Phase space limiting high pressure rate coefficients for the title reaction on ab initio potential energy surfaces have been calculated at 50-600 K. Calculated rigidity factors at different levels of theory are presented. The best limiting high pressure rate coefficient obtained at 300 K, 4.0x10-11cm3 molecule-1 s-1, compares very well with the latest IUPAC recommended value.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Cobos, Carlos Jorge

Reaction Kinetics and Catalysis Letters

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Jointly published by React.Kinet.Catal.Lett.Akadémiai Kiadó, Budapest Vol. 79, No. 2, 263-269and Kluwer Academic Publishers, Dordrecht (2003)0133-1736/2003/US$ 20.00.© Akadémiai Kiadó, Budapest.All rights reserved.RKCL4232LIMITING HIGH PRESSURE RATE COEFFICIENTS FOR THEHO+NO2→HONO2 REACTION ON AB INITIO POTENTIAL ENERGYSURFACESCarlos J. CobosInstituto de Investigaciones  Fisicoquímicas  Teóricas y  Aplicadas (INIFTA),  Departamento deQuímica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CONICET, CICBA,Casilla de Correo 16, Sucursal 4, (1900) La Plata, ArgentinaReceived  October 28, 2002Accepted  January 13, 2003AbstractPhase space limiting high pressure rate coefficients for the title reaction onab initio potential energy surfaces have been calculated at 50-600 K. Calculatedrigidity factors at different levels of theory are presented. The best limiting highpressure rate coefficient obtained at 300 K, 4.0 x 10-11 cm3 molecule-1 s-1,compares very well with the latest IUPAC recommended value.Keywords: Limiting high pressure rate coefficient, potential energy surface,HONO2INTRODUCTION The recombination reaction of HO radical with NO2 to form HONO2 is akey process in both tropospheric and stratospheric chemistry. By removing HOand NO2 into stable HONO2, partially responsible for acid precipitation, thisprocess couples the odd-hydrogen and odd-nitrogen families and terminatesimportant catalytic cycles involving these radicals [1]. Due to the fact thatglobal atmospheric models are particularly sensitive to the rate coefficient ofthis reaction, it has been extensively studied [2-5]. Despite of this,discrepancies remain, mainly at the higher part of the falloff curve thatdescribes the pressure dependence of the rate coefficients. In particular, thelimiting high pressure rate coefficients k∞ recommended for a long time at the264 COBOS: POTENTIAL ENERGY SURFACE NASA compilation [2] is more than a factor of four smaller than that given bythe IUPAC [3]. This fact is consistent with experimental values ranging from1.5x10-11 [6] to 7.5x10-11 cm3 molecule-1 s-1 [7] at 300 K. At present thedifference is smaller, the latest recommended values (1.8±0.2)x10-11cm3 molecule-1 s-1 [4] being and (4.1±2)x10-11 cm3 molecule-1 s-1 [5]. Thediscrepancies mentioned have been partly attributed to differences in the falloffextrapolation procedures employed and most probably to formation of thestable HOONO isomer through an alternative reactive channel. This Letter is concerned with a theoretical study of the title reactionemploying two versions of the statistical adiabatic channel model (SACM) [8-11] coupled with potential energy surfaces based on density functional theory(DFT) and ab initio molecular orbital calculations.THEORETICAL FORMALISM, RESULTS AND DISCUSSION In the frame of the SACM [8] the limiting high pressure rate coefficient fora recombination reaction is given by k∞=frigid k∞(PST) [9]. Here k∞(PST) islimiting high pressure rate coefficient provided by the phase space theory andfrigid is the so-called rigidity factor. k∞(PST) is exclusively determined by theinterplay between the isotropic part of the electronic potential and thecentrifugal potential, and provides an upper bound to the rate coefficients. Onthe other hand, frigid≤1 accounts for the contraction of the available phase spacedue to the anisotropy of the transitional motions. k∞(PST) is calculated as ∞k∞(PST) = (kT/h)(h2/2πµkT)3/2 [1/(2(2+2exp(-201/T))] ∑ (2J+1)exp{-[E0(J)-E0(J=0)]/kT} (1) J=0where k is Boltzmann´s constant, h is Planck´s constant, T is the absolutetemperature, µ is the collisional reduced mass, while the third factor, inbrackets, accounts for electronic degeneracy and the sum takes into accountrelevant centrifugal effects. E0(J) denotes centrifugal energy barriers as afunction of the total angular momentum J, obtained from the maxima of thechannel potential Vcent(J,r)=V(r)+Beff(r)J(J+1). Here V(r) is the electronicpotential along the reaction coordinate r (the HO-NO2 bond distance) andBeff(r)=[A(r)+B(r)]/2 the effective rotational constant. Calculations similar tothe present can be found elsewhere [8,9,11-15]. Different quantum chemical approaches were employed to estimate V(r),while Beff(r) values were derived from fully optimized geometries obtained withthe B3LYP hybrid functional [16,17] in conjunction with the large 6-311++G(3df,3pd) basis set. Ab initio single point energy calculations on DFTCOBOS: POTENTIAL ENERGY SURFACE 265structures were employed to compute the electronic potential. In this way, inaddition to the UB3LYP/6-311++G(3df,3pd) potential (potential I), values forV(r) at the PMP2/6-311++G(2df,2pd)//UB3LYP/6-311++G(3df,3pd) (potentialII) level were calculated. Our best estimations were performed at the highcorrelated coupled cluster singles and doubles approach, including aperturbational estimate of the triple excitations [18]: UCCSD(T)/6-311++G(2df,2pd)//UB3LYP/6-311++G(3df,3pd) (potential III) andUCCSD(T)/cc-pVTZ//UB3LYP/6-311++G(3df,3pd) (potential IV). The 6-311++G(2df,2pd) basis is formed by a total number of 151 basis functionswhile the cc-pVTZ basis contains 134. Coupled cluster methods are relativelyinsensitive to spin contamination and to the multireference character of thewavefunctions. In addition, alfa-beta and spatial spin symmetries weredestroyed by mixing HOMO and LUMO to obtain accurate unrestrictedwavefunctions for singlet states. The Gaussian 98 program [19] was used in allcalculations.Fig. 1. Dependence of the normalized electronic potentials on the HO-NO2 bond distance. ●: UB3LYP/6-311++G(3df,3pd); ▼: PMP2/6-311++G(2df,2pd)//UB3LYP/6-311++G(3df,3pd); ▲:. UCCSD(T)/6-311++G(2df,2pd)//UB3LYP/6-311++G(3df,3pd); ■: UCCSD(T)/cc-pVTZ//UB3LYP/6-311++G(3df,3pd). ---: Morse potential with βeq=2.04Å-1. The solid lines above r=2.1 Å are the results of the fits described inthe text1.5 2.0 2.5 3.00.00.20.40.60.81.0V(r)/Der (Å)266 COBOS: POTENTIAL ENERGY SURFACE To compare the shapes of the potential energy curves, reduced V(r)/Devalues are depicted in Fig. 1. Parts of the potentials relevant in the kineticcalculations (located above 2.1 Å) were fitted with a Varshni potential functionV(r)/De={1-(re/r)exp[-γ(r2-re2)]}2 (with re=1.410 Å) [20]. γ and De values foreach potential are: γ=0.5706 Å-2 and De=49.3 kcal mol-1 (potential I), γ=0.7079Å-2 and De=52.4 kcal mol-1 (potential II), γ=0.8308 Å-2 and De=50.7 kcal mol-1(potential III) and γ=0.8754 Å-2 and De=50.8 kcal mol-1 (potential IV). Astandard Morse potential V(r)/De={1-exp[-β(r-re)]}2 calculated with β=2.04 Å-1[11] is shown in Fig. 1 for comparison. The calculated Morse attractiveinteraction between HO and NO2 is much larger than that predicted employingthe quantum chemical potentials. However, as before, the higher part of theUCCSD(T)/6-311++G(2df,2pd)//UB3LYP/6-311++G(3df,3pd) potential can bevery well represented by using β=4.18 Å-1 (Potential V). As Fig. 1 shows, therest of the calculated potential curves lie between those calculated with thestandard Morse and with the coupled cluster method. Effective rotational constants estimated at the UB3LYP/6-311++G(3df,3pd)level from HO-NO2 values ranging from 1.410 to 3.125 Å were accurately fittedwith the function Beff(r)=0.3071/(1+0.6670(r-re)+0.3090(r-re)2). k∞(PST) valuescalculated with equation (1) and potentials I to V are listed in Table 1.Table 1Calculated k∞(PST) values (in units of cm3 molecule-1 s-1) for reaction HO+NO2→HONO2 atdifferent quantum chemical levels_____________________________________________________________________________  T(K)       Potential I        Potential II          Potential III       Potential IV        Potential V_____________________________________________________________________________    50         5.16x10-11         4.38x10-11           3.90x10-11           3.76x10-11           4.15x10-11  100         6.09x10-11         5.20x10-11           4.64x10-11           4.48x10-11                4.54x10-11  200         6.62x10-11         5.67x10-11           5.09x10-11           4.92x10-11              5.15x10-11  300         6.97x10-11         6.00x10-11           5.40x10-11           5.22x10-11           5.39x10-11  400         7.32x10-11         6.31x10-11           5.69x10-11           5.51x10-11           5.63x10-11  500         7.64x10-11         6.31x10-11           5.97x10-11           5.78x10-11           5.86x10-11  600         7.95x10-11         6.89x10-11           6.25x10-11           6.04x10-11           6.09x10-11_____________________________________________________________________________All calculated rate coefficients exhibit a small positive temperaturedependence. On the other hand, only small basis set effects on k∞(PST) areobserved from calculations performed with potentials III and IV. The presentaccurate  upper  limit  for  the  rate  coefficient  computed  at  300  K  ofCOBOS: POTENTIAL ENERGY SURFACE 2675.3x10-11  cm3 molecule-1 s-1 lies between the above mentioned recommendedNASA [2] and IUPAC [3] k∞ values. This suggests that the latter ones appear tobe too high, probably due to the concurrence of channels forming HONO2 andHOONO. The more recent recommendation available from the IUPAC website[5] gives a value of (4.1±2)x10-11 cm3 molecule-1 s-1 at 200-400 K which islower than the former recommendation but yet higher than that suggested byNASA, (1.8±0.2)x10-11 cm3 molecule-1 s-1 [4]. Combining the values of refs [4] and [5] with our best room temperaturek∞(PST), “experimental” rigidity factors of 0.3 and 0.8 result. Due to the factthat frigid typically ranges from about 0.002 to 0.6 [9,13], the present valueseems to be the highest reported so far. It should be noted that an accurate “apriori” estimation of frigid is a difficult task which requires a correctcharacterization of the transitional modes along the minimum energy path, onlyavailable by high-level ab initio methods. The first SACM approach for frigid isbased on a standard Morse function to represent the radial potential and anexponential decay of the transitional modes, namely ω ≈ ωeexp[-α(r-re)], tomodel the angular potentials [9]. An anisotropic parameter of α/β≈0.5reproduces satisfactorily the experimental k∞ values of a large number ofrecombination reactions [9]. However, for the present system, large α/β valuesof 0.73 and 0.79 are required to reproduce the average consensus value of k∞=3x10-11 cm3 molecule-1 s-1 (frigid=0.56) with either the standard Morse (β=2.04Å-1) or with the potential V (β=4.18 Å-1). The very small frigid=0.008 obtainedwith β=4.18 Å-1 and a normal α/β=0.5 indicates that this reaction behavesanomalously. To our knowledge, no other reactions studied exhibit so large α/βvalues. An improved version named SACM/CT [10] that couples SACM withclassical trajectory calculations on valence potentials has been recentlydeveloped to study capture rate coefficients between two linear rotors formingeither linear or nonlinear complexes. Assuming an energized HONO2 adductwith a perpendicular arrangement of HO and NO2 rotors, Troe [11] estimatesrigidity factors (for α/β=0.5) of 0.82 at 0 K and of about 0.66 at 300 K. Wehave employed the SACM/CT approach using the same molecular input data ofref [11] to calculate k∞=frigid k∞(PST) with our coupled cluster/Morse potential(Potential V). Under this conditions, the frigid(T→0)=0.82 value of ref. [11] isreduced, over the temperature range 200-400 K, to about 0.75. These resultsindicate that the current reaction is close to its phase space limit and, therefore,the importance of an accurate knowledge of k∞(PST) is evident. In addition, themodel predicts frigid(T→0) values of 0.084 and 0.98 for α/β parameters of 0.3and 0.7. The resulting k∞, which is almost independent of temperature undertypical atmospheric conditions, is268 COBOS: POTENTIAL ENERGY SURFACE k∞ = 4.0x10-11 cm3 molecule-1 s-1The estimated value agrees very well with that obtained by Troe [11] fromextrapolation of the falloff curves of ref. [21] of 3.6x10-11 cm3 molecule-1 s-1,and with that recommended by the latest IUPAC compilation of (4.1±2)x10-11cm3 molecule-1 s-1 [5]. On the other hand, recent laser flash photolysis/LIFexperiments by Hippler and co-workers [22] provide convincing evidence forHOONO isomer formation. They were able to separate temporallyHO+NO2+He→HONO2+He and HO+NO2+He→HOONO+He reactions, andmeasure the respective absolute rate coefficients from 5 to 94 atm. It isinteresting to note that the highest value they measure at 430 K, 2.1x10-11cm3 molecule-1 s-1, does not appear to have yet reached the high pressureregime. Finally, if the formation of HONO2 and HOONO are truly separatedprocesses and the experiments of ref. [7] (k∞=7.5x10-11 cm3 molecule-1 s-1) yielda measure of the sum of the rate coefficients, the present results indicate thatsimilar k∞ should be expected for both channels. In summary, the present high-level ab initio potential data implemented inSACM/CT calculations leads to limiting high pressure rate coefficients for thetitle reaction which are in very good agreement with latest IUPACrecommended value [5]. Further quantum chemical studies are beingundertaken to characterize the anisotropic potential in order to improve frigid.Acknowledgements. This work was supported by the Universidad Nacional deLa Plata, the Consejo Nacional de Investigaciones Científicas y Técnicas(CONICET, PIP 0450), the Comisión de Investigaciones Científicas de laProvincia de Buenos Aires (CICBA) and the Agencia Nacional de PromociónCientífica y Tecnológica (PICT 6786).  The author is grateful to Prof. JürgenTroe for helpful discussions.REFERENCES1. H. Johnston: Science, 173, 517 (1971).2. W.B. DeMore, S.P. Sander, D.M. Golden, R.F. Hampson, M.J. Kurylo, C.J. Howard,A.R. Ravishankara, C.E. Kolb, M.J. Molina: Chemical Kinetics and Photochemical Datafor Use in Stratospheric Modeling. Evaluation 12, NASA/JPL, Publication 97-4,Pasadena, CA, 1997.3. R. Atkinson, D.L. Baulch, R.A. Cox, R.F. Hampson, J.A. Kerr, M.J. Rossi, J. Troe:J. Phys. Chem. Ref. Data, 26, 1329 (1997) and references therein.4. S.P. Sander, R.R. Friedl, W.B. DeMore, D.M. Golden, M.J. Kurylo, R.F. Hampson, R.E.Huie, G.K. Moortgat, A.R. Ravishankara, C. E. Kolb, M. J. 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Limiting high pressure rate coefficients for the HO+NO2&→HONO2 reaction on ab initio potential energy surfaces

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Limiting high pressure rate coefficients for the HO+NO2&→HONO2 reaction on ab initio potential energy surfaces

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