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Chemical Physics Letters 450 (2008) 214–220

Ab initio study of sulfur isotope fractionation in thereaction of OCS with OH

Sebastian O. Danielache a,*, Matthew S. Johnson b, Shinkoh Nanbu c, Mette M.-L. Grage b,Chris McLinden d, Naohiro Yoshida a,e,f

a Department of Environmental Science and Technology, Interdisciplinary Graduate School of Science and Engineering,

Tokyo Institute of Technology G1 25, 4259 Nagatsuta, Midori-ku Yokohama City, Kanagawa Prefecture 226-8502, Japanb Department of Chemistry, University of Copenhagen, Copenhagen, Denmark

c Computer and Communication Center, Kyushu University, Station-II for Collaborative Research, Maidashi 3-1-1, Higashi-ku, Fukuoka 812-8512, Japand Meteorological Service of Canada, Downsview, Ont., Canada

e SORST Project, Japan Science and Technology Agency (JST), 4-1-8 Hon-cho, Kawaguchi, Saitama, 332-0012, Japanf Department of Environmental Chemistry and Engineering, Interdisciplinary Graduate School of Science and Engineering,

Tokyo Institute of Technology, 4259 Nagatsuta, Yokohama 226-8502, Japan

Received 30 August 2007; in final form 11 November 2007Available online 24 November 2007

Abstract

The fractionation of sulfur isotopes in the gas-phase reaction of OCS with OH was calculated by ab initio methods. The first reactionstep occurs through a carbon bonded OH–OCS transition state. The activation barrier is 18.4 kJ mol�1 (CCSD(T)/aug-cc-pVDZ levelplus zero-point energy) relative to the reactants. Fractionation constants are �1.4, �2.6 and �6.3‰ for 33S, 34S and 36S respectively.These results bring new insight regarding the origin of stratospheric sulfate aerosols, including the identification of characteristic isotopicfractionations in the lower and middle stratosphere.� 2007 Elsevier B.V. All rights reserved.

1. Introduction

Carbonyl sulfide (OCS) is the most abundant sulfurcompound in the atmosphere. Its reaction with OH isimportant because it represents 80% of the total chemicalsink in the troposphere [1]. The O(3P) reaction plays aminor role in the stratosphere, while photolysis becomesdominant with increasing altitude. The stratospheric sul-fate aerosol (SSA) layer occurs between 17 and 30 km [2].The so-called Junge layer affects the planet’s Albedo andcatalyses the hydrolysis of N2O5, promoting mid-latitudeozone depletion [3]. While volcanic eruptions are an impor-tant source of stratospheric sulfate, they are sporadic andthe source of sulfur in volcanically quiescent times is a mat-ter of debate [1,4]. OCS photolysis is the traditional candi-

0009-2614/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2007.11.054

* Corresponding author. Fax: +84 45 924 5517.E-mail address: Sebastian.d.aa@m.titech.ac.jp (S.O. Danielache).

date [5,6] for the source of SSA. However, some havesuggested that lower stratospheric sulfate aerosols areproduced by SO2 and not by OCS [4]. It has been proposedthat biomass burning affects the amount of OCS enteringthe stratosphere through the tropical tropopause [7].Kinetic isotope effects (KIEs) can provide important addi-tional information concerning the source of SSA. Measure-ments by Leung et al. [7] show a d34S imbalance betweenthe OCS input in the lower stratosphere and SSA if theonly source is OCS photolysis.

The balance between the isotopic enrichment of OCSsources (ocean, soil, biomass burning, CS2 oxidation, etc.)and the fractionation of its loss (vegetation, OH, strato-sphere) determines the distribution of stable isotopes in thetropospheric OCS that is transported to the stratospherewhere it is oxidized to sulfate. In this study we examine therate constant and KIEs for the reaction of the four mostcommon OCS isotopologues with OH using ab initio methods.

Table 1Calculated and experimental bond distances of reactants and finalproducts calculated at MP2/cc-pTVZ, MP2/aug-cc-pTVZ andCCSD(T)/aug-cc-pVDZ (A)

OCS SH OH CO2

OC SC

Expa 1.154 1.563 1.340 0.990 1.164MP2/cc-pVTZ 1.168 1.566 1.339 0.967 1.169MP2/aug-cc-pVTZ 1.169 1.566 1.340 0.969 1.170CCSD(T)/aug-cc-pVDZ 1.173 1.593 1.361 0.980 1.178

a Ref. [33].

S.O. Danielache et al. / Chemical Physics Letters 450 (2008) 214–220 215

Leu and Smith [8] studied the OCS + OH reaction usingdischarge-flow resonance and reported k(298 K) =(6 ± 4) � 10�16 cm3 molecule�1 s�1 and Ea = 20 kJ mol�1;Cheng and Lee [9] reported k = (2 +0.4 �0.8) �10�15 cm3 molecule�1 s�1; Ea = 10 kJ mol�1. Wahner andRavishankara [10] reported k = (1.92 ± 0.25) � 10�15

cm3 molecule�1 s�1 at 298 K from experiments carriedout with pulsed laser-induced fluorescence. The determina-tion of Kurylo and Laufer [11] of (5.66 ± 1.21) �10�14 cm3 molecule�1 s�1 is one of the earliest reports.Experiments by Cheng and Lee [9] and by Wahner andRavishankara [10] are used by IUPAC [12]; k(298 K) =2 � 10�15 cm3 molecule�1 s�1.

There is extensive literature on the application of transi-tion state theory (TST) to isotopic KIEs [13]. A recentstudy examines 34S isotope effects for SO2 + OH [14]. Aseries of isotope effects have been examined by Nielsenand co-workers, see for example [15]. We set out to calcu-late the KIE of the title reaction by calculating the poten-tial energy surface for OCS + OH ? SH + CO2, makinguse of high-level of quantum mechanical methods. Theminimum energy path was confirmed and used to studythe KIEs of the sulfur isotopologues. The implications ofthe results on our understanding of the stratospheric Scycle are discussed.

2. Computational details

Identification of products has been guided by experi-ments [11]. Transition states for the channels leading toSH have been published [16]. A portion of the potentialenergy surface (PES) was re-examined to obtain vibrationalfrequencies and energies. Structures were calculated at theMP2/cc-pVTZ and MP2/aug-cc-pVTZ levels. QST3 andintrinsic reaction coordinate (IRC) calculations confirmedthat the structures connect the reactants and the products.The IRC was computed using mass-weighted Cartesiancoordinates (0.02 amu1/2 Bohr step size). Once the transi-tion states were confirmed, systems were recalculated atthe CCSD/cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels.The structures were also optimized at high levels of theorywith basis sets that reach our computational limits,CCSD(T)/aug-cc-VDZ. All calculations were carried outusing GAUSSIAN 03 [17] and Dunning’s correlation consis-tent cc-pVTZ, aug-cc-pVDZ and aug-cc-pVTZ basis sets.The analysis of the recalculated energy surface applies onlyto 32S. It was assumed that the potential energy surfacedoes not change for different isotopologues, in accordancewith the Born–Oppenheimer approximation. The 32Sgeometries were used in recalculating the isotopologueproperties. The dynamic calculations were carried outusing zero order interpolated transition state theory [18]using the geometries and vibrational frequencies from theab initio calculations. The rate coefficients were calculatedusing improved canonical variational theory [18]. Contri-butions from tunneling were estimated using zero-curva-ture tunneling. The POLYRATE [19] program was used in

the direct dynamic calculations. The methodology is simi-lar to previous work [20,14].

3. Results and discussion

The calculated geometries (Table 1 and Fig. 1) and vibra-tional frequencies for SH, OH, CO2, TS1, TS2, the adductand OCS isotopologues are compared with the availableexperimental data. Calculated vibrational frequencies aretabulated in Table 2 without corrections (vibrational fre-quencies of CO2, OH, SH, TS1, Adduct and TS2 and areavailable as additional information). Calculated propertiesare in good agreement with experimental data and witheach other. Optimized structures at CCSD(T)/aug-cc-VDZ (Fig. 1) are within 0.1 A and calculated frequenciesare within a maximum difference of 50 cm�1 and an averageerror of 27.87 cm�1, 11.05 cm�1, 13.02 cm�1, 13.15 cm�1

for CSSD/cc-pVTZ//MP2/cc-pVTZ, CCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZ, CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVDZ levels respec-tively. The values in parenthesis in Table 2 show the differ-ence in vibrational energy for each isotopologue comparedto 16O12C32S. These comparisons show the ability of thetheoretical method to reproduce the change in vibrationalenergies in isotopologues regardless of the absolute differ-ence between theory and experiments, an important pointwhen kinetic isotopic constants are calculated. It was con-firmed that the largest variation of each TS1 calculated iso-topologue is the vibrational mode corresponding to thesulfur atom (m6 for CCSD/cc-VTZ//MP2/cc-VTZ and m7

for the other calculations). Based on these results wesearched the relevant region of the PES. The reaction isassumed to follow the mechanism summarized in Fig. 2[11,8,16]. Previously published experimental activationenergies are in disagreement by 10 kJ mol�1, the currentlyaccepted value is Ea = 10 kJ mol�1 [8]. The electronic ener-gies and zero-point energies (ZPEs) of the stationary pointsat different theoretical levels and the results of Wilson andHirst [16] are summarized in Table 3. Our results (cf.Fig. 3 and Table 3) show that the energies calculated atCCSD/cc-pVTZ//MP2/cc-pVTZ exceed the literature andthe experimental data. However the results improved whenhigher levels of theory and larger basis set were employed.The energy obtained for TS2 (optimized using CCSD(T)/aug-cc-pDVZ) was smaller than theoretical values in the

Fig. 1. Optimized geometries of CO2, OCS, OH, SH, TS1, TS2 and adduct at CCSD(T)/aug-cc-pTZV. Bond lengths are in Angstroms and angles are indegrees experimental values in brackets [30]. The dihedral angle of TS1 (H–O–C–S) is �79.2�.

216 S.O. Danielache et al. / Chemical Physics Letters 450 (2008) 214–220

literature [16]. Our calculations confirm that OH attacks thecarbon atom to produce the adduct (M1) via TS1, whichhas a barrier height of 18.4 kJ mol�1 (CCSD(T)/aug-cc-pVDZ). The adduct was planar with the OH orientedtoward sulfur. TS1 is the only non-planar structure(Fig. 1) involved with the OH above plane with a dihedralangle (H–O–C–S) of �79.2�, and the angle between OHand carbon atom (H–O–C), 102.9�. There is an internalrotation of OH toward the sulfur atom that links TS1 toM1. Although an adduct with OH oriented toward the oxy-gen atom has been reported [16] our IRC calculations (MP2level) connect TS1 with M1. Decomposition of M1 pro-ceeds by internal transfer of the hydrogen atom from OHto sulfur via a planar four-membered cyclic intermediatetransition state with the hydrogen atom shared betweenthe oxygen and sulfur atoms (Fig. 1, TS2). The energyrequired is larger than that for the formation of M1(48.9 kJ mol�1 at CCSD(T)/aug-cc-pVDZ) even thoughinternal hydrogen transfer is faster than would be expectedfrom classical kinetics, due to tunneling. Once the energysurface was established, structures containing sulfur(OCS, TS1 and M1) were recalculated at the same theoret-ical levels and basis set to obtain the thermochemical prop-erties of the sulfur isotopologues. The Born–Openheimer

approximation was used as we assumed that the surface isinvariant to isotopic substitution. The POLYRATE program[19] made possible zero order interpolated variational tran-sition state theory [18] calculations to determine reactionrates k. The calculated reaction rates at different levels oftheory for 16O12C32S are summarized in Table 4a. The highactivation energy of TS1 obtained using CCSD/cc-pVTZ//MP2/cc-pTVZ produces a very small reaction rate(8.4 � 10�21 cm3 molecule�1 s�1). Increasing levels of the-ory reduce the activation energy to a value of approximately18 kJ and reaction rates to ca. 10�17 cm3 molecule�1 s�1

which resembles previously published theoretical values[16]. Calculations at CCSD(T)/aug-cc-pVDZ of the secondbarrier results in energies that are lower than the data in theliterature [16]. The calculated reaction rate for this barrier(Table 4b) presents a large tunneling effect of a factor of43 and a rate constant of 7.47 � 10�20 cm3 molecule�1 s�1.This rate constant is too small to give a realistic picture ofthe intra-molecular hydrogen transfer process. The experi-mental evidence [8] of SH formation as a reaction productand our results suggest that SH separation from the adductwould have to occur from a vibrationally excited state of theintermediate adduct. The analysis of this possibility isbeyond the scope of this work and may be the objective

Table 2Calculated and experimental frequencies of OCS and several of its isotopologues calculated at different theoretical levels (cm�1)

OC stretching CS stretching Bending

16O12C32S

Exp 2062.20a 866.37b 520.20b

CCSD/cc-pTVZ//MP2/cc-pVTZ 2047.42 880.77 572.79CCSD(T)/aug-cc-pTVZ//MP2/cc-pVTZ 2053.25 879.84 530.83CCSD(T)/aug-cc-pTVZ//MP2/aug-cc-pVTZ 2048.00 878.83 532.63CCSD(T)/aug-cc-pVDZ 2046.65 851.30 510.51

16O12C34S

Exp 2061.45 (0.756) 854.74b (11.629) 519.42b (0.773)CCSD/cc-pTVZ//MP2/cc-pVTZ 2046.70 (0.712) 868.91 (11.862) 572.18 (0.607)CCSD(T)/aug-cc-pTVZ//MP2/cc-pVTZ 2052.46 (0.792) 868.03 (11.814) 530.16 (0.673)CCSD(T)/aug-cc-pTVZ//MP2/aug-cc-pVTZ 2047.20 (0.797) 867.03 (11.798) 531.97 (0.665)CCSD(T)/aug-cc-pVDZ 2045.98 (0.668) 839.81 (11.482) 509.74 (0.773)

16O13C32S

Exp 2009.23a (52.973) 862.10b (4.263) 504.80b (15.393)CCSD/cc-pTVZ//MP2/cc-pVTZ 1993.39 (54.028) 876.28 (4.490) 556.15 (16.633)CCSD(T)/aug-cc-pTVZ//MP2/cc-pVTZ 1998.66 (54.591) 875.53 (4.307) 515.25 (15.587)CCSD(T)/aug-cc-pTVZ//MP2/aug-cc-pVTZ 1993.52 (54.486) 874.54 (4.287) 517.01 (15.628)CCSD(T)/aug-cc-pVDZ 1992.87 (53.779) 846.86 (4.437) 495.32 (15.193)

17O12C32S

Exp 2043.07b (19.134) 848.11b (18.254) 517.55b (2.646)CCSD/cc-pTVZ//MP2/cc-pVTZ 2028.59 (18.821) 869.47 (11.295) 569.02 (3.769)CCSD(T)/aug-cc-pTVZ//MP2/cc-pVTZ 2034.76 (18.493) 868.39 (11.447) 527.58 (3.253)CCSD(T)/aug-cc-pTVZ//MP2/aug-cc-pVTZ 2029.59 (18.412) 867.38 (11.448) 529.35 (3.285)CCSD(T)/aug-cc-pVDZ 2027.60 (19.045) 840.47 (10.821) 507.67 (2.848)

18O12C32S

Exp 2026.15a (36.054) 845.11b (21.254) 514.77b (5.423)CCSD/cc-pTVZ//MP2/cc-pVTZ 2011.98 (35.433) 858.91 (21.859) 565.66 (7.122)CCSD(T)/aug-cc-pTVZ//MP2/cc-pVTZ 2018.44 (34.813) 857.70 (22.144) 524.68 (6.149)CCSD(T)/aug-cc-pTVZ//MP2/aug-cc-pVTZ 2013.34 (34.659) 856.68 (22.147) 526.43 (6.208)CCSD(T)/aug-cc-pVDZ 2010.77 (35.874) 830.36 (20.940) 505.13 (5.383)

18O13C32S

Exp 1971.76b (90.441) 843.41b (22.956) 499.41b (20.787)CCSD/cc-pTVZ//MP2/cc-pVTZ 1956.53 (90.890) 855.34 (25.432) 548.81 (23.975)CCSD(T)/aug-cc-pTVZ//MP2/cc-pVTZ 1962.44 (90.809) 854.28 (25.557) 508.91 (21.924)CCSD(T)/aug-cc-pTVZ//MP2/aug-cc-pVTZ 1957.46 (90.547) 853.29 (25.541) 510.61 (22.027)CCSD(T)/aug-cc-pVDZ 1955.59 (91.058) 826.80 (24.496) 489.76 (20.750)

The values in parenthesis show the deviation between a given isotopologue and the respective value for 16O12C32S.a Ref. [34].b Ref. [35].

OC

S

OH

OCS + OH

O C S

O

H

O

C S

O H

S + C

OC

S

OH

H O2

TS 1

TS 2

Fig. 2. Reaction scheme for the studied reaction mechanism all structuresare planar except TS1 where the dihedral angles (H–O–C–S) is �79.2�.

Table 3Enthalpy of activation TS1, TS2 and Adduct energy relative to reactantsat 298 K calculated at different theoretical levels for the OCS + OHreaction (kJ mol�1)

Theoretical method TS1 Adduct TS2 Products

G2//MP2/6-311Ga 21.08 �74.79 53.75 �149.93CCSD/cc-pTVZ//MP2/cc-pVTZ 38.46 �92.42 80.37 �156.93CCSD(T)/aug-cc-pTVZ//

MP2/cc-pVTZ17.81 �94.99 56.83 �148.27

CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ

18.46 �101.10 56.84 �148.11

CCSD(T)/aug-cc-pVDZ 18.44 �89.26 48.86 �144.52Experimental 10b

a Ref. [16].b Ref. [8].

S.O. Danielache et al. / Chemical Physics Letters 450 (2008) 214–220 217

of future investigations. Further, we do not anticipate thatthis process is associated with a significant isotope effect.

Working on the assumption that the adduct formation isthe rate determining step, the reaction rates calculated using

Adduct

TS1

TS2

OCS + OH

CO2 + SH

-200

-150

-100

-50

0

50

100

Rel

ativ

e ch

ange

in e

ntha

lpy

(kJ

mol

-1)

LiteratureCCSD/cc-pTVZ//MP2/cc-pVTZCCSD(T)/aug-cc-pTVZ//MP2/cc-pVTZCCSD(T)/aug-cc-pTVZ//MP2/aug-cc-pVTZCCSD(T)/aug-cc-PVDZ

Fig. 3. Schematic diagram of the potential energy curves of the reaction OCS + OH CO2 + SH. The values are given by several levels of theory inkJ mol�1 plus ZPE. G2//MP2/aug-cc-pVTZ energies are adapted from literature [16].

Table 4aReaction rates k calculated at different theoretical levels and basis set forTS1, theoretically calculated rate available in the literature and experi-mental data (cm3 molecule�1 s�1)

Theoretical method Reaction rate

G2//MP2/6-311**a 9.8 � 10�17

CCSD/cc-pVTZ//MP2/cc-pVTZ 8.42 � 10�21

CCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZ 3.48 � 10�17

CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ 7.06 � 10�17

CCSD(T)/aug-cc-pVDZ 8.22 � 10�17

Experimentalb 2 � 10�15

a Ref. [16].b Ref. [11].

Table 4bReaction rates (TST) k and zero-curvature tunneling coefficient (ZCT)calculated at different theoretical levels and basis set for TS2(cm3 molecule�1 s�1)

Theoretical method TST TST*ZCT

CCSD/cc-pVTZ//MP2/cc-pVTZ 7.55 � 10�27 2.84 � 10�24

CCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZ 1.02 � 10�23 8.98 � 10�22

CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ 3.09 � 10�21 4.91 � 10�20

CCSD(T)/aug-cc-pVDZ 1.73 � 10�21 7.47 � 10�20

218 S.O. Danielache et al. / Chemical Physics Letters 450 (2008) 214–220

TS1 have a discrepancy of a factor of 23.4 while the activa-tion energy compares very well with the experimental valuesand also with previously published theoretical data [16].Since the purpose of this study is to determine the sulfurKIEs, it is important to verify the change of ZPE and vibra-tional energy of the isotopologues (OCS, TS1, Adduct).Fig. 4 shows the rate of change of ZPE relative to 32S.The linear change in ZPE can be confirmed for most theo-retical levels and molecules. An appreciable difference inthe ZPE change ratio can be observed in the change of

ZPE of the adduct molecule calculated at CCSD(T)/aug-cc-VTZ//MP2/aug-cc-VTZ. It is important to note the sim-ilarity in ZPE change ratio for different theoretical levelsregardless of the level of disagreement with the calculatedk. Another important factor is that all the employed theo-retical methods reproduce the change in vibrational energyof carbonyl sulfide O, C and S isotopologues relative to16O12C32S (Table 2) to an accuracy of a few wavenumbers.Once thermodynamic properties of the isotopologues andtheir respective reaction rates had been calculated, thekinetic isotopic effects were obtained. Throughout thisstudy calculated reaction rates for each isotopologue arecompared to the reaction rate for 16O12C32S and expressedin units of ‰:

e33=34=36S ¼33=34=36k

32k� 1

� �

One feature of the enrichment factor, the goal of the cal-culation, is that many types of errors occurring in both thenumerator and denominator will cancel. The KIEs aresummarized in Table 5, which shows the relative invarianceof the calculated enrichment factor to the level of theoryand basis set, demonstrating a surprisingly high indepen-dence from the disagreement between the theoreticaland experimental k. The calculated KIEs evaluated as theratios between e33S/e34S = 0.539 and e36S/e34S = 2.449 (atCCSD(T)/aug-cc-pVDZ) show some disagreement withthe so-called mass dependent ratios derived from kinetictheory [13], 0.504 and 1.968 for e33S and e36S respectively.Our calculations gave an AAD of 0.5%, possibly related toinaccuracies in the ZPEs. The rate of change of ZPE rela-tive to 32S has an average of 0.24%, therefore small inaccu-racies in the calculation of thermodynamic properties arethe most probable sources of deviations from the massdependent slope, cf. Fig. 4.

99.3

99.4

99.5

99.6

99.7

99.8

99.9

100

32 33 34 35 36 37Sulfur mass in the isotopologue (amu)

Ral

ativ

e ch

ange

of Z

PE re

spec

t to32

S is

otop

olog

ue (

)

TS1

CCSD(T)/aug-cc-pVDZCCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZCCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZCCSD/cc-pVTZ//MP2/cc-pVTZ

Adduct

OCS

Fig. 4. Zero-point energies expressed as relative values to 32S for OCS (j), adduct (d) and TS1 (N) calculated at several levels of theory for isotopomers32S, 33S, 34S and 36S (%).

Table 5Calculated kinetic isotope effect (KIE) based on reaction rates k calculatedat different theoretical levels expressed in per mil units (‰)

Theoretical method e33S e34S e36S

CCSD/cc-pVTZ//MP2/cc-pVTZ �1.15 �2.25 �4.33CCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZ �1.01 �2.42 �7.41CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ �1.43 �2.75 �5.43CCSD(T)/aug-cc-pVDZ �1.38 �2.56 �6.27

0 0.2 0.4 0.6 0.8 110

15

20

25

30

35

40

Loss Fraction

Altit

ude

(km

)

OCS+OHOCS+hνOCS+O

Fig. 5. Model calculated global, annual mean loss fractions for the threechemical sinks of OCS. (Points below the tropopause are not consideredand so, e.g., the tropics do not contribute below �16 km.)

S.O. Danielache et al. / Chemical Physics Letters 450 (2008) 214–220 219

4. Stratospheric model

Diurnally-averaged stratospheric loss rates for the threeOCS loss channels (OH, O(3P) and hm) were calculated as afunction of latitude and altitude for each month using aphotochemical box model [21]. The OCS reaction ratesand photolysis cross sections were taken from the JPL database [22] and a photodissociation quantum yield of unitywas assumed [23]. These rates were applied to monthly,zonal-mean OCS profiles simulated using the Universityof California three-dimensional chemical transport model[24] driven with wind fields from a general circulationmodel [25] and a 475 pptv lower boundary condition. Thesimulated loss rates compare qualitatively well with previ-ously published data [26]. Based on these simulations theannual stratospheric chemical loss of OCS is calculatedto be 7.4 � 1010 g(OCS) year�1, of which 6.7 � 109 g(OCS)year�1 or about 9% is lost through the OCS + OH channel,with nearly all of this occurring in the lowermost strato-sphere. As is evident from Fig. 5, below 16–17 km the dom-inant loss channel is OCS + OH.

It has been estimated that OCS in the troposphere has ad34S = 11‰ [27] and that SSAs have a d34S of 2.6‰ [28].Leung et al. [7] have reported an enrichment factor of+73.8 ± 8.6‰ based on OC32S and OC34S concentrationprofiles between 10 and 20 km. In their work they assume

that photolysis is the main sink yet our results show thatbetween these altitudes OH and O(3P) reactions are impor-tant. Regardless of this the measurement of the large deple-tion in OC34S is an important result that is supported by alaboratory study of the fractionation factor for the photol-ysis of OCS [29] (34e = 67 ± 7‰). These results emphasizethe shortcomings of a model in which OCS photolysis isthe only source of SSA, since SSA (2.6‰) is even lessenriched in 34S than relative tropospheric OCS (11‰).Our results show that OC32S reacts faster, therefore thenegative sign of e34S (�2.56‰ at CCSD(T)/aug-cc-pVDZ).This is in agreement with the depletion observed in SSAalthough it is not enough to explain it, even if SSA wasonly produced by the OCS + OH reaction. Consequently

220 S.O. Danielache et al. / Chemical Physics Letters 450 (2008) 214–220

in order to account for the �8.5‰ difference between thed34S values of tropospheric OCS (11‰) and SSA (2.6‰)the existence of another chemical sink with negative KIEor a source of SSA different from the ones considered inthis work are necessary. The obvious candidate is SO2

(d34S = +30 to �30‰ [27]) transported into the lowerstratosphere [30].

5. Concluding remarks

Ab initio calculations have been carried out to investi-gate the sulfur KIEs for the reaction between OH andOCS. It has been shown using MP2 and CCSD(T) thatthe reaction proceeds via two steps involving the formationof a stable planar adduct with the hydrogen atom orientedtoward the sulfur atom, and a four-membered cyclic com-plex, prior to the separation of an SH radical. CalculatedKIEs show an AAD of 0.5% from the mass dependentslope. According to our model, tropospheric OCS is trans-ported to the lower stratosphere where it is photodissociat-ed and oxidized by OH. The small KIE of 34S may indicatethe relevance of the OCSOH channel for the formation ofSSA. The KIE values of e33S and e36S provide importantinformation for the study of mass-independent effects dur-ing the oxidation of OCS in the stratosphere since the exis-tence of mass-independent effects has been measured byBaroni et al. [31]. The theoretical results together withthe stratospheric model and previous work indicate thatthere is a fundamental change in the isotopic fractionationof OCS removal processes with altitude, due to the changefrom OH-dominated to hv-dominated loss between thelower and middle stratosphere. This effect could be usedto improve our knowledge of the budget of stratosphericsulfate aerosols. The work of Leung et al. [7] presents thevertical profiles of OC32S and OC34S and uses this to calcu-late the enrichment factor for stratospheric photochemis-try. It is a challenging measurement and the isotopicsignal is blurred by mixing [32], and so it is not possibleto see the altitude dependence of the enrichment factor thatwe predict in this Letter. We hope that this topic will be thesubject of future research.

Acknowledgments

The authors thank Sakae Toyoda, Yuichiro Ueno, Hide-ki Nara, and Gilherme Ramos for their kind assistance.M.S.J. and M.M.-L.G. thank the Copenhagen Center forAtmospheric Research, the Villum Kann Rasmussen Fundand the Danish Natural Science Research Council for theirgenerous support.

Appendix A. Supplementary data

Supplementary data associated with this article can befound, in the online version, at doi:10.1016/j.cplett.2007.11.054.

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