Chemical Physics Letters 513 (2011) 31–36

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Chemical Physics Letters

journal homepage: www.elsevier .com/ locate /cplet t

Tunneling in hydrogen and deuterium atom addition to CO at low temperatures

Stefan Andersson a,b,c,d,⇑, T.P.M. Goumans a, Andri Arnaldsson e

a Gorlaeus Laboratories, Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlandsb Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlandsc SINTEF Materials and Chemistry, P.O. Box 4760, 7465 Trondheim, Norwayd Department of Chemistry, Physical Chemistry, University of Gothenburg, 41296 Gothenburg, Swedene Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavík, Iceland

a r t i c l e i n f o

Article history:Received 14 April 2011In final form 22 July 2011Available online 27 July 2011

0009-2614/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.cplett.2011.07.073

⇑ Corresponding author. Present address: SINTEP.O. Box 4760, 7465 Trondheim, Norway.

E-mail address: stefan.andersson@sintef.no (S. And

a b s t r a c t

The hydrogen and deuterium atom addition reactions of CO to form HCO and DCO are addressed byHarmonic Quantum Transition State Theory calculations. Special attention is paid to the reactions at verylow temperatures (5–20 K) where it is found that quantum tunneling leads to substantial rates of reac-tion. This supports experiments in the solid phase, which conclude that these reactions are driven by tun-neling at low temperatures. The calculated kinetic isotope effect of kD/kH = 1/250 is found to be lowerthan the experimentally deduced value of 0.08 for the surface reaction. Possible reasons for this discrep-ancy are discussed.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

The formation of methanol in interstellar space has been one ofthe long-standing mysteries of astrochemistry research. Thepossible gas-phase formation routes have been found to be tooinefficient to explain the observed abundances of methanol [1,2].Hydrogenation of solid carbon monoxide to form HCO at tempera-tures around 10 K was postulated to be the onset of methanol for-mation through consecutive H atom addition [3,4] following thesequence

CO ! HCO ! H2CO ! CH3O ! CH3OH. ð1Þ

The HCO radical was detected in cold matrices (10–25 K) andwas inferred to be formed from the H + CO reaction with a low acti-vation energy [5]. HCO has also been observed in experimentswhere H atoms and CO molecules have been simultaneouslydeposited on cold surfaces (1.3–10 K) [6,7]. Recent experimentalwork on solid CO exposed to H atom irradiation [7–11] confirmedthat also methanol is efficiently formed at 8–20 K. The H + CO reac-tion has a barrier of about 0.13–0.16 eV [12–14], which would leadto insignificant reaction rates at 5–20 K if only classical ‘over-the-barrier’ type dynamics were effective. Therefore, quantum tun-neling seems to be the dominant transition mechanism in thisreaction. Kinetic Monte Carlo modeling of the experimental resultsstrongly suggests that tunneling is important [10], since it wasfound necessary to incorporate temperature dependent barrierheights to the reaction. There have been a number of

ll rights reserved.

F Materials and Chemistry,

ersson).

computational studies on the dynamics and kinetics of the recom-bination reaction of H + CO to form HCO and its reverse reaction,unimolecular dissociation of HCO, for temperatures at and aboveroom temperature [15–20]. However, there has been no previousmolecular simulation study that confirms the importance of tun-neling in this reaction at very low temperatures.

Watanabe et al. [9,10] concluded from their experiments thatthere is an effective kinetic isotope effect of kD/kH = 0.08 in thereactions of D/H atoms with CO adsorbed on an amorphous waterice surface at 15 K. It is likely that the measured effective isotopeeffect is a combination of isotope effects in reaction, diffusion,and/or desorption. Tunneling generally favors the lighter isotopes,while in ‘classical’ barrier transitions, where tunneling is negligi-ble, the isotope effect depends on the type of physical process. Iftunneling is not important, heavier isotopes can be favoredbecause of a lower zero-point energy and as a result often a lowervibrationally adiabatic barrier. The aims of this study are to calcu-late the rate constants including tunneling down to low tempera-tures to establish if tunneling makes the reactions plausible andto estimate how large the isotope effect is in the H/D + CO reaction.

2. Computational methods

Thermal rate constants have been calculated using HarmonicQuantum Transition State Theory (HQTST) [21,22], which is arecent implementation of instanton theory [23–33]. The key con-cept in this methodology is the instanton, which is a first-ordersaddle point of the Euclidean action [31]. It constitutes the quan-tum mechanical analogue of a classical saddle point on theminimum energy path, with the difference that it is the saddle

32 S. Andersson et al. / Chemical Physics Letters 513 (2011) 31–36

point on the minimum action path [31,34]. For a chemical systemthe instanton could be viewed as a dominant tunneling path at agiven temperature [32]. In HQTST the instanton path is repre-sented by a Closed Feynman Path (CFP) [35]. The Euclidean actionof a CFP is calculated as

SE ¼Z �h=kBT

0Hds; ð2Þ

where H is the classical Hamiltonian of the system and s is the mag-nitude of imaginary time [35]. The CFP is discretized so it consists ofa finite number images of the system connected by temperature-dependent springs [36]. Then the calculation of the action becomes[21,22,31]

SE ¼�h

kBT

XP

k¼1

kspðTÞ2

qmodðk;PÞþ1 � qk

��� ���2 þ VðqkÞP

� �

¼ �hkBT

Veff ðq; TÞ; ð3Þ

where P is the number of images, qk are the coordinates of image k,and the spring constants are

kspðTÞ ¼ lPkBT�h

� �2

; ð4Þ

with l being the mass of the degree of freedom in question. Theeffective potential energy surface, Veff, is defined in NP dimensions,where N is the number of degrees of the physical system. The find-ing and optimization of the instanton then becomes a saddle pointsearch in NP dimensions. This is efficiently done by a minimummode following algorithm [37], which only requires first derivativesof the potential, with a Lanczos iterative approach to finding theminimum mode [38]. The HQTST instanton rate constant is calcu-lated as [30]

kinst ¼1

Q r

ffiffiffiffiffiffiffiffiffiS0

2p�h

r1

Ds P0jkj

��� ��� exp½�Veff ðqinst; TÞ=kBT�: ð5Þ

Qr is the reactant partition function, Ds = s/P = �h/kBT is theimaginary time step, kj are the normal mode frequencies of theinstanton chain, and S0 is the action of the ‘zero mode’, whicharises due to permutation of the images in the chain [21,22]. Theproduct of frequencies excludes the zero mode frequency (indi-cated by the prime on the product sign).

A very useful concept in this context is the crossover tempera-ture [27–29,39],

Tc ¼�hX

2pkB; ð6Þ

below which tunneling will dominate thermal rates. The only sys-tem-dependent parameter is X, which is the magnitude of theimaginary normal-mode frequency at a saddle point of the potentialenergy surface. Above Tc the instanton collapses onto this classicalsaddle point and therefore HQTST can only be applied below Tc.At higher temperatures simpler tunneling corrections to a transitionstate theory rate constant often work quite well [22,40].

HQTST was found to give rate constants in excellent agreementwith exact quantum dynamics for model 2D systems down into the‘deep tunneling’ regime at low temperatures [21]. Agreement wasalso good for the H + CH4 gas-phase reaction studied in full dimen-sionality down to 225 K [22]. Close to Tc only on the order of 10images are needed in the CFP to resolve the instanton, at lowertemperatures it is often enough to use about 102 images, and onlyat very low temperatures (Tc/T � 10 and lower T) it is necessary toinclude on the order of 103 images [22].

For the HQTST calculations we used the potential energy surfacefor the HCO system by Werner, Keller, and Schinke (WKS) [19],which was fitted to ab initio data at the MRCI + Q/cc-pVTZ leveland subsequently modified to match the experimental vibrationalspectrum and dissociation energy. The forces were calculated usingfinite differences. The calculations were run using Cartesian coor-dinates, i.e., in 9 degrees of freedom for a triatomic system suchas HCO. In this study the system was treated as a gas-phase unimo-lecular reaction (see Section 3). The general expression for the rateconstant, Eq. (5), is modified to treat a gas phase reaction such thatit is multiplied by the ratio of the rotational partition functions ofthe instanton and the reactant state (see Ref. [22] for details on thistreatment of rotational degrees of freedom). The translational par-tition functions of the instanton and reactant state cancel eachother in a unimolecular reaction.

The optimization of the instantons is performed as described byAndersson et al. [22]. In short, the calculations are run starting at atemperature just below Tc, where the instanton forms a path that isquite close to the classical saddle point. As a starting guess for theinstanton optimization the images of the CFP are distributed clo-sely around the saddle point in the direction of the unstable nor-mal mode. When the instanton has been optimized for onetemperature it is used as a starting guess for an instanton searchat a somewhat lower temperature. This is repeated until the lowesttemperature is reached.

Since the spring constants become weaker as the temperature islowered (cf. Eq. (4)), the instanton at a lower temperature will bemore extended than one at a higher temperature. Therefore, theinstantons at temperatures well below Tc can be quite ‘stretched’and not directly connected to the classical saddle point or the min-imum energy path (see Section 3 and Ref. [22]).

For comparison, standard Transition State Theory calculationshave been performed, here referred to as Harmonic TransitionState Theory (HTST). In these calculations the vibrational partitionfunctions are calculated based on 1D quantum harmonic oscilla-tors. The HTST rate constants are calculated as

kHTST ¼kBT

hQ TS

QR expð�DE=kBTÞ;

where TS and R refer to the classical saddle point (‘transition state’)and reactant, and DE is the energy difference between these twostates. Quantum tunneling through the barrier is not included inthese calculations. As an alternative approach to HQTST for calculat-ing rate constants with the effects of tunneling included we haveemployed the CVT/lOMT (Canonical Variational Transition StateTheory [41] with Microcanonical Optimized Tunneling) methodusing the POLYRATE 2010-A code [42].

3. Results and discussion

The crossover temperatures (Eq. (6)) of H + CO and D + CO werecalculated as 181.8 and 133.6 K, respectively from the saddle pointon the WKS PES (Figure 1 and Table 1). Already from that result it isapparent that tunneling will be the dominant transition mecha-nism at the temperature range of interest (5–20 K). However, thecrossover temperature only indicates the relative importance ofclassical and quantum rate behavior at different temperatures,but it does not tell whether tunneling will be sufficiently efficientat temperatures below Tc for the rate of reaction to be significant.

The HQTST calculations were run from just below Tc down to5 K for both the H + CO and D + CO reactions. It was necessary toinclude 512 images in the CFP to obtain converged rates down to5 K, but 256 images were sufficient down to about 10 K and 128images down to 20 K. For the sake of consistency the resultsreported here are all for 512 image calculations. HTST and CVT/

Figure 1. Stationary points on the WKS PES. Potential energies are relative to theseparated H and CO fragments. The H atom is shown in white, C in grey, and O inred. (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

Table 1Geometries, potential energies, and normal mode frequencies of stationary points onthe WKS PES [19].

H + CO van der Waals complex Saddle point HCO

RHC [Å] – 3.826 1.870 1.117RCO [Å] 1.132 1.132 1.137 1.182aHCO [deg] – 76.8 117.0 124.5E [eV] 0 �0.0034 0.1254 �0.8339x1 [cm�1] – 36 (26) 794i (584i) 1110 (861)x2 [cm�1] – 55 (48) 384 (312) 1888 (1849)x3 [cm�1] 2171 (2171) 2171 (2171) 2127 (2125) 2716 (2022)

Frequencies in parentheses refer to the deuterated system.

Figure 2. Instantons (quantum transition states) for the H + CO and D + COreactions at 5 and 100 K resolved using 512 images in the Feynman path. The Hatom is shown in white, D in yellow, C in grey, and O in red. (For interpretation ofthe references to colour in this figure legend, the reader is referred to the webversion of this article.)

S. Andersson et al. / Chemical Physics Letters 513 (2011) 31–36 33

lOMT calculations were run for temperatures between 5 and200 K. The frequencies used for the vibrational partition functionsin the HTST calculations are given in Table 1.

The experiments we compare with are all performed in the solidphase, simulating the conditions in the interstellar medium, wherean H atom would first adsorb and diffuse on an ice surface beforefinding an adsorption site from which it can react with a co-ad-sorbed CO. Therefore, the reactant state was taken to be the vander Waals minimum between the H atom and CO (Figure 1 and Ta-ble 1) since that is more representative of the condensed phasesystem. The van der Waals well can be seen as a simple approxima-tion to a physisorption well at a solid surface. It should be notedthat this is only a crude approximation as the interaction energywith a single molecule is likely to be smaller than that at a physi-sorption well at the surface and that this treatment neglects otheraspects of the solid-phase reaction, such as diffusion, penetrationand desorption [11], which enter into any experimentally observedreaction rates. However, the main goals of this study is to ascertainwhether tunneling is important at low temperatures and how largethe kinetic isotope effect is for the isolated reaction, i.e., not includ-ing diffusion or desorption. The chosen treatment should be ade-quate for this purpose.

Rate constants for the bimolecular gas-phase reaction have alsobeen calculated for comparison. It should be noted that the instan-tons for the two types of reaction are identical at any given tem-perature. However, if the instanton starts to sample regions ofthe potential energy surface with potential energies below theasymptote, i.e., infinitely separated H and CO, then the bimolecularrate calculations will become unreliable, because the simple

transition state theory-type calculations neglects the influence ofpre-reaction complexes.

A few representative instantons (quantum transition states) areshown in Figure 2. At 100 K the instantons show clear delocaliza-tion of the H and D atoms and to a much lesser extent also ofthe C atom, but they are found in a region close to the classical sad-dle point (cf. Figure 1). At 5 K the instantons extend all the wayfrom the van der Waals minimum to the HCO/DCO product well(cf. Figure 1). Here also the heavier atoms are found to be quite ac-tively involved in tunneling. It is interesting to note that in com-paring the two isotopic reactions in Figure 2, the D atom is lessdelocalized in the instanton than the H atom, which illustrates thatthe tunneling probability is less for D than for H atoms. However,in the D + CO reaction the C atom is apparently more involved inthe tunneling event than for H + CO, since the D + CO instantonshows larger delocalization of the C atom than the correspondingH + CO instanton.

The resulting HQTST rate constants are shown in Figure 3 andTable 2 alongside standard harmonic transition state theory (HTST)rate constants. The HTST results follow a straight-line Arrheniusbehavior, while HQTST shows a behavior typical of tunneling rateswhere at very low temperatures the rate constants become practi-cally temperature independent [28,29]. This is due to tunneling outof the ground state of the reactant, as temperatures have becomeso low that only the ground state is significantly populated. Ittherefore turns out that the rate constants for the H + CO andD + CO reactions remain significant at very low temperatures as al-ready indicated by experiments [5–11]. As seen in Table 2 theinclusion of tunneling in the calculations leads to significant tun-neling factors, j (defined as kHQTST/kHTST), already just below Tc

being 10.7 at 180 K. The rate at 5 K is 140 orders of magnitudehigher than what is estimated from transition state theory withouttunneling.

On closer inspection there are ‘bumps’ in the HQTST rate con-stants around 20 K that can be seen in Figure 3. To ensure thatthese unusual features are not numerical artefacts, we tested theconvergence of the rate constants by increasing the number ofimages of the CFP (up to 1024) and by using stricter convergencecriteria in the instanton optimization. The step size in the finite dif-ference evaluation of the forces was also varied. None of this hadany significant effect on the rate constants and these must thenbe considered to be converged. The bumps in the rate constants

Figure 3. Calculated rate constants for the unimolecular H + CO and D + COreactions between 10 and 200 K.

Figure 4. Calculated rate constants for the bimolecular H + CO and D + CO reactionsbetween 20 and 200 K.

34 S. Andersson et al. / Chemical Physics Letters 513 (2011) 31–36

originate in the product of instanton normal mode frequencies inEq. (5). This seems to be connected to that the extension of theinstanton into the HCO/DCO well becomes restricted below a cer-tain temperature. The ‘ends’ of the instanton are always at thesame potential energy, which can be understood from the alterna-tive description of the instanton as a periodic trajectory on the in-verted potential [23,28,29,33]. The instanton can therefore notextend further into the HCO/DCO well than where the potential en-ergy is equal to that of the van der Waals minimum (cf. Figure 1).The irregularity in the temperature dependence of the product ofinstanton frequencies occurs when the instanton enters the vander Waals well, around 20 K. The instanton frequencies changesomewhat when this occurs, which could be due to a flatter topol-ogy in the van der Waals well than in the barrier region. This couldpoint to a limitation of the use of the harmonic approximation inHQTST. However, the rate constants at temperatures above and be-low the bump are still of the same order of magnitude, so the effectis not dramatic and will not affect the conclusions we draw fromour results. An interesting observation is that the kinetic isotopeeffect, kH/kD, predicted by HQTST is not monotonically increasingwith decreasing temperature between 20 and 5 K (see Table 2).This is likely caused by the irregularity in the rate constants, sincethe ‘bumps’ do not occur at exactly the same temperatures for theH + CO and the D + CO reactions. The van der Waals region of theWKS PES has been shown to be too anisotropic by recent high-levelab initio calculations [43]. It remains unclear whether an improveddescription of this weak interaction would lead to significantchanges in the reaction rate. Efforts will be made to clarify thismatter.

Table 2Unimolecular and bimolecular rate constants for the H(D) + CO reaction.

T/K Unimolecular Bimolecu(s�1) (cm3 s�1)

HQTST CVT/lOMT HTST HQTST

180 1.18(8) 6.96(7) 1.11(7) 7.57(�14130 1.49(7) 1.57(7) 3.64(5) 7.45(�15100 4.63(6) 5.69(6) 8.56(3) 1.92(�15

50 7.02(5) 1.01(6) 5.24(�4) 1.95(�1620 3.98(5) 2.55(5) 5.53(�26) 7.33(�1710 2.15(5) 1.03(5) 1.26(�62) –

8 2.05(5) 7.83(4) 6.55(�81) –5 2.06(5) 4.47(4) 1.10(�135) –

j refers to the ratio of HQTST and HTST unimolecular rate constants for the H + CO reactioreactions. Numbers in parentheses are powers of 10.

In Figure 4 we show the HQTST and CVT/lOMT rate constantsfor the bimolecular H + CO reaction. These are given down to20 K, because as noted above the instantons start to sample nega-tive potential energies and the results will therefore not be reliable.In this case the van der Waals complex is likely to play an activerole in the kinetics and this is not well-treated in this simple tran-sition state theory-type calculation that only considers barriercrossings, as discussed previously. These rate calculations alsoignore recrossings, which will occur due to energy conservationif the system is treated in isolation, since the HCO species will bein a vibrational state that is not bound, but can make the transitionback to reactants. The reported rate constants will only be relatedto observable kinetics if the product HCO complex is stabilizedwith unit efficiency, through collisions and/or radiative deexcita-tion. In Table 2 the calculated rate constants at a number of tem-peratures are summarized. From this table and Figure 4 it can beconcluded that HQTST and CVT/lOMT give remarkably similar re-sults. Only at temperatures below 20 K do the results start to devi-ate more clearly. It should be noted that the lOMT tunnelingcorrection in this case is identical to small curvature tunneling(SCT). The agreement between two such different treatments ofquantum tunneling should lend credibility to the reported results,bearing in mind the neglect in both theories of quantum effectsthat are purely dynamical in nature. For instance, these calcula-tions do not treat the effects of resonances, which have previouslybeen found by explicitly solving the Schrödinger equation forH + CO under the restrictions of zero total angular momentumand a rigid rotor CO [44]. Such resonances may potentially affectthe rate of reaction.

lar j kH/kD

CVT/lOMT HTST

) 4.28(�14) 7.11(�15) 10.7 –) 7.51(�15) 1.82(�16) 41.0 3.19) 2.27(�15) 3.55(�18) 540 11.0) 2.88(�16) 1.46(�25) 1.34(9) 57.3) 8.16(�17) 1.02(�47) 7.20(20) 194

– – 1.70(67) 242– – 3.12(85) 233– – 1.88(140) 257

n. kH/kD is the ratio of HQTST unimolecular rate constants for the H + CO and D + CO

Figure 5. Effective barrier heights for the H + CO and D + CO reactions from HQTSTcalculations. Reactant energy refers to the van der Waals complex.

S. Andersson et al. / Chemical Physics Letters 513 (2011) 31–36 35

The accuracy of the rate constants depends predominantly on thebarrier height and the barrier width. The WKS PES was originally fit-ted to ab initio energy points and then modified to match the exper-imental vibrational spectrum and dissociation energy to highaccuracy [19]. This also lowered the reaction barrier from the ab ini-tio value of 0.169 eV to a lower value of 0.125 eV. This barrier is closeto, but somewhat lower, than the latest theoretical estimate of0.137 eV [14]. It is still considerably higher than the experimentallydetermined gas-phase activation energy, 0.087 ± 0.017 eV [45]. Theuncertainty in the barrier height could lead to an uncertainty in therate constant of a few orders of magnitude at 10 K. The general con-clusions about the feasibility of the reaction and the isotope effectsshould not be affected very much by this since the calculated rateconstants are quite high, indicating highly efficient reactions evenat low temperatures.

The kinetic isotope effect at low temperature turns out to beabout kD/kH = 1/250 (see Table 2), in contrast to the experimentallydeduced isotope effect of 0.08 [9,10]. The experimental value is forthe surface reaction where processes such as diffusion and desorp-tion could show clear isotope effects in addition to the hydrogena-tion reaction. These processes are likely to be more classical innature and therefore the isotope effect could be quite different.

The typical residence times at the surface is expected to belonger for D atoms than for H atoms due to the lower zero-pointenergy and thereby higher activation energy for desorption. Alonger residence time would lead to a higher chance of reactionfor D atoms than H atoms with CO and that would mean that theeffective isotope effect (kD/kH) is larger than that for the isolatedreaction, which is in accord with experimental results.

The experimental barrier heights refer to an ideal reactionwhere HCO does not redissociate upon passing the reaction barrier.Redissociation of the HCO product would result in lowering of theeffective experimental rates compared to the simple one-step bar-rier transition and this would also be reflected in higher effectivebarriers. However, the exact size of such an effect is not possibleto estimate directly from the present calculations.

In order to estimate the effect of the competition between reac-tion and diffusion out of the reactive site at a typical ice-coveredinterstellar grain, we calculated correction factors to the reactionrates that take the diffusion rates into account leading to effectiverate constants, keff = jcorr kreac. These factors are expressed in termsof rate constants for reaction and diffusion and are given byjcorr = kreac/(kreac + kdiff,H + kdiff,CO) [46]. Assuming that CO is immo-bile at low temperatures, the expression reduces to jcorr = kreac/(kreac + kdiff,H). We have used kreac = kHQTST and two different barrierheights for diffusion, Ediff, of 20 and 50 meV that seem to be repre-sentative of diffusion barriers at astrochemically relevant ice sur-faces [47–49]. Further, we assume that the single-jump diffusionrate constant is kdiff = m exp(�Ediff/kBT) with m = 1012 s�1. The totalkdiff,H should include all possible diffusion paths out of the siteand a reasonable assumption is that kdiff,H = 4 kdiff. A diffusion bar-rier of 50 meV has no effect on the effective reaction rate andjcorr = 1 for the relevant temperature range 5–20 K. For a barrierof 20 meV the diffusion of H and D is too slow below 10 K to haveany significant effect, but at 20 K jcorr = 1 � 10�3 for H + CO and6 � 10�6 for D + CO. This would actually give a larger kinetic iso-tope effect than for the isolated reaction, contrary to the compari-son of measured and calculated isotope effects discussed above.The assumption of equal diffusion rates of H and D may be toocrude and differences in the diffusion of H and D should be exam-ined in detail before anything conclusive can be said about thiseffect.

By extracting the effective potential energy, Veff, for the instan-ton (cf. Eqs. (3) and (5)) it is possible to illustrate the lowering ofthe effective activation energy due to tunneling as would be foundfrom an analysis of an Arrhenius type expression. As seen in Figure

5 the effective barrier height drops from the classical value of0.125 eV at and above Tc to 3.3 and 5.4 meV at 5 K for the H + COand D + CO reactions, respectively. These barrier heights are rela-tive to the separated reactants and since we are studying the uni-molecular reaction from the van der Waals minimum, the reactantwell depth of 3.4 meV should be added to the barriers to get the ac-tual barriers for the studied reactions.

This lowering of the effective barrier height supports the con-clusions based on the experiments by van IJzendoorn et al. [5] thatHCO was formed with low activation energy at low temperatures,even though the activation energy at higher temperatures is rela-tively high [12–14]. This also supports the use of temperature-dependent barrier heights in the modeling of the experiments byFuchs et al. [11], even though the actual values differ betweenour pseudo-gas phase reaction and the modeling of the surfacereaction. The experimentally deduced barrier heights for H + COare in the range 34–45 meV between 12 and 16.5 K, while our cal-culated values are 13–19 meV in the same temperature range.Apart from uncertainties in the modeling of the experiments andthe exact level of accuracy of the WKS potential energy surface,this discrepancy could also be an effect of the stronger bindingenergies of H atoms at a surface compared to the loose van derWaals complex studied in our work.

4. Conclusions

We presented the first molecular simulation study of the ratesof the H + CO and D + CO reactions at very low temperatures. Rateconstants were calculated by the HQTST method, which includesquantum tunneling, using an accurate HCO potential energysurface.

The reaction rates were found to be appreciable down to tem-peratures as low as 5 K due to tunneling. This supports experimen-tal results that suggest these reactions to be efficient at lowtemperatures in the solid phase. The kinetic isotope effect wasfound to be kD + CO/kH + CO = 1/250. This cannot directly explainthe experimental isotope effect of 0.08 for the reaction occurringat a water ice surface. However, this effective isotope effect also in-cludes effects specific to surface reactions, such as diffusion anddesorption. If these contributions to the overall rate enhance deu-terium reactivity, then the calculated isotope effect for the isolatedreaction could still be valid. Similar calculations on the correspond-ing surface reactions are therefore needed and form the topic ofongoing research.

36 S. Andersson et al. / Chemical Physics Letters 513 (2011) 31–36

Acknowledgements

We thank Reinhard Schinke for providing the HCO PES andEwine van Dishoeck, Herma Cuppen, Lou Allamandola, HannesJónsson and Geert-Jan Kroes for useful discussions. The Nether-lands Organisation for Scientific Research (NWO) is acknowledgedfor a VENI-fellowship (700.58.404) for TPMG and a CW Top Grantfor funding the work of SA. Part of this work has been performedunder the Project HPC-EUROPA++ project (Project number:211437), with the support of the European Community – ResearchInfrastructure Action of the FP7 ‘Coordination and support action’Programme.

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