INTERSTELLAR COMPLEX ORGANIC MOLECULES AND THE MINIMUM ENERGY PRINCIPLE

Figure 1 shows, for each type of object, the measured abundance ratios (reported in Table 1) as a function of the difference in energy of each isomer, with respect to the most stable one (namely that with the lowest energy). Despite the relative large uncertainty in the abundance ratios,³ this figure shows two striking properties: (1) the most stable isomer is the most abundant; and (2) there is a relationship between the ratio of the most stable isomer abundance with respect to other isomers of the same generic formula and the difference in energy of the two isomers: the larger the energy difference between the two isomers, the larger the abundance ratio between the most stable and less stable isomer.

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These two properties form what we call here the minimum energy principle,⁴ hereafter referred to as the MEP.

In practice, Figure 1 says that what matters mostly in the relative abundance of the isomers of the same generic formula is the relative energy, with just two exceptions in the sample of the 32 detected molecules (cf. the next section).

It is often considered that the different isomers of the same generic formula are the result of different formation and destruction routes and behave like strangers. Against this statement, the MEP suggests that the chemical formation and destruction routes only play secondary roles.

We see at least three possible reasons that would explain the data of Figure 1.

• 1.  
  The isomers of same generic formula reported in Figure 1 have all a common intermediate in their formation and destruction route and the branching ratio from this intermediate/transition state determines the relative abundances of the products.
• 2.  
  There is an equilibration process after reaching the generic formula: internal isomerization with a low activation barrier, assisted isomerization, or catalytic isomerization at the grain/ice surfaces. Such a process would require local thermodynamic equilibrium (LTE) at the time of equilibration;
• 3.  
  There is a selective depletion of one isomer compared to the other.

Most probably, it is a conjunction of these reasons that takes place, with different relative importance according the type of object.

To illustrate the point, we will consider in detail the three molecules which "best" satisfy the MEP (being those with the largest energy differences in Table 2): HOC⁺, HNC₃, and HCNO.

HOC⁺. There is little doubt that HCO⁺ is a gas phase chemistry product: in cold molecular clouds, it is mainly formed by the reaction of CO with H⁺₃, while in PDRs it is the product of reactions with C⁺ and CO⁺. Theoretical calculations (Herbst & Woon 1996) and laboratory experiments (Smith et al. 2002) have studied the isomerization of HOC⁺ into HCO⁺ by reactions with H₂ and established that it has essentially no energy barrier. The fact that the denser and warmer PDRs also have a lower HCO⁺/HOC⁺ ratio supports the idea that isomerization of the rarer isomer HOC⁺ mostly governs the HCO⁺/HOC⁺ ratio in astronomical sources. It is a case (2) example where mediation by H₂ lowers an activation barrier from ∼40 kcal mol⁻¹ to a mere ∼1 kcal mol⁻¹. Such a equilibration process could be efficient for any proton transfer.

HNC₃. It has been so far detected in two sources only, TMC-1 (Kawaguchi et al. 1992b) and IRC10216 (Gensheimer 1997). There is no consensus on the dominant formation routes of HC₃N and HNC₃: either they may both be formed by the electron recombination of the ion HC₃NH⁺, or HC₃N may be formed by the reaction C₂H₂ + CN that does not form HNC₃ (Herbst & Leung 1990). The observed ratio suggests that any difference in the formation or destruction of these two molecules is wiped off by isomerization. In that case, one has also to look for another mechanism, the two extremities of the CCCN chain being too far apart for an easy hydrogen transfer. The most likely mediator is atomic hydrogen via the hydrogen exchange reaction: HNCCC + H → H + NCCCH. It is the equivalent of HNC/NCH addition–elimination reaction that has been shown to divide the intramolecular isomerization barrier by a factor of 8 (Talbi et al. 1996). In the same way, mediation by H₂O via a cyclic hydrogen transfer on the ice (Gardebien & Sevin 2003) could be effective. It is another case (2) example, pertinent to the gas phase and surface chemistry as well.

HCNO. The isomer in Table 2 with the largest energy difference with respect to the most stable is fulminic acid (HCNO), recently discovered in a few molecular clouds by Marcelino et al. (2009). As remarked by these authors, there is not a mother molecule common to HNCO and HCNO and, in principle, they may be formed either in the gas phase or on the grain surfaces. It is certainly worth noticing that in molecular clouds the HNCO/HCNO ratio is smaller than in the hot cores (where only an upper limit exists). This is also often the case for the other isomers of Table 2, and is consistent with the idea that isomerization takes place and that it is more efficient in warmer and denser environments. More observations are necessary to firmly draw a conclusion, but the available data seem to suggest that the relative abundance of HNCO and HCNO is rather determined by their energy difference than the history of their formation, a point of view substantiated by the shape of the potential energy surface (Mebel et al. 1996).

In summary, even if the three pairs of isomers with the largest energy difference possess different formation and destruction routes, the fact that, at the end, the three pairs with the largest energy difference have also the largest abundance ratios is in favor of the idea that isomerization (at some time in the history of these species) is the most important process in determining their relative abundances.

The plot of Figure 1 shows two exceptions to the MEP where the most stable isomer is not the most abundant.

The first molecule is the CH₂=C=CHCN, which has been measured to be more abundant than the most stable isomer of the same generic formula, the CH₃–CC–CN. The observations have been obtained toward the TMC-1 molecular cloud, where Lovas et al. (2006) found that CH₂=C=CHCN is about 4.5 times more abundant than CH₃–CC–CN. Note, however, that the abundance of CH₃–CC–CN is based on one transition only. These authors privilege the thesis that the larger abundance of CH₂=C=CHCN with respect to CH₃–CC–CN is due to the formation route of these molecules. Considering the counter-examples offered by Figure 1, this is not a satisfying enough explanation to us. Something else must be different in these molecules with respect to the other molecules which follow the MEP, should this anomaly be confirmed by other observations.

The other two exceptions to the MEP are both isomers of the generic formula C₂H₄O₂ and refer to the case of acetic acid (CH₃COOH), methyl formate (HCOOCH₃), and glycoaldehyde (CH₂OHCHO). Based on our computations, acetic acid is the most stable isomer. However, in all astronomical sources where it was searched for, acetic acid is at least 10 times less abundant than methyl formate and has about the same abundance as glycoaldehyde. While the latter measurement is subject to a relatively large uncertainty because it refers to one source only and with a relatively large error bar, the fact that methyl formate is at least 10 times more abundant than acetic acid is a robust observational fact, observed in several hot cores and corinos. In fact, the anomaly of these two isomer pairs seems to be the relatively large abundance of methyl formate: if it were 10 to 50 times lower than that observed both acetic acid and glycoaldehyde would fall in the curve of Figure 1 and would respect the MEP. What could then make methyl formate different? Horn et al. (2004) examined the formation routes for methyl formate and could not find any efficient way to form it in the gas phase. They concluded that it is likely formed on the grain surfaces. In this case, we propose that this exception could be the result of a stronger adsorption of CH₃COOH on the grains due to the presence of an acid hydrogen in the COOH group that has no equivalent in methyl formate (M. Lattelais et al. 2009, in preparation). If one considers that these species are coming from independent chemical routes, another possible explanation would be the presence of a high energetical barrier making the isomerization process itself quite impossible. In this case indeed, such a process requires the concerted breaking of two chemical bonds that is very energy demanding and most unlikely.