© ESO, 2015

1. Introduction

Formaldehyde (H₂CO) was the first polyatomic organic molecule detected in the interstellar medium (ISM; Zuckerman et al. 1970). It was detected through the 1₁₁−1₁₀ ground-state rotational transition at 4830 MHz (Snyder et al. 1969), and its distribution was found to be similar to HII and CO in different environments, such as our Galaxy (Davies & Few 1979; Tang et al. 2013, and references therein), and in Galactic radio sources (Downes et al. 1980).

H₂CO has been observed in some comets (Crovisier & Bockeleé-Morvan 1999; Mumma et al. 2005) and in interstellar ices (Keane et al. 2001). Its abundance with respect to water ice varies from 1% to 6% in high (Keane et al. 2001; Dartois 2005) or low (Boogert et al. 2008) mass protostars, or hot corinos (Maret et al. 2004). Gas-phase reactions (Shalabiea & Greenberg 1994) and UV photolysis of H₂O-CO ice (Allamandola et al. 1988; Schutte et al. 1996; Watanabe et al. 2007) can efficiently produce formaldehyde, but surface reactions, such as hydrogenation of CO ice (studied experimentally by Hiraoka et al. 1994, Watanabe & Kouchi 2002, and Madzunkov et al. 2009, and theoretically by Rimola et al. 2014) are needed to explain the observed abundance of H₂CO in the solid phase.

Formaldehyde is a key species for the grain-surface chemistry of interstellar clouds (Schutte et al. 1993a,b). Hidaka et al. (2004) and Fuchs et al. (2009) show that formaldehyde can form methanol (CH₃OH) through H-atom additions or produce CO via H-atom abstractions. Moreover, H₂CO is involved in the formation of large molecules containing C-H, C-O, O-H, and C-N bonds (Schutte et al. 1993b). During the warm-up of the ice on grains, formaldheyde can react with NH₃, H₂O, and itself (H₂CO) to form amines, diols, or [-CH₂-O-]_n groups (Noble et al. 2012b; Theulé et al. 2013; Mispelaer et al. 2013); for this reason, it could be considered a primary precursor of some complex organic materials (Schutte et al. 1993b). In this paper, we present an experimental study showing that formaldehyde reacts with ground-state O(³P) atoms to form CO₂, one of the most abundant species of interstellar ices. Formaldehyde seems to play a crucial role in the chemistry of interstellar ices and, in particular, in the balance between CO₂, CH₃OH, and CO.

This paper is organised as follows. The experimental set-up and methods are described in the next section. In Sect. 3, we present our experimental results showing how H₂CO is consumed by O to form CO₂. In Sect. 4, we present a rate equation model that simulates our results and gives relevant energetic parameters, and we discuss the solid-state network by presenting DFT calculations. In the last section, we discuss the main conclusions and astrophysical implications of this study.

2. Experimental

The experiments were conducted with the FORMOLISM (FORmation of MOLecules in the InterStellar Medium) set-up described extensively elsewhere (Amiaud et al. 2006; Congiu et al. 2012). It consists of a UHV main chamber with a base pressure of 10^-10–10^-11 mbar and two triply differentially pumped atom lines. The ultra-high vacuum chamber contains an oxidised slab of high-oriented pyrolytic graphite (HOPG, 0.9 cm in diameter), operating at temperatures between 8 K and 400 K. The temperature is controlled by a calibrated silicon-diode sensor and a thermocouple (AuFe/Chromel K-type) clamped on the sample holder. Adsorbates and products were probed in situ through Fourier Transform Reflection Absorption InfraRed Spectroscopy (FT-RAIRS) and a quadrupole mass spectrometer (QMS) used for measuring the beam flux and beam composition and for performing the temperature-programmed desorption (TPD) experiments. Amorphous solid water (ASW) ice was grown on the graphite sample, maintained at 120 K, through a leak valve positioned at 2 cm far from the surface.

All the experiments were performed by sending O atoms on formaldehyde ice films previously grown on the cold sample. The two species were deposited by using the same beam line at different times. Figure 1 shows how gaseous formaldehyde is obtained: paraformaldehyde (a white crystalline powder) contained in a pyrex phial is depolymerizated by immersion in a bath at 62 °C. The products of the depolymerization process are H₂CO, CO, and H₂O. Table 1 shows the resulting beam composition measured with QMS (direct beam) at a source pressure of 0.42 mbar as a function of the pumping time. In particular, we report the difference between the signal recorded with the flag¹ open and the signal recorded with the flag closed to account for noise signals.

As shown in Table 1, the ratio between these species varies during the depolymerization process: at the beginning the H₂O/H₂CO ratio is 920/(Mass30+Mass29) ≈ 0.92 and becomes 0 after 90 min of pumping. This means that the sublimation process of paraformaldehyde is able to purify the sample by eliminating the residual H₂O. Similar behaviour concerns the CO/H₂CO ratio, which goes from 1.3 to 0.1; in this case, the resulting gas contains some residual CO even after 90 min of pumping. For this reason, formaldehyde ice films were grown at temperatures higher than those of CO desorption (>55 K). As we discuss in Sect. 3 and Appendix A, we used different isotopologues of formaldehyde to constrain our findings better, i.e., H$\begin{array}{c}\mathrm{12}\\ \mathrm{2}\end{array}$CO, D$\begin{array}{c}\mathrm{12}\\ \mathrm{2}\end{array}$CO, and H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO. In the case of D$\begin{array}{c}\mathrm{12}\\ \mathrm{2}\end{array}$CO, the purity is of about 98%, while for H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO is of 99%. Hereafter we refer to ¹²C simply as C.

Oxygen atoms are generated by (in the ³P ground state) dissociating O₂ molecules in a quartz tube placed within a Surfatron cavity, which can deliver a maximum microwave power of 200 W at 2.45 GHz (Minissale et al. 2014). We studied the electronic state composition of oxygen beam by tuning the energy of the ionizing electrons of the QMS. This technique allows ground state or electronic excited atoms and molecules to be selectively detected, as described in Congiu et al. (2009). We find that our source is free of O(¹D) and O₂(a${}^{\mathrm{1}}\mathrm{\Delta }_{\mathit{g}}^{\mathrm{-}}$) and is composed only of O(³P) and O₂(X${}^{\mathrm{3}}\mathrm{\Sigma }_{\mathit{g}}^{\mathrm{-}}$) (see details in Minissale 2014 and Minissale et al. 2014).

With the microwave source turned on, the dissociation efficiency of O₂ was τ = 70 ± 5%, where τ represents the percentage of dissociated O₂ molecules and τ is proportional to the microwave power used, so it also defines the O/O₂ ratio in the beamline. If τ is 0.7, every ten O₂ molecules, we will have 14 O atoms and 3 O₂ undissociated molecules. Atoms and undissociated molecules are cooled and instantaneously thermalised upon surface impact with the walls of the quartz tube.

We calibrated the molecular beam as described in Amiaud et al. (2007) and Noble et al. (2012). The first monolayer (1 ML = 10¹⁵ molecules cm^-2) of formaldehyde was reached after an exposure time of about 12 min, and 1 ML of O₂ was reached after six minutes, which give a flux of φ_H2CO = (1.3 ± 0.4) × 10¹² and φ_O2off = (3.0 ± 0.3) × 10¹² molecules cm^-2 s^-1, respectively. Once the O₂ discharge is turned on, the O-atom flux is φ_O = 2τφ_O2off = 5.4 × 10¹² atoms cm^-2 s^-1 and the O₂ flux φ_O2on = (1−τ) φ_O2off = 10¹² molecules cm^-2 s^-1.

CO₂ formation was investigated on two different surfaces, ASW and an oxidised slab of HOPG. In Table 2 we display a complete list of experiments providing details on the species and dose of the reactive molecule deposited. Different doses of O (+O₂) were sent onto formaldehyde ice. (The coverage of H₂CO ices was always <2.5 ML.) During each phase (ices growth or O-atom deposition), the surface was held at a given constant temperature. After each O-atom deposition, the products were probed using RAIR spectroscopy. After about 5 ML of oxygen, atoms were deposited, and the surface was heated with a linear temperature ramp of 10 K/min, until the adsorbates had fully desorbed from the surface (around 200 K). For each substrate (ASW ice or graphite), we adopted two deposition temperatures (10 and 60 K). We also performed experiments to determine whether CO₂ was formed via H₂CO + O₂ and H₂CO + O₃. For this purpose, we performed two sets of TPD experiments. First, the H₂CO+O₂ reaction was checked by depositing 2 ML of O₂ on top of H₂CO films. The H₂CO+O₃ reaction was studied through a similar experiment except that H₂CO was deposited on top of O₃. In fact, for technical reasons, we had previously produced ozone via the O+O₂ reaction on the surface at 10 K, eliminated the residual O₂ by heating the surface to 50 K, and only then deposited H₂CO at 60 K.

3. Experimental results

3.1. Oxygenation of H₂CO ices

In this section we present the experimental results showing the products of the reactions H₂CO + O_x (O, O₂, and O₃). The oxygen beam that we used to irradiate formaldehyde also contains O₂ molecules, therefore O₃ can be formed on the surface at temperatures lower than <55 K (Minissale et al. 2014). For this reason, we first studied the reactions H₂CO + O₂/ O₃, then the reaction H₂CO + O. Figure 2 shows three TPD spectra of mass 30 a.m.u. (H₂CO) after depositing 1 ML of H₂CO, 1 ML of H₂CO + O₂, and 1 ML of H₂CO + O₃ on oxidised HOPG held at 10 K . The three TPD curves and their integrated areas are very similar, suggesting that H₂CO has not been consumed by O₂ or O₃.

Actually, this is not a surprising result since the reactions $\begin{array}{ccc}{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}\mathrm{+}{\mathrm{O}}_{\mathrm{2}}& & \mathrm{\to }\mathrm{HCO}\mathrm{+}\mathrm{H}{\mathrm{O}}_{\mathrm{2}}\mathrm{(}\mathrm{\Delta }\mathit{H}\mathrm{=}\mathrm{+}\mathrm{160}\mathrm{kJ}\mathit{/}\mathrm{mol}\mathrm{)}\\ {\mathrm{H}}_{\mathrm{2}}\mathrm{CO}\mathrm{+}{\mathrm{O}}_{\mathrm{3}}& & \mathrm{\to }\mathrm{H}{\mathrm{O}}_{\mathrm{2}}\mathrm{+}\mathrm{HC}{\mathrm{O}}_{\mathrm{2}}\mathrm{(}\mathrm{\Delta }\mathit{H}\mathit{>}\mathrm{200}\mathrm{kJ}\mathit{/}\mathrm{mol}\mathrm{)}\end{array}$are endothermic² and present high (>1600 K/k_b) activation barriers (Michael et al. 1999; Braslavsky & Heicklen 1976). Moreover, the inefficiency of reactions (1) and (2) is confirmed by the absence of newly formed species.

Figure 3 shows the TPD curves of CO₂ (mass 44, left panel) and H₂CO (mass 30, right panel) for three different sequential deposition experiments on oxidised HOPG held at 10 K: 2 ± 0.5 ML of H₂CO, 2 ± 0.5 ML of H₂CO + 5 ± 0.3 ML of O atoms alone, and 5 ± 0.3 ML of O atoms.

The green line represents a control experiment carried out to be certain that CO₂ is not present in the O beam and that carbon dioxide was actually formed on the surface because of H₂CO oxygenation. In fact, a signal at mass 44 (CO₂) is visible in Fig. 3 (left panel) and could come either from the O beam or from oxygenation of residual CO. In either case, it is ten times weaker than the mass-44 signal coming from H₂CO oxygenation experiment (left panel of Fig. 3). For this reason, it is fair to believe that H₂CO ice is consumed upon oxygen irradiation (right panel) and that CO₂ is formed.

Further evidence of H₂CO consumption and CO₂ formation is provided by the RAIR spectra shown in Fig. 4. Curve a in Fig. 4 shows the RAIR spectrum after deposition of 2 ML of H₂CO on an oxidised HOPG held at 60 K to avoid CO adsorption. We assign the band at 1732 cm^-1 to the CO stretch of H₂CO. H₂CO was then exposed to increasing doses of O atoms. Curves b and c in Fig. 4 show the cases of 2 ML H₂CO + 0.8 ± 0.1 and 5 ± 0.4 ML of O atoms. Here two new bands are visible: the first one, peaking between 2349−2345 cm^-1, is assigned to the anti symmetric stretch of CO₂. The second band, peaking at 1047 cm^-1, is due to the ν₃ asymmetric stretching mode of O₃ and is also present in spectrum d, where O atoms were deposited on the bare surface. All the IR bands of interest for this paper are listed in Table 3.

We obtained similar results when the experiments were performed on ASW ices. Figure 5 shows RAIR spectra recorded after irradiation at 10 K, of 2 ± 0.5 ML of H₂CO with increasing doses of oxygen atoms (0, 0.5, 0.8, 1.2, 2, 3.8 ML from curves a to f, respectively). As in the previous case, three main spectral features are visible: at 1048 cm^-1 due to O₃, at 1734 cm^-1 due to the CO stretch of H₂CO, and finally at 2347 cm^-1 where the antisymmetric stretch of CO₂ appeared. Also, we assign the weak and broad band at 1502 cm^-1 to the CH₂ scissoring of H₂CO.

The different substrates (HOPG or compact ASW ice) are responsible for small shifts in the IR features, as well as for a change in the band intensities. Actually, under the same conditions (equal amount of O sent onto H₂CO), HOPG facilitates CO₂ formation slowing down that of O₃, while the ASW substrate favours O₃ formation. This is a consequence of two effects:

• different diffusion constants of O atoms on oxidised HOPG and on ASW ice, i.e., k_diff−HOPG<k_diff−ASW (Congiu et al. 2014);

• different probabilities of chemical desorption for O₂, i.e., ϵ_diff−HOPG>ϵ_diff−ASW (Dulieu et al. 2013; Minissale & Dulieu 2014).

Fast diffusion of O atoms and the low probability of chemical desorption of O₂ on ASW allow O atoms to allotropize into O₂ and into O₃ ([O₃] ≫ [CO₂]). Conversely, on HOPG, the surface density of O₂ decreases due to chemical desorption. The O atoms stay on the surface longer, have a higher probability of reacting with H₂CO and form CO₂( [ O₃ ] ≈ [ CO₂ ]), owing to the lack of O₂ and the lower mobility of O atoms.

3.2. Temperature effects: O-atom irradiation at 55 K

Minissale et al. (2013b; 2014) show that solid-state formation of O₃ is efficient at temperatures lower than 55 K. In fact, temperatures higher than 55 K prevent O₂ adsorption on the surface so O₃ can no longer be formed. Figures 4 and 5 show that O₃ is the main product after H₂CO is exposed to O atoms. To avoid O₃ formation, we thus sent O atoms onto H₂CO ice held at 55 K. Figure 6 shows seven RAIR spectra after O irradiation of 2 ± 0.5 ML of H₂CO, previously adsorbed on ASW, at 55 K (from curve a to g, 0, 0.5, 0.8, 1.2, 2, 3.8 ML of O, respectively, were sent onto H₂CO). The right-hand panel of Fig. 6 shows the integrated areas of the bands at 1732 and 1502 cm^-1 of H₂CO (triangles and circles, respectively) and the one at 2345 cm^-1 of CO₂ (black circles). The spectra of Fig. 6 differ from those in Fig. 5 for two main features: the O₃ band is not present and the band at 2347 cm^-1 (CO₂) increases steadily with O-exposure time. These two main differences, as discussed in detail in the model section, facilitate the evaluation of the H₂CO + O activation barrier.

3.3. Experiments with isotopologues

To confirm the results presented above and for a better understanding of the solid state reaction network, we also performed experiments using another isotopologue of formadehyde, D₂CO. Further experiments in which H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO was used are described in Appendix A.

The top panel of Fig. 7 shows three RAIR spectra recorded after deposition of oxygen atoms (0, 1.4, and 3.8 ML from curves a to c, respectively) on 2 ± 0.5 ML of D₂CO held at 55 K. Three spectral features are apparent. D₂CO is detected through the CO stretch mode at 1680 cm^-1 (decreasing in intensity from a to c) and the asymmetric stretch of CD₂ at 2154 cm^-1; the latter is visible only in spectrum a; the third feature at 2359 cm^-1 is due to the antisymmetric stretch of CO₂ and increases in intensity from spectrum a to spectrum c. Also, a very weak band due to O₃ is visible at 1043 cm^-1 (not shown). The TPD traces in the bottom panel were obtained after deposition of 2 ± 0.5 ML of D₂CO + 3.8 ± 0.3 ML of O atoms on ASW ice. Newly formed CO₂ desorbs between 70 and 90 K and is detected via mass 44. The fraction of D₂CO molecules that did not react desorb between 85 K and 140 K and are detected via the fragments D₂CO⁺ (mass 32) and DCO⁺ (mass 30). TPD results corroborate the previous spectral assignments of the infrared bands and give additional information. Figure 8 shows TPD traces of mass 18, 19, and 20 between 130 and 200 K. The black lines represent TPDs after deposition of 2 ± 0.5 ML of D₂CO on oxidised HOPG held at 55 K, while red lines were obtained by irradiating the same amount of D₂CO with 3.8 ± 0.3 ML of O. The signal at mass 20 comes from the ionisation of heavy water (D₂O⁺): it is almost zero in the black curve, while it has a peak in the red curve. Mass 19 (HDO⁺ and 18 (H₂O⁺ and OD⁺) signals are present in both cases, even if the peak areas of the red curve are twice bigger than the peaks of the black curve. These mass spectra support the formation of D₂O after D₂CO oxygenation. We discuss this point extensively in the next section.

4. Model and discussion

4.1. Quantum chemical calculations on the O + H₂CO reaction

The focus of this paper is on the investigation of solid-state reactions involving formaldehyde ices and oxygen atoms at low temperatures. All the experiments presented in Sect. 3 show that when formaldehyde is exposed to O atoms, H₂CO is consumed and CO₂ is formed. In this section, we describe quantum chemical calculations on O + H₂CO reaction in detail. However, we have used prevalently gas-phase energetic data to carry out our calculations. We would like to stress that solid-state reactivity is somewhat different than the gas-phase one, because of interactions between adsorbate and adsorbent. For this reason, the goal of our quantum chemical calculations is essentially to provide a first estimation of the trend of the different channels studied. The energetic data, present in this section, have to be taken just as qualitative values, since they would be substantially influenced by the solid-state phase chemistry.

Our experimental results are very similar to those obtained by different experimental groups at high (>300 K) temperature in gas phase, i.e. Chang & Barker (1979) and Wellman et al. (1991). Chang & Barker (1979) proposed that CO₂ formation occurs in the following steps:

• 1.

  O-atom addition to the doubly-bonded carbon atom in H₂CO and the following formation of a vibrationally excited triplet of methylenebis(oxy) (H₂CO₂);

• 2.

  H₂CO₂ is formed in the ³B₂ state, and owing to a hydrogen shift, it forms vibrationally excited formic acid (H-atom migration process);

• 3.

  Once formed, the triplet formic acid is decomposed by several pathways (HCO+OH, HCO₂+H, HOCO+H);

• 4.

  Further fragmentation of HOCO and HCO₂ or oxygenation of HCO would lead to CO₂ formation.

On the other hand, Wellman et al. (1991) proposed that H₂CO+O proceeds via a direct hydrogen abstraction (H₂CO+O→OH+HCO), and a secondary reaction of oxygen atoms with HCO may lead to CO₂ formation. In the gas phase, despite some ambiguities, the reaction mainly leads to abstraction products, HCO + OH, through a barrier measured as equal to 1540 K (Klemm 1979; Klemm et al. 1980), with a CO₂ product-branching ratio inferior to 5% (Wellman et al. 1991). We stress that neither Chang & Barker (1979) nor Wellman et al. (1991) have shown direct measurements of HCOOH and HCO. This is consistent with our experimental results. Theoretical calculations (Dupuis & Lester 1984) show that CO₂ production via the addition channel (³OCH₂O, second reaction) should be unlikely, since it involves a transition state above the O + H₂CO entrance channel. Moreover, H₂CO+O could lead to the formation of the Criegee species (CH₂OO) in its triplet state. Nevertheless, we can neglect this channel in our system, thanks to its wide endothermicity (+115 kJ/mol, see Table C.2).

To understand how CO₂ is formed in our system, we carried out a series of DFT calculations (see Appendix C for details). We suppose that H₂CO+O can lead to various products: $\begin{array}{ccc}\mathrm{1}{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}\mathrm{+}{\hspace{0.17em}}^{\mathrm{3}}\mathrm{O}\mathrm{\to }& \mathrm{2}\mathrm{OH}\mathrm{+}{\hspace{0.17em}}^{\mathrm{2}}\mathrm{HCO}& \mathrm{\Delta }\mathit{H}\mathrm{=}\mathrm{-}\mathrm{60}\mathrm{kJ}\mathit{/}\mathrm{mol}\\ \mathrm{\to }& \mathrm{3}\mathrm{OC}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}& \mathrm{\Delta }\mathit{H}\mathrm{=}\mathrm{-}\mathrm{80}\mathit{/}\mathrm{-}\mathrm{70}\mathrm{kJ}\mathit{/}\mathrm{mol}\end{array}$where enthalpies of reactions have been taken from the literature (Baulch et al. 2005, for the first reaction; Dupuis & Lester 1984, for the second value of second reaction) or evaluated in the present work.

In the case of surface reaction (i.e., ice or graphite), the surface interactions have a complex effect on barrier heights (Bromley et al. 2014). For the H + H₂CO reaction on water ice, a small reduction (≈130 K) in the activation barrier was calculated for the addition reaction, while the barrier for abstraction reaction was increased significantly (increased by 725 K) (Goumans 2011). It is reasonable to imagine that the O reaction with H₂CO ice presents a similar effect. To get a better picture of the various mechanisms, we performed theoretical calculations using the Gaussian 09³ package. Calculations details are presented in Appendix C. The energy diagram calculated for the first step of the O + H₂CO reaction (energy values are close to the CCSD(T)/cc-pVTZ and MP2/cc-pVTZ values including zero-point energies, ZPE) is presented in Fig. 9.

The reaction pathway is initiated by the formation of a pre-reactive complex (PRC) O...H₂CO corresponding to a long-range interaction between O atom and H₂CO.

From the PRC, two reactive pathways have been found, one leading to OH + HCO formation through a transition state for H atom abstraction, TS1, and the other leading to oxygen atom addition through TS2 transition state. The energy barrier for the H-atom abstraction depends on the calculation level, ranging from 1 kJ/mol at M06-2X level to 39 kJ/mol at MP2 level and equal to 21 kJ/mol at CCSD(T) level, and the energy barrier for the oxygen atom addition ranging from 30 kJ/mol at M06-2X level to 93 kJ/mol at MP2 level and equal to 53 kJ/mol at CCSD(T) level. Calculations show that in the gas phase, the reaction happens mainly through H atom abstraction with a barrier around 10−20 kJ/mol. They are qualitatively in good agreement with observations, considering that DFT with M06-2X method underestimates the barrier height and MP2 overestimates the barrier (Loison et al. 2014; 2014b). In the case of oxygen-atom addition, it is very unlikely that surface interactions have such an effect on the addition barrier to make this channel important. Moreover, tunneling should be efficient for H-atom abstraction and less efficient for O-atom addition.

The main exit channel for O atom reaction with H₂CO on a cold surface is very likely HCO + OH. The newly formed HCO and OH should have low kinetic energy owing to

• low exothermicity of reaction;

• large amount of available energy localized into vibrational and rotational degrees of freedom.

Probably, HCO and OH will then stay relatively close on the surface and should mainly recombine on the singlet surface (²HCO + ²OH correlate with singlet and triplet surface) without barrier, leading to excited HCOOH**. If some OH and HCO can move on the surface, OH will quickly react with H₂CO leading to H₂O + HCO (Xu et al. 2006; Yetter et al. 1989). The low amount of water formed in the experiments is a strong indication that OH does not move on the surface but rather form HCOOH**. We performed theoretical calculations at the M06-2X level to characterise stationary points in the HCOOH* evolution. Our results (in good agreement with previous calculations for the HCOOH dissociation, Chang et al. 2007) are presented in Fig. 10.

Theoretical calculations on energy transfer from HCOOH* toward phonon modes of the ice is far beyond the scope of this article (and is also far from being well understood). HCOOH* has an internal energy equal to 460 kJ/mol corresponding to the strength of the OC(H)-OH bond, so well above the dissociation barrier towards H₂ + CO₂ and H₂O + CO.

To estimate the evolution of excited HCOOH** and its unimolecular decomposition, we use our experimental results showing that neither HCOOH nor H₂O were formed and then we mainly consider CO₂ + H₂ formation. That CO₂ + H₂ is favoured is in good agreement with theoretical calculations for the H + HOCO reaction (Yu & Francisco 2008) leading to similar HCOOH** energized adducts. The most surprising experimental result is the low amount of HCOOH stabilized, which should be a function of energy relaxation efficiency through surface interaction. The low efficiency of HCOOH stabilization in our experiments clearly shows the complexity of surface reactions, and it is definitively an important experimental result because the competition between adduct stabilization and bimolecular exit channel happens for a majority of surface reactions (i.e., C + NO → CN + O/CO + N/CNO/NCO, CH + CH₄ → C₂H₅/ C₂H₅ + H,H + HO₂ → H₂O₂/ OH + OH/H₂ + O₂, H₂O + O, and so on). We propose the following simplified chemical pathways:

• a.1)

  H₂CO + O → (OH + HCO)_cage

• a.2)

  (OH + HCO)_cage → HCOOH^∗∗

• a.3)

  HCOOH^∗∗ → (CO₂ + H₂) or (H₂O + CO)

• b)

  O + O → O₂

• c)

  O₂ + O → O₃

• d)

  O + CO → CO₂

where reaction a1 has a barrier of 335 K (fitted using E_Odiff = 700 K, see previous section). Reactions a2 (radical-radical reaction), b, and c have no barrier; reaction a3 presents a 95%−5% (±5%) branching ratio; and reaction d presents a barrier of 600 K (Minissale et al. 2013a).

In the next section, we describe the model used to evaluate the activation barrier of the H₂CO + O reaction.

4.2. Evaluation of the H₂CO+O barrier

In this section we present the model used to fit our experimental data and, in particular, to evaluate the activation barrier of the H₂CO + O reaction. The model is composed of a set of five differential equations that account for the surface population of H₂CO, O atoms, O₂, O₂, and CO₂ (see Appendix B for further details). In fact, we considered only the most abundant species present on the surface, and the three main reaction pathways:

• a)

  H₂CO + O → CO₂ + H₂

• b)

  O + O → O₂

• c)

  O₂ + O → O₃.

H₂ was not included in our model, since our experiments were performed at high surface temperature and H₂ has a very short residence time under these conditions. In any case, H₂ is inert at low temperature and cannot affect the surface density of other species. The surface reactions listed above can occur through two mechanisms: the Eley-Rideal (ER) and the Langmuir-Hinshelwood (LH) mechanisms. In the ER mechanism one molecule is already adsorbed on the surface, and the other comes from the gas phase (i.e., the beam line). The ER becomes more efficient as the surface coverage increases. In the LH mechanism, both molecules are physisorbed to the surface, and they can meet each other by diffusing on the surface and eventually react. LH is highly dependent on the surface temperature. With these considerations in mind, we chose to fit the data of Fig. 6 (right panel) to give a more precise evaluation of the H₂CO+O activation barrier. Actually, the physicochemical conditions in these experiments allow us to simplify our model and reduce the errors:

• O-atom diffusion is very fast, and the majority of adsorbed O atoms are consumed through reaction (b);

• reaction (c) can be neglected, since it is impeded by O₂ desorption⁴;

• reaction (a) is more likely to occur via ER, since O atoms are deposited on the H₂CO ice.

Clearly the last point does not exclude that reaction (a) could occur via the LH mechanism, and this actually represents the main source of error in the barrier determination. The LH mechanism depends strongly on the O-atom diffusion barrier (E_Odiff), one of the free parameters of the model. The barrier E_Odiff is a pure thermal diffusion barrier since quantum effects are negligible at high temperatures (Minissale et al. 2013a), and it has an upper limit of 900 K/k_b (Cazaux et al. 2010) and a lower limit given by ozone formation in our experiments (<0.05 ML). A value lower than 600 K/k_b for E_Odiff increases the efficiency of reaction (b) and produces more than 0.05 ML of ozone. Within these two boundaries, the total amount of CO₂ formed via LH changes by 20%, if E_Odiff = 900 K/k_b, or 5%, if E_Odiff = 600 K/k_b. This indetermination, as we see below, complicates the evaluation of the activation barrier E_a of reaction (a), the second free parameter of the model. A priori, E_a is a positive real number and becomes zero in the case of a barrierless reaction. Figure 11 shows the results of the model (lines) compared with experimental data. We used four values for E_a: 550 K/k_b (panel α), 390 K/k_b (panel β), 280 K/k_b (panel γ), and 200 K/k_b (panel δ). We varied E_Odiff in the 600−900 K/k_b range, and Fig. 11 shows the four cases: 600, 700, 800, and 900 K/k_b. Panel α shows that a value of E_a that is too high (>550 K/k_b) is not able to fit our data for any value of E_Odiff: small amounts of CO₂ are formed, small amounts H₂CO are consumed, and a large amount of ozone is formed. On the other hand, a value that is too small (<200 K/k_b) for E_a has an opposite effect, CO₂ is formed too rapidly and H₂CO is consumed too quickly by O atoms (panel δ). Couples of values of E_a and E_Odiff ranging in 390−280 K/k_b and 600−900 K/k_b, respectively (panels β and γ), give an excellent fit to the experimental data. Because the fit depends on two parameters, we are not able to give a precise value of the activation barrier of reaction (a). However, we have to stress that a given choice of E_Odiff, automatically determines the value of E_a: by using E_Odiff = 700 ± 150 K/k_b, we found E_a = 335 ± 55 K/k_b.

The activation barrier that we have found for solid state reaction H₂CO+O (>300 K) is lower than gas phase barrier (>1560 K, Wellman et al. 1991). The reason for such a low activation barrier is probably the catalytic effect of the surface.

5. Astrophysical conclusions

In this paper we have shown that O(³P) atoms are able to react with H₂CO on cold surfaces, such as amorphous water or oxidised graphite, under conditions encountered in interstellar dense clouds. Using a model, we estimated a value of 335 ± 55 K/k_b for its activation barrier, and CO₂ was found to be the main product of the reaction. This reaction is relevant to astrochemistry because it may account for CO₂ abundances, as well as for CH₃OH ones, in interstellar ices. Actually, carbon dioxide is one of the most common and abundant types of ice, and it has been detected in many interstellar environments, from comets (Ootsubo et al. 2010) to other galaxies (Shimonishi et al. 2010; Oliveira et al. 2011). Its high abundances observed in interstellar ices are explained through some solid-phase reactions. Energetic formation processes leading to efficient formation of CO₂ include irradiation of CO ices (pure or mixed with H₂O) with photons, charged particles or electrons (Ioppolo et al. 2009; Laffon et al. 2010). On the other hand, Whittet et al. (1998) invoke chemical pathways occurring without the addition of energy to explain the CO₂ detection in those interstellar environments where a lack of UV photons forbids ice processing (i.e., molecular cloud Taurus). To date, only two (non energetic) pathways were considered:

• d)

  CO + O → CO₂

• e)

  CO + OH → CO₂ + H.

Roser et al. (2001) and Raut & Baragiola (2011) successfully showed that the formation of CO₂ is possible through reaction (d). Recently, Minissale et al. (2013b) have confirmed these results and estimated an activation barrier of about 600 K/k_b. Recently, Noble et al. (2011) and Oba et al. (2011) have shown experimentally the CO₂ formation through reaction (e), but no consistent values were obtained for the activation barrier. In this paper, we showed that also reaction (a) (H₂CO+O → CO₂+H₂) can efficiently form CO₂ in the ISM. Moreover, this reaction can help to explain the CH₃OH abundances variability (from <3% to 25−30% with respect to water) in interstellar ices (Dartois et al. 1999; Whittet et al. 2011). Formation of CO₂ and CH₃OH in “hot” environments (high UV fluxes or/and T_grain> 50 K) can be explained through energetic processing of icy mantles (Moore & Hudson 1999; Ioppolo et al. 2009, and references therein), but as opposed to CO₂, CH₃OH formation is strongly dependent on the ice composition.

In cold environments, where energetic routes are not efficient, methanol and carbon dioxide are believed to form via the solid state reactions shown in Fig. 12 and listed in Table 4. In summary, we can say that:

• CH₃OH is formed via four CO hydrogenations (with a total energy barrier >800 K/k_b, Fuchs et al. 2009), leading to the formation of two unstable products, HCO and CH₃O, and one stable molecule, namely H₂CO;

• CO₂ is formed following three different chemical pathways: reaction (a), (d), and (e);

• H₂CO is a precursor not only of CH₃OH, but also of CO₂.

These considerations can have two consequences for the CH₃OH/CO₂ ratio in interstellar ice: (1) where large abundances of atomic oxygen (O/H ratio >0.1) are observed (i.e., Sgr B2 and L1689N2), the CH₃OH/CO₂ ratio tends to zero; (2) where low O/H ratios (<0.1) are observed, the increase in CH₃OH/CO₂ ratio is difficult to predict a priori because it may depend on other factors. For example, the large CO hydrogenation energy barrier and H₂CO+O reaction could hinder CH₃OH formation and favour CO₂ formation.

Online material

Appendix A: Additional experiments

To validate the formation of carbon dioxide, we performed further experiments using the H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO isotopologue of formaldehyde: the results are presented below. The top panel in Fig. A.1 shows three RAIR spectra recorded after irradiation of 2 ± 0.5 ML of H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO with increasing doses of oxygen atoms (0, 1.4, and 3.8 ML, respectively from a to c spectra) on oxidised HOPG at 55 K. Three main features are visible: at 1502 and 1697 cm^-1 due to H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO, ¹³CH₂ scissoring and ¹³CO stretch mode, respectively; at 2285 cm^-1 due to the antisymmetric stretch of ¹³CO₂. Moreover, a very weak band due to O₃ is present at 1042 cm^-1 (not shown). Each IR band varies in intensity from curve to curve. In particular, the H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO bands decrease from spectrum a to spectrum c, and the reverse occurs to the bands of ¹³CO₂. This indicates that H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO is consumed and ¹³CO₂ is formed subsequently to O irradiation. The infrared assignments are confirmed by TPD results shown in the bottom panel of Fig. A.1. These TPD traces were obtained after deposition of 2 ± 0.5 ML of ${\mathrm{H}}_{\mathrm{2}}^{\mathrm{13}}\mathrm{CO}\mathrm{+}\mathrm{3.8}\mathrm{\pm }\mathrm{0.3}$ ML of O atoms on oxidised HOPG held at 60 K. Newly formed ¹³CO₂ desorbs between 70 and 90 K and is detected via mass 45. Unreacted H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO molecules desorb between 85 and 140 K and are detected via two fragments: ⁺H$\begin{array}{c}\mathrm{13}\\ \mathrm{2}\end{array}$CO (mass 31) and ⁺H¹³CO (mass 30).

Appendix B: Rate equations

The model used to fit our experimental data is very similar to the one described in Minissale (2014) and Minissale et al. (2013b; 2014). It is composed of five differential equations, one for each of the species considered: H₂CO molecules, deposited on the surface; O atoms, coming exclusively from the beam; O₃ and CO₂, formed only on the surface; and finally O₂, coming both from the beam and formed on the surface. Each differential equation is composed of different terms:

• positive terms indicate a contribution to the increase in the surface density of the species, i.e., a molecule (or atom) arrives from the gas phase or is formed on the surface;

• negative terms indicate a decrease in the surface density of the species, i.e., a molecule (or atom) is consumed on the surface or desorbs and returns to the gas phase.

Likewise, the terms involving the ER and LH mechanisms are independent of one another, thus we are able to determine the amount of a species formed (or consumed) via the ER or the LH mechanism. For the sake of simplicity, the differential equations were divided into two sets, accounting for the two formation mechanism separately. Below is the list of equations governing the CO₂ formation by the ER mechanism: $\begin{array}{ccc}& & {\mathrm{O}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}\mathrm{2}\mathit{\tau }\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}\mathrm{(}\mathrm{1}\mathrm{-}\mathrm{2}{\mathrm{O}\mathrm{-}\mathrm{O}}_{\mathrm{2}}\mathrm{)}\mathrm{-}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{\tau }\mathrm{)}\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}\mathrm{O}\\ & & \mathrm{-}{\mathit{r}}_{\mathrm{aER}}\mathrm{2}\mathit{\tau }{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}\mathrm{-}\mathrm{O}\hspace{0.17em}{\mathit{r}}_{\mathrm{Des}{\mathrm{o}}_{\mathrm{O}}}\\ & & {\mathrm{O}}_{\mathrm{2}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{\tau }\mathrm{)}\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}\mathrm{(}\mathrm{1}\mathrm{-}\mathrm{O}\hspace{0.17em}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{ϵ}\mathrm{\left)}\mathrm{\right)}\mathrm{-}\mathrm{2}\mathit{\tau }\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}{\mathrm{O}}_{\mathrm{2}}\\ & & \mathrm{+}\mathrm{2}\mathit{\tau }\hspace{0.17em}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{ϵ}\mathrm{)}\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}{\mathrm{O}\mathrm{-}\mathrm{O}}_{\mathrm{2}}\hspace{0.17em}{\mathit{r}}_{\mathrm{Des}{\mathrm{o}}_{{\mathrm{O}}_{\mathrm{2}}}}\\ & & {\mathrm{O}}_{\mathrm{3}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}\mathrm{(}\mathrm{1}\mathrm{-}\mathit{\tau }\mathrm{)}\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}\mathrm{O}\mathrm{+}\mathrm{2}\mathit{\tau }\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}{\mathrm{O}}_{\mathrm{2}}\\ & & {{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}\mathrm{-}{\mathit{r}}_{\mathrm{aER}}\hspace{0.17em}\mathrm{2}\mathit{\tau }\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}\\ & & {\mathrm{CO}}_{\mathrm{2}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}{\mathit{r}}_{\mathrm{aER}}\hspace{0.17em}\mathrm{2}\mathit{\tau }\hspace{0.17em}{\mathit{\phi }}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{off}}\hspace{0.17em}{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}\mathit{.}\end{array}$O, O₂, O₃, H₂CO, and CO₂ are the surface densities (expressed in fractions of ML) of the species, τ is the dissociated fraction of O₂ defined in Sect. 2, φ_O2off is the flux (0.003 cm^-2 s^-1) of O₂, ϵ is the evaporation probability – due to chemical desorption − of O₂ formed on the surface (Dulieu et al. 2013), and $\begin{array}{ccc}& & {\mathit{r}}_{\mathrm{aER}}\mathrm{=}{\mathrm{e}}^{\mathrm{-}\frac{{\mathit{E}}_{\mathit{a}}}{{\mathit{T}}_{\mathrm{eff}}}}\\ & & {\mathit{r}}_{\mathrm{Des}{\mathrm{o}}_{\mathrm{O}}}\mathrm{=}\mathit{\nu }\hspace{0.17em}{\mathrm{e}}^{\frac{\mathrm{-}{\mathit{E}}_{\mathrm{Odes}}}{\mathit{T}}}\\ & & {\mathit{r}}_{\mathrm{Des}{\mathrm{o}}_{{\mathrm{O}}_{\mathrm{2}}}}\mathrm{=}\mathit{\nu }\hspace{0.17em}{\mathrm{e}}^{\frac{\mathrm{-}{\mathit{E}}_{{\mathrm{O}}_{\mathrm{2}}\mathrm{des}}}{\mathit{T}}}\mathit{,}\end{array}$are the reaction probability of H₂CO+O via ER and the desorption probabilities of O and O₂, respectively; ν = 10¹² is the trial frequency for attempting a new event. Finally, simple calculations show that 2τφ_O2off and (1 − τ)φ_O2off are the O and O₂ flux, respectively, when the discharge is on. Similarly, as for CO₂ formation by the LH mechanism, we have $\begin{array}{ccc}& & {\mathrm{O}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}\mathrm{-}\mathrm{4}\hspace{0.17em}{\mathit{k}}_{\mathrm{Odiff}}\hspace{0.17em}\mathrm{O}\hspace{0.17em}\mathrm{O}\mathrm{-}{\mathit{k}}_{\mathrm{Odiff}}\hspace{0.17em}\mathrm{O}\hspace{0.17em}{\mathrm{O}}_{\mathrm{2}}\\ & & \mathrm{-}{\mathit{r}}_{\mathrm{aLH}}\hspace{0.17em}{\mathit{k}}_{\mathrm{Odiff}}\hspace{0.17em}\mathrm{O}{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}\mathrm{-}\mathrm{O}\hspace{0.17em}{\mathit{r}}_{\mathrm{Des}{\mathrm{o}}_{\mathrm{O}}} \\ & & {\mathrm{O}}_{\mathrm{2}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}\mathrm{2}\hspace{0.17em}{\mathit{k}}_{\mathrm{Odiff}}\hspace{0.17em}\mathrm{O}\hspace{0.17em}\mathrm{O}\hspace{0.17em}\mathit{ϵ}\mathrm{-}{\mathit{k}}_{\mathrm{Odiff}}\hspace{0.17em}\mathrm{O}\hspace{0.17em}{\mathrm{O}}_{\mathrm{2}}\\ & & \mathrm{-}{\mathrm{O}}_{\mathrm{2}}\hspace{0.17em}{\mathit{r}}_{\mathrm{Des}{\mathrm{o}}_{{\mathrm{O}}_{\mathrm{2}}}} \\ & & {\mathrm{O}}_{\mathrm{3}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}{\mathit{k}}_{\mathrm{Odiff}}\hspace{0.17em}\mathrm{O}\hspace{0.17em}{\mathrm{O}}_{\mathrm{2}} \\ & & {\mathrm{H}}_{\mathrm{2}}{\mathrm{CO}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}\mathrm{-}{\mathit{r}}_{\mathrm{aLH}}\hspace{0.17em}{\mathit{k}}_{\mathrm{Odiff}}\hspace{0.17em}\mathrm{O}\hspace{0.17em}{\mathrm{H}}_{\mathrm{2}}\mathrm{CO} \\ & & {\mathrm{CO}}_{\mathrm{2}}^{\mathrm{\prime }}\mathrm{\left(}\mathit{t}\mathrm{\right)}\mathrm{=}{\mathit{r}}_{\mathrm{aLH}}\hspace{0.17em}{\mathit{k}}_{\mathrm{Odiff}}\hspace{0.17em}\mathrm{O}\hspace{0.17em}{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}\mathit{,} \end{array}$where $\begin{array}{ccc}& & {\mathit{k}}_{\mathrm{Odiff}}\mathrm{=}\mathit{\nu }\hspace{0.17em}{\mathrm{e}}^{\frac{\mathrm{-}{\mathit{E}}_{\mathrm{Odiff}}}{\mathit{T}}}\\ & & {\mathit{r}}_{\mathrm{aLH}}\mathrm{=}{\mathrm{e}}^{\frac{\mathrm{-}{\mathit{E}}_{\mathit{a}}}{\mathit{T}}}\end{array}$are the thermal diffusion probability of O atoms and the reaction probability of H₂CO+O via LH, respectively. The activation barrier E_a is derived inverting the normalized Arrhenius equation: ${\mathit{E}}_{\mathit{a}}\mathrm{=}\mathrm{-}{\mathit{k}}_{\mathit{b}}\hspace{0.17em}{\mathit{T}}_{\mathrm{eff}}\hspace{0.17em}\log \mathrm{\left(}{\mathit{r}}_{\mathrm{aER}\mathit{,}\mathrm{LH}}\mathrm{\right)}\mathit{,}$(B.16)with either r_aER or r_aLH according to the mechanism at play. Here $\begin{array}{ccc}{\mathit{T}}_{\mathrm{eff}}& \mathrm{=}& \mathit{\mu }\left(\frac{{\mathit{T}}_{\mathrm{solid}}}{{\mathit{m}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}}}\mathrm{+}\frac{{\mathit{T}}_{\mathrm{gas}}}{{\mathit{m}}_{\mathrm{O}}}\right)\mathrm{=}\mathrm{280}\mathrm{K}\mathrm{forER,and}\\ {\mathit{T}}_{\mathrm{eff}}& \mathrm{=}& \mathit{\mu }\left(\frac{{\mathit{T}}_{\mathrm{solid}}}{{\mathit{m}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{CO}}}\mathrm{+}\frac{{\mathit{T}}_{\mathrm{solid}}}{{\mathit{m}}_{\mathrm{O}}}\right)\mathrm{=}\mathrm{55}\mathrm{K}\mathrm{forLH}\end{array}$(see Minissale et al. 2013b for more details).

Appendix C: Theoretical calculations

The geometries (Fig. C.1) and energies (Tables C.1 and C.2) were optimized either using DFT with the hybrid meta exchange-correlation functional M06-2X or using classical MP2 method, both methods coupled to the Dunning’s correlation (Dunning 1989) consistent polarized valence triple zeta basis set cc-pVTZ. The highly nonlocal M06-2X functional developed by Truhlar et al. (Zhao & Truhlar 2008) is relatively well suited to structures and energetics calculations of the transition states even though this method slightly underestimates barrier energy. We then also calculate the barrier height using full optimized MP2

method, as well as single point CCSD(T) with MP2 geometries in some cases. The unrestricted Hartree-Fock (UHF) formulation has been used since it is a convenient way to describe open-shell and bond-breaking processes. Its use is justified in our study by the fact that we did not observe any significant spin contamination for all the stationary points explored, the quantum average value ⟨S2⟩ of the square of the total spin operator remaining close to 2.00, i.e. the characteristic value for a triplet state. Full geometry optimization was performed throughout. We checked carefully that all the saddle points found are correctly connected to two minima and are characterized by the existence of only one negative eigenvalue of the Hessian matrix corresponding to an imaginary frequency in the normal mode analysis.

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Acknowledgments

The LERMA-LAMAp team in Cergy acknowledges the support of the national PCMI programme founded by CNRS. M.M. acknowledges financial support by LASSIE, a European FP7 ITN Community’s Seventh Framework Programme under Grant Agreement No. 238258. M.M. also thanks Dr. M. E. Palumbo and Dr. E. Dartois for fruitful discussions.

References

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