Experimental and theoretical investigation of rate coefficients of the reaction S(P-3)+OCS in the temperature range of 298-985 K

OCS in the temperature range of 298 – 985 K

Chih-Wei Lu, Yu-Jong Wu, Yuan-Pern Lee, R. S. Zhu, and M. C. Lin

Citation: The Journal of Chemical Physics 125, 164329 (2006); doi: 10.1063/1.2357739 View online: http://dx.doi.org/10.1063/1.2357739

View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/125/16?ver=pdfcov Published by the AIP Publishing

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Experimental and theoretical investigation of rate coefficients

of the reaction S

_„

3

P

_{…+OCS in the temperature range of 298–985 K}

Chih-Wei Lu and Yu-Jong Wu

Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan

Yuan-Pern Leea兲

Department of Applied Chemistry, National Chiao Tung University, Hsinchu 30010, Taiwan; Institute of Molecular Science, National Chiao Tung University, Hsinchu 30010, Taiwan; and Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan

R. S. Zhu

Department of Chemistry, Emory University, Atlanta, Georgia 30322

M. C. Linb兲

Department of Applied Chemistry, National Chiao Tung University, Hsinchu 30010, Taiwan; Institute of Molecular Science, National Chiao Tung University, Hsinchu 30010, Taiwan; and Department of Chemistry, Emory University, Atlanta, Georgia 30322

共Received 14 April 2006; accepted 30 August 2006; published online 27 October 2006兲

The reaction S共3_{P兲+OCS in Ar was investigated over the pressure range of 50–710 Torr and the}

temperature range of 298– 985 K with the laser photolysis technique. S atoms were generated by photolysis of OCS with light at 248 nm from a KrF excimer laser; their concentration was monitored via resonance fluorescence excited by atomic emission of S produced from microwave-discharged SO2. At pressures less than 250 Torr, our measurements give k共298 K兲

=共2.7±0.5兲⫻10−15_cm3_molecule−1_s−1_{, in satisfactory agreement with a previous report by Klemm}

and Davis 关J. Phys. Chem. 78, 1137 共1974兲兴. New data determined for 407–985 K connect rate coefficients reported previously for T艌860 and T艋478 K and show a non-Arrhenius behavior. Combining our results with data reported at high temperatures, we derived an expression k共T兲 =共6.1±0.3兲⫻10−18_T1.97±0.24_{exp关−共1560±170兲/T兴 cm}3_molecule−1_s−1 _{for 298艋T/K艋1680. At}

298 K and P艌500 Torr, the reaction rate was enhanced. Theoretical calculations at the G2M共CC2兲 level, using geometries optimized with the B3LYP/ 6-311+ G共3df兲 method, yield energies of transition states and products relative to those of the reactants. Rate coefficients predicted with multichannel Rice–Ramsperger–Kassel–Marcus 共RRKM兲 calculations agree satisfactorily with experimental observations. According to our calculations, the singlet channel involving formation of SSCO followed by direct dissociation into S2共a1⌬g兲+CO dominates below 2000 K; SSCO is formed via intersystem crossing from the triplet surface. At low temperature and under high pressure the stabilization of OCS2, formed via isomerization of SSCO, becomes important; its formation and

further reaction with S atoms partially account for the observed increase in the rate coefficient under such conditions. © 2006 American Institute of Physics.关DOI:10.1063/1.2357739兴

I. INTRODUCTION

Carbonyl sulfide共OCS兲 commonly serves as a photolytic source of atomic sulfur in laboratories partly because the photofragment CO is practically inert. At large concentra-tions, the secondary reaction

S共3_{P兲 + OCS → products 共1兲}

becomes important. Measurements of the rate coefficient k1

at temperatures above 860 K using a shock tube and atomic absorption1–4 yield results somewhat consistent with the ac-tivation energy, with Ea/ R in the range of 3400– 4560 K and the Arrhenius preexponential factor A in the range of

共39–100兲⫻10−12_cm3_molecule−1_s−1_{, except an earlier}

ex-periment that employed a shock tube with mass spectromet-ric product detection and yielded an erroneously small value of k1= 1.0⫻10−12cm3molecule−1s−1 at 2570 K.5 In

con-trast, reported rate coefficients near 298 K using various de-tection methods differ significantly, in a range of 共0.2–54兲 ⫻10−15_cm3_molecule−1_s−1_.6–9

TableIsummarizes rate coef-ficients reported for this reaction.

No experimental data exist for temperatures between 478 and 860 K. Extrapolation of the Arrhenius equation de-termined at high temperature yields k1 at 298 K of 0.01–0.1

times the experimental values. A non-Arrhenius behavior for reaction共1兲 is thus indicated and warrants further character-ization.

The reaction might proceed via various exothermic prod-uct channels:

a兲_{Author to whom correspondence should be addressed. Electronic mail:}

yplee@mail.nctu.edu.tw

b兲_{Author to whom correspondence should be addressed. Electronic mail:}

chemmcl@emory.edu

THE JOURNAL OF CHEMICAL PHYSICS 125, 164329共2006兲

0021-9606/2006/125共16兲/164329/10/$23.00 125, 164329-1 © 2006 American Institute of Physics

S共3P兲 + OCS共1⌺+兲 → CO共X1⌺+兲 + S₂共X3⌺g−兲, 共1a兲 ⌬H0= − 28.8 kcal mol−1, → M OCS2共1A1兲, 共1b兲 ⌬H0⬵−26 kcal mol−1, → M SSCO共1_A 1兲, 共1c兲 ⌬H0⬵−12 kcal mol−1.

The enthalpy of reaction for 共1a兲 is derived based on the reported enthalpies of formation of 66.20共S兲, −33.08 共OCS兲, −26.42 共CO兲, and 30.74 kcal mol−1 _共S

2兲, respectively;10

those of reactions共1b兲and共1c兲are estimated from quantum-chemical calculations, to be described hereafter. The pres-ence of reaction 共1b兲 was proposed by Basco and Pearson when they tried to explain their kinetic data for formation of S2 following flash photolysis of CS2 and OCS.11 The other

two possible reaction channels, S共3 P兲 + OCS共1⌺+兲→ M SOCS共1 A

⬘

兲, 共1d兲 ⌬H0⬵ 21 kcal mol−1, S共3

P兲 + OCS共1⌺+兲 → CS共1⌺+兲 + SO共3⌺−兲, 共1e兲

⌬H0⬵ 35.1 kcal mol−1,

are unimportant at low temperatures because they are quite endothermic. There has been no theoretical study of the ki-netics of reaction共1兲.

We have earlier identified carbon disulfide S oxide 共OSCS兲 and dithiiranone 共OCS2兲 using matrix isolation and

infrared absorption techniques.12Irradiation of an Ar matrix sample containing O3 and CS2 with light at 248 nm from a

KrF excimer laser yielded new absorption lines at 1402.1, 1056.2, and 622.3 cm−1; these features were assigned to CvS stretching, OuS stretching, and SuC stretching

modes, respectively, of OSCS. Annealing of this matrix to 30 K yielded new lines in a second set at 1824.7 and 617.8 cm−1, assigned to CvO stretching and OCS bending modes of OCS2, respectively. Calculations using

density-functional theory 共B3LYP/aug-cc-pVTZ兲 predicted four stable isomers: OCS₂, SSCO, OSCS, and SOCS, listed in order of increasing energy. According to calculations, OCS₂ has a C_2v symmetry and is the most stable; OSCS, SSCO, and SOCS are all planar. Calculated vibrational wave num-bers, IR intensities, and 34S- and 18O-isotopic shifts for OSCS and OCS₂ fit satisfactorily with experimental results. In this work, we have performed experiments on the reaction of S + OCS at pressures 50– 710 Torr of Ar and ex-tended rate measurements from 298 to 985 K to bridge the region T艋478 K with a small activation energy and the re-gion T艌860 K in which the reported rate coefficients show an activation energy corresponding to Ea/ R = 3400– 4560 K. The pressure dependence of rate coefficients at 298 K was investigated to confirm the existence of an adduct-formation channel under such conditions. We also performed detailed theoretical calculations to predict rate coefficients and to identify important channels in this reaction at various tem-peratures and pressures.

II. EXPERIMENTS

The experimental setup was described in detail previously;13–15 only a brief description follows here. The reaction vessel is a six-way tubular quartz cross 共with a di-ameter of 40 mm兲 with two sidearms of length ⬵15 cm and with Brewster windows for laser photolysis. A temperature controller共Omega CN9000兲 regulated the temperature of the reactor through resistive heating. S atoms were produced on photolysis of OCS with radiation from a pulsed KrF excimer laser at 248 nm共0.5–19 mJ cm−2_{, 0.5– 3 Hz兲. Excess Ar gas}

was added to the system to ensure that S共1_{D兲 was quenched}

before reaction.16A microwave-discharge lamp with a flow-ing gas mixture of SO2⬃0.10% in He produced emission in

the transitions S共3_S兲-S共3_P

2,1,0兲 at 180.73, 182.03, and

TABLE I. Summary of reported experimental rate coefficients using various methods.

Temperature 共K兲 Pressure共gas兲 共Torr兲 k共⬃298 K兲 共10−15_兲a A 共10−12_兲a Ea/ R 共K兲 Methodb Reference

301 n.a. 艌0.17 FP/GC and MS Breckenridge and Taube共BT兲 共Ref.8兲 n.a. n.a. 54 Gunning and Strausz共GS兲共Ref.9兲 298–478 1294共OCS/CO2兲 16 83 2525 FP/GC and MS Jakubowski et al.共JALSGS兲 共Ref.7兲

233–445 20–200共Ar兲 3.48± 0.39 1.52± 0.20 1830± 60 FP/RF Klemm and Davis共KD兲 共Ref.6兲 860–1680 n.a. 50± 8 3730± 220 ST/ABS Shiina et al.共SOYMM兲 共Ref.1兲 1140–1680 930–1740共Ar兲 39± 12 3400± 110 ST/ABS Oya et al.共OSTM兲 共Ref.2兲 1200–1670 450–1500共Ar兲 99.7 4560 ST/ABS Woiki et al.共WMR兲 共Ref.4兲 1750–2990 375–1035共Ar兲 6.6c ST/ABS Woiki and Roth共WR兲 共Ref.3兲

2570 365共Ar兲 1.0d ST/MS Hay and Berford共HB兲 共Ref.5兲 298–958 50–710共Ar兲 2.7± 0.5 e e LP/RF This work

a_{In units of cm}3_molecule−1_s−1_.

b_{FP: flash photolysis; LP: laser photolysis; ST: shock tube; ABS: absorption; RF: resonance fluorescence; GC: gas chromatography; and MS: mass}

spectrom-etry.

c_{k共1800–2200 K兲=6.6⫻10}−12_cm3_molecule−1_s−1_. d_{k共2570 K兲=1.0⫻10}−12_cm3_molecule−1_s−1_.

e_{k共T兲=共6.63±0.33兲⫻10}−20_T2.57±0.19_{exp关−共1180±120兲/T兴 cm}3_molecule−1_s−1_{for the temperature range of 233– 1680 K.}

182.62 nm, respectively; the emission, collected with a lens 共S1-UV, focal length f =5 cm, passing wavelength ⬎170 nm兲, and excited S atoms in the reaction vessel for their detection.

The fluorescence was collected along an axis perpen-dicular to both photolysis laser and probe beams with a MgF2lens 共f =5 cm兲 and detected with a solar-blind

photo-multiplier tube 共EMR 541G-09兲. The signal was amplified with a low-noise amplifier 共Stanford Research Systems, SR570兲 before being recorded with a digital oscilloscope 共Tektronix, TDS-620B, 2.5 G sample s−1_{, 500 MHz}

band-width兲. Temporal profiles for fluorescence of S were typi-cally averaged over more than 500 laser pulses before being transferred to a computer for further processing.

OCS 共99.98%, Matheson兲 was purified on distillation from trap to trap. A 20% mixture of OCS in Ar was prepared with standard gas-handling techniques. He 共99.9995%兲 and Ar共99.9995%, both from AGA Specialty Gases兲 were used without further purification. The flow rates of He, Ar, and the OCS/ Ar mixture were monitored with mass flow meters 共Ty-lan FM360兲 that were calibrated with a wet testmeter or by the pressure increase in a calibrated volume before and after experiments.

Typical experimental conditions were as follows: total flow rate FT= 10.7– 13.3 STP cm3s−1 共STP=1 atm and 273 K兲, reaction temperature T=298–985 K, total pressure

P = 50– 710 Torr, 关OCS兴=3.62⫻1013_{− 1.05⫻10}17 _molecule

cm−3_{, 关S兴=共0.49–71.1兲⫻10}11 _{molecule cm}−3_{, 关Ar兴}

=共0.50–23.2兲⫻1018_{molecule cm}−3_{, probed intervals of}

decay= 20␮s − 90 ms, and mean flow speed of the gaseous mixture␷= 0.8– 29.8 cm s−1_.

III. COMPUTATIONAL METHODS

The geometries of the reactants, intermediates, transition states, and products of the title reaction were optimized at the B3LYP/ 6-311+ G共3df兲 level of theory with Becke’s three-parameter nonlocal exchange functional17 and the nonlocal correlation functional of Lee et al.18Single point energies of all species were refined by the G2M共CC2兲 共Ref.19兲 method

using geometries and zero-point energies obtained at the B3LYP/ 6-311+ G共3df兲 level. For the surface intersection points 共MSX1 and MSX2兲, their geometries were located using the state-averaged complete active space self-consistent field共CASSCF兲 method.20Six electrons in six ac-tive spaces were used with 6-31+ G共d兲 basis set. Because no symmetry was constrained in the geometry optimization, the default option in the GAUSSIAN program was used for the selection of the active space and electrons in the CASSCF calculation; the active space is defined assuming that the electrons come from the highest occupied orbitals in the ini-tial guess determinant and that the remaining orbitals re-quired for the active space come from the lowest virtuals of the initial guess. To be consistent with other species, vibra-tional wave numbers of these intersection points were ap-proximately calculated at the B3LYP/ 6-311+ G共3df ,2p兲 level on the singlet surface. Imaginary wave numbers 293.8i and 420.1i cm−1 were obtained for MSX1 and MSX2, re-spectively, indicating that these points appear to have

transi-tion state characters. We confirm with GAUSSVIEW that MSX1 connects to the reactants and SSCO and MSX2 con-nects to the reactants and OCS2. The total G2M共CC2兲 energy

with zero-point energy共ZPE兲 correction is calculated as fol-lows:

E关共G2M共CC2兲兲兴 = Ebas+⌬E共+ 兲 + ⌬E共2df兲 + ⌬E共CC兲

+⌬

⬘

+⌬E共HLC,CC2兲 + ZPE共3df,2p兲, in which

Ebas= E关PMP4/6-311G共d,p兲兴,

⌬E共+ 兲 = E关PMP4/6-311 + G共d,p兲兴 − Ebas,

⌬E共2df兲 = E关PMP4/6-311G共2df,p兲兴 − Ebas,

⌬E共CC兲 = E关CCSD共T兲/6-311G共d,p兲兴 − Ebas,

⌬

⬘

= E关UMP2/6-311 + G共3df,2p兲兴 − E关UMP2/6-311 + G共2df,p兲兴 − E关UMP2/6-311 + G共d,p兲兴 − E关UMP2/6-311共d,p兲兴,

⌬E共HLC,CC2兲 = − 5.78n␤− 0.19n␣

共in units of mhartree兲,

in which n_␣ and n_␤ are the numbers of valence electrons,

n_␣艌n_␤, and HLC indicates a higher level correction. For comparison, single point energies were also calculated at the CCSD共T兲/6-311+G共3df兲 level based on the structures at the B3LYP/ 6-311+ G共3df兲 level, expressed as CCSD共T兲/6 -311+ G共3df兲储B3LYP/ 6-311+ G共3df兲. Calculations of the

intrinsic reaction coordinate21共IRC兲 were performed to con-nect each transition state with designated reactants and prod-ucts. All calculations were carried out withGAUSSIAN 03.22

Various statistical models for nonadiabatic reactions based on transition state theory 共TST兲 have been developed and applied to a number of reactions.23–34All are based on the assumption that the minimum energy crossing point rep-resents the transition state for the adiabatic reaction; the den-sity of states of the transition state in the TST 共or Rice– Ramsperger–Kassel–Marcus, RRKM兲 rate equation is then multiplied by “hopping probability” related to the spin-orbit coupling strength to correct the rate computed using the stan-dard transition state theory for adiabatic processes. The re-sults show that the one-dimensional treatment of the surface hopping probability often gives rate constants from about a factor of 2共Ref.34兲 to one to two orders of magnitude lower

than experimental values.29,33In this work, the hopping prob-ability via MSX1 and MSX2 was assumed to be unity. The standard adiabatic TST 共or RRKM兲 theory as described in the following sections was employed to calculate rate con-stants.

The rate coefficients for various reaction channels were calculated with a multichannel RRKM 关VARIFLEX兴 code

共Ref. 35兲 which solves the master equation36,37 involving multistep vibrational energy transfers for the excited inter-mediate SSCO or OCS2. The Lennard-Jones共LJ兲 parameters

164329-3 _{Rate coefficients of S共}3_{P兲+OCS J. Chem. Phys. 125, 164329共2006兲}

required for the RRKM calculations for the quenching of SSCO and OCS2 were approximately taken the same as

those of CS2, with ␧/k=414.6 K and ␴= 4.575 Å.38 LJ

pa-rameters for Ar,␧/k=114 K and␴= 3.47 Å, were also taken from Ref. 38. The exponential-down model with ␣ = 400 cm−1 _{was employed for collisional deactivation. For}

the channels involved in two wells, a rigorous way of pre-dicting their kinetics is to solve the time-dependent master equation共ME兲 which denotes a set of coupled integral dif-ferential equations of motion for populations of specific en-ergy levels of the reactive intermediates:

⳵gi共E,t兲 ⳵t =␻

冕

E_0i

⬁

Pi共E,E

⬘

兲gi共E

⬘

,t兲dE

⬘

−␻gi共E,t兲 − ki共E兲gi共E兲 + r共E,t兲

in which gi共E,t兲 is the population of energy level E in well i at time t,␻is the collisional frequencies, E0i is the

ground-state energy of well i, Pi共E,E

⬘

兲 is the transition probability for a molecule in well i with energy E

⬘

to go on collision to another state in the same well with energy E, ki共E兲 is the total rate constant of decay via all isomerization and decom-position channels open from well i at energy E, and r共E,t兲 is the rate of formation for species i with energy E from the chemical activation and isomerization channels. The ME was solved in a matrix form with a method based on the House-holder’s tridiagonalization algorithm.39 More details about the implementation of the time-dependent ME/RRKM analy-sis inCHEMRATE共Ref.40兲 are available in a series of

publi-cations by Tsang and co-workers.41–43 The accuracy of the method implemented inCHEMRATEwas found to be adequate after examination through extensive comparisons with ex-perimental and theoretical data for the reactions of phenyl with acetylene44 and ethylene.45For the abstraction reaction channel not involving an intermediate, conventional TST theory was used to calculate the rate. Energies of the inter-mediates and transition states calculated at the G2M共CC2兲 level were used in the calculation of rate coefficients because the heats of reaction predicted by the method agree better with experimental values共vide infra兲.

IV. RESULTS AND DISCUSSION

A. Experimental rate coefficient below 250 Torr All experiments were performed under pseudo-first-order conditions with关OCS兴/关S兴 greater than 610. The initial concentration of S,关S兴₀, was estimated from the absorption cross section 共2.36⫻10−20_cm2_{兲 of OCS and quantum yield}

⌽共S兲=0.72±0.08 at 248 nm,46

and the fluence of the pho-tolysis laser. The concentration of S atoms, 关S兴t, follows an exponential decay. The apparent pseudo-first-order rate coef-ficient kIa is derived with the equation

ln共关S兴t/关S兴0兲 = − kIat + at2+ bt3, 共2兲

in which t is the reaction time and a and b are fitting param-eters to account for secondary reactions.

To derive accurate rate coefficients, we employed a model comprising the following reactions:

S共3 P兲 + OCS共1⌺+兲 → CO共X1⌺+兲 + S2共X3⌺g −_{兲, 共1a兲} ⌬H0= − 28.8 kcal mol−1, → M OCS2共1A1兲, 共1b兲 ⌬H0⬵−26 kcal mol−1, S + OCS2→ S2+ OCS, 共3兲

FIG. 1. Derived k_1aI _{as a function of 关OCS兴 at various temperatures. 共a兲}

298 K, 50 Torr, symbol䊊; 298 K, 250 Torr, symbol 쎲; 407 K, 50 Torr, symbol 䉱; 407 K, 250 Torr, symbol 䊐; 506 K, 50 Torr, symbol 䉮; 250 Torr, symbol䊏. 共b兲 613 K, 50 Torr, symbol 〫; 255 Torr, symbol 쎲; 758 K, 50 Torr, symbol䉱; 985 K, 50 Torr, symbol 䉮. The data at 613 K and 500 Torr共symbol 䊐兲 were not included in the fitting.

S + S2→

M

S3. 共4兲

The calculated temperature dependence of the bimolecular rate coefficients k_1bII and k₄IIIat 50 Torr can be represented by

k_1bII共T兲 = 9.08 ⫻ 107T−7.59

⫻exp关− 共3330/T兲兴 cm3_molecule−1_s−1 _共5兲

and

k₄III共T兲 = 5.33 ⫻ 10−20_T−4.12

⫻exp关− 共625/T兲兴 cm6_molecule−2_s−1_{, 共6兲}

to be discussed later. The rate coefficient of reaction 共3兲 is expected to be on the order of 10−10_cm3_molecule−1_s−1

be-cause we found no barrier for this reaction.

We modeled observed temporal profiles of关S兴twith re-actions 共1a兲, 共1b兲, 共3兲, and 共4兲, with a commercial kinetic modeling program FACSIMILE;47 rate coefficients listed in

Eqs. 共5兲 and 共6兲 were unaltered and the pseudo-first-order rate coefficient of reaction共1a兲, k_1aI , was varied to yield the best fit. According to our simulations, reactions共1b兲and共3兲 are unimportant under our experimental conditions, and re-action共4兲 only has a small effect on the decay of S atoms. Values of k_1aI thus derived are 78%–99% those of kIa_derived

with Eq. 共2兲, supporting that reactions 共1b兲 and共3兲 are un-important under these conditions.

Values of k_1aI determined with various concentrations of OCS at temperatures 298, 407, 506, 613, 758, and 985 K are plotted in Fig.1; the slope of the line fitted with least squares yields the bimolecular rate coefficient k1a at each

tempera-ture, as listed in TableII. Because reaction共1a兲is dominant for reaction 共1兲 under these conditions, we use values of k1a to represent k1. At 298 K, k1=共2.70±0.11兲

⫻10−15_cm3_molecule−1_s−1_{; unless otherwise noted, the}

un-certainty represents one standard error in fitting. In these experiments, rate coefficients remained the same while 关S兴0

was varied by a factor of 12 and the total pressure was varied from 50 to 250 Torr. The combined systematic error 共mea-surements of flow rates, pressure, and temperature兲 of our system is estimated to be⬃9%, and the error in deriving k_1aI and its dependence on关OCS兴 is ⬃15%. Hence, we estimate an error ⬃18% for k1 and recommend a rate coefficient of

共2.7±0.5兲⫻10−15_cm3_molecule−1_s−1_{at 298 K. The value of}

k1 at 298 K determined in this work is within experimental

uncertainties of the previous report of k1=共3.48±0.39兲

⫻10−15_cm3_molecule−1_s−1 _{by Klemm and Davis,}6

but is smaller than two previous reports of rate coefficient deter-mined relative to that of the reaction

S共3

P兲 + C2H4→ products. 共7兲

Jakubowski et al.7and Gunning and Strausz9reported ratios of k₇/ k₁= 83 and 25, respectively; the recommended rate co-efficient of k₇ is 1.35⫻10−12_cm3_molecule−1_s−1_,48

which yields k₁/ 10−15_cm3_molecule−1_s−1_{= 16 and 54, respectively.}

Even when the smallest reported value of k₇= 4.95 ⫻10−13_cm3_molecule−1_s−1 _{共Ref. 49兲 is used, the derived}

values of k1/ 10−15cm3molecule−1s−1= 6 and 20 are still

much greater than ours at 298 K.

Rate coefficients k1 determined at 298, 407, 506, 613,

758, and 985 K are listed in TableII; they are also compared with the previous data in Fig. 2 in which lines of various types are drawn for only the range of temperature investi-gated. Our data of k1 increase from 共2.7±0.5兲

⫻10−15_cm3_molecule−1_s−1 _{at 298 K to共1.04±0.19兲}

⫻10−12_cm3_molecule−1_s−1_{at 985 K, showing a distinct}

de-viation from a linear Arrhenius form, but connecting satis-factorily data for T⬎860 K by Shiina et al.,1Oya et al.,2and Woiki et al.3 and those for T = 233– 445 K by Klemm and Davis.6

TABLE II. Bimolecular rate coefficients k1at various temperatures.

T

共K兲

P

共Torr兲 共10关S兴11_兲a 关OCS兴_共1014_兲a _共10关Ar兴17_兲a

k1 共cm3_molecule−1_s−1_兲 298 51–250 9.0–42.8 5.45–362 16.4–79.9 共2.7±0.5兲⫻10−15 407 50 10.5 7.68–32.0 11.9 共1.5±0.2兲⫻10−14 506 50–250 1.87–7.65 1.39–132 9.5–49.3 共5.0±0.8兲⫻10−14 613 50–255 0.81–9.75 0.60–107 7.9–40.2 共1.3±0.2兲⫻10−13 758 50 0.84 0.63–17.3 6.4 共3.6±0.5兲⫻10−13 985 51 0.49 0.36–13.3 5.0 共1.0±0.2兲⫻10−12 a_{In units of molecule cm}−3_.

FIG. 2. Arrhenius plots of k1for the reaction S + OCS→S2+ CO. Our data

are shown as symbol쎲 with a fitted equation shown as a thick solid line. Those of Klemm and Davis共Ref.6兲 are shown as symbol 䊊 with a fitted equation shown as a dotted line. Other previous results are shown as lines of various types drawn for the temperature range of study. A combination of first characters of each author’s last name is used to indicate previous re-ports, as listed in TableI.

164329-5 _{Rate coefficients of S共}3_{P兲+OCS J. Chem. Phys. 125, 164329共2006兲}

Fitting our results alone yields an expression for the rate coefficient in the range of 298艋T/K艋985:

k1共T兲 = 共2.86 ± 0.14兲 ⫻ 10−24T3.97±0.12

⫻exp关− 共580 ± 60兲/T兴 cm3_molecule−1_s−1_{. 共8兲}

When combined with data for T⬎860 K reported by Oya et

al.,2 Woiki et al.,3 and those for T = 233– 445 K by Klemm and Davis.,6we derive a general expression

k₁共T兲 = 共6.63 ± 0.33兲 ⫻ 10−20T2.57±0.19

⫻exp关− 共1180 ± 120兲/T兴 cm3_molecule−1_s−1_,

共9兲 for 233艋T/K艋1680. This equation reproduces reported rate coefficients within 25% except a few data points.

B. Experimental rate coefficient at high pressures We performed experiments also under high pressures. Although the decay deviates little from pseudo-first-order ki-netics, a significant enhancement of an apparent pseudo-first-order rate coefficient kIa_{, derived according to Eq. 共2兲, was}

observed for PT= 500 and 710 Torr at 298 K. Figure3shows a representative semilogarithmic plot of temporal profiles of 关S兴 observed when a flowing gas mixture containing OCS and Ar at 710 Torr and 298 K was irradiated at 248 nm; the concentration of OCS was 0.66, 1.03, and 5.31⫻1016_{molecule cm}−3_{. Values of k}

1/ 10−14cm3

molecule−1_s−1 _{were determined to be 5.0, 4.0, and 1.03 for}

关OCS兴/1016_{molecule cm}−3_{= 0.66, 1.03, and 5.31 under a}

to-tal pressure of 710 Torr at 298 K. In contrast, values of kIa

determined with various concentrations of OCS under a total pressure of 50, 255, and 510 Torr at 613 K are unaltered, as shown in Fig. 1. The observation indicates that, at low tem-perature and under high pressure, the channel involving for-mation of an adduct likely becomes important. We employed theoretical calculations to understand the mechanism, as dis-cussed in the following section.

C. Potential-energy surfaces and reaction mechanism Our calculations show that several triplet and singlet in-termediates and transition states are involved in the reaction S共3

P兲+OCS 共X1兺+兲 to produce S2共X3兺g

−_兲+CO共X1_兺+_{兲 and}

S2共a1⌬g兲+CO共X

1_兺+_{兲. Optimized geometries of the}

inter-FIG. 3. Semilogarithmic plot of temporal profiles of关S兴t observed after

photolysis of a sample containing OCS and Ar. T = 298 K, P = 710 Torr, 关Ar兴=2.3⫻1019_{molecule cm}−3_{, and 关OCS兴/10}16_{molecule cm}−3_{= 0.66 共a兲,}

1.03共b兲, and 5.31 共c兲. The solid line represents fitted results according to a model described in the text.

FIG. 4. Optimized geometries of transition states and intermediates of the S + OCS system at the B3LYP/ 6-311+ G共3df兲 level, with bond lengths in angstrom and bond angles in degree.

mediates and transition states involved in the reaction are shown in Fig.4. The energy diagrams for singlet and triplet surfaces calculated with the G2M共CC2兲 and CCSD共T兲/6-311+ G共3df兲储B3LYPY/ 6-311+ G共3df兲 methods are

pre-sented in Fig. 5; values derived with the latter method are listed parenthetically. At the G2M共CC2兲 and CCSD共T兲/6-311+ G共3df兲储B3LYPY/ 6-311+ G共3df兲 levels, predicted

en-thalpies of reaction for S共3

P兲+OCS共1兺+兲→CO共X1兺+兲

+ S₂共X3兺_g−兲, −25.9 and −24.2 kcal mol−1 _{respectively, are}

10% and 16% smaller than the value obtained from JANAF, −28.8 kcal mol−1_.10

For formation of CO 共X1兺+兲 + S2共a1⌬g兲, the predicted enthalpies of reaction are −11.8 and −8.1 kcal mol−1, respectively, at the G2M共CC2兲 and the CCSD共T兲/6-311+G共3df兲储B3LYPY/ 6-311+ G共3df兲 levels; experimental value from JANAF is −15.4 kcal mol−1_{. For the}

production of SO 共3兺−兲+CS共1兺+兲, the predicted enthalpies of reaction of 38.5 and 41.3 kcal mol−1 at the above levels may be compared with the JANAF value of 35.1 kcal mol−1_.

The heat of formation of CS in JANAF共Ref.10兲 has a large

error of⬃6 kcal mol−1. The predicted enthalpies of reaction at the G3B3 level50for these three channels, −25.6, −9.8, and 37.0 kcal mol−1_{, are in good agreement with values −25.9,}

−11.8, and 38.5 kcal mol−1 derived at the G2M共CC2兲 level. Comparing the enthalpies of reaction, we found that the val-ues obtained at the G2M共CC2兲 level are closer to the experi-mental data. Accordingly, in the following text, values ob-tained at the G2M共CC2兲 level are cited. Predicted vibrational wave numbers and rotational parameters for the reactants, intermediates, transition states, and products are summarized in TableIII. The experimental vibrational wave numbers are

also listed in Table III for comparison;12 predicted vibra-tional wave numbers deviate by less than 3% from experi-mental values.

Figure 5 shows that the triplet surface with the lowest energy proceeds via TS1 with a barrier of 11.9 kcal mol−1to form S2共X3兺g−兲+CO共X1兺+兲. The other triplet channel, pro-ceeding via TS2 to form triplet OCS2共3B1兲 followed by

de-composition to S₂共X3兺_g−兲+CO共X1兺+兲 via TS3, has a much greater barrier. The reaction might also proceed via singlet surfaces by curve crossing via MSX1 and MSX2. Crossing via MSX1 at 3.3 kcal mol−1 _{produces SSCO 共}1_A

_⬘

_{兲, which}

lies at −11 kcal mol−1_{relative to the reactants and might}

sub-sequently decompose to S2共a1⌬g兲+CO共X1兺+兲 via TS5 共with a barrier 8.7 kcal mol−1_{兲. SSCO 共}1_A

_⬘

_{兲 may also}

isomer-ize to OCS2共1A1兲, lying at 26.2 kcal mol−1 below the

reac-tants, via TS4 with a barrier of 1.1 kcal mol−1_{. Crossing via}

MSX2 at 8.5 kcal mol−1 _{leads to formation of OCS} 2共1A1兲

directly. At low temperatures OCS2is unlikely to decompose

to S₂共a1⌬_g兲+CO共X1兺+兲 because the energy of TS6 is about 15.7 kcal mol−1above the reactants S共3P兲+OCS共X1兺+兲. The

predicted small barrier at TS4 for SSCO isomerization to OCS2 is consistent with our earlier observation in low

tem-perature matrices.

At low temperature and low pressure, crossing via MSX1 to form singlet SSCO, followed by decomposition of SSCO via TS5 to form S₂共a1⌬_g兲+CO共X1兺+兲, is the most important path. At higher temperatures, the direct abstraction channel via TS1 on the triplet surface becomes important; observed that activation energy of 7 – 9 kcal mol−1 at high temperatures is consistent with a predicted barrier of 11.9 kcal mol−1for TS1.

FIG. 5. Potential-energy diagrams for the S + OCS reaction based on energies calculated at the G2M共RCC2兲储B3LYP/ 6-311+ G共3df兲 level. Values in parentheses are calculated at the CCSD共T兲/6-311+G共3df兲储B3LYP/ 6-311+ G共3df兲 level. Energies are listed in kcal mol−1_.

164329-7 _{Rate coefficients of S共}3_{P兲+OCS J. Chem. Phys. 125, 164329共2006兲}

Calculations based on transition state and RRKM theo-ries were carried out with theVARIFLEX共Ref.35兲 and CHEM-RATEcodes共Ref.40兲 for the overall reaction,

S共3

P兲 + OCS → products 共1兲

via the following possible channels:

S + OCS→ TS1 → S₂共X3⌺g−兲 + CO共X1⌺+兲, 共1a-1兲 S + OCS ——→ MSX1 SSCO共1A

⬘

兲 → TS5 → S₂共a1⌬g兲 + CO共X1_⌺+_{兲, 共1a-2兲} S + OCS ——→ MSX2 OCS2共1A1兲 → TS6 → S2共a1⌬g兲 + CO共X1_⌺+_{兲, 共1a-3兲} S + OCS ——→ MSX1 SSCO共1 A

⬘

兲 → TS4 → OCS2共1A1兲, 共1b-1兲 S + OCS ——→ MSX2 OCS2共1A1兲. 共1b-2兲

The following scheme was used to couple all of the forward and reverse channels involved in the reactions:

S₂共a1⌬g兲 + CO

↑

S + OCS
k1 SSCO*_{共M兲 → SSCO + M}

↓

S + OCS
OCS₂*共M兲 → OCS2+ M

↓

S2共a1⌬g兲 + CO

For the constant prediction, the potential-energy surface 共PES兲 obtained by both G2M共CC2兲 and CCSD共T兲/6-311 + G共3df兲储B3LYP/ 6-311+ G共3df兲 methods have been tested

using the above reaction scheme; the result of the calculation based on the crossing energies at MSX1 obtained by the two methods 共see Fig. 5兲, 3.3 and 5.3 kcal mol−1_{, respectively,}

shows that the S disappearance rate is overpredicted by a factor of 2.4 at 300 K and 68% at 1000 K by the former method, and is underpredicted by 80% and 36% at the above two temperatures by the latter method. However, if the energy at MSX1 is adjusted up and down by 1.0 kcal mol−1 _{from those of G2M共CC2兲 and}

CCSD共T兲/6-311+ G共3df兲储B3LYP/ 6-311+ G共3df兲, respectively, to 4.3 kcal mol−1_{, calculations based on both PES’s lead to}

es-sentially the same values 关see Fig. 6共b兲兴, which also agree closely with experimental results over the temperature range studied. It should be mentioned that if the average frequen-cies calculated on the singlet and triplet surfaces at MSX1 and MXS2 were used, the predicted total rate constants in-crease by about 10% and 15% at 300 and 1000 K, respec-tively; the difference is well within the experimental scatters. The predicted individual and total rate constants based on the G2M共CC2兲 energetics and the frequencies on the singlet

sur-face for MSX1 with the 4.3 kcal mol−1 _{barrier, as described}

above, can be expressed as

k1a-1共T兲 = 4.65 ⫻ 10−14T0.93 ⫻exp关− 共5980/T兲兴 cm3_molecule−1_s−1_{, 共10兲} k_1a-2共T兲 = 1.27 ⫻ 10−14_T0.96 ⫻exp关− 共2239/T兲兴 cm3_molecule−1_s−1_{, 共11兲} k1a-3共T兲 = 3.99 ⫻ 10−21T2.50 ⫻exp关− 共4769/T兲兴 cm3_molecule−1_s−1_{, 共12兲} k1b-1共T兲 = 7.65 ⫻ 109T−8.22 ⫻exp关− 共4206/T兲兴 cm3_molecule−1_s−1_{, 共13兲} k1b-2共T兲 = 1.81 ⫻ 107T−6.98 ⫻exp关− 共6046/T兲兴 cm3_molecule−1_s−1_{. 共14兲}

The predicted total rate coefficients 共k1a-1+ k1a-2+ k1a-3

+ k1b-1+ k1b-2兲 are expressed as

k₁共T兲 = 1.43 ⫻ 10−16T1.58

⫻exp关− 共1940/T兲兴 cm3_molecule−1_s−1_{, 共15兲}

in which k1b-1共T兲 and k1b-2共T兲 were calculated for

P = 50 Torr. The equations are in the temperature range

of 298– 2500 K. At 298 K, k1b-1= 2.6⫻10−17 and

k1b-2= 1.50⫻10−19cm3molecule−1s−1; for T⬎1000 K, k1b-1

TABLE III. Vibrational wave numbers and rotational parameters for the reactants, intermediates, transition states, and products of the S + OCS reac-tion computed with the B3LYP/ 6-311+ G共3df兲 method. Bold values in pa-rentheses are experimental data taken from Ref.12.

Species Ia, Ib, Ic共GHz兲 Vibrational wave numbers 共cm−1兲

SO共a1⌬兲 21.4 1156.6 SO共X3_⌺−_{兲 21.4 1157.2} CS共X1_⌺+_{兲 24.7 1312.2} S2共a1⌬g兲 8.7 712.0 3_S 2共X3⌺g兲 8.7 716.1 CO共X1⌺+兲 58.3 2217.1 OCS共X1_⌺+_{兲 6.1 531.3, 531.3, 879.4, 2115.5} OCS2共1A1兲 6.6, 5.5, 3.0 363.0, 444.6, 523.9, 611.6共617.8兲, 666.5, 1882.1共1824.7兲 OCS2共3B1兲 6.4, 4.8, 2.7 288.2, 384.4, 510.9, 556.2, 611.0, 1801.8 SSCO共1A⬘兲 12.2, 2.9, 2.3 112.7, 402.3, 468.8, 502.9, 723.4, 2093.4 OSCS共1_{A⬘兲 30.2, 2.2, 2.0 134.7, 291.0, 488.0, 626.2共622.3, 620.5兲,} 1062.4共1056.2,1052.7兲, 1446.3 共1402.1, 1404.7兲 SOCS共1A⬘兲 123.3, 1.6, 1.6 63.7, 294.4, 436.4, 481.8, 904.9, 2036.0 TS1 11.9, 2.5, 2.1 336.1i, 134.0, 392.2, 435.5, 620.7, 1967.7 TS2 6.0, 4.0, 2.4 312.1i, 222.9, 397.1, 506.7, 755.7, 1998.3 TS3 12.1, 3.2, 2.5 417.5i, 274.0, 481.3, 588.8, 932.6, 1424.2 TS4 8.6, 3.8, 2.6 230.2i, 326.2, 468.5, 482.9, 796.3, 2106.7 TS5 11.2, 2.4, 2.0 239.2i, 64.4, 128.4, 281.9, 656.3, 2117.0 TS6 11.9, 3.2, 2.5 408.7i, 265.8, 499.8, 599.7, 964.1, 1426.8 TS7 17.4, 2.8, 2.4 487.7i, 293.4, 372.1, 615.5, 809.5, 1507.9 TS8 75.9, 1.5, 1.5 463.2i, 6.5, 186.9, 282.4, 938.9, 1242.5 MSX1 9.4, 2.5, 2.0 293.8i, 115.2, 454.2, 481.4, 587.9, 2078.8 MSX2 8.6, 2.7, 2.0 420.1i, 97.8, 359.8, 438.7, 449.6, 1528.8

is less than 2.5⫻10−17_cm3_molecule−1_s−1_{. For the channels}

via MSX1 and MSX2, the calculations assume a unity prob-ability for crossing from the triplet surface to the singlet surface. In view of the fact that the system involves two sulfur atoms, this assumption is expected to be valid.

Channel 共1a-2兲 is clearly the dominating path at tem-peratures below 1500 K, whereas channel 共1a-1兲 becomes non-negligible at temperatures above 1500 K, resulting in a more rapid increase of the rate coefficient at high tempera-tures. Formation rate of S2共a1⌬g兲+CO 共X

1_兺+_{兲 via the}

in-termediate OCS2 共1A1兲 is negligible because of the higher

barrier of TS6. Rate coefficients for each channel and the total rate coefficient, Eqs.共10兲–共15兲, are plotted in Fig.6共a兲; the total rate constants predicted using the PES obtained by the above two methods and those with 1.0 kcal mol−1 adjust-ment for MSX1 are plotted in Fig. 6共b兲, the experimental results are also plotted for comparison. The total rate

coeffi-cient with MSX1 = 4.3 kcal mol−1 _{agrees satisfactorily with}

experimental results in this work, and also with those at high temperatures reported by Shiina et al.,1 Oya et al.,2 and Woiki et al.3

D. Kinetic modeling for reactions under high pressure at low temperature

According to calculations, the stabilization of SSCO that was formed via MSX1 is negligible because the barrier for further reaction is small. Stabilization of OCS2 via channels

共1b-1兲 and 共1b-2兲 is negligibly small at low pressure, but becomes important at higher pressures. The pressure depen-dences of k1b-1 and k1b-2at 298 K in the pressure range of

0.0263– 1.316 atm were calculated to be

k1b-1关M兴 = 1.76 ⫻ 10−16共P/P0兲0.56 ⫻exp关− 共0.01287P0_{/P兲兴 cm}3_molecule−1_s−1 共16兲 and k1b-2关M兴 = 9.25 ⫻ 10−19共P/P0兲0.56 ⫻exp关− 共0.0129P0_{/P兲兴 cm}3_molecule−1_s−1_, 共17兲 in which P0 _{represent the pressure, 1 atm, of the}

standard state. At 298 K, k1b-1 关M兴 is

3.15⫻10−17_cm3_molecule−1_s−1 _{at 50 Torr, whereas k} 1b-1

关M兴 becomes 1.65⫻10−16_cm3_molecule−1_s−1 _{at 700 Torr.}

The stabilization of OCS2 via channel 共1b-2兲 is negligible,

with k1b-2 关M兴=1.66⫻10−19cm3molecule−1s−1 at 50 Torr

and k1b-2关M兴=8.71⫻10−19cm3molecule−1s−1 at 700 Torr.

We modeled observed temporal profiles of关S兴t with the mechanism described in Sec. IV A关Eqs.共1a兲,共1b兲,共3兲, and

共4兲兴 using the modeling programFACSIMILE;47the rate coef-ficient k1a obtained under 250 Torr remains unaltered. The

values of k1b-1= 1.65⫻10−16cm3molecule−1s−1 for P

= 700 Torr and T = 298 K were used for k1b. The pressure

dependences of k4 at 298 K in the pressure range of

0.0263– 2.63 atm was calculated to be

k4关M兴 = 4.11 ⫻ 10−12共P/P0兲0.76

⫻exp关− 共0.00995P0_{/P兲兴 cm}3_molecule−1_s−1_,

共18兲 with k4 关M兴=3.83⫻10−12cm3molecule−1s−1 at 700 Torr

and 298 K. Simulated decay curves are shown as solid lines in Fig.3; they are in satisfactory agreement with experimen-tal observation. The enhancement in rate coefficient results partially from the increase in k1b-1 共⬃40% of k1a兲 and

par-tially from secondary reactions of S with OCS2 and S2; the

latter was also enhanced at high pressure. V. CONCLUSION

Rate coefficients for the reaction of S with OCS in the temperature range of 298– 985 K have been determined. Our result at 298 K, k1=共2.7±0.5兲⫻10−15cm3molecule−1s−1, is

consistent with a previous measurement by Klemm and Davis.6Our new data in the range of 407– 985 K fill the gap

FIG. 6. 共a兲 Theoretically predicted rate coefficients for the reaction S + OCS→products. Channel 共1a-1兲: via TS1 on the triplet surface; channel 共1a-2兲: via SSCO and TS5 on the singlet surface; channel 共1a-3兲: via OCS2

and TS6 on the singlet surface; channel共1b-1兲: via SSCO and TS4 to form OCS2on the singlet surface; channel共1b-2兲: via MSX2 to form OCS2on the

singlet surface; solid line: total rate coefficient.共b兲 Comparison of experi-mental and calculated total rate coefficients. 쎲: experiment; dotted and dashed lines: calculated, using the PESs obtained at the G2M共CC2兲 and CCSD共T兲/6-311+G共3df兲储B3LYP/ 6-311+ G共3df兲 levels without any ad-justment; thick and thin solid lines: calculated, based on the PESs predicted by the two methods using the same 4.3 kcal mol−1 _{energy at MSX1,}

respectively.

164329-9 _{Rate coefficients of S共}3_{P兲+OCS J. Chem. Phys. 125, 164329共2006兲}

between reported rate coefficients for T艋478 K and T 艌860 K. From the combined available data, rate coefficients fit well with the equation k1 共T兲=共6.63±0.33兲

⫻10−20_T2.57±0.19_{exp关−共1180±120兲/T兴 cm}3_molecule−1_s−1

for the temperature range of 233– 1680 K; listed uncertain-ties represent one standard error in fitting. Theoretical

calcu-lations based on a PES computed at the

G2M共CC2兲储B3LYP/ 6-311+ G共3df兲 level indicate that, at

low temperature, the reaction proceeds via curve crossing to the singlet surface to form SSCO, followed by decomposi-tion to S2共a1⌬g兲+CO共X1兺+兲; at high temperatures, a direct abstraction reaction to form S2 共X3兺g−兲+CO共X1兺+兲 on the triplet surface becomes competitive. Predicted total rate co-efficients agree with experiments throughout the temperature range under investigation. According to calculations, the sta-bilization of OCS2 is enhanced under high pressures and at

low temperature. Secondary reactions of S with OCS2and S2

result in an enhanced decay of 关S兴, as was observed in our experiments.

ACKNOWLEDGMENTS

One of the authors共Y.P.L.兲 thanks the National Science Council of Taiwan共Grant No. NSC95-2119-M-009-032兲 and National Chiao Tung University for support. Another author 共R.S.Z.兲 thanks the Office of Naval Research, US Navy 共Contract no. N00014-89-J1949兲 for support. Also one of the authors 共M.C.L.兲 acknowledges support from the Taiwan Semiconductor Manufacturing Company for the TSMC dis-tinguished professorship and the National Science Council of Taiwan for a distinguished visiting professorship.

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