ORIGINAL RESEARCH published: 21 April 2021 doi: 10.3389/fspas.2021.659494 Formation of Interstellar Silicate Dust via Nanocluster Aggregation: Insights From Quantum Chemistry Simulations Albert Rimola 1* and Stefan T. Bromley 2,3* 1 Departament de Química, Universitat Autònoma de Barcelona, Bellaterra, Spain, 2 Departament de Química Física, Institut de Química Teòrica i Computacional (IQTC), Universitat de Barcelona, Barcelona, Spain, 3 Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain The issue of formation of dust grains in the interstellar medium is still a matter of debate. One of the most developed proposals suggests that atomic and heteromolecular seeds bind together to initiate a nucleation process leading to the formation of nanostructures resembling very small grain components. In the case of silicates, nucleated systems can result in molecular nanoclusters with diameters ≤ 2 nm. A reasonable path to further increase the size of these proto-silicate nanoclusters is by mutual aggregation. The Edited by: present work deals with modeling this proto-silicate nanocluster aggregation process Ankan Das, Indian Centre for Space Physics, India by means of quantum chemical density functional theory calculations. We simulate Reviewed by: nanocluster aggregation by progressively reducing the size of a periodic array of initially Shubhadip Chakraborty, well-separated nanoclusters. The resulting aggregation leads to a set of silicate bulk UMR6251 Institut de Physique de structures with gradually increasing density which we analyze with respect to structure, Rennes (IPR), France Natalia Inostroza, energetics and spectroscopic properties. Our results indicate that aggregation is a Autonomous University of Chile, Chile highly energetically favorable process, in which the infrared spectra of the finally formed *Correspondence: amorphous silicates match well with astronomical observations. Albert Rimola albert.rimola@uab.cat Keywords: interstellar medium, silicate grains, periodic DFT simulations, infrared spectra, nanocluster Stefan T. Bromley aggregation s.bromley@ub.edu Specialty section: INTRODUCTION This article was submitted to Astrochemistry, Interstellar matter consists of gaseous molecules and submicron solid state particles commonly a section of the journal referred to as dust grains. Ninety nine percentage of the interstellar mass belongs to the former Frontiers in Astronomy and Space group while a meager 1% to the latter one. This matter is not evenly distributed and often Sciences accumulates in condensed regions between stars, forming interstellar clouds (Tielens, 2013; van Received: 27 January 2021 Dishoeck, 2014). Despite making up only a tiny fraction of the interstellar mass, dust grains are Accepted: 16 March 2021 pivotal constituents which assist in the build-up the molecular diversity and complexity of the Published: 21 April 2021 interstellar medium (ISM) (Williams and Herbst, 2002; Hama and Watanabe, 2013). Indeed, the Citation: formation of different simple molecules [some of them of fundamental relevance such as H2 , Rimola A and Bromley ST (2021) (Kerkeni and Bromley, 2013; Vidali, 2013; Navarro-Ruiz et al., 2014a, 2015, 2016) H2 O (van Formation of Interstellar Silicate Dust via Nanocluster Aggregation: Insights Dishoeck et al., 2013; Molpeceres et al., 2019) and CH3 OH (Watanabe et al., 2003; Rimola et al., From Quantum Chemistry 2014)] as well as complex organic molecules (Öberg, 2016; Herbst, 2017; Zamirri et al., 2019b) Simulations. (e.g., CH3 CHO or NH2 CHO) (Enrique-Romero et al., 2016, 2019; Rimola et al., 2018) has been Front. Astron. Space Sci. 8:659494. postulated to exclusively occur on the surface of grains. Co-adsorption at catalytic surface sites doi: 10.3389/fspas.2021.659494 accelerate these formation reactions, which would not otherwise occur in the gas phase. Frontiers in Astronomy and Space Sciences | www.frontiersin.org 1 April 2021 | Volume 8 | Article 659494 Rimola and Bromley Silicate Nanocluster Aggregation In the ISM, dust particles can be found as bare grains fragments (Jones et al., 1996; Hirashita and Kobayashi, 2013). of refractory materials or covered in ices, depending on the There is also laboratory evidence that small silicate dust grains conditions of the interstellar clouds where they are found. may (re)form in the ISM (Rouillé et al., 2014). It is thus estimated In diffuse clouds the temperature is typically between 50– that the ISM could contain a significant population of nano-sized 100 K with gas densities in the range 10–102 cm−3 . Here, bare proto-silicates (Li and Draine, 2001b), which will eventually form grains predominate because UV photons can penetrate the part of the diffuse and dense clouds. cloud, destroying any molecular complex species. Grains consist Interestingly, proto-silicate nanoclusters have properties that of either carbonaceous materials (Ehrenfreund and Charnley, match relatively well with the physico-chemical features of very 2000; Tielens, 2008) or silicates (Henning, 2010) (i.e., refractory small grain (VSG) components (of size ≤ 20 nm) (Li and Draine, materials), depending on the C/O ratio where they nucleate, grow 2001a; Rouillé et al., 2014), the optical properties of which and form. In dense molecular clouds (with temperatures as low cannot be described by bulk material measurements. VSGs may as 5–10 K and a gas density of ∼104 cm−3 ), the low permeability be responsible for the UV bump in the IS extinction curve of UV photons into the cloud allows the formation/accretion of and a significant fraction of the mid-IR emission (Rapacioli simple volatile species, which convert into ice mantles covering et al., 2005; Pilleri et al., 2012, 2015). Although carbonaceous the refractory grains. The most predominant component of the materials (e.g., polycyclic aromatic hydrocarbons, hydrogenated interstellar ices is H2 O, but other species are also relatively amorphous carbon) have been advocated to be the main abundant, such as NH3 , CO, CO2 , and CH3 OH (Boogert et al., constituent of VSGs, there could also be a significant component 2015). formed from proto-silicate nanoclusters/nanoparticles. VSG Most bare interstellar grains are made of silicates, which proto-silicates can be understood as intermediate species from are a class of naturally occurring inorganic materials with which larger silicates (i.e., grain monomers) are formed from a large diversity in chemical composition and structural the nucleation seed. A reasonable process would involve the properties. All silicates are based on the [SiO4 ]4− building production of different proto-silicate nanoclusters driven by block with divalent cations compensating the negative charge. harsh external phenomena (e.g., cosmic ray hits or shock In interstellar grains the most common cation is Mg2+ , waves) and subsequent aggregation by intermolecular attractive followed to a lesser extent by Fe2+ , as dictated by the relative forces between nanoclusters. Interestingly, since nanoclusters are interstellar abundances. Two main classes of interstellar silicates inherently not crystalline-like (Escatllar et al., 2019; Zamirri et al., have been identified: olivines and pyroxenes, with general 2019a), direct aggregates are expected to exhibit an amorphous chemical compositions Mg2x Fe(2−2x) SiO4 and Mgx Fe(1−x) SiO3 structural state. (x = 0–1), respectively. These interstellar grain silicates are Quantum chemical computations have been used to usually structurally amorphous, although crystalline silicates investigate on the physico-chemical properties of interstellar have also been detected (Molster and Kemper, 2005). Evidence silicates (Goumans and Bromley, 2011; Kerkeni and Bromley, of amorphicity is provided by astronomical infrared (IR) 2013; Navarro-Ruiz et al., 2014a,b; Navarro-Ruiz et al., 2015, observations, where mid-IR measurements show two broad 2016; Oueslati et al., 2015; Kerkeni et al., 2017, 2019; Molpeceres bands centered at 9.7 µm (∼1,100 cm−1 ) and 18 µm (∼550 et al., 2019), demonstrating the extreme usefulness of this cm−1 ) (Henning, 2010), attributed to the ν(SiO) stretching and approach by providing unique results at an atomic scale δ(OSiO) bending modes. These bands are usually found to be related to their structure, reactivity and vibrational features. heavily broadened, which is indicative of the wide distribution In the present work, the aggregation between proto-silicate of bond lengths and angles characteristic of amorphous systems. nanoclusters to form silicate bulk aggregates is investigated We note that this assignment of broadened bands to amorphous by means of quantum chemical simulations. To this end, a silicate grains should be used with care in the case of very small modeling strategy based on the gradual reduction in size of grains (Zamirri et al., 2019a). a periodic unit cell centered on a proto-silicate nanocluster, The elementary steps leading to silicate grain formation is not thus decreasing the distance between repeated nanoclusters, is yet fully understood. The commonly held current view is that employed. The resulting increasingly condensed systems during silicate dust nucleates in outflows of dying stars, in which atomic this procedure have been analyzed from a structural, energetic and molecular seeds bind together to initiate the nucleation and spectroscopic points of view giving new insights into the process (Weinberger, 2005; Ercolano et al., 2007; Jones, 2007; plausibility of the proto-silicate aggregation processes. Matsuura et al., 2011). Some thermodynamically viable pathways for the initial stages of silicate nucleation in circumstellar environments have been studied by computational chemistry METHODS techniques, indicating that heteromolecular aggregation of Mg, SiO and H2 O could be a plausible mechanism, rather than direct Theoretical calculations were carried out with the CRYSTAL14 nucleation of atomic O, Mg and Si (Goumans and Bromley, code (Dovesi et al., 2014); a program dedicated to simulating 2012, 2013). The silicate dust grains formed in such processes all-electron periodic and molecular systems. Simulations were are thought to be of the order 0.1 µm in diameter (dust grain performed with density functional theory (DFT) calculations monomers) when they leave the star and enter the ISM. There, using the hybrid B3LYP functional (Lee et al., 1988; Becke, these grains are subject to supernovae shockwaves and dust 1993) in combination with the following Gaussian basis grain collisions which shatter these grains into small nanosized sets: (8s)-(511sp)-(1d) for Mg, (8s)-(6311sp)-(1d) for Si, Frontiers in Astronomy and Space Sciences | www.frontiersin.org 2 April 2021 | Volume 8 | Article 659494 Rimola and Bromley Silicate Nanocluster Aggregation and (8s)-(411sp)-(1d) for O. A reliable performance of this methodology for simulating the structure and spectroscopic properties of silicates is evidenced by different theoretical works, where results of DFT calculations using the B3LYP functional are found to compare very well with experimental measurements related to IR, Raman and reflectance spectroscopy (Noel et al., 2006; De La Pierre et al., 2011, 2013; Navarro-Ruiz et al., 2014b; Martínez-González et al., 2018). The shrinking factor of the reciprocal space net was set to 3, defining a total of 14 k points in the irreducible Brillouin zone (IBZ) (Monkhorst and Pack, 1976). The overlap integrals controlling the Coulomb and exchange series were set to 10−6 and 10−16 . The SCF criterion was set to 10−7 Hartrees. Geometry optimizations were performed using the quasi-Newton algorithm, combining the quadratic step (BFGS scheme) with a linear one (Civalleri et al., 2001; Doll, 2001). Simulated IR spectra were obtained by computing the vibrational frequencies of the studied systems at the Ŵ point (point k = 0 in IBZ) within the harmonic approximation. The Hessian matrix was obtained numerically (i.e., via the central difference formula), in which second-energy derivatives are calculated by displacing each of the 3N optimized nuclear positions by a small amount (u = 0.003 Å) (Pascale et al., 2004). The SCF criterion convergence to numerically construct the Hessian matrix was set to 10−11 Hartrees in order to ensure sufficiently accurate numerical derivatives for calculating frequencies. IR intensity values of the normal modes were calculated through the variation of the dipole moment along the corresponding modes using a set of localized Wannier functions (Zicovich-Wilson et al., 2001, 2002). We note that anharmonicity is very unlikely to be significant in our systems as they do FIGURE 1 | Optimized silicate structures derived from the progressive not contain light atoms (e.g., H) and the aggregation process reduction of the periodic unit cell size as a strategy to mimic proto-silicate is interpreted to occur at the very low temperatures of the aggregation. For Sil-1_1, Sil-1_2, and Sil-1_3, unit cell parameters were fixed to the initial values, while for Sil-1_4, Sil-1_5, and Sil-1_6 they were included in ISM, and thus only low energy vibrational states are populated. the optimization process. Atom color key: Si—yellow, Mg—blue, O—red. Accordingly, we consider the harmonic approximation to be sufficiently accurate for the description of the vibrational spectra. Visualization and manipulation of the structures, including visual inspection of the calculated frequencies for band assignment, have been carried out with the MOLDRAW Construction of Aggregated Silicates program (Ugliengo et al., 1993). Figures were rendered with the The initial structure from which the aggregated silicate systems POVRAY program. are generated is the Mg6 Si3 O12 nanocluster (Sil-0 in Figures 1, 2), which has the forsterite stoichiometry (i.e., Mg2 SiO4 ) and contains three formula units. Sil-0 was found as one of the most energetically stable nanocluster isomers of this size in RESULTS AND DISCUSSION global optimization searches using Monte Carlo basin hopping approach (Escatllar et al., 2019). In Escatllar et al. (2019) The underlying idea is to assess if aggregation of proto-silicate DFT based calculations were carried out using the PBE0 nanoclusters can result in the formation of silicate grains present hybrid functional, while our work employed the B3LYP hybrid in the ISM. To this end, construction of bulk silicate structures functional. Despite this methodological difference, structural from gradually bringing together molecular silicate nanoclusters parameters for Sil-0 provided by both methods compare was firstly performed. Then, a structural and energetic analysis extremely well. of the obtained structures was carried out to assess the stability Our “virtual” aggregation process (represented in Figures 1, of these aggregates with respect to the respective bulk crystalline 2) is explained as follows. The first step was to apply periodic silicate system. Finally, simulated IR spectra were compared boundary conditions to Sil-0. That is, the nanocluster was with observational data for actual IR silicates in the ISM. introduced inside a cubic box (i.e., the unit cell) that was repeated Cartesian/fractional coordinates of the studied systems are periodically in the three spatial dimensions. The initial lattice available in the Supplementary Material. parameters of the unit cell were set to a = b = c = 12 Å and Frontiers in Astronomy and Space Sciences | www.frontiersin.org 3 April 2021 | Volume 8 | Article 659494 Rimola and Bromley Silicate Nanocluster Aggregation TABLE 1 | Densities (in g cm−3 ) and lattice cell parameters (distances in Å and angles in degrees) of the periodic silicate structures shown in Figures 1, 2. Density a b c α β γ Figure 1 Sil-1_1 0.403 12.0 12.0 12.0 90.0 90.0 90.0 Sil-1_2 0.697 10.0 10.0 10.0 90.0 90.0 90.0 Sil-1_3 0.956 9.0 9.0 9.0 90.0 90.0 90.0 Sil-1_4 1.687 7.804 7.918 6.809 83.3 94.1 82.9 Sil-1_5 2.451 7.821 7.544 5.643 111.7 111.8 75.0 Sil-1_6 2.940 7.5 6.1 5.8 101.1 72.3 77.4 Sil-1_4ca 1.361 8.0 8.0 8.0 90.0 90.0 90.0 Sil-1_6ca 2.032 7.0 7.0 7.0 90.0 90.0 90.0 Figure 2 Sil-2_1 0.403 12.0 12.0 12.0 90.0 90.0 90.0 Sil-2_2 0.697 10.0 10.0 10.0 90.0 90.0 90.0 Sil-2_3 0.956 9.0 9.0 9.0 90.0 90.0 90.0 Sil-2_4 1.994 8.228 5.746 7.770 95.5 88.4 73.2 Sil-2_5 2.914 5.143 7.729 6.489 87.6 96.9 69.7 Sil-2_6 2.988 5.822 7.573 6.319 93.8 116.0 69.5 Sil-2_4ca 1.361 8.0 8.0 8.0 90.0 90.0 90.0 Sil-2_5ca 2.032 7.0 7.0 7.0 90.0 90.0 90.0 Sil-2_6ca 2.371 6.0 7.0 7.0 90.0 90.0 90.0 forsterite 3.150 4.789 10.254 6.009 90.0 90.0 90.0 a These structures (not shown in Figures 1, 2) derive from optimisations in which the unit cell parameters were fixed. For comparison, the same data for bulk forsterite Mg2 SiO4 crystal is also included. FIGURE 2 | Optimized silicate structures derived from the progressive reduction of the periodic unit cell size as a strategy to mimic proto-silicate Once this situation was reached (i.e., interaction between aggregation. For Sil-2_1, Sil-2_2, and Sil-2_3, unit cell parameters were fixed to the initial values, while for Sil-2_4, Sil-2_5, and Sil-2_6 they were included in replicated nanoclusters), during this aggregation phase both the optimization process. These structures result from the aggregation of the internal atomic positions and lattice cell parameters were same nanocluster as shown in Figure 1, but with a different initial rotational optimised in order to better allow the interacting nanoclusters to orientation within the periodic unit cell. Atom color key: Si—yellow, Mg—blue, reach a stable relaxed energy minimum. This final aggregation O—red. process led to the formation of several extended amorphous silicates with different structures and densities (see Sil-1_4, Sil- 1_5, and Sil-1_6 and Table 1). α = β = γ = 90◦ . Once the periodic system was generated, the Finally, we note that the structures of the resulting amorphous atomic positions of the nanocluster were optimized, keeping the silicates derived from our aggregation procedure depend on the lattice parameters fixed to avoid interactions between replicated initial orientation of the nanocluster inside the periodic box. This nanoclusters. Due to the relatively large values of a, b and c, the effect is shown in the aggregated structures in Figures 1 and 2, first system is simply a relatively isolated Sil-0 nanocluster inside respectively, where in the latter case, the nanocluster was rotated the unit cell, which keeps its molecular structure (see Sil-1_1 45◦ with respect to the c axis as compared to the former. This in Figure 1), meaning that there are no significant interactions change in initial conditions was found to significantly influence between periodically replicated nanoclusters. the detailed atomic structures during aggregation, especially From this starting point, the values of a, b and c were those generated in the final aggregation steps, in which the unit progressively decreased (shown in Figure 1), hence reducing the cell parameters were optimized (e.g., compare Sil-1_4, Sil-1_5 size of the unit cell, in which the internal atomic positions of and Sil-1_6 with Sil-2_4, Sil-2_5, and Sil-2_6, respectively). the system were relaxed with fixed lattice parameters. With each reduction in cell size, the replicated nanoclusters were closer to Structural and Energetic Analysis each other (see Sil-1_1 and Sil-1_2 structures of Figure 1), up Figures 1, 2 show the optimized silicate systems adopting to a point in which interaction between nanoclusters took place. the abovementioned nanocluster aggregation procedure. The Indeed, structure Sil-1_3 of Figure 1 shows the formation of first generated structures (Sil-1_1/Sil-2_1 and Sil-1_2/Sil-2_2 in Mg-O bonds between two adjacent nanoclusters. At this point, Figures 1, 2) are periodic arrays of isolated silicate nanoclusters. we can consider that aggregation is starting to occur. Since these structures do not significantly interact with respective Frontiers in Astronomy and Space Sciences | www.frontiersin.org 4 April 2021 | Volume 8 | Article 659494 Rimola and Bromley Silicate Nanocluster Aggregation images (the closest inter-cluster distances are ≈6.1 Å and ≈4.0 Å, respectively), they do not suffer structural variation with respect to the original nanocluster. The first replica-interacting systems (structures Sil-1_3 and Sil-2_3 in Figures 1, 2) show the formation of Mg-O bonds between images forming a square (MgO)2 ring. These interactions take place when the unit cell parameters are a = b = c = 9 Å. This suggests that inter-cluster Mg-O interactions could trigger the silicate aggregation between nanoclusters. This is reasonable since interaction between these two atom types is essentially electrostatic (i.e., formally between Mg2+ and O2− ions). From these initially interacting structures, slight reduction of the unit cell size, followed by full geometry optimization, quickly leads to the formation of extended porous silicates, namely, silicates with cavities inside the structures (see Sil- 1_4 and Sil-2_4 structures in Figures 1, 2). Indeed, in both systems, the nanocluster replicas interact along the three periodic directions in such a way that a cavity between them is created. These pores have diameters of ≈7–8 Å, which is a suitable size to encapsulate small gaseous molecules. Thus, if the proto- silicate nanoclusters were capable to possess adsorbed molecules on their surfaces, they could potentially be retained during the aggregation process and finally become confined inside the formed porous. Further reduction of the unit cell size leads to the formation of dense silicates (see e.g., Sil-1_6) with no pores. Interestingly, these compressed systems appear to be totally amorphous materials since the atomic positions do not seem to follow any regularity in space. This amorphous nature will be further explored by their simulated IR spectra (see below). The relative energy of these “generated + optimized” systems FIGURE 3 | Relative energies (in kcal mol−1 ) of the Mg6 Si3 O12 -based aggregates with respect to the bulk forsterite Mg2 SiO4 crystal as a function of with respect to that of the forsterite bulk Mg2 SiO4 crystal their density. Values are normalized with respect to the four Mg2 SiO4 units (considered here as our reference system) as a function of system present in the crystalline unit cell: (A) for systems shown in Figure 1; (B) for density is reported in Figure 3. The values of these energies are systems shown in Figure 2. Values labeled by triangles refer to compressed also reported in Table 2. Values are normalized with respect to structures without optimizing their unit cells (see text for more details). Arrows the four Mg2 SiO4 units present in the crystalline unit cell. The indicate the system formed upon full geometry (i.e., atomic positions + cell parameters) optimization. The molecular nanocluster system is considered to energy plots can also be understood as the energy variation of the have density 0 g cm−3 , as the lattice parameters are effectively infinite. systems with respect to the distance between proto-silicate units, where a high density implies a smaller inter-silicate distance and vice versa. Among the different silicates studied here, crystalline forsterite is the most stable one, while the molecular limited to a strained (MgO)2 ring. However, for the subsequent nanocluster is the least stable. This is not surprising as: (i) increasingly interacting systems, relative energies significantly for extended systems crystalline structures tend to be more drop: the porous silicates lie 170–200 kcal mol−1 above the energy stable than amorphous ones, and (ii) nanoclusters have a high of forsterite and the corresponding relative energies our densest percentage of undercoordinated surface atoms resulting in highly silicates are <100 kcal mol−1 . reconstructed and strained non-crystalline structures (Escatllar In the plots in Figure 3, the relative energies of compressed et al., 2019), leading to large instabilities. In our case, the isolated systems without optimized unit cell parameters are also Mg6 Si3 O12 nanocluster is approximately 390 kcal mol−1 higher represented (gray triangle points). The arrows indicate the in energy than crystalline bulk Mg2 SiO4 . resulting structures when full optimization (i.e., atomic positions For periodic structures without interactions between replicas, + cell parameters) was performed from those without optimizing their energetic stability is, as expected, the same as the Mg6 Si3 O12 the unit cell. These later structures are more energetically nanocluster. Once interaction between clusters begins, the unstable than their optimized unit cell analogues as the relative energies of the system with respect to forsterite decreases. constrained cell parameters lead to artificially overly compressed For the first interacting systems, relative energies are still structures which exhibit high geometrical strains. Therefore, we relatively high (330–345 kcal mol−1 ), as the interaction is do not consider these systems as representative. Frontiers in Astronomy and Space Sciences | www.frontiersin.org 5 April 2021 | Volume 8 | Article 659494 Rimola and Bromley Silicate Nanocluster Aggregation TABLE 2 | Relative energies (in kcal mol−1 ) of the periodic silicate structures shown in Figures 1, 2 with respect to the bulk forsterite Mg2 SiO4 crystal (per unit formula). Figure 1 Rel. E Figure 2 Rel. E Sil-0 390.5 Sil-0 390.5 Sil-1_1 388.4 Sil-2_1 388.4 Sil-1_2 381.8 Sil-2_2 381.8 Sil-1_3 345.7 Sil-2_3 327.8 Sil-1_4 205.8 Sil-2_4 168.0 Sil-1_5 135.1 Sil-2_5 67.9 Sil-1_6 82.8 Sil-2_6 66.0 Sil-1_4ca 224.5 Sil-2_4ca 261.8 Sil-1_6c a 289.5 Sil-2_5ca 196.9 Sil-2_6ca 199.0 Their representation as a function of the corresponding densities is shown in Figure 3. a These structures (not shown in Figures 1, 2) derive from optimizations in which the unit cell parameters were fixed. Analysis of Simulated IR Spectra Figure 4 shows the simulated IR spectra associated with the silicate structures reported in Figures 1 (black spectra) and 2 (red spectra), while Table 3 reports the calculated intensities and the vibrational mode assignment of the IR bands presented in Figure 4. For the sake of comparison, IR data related to the crystalline Mg2 SiO4 forsterite is also included. In Figure 4, gray shading indicates the positions of the IR bands for general interstellar silicates obtained from astronomical observations, which are centered at ca. 1,000 cm−1 and ca. 550 cm−1 . The IR spectra of the molecular nanocluster and the crystalline bulk are also available in the literature (Navarro-Ruiz et al., 2014b; Martínez-González et al., 2018; Escatllar et al., 2019). The forsterite spectrum shows a set of well-defined, relatively sharp IR bands (Figure 4g). Bands peaked between 1,000 and 800 cm−1 are assigned to the ν(Si-O) stretching modes, those FIGURE 4 | Calculated IR spectra of the silicate aggregates. The calculated IR between 600 and 500 cm−1 to δ(O-Si-O) bending modes, those spectra of the Mg6 Si3 O12 nanocluster and the crystalline forsterite bulk are also included. Gray shading indicates the bands from observational around 400 cm−1 to rotational motions of the SiO4 tetrahedra, measurements, centered at ca. 1,000 and 550 cm−1 , the width of which being and those around 350 cm−1 to translational motions of the the corresponding full width at half maximum (FWHM) ranges [from Henning metal cations. In contrast, the IR spectrum of the Mg6 Si3 O12 (2010)]. Black spectra are those for the systems shown in Figure 1 (Sil-1_1 is nanocluster (Figure 4a) displays a wider variety of bands. This omitted because it is equal to Sil-0). Red spectra are those for the systems shown in Figure 2 (Sil-2_1 is omitted because it is equal to Sil-0). The spectra is due to the nanocluster’s lack of internal symmetry, which splits are superimposed to show that irrespective of the aggregation process route the IR bands into several signals because of the non-equivalent the final dense structures are very similar observationally. (a) Sil-0, (b) Sil-1_2 vibrations of the moieties. Despite this, IR assignments can also and Sil-2_2, (c) Sil-1_3 and Sil-2_3, (d) Sil-1_4 and Sil-2_4, (e) Sil-1_5 and be grouped in a similar way as the crystalline ones. Sil-2_5, (f) Sil-1_6 and Sil-2_6, and (g) forsterite crystalline Mg2 SiO4 bulk. In relation to the progressively reduced silicates, the IR spectra Intensities are normalized to 100 with respect to the most intense band and accordingly they are in arbitrary units. of the periodic non-interacting replicas systems (Sil-1_2 and Sil- 2_2 of Figures 1, 2, respectively) are, expectedly, almost identical than that of the molecular nanocluster (compare spectra of Figure 4a with b). Changes start when the replicas of adjacent cells start to interact (Sil-1_3 and Sil-1_4 of Figure 1, and Sil-2_3 into a more continuous band through the 1,200–800 cm−1 range. and Sil-2_4 of Figure 2). Because of the presence of the newly Due to this, the regions between the stretching vibrations and formed Mg-O bonds, some new bands assigned to the ν(Mg-O) the rest of vibrations are more clearly differentiated in two appear; in particular, the bands around 1,000 cm−1 (see spectra of broad bands. Such a differentiation is even more defined in Figures 4c,d), which were lacking in the non-interacting-replicas the periodic fully interacting-replicas systems (i.e., Sil-1_5 and systems. The presence of these new bands converts the IR profiles Sil-1_6 of Figure 1 and Sil-2_5 and Sil-2_6 of Figure 2). For these Frontiers in Astronomy and Space Sciences | www.frontiersin.org 6 April 2021 | Volume 8 | Article 659494 Rimola and Bromley Silicate Nanocluster Aggregation TABLE 3 | Calculated frequencies and intensities, and assignment of the TABLE 3 | Continued corresponding vibrational modes of the IR bands for the studied systems. System Frequency Intensity System Frequency Intensity Vibrational System Frequency Intensity System Frequency Intensity Vibrational (cm−1 ) (km/mol) (cm−1 ) (km/mol) mode (cm−1 ) (km/mol) (cm−1 ) (km/mol) mode 151 481.6 Transl. Mg Sil-0 1,109 159.5 ν(Si-O) 915 202.3 ν(Si-O) Sil-1_5 1,022 381.7 Sil-2_5 993 209.0 ν(Si-O) 852 145.5 ν(Si-O) 992 408.7 931 214.9 ν(Si-O) 749 142.7 ν(Si-O) 879 419.5 869 211.4 ν(Si-O) 579 455.6 δ(O-Si-O) 823 198.1 ν(Si-O) 397 418.5 δ(O-Si-O) 730 120.9 724 132.8 ν(Mg-O) 321 401.5 Transl. Mg 598 375.8 645 219.9 ν(Mg-O) 221 484.9 Transl. Mg 536 387.4 495 435.3 δ(O-Si-O) 427 310.5 427 480.3 δ(O-Si-O) Sil-1_1 1,105 140.9 Sil-2_1 1,105 150.5 ν(Si-O) 334 183.0 271 550.3 Transl. Mg 915 168.6 915 173.7 ν(Si-O) 252 120.7 157 311.2 Transl. Mg 854 122.7 854 127.1 ν(Si-O) 742 121.4 740 132.0 ν(Si-O) Sil-1_6 984 243.0 Sil-2_6 944 277.2 ν(Si-O) 578 378.4 577 406.8 δ(O-Si-O) 933 184.9 899 256.0 ν(Si-O) 395 354.5 395 363.6 δ(O-Si-O) 848 180.4 845 226.0 ν(Si-O) 322 344.6 323 374.6 Transl. Mg 693 114.6 676 232.2 ν(Mg-O) 221 410.6 221 426.6 Transl. Mg 631 259.1 ν(Mg-O) 523 363.1 559 457.8 δ(O-Si-O) Sil-1_2 1,095 180.4 Sil-2_2 1,097 207.5 ν(Si-O) 452 406.9 502 479.4 δ(O-Si-O) 932 216.9 928 241.5 ν(Si-O) 431 487.9 δ(O-Si-O) 853 150.8 858 164.7 ν(Si-O) 296 467.4 285 582.3 Transl. Mg 743 143.4 739 170.1 ν(Si-O) 187 371.8 208 547.4 Transl. Mg 660 385.8 567 522.5 δ(O-Si-O) 555 450.7 394 480.1 δ(O-Si-O) forsterite 982 1413.3 ν(Si-O) 391 435.5 315 481.5 δ(O-Si-O) 874 2659.8 ν(Si-O) 292 427.9 215 550.5 Transl. Mg 614 463.5 δ(O-Si-O) 220 507.4 Transl. Mg 514 641.8 δ(O-Si-O) 416 1288.5 Rot. SiO4 Sil-1_3 1,086 119.3 Sil-2_3 1,118 101.2 ν(Si-O) 350 1035.7 Rot. SiO4 946 181.9 1,027 131.3 ν(Si-O) 293 806.4 Transl. Mg 916 178.9 930 282.8 ν(Si-O) + ν(Mg-O) The simulated spectra are shown in Figure 4. 842 190.9 797 154.5 ν(Si-O) 796 193.9 ν(Si-O) 656 347.0 692 226.7 δ(O-Si-O) 572 539.4 527 536.5 ν(Mg-O) systems, the IR spectra match well those of the bulk amorphous 419 520.3 402 500.6 δ(O-Si-O) Mg2 SiO4 silicates, namely, two very broad bands between 1,100 322 601.3 333 564.7 Transl. Mg and 800 cm−1 and between 600 and 200 cm−1 (see spectra of 217 561.8 168 531.9 Transl. Mg Figures 4e,g). These IR features are in good agreement with those of large amorphous silicate models (Martínez-González 172 544.6 Transl. Mg et al., 2018) and observational measurements (Henning, 2010). Sil-1_4 1,078 170.5 Sil-2_4 1,159 165.0 ν(Si-O) In view of these results, the first interacting-replicas systems (Sil- 1,021 174.0 1,078 207.7 ν(Si-O) 1_3, Sil-1_4, Sil-2_3, and Sil-2_4) can be considered as transient 903 184.8 1,009 259.0 ν(Si-O) states involved in the aggregation processes from proto-silicate 850 118.3 883 178.4 ν(Si-O) nanoclusters to amorphous silicates. 708 214.2 756 202.5 ν(Mg-O) It is finally worth mentioning that the superimposition of 649 291.0 634 472.7 ν(Mg-O) the two sets of spectra shown in Figure 4, from the Sil-1 and 520 369.1 503 432.2 δ(O-Si-O) Sil-2 aggregation, although having different initial conditions, 406 446.5 430 478.9 δ(O-Si-O) tend to produce bulk amorphous silicates with very similar 302 479.0 362 532.5 Transl. Mg IR profiles. This is an important fact because is suggests that, 172 399.8 190 516.1 Transl. Mg irrespective of the detailed route of the aggregation process, the resulting structures arising from each aggregation process are (Continued) very similar observationally. Frontiers in Astronomy and Space Sciences | www.frontiersin.org 7 April 2021 | Volume 8 | Article 659494 Rimola and Bromley Silicate Nanocluster Aggregation CONCLUSIONS In summary, our results provide evidence that formation of interstellar silicate grains through proto-silicate aggregation is In this work we investigate theoretically the aggregation of proto- a feasible process, since the aggregation steps are energetically silicate nanoclusters (i.e., small silicate clusters) as a way to form favorable and the final amorphous systems exhibit IR properties interstellar silicate grains. The study is performed by means in fair agreement with those obtained observationally. of periodic quantum mechanical simulations using DFT based calculations employing the hybrid B3LYP functional; a method DATA AVAILABILITY STATEMENT known to be reliable for modeling silicate systems. Using a stable Mg6 Si3 O12 nanocluster as initial guess structure The original contributions presented in the study are included to form silicate aggregates, the adopted strategy to simulate the in the article/Supplementary Material, further inquiries can be aggregation process is based on the progressive reduction in size directed to the corresponding author/s. of a 3D periodic unit cell centered on the nanocluster. Upon decreasing the lattice parameters, the nanocluster replicas in AUTHOR CONTRIBUTIONS adjacent unit cells start to interact to form extended Mg2 SiO4 silicate materials with progressively increasing density. All authors participated in the initial conception of the research Our results indicate that the first interaction between idea and in the discussion of the results. AR did the quantum nanocluster replicas takes place between Mg and O atoms, chemical simulations and participated in the writing and editing forming (MgO)2 rings. These tenuously linked intermediate- of the manuscript. SB participated in the writing and editing of aggregated systems exhibit internal cavities rendering them as the manuscript. nanoporous materials. Further reduction in size of the periodic box gives rise to systems in which the porosity disappears, leading FUNDING to dense amorphous materials. Energetic analysis of the resulting structures shows that all This project has received funding from the European of them lie higher in energy than the forsterite Mg2 SiO4 crystal Research Council (ERC) under the European Union’s bulk. The most unstable system is the isolated Mg6 Si3 O12 Horizon 2020 research and innovation programme grant proto-silicate nanocluster (ca. 400 kcal mol−1 with respect to agreement no. 865657 for the project Quantum Chemistry on forsterite per formula unit). Once proto-silicate replicas start to Interstellar Grains (QUANTUMGRAIN). We acknowledge interact, corresponding relative energies significantly decrease. financial support from the Spanish Ministerio de Ciencia, The porous systems lie ca. 170–200 kcal mol−1 above the Innnovación y Universidades (projects CTQ2017-89132- forsterite, while the densest non-porous materials are <100 kcal P, RTI2018-095460-B-100, and MDM-2017-0767 via the mol−1 the crystalline bulk. This increasingly stabilization of the Spanish Structures of Excellence María de Maeztu program) systems formed during the compression is indicative that the and the Generalitat de Catalunya (projects 2017SGR1323 aggregation process does not present energetic hindrances, at and 2017SGR13). least thermodynamically and at very low temperatures. The IR spectra of non-interacting replica systems are ACKNOWLEDGMENTS practically identical to the isolated Mg6 Si3 O12 nanocluster, whereas for the interacting cases additional bands arise. For AR is indebted to the Ramón y Cajal program. The Red the porous systems, particular bands at ca. 900 cm−1 appear Española de Supercomputación (RES) and Consorci de Serveis due to the new ν(Mg-O) vibrations, while for the densest Universitaris de Catalunya (CSUC) are also acknowledged for the ones two very broad bands at 1,100–800 cm−1 and 600–200 provision of supercomputing time. cm−1 are exhibited. 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What can infrared spectra tell us about the crystallinity of author(s) and the copyright owner(s) are credited and that the original publication nanosized interstellar silicate dust grains? ACS Earth Space Chem. 3, 2323–2338. in this journal is cited, in accordance with accepted academic practice. No use, doi: 10.1021/acsearthspacechem.9b00157 distribution or reproduction is permitted which does not comply with these terms. Frontiers in Astronomy and Space Sciences | www.frontiersin.org 10 April 2021 | Volume 8 | Article 659494