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Chemical Physics 332 (2007) 162–175

A detailed trajectory study of the OH + CO! H + CO2 reaction

Ernesto Garcia a, Amaia Saracibar a, Leire Zuazo a, Antonio Lagana b,*

a Departamento de Quımica Fısica, Universidad del Paıs Vasco, 01006 Vitoria, Spainb Dipartimento di Chimica, Universita di Perugia, via elce di sotto, 806123 Perugia, Italy

Received 4 September 2006; accepted 9 November 2006Available online 16 November 2006

Abstract

Extensive quasiclassical trajectory calculations of the rate coefficients, cross sections and product distributions of the OH + CO reac-tion have been carried out. From the detailed comparison of the values obtained on the most popular potential energy surfaces proposedin the literature an evaluation of the suitability of these surfaces for modeling the reactive process is made.� 2006 Elsevier B.V. All rights reserved.

Keywords: Molecular dynamics; Kinetics; Isotopic effects; Potential energy surfaces; Quasiclassical trajectories

1. Introduction

Extensive theoretical [1–18] and experimental [19–36]investigations have been carried out for the OH + CO!H + CO2 reaction. Similar calculations and experimentshave also been carried out for the reverse H + CO2!OH + CO reaction [37–45] as well as for related isotopicvariants. Previous work is reviewed in Ref. [46]. The highinterest for this reaction from both theoretical and experi-mental viewpoints is confirmed by the presence of invitedtalks in top international conferences and workshops onreactive dynamics (see for recent examples Refs. [47,48]).

The present paper focuses on the direct reactionOH + CO! H + CO2. This reaction is an important com-ponent of hydrocarbon combustion models since it con-tributes to the propagation of H and constitutes the mainsource of CO2 [49]. Also in atmospheric chemistry theOH + CO reaction plays a central role. This reaction is,in fact, the primary mechanism of loss for troposphericCO and a remarkable source of tropospheric ozone andCO2 (through the HO2 radical formed by the producthydrogen and molecular oxygen) [50].

Thermal rate coefficients, k(T), for the OH + CO!H + CO2 reaction have been measured over an interval

0301-0104/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2006.11.010

* Corresponding author.E-mail addresses: lag@dyn.unipg.it, noelia@dyn.unipg.it (A. Lagana).

of temperature T ranging from 80 to 2800 K. The valuerecommended by IUPAC for a temperature of 298 K is1.3 · 10�13 cm3 molecule�1 s�1 [51]. The measured valuesshow a strong non-Arrhenius dependence on temperature.At low temperature (below 500 K), they are nearly inde-pendent of T. On the contrary, at temperatures higher than500 K they sharply increase with T. Fits to measured ratecoefficients were produced using an RRKM approach.From them analytical expressions for the temperaturedependence of the thermal rate coefficient were derived[33,34,52].

Kinetic studies were also performed to investigate therole played by initial vibrational excitation of the OHand CO reactant molecules [21,23,26]. The CO vibrationalexcitation is inefficient to enhance reactivity. On the con-trary, when OH is promoted to the first excited vibrationallevel the reactivity increases by a factor of 7 at roomtemperature.

Absolute cross sections of the OH + CO reaction weremeasured by Wolfrum and co-workers [25,32] using theLP-LIF (laser photolysis – laser induced fluorescence)‘‘pump–probe’’ technique. OH radicals were produced byUV photolysis of H2O2. Wide Gaussian rotational energy(Erot) distributions having a maximum either at j = 6 orat j = 12 (depending on the frequency used for the excita-tion) were obtained. Wide Gaussian distributions havinga maximum either at 18.9 or at 26.1 kcal mol�1 were

E. Garcia et al. / Chemical Physics 332 (2007) 162–175 163

obtained also for translational energy (Etr). The measuredvalues of the cross section are 0.3 ± 0.1 and 1.2 ± 0.3 A2

depending on whether the collision energy is 18.9 or26.1 kcal mol�1 [32]. These values do not easily match withprevious experimental indications which lead to a cross sec-tion value of 19 ± 10 A2 at a collision energy of30.4 kcal mol�1 [25] (this value is believed to be overesti-mated because of the assumptions made when elaboratingmeasured intensities [14]).

Cross sections of the OH + CO reaction were also mea-sured by Casavecchia and collaborators using a crossedbeam apparatus detecting the CO2 product [28,30,31].The product center-of-mass angular (quoted in the litera-ture either as P(H 0) or PAD) and translational energy(quoted in the literature either as P ðE0trÞ or PTD) distribu-tions were obtained from the experiment at the followingtwo collision energy values: Etr = 8.6 and 14.1 kcal mol�1

(as usual product quantities are primed, reactant quantitiesare unprimed). The corresponding PADs of CO2 obtainedby deconvoluting the distributions in the laboratory angleexhibit a bimodal forward-backward structure (thoughwith a strong forward bias with respect to the directionof the OH beam). This feature was interpreted by theauthors as an indication that the reaction proceeds throughthe formation of an intermediate complex. The PTDs peakat about the same value of the product translational energyðE0tr ¼ 28 kcal mol�1Þ at both values of the reactant colli-sion energy of the experiment. However, the distributionis narrower at low Etr while it is quite broader at highEtr. This was rationalized in terms of a strong repulsiveinteraction between CO2 and H in the exit channel.

On the theoretical side a pioneering role has been playedby Schatz and his collaborators [11,37,38,53] who pro-duced and refined along the years a widely used potentialenergy surface (PES). Other PESs have been proposed bythe authors of Refs. [14,54,55] though without reachingthe same level of popularity.

Aim of the present paper is to contribute to the analysisof the suitability of the proposed PESs to reproduce exper-imental findings reported in the literature by running mas-sive batches of quasiclassical trajectories (QCT) using acrossed beam simulator [56] based on computing grid tech-nologies. To this end, particular care was taken to ensurethe convergence of the trajectory integrations. On thisaspect a comparison is made with the results of the QCTcalculations of Schatz and collaborators [11,12]. Othercomparisons are made with the QCT results of Kroesand collaborators [14] and with the quantum dressed clas-sical (QDC) method calculations of Billing et al. [10]. Acomparison is also made with transition state (TST) calcu-lations [8].

No comparison is made in this work with full quantumcalculations because available quantum results are stilleither of the reduced dimensionality type [2,4,5] or limitedto zero total angular momentum [9,12,13,15–17]. However,a previous comparison of classical versus (time dependent)quantum probabilities carried out at for vOH = jOH =

vCO = jCO = 0 and J = 0 (J is the total angular momentumquantum number) indicates that QCT probabilities arealways higher than quantum ones. This is true for thewhole range of collision energies considered (up to8 kcal mol�1) and in particular at low collision energies(for example, at a collision energy of 1.4 kcal mol�1 QCTprobabilities are 10 times larger than quantum ones [12]).

The paper is organized as follows: in Section 2 the func-tional formulation of the potential energy surfaces used fordynamical calculations and their main features are illus-trated. In Sections 3–5 a detailed discussion of calculatedrate coefficients and relevant isotopic effects (Section 3),reactive cross sections (Section 4) and product distributions(Section 5) is given. In Section 6 some conclusions aredrawn.

2. The potential energy surfaces used for calculations

The first full-dimensional PES for dynamical calcula-tions of the reactive properties of the OH + CO systemwas proposed by Schatz and co-workers in 1987 [37]. ThisPES is based on the many-body expansion approach [57].Accordingly, the potential energy is articulated as follows:

V ¼ V ð2ÞOH þ V ð2ÞCH þ V ð2Þ0O Hþ V ð2ÞCO þ V ð2Þ0OO þ V ð2Þ0CO

þ V ð3ÞHCO þ V ð3Þ0HCO þ V ð3Þ0HOO þ V ð3Þ0OCO þ V ð4ÞHOCO ð1Þ

with O and O 0 being the first and the second oxygen atomsof the system and V(2), V(3) and V(4) the two, three and fourbody terms, respectively, of the many body expansion. Thetwo and three body terms consist of polynomials in the re-lated internuclear distances multiplied by damping func-tions to make them vanish at large distances. The fourbody term consists of products of polynomials (of the samekind as those used for the two and three body terms) andGaussians enforcing the reproduction of the ab initio sta-tionary points. This has been subsequently modified[38,53] to smooth down singularities occurring during thenumerical evaluation of the potential energy (and its deriv-atives) and better reproduce the ab initio values of Ref.[37].

Further improvements were recently introduced usingthe same many-body expansion (Eq. (1)) to fit a new setof ab initio data [54,58,59]. The introduced modificationsfurther smoothed the surface and made it more accuratelyreproduce the stationary points. In this way the YMS [54]and LTSH [11] PESs were produced. The improvement ofLTSH over the previous PES of Schatz and collaboratorswas concerned both with the parameters of the four bodyterm V(4) and the modelling of the long range part of theOH + CO entrance channel. A modified version of theLTSH PES (called by the authors mod-LTSH) was alsoproduced [12] to single out the influence on the dynamicsof the wells located in the reactant channel by suppressingthe long range tail of the surface in the reactant region.

A different functional representation was adopted byBowman et al. [55]. Their PES is based on a Shepard

164 E. Garcia et al. / Chemical Physics 332 (2007) 162–175

interpolation [60] of the ab initio potential energy valuesby adopting a reduced dimensionality (three degrees offreedom) functional. The coordinates used for this pur-pose are the OH and CO internuclear distances and thedistance between the center of mass of the OH and COdiatoms. Finally, very recently, another full-dimensionalPES (Leiden) has been reported in the literature [14].The Leiden PES is also based on a Shepard interpolationof a set of 1250 electronic ab initio values generated iter-atively using the Collins’ GROW program [61]. Themethod requires both the ab initio energies and their firstand second derivatives.

In the dynamical study reported in this paper we focusour attention on the YMS and LTSH PESs not only becauseit has been possible to obtain from the authors a copy of therelated FORTRAN routines, but also because these twoPESs are extensively discussed in the literature. The maincharacteristic of these PESs (and of the Leiden PES as well)is the rather complex structure of the minimum energy path(MEP). This can be clearly seen in Fig. 1 where the main sta-tionary points of the YMS PES are shown (those of theLTSH PES, not given in the figure for aim of clarity, are sim-ilar). In the entrance channel there are two wells associatedwith the two linear complexes OH–CO and OH–OC (withthe former being deeper). Each well is followed by a barrierlocated in the entrance OH + CO channel. The two barriersare small (the smaller lies below the asymptotic energy of the

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0

5

10 10

Ene

rgy

/ kca

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-1

Ene

rgy

/ kca

l mol

-1

OH+CO

OH-CO

t-HO.CO

t-HOCO

-HOCO

c-HOCO

t-HOCO - HCO2

c-H.OCO

H+CO2

C2v

-HCO2

C2v

-HCO2 - H+CO

2

OH-OC

c-HO.CO

5

0

Fig. 1. A schematic representation of the stationary points of the YMSPES.

reactants). The key feature of the MEP connecting reactantsto products in the strong interaction region is a pair of deepwells corresponding to the cis and trans (the latter is thedeepest) geometries associated with a planar HOCO com-plex. These wells are separated by a relatively high barrierassociated with a non-planar geometry. From each of thesetwo HOCO wells departs a different path to the H + CO2

product valley. The first path connects the cis-HOCO com-plex directly to the products through a high barrier. The sec-ond path connects the trans-HOCO complex to another (lessdeep) well stabilizing another complex (with a C2v symme-try) through a barrier higher than that of the cis-HOCOcomplex. A further low barrier separates the C2v complexfrom the products.

A crucial feature of both the YMS and LTSH PESs isthe formulation of the V(4) term of the many body expan-sion of Eq. (1) because it causes instabilities during thenumerical integration of the motion equations and, as aconsequence, a poor conservation of the total energy [11].To improve the accuracy of the derivatives and the conser-vation of the total energy we checked the effect of bothvarying the integration time step and changing the numer-ical evaluation technique for calculating the potentialderivatives (considering one (forward), two and sevenpoints methods [63]). In addition, we compared the accu-racy of the numerical derivation against the analyticalone. For the numerical integration a time step of 0.24 fswas found to lead to a good compromise between totalenergy conservation and trajectory integration time. As aresult of this check we found also that, while a change inthe method and in the step used for the numerical evalua-tion of the potential derivatives does not lead to a signifi-cant difference in the accuracy of the integration of theequations of motion, the adoption of their analytical for-mulation (as done in the case of the YMS PES) does,indeed, lead to quite a reduction of non-converged trajecto-ries though not to their disappearance.

The possibility of integrating massive batches of trajecto-ries on a distributed platform allowed us to set boundariesto energy conservation stricter than those used for previousinvestigations [11]. In particular, we reduced the tolerancefor the total energy drift during the trajectory integrationto ±0.04 kcal mol�1 (the same deviation accepted for thecalculated ab initio electronic energies in the long rangeregion taken as asymptotic) and discarded all the trajecto-ries exceeding that limit. The setting of more severe bound-aries to total energy conservation has an obvious differentimpact on the calculated values of reactive and non-reactiveproperties. In fact, in general, the fraction of reactive trajec-tories discarded for this reason turns out to be much largerfor reactive than for non-reactive ones. This also impliesthat the reactive probabilities computed in our calculationsare always lower than those reported in Ref. [11].

The quasiclassical calculations were performed by run-ning a modified version of the program VENUS [62] cus-tomized to incorporate the mentioned PES routines. Asalready mentioned analytical derivatives were used for

E. Garcia et al. / Chemical Physics 332 (2007) 162–175 165

the YMS surface while a forward differentiation algorithmwas used for the LTSH one. As in Ref. [11] a time step of0.24 fs was used to integrate the trajectories on both sur-faces. Initial and final distances were set at 8.0 A for theYMS PES so as to guarantee that the corresponding poten-tial energy values differ from the asymptotic limit less than0.04 kcal mol�1. On the contrary, for the LTSH PES theinitial and the final distances were set equal to 6.3 Abecause beyond that limit no ab initio points are availableto support the spline fitting of the long range interaction.The adopted value for the maximum impact parameterhas been optimized for each surface and set of initial con-ditions. The number of integrated trajectories was also var-ied in the various runs depending on the accuracy requiredfor the specific property being considered.

3. Rate coefficients

A first comparison of theoretical results with experimen-tal data (and therefore a first evaluation of the suitability ofthe PESs considered) is carried out here by considering thevalues of thermal rate coefficients in an interval of temper-ature ranging from 80 K to 3000 K. The computationswere performed by selecting the values of initial transla-tional and rotational energies so as to mimic the Boltz-mann distribution at the considered temperature. Initialvibrational energies were selected to correspond to one ofthe relevant quantum states of the reactants: vOH = 0 and1 for OH and vCO = 0, 1, 2 and 3 for CO. The thermalizedrate coefficients were evaluated by properly averaging therelevant vibrational state specific rate coefficients. Thevalue of the maximum impact parameter was varied withtemperature and with the initial vibrational state of thereactants (sometimes its value had to be chosen to be quitelarge). For instance, at T = 500 K, vOH = 0 and vCO = 2 amaximum impact parameter value of 3.6 A was usedfor the calculations performed on the YMS PES, while forthe calculations performed under the same conditions onthe LTSH PES a value of 2.6 A was found to be adequate.

For each set of initial conditions the number of calcu-lated trajectories was chosen to be large enough to makethe statistical error of the rate coefficient (after discardingtrajectories poorly conserving total energy) lower than5%. For instance, at T = 298 K and vOH = vCO = 0 morethan 1,500,000 and 1,800,000 trajectories were integratedfor the YMS and the LTSH surfaces, respectively, whileat T = 2000 K and vOH = vCO = 0 the integration of200,000 and 300,000 trajectories was found to be sufficient.Calculated values of the rate coefficients were scaled usingthe statistical factor of 1/2 (to account for the doubledegeneracy of the OH(2P) electronic state).

The QCT estimates of the thermalized rate coefficientfor the OH + CO! H + CO2 reaction calculated on theYMS and LTSH PESs are shown in Fig. 2 (it has to bepointed out here that no correction whatsoever was intro-duced for the zero point energy). In the same figure, thevalues calculated on the YMS surface [8] using the

CCUS/SCT (competitive canonical unified statistical the-ory [64] with small curvature tunneling correction [65]) ver-sion of the TST method and using the QDC (quantumdressed classical) method [6] are also given for comparisontogether with fits to experimental data [33,34,52] (it isworth recalling here that our LTSH results of Fig. 2 aresmaller than those of Ref. [12] due to the adoption of moredrastic energy conserving boundaries). For sake of simplic-ity, we do not show in the figure the plot of the rate coef-ficients calculated using the mod-LTSH PES [17] (as amatter of fact mod-LTSH results are about 70% of theLTSH ones at low temperature and such a difference tendsto vanish as temperature increases).

The figure shows that both measured and calculated ratecoefficients undergo a clear change in slope in the tempera-ture interval ranging from 500 to 700 K implying, so far, alarge activation energy at high temperature and a low acti-vation energy at low temperature. Calculated values, how-ever, show a slope steeper than that of measured data.This feature is more pronounced for values calculated onthe YMS PES. In fact, the rates calculated at low tempera-tures are nearly temperature independent and constantlylower than experimental data (e.g., about a factor of 6 atT = 200 K). On the contrary, at high temperature, theQCT rates are larger than the experimental ones (e.g., abouta factor of 2 at T = 2000 K). Also for the LTSH PES, thevariation of slope at high and low temperature is steeperthan the one found in the experiment. As a matter of factQCT rates calculated on the LTSH PES at high temperatureare similar to the measured ones, while at low temperaturethey are definitely smaller (e.g., a factor of 10 at T = 200 K)and exhibit a non-negligible decrease with the inverse of T.It is worth noting here that the rate coefficients calculatedon the YMS PES are larger than those calculated on theLTSH PES in the whole range of temperature by about afactor of 2. A particular difference between the YMS andLTSH results is the value calculated for the threshold tem-perature. In fact, at about T = 80 K the value calculated onthe LTSH PES decreases slowly while that calculated on theYMS PES suddenly drops one order of magnitude in goingfrom T = 100 K to 80 K. This feature is usually associatedwith the fact that the width of the reaction channel at thesaddle is narrower (at the relevant energies) than the localamplitude of the vibration of the system.

As to the comparison between QCT and TST results(both performed on the YMS PES), TST rates are alwayshigher than the QCT ones (e.g., at T = 200 K the ratio isabout 6 and it decreases to 1.5 at T = 2000 K). Intuitively,such a difference could be rationalized in terms of the inclu-sion of the tunneling effects in the TST treatment (whilethis is not so in QCT treatments). The difference, however,cannot be entirely due to tunneling (the ratio between theTST values of the rate coefficient calculated by includingand excluding the tunneling correction is 1.12 at 200 Kand 1.03 at 500 K [8]). As a matter of fact TST and QCTresults almost coincide at very low temperature (e.g.,T = 80 K). A more convincing rationalization of the

0 1 2 3 4 5 6 7 8 9 10 11 12 131000 K/ T

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QCT-YMSQCT-LTSHTST-YMS [8]QDC-YMS [10]Fulle et al [33]Golden et al [34]Senosiain et al [52]

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

1000 K/ T

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Fig. 2. QCT thermalized rate coefficients calculated for the OH + CO reaction using the YMS (solid circles) and LTSH (solid squares) PESs plotted as afunction of the inverse temperature for the whole investigated temperature range (upper panel) and the zoomed high temperature range (lower panel).Corresponding values calculated on the YMS surface using the CCUS/SCT version of the TST method [8] and the QDC method [10] are plotted as opendiamonds and open triangles, respectively. Curves fitted to experimental results taken from Refs. [33,34,52] are also plotted as dashed-dotted, dashed andsolid lines, respectively.

166 E. Garcia et al. / Chemical Physics 332 (2007) 162–175

difference between TST and QCT results is the lower valid-ity of the transition state model treatment (especially asenergy increases) for systems having a PES with a complexstructure (like OH + CO). In connection with that, how-ever, it is worth pointing out here that at very low temper-ature (e.g., T = 80 K), at which TST assumptions betterapply, not only the absolute value of the rate coefficientis closer to QCT ones but so is also its decrease with tem-perature (one order of magnitude). This confirms also thatthe sharp drop off of the reactivity on the YMS PES is apeculiar feature of its low energy region. In the extremelylow energy region it may happen, however, that isolatedtrajectories find peculiar ways of reaching the product val-

ley because of the structured nature of the PES and themissing constraint for the zero point energy.

As to the comparison between QCT and QDC rate coef-ficients calculated on the YMS PES at low temperature thelatter are significantly larger than the former (ratios are 2.6and 3.5 at 500 K and 100 K, respectively). However, theirvalues are always smaller than TST ones with deviationslarger than what one might expect from a pure tunnelingeffect (see Ref. [52]). This indicates that also the deviationof QDC from QCT results is due to the dynamical approx-imations built in into the QDC method. This confirmsagain that further efforts should be paid to revise the poten-tial energy surface before carrying out full dimensional

E. Garcia et al. / Chemical Physics 332 (2007) 162–175 167

quantum calculations (as also implied by the outcome ofthe preliminary quantum calculations of Refs. [47,48]).

Thermal rate coefficients were measured for vibration-ally excited OH [21,26] and CO [23] reactants atT = 298 K. Measurements of k(Ttr = Trot = 298 K,Tvib)with Ttr, Trot and Tvib being the translational, rotationaland vibrational temperatures, respectively, are also avail-able for Tvib = 298, 1400 and 1800 K. For vOH = 1 andvCO = 0, the calculations performed at T = 298 K did notconverge. On the contrary, convergence was obtained forcalculations performed for excited CO. The values fork(Ttr = Trot = 298 K,Tvib = 298, 1400, 1800 K) were esti-mated by properly weighing the vibrationally state specific(for CO) rate coefficients.

The extension of QCT calculations to vibrationally statespecific thermal rate coefficients gave the following values:0.31, 0.54, 0.71 · 10�13 cm3 molecule�1 s�1 for the YMSPES and 0.17, 0.19, 0.20 · 10�13 cm3 molecule�1 s�1 forthe LTSH PES at Tvib = 298, 1400, 1800 K, respectively.These values deviate from the corresponding experimentaldata ((1.51 ± 0.56), (1.36 ± 0.50), and (1.30 ± 0.48) ·10�13 cm3 molecule�1 s�1, respectively) by a factor rangingfrom 5 to 2 for the YMS PES and from 9 to 7 for the LTSHPES. Moreover, while QCT results obtained on the YMSPES predict an increase of the rate coefficients with vibra-tional temperature, this is not so for both calculated (on theLTSH PES) and experimental results.

A detailed illustration of the effect of vibrational excita-tion of the reactant molecules on the rate coefficient isshown in Fig. 3. In the figure the rate coefficients calculatedon the YMS (top panel) and the LTSH (bottom panel) PESsfor several values of vCO and vOH are plotted as a function ofthe temperature. The low temperature values for vOH = 1and vCO = 0 are not shown because not converge.

As apparent from the figure, the excitation of the OHmolecule to the next upper vibrational state leads to a sig-nificant enhancement of the reactivity. For instance, thevalue of the rate coefficient calculated at T = 600 K is lar-ger (by a factor of 9.0 and 4.3) than the correspondingground state result for the YMS and LTSH PESs, respec-tively. At T = 3000 K the above mentioned factorsdecrease to 1.7 and 2.0. The enhancement obtained by pro-moting the OH molecule to its first excited vibrational levelis definitely larger than the one obtained when vibration-ally exciting the CO molecule. For example, at T =600 K, a factor of 6.3 and 1.7 is found when vOH = 0 andvCO = 2 (the vibrational energy of the state vCO = 2 ishigher than that of the state vOH = 1). This suggests thatthe vibrational motion of the OH molecule (especially inthe case of the LTSH PES as shown by the plots of the bot-tom panel of Fig. 3) largely channels the system to progressalong the reaction coordinate. On the contrary, the vibra-tional motion of the CO molecule does not seem to be par-ticularly efficient in enhancing the reactivity in spite of thefact the time dependent J = 0 full dimensional calculationsshow this effect to be appreciable [15,18]. However, thelarge increase of the reactivity obtained at low temperature

on the YMS PES (the enhancement factor is 7, 17, and 31for vCO = 1,2,3, respectively, at T = 298 K) seems to indi-cate that at low energy this PES channels the CO vibrationinto the motion along the reaction coordinate. Graphicalstudies show, indeed, that the coupling occurs mainly dur-ing the residence of the HOCO complex inside the relatedpotential energy well.

The ratio k(vOH = 0,vCO = 1)/k(vOH = 0,vCO = 0) hasbeen used to estimate the overall rate of the OH + CO reac-tion at high temperature (for temperatures above 1500 K anuncertainty of 1% in the ratio leads to an uncertainty in therate coefficient of 11% [29]). Ref. [29] quotes a value of 0.5for this ratio. Experimental results of Ref. [23] indicate thatan increase of the vibrational temperature (and conse-quently an increase of the population of the excited vibra-tional states) leads to a decrease of the reactivity. Thisbehaviour is clearly in contrast with the results of theQCT calculations performed at T = 3000 K on both YMSand LTSH PESs for which the ratio k(vOH = 0, vCO = 1)/k(vOH = 0, vCO = 0) is equal to 1.2 and 1.1, respectively.

The accuracy of the used OH + CO PESs was alsotested by comparing the calculated and experimental isoto-pic ratios. For the OH + CO! H + CO2 reaction and itsisotope variant OD + CO! D + CO2 experimental esti-mates of the rate coefficients have been obtained at severaltemperatures. From these and from other data of the liter-ature an analytical formulation of the temperature depen-dence of the isotopic effect was given [34]. Experimentaldata are also available for several CO isotopomers. In par-ticular, the effect of using 13C and 18O isotopes on the valueof the rate coefficient was measured [22,35]. Also, the OHradical reaction rate of 12C16O relative to 13C16O, 12C18Oand 13C18O and the reaction rate of 12C17O relative to12C18O were measured at T = 295 K [36].

To study the effect of the OH/OD substitution, QCTcalculations were performed (only on the YMS PES) forthe OD + CO! D + CO2 reaction at T = 150, 200, 250,298, 350 K, i.e., in the same range of temperatures investi-gated by the experiment. In these calculations the value ofthe maximum impact parameter was set equal to 3.4 A (asfor the OH + CO reaction at the same temperature). Morethan 2,000,000 (2,500,000 at T = 150 K) trajectories wereintegrated for each temperature and the error in the ratecoefficients (once discarded the trajectories poorly conserv-ing total energy) was smaller than 6%.

The QCT rate coefficients calculated for the OD + COreaction agree with the experimental data in decreasing withthe temperature although, as already found for OH + CO,in contrast with the experimental findings, its decrease is fas-ter. As to the OH + CO reaction, in the temperature rangeconsidered, the QCT values are roughly a factor of 2 smallerthan experimental data (with the exception of that calcu-lated at T = 150 K for which the factor is 3). The calculatedisotopic ratio k(OH + CO)/k(OD + CO) is 1.69 ± 0.23,0.85 ± 0.11, 0.88 ± 0.11, 0.97 ± 0.11, 0.85 ± 0.09 at T =150, 200, 250, 298, 350 K, respectively. These values differnon-negligibly from the experimental results. In fact, the

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(vOH

=0,vCO

=0)(v

OH=0,v

CO=1)

(vOH

=0,vCO

=2)(v

OH=0,v

CO=3)

(vOH

=1,vCO

=0)

Fig. 3. QCT vibrational-specific rate coefficients for the OH + CO reaction using the YMS (top panel) and LTSH (lower panel) PESs plotted as a functionof the inverse temperature for vOH = 0, vCO = 0 (circles connected by solid lines), vOH = 0, vCO = 1 (squares connected by long dashed lines), vOH = 0,vCO = 2 (triangles-up connected by short dashed lines), vOH = 0, vCO = 3 (triangles-down connected by dotted lines) and vOH = 1, vCO = 0 (diamondsconnected by dashed dotted lines).

168 E. Garcia et al. / Chemical Physics 332 (2007) 162–175

calculated isotopic ratio shows, at T P 200 K, more reactiv-ity for the OD than for the OH radical. This contrasts theexperimental results (e.g., the isotopic ratio is 2.6 and 1.7at T = 200 and 350 K, respectively).

To study the effect of isotopically substituting the COmolecule, QCT calculations were performed (only on theYMS PES) for the reactions OH + 12C16O, OH + 12C17O,OH + 12C18O, OH + 13C16O, OH + 13C17O and OH +13C18O at T = 295 K. The maximum impact parameterwas set at 3.4 A. More than 2,500,000 trajectories for eachreaction were integrated in order to obtain an error smallerthan 4.5%.

The values of QCT rate coefficients calculated (only onthe YMS PES) for the reactions OH + 12C16O,

OH + 12C17O, OH + 12C18O, OH + 13C16O, OH + 13C17Oand OH + 13C18O at T = 295 K are (2.62 ± 0.11),(2.42 ± 0.11), (2.17 ± 0.09), (2.26 ± 0.10), (2.32 ± 0.10)and (2.35 ± 0.10) · 10�14 cm3 molecule�1 s�1, respectively.These results show that there is no significant effect onthe rate coefficient when varying the mass either of C orof O in the CO molecule. This is true for all the O isotopes.This is also true when varying the O mass with 13C. On thecontrary, a slight decrease of the rate coefficient with theoxygen mass is found for12C.

Contrary to the experimental findings, results of QCTcalculations clearly evidence that all the isotopomers ofCO heavier than 12C16O are efficient when reactingwith OH. It happens, in fact, that the klight/kheavy ratio

E. Garcia et al. / Chemical Physics 332 (2007) 162–175 169

calculated for the 12C17O, 12C16O, 13C17O and 13C18O iso-topomers, relative to the OH + 12C16O reaction, are1.09 ± 0.09, 1.21 ± 0.10, 1.16 ± 0.10, 1.13 ± 0.10 and1.12 ± 0.10, respectively. The corresponding experimentalvalues are 0.943 ± 0.0045, 0.959 ± 0.0037 and 0.946 ±0.0110 for the 12C18O, 13C16O and 13C18O isotopomers[36] and 0.992 and 0.989–0.982 (at zero pressure anddepending on the bath gas) for the 13C16O and 12C18O[22,35] ones. Only the k(12C17O)/k(12C18O) ratio has avalue of 1.12 ± 0.10 that falls within the error bars of theexperimental data (1.013 ± 0.0049) [36]. The disagreementbetween theory and experiment is even larger when thecomparison of the mass-independent oxygen isotope frac-tionation (i.e., the excess of 17O relative to the naturalabundance ratio between 17O and 18O) is considered. Infact, QCT results predict a value of �22% while the exper-imental value gives +2% [35].

4. Cross sections

Due to the difficulty of deriving detailed indications onthe reactive process from thermal rate coefficients (becauseof their highly averaged nature) we extended the computa-tions to the value of the reactive cross section. To this endbatches of trajectories mimicking the experimental condi-tions of Ref. [32] were run. This means that OH and COwere set at their ground vibrational state with the latterhaving a thermal (300 K) rotational distribution. Theremaining conditions were set as follows:

(1) (case a) a Gaussian collision energy distribution (witha maximum at 18.9 kcal mol�1 and a FWHM of8.8 kcal mol�1) and a Gaussian rotational distribu-tion for OH (with a maximum at jOH = 7 and aFWHM of 8);

18 20 22

Translational e

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Cro

ss s

ectio

n / A

2

Wolfrum et al [32]QCT-YMSQCT-LTSHQCT-LTSH [14]QCT-Leiden [14]

Fig. 4. QCT cross sections calculated for the OH + CO reaction using the YMenergy. Experimental values of Ref. [32] are given as diamonds. QCT cross secLTSH (triangles up) and Leiden (triangles down) PESs are also shown.

(2) (case b) a Gaussian collision energy distribution (witha maximum at 26.1 kcal mol�1 and a FWHM of10.6 kcal mol�1) and a Gaussian rotational distribu-tion for OH (with a maximum at jOH = 12 and aFWHM of 7).

To compute the value of the cross section for these twocases batches of trajectories varying from 350,000 to600,000 were integrated depending on the collision energyand on the surface used. The large number of integratedtrajectories allowed us to keep the statistical error as lowas 1% in spite of the fact that, as already mentioned, alot of trajectories had to be discarded because of the smalltolerance boundaries adopted for total energy conservation(±0.04 kcal mol�1). The maximum impact parameter wasset equal to 2.6 and 2.4 A for the YMS and the LTSHPESs, respectively. As in the case of calculated rate coeffi-cients, computed cross section values were scaled using thestatistical factor of 1/2 (to account for the double degener-acy of the OH(2P) electronic state).

The comparison of the calculated cross sections withcorresponding experimental values is given in Fig. 4. Inthe figure the QCT values of Ref. [14] calculated usingthe LTSH and the Leiden PESs by setting the collisionenergy at 18.9 and 26.1 kcal mol�1 (the maximum of theGaussian distributions in the two measurements), the rota-tional state of the CO molecule at 7 (the most populatedstate at 300 K) and the rotational state of the OH moleculeat 7 and 12 (the maximum of the experimental Gaussiandistributions corresponding to the two cases), are shown.Values taken from the literature have been scaled by a fac-tor 1/2. The figure shows also that theoretical cross sectionsdo not agree with experimental results not only for theabsolute value but also for the energy dependence. In fact,the dependence of the calculated cross sections on the col-

24 26

nergy / kcal mol-1

S (circles) and LTSH (squares) PESs plotted as a function of the collisiontion values taken from Ref. [14] scaled by a factor 1/2 calculated using the

170 E. Garcia et al. / Chemical Physics 332 (2007) 162–175

lision energy shows a slope significantly flatter than thatfound by the experiment. The comparison of the absolutevalues is difficult because experimental data have beenquestioned and a revision of the calibration method hasbeen suggested [14,66]. The cross section values calculatedusing the YMS PES are approximately 2.5 times largerthan those calculated using the LTSH and the LeidenPESs. This may be associated with the larger depth ofthe entrance channel wells and with the slimmer width ofthe transition state barriers of the YMS PES.

A last comment is deserved by the difference between thecross section values we calculated on the LTSH PES andthose quoted in Ref. [14]. This is due not only to the differ-ent use of the statistical factor but also to the differentboundaries adopted for total energy conservation and tothe different selection of initial conditions (Gaussian distri-bution in our case, single energy in Ref. [14]).

More extended calculations were performed to deter-mine the value of the cross section for reagent translationalenergies differing from the experimental ones and falling inthe range 0.05–40 kcal mol�1. The calculations were per-formed by considering both the OH and the CO moleculesin their ground rovibrational states. To this end, batches oftrajectories varying from 30,000 to 60,000 at high energyand from 1,000,000 to 2,000,000 at low energy were inte-grated for the YMS and LTSH PESs, respectively. In thiscase too, the number of trajectories discarded becausepoorly conserving total energy is large and different forreactive and non-reactive events. As a matter of fact, theyrange from 15% to 50% for reactive events and sum up to amaximum of 5% for non-reactive ones on the YMS PES.On the contrary, in the case of the LTSH PES they rangefrom 55% to 85% for reactive events and sum up to a max-imum of 15% for non-reactive ones. However, due to the

0 5 10 15

Translational e

0.0

0.1

0.2

0.3

0.4

Cro

ss s

ectio

n / A

2

QCT-YMSQCT-LTSHQCT-LTSH [11]QCT-Leiden [14]

Fig. 5. QCT cross sections calculated for the OH + CO reaction using the YMenergy. QCT cross section values taken from Refs. [11,14] scaled by a facto(triangles down) PESs are also shown.

large number of calculated trajectories the error madewhen estimating the cross section value is as low as 3% athigh energies and 6% at the lowest energy considered.The value of the maximum impact parameter was variedaccording to the collision energy from 2.6 A (at highenergy) to 4.0 A (at low energy).

In Fig. 5, the theoretical estimates of the cross sectionare plotted as a function of the collision energy for a quitelarge collision energy interval (0.05–40 kcal mol�1). Theexcitation function has the typical behaviour of those ofbarrier controlled reactions (yet we have been unable tosingle out a clear threshold energy value that may suggestthe coming into play, at low collision energy, of reactivecontributions following peculiar paths to products). Forthe sake of comparison also the excitation functionsquoted in Refs. [11,14] and calculated on the LTSH andthe Leiden PESs are plotted in the same figure. As appar-ent from the figure, the cross section values computed onthe YMS PES show a pronounced increasing trend (withEtr) starting at Etr = 3 kcal mol�1 and reaching a plateauof 0.4 A2 at Etr = 25 kcal mol�1. On the contrary, thecross sections calculated on both the LTSH and the Lei-den PESs show still a continuous positive trend thoughwithout reaching a plateau in the same range of transla-tional energy. Another important difference of the crosssection calculated on the LTSH PES, with respect to thatcalculated on the YMS PES, is its smaller absolute value(that instead is similar to the one obtained on the LeidenPES).

Finally, also the effect of rotationally exciting the reac-tant CO molecule has been investigated. The calculationsconfirm the findings of Ref. [11] which indicate that a var-iation of rotational energy enhances reactivity only at lowcollision energy.

20 25 30 35 40

nergy / kcal mol-1

S (circles) and LTSH (squares) PESs plotted as a function of the collisionr 1/2 calculated using, respectively, the LTSH (triangles up) and Leiden

E. Garcia et al. / Chemical Physics 332 (2007) 162–175 171

5. Reaction probabilities and product distributions

More detailed information on the reaction dynamicsand on the accuracy of the PES adopted can be obtainedby analyzing the probabilities calculated on it and compar-ing their values with even more detailed molecular beamdata [28,30,31]. Usually, this comparison is carried outfor PTDs and PADs.

To work out a theoretical estimate of the PADs and thePTDs of the OH + CO reaction at the conditions of theexperiment, we performed QCT calculations on boththe YMS and LTSH PESs by setting the collision energyat 8.6 and 14.1 kcal mol�1 and the rovibrational energyof both the OH and CO molecules as that of their groundstate. Batches of more than 1,000,000 trajectories were cal-culated using a maximum impact parameter of 2.6 and2.4 A for the YMS and the LTSH PESs, respectively. Fol-

0 30 60

Scattering Angle

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Prob

abili

ty

Etr=8.6 kcal mol-1

Etr=14.1 kcal mol-1

Fig. 6. Product angular distribution for the OH + CO! H + CO2 reaction epanel). Experimental values of Ref. [31] are given as a solid line (no error bars aare given as a dashed line while those calculated on the LTSH PES are given

lowing the already mentioned criterion of total energy con-servation during the trajectory integration, 2–3% and 3–5%of the non-reactive trajectories and 19–30% and 66–73% ofthe reactive trajectories were rejected for the YMS and theLTSH PESs, respectively.

Fig. 6 shows the product angular distributions calcu-lated on the YMS and LTSH surfaces at the two collisionenergy values of the experiment. As apparent from the fig-ure, calculated PADs show an almost symmetric back-ward–forward double peak structure with a slightpreference for the backward direction (with respect to theOH velocity). The backward–forward shape of the PADis usually interpreted as a result of the formation of anintermediate complex and this is, indeed, what is confirmedby the analysis of the calculated trajectories.

However, as shown by Fig. 6, the shape of the PADmeasured at the two energies considered in the crossed

90 120 150 180

/degrees

ExpQCT-YMSQCT-LTSH

valuated at Etr = 14.1 kcal mol�1 (upper panel) and 8.6 kcal mol�1 (lowerre given to keep the figure simple). QCT values calculated on the YMS PESas a dotted line. Distributions are normalized to the maximum.

172 E. Garcia et al. / Chemical Physics 332 (2007) 162–175

beam experiment has a definite backward peak placed ontop of a fairly large background backward–forward pla-teau. This implies that, in addition to the already men-tioned formation of an intermediate complex, the systemmay react also in a more direct way and a competitionbetween more than one concomitant reaction mechanismsof different dynamical nature (microscopic branching)may occur at least for a certain range of collision energies.

In spite of the fact that PADs calculated on both theYMS and the LTSH surfaces show an almost identicalsymmetric backward–forward distribution, the relatedproduct translational distributions calculated on the samesurfaces show clear differences. As a matter of fact, thePTDs calculated on the YMS PES have a maximumdepending on the reactant collision energy (that is located

0 5 10 15

Product Translatio

0.0

0.2

0.4

0.6

0.8

1.0

ExpQCT-YMSQCT-LTSH

0.0

0.2

0.4

0.6

0.8

1.0

Prob

abili

ty

Etr=8.6 kcal mol-1

Etr=14.1 kcal mol-1

Fig. 7. Product translational energy distribution for the OH + CO!H8.6 kcal mol�1 (lower panel). Experimental values of Ref. [31] are given as acalculated on the YMS PES are given as a dashed line while those calculated onthe maximum.

at E0tr ¼ 19 and 21 kcal mol�1 for reactant collision ener-gies of 8.6 and 14.1 kcal mol�1, respectively). On the con-trary the PTDs calculated on the LTSH PES at the samecollision energies have both a maximum at E0tr ¼23 kcal mol�1 (see Fig. 7). The PTDs are basically symmet-ric (the average product translational energies are coinci-dent with the value at the maxima) with the distributionscalculated at Etr = 14.1 kcal mol�1 being slightly broaderthan the ones calculated at Etr = 8.6 kcal mol�1. Largerdifferences are shown by the PTDs. Those calculated onthe LTSH PES are, in fact, systematically closer to theexperimental distribution than those calculated on theYMS one. However, none of the calculated PTDs coincideswith the corresponding experimental data. These resultsback the idea of a further source of inaccuracy in the pro-

20 25 30 35 40

nal Energy / kcal mol-1

+ CO2 reaction evaluated at Etr = 14.1 kcal mol�1 (upper panel) andsolid line (no error bars are given to keep the figure simple), QCT values

the LTSH PES are given as a dotted line. Distributions are normalized to

E. Garcia et al. / Chemical Physics 332 (2007) 162–175 173

posed PESs due to a wrong long behaviour of the PES inthe exit channel. Indeed, the comparison indicates that inthe present case both the YMS and the LTSH surfaceshave an inaccurate repulsive character (though the formerseems to be less accurate than the latter).

Further investigations were performed to study the roleplayed by the rotational temperature (the jCO = 1,2,3,4rotational states were considered) of the CO molecule.Related calculations were performed only on the YMSPES by integrating smaller batches of trajectories (about100,000 per run). Results are sketched in Figs. 8 and 9.Both the calculated PADs and PTDs indicate that anincrease of the CO rotational energy does not appreciablyaffect the product distributions and that the above men-tioned differences between calculated and measured PADsand PTDs are to be mainly ascribed to structural deficien-cies of the considered PESs.

0 30 60

Scattering An

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Prob

abili

ty

Etr=8.6 kcal mol-1

Etr=14.1 kcal mol-1

Fig. 8. Product angular distribution for the OH + CO(jOH = 0,1,2,3,4)!8.6 kcal mol�1 (lower panel) using the YMS surface. Distributions are normal

6. Conclusions

The extensive quasiclassical trajectory calculationsreported in this paper have achieved two important objec-tives in working out the theoretical estimates of the obser-vable properties of the OH + CO reaction:

(a) an unprecedentedly obtained accuracy in determiningrate coefficients, cross sections and probabilities;

(b) a clear indication that, though still within the limits ofa quasiclassical treatment, the used PESs are not fullysuitable for dynamical studies.

As to the first aspect, this is the result of the efforts spentin building grid enabled molecular simulators allowing theconcurrent running of large batches of trajectories and pro-viding a remedy to the too large trajectory rejection rate

90 120 150 180

gle /degrees

j=0j=1j=2j=3j=4

H + CO2 reaction evaluated at Etr = 14.1 kcal mol�1 (upper panel) andized to the maximum.

0 5 10 15 20 25 30 35 40

Product Translational Energy / kcal mol-1

0.0

0.2

0.4

0.6

0.8

1.0

j=0j=1j=2j=3j=4

0.0

0.2

0.4

0.6

0.8

1.0

Prob

abili

ty

Etr=8.6 kcal mol-1

Etr=14.1 kcal mol-1

Fig. 9. Product translational energy distribution for the OH + CO(jOH = 0,1,2,3,4)!H + CO2 reaction evaluated at Etr = 14.1 kcal mol�1 (upperpanel) and 8.6 kcal mol�1 (lower panel) using the YMS surface. Distributions are normalized to the maximum.

174 E. Garcia et al. / Chemical Physics 332 (2007) 162–175

(due to the poor total energy conservation during the inte-gration of classical dynamics equations).

As to the second aspect, this is the result of the effortsspent to compare calculated and measured observableproperties of the system. As a matter of fact, the YMSPES was found to lead to less accurate predictions of prod-uct distributions (suggesting that its exit channel should bemade more repulsive in order to allocate more translationalenergy into the products) while the LTSH one was found tolead to less accurate predictions of rate coefficients andcross sections (suggesting that its entrance channel shouldbe made more attractive in order to funnel more direct col-lision into reaction). However, both PES were still found tolead to a large fraction of poorly total energy conservingtrajectories despite the improvements introduced in thecomputational procedures (like the use of analytical deriv-atives or of more accurate numerical algorithms). This

means that a proper solution to represent the interactionwould be the adoption of a smoother functional form.

Acknowledgments

Partial financial support from MEC, MIUR, ASI andCNR is acknowledged. This work has been carried out asa part of the COST in Chemistry European CooperativeProject D23/0003/01. Computational assistance and re-sources were provided by the SGI/IZO-SGIker at theUPV/EHU (supported by the Spanish Ministry of Educa-tion and Science and the European Social Fund).

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