The Case of H$_2$C$_3$O Isomers, Revisited: Solving the Mystery of the Missing Propadienone

TL;DR

This study uses quantum chemical calculations to explain why the propadienone isomer of H$_2$C$_3$O remains undetected in space, revealing that kinetic factors, not just stability, govern interstellar molecule abundances.

Contribution

The paper demonstrates that barrierless destruction of propadienone explains its absence, emphasizing the role of kinetics over thermodynamics in astrochemical isomer distributions.

Findings

Propadienone destruction is barrierless and exothermic.

Radical CH$_2$CHCO reacts with H to form detectable propenal.

Kinetic effects explain the non-detection of certain isomers.

Abstract

To date, two isomers of H$_2$C$_3$O have been detected, namely, propynal (HCCCHO) and cylclopropenone (c-H$_2$C$_3$O). A third, propadienone (CH$_2$CCO), has thus far eluded observers despite the fact that it is the lowest in energy of the three. This previously noted result is in contradiction of the minimum energy principle, which posits that the abundances of isomers in interstellar environments can be predicted based on their relative stabilities - and suggests, rather, the importance of kinetic over thermodynamic effects in explaining the role of such species. Here, we report results of \textit{ab initio} quantum chemical calculations of the reaction between H and (a) HC$_3$O, (b) H$_2$C$_3$O (both propynal and propadienone), and (c) CH$_2$CHCO. We have found that, among all possible reactions between atomic hydrogen and either propadienone or propynal, only the destruction of propadienone is barrierless and exothermic. That this destruction pathway is indeed behind the non-detection of CH$_2$CCO is further suggested by our finding that the product of this process, the radical CH$_2$CHCO, can subsequently react barrierlessly with H to form propenal (CH$_2$CHCHO) which has, in fact, been detected in regions where the other two H$_2$C$_3$O isomers are observed. Thus, these results not only shed light on a previously unresolved astrochemical mystery, but also further highlight the importance of kinetics in understanding the abundances of interstellar molecules.

Tables

Table 1. Table 1: Overview of reaction energies ( Δ r ​ E subscript Δ r 𝐸 \Delta_{\text{r}}E ) and activation barriers ( Δ ​ E A Δ subscript 𝐸 A \Delta E_{\text{A}} ) in kJ mol -1 of all reactions studied.

Label	Reaction	${\Delta }_{\text{r}}E$	$\Delta E_{\text{A}}$
(R1)	\ceH + HC3O $\to$ \ceCH2CCO	$-$363.2	0.0
(R2)	\ceH + HC3O $\to$ \ceHCCCHO	$-$340.3	0.0
(R3)	\ceH + CH2CCO $\to$ \ceHC3O + H2	$-$58.2	18.4
(R4)	\ceH + CH2CCO $\to$ \ceCH2CHCO	$-$246.5	0.0
(R5)	\ceH + CH2CCO $\to$ \ceCH2CCOH	$-$117.2	38.1
(R6)	\ceH + CH2CCO $\to$ \ceCH2CCHO	$-$169.7	$\gg$
(R7)	\ceH + CH2CCO $\to$ \ceCH3CCO	$-$205.4	6.2
(R8)	\ceH + HCCCHO $\to$ \ceCCCHO + H2	128.1	128.1
(R9)	\ceH + HCCCHO $\to$ \ceHC3O + H2	$-$76.5	11.7
(R10)	\ceH + HCCCHO $\to$ \ceCHCCHOH	$-$168.8	26.9
(R11)	\ceH + HCCCHO $\to$ \ceCHCCH2O	$-$74.6	23.8
(R12)	\ceH + HCCCHO $\to$ \ceCHCHCHO	$-$164.5	18.9
(R13)	\ceH + HCCCHO $\to$ \ceCH2CCHO	$-$192.7	11.3

Equations

$$T_{\mathrm{c}}=\frac{\hslash {\omega }_{\mathrm{b}}}{2\pi k_{\mathrm{b}}},$$

$$\text{ce}H+HC3O->CH2CCO$$

$$\text{ce}H+HC3O->HCCCHO$$

$$\text{ce}H+CH2CCO->HC3O+H2.$$

$$\text{ce}H+CH2CCO->CH2CHCO$$

$$\text{ce}H+CH2CHCO->CH2CHCHO$$

$$\text{ce}HCCCHO+2H->CH2CHCHO.$$

Full text

Here, we report results of ab initio quantum chemical calculations of the reaction between H and (a) \ceHC3O, (b) \ceH2C3O (both propynal and propadienone), and (c) \ceCH2CHCO. We have found that, among all possible reactions between atomic hydrogen and either propadienone or propynal, only the destruction of propadienone is barrierless and exothermic. That this destruction pathway is indeed behind the non-detection of \ceCH2CCO is further suggested by our finding that the product of this process, the radical \ceCH2CHCO, can subsequently react barrierlessly with H to form propenal (\ceCH2CHCHO) which has, in fact, been detected in regions where the other two \ceH2C3O isomers are observed. Thus, these results not only shed light on a previously unresolved astrochemical mystery, but also further highlight the importance of kinetics in understanding the abundances of interstellar molecules.

astrochemistry — ISM: abundances — ISM: clouds — ISM: molecules — molecular processes

††journal: ApJ††software: Turbomole (TURBOMOLE, 2018), ChemShell (Sherwood et al., 2003; Metz et al., 2014), DL-Find (Kästner et al., 2009), Molpro (Werner et al., 2010)

1 Introduction

In a recent survey by McGuire (2018), it was noted that, to date, approximately 200 different individual molecular species have been detected in either interstellar or circumstellar regions. As observing facilities and observational techniques have become more sophisticated, larger and more complex molecules have been detected, including a number of isomers - one of the most notable being the branched form of propyl cyanide (\ceC3H7CN) (Belloche et al., 2014).

Uncovering the chemical mechanisms behind the observed relative abundances of these isomers remains one of the major challenges in astrochemistry today, and as increasingly complex molecules are detected this problem will only grow more acute. For example, the abundances of \ceH2C3O isomers have posed a longstanding astrochemical conundrum. The first such species to be detected was propynal (\ceHCCCHO), observed by Irvine et al. (1988) in the cold core TMC-1. The cyclic molecule cyclopropenone (\cec-H2C3O) was later seen by Hollis et al. (2006) towards Sgr B2(N) using the GBT. There is also a third form, propadienone (\ceCH2CCO), which was calculated to be the most stable of the three (Komornicki et al., 1981; Maclagan et al., 1995; Ekern et al., 1996; Scott & Radom, 2000; Karton & Talbi, 2014), however, this last form has thus far proven elusive.

One such attempt to detect propadienone was made by Loomis et al. (2015), who searched for isomers of \ceH2C3O in archival data from the PRIMOS survey of Sgr B2(N).111https://www.cv.nrao.edu/PRIMOS There, they reported detections of cyclopropenone and propynal but a non-detection of \ceCH2CCO. In that work, Loomis and coworkers interpreted their results as highlighting the influence of some as yet unknown reaction that favored either the production of propynal and cyclopropenone and/or the destruction of propadienone.

More recently, Loison et al. (2016) reported the non-detections of propadienone towards a number of starless cores and molecular clouds, despite having detected both cyclopropenone and propynal. Based on these observational results, as well as those from detailed chemical modeling, they too concluded that the abundances of the \ceH2C3O molecules were kinetically, rather than thermodynamically controlled. Loison and coworkers speculated that the primary contributing factor behind the observed abundances of these isomers were differing formation routes. However, the results of their simulations regarding propadienone were mixed, with its calculated abundance being within the observational error of their upper limit for at least sources with typical densities of $\sim 10^{4}$ cm*-3* at relevant timescales. Thus, despite evidence suggesting the impact of some key chemical reactions on the abundance of propadienone, their identities remained mysterious.

Here, we report the results of ab initio quantum chemical calculations of the reaction \ceH + HC3O, as well as hydrogen additions to a number of related species, including propynal and propadienone. Though this study was motivated by the recent detections of \ceHC5O (McGuire et al., 2017) and \ceHC7O (McGuire et al., 2017; Cordiner et al., 2017), in performing these calculations we have uncovered the likely chemical pathways responsible for the puzzling lack of \ceCH2CCO.

Secondarily, our findings shed additional light on the validity of using thermodynamics to predict molecular abundances in the ISM, more generally, and highlight the central importance of chemical activation energy barriers, i.e. kinetics. Such an attempt to make sense of observational results was made by Lattelais et al., who proposed a general rule based on a comparison between observational data and the results of quantum chemical calculations (Lattelais et al., 2009, 2010, 2011). This guideline, which they called the “minimum energy principle” (hereafter MEP), states that the relative abundances of different isomers in the same region could be estimated based on the energy differences between them, with the most stable being the most abundant. However, even in their first work on the MEP, Lattelais et al. (2009) noted exceptions, for instance, species with the formula \ceC2H4O2. Thus, though the aim of this work is neither to further challenge the already dubious MEP nor to again demonstrate - as we have previously done in Loomis et al. (2015) - that the \ceH2C3O isomers violate said principle, our results do provide further evidence for the centrality of kinetics in understanding the theoretical basis behind interstellar isomer abundances.

The rest of this letter is as follows: in §2 we give an overview of the methods and tools used in this study, in §3 our results are presented, and their astrochemical implications are discussed in §4, finally, our conclusions are summarized in §5.

2 Computational Details

We used unrestricted density functional theory (DFT) with the PW6B95 functional (Zhao & Truhlar, 2005) and the def2-TZVP basis set (Schäfer et al., 1994). These calculations were done in Turbomole (TURBOMOLE, 2018) accessed via ChemShell (Sherwood et al., 2003; Metz et al., 2014). The geometry optimizations and instanton calculations were done in DL-Find (Kästner et al., 2009) through ChemShell. All molecular degrees of freedom were optimized in all cases. No symmetry was imposed on the molecules. For radical-radical reactions, like \ceH + HC3O, an unrestricted broken-symmetry wave function was used with overall as many spin-up as spin-down electrons, but finite spin density on both radicals. Although a gas-phase model was used, rate constants were calculated with an implicit surface model (Meisner et al., 2017). Benchmarks were performed for individual geometries on the coupled-cluster level UCCSD(T)-F12a (Adler et al., 2007) with a restricted Hartree–Fock reference and the cc-pVTZ-f12 basis set (Peterson et al., 2008) in Molpro (Werner et al., 2010).

Minima and transition state structures were verified by frequency calculations from numerical Hessians in DL-Find. Energies are reported including the harmonic vibrational zero point energy. Barrierless processes were identified by starting energy minimizations from the separated reactants. An optimization ending up in the product minimum demonstrates a barrierless path.

Bimolecular rate constants were calculated using instanton theory (Miller, 1975; Coleman, 1977) as implemented in DL-Find (Rommel et al., 2011) below the crossover temperature,

[TABLE]

with $\hbar$ and $k_{\mathrm{b}}$ being the reduced Planck and Boltzmann constants, respectively, and $\omega_{\mathrm{b}}$ the absolute value of the imaginary frequency at the transition state. The instanton path was discretized with 40 replicas, except for the calculations at 55 K and 50 K for the reaction \ceH + CHCCHO $\rightarrow$ \ceHC3O + H2, where 78 replicas were used. Convergence with respect to the number of replicas was confirmed by using more replicas at one low temperature. Through the use of both a well-established correction (Kryvohuz, 2013; McConnell & Kästner, 2017) close to the crossover temperature and the use of reduced instanton theory (Kryvohuz, 2013) above that temperature, a continuous curve over the full temperature range was achieved.

3 Results and Discussion

The results of our geometry optimizations of the molecule \ceHC3O show that it is not linear. Rather, in agreement with QCISD calculations by Wang & Cooksy (1996) and Cooksy et al. (1995), we found two main configurations, namely, one with a bend on the CO-end, and another with the bend on the CH-end, with the latter being more stable.

As shown in Table 1, in which the results of our calculations are listed for reactions labeled (R1)-(R13), we further found the first two,

[TABLE]

[TABLE]

to be barrierless and exothermic in both the product channels. Thus, both (R1) and (R2) should be efficient formation routes for propynal and propadienone on interstellar dust-grain surfaces. Using DFT (PW6B95/def2-TZVP), we found the formation of \ceCH2CCO to be exothermic by 363.2 kJ mol*-1* and the formation of HCCCHO to be exothermic by 340.3 kJ mol*-1*. However, the branching ratio between the two is likely to be more sensitive to the orientation of the reactants than on the exothermicities of these two reactions. In addition, while \ceCH2CCO is more stable than HCCCHO by 22.9 kJ mol*-1* using DFT, it is slightly less stable (by 0.7 kJ mol*-1*) using CCSD(T)-F12a/cc-pVTZ-F12. By comparison, \cec-H2C3O is found to be 24.7 kJ mol*-1* less stable than \ceCH2CCO by DFT and 26.3 kJ mol*-1* by CCSD(T)-F12a/cc-pVTZ-F12. These data are consistent with previous data from W2-F12 theory by Karton & Talbi (2014), who find \ceCH2CCO to be the most stable isomer, followed by \ceHCCCHO at 2.5 kJ mol*-1* and \cec-H2C3O at 29.2 kJ mol*-1* and broadly consistent with older calculations at lower levels of theory (Komornicki et al., 1981; Maclagan et al., 1995; Ekern et al., 1996; Scott & Radom, 2000). We find \ceCH2CCO to be bent at the $\beta$ carbon atom (see Fig. 1) by 150 degrees, which is close to the 140 degrees found by Scott & Radom (2000) using MP2 theory.

Thus, while both \ceCH2CCO and HCCCHO can be formed by hydrogenation of \ceHC3O, they show different stabilities with respect to further hydrogenation. Here, we have further studied the hydrogen addition reactions to all atoms of both propynal and propadienone, as well as the hydrogen abstraction reaction

[TABLE]

An examination of the energetics of these processes, summarized in Table 1, shows that they are all exothermic. Surprisingly, though, only the reaction

[TABLE]

was found to be barrierless, with the energy along the path of H approaching \ceCH2CCO depicted in Fig. 1. By contrast, the other channels have barriers larger than 6.2 kJ mol*-1*. Thus, the formation of \ceCH2CHCO is significantly faster than all alternative channels. Our results also confirm that subsequent reaction between this radical and atomic hydrogen

[TABLE]

is likewise barrierless and results in the formation of propenal, also known as acrolein. For reaction (R6), i.e. \ceH + CH2CCO $\rightarrow$ \ceCH2CCHO, we failed to find an accurate transition state, but the calculations of the reaction path clearly indicate that the barrier is quite large.

As with propadienone, hydrogen atoms can react with propynal, HCCCHO, leading to hydrogen additions and abstractions. However, unlike the case with \ceCH2CCO, the results of our calculations show that all of these reactions involving \ceHCCCHO either have a barrier or (abstraction of the aliphatic H) are endothermic. Thus, at the low temperatures of molecular clouds, they will be significantly slower than the barrierless process destroying \ceCH2CCO. Of the six possible reactions, hydrogen abstraction leading back to \ceHC3O (R9) and hydrogen addition leading to \ceCH2CCHO (R13) have the lowest barriers, 11.7 and 11.3 kJ mol*-1*, respectively. Their rate constants are plotted in Figure 2. They are rather similar, which can be expected from the similar barriers. Overall, the rate constants of both reactions are rather low: at 100 K they are $8.5\cdot 10^{-16}$ cm3 s*-1* and $2.4\cdot 10^{-16}$ cm3 s*-1* while at 50 K, the lowest temperature for which we performed instanton calculations, they are merely $1.1\cdot 10^{-17}$ cm3 s*-1* and $3.7\cdot 10^{-18}$ cm3 s*-1*. In sum, our calculations reveal that propynal is rather stable against reaction with H atoms, unlike propadienone, which will be efficiently destroyed by atomic hydrogen on both grain surfaces and in the gas.

4 Astrochemical Implications

Atomic hydrogen is a known component of even dense molecular clouds, where it is produced mainly via the cosmic ray-driven dissociation of \ceH2 (Padovani et al., 2018). Thus produced, these atoms can adsorb onto the surface of interstellar dust grains, where their high mobilities make reactions between them and other grain species one of the dominant formation routes for complex organic molecules in the ISM (Herbst & van Dishoeck, 2009). Cosmic rays can also drive the formation of atomic hydrogen within interstellar ices via radiolytic dissociation (Shingledecker et al., 2018; Shingledecker & Herbst, 2018). Therefore, given the ubiquity of H in the gas, as well as both on and in dust-grain ice mantles, our finding that H atom addition to \ceCH2CCO (R4) is barrierless and exothermic provides a compelling explanation as to why this most stable \ceH2C3O isomer has remained undetected in sources over a wide range of physical conditions (Loomis et al., 2015; Loison et al., 2016).

Our hypothesis that reaction (R4) is indeed the long-sought process underlying the consistent non-detections of propadienone is further supported by both previous observational and experimental studies. For example, in Zhou et al. (2008) it was shown that, in a mixed CO:\ceC2H2 ice at 10 K irradiated by high-energy electrons under ultra-high vacuum, the formation of both cyclopropenone and propynal could be observed, though interestingly, no firm detection of propadienone could be made. There, atomic hydrogen was efficiently formed throughout the ice via the dissociation of acetylene, which could then quickly destroy \ceCH2CCO even at the very low temperatures at which the experiment was carried out.

Another finding suggestive of the importance of reaction (R4) was the detection by Hollis et al. (2004) of propenal (\ceCH2CHCHO) in Sgr B2(N), where \ceHCCCHO and \cec-H2C3O have been seen (Loomis et al., 2015). In the paper reporting their detection, Hollis et al. proposed the following formation route for \ceCH2CHCHO:

[TABLE]

However, as the results of our calculations show, a much more energetically favored precursor is in fact \ceCH2CCO. If reaction (R4) followed by (R14), as opposed to (R15) is the dominant formation route for \ceCH2CHCHO then, in a sense, propadienone might be hiding in plain sight as propenal, rather than missing.

More generally, our results support the claim made by Loomis et al. (2015) that molecular abundances in interstellar environments, even in hot cores like Sgr B2(N), are ultimately kinetically controlled, i.e. governed by reaction barriers rather than the thermodynamic stabilities of individual species. Moreover, as one can glean from an overview of the data in Table 1, it is often not possible to intuit the presence or size of such barriers, particularly for neutral-neutral reactions not involving two radicals. Thus, detailed quantum chemical calculations are essential astrochemical tools that can, as shown here, shed light on the underlying processes which give rise to seemingly perplexing observational results.

Finally, these data both strengthen the chemical connection between unsaturated carbon chain species like \ceHC3O and nearly saturated organic molecules, such as \ceCH2CHCHO, and suggest that other members of the HCnO ($n=3-7$) family - as well as perhaps similiar carbon-chain species like the ubiquitous cyanopolyynes - might likewise serve as backbones for more complex molecules (McGuire et al., 2018).

5 Conclusions and Outlook

We have carried out calculations of reactions between atomic hydrogen and \ceHC3O, \ceCH2CCO, and \ceHCCCHO. Our main findings are the following:

that \ceH + HC3O, (R1)-(R2), is both barrierless and exothermic, and leads to either propadienone (\ceCH2CCO) or propynal (\ceHCCCHO), with the orientation of the reactants being the main factor influencing which of these two products is formed, 2. 2.

that the reactivity of propynal and propadienone with H are starkly different, with only \ceH + CH2CCO -> CH2CHCO (R4) being both barrierless and exothermic, 3. 3.

that the above finding serves as a compelling explanation as to why attempts to detect propadienone have been consistently negative and, 4. 4.

that the subsequent barrierless exothermic reaction of \ceCH2CHCO with H, shown in (R14), yields propenal (\ceCH2CHCHO) which has been observed in Sgr B2(N).

These findings are in agreement with recent work by Garrod et al. (2017), who examined the formation mechanisms of both the branched (\cei-C3H7CN) and straight-chain (\cen-C3H7CN) forms of propyl cyanide in detail. As with propadienone, the more stable isomer (\cei-C3H7CN) was found to be less abundant than \cen-C3H7CN (Belloche et al., 2014). Interestingly, it was found by Garrod et al. (2017) that kinetic factors - specifically the rates of reaction with H and CN and the relative efficiencies of the addition of these radicals to either secondary or terminal carbon atoms - were essential for accurately reproducing the $i$:$n$ ratio.

Thus, though the focus of this work was on explaining the consistent non-detections of propadienone and not on disproving the already questionable MEP, our results further reinforce the central role of kinetics in understanding the behavior of interstellar isomers, even in comparatively warm environments like star forming regions. Unfortunately, this makes interpreting observed abundances more challenging since even similar species, like propynal and propadienone, can display quite different reactivities. Thus, as the variety and complexity of known interstellar molecules continues to increase, so too will the importance of detailed experiments or quantum chemical calculations in understanding the chemical basis underlying observational results.

CNS gratefully acknowledges the support of the Alexander von Humboldt Foundation. This work was financially supported by the European Union’s Horizon 2020 research and innovation program (Grant Agreement Number 646717, TUNNELCHEM).