CONTRIBUTIONS FROM GRAIN SURFACE AND GAS PHASE CHEMISTRY TO THE FORMATION OF METHYL FORMATE AND ITS STRUCTURAL ISOMERS

In the GWWH08 study, the photodissociation pathways for methanol on grain surfaces include

$$\begin{eqnarray} \hbox{CH}_3\hbox{OH} + \hbox{h}\nu &\rightarrow & {}\hbox{CH}_3 + {}\hbox{OH}, \end{eqnarray} \tag{ 1a }$$

$$\begin{eqnarray} \hspace{5pc}&\rightarrow & {}\hbox{CH}_2\hbox{OH} + \hbox{H}, \end{eqnarray} \tag{ 1b }$$

$$\begin{eqnarray} \hspace{4.5pc}&\rightarrow & \hbox{CH}_3\hbox{O} + \hbox{H}. \end{eqnarray} \tag{ 1c }$$

In the GWWH08 study, the methanol photodissociation branching ratios for the above pathways were assumed to be 60:20:20 (1a:1b:1c) for all photodissociation processes; hereafter, we denote this set of branching ratios as the "standard" branching ratios.

In the current study, only the branching ratios for the cosmic-ray-induced photodissociation of methanol were altered, so that direct comparison could be made to the previous work. Four sets of methanol photodissociation branching ratios were used, and these trials are summarized in Table 1. The other sets of photodissociation branching ratios beyond the standard values were chosen to test the extreme cases for each specific product channel dominating the dissociation.

Each entry in Table 1 was used for a corresponding set of gas phase reactions, grain surface reactions, or both. The labeling scheme used hereafter is as follows: label = prefix_ suffix_timescale, where prefixes are B (both grain surface and gas phase methanol photodissociation channels), S (grain surface methanol photodissociation channels only), G (gas phase methanol photodissociation channels only). Suffixes are listed in Table 1, and the timescale is either S (1 × 10⁶ yr), M (2 × 10⁵ yr), or F (5 × 10⁴ yr). In the cases where the sets contained altered methanol photodissociation branching ratios only for the grain surface or gas phase reaction sets, the default values for the unaltered reactions were set to the "standard" values. For example, the trial with methanol photodissociation branching ratios emphasizing the hydroxymethyl channel set to 90% on the grain surface (1a:1b:1c = 5:90:5) and tested at a medium warm-up timescale is labeled as "S_hydroxymethyl_M," and the gas phase methanol photodissociation branching ratios were set to 1a:1b:1c = 60:20:20.

Pate and coworkers (J. Neill et al. 2011, in preparation) have suggested that Fischer esterification reactions between formic acid and methanol may be feasible gas phase formation routes for methyl formate. For this study, we tested two Fischer esterification mechanisms: the standard esterification mechanism with formic acid as the protonated reactant and a second esterification reaction with methanol as the protonated reactant. These two mechanisms and the steps taken to incorporate them into the model are described below.

2.2.1. Route 1: Protonated Formic Acid + Methanol

The Fischer esterification reaction between protonated formic acid and methanol (hereafter referred to as Route 1) leads to protonated methyl formate:

$$\begin{equation} \hbox{HCOOH}_2^+ + \hbox{CH}_3\hbox{OH} \rightarrow \hbox{CH}_3\hbox{OCOH}_2^+ + \hbox{H}_2\hbox{O}. \end{equation} \tag{ 2 }$$

This reaction was added to the reaction network and classified as a gas phase ion–molecule reaction with the standard rate expression. Additional related reactions, including the proton transfer between methanol and formic acid, and a set of ion–neutral reactions involving formic acid, were also added to the network. The list of new reactions added to the network for Route 1 and the associated information for their rate coefficients are given in Table 2.

Table 2. Changes to the Reaction Network Based on Route 1

Reactants	Products	Rate Coefficient Termsa			Reference
		α	β	γ
HCOOH+2 + CH3OH	CH3OCOH+2 + H2O	2.00 × 10−9 b	−0.5	2810	1
CH3OH+2 + HCOOH	CH3OH + HCOOH+2	3.63 × 10−9	−0.5	685	2
HCOOH+2 + CH3OH	CH3OH+2 + HCOOH	2.29 × 10−9	−0.5	0	3
CH+5 + HCOOH	HCOOH+2 + CH4	3.00 × 10−9	−0.5	0	2
H+3 + HCOOH	HCO+ + H2O + H2	3.90 × 10−9	−0.5	0	2, 4
He+ + HCOOH	HCO+ + OH + He	9.00 × 10−10	−0.5	0	4
C+ + HCOOH	HCO+ + OH + C	8.00 × 10−10	−0.5	0	4
N2H+ + HCOOH	HCOOH+2 + N2	1.70 × 10−9	−0.5	0	2
H2CN+ + HCOOH	HCOOH+2 + HCN	1.40 × 10−9	−0.5	0	2
H3S+ + HCOOH	HCOOH+2 + H2S	2.00 × 10−9	−0.5	0	2
H2COH+ + HCOOH	HCOOH+2 + H2CO	2.00 × 10−9	−0.5	0	2

Notes. ^ak(T) = α(T/300)^βexp(−γ/T) cm³ s⁻¹. ^bThe rate coefficient used here is identical with an estimate based on the Su-Chesnavich theory for reactions between ions and polar neutrals (Woon & Herbst 2009) in the temperature range 10–300 K. References. (1) J. Neill et al. 2011, in preparation; (2) Freeman et al. 1978a; (3) Feng & Lifshitz 1994; (4) Freeman et al. 1978b.

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In addition to the new gas phase formation reactions, additional modifications were made to the network for the dissociative recombination (DR) reactions of protonated formic acid. These changes were based on the recent DR study of protonated formic acid at CRYRING (Vigren et al. 2010). In the original network, the following DR reactions for protonated formic acid were present:

$$\begin{equation} \hbox{HCOOH}_2^+ + e^- \rightarrow \hbox{CO}_2 + \hbox{H}_2 + \hbox{H} \end{equation} \tag{ 3 }$$

$$\begin{equation} \hbox{HCOOH}_2^+ + e^- \rightarrow \hbox{HCOOH} + \hbox{H}. \end{equation} \tag{ 4 }$$

In the present study, Reaction 3 was replaced with

$$\begin{equation} \hbox{HCOOH}_2^+ + e^- \rightarrow \hbox{HCO} + \hbox{OH} + \hbox{H}. \end{equation} \tag{ 5 }$$

As is shown in Table 3, the DR reactions and their rate coefficients were changed to reflect the new CRYRING measurements.

Table 3. Protonated Formic Acid DR Reactions

Reaction	Previous Rate Coefficient	New Rate Coefficient
	(cm3 s−1)	(cm3 s−1)
3	k(T) = 2.85 × 10−7(T/300)−0.5	0
4	k(T) = 1.5 × 10−8(T/300)−0.5	k(T) = 1.1 × 10−7(T/300)−0.78
5	0	k(T) = 7.3 × 10−7(T/300)−0.78

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2.2.2. Route 2: Protonated Methanol + Formic Acid

A second esterification reaction leading to protonated methyl formate, this time involving protonated methanol and formic acid, was added to the network:

$$\begin{equation} \hbox{CH}_3\hbox{OH}_2^+ + \hbox{HCOOH} \rightarrow \hbox{CH}_3\hbox{OCOH}_2^+ + \hbox{H}_2\hbox{O}. \end{equation} \tag{ 6 }$$

This pathway is hereafter referred to as Route 2. Here, the product can be either the cis or trans stereoisomer of protonated methyl formate. The pathway leading to the cis stereoisomer involves a 1320 K barrier, while the reaction leading to the trans stereoisomer does not have a barrier. These reactions were added to the network, where the α term in the rate coefficient expression was based on the experimental results of Freeman et al. (1978a), which gave a total rate coefficient of 3.7 × 10⁻¹⁰ cm³ s⁻¹ at 300 K. In this study, the measurements focused on the proton-transfer reaction, rather than the formation of protonated methyl formate. The total rate coefficient determined for the proton-transfer reaction is higher than the values used in the model for other similar reactions. It is not clear from this study whether the protonated methyl formate channel could have contributed to the overall rate measured in this experiment, but it is possible if this value was determined by monitoring the reactants and the assumption was made that the proton-transfer reaction was the only reaction channel. Based on this fact, and the unusually high value for the proton-transfer reaction rate determined in this study, it is reasonable to assume that the protonated methyl formate formation channel may have contributed to the overall measured value of the rate coefficient. We therefore used the more typical value for the proton-transfer reaction rate coefficient of 1.9 × 10⁻¹⁰ cm³ s⁻¹ and derived from this a total rate coefficient for Route 2 of 1.8 × 10⁻¹⁰ cm³ s⁻¹. The rate coefficient information for the two esterification reactions leading to cis and trans protonated methyl formate via Route 2 is given in Table 4. An α value of 1.8 × 10⁻¹⁰ was used for both reactions involved in Route 2, based on the assumption that the two reactions would have equal α values. Here, the barrierless reaction leading to the trans conformer of protonated methyl formate dominates the total rate coefficient for this process.

Table 4. Changes to the Reaction Network Based on Route 2

Reactants	Products	Rate Coefficient Termsa
		α	β	γ
CH3OH+2 + HCOOH	cis-CH3OCOH+2 + H2O	1.8 × 10−10	−0.5	1320
CH3OH+2 + HCOOH	trans-CH3OCOH+2 + H2O	1.8 × 10−10	−0.5	0

Note. ^ak(T) = α(T/300)^βexp(−γ/T) cm³ s⁻¹.

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In addition to the new reactions outlined above, the reaction network was modified so that a distinction was made between the cis and trans stereoisomers of methyl formate and its protonated counterpart. The reaction energies of the stereoisomers are quite different in each case and can therefore lead to different chemical pathways. Structurally, the two stereoisomers of methyl formate differ in the orientation of the –CH₃O group relative to the –CHO group, with the trans species being 2880 K higher in energy than the cis species (J. Neill et al. 2011, in preparation). The protonated versions of the cis and trans stereoisomers have similar structures to their neutral counterparts, but in this case the trans species is lower in energy by 2880 K. In the reaction network, the stereoisomers of both neutral and protonated methyl formate are distinguished as separate species, differing only in their label and their respective reaction rates. The overall chemistry was assumed to be the same for the two stereoisomers in each case. All reactions involving the neutral and protonated forms of methyl formate were duplicated so that a complete set of reactions was included for each stereoisomer. The gas phase reactions of each stereoisomer are shown in Table 5. Here, the α term in the rate coefficient expression for the cis conformer was used for the trans conformer. DR reactions leading to neutral methyl formate from protonated methyl formate were assumed to proceed with no conformational change (i.e., the structure of the ion is retained in the neutral product).

Only one form of methyl formate was included in the list of grain surface species, and this molecule was not distinguished as either cis or trans. However, for reactions on surfaces that produce gas phase methyl formate, the reaction was duplicated in the same manner as the gas phase reactions so that both stereoisomers could be included. The rates for those reactions involving the trans stereoisomer were scaled using a Boltzmann factor based on the energy difference between the two stereoisomers and assuming a temperature of 50 K. This temperature was selected because GWWH08 showed that the heavy radicals involved in these reactions become mobile on the grain surface and react in the 30–70 K temperature range. As is shown in Table 6, the values of the α term in the rate coefficient expression for the grain surface reactions involving the gas phase trans species were therefore scaled by 10⁻²⁵ (i.e., e^{−(2880 K/50 K)}) with respect to the reactions involving the gas phase cis species. Only grain surface reactions that involved one gas phase molecule were included in the model, following the convention used in previous modeling studies (Garrod et al. 2007).

The results of the trials where only methanol photodissociation branching ratios were modified are shown in Figures 1–3. For the sake of simplification, only molecules that have been identified in the Sgr B2(N-LMH) hot core source have been included. Figure 1 compares the peak abundances determined using the standard branching ratios from GWWH08 and those predicted using grain surface branching ratios that emphasize the methoxy (CH₃O) channel. The slow warm-up timescale is shown for comparison in Figure 1, as this is the appropriate timescale for a high-mass hot core such as Sgr B2(N). Examination of Figure 1 reveals that the S_Methoxy_S trial gives a peak methyl formate abundance that is in better agreement with the observed abundance than the standard methanol photodissociation branching ratios used in GWWH08.

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As is shown in more detail in Figure 2, the "Methoxy" branching ratios give the best match between observations and peak abundances for methyl formate, but both the acetic acid and glycolaldehyde peak abundances better match observations when the "Methyl" branching ratios are used. It should be noted here that the differences between these two trials for these two molecules are of the same magnitude as the estimated 20% uncertainty in the observational numbers. It is unclear from these results which set of branching ratios gives the best overall match to the relative abundances observed in Sgr B2(N). The set of branching ratios favoring the methoxy channel agrees qualitatively with gas phase laboratory measurements, which determined the overall branching fraction for the combined CH₃O and CH₂OH channels to be ∼0.75 (Hagege et al. 1968). To our knowledge, no gas phase or condensed phase laboratory measurements have yet distinguished between these two channels through direct measurements of the products. In contrast, neither set of branching ratios that gives a reasonable match to the Sgr B2(N) abundances agrees with the results of a recent laboratory study of methanol ice photodissociation, where the CH₂OH channel was found to dominate the other two pathways (Öberg et al. 2009). Regardless, it is clear that an increase in the methanol photodissociation branching fraction that leads to the methoxy channel is required to explain the methyl formate abundance observed in Sgr B2(N).

Despite the agreement observed in the S_Methoxy_S trial for methyl formate, and reasonable agreement in this trial for acetic acid, the predicted peak abundance for glycolaldehyde in all trials is more than an order of magnitude higher than that observed in Sgr B2(N-LMH). Glycolaldehyde is known to be cold (<50 K) and extended (>60'') in this source (Hollis et al. 2004), unlike its structural isomers methyl formate and acetic acid, which are both compact hot core molecules (Snyder 2006). The peak abundance for glycolaldehyde occurs at a long timescale and high temperature in the model. If shocks released significant quantities of glycolaldehyde into the cold gas in the outer shells of the Sgr B2(N) hot core, then it is unrealistic to compare the peak gas phase abundance for glycolaldehyde in the model to the observed abundance. Direct comparison with the grain surface peak abundance is also not reasonable, because not all of the grain surface species would necessarily be released into the gas by the shock. Even if all grain surface glycolaldehyde was released by shocks into the gas phase, some fraction of the released glycolaldehyde would accrete back onto the grain at the lower temperatures of the outer envelope. Therefore, the only reasonable point of comparison is the T = 80–120 K range where significant evaporation of grain surface glycolaldehyde is occurring. Indeed, the glycolaldehyde fractional abundance of (2–4)×10⁻¹¹ predicted by the model at T ∼ 100 K matches the value of 4 × 10⁻¹¹ observed in Sgr B2(N-LMH).

Looking beyond the influence of the grain surface photodissociation branching ratios, these trials reveal two other interesting trends. As is shown in Figure 2, the gas phase branching ratios have no influence on the peak abundances of COMs. This is to be expected, as the dominant formation mechanisms for these species are grain surface pathways. Additional examination of the results reveals that a change in warm-up timescale in addition to changes in the grain surface branching ratios can have a large influence on the peak abundances for COMs, as is illustrated by Figure 3. Fast warm-up timescales allow less time for grain surface chemistry, and so the more complex species are not formed efficiently under these conditions. This is especially true for a species such as acetic acid that forms from secondary radicals, as is evident in Figure 3. The longest warm-up timescale corresponds to the formation of a high-mass hot core, and indeed this timescale gives the best match to the observed Sgr B2(N-LMH) abundances. Longer warm-up timescales should result in more chemical complexity, in agreement with the rich molecular complexity observed in high-mass hot cores such as Sgr B2 and Orion.

The results of the trials including the new gas phase routes to form methyl formate (i.e., Routes 1 and 2) are shown in Figures 4 and 5. Figure 4 shows the peak abundances for COMs using both the B_Standard_S and the S_Methoxy_S branching ratios, both with and without the new gas phase reactions, compared to the abundances observed in Sgr B2(N-LMH). The inclusion of the new gas phase formation routes for methyl formate yields no change in the model predictions for the peak abundances for any trials.

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Detailed analysis indicates that no changes occur for the cis-methyl formate abundance when Routes 1 and 2 are included, regardless of temperature, although the results from trials including these new gas phase reactions do indicate that trans-methyl formate should be an abundant molecule in hot cores. The time evolution plot of Figure 5 reveals that at T < 55 K, gas phase trans-methyl formate is slightly higher in abundance than gas phase cis-methyl formate because it is formed in the gas via Route 2. In the range T = 55–100 K, cis-methyl formate is produced via grain surface chemistry, and this formation route dominates its formation over the new gas phase routes. The gas phase cis-methyl formate abundance peak occurs at T ∼ 80 K; at this temperature, the relative abundance ratio of cis/trans is 2.3 × 10⁸. Above T = 100 K, the grain surface production routes to methyl formate no longer contribute significantly to the cis-methyl formate gas phase abundance. The gas phase abundance of trans-methyl formate begins to rise dramatically at these higher temperatures because of its formation via Route 2, while the gas phase abundance of cis-methyl formate decreases gradually as it is destroyed through gas phase processes and is no longer replenished via grain surface chemistry. The two conformers begin to approach a similar gas phase abundance at higher temperatures and long timescales, and the relative abundance ratio of cis/trans is 2.67 at T = 200 K.

Although the peak abundances do not change when Routes 1 and 2 are included, small changes are observed in the time evolution plots for formic acid and acetic acid. These changes arise from the adjustment of the protonated formic acid DR rates reflected in Table 3. The formic acid abundance in the gas phase increases at temperatures below 100 K because the rate of its formation via Reaction 4 is increased over the rate used in GWWH08. This results in an increase in formic acid abundance on the grain (via accretion of the gas phase neutral) and acetic acid abundance in the gas (via its formation from formic acid in grain surface reactions and subsequent evaporation). No change is observed at T > 100 K between the two sets of trials (i.e., with and without Routes 1 and 2) for any species examined here other than trans-methyl formate.

The methyl formate stereoisomers can be used as a gauge of the validity of the gas phase chemistry examined in this model, as trans-methyl formate should be observable in the Sgr B2(N-LMH) source if it forms from the mechanisms included here. Its presence will also allow a test of the physical model assumed for comparison to Sgr B2, as the abundance ratios directly probe the temperature at which methyl formate is released from grains. The fractional abundance of cis-methyl formate in Sgr B2 is 1.9 × 10⁻⁸. The expected thermodynamic ratio between the two isomers is 10⁻²⁵ (i.e., e^{−(2880 K/50 K)}), but the model predicts the fractional abundance of trans-methyl formate to be 1 × 10⁻¹¹ at high temperatures (i.e., T > 100 K) and long timescales. The rotational spectrum of trans-methyl formate has now been recorded up to 26 GHz, and initial observational searches indicate its presence in Sgr B2 (J. Neill et al. 2011, in preparation). No quantitative information about its temperature or abundance is yet available. Additional higher frequency laboratory studies are required before its physical properties in a hot core can be probed.

In addition to using stereoisomers as probes of the chemistry and physics included in this model, the model now provides predictions for ion abundances that are based on a more realistic chemical network. Imaging observations that compare the distribution of these ions to their neutral counterparts could reveal their role in the chemical processing of material in hot cores. A direct spatial correlation between the ion and its neutral counterpart might indicate formation of the neutral species from the electron recombination reactions of its protonated counterpart. If an anti-correlation is observed, however, then the conclusion could be drawn that the neutral forms from grain chemistry, and is subsequently ionized in the gas phase after release from the grain. Regardless, these species hold great promise for unveiling the true chemical mechanisms leading to the formation and destruction of COMs in interstellar clouds. The peak abundances predicted for protonated methanol (2 × 10⁻¹¹) and protonated cis-methyl formate (8 × 10⁻¹¹) indicate that both of these ions should be observable in the Sgr B2 source. The predicted peak abundances for protonated formic acid (1 × 10⁻¹³) and protonated trans-methyl formate (6 × 10⁻¹⁴) indicate that detection of these ions will be observationally challenging.