Predictions of the sulfur and carbon kinetic isotope effects in the OH + OCS reaction

Chemical Physics Letters 531 (2012) 64–69

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Predictions of the sulfur and carbon kinetic isotope effects in the OH + OCS reaction J.A. Schmidt a,⇑, M.S. Johnson a, Y. Jung b, S.O. Danielache c, S. Hattori d, N. Yoshida d a

Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark Graduate School of EEWS, KAIST, Daejeon 305-701, Republic of Korea c Tokyo Institute of Technology, Department of Earth and Planetary Science, Meguro-ku, Tokyo 152-8551, Japan d Tokyo Institute of Technology, Department of Environmental Chemistry and Engineering, G1-17, Nagatsuta-cho, Yokohama 226-8502, Japan b

a r t i c l e

i n f o

Article history: Received 22 December 2011 In final form 14 February 2012 Available online 23 February 2012

a b s t r a c t The 34 S and 13 C isotopic fractionations in the OCS + OH reaction are investigated using RRKM-theory. The reaction proceeds via different channels, at low pressures a channel leading to CO + SOH dominates. While with increasing pressure an adduct forming channel becomes competitive. The resulting overall rate constant is not strongly dependent on pressure and agrees well with experiments. The competition between channels makes the fractionation constants highly pressure dependent, however the sulfur-34 fractionation constant varies only from about 5 ‰ to 0 ‰ in the troposphere and lower stratosphere. The carbon-13 isotopic fractionation is stronger; between 40 ‰ and 70 ‰ in the troposphere and lower stratosphere. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Carbonyl sulfide (OCS) has been recognized as an important constituent of the atmosphere since its discovery in tropospheric air [1]. The atmospheric mixing ratio of OCS has increased from 1 between 0.3 and 0.4 ppb (parts-per-billion i.e. nmol mol ) in pre-industrial times to about 0.5 ppb today making it the most abundant sulfur containing compound in the atmosphere [2,3]. Its sources include direct and indirect emission from the ocean and various anthropogenic sources e.g. from fuel combustion and coal gasification [4,5]. Other natural sources such as volcanoes and forest fires also contribute to the global OCS budget which currently has very large uncertainties [4,5]. OCS is relatively resistent to oxidation by OH and Oð3 PÞ. Despite this the OH reaction is the main sink of atmospheric OCS together with uptake by vegetation, soil and the ocean [5]. Photolysis of OCS is slow in the troposphere but becomes important in the stratosphere. Of the three in situ sinks (OH, Oð3 PÞ and photolysis) the reaction with OH is by far the strongest [4–6]. The tropospheric lifetime of OCS is long (1–6 years [4,7]) which allows OCS to be transported into the stratosphere [8] where the lifetime is even longer (64  21 years [9]). The atmospheric sink reactions lead to sulfur dioxide, and OCS is therefore a significant source of stratospheric SO2 . Crutzen [8] suggested that the conversion of this SO2 to sulfate would in turn be a significant non-volcanic background source of the stratospheric sulfate aerosol (SSA) layer [10]. This layer is important

⇑ Corresponding author. E-mail address: [email protected] (J.A. Schmidt). 0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2012.02.049

because it can enhance stratospheric ozone depletion [11] and influences Earth’s radiative balance [4,12]. Analysis of the distributions of stable isotopes in atmospheric trace gases provides additional information about sources, reactions and transport relative to what can be learned from species concentrations alone [13]. Given improvements in technology it is possible to obtain increasingly detailed isotopologue distributions from remote sensing data (e.g. Refs. [9,14]) in addition to what can be learned from in situ sampling (e.g. Refs. [15]). Another example is that the distributions of sulfur isotopes found in geological samples [16] and ice cores [17] are in some cases explained by atmospheric photochemistry. We have focused on isotope effects in the atmospheric sulfur cycle in a series of studies [6,16,18– 20]. One goal is to refine estimates of the sources of SSA to identify how human activity will effect this important element of the climate system. With regards to carbonyl sulfide, the distributions of 13C and 34S are of particular interest due to their abundance (1.1% and 4.4%, respectively) giving ease of detection, their varied kinetic isotope effects and in the case of sulfur its central role in the atmospheric sulfur cycle. There have been several experimental studies of the OH + OCS reaction [21–25]. Leu and Smith [23] measured the rate constant at low total pressure ( 2—5 mbar) between 300 and 520 K and found k ¼ ð0:6  0:4Þ  1015 cm3 s1 at 300 K. During the reaction both SH and HSO were detected. Intuitively one might expect the reaction to be similar to the CS2 + OH reaction which is known to form an adduct that may react with O2 [26]. Adduct forming reactions rely on third body collisional energy transfer and such reactions are therefore usually dependent on total pressure. Wahner and co-workers [25] studied the influence of temperature (245 and 298 K), total pressure and O2 partial pressure on the rate

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constant. Different bath gasses (He, N2 and SF6) were used and the total pressure was varied from 125 to 480 mbar while the O2 partial pressure was varied from 0 to 48 mbar. The rate constant (k ¼ ð1:96  0:25Þ  1015 cm3 s1 at 298 K) was found to be insensitive to both total pressure and O2 to within the experimental uncertainty. Cheng and Lee [24] measured the rate constant at low total pressures and different temperatures from 255 to 483 K. The rate constant (k ¼ ð2:0  0:8Þ  1015 cm3 s1 at 300 K) was found to be independent of total pressure and O2 at all temperatures. Wilson and Hirst [27] presented the first theoretical study of the reaction. Two reaction paths were located: the first path can be described as an addition reaction to the C@S double bond where the O atom of the hydroxyl radical forms a bond to the C atom in OCS forming an adduct. The adduct can either stabilize, dissociate backwards into the reactant channel or dissociate forward into a SH + CO2 product channel. They found the barrier for dissociation into the product channel to be very high and dissociation into this channel would therefore be slow even at high temperatures (500 K). The second reaction path can be described as metathesis where OH attacks the terminal S forming CO and SOH products. The barrier for this path is lower. A later study by Danielache et al. [6] used transition state theory to study the isotopic fractionation in the adduct forming channel in the high pressure limit, i.e. when any formed meta-stable adduct complex is immediately stabilized by collisions with the bath gas, and found that for this process sulfur isotopic fractionation is small. In this Letter we consider both the adduct forming channel and the CO + SOH forming channel and calculate the isotopic fractionation constant as a function of pressure and temperature. We also consider dissociation of the adduct into the CO2 + SH product channel.

angular momentum J, while Ni ðE; JÞ is the sum of states at the transition state leading into sub-channel Bi and h is Planck’s constant. The density of states and sum of states were calculated using the Extended Beyer Swinehart algorithm [30] (an energy grain size of 1 cm1 was used) and tunneling corrections were included using the method of Miller [31]. The relevant stationary points on the ground state potential energy surfaces (PES) were located using the CCSD method [32,33] and the aug-cc-pVTZ orbital basis set. [34,35] The structures are shown in Figure 1 (the structures in the ‘‘xyz’’ file format are included in Supporting information). Harmonic vibrational frequencies at the stationary points were obtained using the same level of theory for all relevant isotopologues and are given in Supporting information. The calculated vibrational frequencies and rotational constants for the different isotopologues of OCS are compared to experimental values in Table 1. The reaction barriers were refined by performing single point CCSD(T) [36,37] calculations at the obtained reactant, transition state and product geometries using the aug-cc-pVTZ and aug-cc-pVQZ [34,35] basis sets followed by extrapolations to the complete basis set limit using the scheme of Halkier et al. [38] The energies with and without zero point energy (ZPE) correction are given in Table 2. All computational

2. Methodology Two reaction channels are important for the OH + OCS reaction [27]. First, OH radical attack on the S-atom can lead to rupture of the SAC bond (channel A),

OH þ OCS ! SOH þ CO Alternatively OH can add into one of the double bonds in OCS and form a ro-vibrationally excited adduct where OH is bound to the C atom which may then react further (channel B),

OH þ OCS ! OCðOHÞS ! productðsÞ The excited adduct will either redissociate into the reactant (subchannel B1),

OCðOHÞS ! OH þ OCS dissociate into a product channel (sub-channel B2),

OCðOHÞS ! CO2 þ SH or be collisionally stabilized (sub-channel B3),

OCðOHÞS þ M ! OCðOHÞS þ M

Figure 1. Critical points on the OCS + OH potential energy surface. Relevant points for channels (A) and (B) are shown in Panel (a) and (b), respectively.

Low pressure will make bath collisions less likely and thus favor dissociation (i.e. sub-channel B1 and B2), while at sufficiently high pressures sub-channel B3 will dominate over B1 and B2. The rate constant for dissociation into the reactants (B1) and products (B2) can be calculated using the RRKM approximation [28,29],

ki ðE; JÞ ¼

Ni ðE; JÞ ; h qðE; JÞ

ð1Þ

where the index i is either 1 (sub-channel B1) or 2 (sub-channel B2) and qðE; JÞ is density of states of the adduct at energy E and total

Table 1 The vibrational frequencies (mi ) and rotational constants (B) for the isotopologues of OCS. All values are in cm1 and the numbers in parenthesis are experimental values [42,43]. Species

m1

m2

m3

B

O12C32S O12C34S O13C32S

538.7 (520.2) 537.9 (519.4) 522.7 (504.8)

876.0 (866.4) 864.1 (854.7) 871.0 (862.1)

2131.3 (2062.2) 2130.7 (2061.4) 2076.3 (2009.2)

0.202 (0.203) 0.197 (0.198) 0.202 (0.202)

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Table 2 1 The electronic energies and the ZPE corrected energies (in kJ mol ) of the critical geometries for the different isotopes. Ee OCS + OH TS1 TS2 TS3 Adduct SH + CO2 CO + SOH

0.00 13.18 50.48 19.15 124.44 147.20 15.26

E0 ð12 C;32 SÞ

E0 ð12 C;34 SÞ

E0 ð13 C;32 SÞ

46.90 68.10 96.95 73.07 59.64 – –

46.81 68.01 96.91 72.99 59.71 – –

46.35 67.62 96.36 72.75 60.28 – –

2.1. Isotopic fractionation The enrichment of a given isotope, e.g. 34S, in a sample is commonly quantified in terms the relative isotope ratio difference (or isotope delta) defined as,

chemistry calculations were carried out using the MOLPRO 2010.1 program package ([39]). The channel A rate constant can be calculated using transition state theory with the Wigner tunneling correction. In the high pressure limit (when B3 completely dominates B1 and B2) the channel B rate constant can also be calculated using this approach (cf. Chapter 8 of Ref. [29]),

Z 1 X 1 dE NðE; JÞ eE=kT ; hQR J 0

ð2Þ

where Q R is the partition function of the reactants and NðE; JÞ is the sum of states at the relevant transition state. Note that in Eq. (2) and the equations that follow the energy is normalized such that the zero point energy of the reactant pair is 0. At sufficiently low pressures sub-channel B3 can be ignored and a competition exists between dissociation into B1 and B2. The branching ratio for dissociation into product channel B2 is,

k2 ðE; JÞ N 2 ðE; JÞ ¼ : k1 ðE; JÞ þ k2 ðE; JÞ N1 ðE; JÞ þ N2 ðE; JÞ

kB2

ð3Þ

As will be shown below sub-channel B2 can be ignored under atmospheric conditions (temperature ranging from 200 to 300 K and pressure from 1 to 1000 mbar). In the low pressure limit the overall Channel B rate becomes proportional to the bath gas number density, ½M, and a termolecular rate constant can be calculated using [29],

k0 ¼

Z x X QR

J

R  1; Rref

ð6Þ

where 34 Rref is the ½34 S : ½32 S ratio in a reference, with Vienna Canyon Diablo Troilite (VCDT) being a typical reference for sulfur. A relative isotope ratio difference for carbon-13 (d13 C) can be defined in a similar way. The potential of a reaction, e.g. OH + OCS, to produce isotopic enrichment or depletion in a resovoir species such as OCS is commonly quantified using the isotopic fractionation constant, 34

34

¼

k  1; k

ð7Þ

where k and 34 k are the rate constants associated with the OH + O12 C32 S and OH + O12 C34S reactions, respectively. A carbon13 fractionation constant (13) can be defined in a similar way. Since both d 34S, d 13C, 34 and 13 are typically quite close to zero it is common to denote them in units of per mil (‰). 3. Results and implications

At low pressures the rate constant for producing SH + CO2 can therefore be obtained using,

Z 1 X 1 N 1 ðE; JÞN2 ðE; JÞ E=kT ¼ dE : e hQR J N1 ðE; JÞ þ N2 ðE; JÞ 0

34

d34 S ¼ 34

Figure 2 shows the unimolecular rate constants for dissociation into sub-channels B1 and B2. Below the barrier for dissociation into 1 B1 ð 21 kJ mol ) the rate constant is tunneling controlled and decreases exponentially with lower energy. Redissociation into reactants is several orders of magnitude faster than dissociation 1 into products at the important energies around  21 kJ mol due to the much higher barrier for dissociation into B2, see Table 2. The B2 rate constant is therefore very small (1:54  1018 cm3 s1 at 300 K). Note that the B2 rate constant becomes comparable to the rate constant for forming the adduct at pressures on the order

1

dE qðE; JÞ eE=kT ;

ð4Þ

9

10

0

where x is the bimolecular collision rate for the adduct colliding with N2 (the most likely bath gas molecule) in units of cm3 s1 . Note that k0 is given in units of cm6 s1 and ½Mgk0 yields a rate constant in cm3 s1 , where g is collision efficiency and ½M is the bath gas density. The channel B rate constant in the intermediate pressure range can be obtained using the formula introduced by Troe [40] to interpolate between the high and low pressure limits, 2 1 ½Mgk0 kð½MÞ ¼ F ð1þlog10 ð½Mgk0 =k1 Þ Þ ; 1 þ ½Mgk0 =k1

8

10

ki(E;J) / s-1

kTST ¼ k1 ¼

reaction at intermediate pressure would be obtained by setting up an energy transfer model and solving the Master Equation (cf. Ref. [29]). The Troe formula approach is attractive due to its ease of use and its cost in terms of computer resources. In all cases the rate constants were calculated using our STATRATE program package.

k1(E;J)

7

10

6

10

ð5Þ k2(E;J)

5

where F depends both on temperature and the reaction in question, however under atmospheric conditions F is nearly temperature independent and approximately equal 0:8. We fix F to 0:6 since this has been found to work well for a large number of reactions [41]. The use of the Troe formula is crude in the sense that it does not take into account detailed isotope effects between the adduct and bath gas at intermediate pressure (it merely interpolates between high and low pressure). A more sophisticated description of the

10

4

10

10

15

20

25

30

35

E / kJ mol-1 Figure 2. The unimolecular rate constants (Eq. (1)) for dissociation into the reactant (B1) and HS + CO2 product (B2) channels for J = 0 (full line) and J = 30 (broken line).

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(a)

(a) -16

4

4.2

1.5 1 0.5

4.4

T-1 / 10-3 K-1

0 200

3

k / 10-16 cm3 s-1

2.5

kA + kB

(b)

2

1

kA

0.5 0 0 10

3

220

240 260 T/K

280

300

0

2.5

1.5

kB

1

T = 300 K 2

10

10

3

10

P / mbar Figure 3. The rate constants for the different reaction channels as a function of temperature (Panel (a)) and pressure (Panel (b)). kA and kB were calculated using Eqs. (2) and (4), respectively.

of 1 mbar, however at such low pressures the A channel rate constant is orders of magnitude faster and will dominate, and the B2 sub-channel can therefore be ignored. Figure 3 shows the overall rate constant and rate constants for channel A and B as functions of temperature (upper panel) and pressure (lower panel). Channel B is slightly dominant around 1 bar but as the pressure is lowered channel A quickly becomes dominant. At standard conditions the calculated total rate constant is 0:28  1015 cm3 s1 which compares well with room temperature experimental values of ð0:6  0:4Þ  1015 cm3 s1 [23], ð2:0  0:8Þ  1015 cm3 s1 [24] and ð1:96  0:25Þ  1015 cm3 s1 [25]. Note that these experiments were often performed at low pressures (e.g. 5 mbar [23]) and no pressure dependence was observed. Our calculations are consistent with this observation and show only minor pressure dependence changing by less than a factor of 3 from 1 to 1000 mbar. Around 5 mbar the calculations show almost no pressure dependence. Figure 4 shows contours of the overall rate constant (upper panel) and 34S fractionation constant (lower) as functions of pressure and temperature. The temperature variations observed in the troposphere and stratosphere have a larger effect on the overall rate constant than the variations in pressure, as shown by the almost vertical contour plot in Figure 4a. However, the opposite is true for the fractionation constant which is largely independent of temperature but significantly dependent on pressure due to competition between the different reaction channels, as shown by the almost horizontal contour plot in Figure 4b. The simple (TST type) barrier crossing reactions such as channel A and channel B in the high pressure limit have negative fractionation constants. The reduced reactivity of the heavy isotopes can in part be explained by changes in the vibrational zero point energy of the reactants and transition states which increases the height of the reaction barrier and partly by the reactant density of states which is higher for the heavy isotopes thereby increasing the reactant partition function (see Eq. (2)). In contrast channel B in the low

log10(p / mbar)

(b)

1e-16

3.8

2

7 1e-1

3.6

-16

7

18

3.4

1e

-1

1e-

kA

-18

10

log10(p / mbar)

k / cm3 s-1

kB (0.1 bar)

-17

10

1e

2.5

kB (1 bar)

10

3

-6

20

-6 1.5

-6

-12

1 0.5 -18 0 200

-12

-12

-18 -18

220

240 260 T/K

280

300

Figure 4. Panel (a) shows contour plots for the total rate constant (kA þ kB ) in units of cm3 s1 and Panel (b) shows the 34S fractionation constant in ‰ (Eq. (7)) in both panels as functions of temperature and pressure.

pressure limit has positive fractionation constant ð34  ¼ 16‰ and 13  ¼ 32‰ at 300 K). At low pressure a competition exists between stabilization and redissociation of the ‘‘hot’’ adduct. The energy spacing between the ro-vibrational states of adduct is smaller for the heavy isotopes and they therefore have larger density of states which lowers the redissociation rate and thus increases the chance of a stabilizing collision which results in a positive fractionation constant. At 1 mbar channel A dominates making the fractionation constant very negative but as the pressure is increased channel B becomes more important and the fractionation constant increases (Figure 4b). To see how the 34S and 13C fractionation constants change approximately throughout the troposphere and stratosphere we calculated 34  and 13  as a function of altitude using the US Standard Atmosphere. The temperature and pressure profiles of the atmosphere are shown along side the fractionation constants in Figure 5. As seen in Panel (c) of the figure, the sulfur-34 fractionation constant is small below 20 km, between 0‰ and 5‰. In the troposphere (at high pressure) where the adduct forming channel dominates the fractionation constant is very close to zero. In the stratosphere the magnitude of 34  is larger but here the OH + OCS reaction is less important due to photolysis, which is the most important OCS sink in the stratosphere. In all it is seen that the OH + OCS reaction produces only moderate sulfur isotopic fractionation. This suggests that the pool of OCS that is transported to stratosphere (i.e. avoids oxidation in the troposphere) will carry an sulfur isotopic signature that is very similar to that of tropospheric OCS. The carbon-13 isotopic fractionation (Panel (d)) is stronger; around 40‰ in the troposhere and decreasing to between 50‰ and 70‰ in the lower stratosphere. Thus, simultaneous measurements of the vertical profiles of d 13C(OCS) and

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J.A. Schmidt et al. / Chemical Physics Letters 531 (2012) 64–69

(a)

(b)

40

z / km

30 20 10 0

(c)

0

200

400 600 P / mbar

800

1000

200

220

240 260 T/K

280

300

-80

-70

-50

-40

(d)

40

z / km

30 20 10 0 -20

-15

-10

-5

0

-90

34

Figure 5. The pressure (Panel (a)), temperature (Panel (b)), standard atmosphere.

34

-60

13

ε / per mil

ε / per mil

S fractionation constant (Panel (c)) and

13

C fractionation constant (Panel (d)) as function of altitude in the US

d 34S(OCS) would provide information on the relative contributions of the OCS sink reactions and on the amount and isotopic composition of resulting sulfate aerosols.

Culture, Sports, and Technology (MEXT), Japan. S.H. is supported by Grant in Aid for JSPS Research Fellows (DC1 (No. 22-7563)) and Global COE program ‘Earth to Earths’ of MEXT, Japan.

4. Conclusions

Appendix A. Supplementary data

The OH + OCS reaction can proceed via a pressure independent metathesis channel (A) and pressure dependent adduct forming channel (B). Both channels were considered in this study using RRKM theory. The calculated overall rate constant at room temperature is weakly pressure dependent (approximately 0:2  1015 cm3 s1 and 0:3  1015 cm3 s1 at 0.2 and 1.0 bar, respectively) and compares fairly well with experimental room temperature rate constants obtained at different pressures. Using the US standard atmosphere, this study predicted the sulfur-34 isotopic fractionation in the troposphere and lower stratosphere to be weak (between 0 and 5‰) while carbon-13 fractionation is stronger (around 40‰ in the troposhere and decreasing to between 50 and 70‰ in the lower stratosphere). Since the reaction with OH is the most important sink for OCS in the troposphere the results of this study suggest that OCS transported to the stratosphere will carry an S-isotope abundance similar to that of tropospheric OCS.

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2012.02.049.

Acknowledgments We gratefully acknowledge the excellent feed-back and suggestions provided to us by an anonymous reviewer. We thank the IntraMIF project in the European Community’s Seventh Framework Programme (FP7/2007-1013) under Grant Agreement No. 237890 for support. Y.J. acknowledges the support of WCU Program (R31-2008-000-10055-0) through the NRF of Korea. S.O.D., S.H. and N.Y. are supported by Global Environmental Research Fund (A-0904) of the Ministry of the Environment, Japan, and Grant in Aid for Scientific Research (S) (23224013) of Ministry of Education,

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