INVESTIGATING THE MINIMUM ENERGY PRINCIPLE IN SEARCHES FOR NEW MOLECULAR SPECIES—THE CASE OF H₂C₃O ISOMERS

A long-standing goal of astrochemistry is to understand the physical and chemical evolution of interstellar sources through molecular observations. The formation and destruction of complex organic molecules are affected by the source conditions; observed molecular abundance ratios preserve information about the physical evolution of the region, acting as a chemical fingerprint. Extracting this information has proven to be exceedingly difficult, however, for even the simplest sources. Due to complex source structure, incomplete molecular inventories of sources, vast networks of molecular interactions, and only a partial understanding of interstellar chemical formation pathways, it is challenging to create models sufficiently accurate to predict observations (Quan & Herbst 2007).

Numerous efforts have sought to address these issues by establishing complete molecular inventories for molecule-rich sources and characterizing basic conditions and abundances (e.g., Neill et al. 2014; Crockett et al. 2014), and creating complete reaction networks with accurate reaction dynamics (e.g., Garrod et al. 2008; Garrod 2013). Still, the low densities, low temperatures, and long timescales of molecular processes in the interstellar medium (ISM) present a significant challenge to relating laboratory reaction dynamics and mechanisms to those occurring in the ISM (Laas et al. 2013). Whether the reactions governing the formation of complex molecules are primarily under kinetic or thermodynamic control is of particular interest, as this significantly affects molecular abundance ratios and the formation of prebiotically relevant molecules (Garrod et al. 2008; Lovas et al. 2010).

Observations of molecular isomers provide a unique tool for directly probing hypotheses about reaction mechanisms in the ISM, as their formation and destruction routes directly influence their abundance ratios (Hollis et al. 2006). While this is true for all molecules, isomers are particularly useful as they present a similar level of chemical complexity, and have the same constituent atoms, simplifying the problem tremendously. This approach has historically proven to be fruitful; hypotheses of the formation chemistry of HCN led to the detection of its isomer, HNC (Snyder & Buhl 1971), and comparisons between the abundances and distributions of conformational isomers of methyl formate, ethanol, and vinyl alcohol have yielded important information about their formation pathways (Neill et al. 2012; Pearson et al. 1997; Turner & Apponi 2001). Thus, understanding the root causes of molecular abundance ratios and accurately predicting which isomers are most likely to be observed is a highly desirable goal. Comparing abundance ratios with the conversion barriers and zero-point energy differences between the different isomers can elucidate whether a thermal process or a kinetically controlled formation mechanism is primarily responsible in determining the ratio.

Recently, (Lattelais et al. 2009, 2010, 2011) investigated the relative abundances of 32 detected molecular isomers and suggested that there exists a "minimum energy principle" (MEP), generally applicable across a number of astronomical environments. According to this principle, the isomer with the lowest zero-point bonding energy (i.e., the most energetically stable isomer) should be the most abundant, and thus most easily detected. Lattelais et al. (2009) include a wide variety of sources in this analysis, including molecular clouds, hot cores/corinos, photodissociation regions, and asymptotic giant branch stars, and do not note any differences in trends between these sources. Importantly, they make no mention of attempting to exclude sources where LTE assumptions would be unlikely to hold, and instead assert that LTE effects may be general across all sources used in their analysis. C₄H₃N and C₂H₄O₂ are noted as exceptions to the principle, but are dismissed by calling the abundance measurements of the former into question and proposing differential adsorption rates onto grains for the latter (Lattelais et al. 2009, 2010). However, studies of other common isomers (e.g., HCN/HNC) have shown that abundances and emission strength are dependent on the local environment, suggesting that there must be more to the picture than bonding energy ratios (see, e.g., Sarrasin et al. 2010, and references therein). We therefore assert that the chemical formation route and physical conditions of these species, especially complex organics, are more significant in establishing relative abundance ratios than the zero-point bonding energies, and thus the MEP is not generally applicable as proposed by Lattelais et al. (2009, 2010, 2011).

Toward this end, we have fully characterized the spectra of the three isomers of C₃H₂O toward the well-studied molecular region Sgr B2(N). The relative bonding energies of these isomers are shown in Figure 1. Based on these bonding energies and with no other prior knowledge, the MEP would predict the most stable isomer, propadienone (CH₂CCO), to be observed as the most abundant of the three isomers (Karton & Talbi 2014). However, propadienone has never been detected toward an astronomical source, while both propynal and cyclopropenone have been detected in molecular clouds (Irvine et al. 1988; Hollis et al. 2006). We present evidence for the detection of the two higher energy isomers cyclopropenone (c-C₃H₂O) and propynal (HCCCHO), along with evidence of the non-detection of propadienone toward Sgr B2(N). We interpret this to show that chemical formation pathways, which may be under kinetic control, have a more pronounced effect on final isomer abundances than thermodynamic effects such as the MEP.

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Sgr B2(N) is one of the preeminent sources for complex molecule detections, and the majority of all molecules used in the analysis of Lattelais et al. (2009) have been detected there, thus it serves as a reasonable source to test the predictions of the MEP. Sgr B2(N) has a heterogeneous temperature and density structure, with both a hot-core and a colder, less dense envelope, yielding multiple velocity components and a complex chemistry (Belloche et al. 2013). For a full discussion of the effect of this structure on molecular inventories of the respective regions, see Neill et al. (2014). Significantly, many of the large complex organic molecules observed toward Sgr B2(N) (including some traditionally considered to be hot-core molecules) have been seen to have sub-thermal emission, with significant non-LTE effects (Neill et al. 2012; Loomis et al. 2013; Zaleski et al. 2013, and references therein). These molecules have very low rotational temperatures, suggesting that they are extended and belong to the envelope, but the non-LTE effects make determinations of column density and temperature extremely difficult without collisional cross-sections (Faure et al. 2014). As all three of the molecules searched for in this study would be expected to originate in colder environments, these non-LTE effects are likely very relevant, and are discussed in Section 4.1.

All known strong (predicted to be above the measured noise limit at a characteristic excitation temperature of 10–50 K) rotational transitions of cyclopropenone, propynal, and propadienone between 4 GHz and 50 GHz were searched for in publicly available data from the PRIMOS survey of Sgr B2(N), a NRAO key project on the Robert C. Byrd Green Bank Telescope (GBT) from 2008 January through 2011 July.¹² An LSR source velocity of +64 km s⁻¹ was assumed, and antenna temperatures were recorded on the $T_A^*$ scale (Ulich & Haas 1976) with estimated 20% uncertainties. Data were taken in position-switching mode, with 2 minute scans toward the on position (αJ2000 = 17^h47^m198, δJ2000 = −28°22'170) and toward the off position, 1° east in azimuth. Additional details of PRIMOS survey observations can be found in Neill et al. (2012). Rest frequencies for all transitions were obtained from the Splatalogue database.^13,14

3.1. Cyclopropenone

Nine low-energy, high line-strength transitions of cyclopropenone were identified in absorption in PRIMOS data. Of these, six had been previously identified by Hollis et al. (2006) at lower sensitivity and spectral resolution (see Table 1). All observed transitions were a-type (μ_a = 4.39(06) D) (Benson et al. 1973), with six R-branch transitions (ΔJ = −1) and three Q-branch (ΔJ = 0). Three higher energy (J > 4) Q-branch transitions were not observed. This encompasses all strong transitions within the PRIMOS frequency coverage, with the exception of the 2₁₂–1₁₁ transition where observational data were not available.

Table 1. Observed Transitions of Cyclopropenone

Transition	Frequencya,b	Eu	Sijμ2	64 km s−1		82 km s−1
J$^{\prime }_{kk}$–J$^{\prime \prime }_{kk}$	(MHz)	(K)	(D2)	Δ$T_{A}^{*}$c (mK)	ΔV c (km s−1)	Δ$T_{A}^{*}$c (mK)	ΔV c (km s−1)
211–212	4632.79	3.34	48.19	−57.2(5.4)	14.8(0.9)	−32.1(4.6)	15.1(1.2)
312–313d	9263.49	5.48	33.76	−29.1(6.1)	15.9(0.5)	−10.0(0.9)	12.4(1.1)
413–414d	15427.90	8.33	26.12	−12.1(0.6)	11.6(0.6)	−5.4(0.7)	12.0(0.8)
514–515	23105.58	11.88	21.41	<5.0	...	<5.0	...
615–616	32255.63	16.14	18.27	<10.7	...	<10.7	...
716–717	42808.10	21.08	16.10	<7.3	...	<7.3	...
101–000d	14105.74	0.68	19.27	−6.7(0.7)	7.2(0.9)	<2.2	...
212–111	26667.02	3.12	86.73	...	...	...	...
202–101	28139.89	2.03	38.52	−133.6(4.2)	8.6(0.3)	−48.9(4.5)	6.4(0.5)
211–110	29755.51	3.34	86.73	−83.2(8.8)	8.2(0.5)	−22.9(7.3)	14.2(2.4)
313–212d	39956.70	5.04	154.15	−66.5(3.1)	6.0(0.3)	−32.9(3.0)	5.9(0.6)
303–202d	42031.94	4.04	57.71	−74.5(1.9)	15.3(0.4)	−40.3(2.2)	9.4(0.5)
312–211d	44587.40	5.48	154.1	−46.9(2.1)	11.7(0.6)	−34.4(1.8)	12.5(0.9)

Notes. ^aBeam sizes, efficiencies, and continuum temperatures for each respective frequency can be found in Hollis et al. (2007). ^bRest frequencies are all taken from Splatalogue; see Section 2 for complete references. ^cThe uncertainties for the intensities and line widths are type B, k = 1 (1σ) (Taylor & Kuyatt 1994). ^dPreviously detected with the GBT with lower sensitivity and spectral resolution (Hollis et al. 2006).

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All detected transitions were observed at a nominal rest velocity of v_LSR = +64 km s⁻¹, with a second, weaker, v_LSR = +82 km s⁻¹ component observed for all transitions other than 1₀₁–0₀₀; consistent with other molecular detections with the GBT toward Sgr B2(N) (see, e.g., Hollis et al. 2004a; Remijan et al. 2008, and references therein). Observations of all Q- and R-branch transition rest frequencies within the PRIMOS coverage are presented in Figures 2 and 3, respectively.

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As seen in Figure 3, the 2₁₁–1₁₀ transition is blended with a hydrogen recombination line (H(94)δ) at 29575.189 MHz. Additionally, the v_LSR = +64 km s⁻¹ component of the 3₁₃–2₁₂ transition is partially blended with the 2₀₂–1₀₁, v = 1 transition of NH₂CN in emission. Best-fit Gaussian line widths and peak intensities, or respective upper limits, are reported in Table 1. The 2₁₁–1₁₀ transition was simultaneously fit in absorption against a modeled Gaussian emission profile for the H(94)δ recombination line.

3.2. Propynal

Six uncontaminated, low-energy, high line-strength transitions of propynal were identified in absorption. One of these had been previously been detected by Hollis et al. (2004b) with lower sensitivity and spectral resolution (see Table 2). Three of the identified transitions were k_a = 0 a-type (μ_a = 2.359(18) D), and three were b-type (μ_b = 1.48(22) D) (Brown & Godfrey 1984). Of the remaining twelve low-energy, high line-strength transitions predicted to be possibly observable, six were not observed above the noise level, five were contaminated by blends with other molecule emission features (see Figure 4), and frequency coverage was not available for one transition. Notably, although multiple k_a = 0 a-type transitions were observed with strong absorption, no k_a = 1 a-type transitions were detected.

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Table 2. Observed Transitions of Propynal

Transition	Frequencya,b	Eu	Sijμ2	64 km s−1		82 km s−1
$J^{\prime }_{kk}$–$J^{\prime \prime }_{kk}$	(MHz)	(K)	(D2)	Δ$T_{A}^{*}$c (mK)	ΔV c (km s−1)	Δ$T_{A}^{*}$c (mK)	ΔV c (km s−1)
515–606	5044.66	9.64	5.58	−36.4(2.2)	20.3(1.8)d	−26.1(2.3)	20.3(1.8)d
414–505e	15146.04	7.44	4.43	−20.3(1.2)	9.9(0.6)	−14.5(1.3)	10.3(0.9)
313–404	25100.65	5.68	3.30	−20.4(1.5)	10.1(0.8)	−16.6(1.6)	8.3(0.9)
212–303	34903.64	4.36	2.18	<8.7	...	<8.7	...
111–202	44550.03	3.48	1.09	<8.6	...	<8.6	...
101–000	9325.81	0.45	5.56	<3.8	...	<3.8	...
212–111	18325.56	4.36	8.35	Blend	...	Blend	...
202–101	18650.31	1.34	11.13	−16.8(1.6)	7.2(0.7)	−14.1(1.5)	4.9(0.6)
211–110	18978.79	4.41	8.35	<3.6	...	<3.6	...
313–212	27487.45	5.68	14.84	Blend	...	<8.3	...
303–202	27972.13	2.68	16.69	Blend	...	Blend	...
312–211	28467.15	5.77	14.84	...	...	...	...
414–313	36648.20	7.44	20.87	<11.2	...	<11.2	...
404–303	37290.10	4.47	22.26	−52.7(-4.1)	5.8(0.5)	<16.4	...
413–312	37954.95	7.60	20.87	Blend	...	Blend	...
515–414	45807.70	9.64	26.71	<9.5	...	<9.5	...
505–404	46602.80	6.71	27.82	−28.8(2.1)	5.6(0.3)	−23.4(1.7)	4.0(0.4)
514–413	47440.40	9.87	26.71	Blend	...	<9.2	...

Notes. ^aBeam sizes, efficiencies, and continuum temperatures for each respective frequency can be found in Hollis et al. (2007). ^bRest frequencies are all taken from Splatalogue; see Section 2 for complete references. ^cThe uncertainties for the intensities and line widths are Type B, k = 1 (1σ) (Taylor & Kuyatt 1994). ^dDue to blended velocity components, line widths were shared during fitting. ^ePreviously detected with the GBT with lower sensitivity and spectral resolution (Hollis et al. 2004b).

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Irvine et al. (1988) suggested that the k_a = 1 transitions of propynal may be weaker than predicted by a thermal model due to b-type transitions transferring k_a = 1 population into the k_a = 0 state; this behavior has also been observed in HNCO (Hocking et al. 1974). Irvine et al. used a collisional model to predict corrected k_a = 1 intensities for their detection in TMC-1, and determined an approximate intensity in agreement with their tentative 2σ–3σ detection of the 2₁₁–1₁₀ transition using the NRAO 140 ft. If this model is correct, a rough scaling to our observations would explain the lack of k_a = 1 detections, with all predicted intensities below the observed noise level.

All detected transitions were observed at a nominal rest velocity of v_LSR = +64 km s⁻¹, with an additional, weaker, v_LSR = +82 km s⁻¹ component observed for all transitions other than 4₀₄–3₀₃, where the noise level is comparable to the expected intensity of the v_LSR = +82 km s⁻¹ component. Observations of all a-type and b-type transition rest frequencies within PRIMOS coverage are presented in Figures 4 and 5, respectively. Best-fit Gaussian line widths and peak intensities, or respective upper limits, are reported in Table 2. All features were observed with line widths of ∼4–10 km s⁻¹ with the exception of the 5₁₅–6₀₆ transition, where the velocity components were blended due to low signal-to-noise ratio and line widths were therefore fixed together during fitting, possibly artificially broadening the fit width.

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3.3. Propadienone

No transitions of propadienone were identified in PRIMOS data. Of the known transitions between 4 GHz and 50 GHz, only a-type transitions (μ_a = 2.156 D, μ_b = 0.7914 D) (Brown et al. 1981) are predicted to be strong enough to be observed in PRIMOS data. It is important to note that the slight bend of the C₃O chain in propadienone causes a small barrier, creating two tunneling states separated by a small (0.1198 cm⁻¹) energy difference. a-type transitions occur within each substate while b-type transitions occur between the two tunneling states (Brown et al. 1987). b-type transitions within PRIMOS frequency coverage are predicted to be significantly weaker due to a lower dipole moment and high upper state energies. Observations of all a-type transition rest frequencies within the PRIMOS coverage are presented in Figure 6 and upper limits on all a-type transition intensities are given in Table 3.

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Table 3. Observed Transitions of Propadienone

Transition	Frequencya,b	Eu	Sijμ2	64 km s−1		82 km s−1
$J^{\prime }_{kk}$–$J^{\prime \prime }_{kk}$	(MHz)	(K)	(D2)	Δ$T_{A}^{*}$ (mK)	ΔV (km s−1)	Δ$T_{A}^{*}$ (mK)	ΔV (km s−1)
101–000	8645.16	0.41	4.65	<3.4	...	<3.4	...
212–111	17164.49	8.39	20.92	No data	...	No data	...
202–101	17290.18	1.24	9.30	No data	...	No data	...
211–110	17422.33	8.41	20.92	No data	...	No data	...
313–212	25746.59	9.63	37.19	<3.4	...	<3.4	...
303–202	25934.97	2.49	13.95	<3.6	...	<3.6	...
312–211	26133.34	9.66	37.19	<5.4	...	<5.4	...
414–313	34328.55	11.27	52.29	<3.3	...	<3.3	...
404–303	34579.38	4.15	18.60	<8.0	...	<8.0	...
413–312	34844.16	11.34	52.29	<9.2	...	<9.2	...
515–414	42910.28	13.33	66.93	<6.9	...	<6.9	...
505–404	43223.30	6.22	23.24	<8.6	...	<8.6	...
514–413	43554.72	13.43	66.94	<7.6	...	<7.6	...

Notes. ^aBeam sizes, efficiencies, and continuum temperatures for each respective frequency can be found in Hollis et al. (2007). ^bRest frequencies are all taken from Splatalogue; see Section 2 for complete references.

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Although our observational results support a detection of cyclopropenone and propynal and a non-detection of propadienone, it is important to additionally examine their abundance ratios. It may be possible for a given isomer to be more abundant, yet not detected, due to inherent line strengths or excitation issues. Using the formulation in Hollis et al. (2004a), and assuming a temperature of 15 K, similar to other cold large organics detected with the PRIMOS survey, we calculate column densities of ∼10¹² cm⁻² for cyclopropenone, ∼10¹³ cm⁻² for propynal, and an upper limit of <10¹¹ cm⁻² for propadienone. Thus, if propadienone was actually equal in abundance to cyclopropenone or propynal, we would expect to see features 10–100 times the noise level, yet no such features are observed. These calculations assume continuum temperatures for Sgr B2(N) from Hollis et al. (2007), as well as LTE conditions. We wish to stress that our observations are not fit particularly well with these assumptions, suggesting that a large number of the observed lines are sub-thermally excited. If these features arise from non-LTE conditions, this may call into question our derived column densities, but would also invalidate the assumptions necessary for the MEP, strengthening our assertion that thermodynamically driven processes do not control the bulk of interstellar abundance ratios.

These results answer calls for further observational tests of the MEP from theoretical studies investigating the relative energies of multiple isomer families (Lovas et al. 2010; Karton & Talbi 2014). In particular, Karton & Talbi (2014) explicitly note that within the C₃H₂O isomer family, propadienone should be detected based on the predictions of the MEP and suggest further observational searches for the molecule. Its non-detection now leaves us with the question as to which synthesis routes result in the formation of cyclopropenone and propynal but not propadienone.

4.1. Formation Chemistry on Grain Surfaces

In the ISM, dust grains serve as catalysts for much of the rich organic chemistry that is observed (Herbst & van Dishoeck 2009). Zhou et al. (2008) studied the non-equilibrium grain-ice chemistry in cold (∼10 K) regions of the ISM, finding that cyclopropenone is formed on grain surfaces via reactions between triplet CO and C₂H₂, i.e.,

$$\begin{equation} \mathrm{CO} + \mathrm{C_2H_2} \rightarrow \mathrm{c-C_3H_2O}, \end{equation} \tag{ 1 }$$

and that propynal is formed in the bulk by carbon monoxide and acetylene through a radical pair reaction, i.e.,

$$\begin{equation} \mathrm{CO} + \mathrm{C_2H_2} \rightarrow [\mathrm{HCO-CCH}]^* \rightarrow \mathrm{HCCCHO}. \end{equation} \tag{ 2 }$$

Zhou et al. (2008) found that cosmic ray protons (∼10 MeV) are likely the source of energy that drives these reactions, inducing a C–H cleavage in collisions with acetylene that initiates reactions (1) and (2). Experimental results from ultra-high vacuum irradiation of ice samples showed that the two metastable isomers of C₃H₂O were produced, with only a tentative detection of propadienone. The molecules formed in this way can then enrich the gas-phase abundance through sublimation, a particularly likely scenario in star-forming regions such as Sgr B2(N).

4.2. Gas-phase Formation Chemistry

In addition to formation pathways involving grain chemistry, there are several gas-phase reactions that are thought to produce cyclopropenone and propynal, but no feasible reactions have been proposed for propadienone production (Kwon et al. 2006; Petrie 1995; Irvine et al. 1988). A study by Quan & Herbst (2007) attempted, in part, to reproduce the observed abundance of c-C₃H₂O in Sgr B2(N). Their network included the gas-phase formation pathway:

$$\begin{equation} \mathrm{C_3H^+} + \mathrm{H_2} \rightarrow \mathrm{c-C_3H_3^+} + h\nu \end{equation} \tag{ 3 }$$

$$\begin{equation} \mathrm{c-C_3H_3^+} + e^- \rightarrow \mathrm{c-C_3H_2} + \mathrm{H} \end{equation} \tag{ 4 }$$

$$\begin{equation} \mathrm{c-C_3H_2} + \mathrm{O}(^3P) \rightarrow \mathrm{c-C_3H_2O}. \end{equation} \tag{ 5 }$$

Recently, the reactant C₃H⁺ in reaction (3) was detected in Sgr B2(N), suggesting the validity of this gas-phase formation route as a possible source of C₃H₂ (McGuire et al. 2013). The abundance of the cyclic form of C₃H₂ has been estimated to be 50–150 times greater than the linear form of C₃H₂ toward Sgr B2(N) (Cernicharo et al. 1999), suggesting that it has the potential to be a parent molecule of c-C₃H₂O (Matthews & Irvine 1985). The model of Quan & Herbst (2007) was unable to reproduce the observed abundance of c-C₃H₂O in Sgr B2(N), but this is not too surprising, given that they did not include grain–surface reactions for the formation of cyclopropenone in their network.

4.3. Interpretation of This Case Study and Conclusions

R.A.L. gratefully acknowledges funding from an NSF Graduate Research Fellowship and the Virginia Space Grant Program, as well as support from the College Science Scholars program at the University of Virginia. B.A.M. gratefully acknowledges funding from an NSF Graduate Research Fellowship, and G. A. Blake for his support. We thank an anonymous referee for important comments. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.