Theoretical Study of the NH 2 + C 2 H 2 Reaction

Transcription

1 J. Phys. Chem. A 1998, 102, Theoreticl Study of the NH 2 + C 2 H 2 Rection L. V. Mosklev nd M. C. Lin* Deprtment of Chemistry, Emory UniVersity, Atlnt, Georgi ReceiVed: Jnury 20, 1998; In Finl Form: April 3, 1998 The potentil energy surfce of the mino rdicl rection with cetylene hs been studied by the b initio moleculr orbitl method, nd the rection rte hs been computed by multichnnel RRKM clcultion. At the highest G2M(RCC) level of theory, the brrier height for the ddition step ws clculted to be 8.24 kcl/mol, producing solely the HCCH-trns mino-vinyl rdicl. The dduct cn further undergo NH 2 -for-h displcement decomposition nd severl isomeriztion rections. The RRKM clcultion ws crried out for the lowest energy pth, nd the result indictes tht the rte constnt is expected to be pressure-dependent due to incresed redissocition rte t low pressures. Kinetic modeling performed under experimentl conditions revels substntil effect of secondry rections on the observed NH 2 decy rtes. This my explin the low ctivtion energies reported for this rection. I. Introduction The midogen (or mino) rdicl, NH 2, is isoelectronic with CH 3 nd OH. These rdicl species re relevnt to fossil fuel combustion rections. NH 2 plys pivotl role in the therml deno x process nd in N-contining fuel chemistry. 1 The rections of NH 2 with hydrocrbons, prticulrly smll unsturted ones such s C 2 H 2 nd C 2 H 4, re lso importnt to the tmospheric chemistry of Jupiter nd Sturn involving NH 3, CH 4, nd their photochemicl derivtives. 2,3 The mechnisms of these rections hve not been sufficiently chrcterized. For the rection of interest to the present study, NH 2 + C 2 H 2, four independent investigtions employing different methods of rection rte determintion hve been reported Hck et l. 12 first mesured the rte constnt by dischrge-flow/lserinduced fluorescence (DF/LIF) technique using He s crrier gs t 1 Torr pressure in the temperture rnge K. The reported rte constnt, k ) T cm 3 /(mol s), exhibits strong negtive temperture dependence. Bosco nd co-workers, 13 on the other hnd, observed positive temperture dependence with k ) e -1850/T cm 3 /(mol s), employing flsh photolysis/lser-induced fluorescence (FP/LIF) method t Torr (Ar dilution) in the temperture rnge K. A similr study by Lesclux nd co-workers 10 used flsh photolysis/visible bsorption (FP/VA) technique t K with Torr C 2 H 2 without dilution. Their result, k ) e -2780/T cm 3 /(mol s), grees resonbly well with tht of Bosco, but differs significntly from tht of Hck. More recently, Hennig nd Wgner 11 investigted the rection t high tempertures behind incident shock wves ( K) t Ar pressures centering t 350 Torr. They reported k ) (3.7 ( 0.4) e -5700/T cm 3 /(mol s), giving the ctivtion energy s high s 11.3 kcl/mol. Theoreticlly, we must sk: Wht is the origin of the lrge sctter in the reported ctivtion energies (which vry from c. -5 to +11 kcl/mol) nd wht is the mechnism involved nd * Corresponding uthor. E-mil ddress: chemmcl@emory.edu. the mjor products formed over the rnges of temperture nd pressure investigted? To ddress these questions, we crried out detiled b initio moleculr orbitl (MO) nd RRKM clcultions to elucidte the mechnism of the rection nd to clculte the rte constnts for the formtion of vrious products ccessible t tempertures from 250 to 2500 K. In ddition, we hve performed kinetic modeling for the decy of NH 2 rdicls under the conditions employed by Hck, 12 Stief, 13 Lesclux 10 nd co-workers to exmine the potentil effect of secondry rections. The results of this investigtion re presented herein. II. Computtion Procedure A. Ab Initio MO Clcultions. The G2M theoreticl model employed in the present clcultion, hs been extensively described elsewhere. 5 The method modifies the originl G2 technique 4 for pplictions to lrger open shell systems. The following is brief description of the clcultion procedure. The most elborte RCC version of G2M hs been employed, s recommended for systems with one to three hevy toms. Accordingly, the geometries of ll the rectnts, products, nd trnsition sttes were fully optimized using the hybrid density functionl B3LYP method (Becke s threeprmeter nonlocl exchnge functionl 6 with the nonlocl correltion functionl of Lee, Yng, nd Prr 7 ) with the 6-311G- (d,p) bsis set. Vibrtionl frequencies were obtined t the sme level of theory for chrcteriztion of the nture of the sttionry points nd zero point energy (ZPE) corrections. The G2M(RCC) energy ws clculted for ech optimized structure s follows: 5 E[G2M(RCC)] ) E[PMP4/6-311G(d,p)] + E(+) + E(2df,p) + E(RCC) + + E(HLC) + ZPE[B3LYP/6-311G(d,p)] S (98) CCC: $ Americn Chemicl Society Published on Web 05/15/1998

2 4688 J. Phys. Chem. A, Vol. 102, No. 24, 1998 Mosklev nd Lin Figure 1. (A) Optimized (B3LYP) geometries of the vrious species involved in the rection of the NH 2 rdicl with cetylene. (B) Optimized (B3LYP) geometries of the vrious trnsition sttes involved in the rection of the NH 2 rdicl with cetylene. where E(+) ) E[PMP4/6-311+G(d,p)] - E[PMP4/6-311G(d,p)] E(2df,p) ) E[PMP4/6-311G(2df,p)] - E[PMP4/6-311G(d,p)] E(RCC) ) E[RCCSD(T)/6-311G(d,p)] - E[PMP4/6-311G(d,p)] ) E[MP2/6-311+G(3df,2p)] - E[MP2/6-311G(2df,p)] - E[MP2/6-311+G(d,p)] + E[MP2/6-311G(d,p)] E(HLC) )-5.71n β n R where n R nd n β re the numbers of R nd β vlence electrons, respectively, nd the numericl coefficients re given in units of mhrtree. The frequencies nd ZPE clculted t the B3LYP/6-311G- (d,p) level were used without scling. All the moleculr orbitl clcultions were performed with the GAUSSIAN94 progrm pckge 8 except those of RCCSD(T), which were crried out using the MOLPRO96 9 progrm. B. Multichnnel RRKM Clcultions. The effects of temperture nd pressure on the rte of the NH 2 + C 2 H 2 rection were exmined for the lowest energy pth (Figure 3) with the inclusion of the dectivtion of the chemiclly ctivted dducts denoted by : NH 2 + C 2 H 2 y\z t-h b - 2 NCHCH y\z -b c-h 2 NCHCH 98 c H 2 NC 2 H + H (1) t-h 2 NC 2 H 2 + M f t-h 2 NC 2 H 2 + M (2) c-h 2 NC 2 H 2 + M f c-h 2 NC 2 H 2 + M (3) Severl multichnnel, coupled systems of this type hve been treted in this lbortory erlier, e.g., the rection of NH 2 with NO producing OH + HN 2 nd H 2 O + N 2 vi two long-lived intermedites, H 2 NNO nd HNNOH. 14 The sme computer progrm employed for the NH 2 + NO rection ws used in the present clcultion. III. Results nd Discussion The geometries of the rectnts, intermedites, products, nd connecting trnsition sttes re summrized in Figure 1(A) nd (B). The schemtic potentil energy profile of the entire system is shown in Figure 2. The computed energetics by vrious methods nd the moleculr prmeters for the species relevnt to RRKM clcultions re presented in Tbles 1 nd 2, respectively. Here, nd in the discussion below, ll the energies re relted to the rectnts, unless otherwise noted. A. Rection of Amidogen with Acetylene. Two options re open for the first rection step, nmely, ddition to the triple bond nd the bstrction of hydrogen tom by the NH 2 rdicl.

3 Theoreticl Study of the NH 2 + C 2 H 2 Rection J. Phys. Chem. A, Vol. 102, No. 24, Figure 2. Schemtic energy digrm for the potentil energy surfce of the NH 2 + C 2H 2 rection. Energies re obtined from the G2M(RCC) clcultion. Figure 3. Lowest energy pth used in RRKM clcultions on the NH 2 + C 2H 2 system. The ltter is shown to hve high brrier of kcl/mol nd is, therefore, of minor importnce for the rection kinetics. Our investigtion hs thus been focused on the ddition chnnel nd the further trnsformtions of the dduct. The trnsition stte for NH 2 ddition to C 2 H 2, represented on the digrm s TS1, lies 8.24 kcl/mol bove the rectnts t our G2M(RCC) level. It hs C s symmetry, the two hydrogen toms of the mino group being out of plne. However, in the

4 4690 J. Phys. Chem. A, Vol. 102, No. 24, 1998 Mosklev nd Lin TABLE 1: Reltive Energies (ZPE-Corrected, in kcl/mol) for Species nd Trnsition Sttes Involved in the Rection of Amino Rdicl with Acetylene species nd trnsition sttes ZPE B3LYP/6-311G(d,p) UMP2/6-311+G(3df,2p) PMP4/6-311G(2df,p) RCCSD(T)/6-311G(d,p) G2M(RCC) NH 2( 2 B 1) + C 2H 2( 1 g+ ) b TSbstr NH 3( 1 A 1) + C 2H( 2 + ) TS trns-nh 2C 2H cis-nh 2C 2H TS TS NH 2CCH( 1 A ) + H TS TS3iso NH 2CCH 2( 1 A ) TS NHCHCH TS TS NHCCH 2( 1 A ) + H ZPE is clculted t the B3LYP/6-311G(d,p) level. b The totl energies (in hrtree) for the NH 2 + C 2H 2 system re B3LYP/6-311G(d,p), ; MP2/6-311G(d,p), ; MP4/6-311G(d,p), ; MP2/6-311+G(d,p), ; MP4/6-311+G(d,p), ; MP2/6-311G(2df,p), ; MP4/6-311G(2df,p), ; MP2/6-311+G(3df,2p), ; RCCSD(T)/6-311G9d,p), dduct, the hybridiztion chnges to sp 2 ; tht is, the geometry of the N-center is lmost plnr nd twisted reltive to the TS structure, so tht the C s symmetry is not preserved. This symmetry brekdown t some point long the rection coordinte is cusing splitting of the pth or double pth degenercy on going from the product to TS1. To be ccurte, we crried out n IRC procedure which enbled us to observe the geometry chnge in the course of the rection. An IRC (intrinsic rection coordinte) nlysis reveled dditionlly tht the product formed hs trns-structure in the outermost CH bond orienttion. However, we were unble to locte ny other trnsition stte different from TS1 tht would relte the lterntive cis-structure nd the rectnts. The geometries of the two isomers re similr (with the exception of one ngle) nd so re their energies, nd kcl/mol reltive to the rectnts, the deeper minimum corresponding to cis-isomer. The conversion brrier is smll, less thn 3 kcl/mol from trns to cis. Therefore, t modertely high tempertures the interchnge occurs fst enough to render the two structures indistinguishble. B. Hydrogen Atom Migrtion. We considered two possibilities for the hydrogen tom migrtion to form more stble rdicls NH 2 -CdCH 2 nd NH-CHdCH 2. The ltter is remrkbly stbilized by electronic resonnce (its energy is kcl/mol lower compred to trns-nh 2 C 2 H 2 ). The two corresponding trnsition sttes (defined s TS3iso nd TS4) hve close energies, nd kcl/mol bove the rectnts, respectively, the former being linked to the trns-isomer wheres the ltter is llied with the cis-isomer. NH 2 CdCH 2 product cn be formed from the cis-intermedite s well; this process refers to TS3 nd requires much higher ctivtion energy. C. Dehydrogention. At high tempertures, ll rdicl intermedites re expected to lose hydrogen tom, forming stble molecules. Kicking off the hydrogen tom from cis- NH 2 -CHdCH produces minocetylene NH 2 -CtCH. Similrly to the NH 2 ddition to the triple bond of cetylene, H ddition to NH 2 -CtCH occurs stereospecificlly; tht is, only cis-nh 2 -CHdCH is formed. This ws confirmed by IRC rection pth nlysis. The corresponding brrier height for the forwrd rection is kcl/mol. The hydrogen tom loss by the two other intermedites, NH 2 CCH 2 nd NHCHCH 2, leds to n isomeric product, HNdCdCH 2, which is kcl/ mol more stble thn its counterprt. In fct, NH 2 CCH 2 cn lso decompose to NH 2 -CtCH, but becuse of high endothermicity, this chnnel is not importnt to the overll rection rte. D. Rte Constnts for the Rection vi the Lowest Energy Pths. The lowest energy pths for the rection of NH 2 with C 2 H 2 nd the decomposition of the H 2 NC 2 H 2 (cis + trns) dducts re depicted in Figure 3. Becuse of the smll energetic nd structurl difference between the cis- nd trns-h 2 NC 2 H 2 isomers, these two dducts were treted to be the sme, nd only single well ws ssumed in our RRKM clcultions. The rte constnt for the disppernce of the NH 2 rdicl in the presence of n excess mount of C 2 H 2, s employed under ll pseudo-first-order conditions, is controlled primrily by the ddition step () vi TS1 t low tempertures nd t pressures greter thn 10 Torr (s in the studies by Bosco 13 nd Lesclux 10 nd their co-workers). At lower pressures, employed in Hck s experiment (p ) 1 Torr), the redissocition of the excited dduct H 2 NC 2 H 2 becomes competitive with the dectivtion process. The mesured rte constnt is thus pressure-dependent. The pressure dependency becomes greter when the temperture of the system increses becuse of the incresing redissocition rte. The pressure effect is expected to diminish when the temperture of the system reches tht of the shock tube study by Wgner nd co-workers, T > 1500 K, becuse of the ccessibility of higher energy decomposition chnnels producing H toms vi the direct decomposition nd indirect isomeriztion/ decomposition chnnels s shown in Figure 3. The clculted rte constnts for the disppernce of NH 2 t different pressures hve been fitted to the following Arrhenius equtions: k ) T 1.67 e -2559/T 250 K e T e 500 K k ) T -0.2 e -4689/T 500 K e T e 2000 K k(350 Torr) ) T e -3779/T 250 K e T e 500 K k(350 Torr) ) T 8.31 e 3740/T 500 K e T e 2000 K k(1 Torr) ) T e -2964/T 250 K e T e 500 K

5 Theoreticl Study of the NH 2 + C 2 H 2 Rection J. Phys. Chem. A, Vol. 102, No. 24, TABLE 2: Moleculr nd Trnsition-Stte Prmeters Used for RRKM Clcultions on the NH 2 + C 2 H 2 System species or trnsition stte E rel (kcl/mol) I I bi c (g 3 cm 6 ) b ν (cm -1 ) species or trnsition stte E rel (kcl/mol) I I bi c (g 3 cm 6 ) ν (cm -1 ) NH TS i C 2H b 643 NHCHCH TS i 826 TS i NH 2C 2H 2 (verge TS i 1078 of cis nd trns) Energies reltive to the rectnts re given s clculted by G2M(RCC)//B3LYP/6-311G(d,p), except the TS1, for which the energy ws lowered by 2 kcl/mol; the geometries nd vibrtionl frequencies re computed t the B3LYP/6-311G(d,p) level of theory. b For the cetylene molecule we give I I b in g 2 cm 3 (I c ) 0). Figure 4. Arrhenius plot of rte dt for the rection NH 2 + C 2H 2. RRKM result with the b initio brrier lowered by 2.0 kcl/mol; [10], [12], [11], nd [13] re experimentl dt. nd re lso presented in Figure 4 in comprison with experimentl dt. To quntittively ccount for the lowtemperture dt of Bosco et l. 13 nd Lesclux nd co-workers 10 (they re in close greement), the clculted ddition brrier ws lowered from 8 to 6 kcl/mol. The result of Hck et l. 12 obtined t 1 Torr He pressure with negtive ctivtion could not be resonbly ccounted for, however. The pprent lrge devition between theory nd experiment, prticulrly tht of Hck, results from the combintion of pressure nd secondry rection effects. In the Appendix, we summrize the results of kinetic modeling of NH 2 decy rtes employing experimentl conditions Figure 5. Kinetic modeling of the C 2H 2 + NH 2 rection under Bosco conditions (25 Torr): (1) Bosco; 13 (O) modeling result. Rte constnts re given in cm 3 mol -1 s -1. reported by these uthors. Using the predicted rte constnt clculted t 1 Torr pressure, we found tht Hck s NH 2 decy rtes were enhnced significntly by fst side rections such s NH 2 + NH 2 nd NH 2 + NH 2 C 2 H 2. We hve lso exmined the effects of secondry rections on the results of Bosco 13 nd Lesclux 10 under individul experimentl conditions. Surprisingly, both sets of dt obtined under the [C 2 H 2 ]. [NH 2 ] pseudo-first-order conditions were not immune to the effects, prticulrly t lower tempertures, t which the ddition rection becme slower nd the fster rdicl-rdicl rections becme competitive despite their lower concentrtions, becuse the kineticlly modeled rte constnts for NH 2 decy exhibit 1-2 kcl/mol higher ctivtion energies thn originlly reported (see Figures 5-7 nd the discussion in the Appendix for detil).

6 4692 J. Phys. Chem. A, Vol. 102, No. 24, 1998 Mosklev nd Lin TABLE 3: Mechnisms Used for the NH 2 + C 2 H 2 Rection rection A B C remrks Modeling under Bosco 13 Conditions 1. NH 2 + C 2H 2 ) NH 2C 2H b 2. NH 2 + NH 2 + M ) N 2H 4 + M C 2H 2 + H + M ) C 2H 3 + M C 2H 2 + H ) H 2 + C 2H C 2H 3 + NH 2 ) NH 3 + C 2H c Modeling under Lesclux 10 Conditions 1. NH 2 + C 2H 2 ) NH 2C 2H b 2. NH 2 + NH 2 ) N 2H NH 2 + NH 2 ) NH 3 + NH NH 2C 2H 2 + NH 2 f NH 2C 2H 2NH c 5. NH 2C 2H 2 + NH 2 f NH 2C 2H + NH c 6. NH 2C 2H 2 + H f NH 2C 2H c 7. NH 2C 2H 2 + C 2H 2 f NH 2C 4H c 8. C 2H 2 + H ) C 2H C 2H 2 + H ) H 2 + C 2H C 2H 3 + NH 2 f NH 2C 2H c 11. C 2H 3 + NH 2 ) NH 3 + C 2H c 12. C 2H 3 + NH ) NH 2 + C 2H c 13. NH 2 + H ) NH c 14. NH 2 + H ) NH + H H + H + M ) H 2 + M NH 2 + C 2H ) NH + C 2H c Modeling under Hck 12 Conditions 1. NH 2 + C 2H 2 ) NH 2C 2H d 2. NH 2 + NH 2 + M ) N 2H 4 + M NH 2 + NH 2 ) NH 3 + NH NH 2C 2H 2 + NH 2 f NH 2C 2H 2NH c 5. NH 2C 2H 2 + NH 2 f NH 2C 2H + NH c 6. NH 2C 2H 2 + C 2H 2 f NH 2C 4H c 7. NH 2 + H ) NH c 8. NH 2 + C 2H ) NH + C 2H c The rte constnts re given by k ) AT B e -C/T in units of cm 3, mol, nd s. b The rte constnts were obtined by fitting to NH 2 decys observed in the corresponding experimentl studies. c Assumed. d RRKM prediction for 1 Torr. Figure 6. Kinetic modeling of the C 2H 2 + NH 2 rection under Lesclux conditions (50 Torr): (1) Lesclux; 10 (O) modeling result. Rte constnts re given in cm 3 mol -1 s -1. The theoreticlly clculted results presented for 350 Torr Ar duplicting the condition employed by Hennig nd Wgner 11 exhibit strong nonliner behvior becuse of the redissocition of NH 2 C 2 H 2 t moderte tempertures ( K), beyond which the vlue of the rte constnt turns up shrply, resulting from the opening of the exit chnnels s mentioned bove. The predicted vlue in the K region grees resonbly with the mesured result of Hennig nd Wgner. Under hightemperture conditions, the NH 2 -for-h displcement process NH 2 + C 2 H 2 h NH 2 C 2 H 2 f NH 2 C 2 H + H (4) becomes dominnt, s illustrted in Figure 4. A similr observtion ws mde for the isoelectronic CH 3 + C 2 H 2 rection. 21 Figure 7. Kinetic modeling of the C 2H 2 + NH 2 rection under Hck conditions (1 Torr): (1) Hck; 12 (9) RRKM; (O) modeling result. Rte constnts re given in cm 3 mol -1 s -1. To complete the nlysis, we employed tunneling correction for the high energetic chnnels b nd c (eq 1). This test reveled tunneling effects on the overll rte to be negligible. IV. Conclusion We performed detiled investigtion of the NH 2 + C 2 H 2 rection mechnism combining high-level MO nd sttisticl theory clcultions. The clculted brrier for the ddition step is 8.24 kcl/mol t the G2M(RCC) level. With the exception of the NH 2 -for-h displcement products, NH 2 C 2 H + H nd NHCCH 2, ll dducts nd their isomers, NH 2 C 2 H 2 (-HCCHtrns nd -HCCH-cis) were found to be more stble thn the rectnts, NH 2 + C 2 H 2. Therefore, the rection is expected to produce predominntly these isomeric products. Multichnnel RRKM clcultions were crried out for the lowest energy pth including hydrogen loss by the dduct or

7 Theoreticl Study of the NH 2 + C 2 H 2 Rection J. Phys. Chem. A, Vol. 102, No. 24, its isomeriztion to llyl nlogue, NHCHCH 2, followed by dissocition to form NHCCH 2 + H. The low conversion brrier between cis- nd trns-dducts enbled us to tret them s single well. Our clcultion revels tht the rte constnt for the NH 2 disppernce is controlled primrily by the ddition step. The rection rte is expected to be pressure-dependent due to the incresed redissocition rte of the ctivted dduct t low pressures. The pressure effect is diminished t tempertures bove 1000 K becuse of the ccessibility of higher energy decomposition chnnels nd indirect isomeriztion/ decomposition chnnels. Kinetic modeling performed under experimentl conditions revels substntil effect of secondry rections on the observed NH 2 decy rtes. This explins the lrge sctter in the reported rte constnts nd ctivtion energies obtined under vrying experimentl conditions. Acknowledgment. The uthors grtefully cknowledge the support received from the Deprtment of Energy, Office of Bsic Energy Sciences, Division of Chemicl Sciences, through Contrct DE-FGO2-97ER Also, we re thnkful to the Cherry L. Emerson Center for Scientific Computtion for the use of vrious progrms nd computing fcilities. Appendix. Modeling of the NH 2 Decy Rtes under Vrious Experimentl Conditions We ttempted to model the effect of secondry rections on the NH 2 decy rtes for the three sets of experimentl dt by Bosco et l., 13 Lesclux et l., 10 nd Hck et l. 12 to ccount for the effective lower ctivtion energy s compred to the theoreticl prediction. In the study of Bosco et l., the NH 2 decy ws mesured by the flsh photolysis technique combined with time-resolved detection of NH 2 vi lser-induced fluorescence under [C 2 H 2 ]. [NH 2 ] conditions with [NH 2 ] 0 estimted s molecule cm -3 t typicl 1 Torr mmoni prtil pressure nd Torr totl pressure. The modeling ws performed for 25 Torr totl pressure with the mechnism given in Tble 3, where the rte of rection 1 ws vried to fit the experimentlly observed decy rtes (under the reported pseudo-first-order conditions). Our modeling (see Figure 5) predicts steeper slope for the disppernce of NH 2 vi the ddition step, with the ctivtion energy of 3.95 kcl/mol compring with the reported vlue of 3.36 kcl/mol. In similr mnner, we modeled the experiment by Lesclux et l., 10 who lso used flsh photolysis combined with the lser resonnce bsorption technique. In tht study, the initil concentrtion of the NH 2 rdicl ws molecule cm -3. Acetylene ws used s bth gs. Therefore, in the mechnism (Tble 3) the cetylene secondry rections re plying n importnt role. We hve modeled severl points t 50 Torr totl pressure nd observed substntil effect of secondry rections, s illustrted in Figure 6. Hck et l. 12 mesured the NH 2 decy in bout the sme region s the two studies discussed bove, but t lower pressures ( 1 Torr) using dischrge flow system with the lser-induced resonnce fluorescence detection of NH 2, which ws generted in the F + NH 3 f HF + NH 2 rection. The modeling bsed on the RRKM-predicted (for 1 Torr) rte constnt shows n enormous devition due to side rections (Figure 7). Our preliminry b initio clcultion predicts the formtion of the NH 2 HF moleculr complex, which is 9.7 kcl/mol [B3LYP/ 6-311G(d,p) level] more stble thn the isolted species. This my ffect the observed NH 2 decy rte s well. References nd Notes (1) Miller, J. A.; Bowmn, C. T. Prog. Energy Combust. Sci. 1989, 15, 287. (2) () Kye, J. A.; Strobel, D. F. Icrus 1983, 54, 417. (b) Strobel, D. F. Int. ReV. Phys. Chem. 1983, 3, 145. (3) Young, Y. L.; Allen, M.; Pinto, J. P. Astrophys. J. Suppl. Ser. 1984, 55, 465. (4) () Curtiss, L. A.; Rghvchri, K.; Trucks, G. W.; Pople, J. A. J. Chem. 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