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A Theoretical Investigation of the Reaction Between Glycolaldehyde and H+ and Implications for the Organic Chemistry of Star Forming Regions

The characterization of one of the possible pathways in the reaction between H+ and glycolaldehyde (the channel leading to COH + CH3OH+) has been carried out by performing electronic structure calculations of the stationary points along the minimum energy path. We have employed different theoretical methods verifying that, while geometry optimizations can be performed with a relatively low level of theory, quantitative results for the energies require higher level calculations. The same methodology will be applied to the complete scheme of the title reaction as well as similar processes which are needed to characterize the destruction routes of interstellar complex organic molecules.


Introduction
Interstellar medium (ISM) is the non-condensed matter in between stars and their planetary system objects in our Galaxy. It is composed of gas (with the main component being hydrogen) and dust distributed in an inhomogeneous way. On average the number density is extremely low (as low as *0.1 particles per cm 3 in the diffuse warm and ionized regions), but there are regions where baryonic matter becomes denser, the so-called molecular clouds (*10 4 particles per cm 3 ). In some of those regions, new solar systems are formed [1]. The observation of organic molecules of some complexity (hereafter iCOMs for interstellar complex organic molecules) in star-forming regions (for a recent survey see [2]) has aroused plenty of interest, since those organic molecules can be the legacy of interstellar chemistry to newly formed planets, thus seeding them with relatively complex organic molecules that behave as the building blocks of life [1,[3][4][5][6][7]. Among the most interesting iCOMS, glycolaldehyde (HCOCH 2 OH) is the smallest molecule containing both a hydroxyl group and a carbonyl group, thus resembling a sugar. The formation of glycolaldehyde is an intermediate step towards sugars in the formose reaction and, therefore, it is believed to have a strong prebiotic potential. Its detection in high mass and low mass star forming regions [8][9][10][11][12] has posed the question of how a molecule with this degree of complexity can be formed in the harsh conditions of the interstellar medium. Various formation mechanisms have been envisaged involving either gas-phase chemistry or reactions occurring on the icy mantles of interstellar dust grains [13][14][15][16][17]. In particular, the sequence of two neutralneutral reactions seems to be very promising since it is able to reproduce the relative abundance of ethanol (the "mother" molecule) and glycolaldehyde in low mass [13] and high mass [12] star forming regions.
In both cases, whether released in the gas phase from the sublimating icy mantles of the interstellar dust grains or formed directly in the gas phase, to build up realistic astrochemical models and account for the observed abundances it is necessary to characterize the destruction routes of each species in the gas phase. Unfortunately, there are no data available in the literature concerning the possible destruction routes of glycolaldehyde. In the conditions of the ISM, most molecules are consumed by their reactions with energetic ions, such as HCO + , H 3 + , He + and H + (see for instance [18]), which are abundant in the ISM. While in the case of the reactions with the ions HCO + and H 3 + the most probable outcome is a proton transfer mechanism and in the case of He + only a charge transfer mechanism is possible, the collisions of interstellar molecules with H + can occur either by charge transfer (in this case the molecule is ionized and can also undergo dissociative ionization) or by a real chemical reaction, in which H + adds to the molecule and a reaction pathway starts.
Given the paucity of information on the processes following the interaction of iCOMs with H + , in our laboratory we have decided to start a systematic investigation of these processes by resorting to electronic structure calculations of the stationary points along the relevant potential energy surfaces (PESs) and kinetics estimates. In this contribution, we present the first results concerning the reactive pathway Different theoretical methods have been tested and compared to assess their performance and select the best method for our planned systematic investigation of iCOMs reactions.

Computational Details
The characterization of the PES for the reaction (3) has been performed by locating the lowest stationary points with different computational strategies listed in Table 1.
Glycolaldehyde is characterized by four possible conformers, among which the ciscis structure is the most stable one because of an intramolecular hydrogen bond. Therefore, we have performed our calculations starting from the cis-cis conformer (see Fig. 2). As an example, the structures of this conformer of glycolaldehyde as obtained with the different methods are reported in Fig. 1. A few other stationary points have been also characterized using the methods listed in Table 1.
Subsequently, the geometries of all the stationary points, including reactants and products, have been optimized only at the B3LYP level of theory [19,20], in conjunction with the correlation consistent aug-cc-pVTZ basis set [21][22][23]. Harmonic vibrational frequencies have been computed at the same level of theory, in order to define the nature of the identified stationary points, i.e., minimum if all the frequencies are real, saddle point if there is one and only one imaginary frequency. The identified saddle point has been assigned through Intrinsic Reaction Coordinates (IRC) calculations [24,25]. The zero-point-energy correction (computed using the scaled harmonic vibrational frequencies) has been added in order to correct the energies at 0 K. All calculations have been repeated (to assess the accuracy of the obtained data) with the double hybrid B2PLYP functional in addition to the contribution of the semiempirical dispersion considered in the D3BJ model (B2PLYPD3) [26,27], with the same aug-cc-pVTZ basis set. In the end, coupled-cluster single and double excitations augmented by a perturbative treatment of the triple excitations (CCSD(T)) [28][29][30] calculations have been performed with the same basis set and the B2PLYPD3/aug-cc-pVTZ optimized geometries, following a computational scheme which has been used in previous cases [31][32][33][34][35][36][37][38]. In addition, computational work has been carried out in order to establish which combination of method and basis set would be the most suitable one for the analyzed reaction. All calculations have been performed using Gaussian 09 [39] while the analysis of the vibrational frequencies has been done using Avogadro [40,41]. Table 1. List of combinations method/basis set used.

Results and Discussion
The complete potential energy surface obtained for the reaction (3) is reported in Fig. 2, with the geometries optimized at the B3LYP/aug-cc-pVTZ level of theory. In particular, in the figure the energies have been reported at the B3LYP/aug-cc-pVTZ (in red), B2PLYPD3/aug-cc-pVTZ (in black) and CCSD(T)/aug-cc-pVTZ (in black, in parentheses) levels of theory. In order to have an analysis of the minimum energy path, the more accurate CCSD(T) energies are considered.
There are two possible attack sites for the incoming free proton. In the initial approach analyzed in this work, the reaction starts with a barrierless addition of the proton to the oxygen of the carbonyl group of the molecule, leading to the formation of MIN1, in which a new O-H bond is formed at a distance of 0.977 Å, while the value of the C-O bond length goes from 1.206 Å to 1.261 Å, indicating a double-to-single bond variation. The energy of the stationary point, with respect to the reactant energy asymptote, taken as a reference, is −826.6 kJ/mol. The alternative additional initial approach can feature, instead, the addition of H + on the oxygen of the hydroxyl group (the investigation of this pathway is currently under way). Starting from MIN1, it is possible to obtain the second minimum in the PES, named MIN2. In this case the C-C bond is broken and two fragments are formed: HCOH and CH 2 OH. In this structure, the hydrogen atom linked to the carbon in the HCOH fragment strongly interacts with the carbon atom in the CH 2 OH fragment at a distance of 1.351 Å and the total charge is distributed over the complex. The relative energy of MIN2, with respect to the reactant energy asymptote, is −503.9 kJ/mol. The transition from MIN1 to MIN2 is possible through the overcoming of a barrier of 433.7 kJ/mol. The related transition state, TS1, clearly shows the breaking of the C-C bond. The distance between the two C atoms, indeed, is increased up to 2.146 Å. The analysis of the vibrational frequencies for TS1 allows us to notice the interaction of the H in the HCOH fragment with the carbon atom in the CH 2 OH moiety. The distance between the two mentioned atoms is 1.924 Å. Once formed, MIN2 directly leads to the formation of the two products (HCO and CH 3 OH + ), located at 211.2 kJ/mol below the reactant energy asymptote. No transition states have been found for this process. In general, it is possible to notice that all the identified stationary points lie below the reactant energy asymptote, so the reaction is globally exothermic and can take place in the harsh conditions of the interstellar medium.
The analysis of the stationary points in the PES has been performed at different levels of theory; in Figs. 3, 4 are reported the values of the bond lengths (in Å) resulting from the geometry optimized at B3LYP/aug-cc-pVTZ (in red) and B2PLYPD3/aug-cc-pVTZ (in black) level of theory. As can be seen from the reported data, there are no particular differences in the bond lengths evaluated with the two different computational strategies. The only appreciable difference is shown in the C-H interaction in TS1, in which the chemical bond is not completely formed. In this case the B2PLYPD3/aug-cc-pVTZ combination provides a length which is 0.031 Å lower than the one resulting from the B3LYP/aug-cc-pVTZ calculation. A different behavior can be seen from the analysis of the energies. In Tables 2, 3, 4 are reported the enthalpy changes and barrier heights at 0 K, computed at the three previously mentioned levels of theory.
Since the geometries of the different stationary points are very similar, it is possible to conclude that the differences in energies are related to the differences in the two methods. In particular the B2PLYPD3 functional, in addition to the D3BJ dispersion, includes a contribution related to second order perturbation theory, which can be considered the origin of the noticed differences. The same conclusion can be reached considering the results coming from the use of different methods and basis sets. As can be seen in the results shown in Fig. 1, in the case of glycolaldehyde there are no particular differences in the values of the bond lengths evaluated at different levels of theory. The results are, instead, more varied for the MIN2 and TS1 structures. The main differences can be noticed when the B3LYP functional is used in conjunction with the STO-3G basis set. From a comparison with the cases in which the same functional is used together with other different basis sets, it can be concluded that the differences in the bond lengths derive mainly from the use of the STO-3G basis set, which is less accurate since it is a minimum basis set. From an energetic point of view, it can be noticed that the combination that most differs from the reference (which in this case is the CCSD(T) energy calculation) is once again due to the use of the STO-3G basis set. The values of the energy obtained at different levels of theory are shown in Table 5. In some cases, the results obtained at the B3LYP level of theory seem to be closer to the CCSD(T) values (which is considered the best approach) than the ones obtained at the B2PLYPD3 level. However, the B2PLYPD3/aug-cc-pVTZ approach tends to give a more accurate estimate for the barrier heights, a crucial aspect when it comes to deriving rate coefficients and product branching ratios (Figs. 5 and 6).

Conclusion
In this work, different ab initio methods have been employed for the study of the reaction between H + and glycolaldehyde with the addition site on the oxygen of the carbonyl group and with the formation of COH and CH 3 OH + . The aim was to define the best compromise between chemical accuracy and computational costs. The best approach will be later employed in our systematic investigation of this and similar reactions. From the data analyzed we can conclude that relatively low-level calculations, such as B3LYP/aug-cc-pVTZ, can be used for geometry optimization and harmonic vibrational frequencies calculations. However, the energy must be evaluated at a higher level of theory, e.g. CCSD(T), in order to obtain more accurate values and construct a realistic potential energy surface. This conclusion is in agreement with previous work.
The reaction channel investigated in this contribution is only part of the PES of the glycolaldehyde-H + system. The global PES is expected to be much more complex with other possible exit channels (namely, those leading to the products HCOH + + H 2 COH, HCOH + H 2 COH + , H 2 + HCOHCHO + , H 2 O + CH 2 COH + , H 2 + OCCH 2 OH + , H 3 O + + OCCH 2 and H 2 O + CH 3 CO + ). Another complication is due to the presence of a second site for H + addition. Having verified that a combined B3LYP/aug-cc-pVTZ and CCSD(T) approach is a viable method to characterize the PES of this system, further investigations complemented by kinetics calculations are needed. We aim to complete those calculations to provide reliable estimates of the rate coefficients to be employed in astrochemical models.