An Ab Initio Computational Study of Binding Energies of Interstellar Complex Organic Molecules on Crystalline Water Ice Surface Models

The interstellar medium (ISM) is the region between the stars consisting of matter and energy. The ISM presents a vast range of physical conditions, with temperatures spanning from 10 K to 10⁶ K, and densities varying from 10^–4 to 10⁸ cm^–3 [1]. The interstellar matter is composed of gaseous material (such as atoms, molecules, and ions) and solid constituents (like submicron carbonaceous and silicate dust grains) [2]. In the cold (10 K) and dense (10⁴ cm^–3) environments of prestellar cores [3], also known as interstellar dark molecular clouds, volatile species such as H₂O, CO, CO₂, NH₃, CH₃OH, and CH₄ freeze-out onto the dust grain surfaces forming ice mantles, predominantly of amorphous H₂O ices and apolar CO ices [4].

As the gravitational collapse of the cold cloud proceeds, the interstellar gaseous material emits IR radiation, resulting in warm (100 K) inner envelopes around the low-mass protostar known as hot corinos, which provide viable conditions for rich grain surface chemistry, such as the formation of interstellar complex organic molecules (iCOMs), i.e., chemical compounds containing 6–13 atoms, of which at least one is C [5]. Although the complex species present in the cold regions are generally unsaturated and exotic, the warm cores in young stellar objects contain saturated (hydrogen-rich) complex organic molecules [6]. Despite being formed on the icy dust grains, as the temperature in the hot corinos reaches the mantle sublimation temperature, the species frozen in the ice mantles are released into the gas phase, where they can be detected and observed via their rotational spectra [7].

The molecules require energy to desorb from the grain surfaces. If the chemical, thermal, or radiative energy acquired by the molecule is higher than its interaction energy (i.e., binding energy, BE) with the icy surface, the species can evaporate into the gas phase. In case the acquired energy is a fraction of the BE, the molecules diffuse on the grain surface which is a critical step for chemical reactions to occur [7]. Therefore, obtaining highly accurate BE values of chemical compounds on dust grains is of utmost importance. Moreover, they are important input parameters in gas-grain astrochemical modelling for the characterization of the chemical composition and evolution of the ISM. The molecular species can interact with the icy grain surfaces by either forming chemical bonds (chemisorption), or via weaker (e.g., hydrogen bonding or dispersion) interactions (physisorption). This work focuses on the physical adsorption of iCOMs on a crystalline water ice surface model.

While techniques such as temperature programmed desorption (TPD) are used to estimate BEs experimentally, they are unable to accurately reproduce the extreme and diverse interstellar conditions in the laboratory setup. Hence, quantum chemical calculations provide a robust alternative to determine accurate BEs. This work, therefore, aims to add to the existing network of BEs those of some iCOMs recurrently found in astronomical observations, some of which, furthermore, might be regarded as potential prebiotic precursors.

In this work, the BEs of 13 closed-shell species have been calculated at various levels of theory adopting a periodic approach. Structural optimizations for the adsorption of iCOMs on the crystalline ice surface were carried out using the density functional theory (DFT), with the CRYSTAL17 program package [8]. The hybrid B3LYP functional [9‐11] was utilized, along with Grimme’s DFT-D3 correction with the Becke-Johnson damping [12, 13] for the treatment of London-dispersion interactions, and an Ahlrichs triple zeta valence (TZV) basis set with polarization functions (henceforth referred to as B3LYP-D3(BJ)/Ahlrichs-TVZ*). Due to the use of finite basis set, the basis set superposition error (BSSE) was encountered, which has been treated using the counterpoise method (CP) [14] as follows:where ΔE is the interaction energy and ΔE^CP is the BSSE-corrected interaction energy using the CP method. The calculated binding energies are defined as the inverse of ΔE^CP:In addition to the computationally costly B3LYP-D3(BJ)/Ahlrichs-TVZ* calculations, the significantly cheaper semi-empirical HF-3c treatment has also been applied for the geometry optimization of the adsorbate/ice complexes. This method uses the MINIX basis set, along with three a posteriori corrections pertaining to London dispersion interactions, BSSE, and short-range deficiencies arising due to the minimal basis set [15]. In order to further improve the HF-3c BEs, single-point energy calculations at B3LYP-D3(BJ)/Ahlrichs-TVZ* on the HF-3c optimized geometries were performed. This relatively accurate yet computationally cost-effective method (hereafter referred to as DFT//HF-3c) can be further employed to calculate BEs on more realistic (i.e., larger and amorphous) ice models, where full DFT treatment is unfeasibly costly.

In order to check the accuracy of the DFT calculated BEs, the CCSD(T) method has been employed, with the Gaussian16 software package [16], along with correlation consistent basis sets extrapolated to the complete basis set limit (CBS). Due to the exceedingly high computational cost of the CCSD(T)/CBS method, an ONIOM2-like approach has been applied, in which the molecules involved in the binding (the model zone, i.e., the iCOMs and three/four water molecules, depending on the size of the iCOM) are treated at CCSD(T), while computing at DFT for the whole system [17]. By following this ONIOM2-like scheme, the BEs are given as:

The water ice surface has been modelled using the bulk of the proton ordered crystalline structure of P-ice. A 2D-periodic slab model has been defined by cutting along the (010) surface [18‐20]. The slab has a null electric dipole moment along the non-periodic z-axis. The slab model consists of twelve atomic layers involving 24 water molecules per unit cell, with cell parameters |a| = 8.980 Å and |b| = 7.081 Å. Due to the larger size of CH₃CH₂CN, a 2 × 1 supercell was used to ensure that the intermolecular interactions with the ice slab are predominantly considered, and spurious lateral interactions between adjacent unit cells are avoided.

In this work, the BEs of 13 iCOMs (shown in Fig. 1) have been computed on the crystalline (010) water ice surface model. All the compounds are closed-shell species and, except HCOOH, comprise of 7–11 atoms. They contain different functional groups that determine their adsorption properties.

Based on likely hydrogen bond (H-bond) patterns, the iCOMs can be divided into two different categories: (i) iCOMs containing both H-bond donors and acceptors, due to the presence of hydrogen atoms chemically bonded to electronegative constituents, and (ii) iCOMs containing H-bond acceptors only, due to the presence of electronegative atoms such as O or N.

In this work, the BEs of 13 iCOMs (i.e., CH₃COOH, CH₃CH₂OH, HOCH₂CH₂OH, HCOOH, HOCH₂CHO, c-CH₂CH₂O, CH₃CHO, CH₃COCH₃, CH₃CH₂CN, CH₃COOCH₃, HCOOCH₃, CH₃NCO, and CH₃CH₂CHO) on a P-ice based crystalline (010) water ice surface model have been computed by means of periodic quantum chemical calculations. With the aim to provide accurate BEs to be used as input parameters in astrochemical models, the B3LYP-D3(BJ)/Ahlrichs-TVZ* level of theory has been employed. Additionally, a computationally cheaper DFT//HF-3c scheme has been used in order to compare its accuracy with the DFT level for further application in amorphous water ice systems. BE refinements have been carried out at CCSD(T)/CBS level of theory using the ONIOM2 methodology to compare the DFT results with the “gold-standard” accuracy provided by the coupled cluster method.

The results reveal that some iCOMs (CH₃COOH, CH₃CH₂OH, HOCH₂CH₂OH, HCOOH, and HOCH₂CHO) can act as both H-bond donors and acceptors when adsorbed on the water ice surface. The BEs of such species are significantly higher (nearly 25–30 kJ mol⁻¹) than the molecules that can only act as H-bond acceptors. This indicates that the former species are much strongly bonded to the ice surface than the latter counterparts due to larger H-bond cooperativity. On the other hand, it has been observed that dispersion accounts for a major fraction of the total BE in the case of iCOMs with H-bond acceptors only, while the dispersion contribution is lower in species with high BE values.

The comparison of BEs between those obtained at the full DFT level with those refined at CCSDT//DFT shows an excellent correlation, indicating that the B3LYP-D3(BJ) functional yields accurate energy estimation for the adsorbate/ice systems. Furthermore, DFT//HF-3c results correlate well with the full DFT treated ones, thereby indicating that the DFT//HF-3c scheme is a cost-effective level of theory to be utilized for the calculation of BEs on amorphous ice systems, which require a larger unit cell to account for the lack of long-range order and varied binding sites on the surface.