about 2–4 kcal/mol more stable than the
corresponding products (Fig. S1).
As illustrated in Fig. S1a–1d, it can also be found that the ΔE decrease in the same
channel in the following order: ΔEformaldehyde > ΔEacetaldehyde > ΔEpropanal > ΔEbutanal. For example,
for the syn-RO-abs1 channel, the ΔEs of four investigated aldehydes are 21.86, 18.79, 18.11 and
17.48 kcal/mol, respectively. This implies that the rate constants should increase with
increasing the carbon number of aldehydes. The above phenomena may be due to the
electronic effect of the alkyl group, which increases the electronic density at the carbonyl
carbon, favoring the abstraction of the hydrogen atom (Alvarez-Idaboy et al., 2001). In
addition, we can also find that the ΔEP of the channels with the reactant-like TS is lower than
those with the product-like TS. For example, for the reaction of formaldehyde with NO2, the
ΔEP of the syn-RO-abs1 channel with the reactant-like TS is 10.00 kcal/mol, which is about 7
kcal/mol lower than that of the RN-abs1 channel with product-like TS (Fig. S1).
It is known that the accurate knowledge of the reaction enthalpies ( ΔH 0298 ) is important
parameter to determine the thermodynamic properties and the kinetics of atmospheric
processes. The reaction enthalpies of each channel are calculated and listed in Tables S3–S4.
The calculated reaction enthalpies are 10.09 (formaldehyde) and 11.16 (acetaldehyde)
kcal/mol for the syn-RO-abs1 channel in this paper, which are in excellent agreement with the
corresponding energies [9.9 ± 0.9 and 12.41 ± 1.6 kcal/mol, respectively (Table S3)]
calculated by the experimental standard heats of formation (Berkowitz et al., 1994; Chase et
al., 1998; Frenkel et al., 1994; Lias et al., 1998; NIST). For other channels, it is difficult to
make a direct comparison of the theory with the experiment for the enthalpies due to lack of
the experimental data. However, in view of the good agreement obtained above two channels,
it is expected that the calculated enthalpies of other channels are reliable.
3.2. Reaction Kinetics
To estimate the kinetics of the reactions of LMW aldehydes (C1–C4) with NO2 in other
temperatures where no experimental data are available, the modified Arrhenius formulas
within the temperature ranges of 200–360 K and 360–2000 K are listed in Table 1 and Tables
S5–S6, respectively. The pre-exponential factor, the activation energy, and the rate constants
can be obtained from these Arrhenius formulas.
3.2.1. Low Temperature Measurements
In order to simulate the real atmospheric reactions occurred at the temperature range
from the earth surface to the tropopause, the rate constants was investigated within the
temperature range of 200–360 K. The temperature dependences of the branching ratios are
presented in Fig. S2a–2d. See from figure, it can be found that except the syn-RO-abs1 and RNabs1
channels, the contribution of other channels are not more than 0.1%, implying that the
syn-RO-abs1 and RN-abs1 channels are two major channels and other channels can be negligible
within the temperature range of 200–360 K. This is consistent with the analysis for the
potential barrier heights of these channels mentioned above. Thus, in the following study, the
syn-RO-abs1 and RN-abs1 channels will be mainly focused. And, the total CVT/SCT rate
constants obtained as the sum of the individual rate constants associated with the syn-RO-abs1
and RN-sbs1 channels are shown in Fig. 5a–5d along with the available previous experimental
values (Christie et al., 1967; Davis et al., 1972; Jaffe et al., 1974).
For the reaction of formaldehyde with NO2, seen from Fig. S2a, the syn-RO-abs1 channel
is predominant pathway with the ratio nearly 100% within the temperature range of 200–360
K, and the total rate constants are almost equal to that of syn-RO-abs1 channel. The rate
constants of formaldehyde with NO2 at the BMC-CCSD//MPWB1K method were compared
at the CCSD(T)//MPWB1K method, and it was found that the rate constants at both methods
are almost the same. For example, at 298 K, the rate constant is 1.65 × 10-25 cm3 molecule-1 s-1
with the former method, and is 3.60 × 10-25 cm3 molecule-1 s-1 with the latter method (Fig. 5a).
As for the reaction of acetaldehyde with NO2, the dominant reaction channel is still syn-ROabs1
channel. The rate constants, as illustrated in Fig. 5b, are in excellent agreement with the
experimental values measured by Christie et al. (Christie et al., 1967), while slightly
underestimate the experimental values of Davis et al. (Davis et al., 1972). For instance, at 298
K, the obtained CVT/SCT rate constant is 1.43×10-24 cm3 molecule-1 s-1. This value perfectly
match the experimental value of 1.55×10-24 cm3 molecule-1 s-1 (Christie et al., 1967), while is
lower than that of 1.84×10-23 cm3 molecule-1 s-1 (Davis et al., 1972). As for the reaction of
butanal with NO2, as shown in Fig. 5d, the calculated CVT/SCT rate constants are also close
to the available experimental values (Jaffe et al., 1974) with the largest deviation within a
factor of 1.9 within the temperature range of 250–360 K. As indicated in the above results, the
good match was observed between the theoretical results and the experimental values for
above three aldehydes. Therefore, for the reaction of propanal with NO2, despite the absence
of the available experimental values, the calculated rate constants should be reliable. As
shown in Fig. S2c–2d, like formaldehyde and acetaldehyde, the syn-RO-abs1 channels are still
major pathway for propanal and butanal, and the total rate constants are almost equal to that
of syn-RO-abs1 channel within the investigated temperature range. Therefore, as for the
reactions of LMW aldehydes (C1–C4) with NO2, the acyl radical and syn-HONO are the
dominated products, and alkyl aldehydes radicals and adducts will be difficult to form within
the low temperature range of 200–360 K.
The total rate constants of four LMW aldehydes (C1–C4) with NO2 are summarized in
Fig. 6. At 298 K, the CVT/SCT values are 1.65 × 10-25, 1.43 × 10-24, 3.39 × 10-24 and 1.83 ×
10-23 cm3 molecule-1 s-1 for four LMW aldehydes (C1–C4) , respectively. We can found that
the total rate constants increase with increasing carbon number of aldehydes. That is, with
increasing the size of the R group in RCHO, the total rate constants increase in the order of
kformaldehyde < kacetaldehyde < kpropanal < kbutanal, in accordance with the analysis results from the
ΔEs. However, Jaffe and Wan found that the activities of four LMW aldehydes (C1–C4)
0
depend on the aldehydic C–H bond energy ( D298
(C − H ) ) and very little relative to the size
of the R group in RCHO (1974). Thus, in order to confirm their hypothesis, the dissociation
0
energies ( D298
) of the four aldehydes were calculated at the BMC-CCSD//MPWB1K/60
311G(d,p) level, and listed in Table S7. From the Table, the calculated D298
(C − H ) in the
four aldehydes are obtained as 87.24 (formaldehyde), 88.26 (acetaldehyde), 88.63 (propanal)
0
0
and 88.21 kcal/mol (butanal) with the order of D298
(C − H ) formaldehyde < D298
(C − H ) acetaldehyde <
0
0
D298
(C − H ) propanal > D298
(C − H ) bu tan al . Two calculated data of formaldehyde and
acetaldehyde are all in excellent agreement with the experimental values of 88.04 ± 0.16 and
89.4 ± 0.3 kcal/mol in previously published reference (Alvarez-Idaboy et al., 2001). This
discrepancy between our calculated data and experimental results (Jaffe et al., 1974) may be
explained that the activities of LMW aldehydes are not only relative to the aldehydic C-H
bond energy, but also affected by the steric effect and electronic effect of the alkyl group
within long-chain LMW aldehydes.
3.2.2. High Temperature Measurements
Since aldehydes and NO2 are all key important initial decomposition products in the
combustion of cyclic nitramine solid propellants (Xu et al., 2003), Thus, the reactions kinetics
of LMW aldehydes (C1–C4) with NO2 within the high temperature range of 360–2000 K was
also investigated in order to simulate this high temperature combustion processes. The total
CVT/SCT rate constants as well as the corresponding available experimental values (Christie
et al., 1967; Davis et al., 1972; He et al., 1989; Jaffe et al., 1974; Lin et al., 1990; Mcdowell et
al., 1950; Pedler et al., 1957; Pollard et al., 1949) are plotted in Fig. S3a–3d. For the reaction
of formaldehyde with NO2, the rate constants are consistent with the experimental values
obtained by Pollard et al (1949) within the temperature range of 391–457 K and by Lin et al.
(1990) within the temperature range of 1143–1653 K, while are somewhat lower than the
results measured by He et al. (1989) within the temperature range of 393–476 K. For example,
the fitted two-parameter expression from the CVT/SCT rate constants within 391–457 K is k
= 2.41 × 10-14 exp (–7812/T) cm3 molecule-1 s-1, in line with the experimental expression of k
= 2.16 × 10-14 exp (–7600/T) cm3 molecule-1 s-1 (Pollard et al., 1949). As shown in Fig. S3b,
for the reaction of acetaldehyde with NO2, our calculated rate constants are much closer to the
experimental values of Pedler and Pollard (1957) than those of Davis et al. (1972) and
Mcdowell et al. (1950). With respect to the reaction of butanal with NO2, our calculated
CVT/SCT values (Fig. S3d) are consistent with the only obtained experimental data by Jaffe
and Wan within the temperature range of 360–390 K (1974). For example, the CVT/SCT
value is 5.22 × 10-21 cm3 molecule-1 s-1 at 390 K, while the experimental result is 4.69 × 10-21
cm3 molecule-1 s-1.
Similar to the low temperature, the syn-RO-abs1 channel is still major pathway of the
reactions of LMW aldehydes (C1–C4) with NO2 within the temperature range of 360 to 2000
K (Fig. S4a–4d). However, the contribution of RN-abs1 channel can not be neglected within
higher temperature range. For example, for four LMW aldehydes (C1–C4), the branching
ratio of kN-abs1/k are 4%, 1%, 0% and 1% at 500 K, whereas are 45%, 7%, 3% and 14% at
2000 K, respectively. Thus, the acyl radical, syn-HONO and HNO2 are the dominated
products within high temperature range of 360–2000 K. Nevertheless, the formation of
HONO and HNO2 should be meaningful, because the isomerization reactions HONO
HNO2 should occur rapidly in the combustion conditions due to the low transformed energy
barrier of about 46 kcal/mol (Lu et al., 2000). Furthermore, the CVT/SCT rate constants also
increase with increasing carbon number of aldehydes in the high temperature (Fig. 6).
4. Environmental Implications
Aldehydes and NO2 are all the important air pollutants, which are almost ubiquitous in
the indoor and outdoor environment. Although the observed rate constant values for the
reactions of aldehydes with NO2 are smaller than those with OH in the troposphere, in some
special regions of the developing country, for example the Pearl River Delta, South China, the
NO2 emission is still huge and the pollution and reaction mechanism are still very significant.
Thus, the investigation of their reactions may be valuable for better understanding of air
pollution mechanism at the environmental temperature and the combustion possibility in
some extreme high temperature.
In this study, we put forward an effective method (BMC-CCSD) to predict the rate
constants and to probe the mechanisms of the atmospheric reactions of LMW aldehydes (C1–
C4) with NO2. The theoretical results found that the order of the reactivity for the reactions
calculated in this work is kformaldehyde < kacetaldehyde < kpropanal < kbutanal, implying that relative
long-chain LMW aldehydes are more reactive toward NO2 than those short-chain LMW
aldehydes in the atmospheric environment. From the mechanistic study, whether at the low or
high temperature range, the acyl radical and HONO are all found as the dominated
intermediates. In fact, the product HONO is considered as a harmful pollutant at atmospheric
environment due to its mutagenic and carcinogenic properties. First of all, the exposure of
HONO will influence the health of the lung function or eye-provocation at a short timescale
(Kleffmann, 2007). Secondly, due to chemically relatively stable, the primary product HONO
can be possibly accumulated at low temperatures (Lu et al., 2000), and thus may cause acid
deposition. Finally, HONO can be found as a major source of hydroxyl radical (•OH) close to
the ground surface during daytime (Kleffmann, 2007). And it is well known that •OH is the
major oxidant responsible for the degradation of most pollutants in the atmosphere and is thus
called the “detergent of the atmosphere”. Thus, the formation, identification and
quantification of HONO sources in atmospheric environment are all ongoing and significant
topic.
Acknowledgements
This is contribution No. IS-XXXX from GIGCAS. We thank Professor Donald G. Truhlar for
providing the POLYRATE program. This work was financially supported by the Science and
Technology Project of Guangdong Province, China (2009A030902003, 2011A030700003,
and 2009B091300023) and China Postdoctoral Science Foundation (201104371 and
20100480785).
Supporting information:
1) Detailed descriptions of the computational methods and comparison of method; 2) Details
0
and hardness; 3) Arrhenius formulas for
on frequencies for species, ΔH 0298 , PES profile, D298
each channel over the temperature range of 200–360 K and 360–2000 K. Supporting
information associated with this article can be found, in the online version, at doi: XXXX.
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Table 1
Calculated Modified Arrhenius Fit Parameters for k = ATn'e-B/T
a
b
T range
A
n'
reaction
a
B
formaldehyde + NO2 →
200–360
1.61 × 10-39
8.24
4380
products
360–2000
1.01 × 10-33
6.48
5477
acetaldehyde + NO2 → 200–360
products
360–2000
1.40 × 10-35
7.60
4663
1.25 × 10-28
5.06
5899
propanal + NO2 →
200–360
2.15 × 10-36
7.30
4767
products
360–2000
1.51 × 10-27
4.81
5947
butanal + NO2 →
200–360
6.17 × 10-36
7.70
4521
products
360–2000
4.72 × 10-27
4.89
5945
a
Units in Kelvin.
b
Units in cm3 molecule-1 s-1.
constant(Zheng et al., 2010).
c
B =
E
, E = Ea – nRT, R is the gas
R
FIGURE CAPTIONS
Fig. 1. Potential mechanisms for the reactions of formaldehyde with NO2 embedded with
molecular structure (in Å or °) and the energies (in kcal/mol). Structure is calculated at
the MPWB1K/6-311G(d,p) level of theory; the energies is calculated at the BMCCCSD//MPWB1K/6-311G(d,p) level of theory.
Fig. 2. Potential mechanisms for the reactions of acetaldehyde with NO2 embedded with
molecular structure (in Å or °) and the energetics (in kcal/mol) obtained at the BMCCCSD//MPWB1K/6-311G(d,p) level of theory. Structure is calculated at the
MPWB1K/6-311G(d,p) level of theory; the energies is calculated at the BMCCCSD//MPWB1K/6-311G(d,p) level of theory.
Fig. 3. Potential mechanisms for the reactions of propanal with NO2 embedded with
molecular structure (in Å or °) and the energies (in kcal/mol). Structure is calculated at
the MPWB1K/6-311G(d,p) level of theory; the energies is calculated at the BMCCCSD//MPWB1K/6-311G(d,p) level of theory.
Fig. 4. Potential mechanisms for the reactions of butanal with NO2 embedded with molecular
structure (in Å or °) and the energies (in kcal/mol). Structure is calculated at the
MPWB1K/6-311G(d,p) level of theory; the energies is calculated at the BMCCCSD//MPWB1K/6-311G(d,p) level of theory.
Fig. 5. Plot of the CVT/SCT rate constants calculated at the BMC-CCSD//MPWB1K and the
available experimental values vs 1000/T between 200 and 360 K for the reactions of (a)
formaldehyde with NO2, (b) acetaldehyde with NO2, (c) propanal with NO2, (d) butanal
with NO2. Exptl. 1 from (Davis et al., 1972); Exptl. 2 from (Christie et al., 1967); Exptl.
3 from (Jaffe et al., 1974).
Fig. 6. Plot of the CVT/SCT rate constants vs 1000/T between 200 and 2000 K for the
reactions of NO2 with LMW aldehydes (C1–C4).
1E-10
1E-10
a
1E-15
1E-15
3
-1 -1
rate constant (cm molecule s )
1E-20
1E-20
kCVT/SCT(CCSD(T)//MPWB1K)
1E-25
1E-25
1E-30
1E-30
kCVT/SCT
1E-35
1E-40
1E-10
Exptl. 1
kCVT/SCT
Exptl. 2
1E-35
acetaldehyde
formaldehyde
3.0
3.5
4.0
4.5
5.0
1E-40
3.0
3.5
4.0
4.5
5.0
--
c
1E-10
1E-15
1E-15
1E-20
1E-20
kCVT/SCT
1E-25
d
1E-25
1E-30
kCVT/SCT
Exptl. 2
1E-30
1E-35
1E-35
propanal
butanal
1E-40
b
3.0
3.5
4.0
4.5
5.0
1E-40
3.0
-1
1000/T (K )
3.5
4.0
4.5
5.0
Formaldehyde
Acetaldehyde
Propanal
Butanal
1E-15
1E-18
3
-1 -1
rate constant (cm molecule s )
1E-12
1E-21
1E-24
1E-27
1E-30
1
2
-1
1000/T (K )
3
4
5