Reaction Pathway and Rovibrational Analysis of Aluminum Nitride Species as Potential Dust Grain Nucleation Agents

A dust nucleating agent may be present in interstellar or circumstellar media that has gone seemingly undetected and unstudied for decades. Some analyses of the Murchison CM2 meteorite suggest that at least some of the aluminum present within condensed as aluminum nitrides instead of the long-studied, but heretofore undetected suite of aluminum oxides. The present theoretical study utilizes explicitly correlated coupled cluster theory and density functional theory to provide a formation pathway from alane (AlH3) and ammonia to the cyclic structure Al2N2H4, which has the proper Al/N ratio expected of bulk aluminum nitrides. Novel rovibrational spectroscopic constants are computed for alane and the first two formed structures, AlNH6 and AlNH4, along the reaction pathway for use as reference in possible laboratory or observational studies. The ν 8 bending frequency for AlNH6 at 755.7 cm−1 (13.23 μm) presents a vibrational transition intensity of 515 km mol−1, more intense than the antisymmetric C−O stretch of carbon dioxide, and contains a dipole moment of 5.40 D, which is ∼3× larger than that of water. Thus, the present reaction pathway and rovibrational spectroscopic analysis may potentially assist in the astrophysical detection of novel, inorganic species which may be indicative of larger dust grain nucleation.


INTRODUCTION
Previous study (Zinner et al. 1991) of the Murchison CM2 chondritic meteorite seems to suggest the aluminum present within condensed as a form of aluminum nitride rather than the more commonly assumed aluminum oxides.However, aluminum nitride clusters must compete with these aluminum oxides during dust grain nucleation and further formation.Alumina (Al 2 O 3 ) is a common aluminum oxide that has been theorized as a major contributor to both bulk aluminum oxides and their use in dust grain nucleation and formation in the interstellar medium (ISM) and in circumstellar media (CSM) (Gail & Sedlmayr 1998, 1999;Gobrecht et al. 2016).One of the most commonly attributed spectral features for bulk alumina's Al−O vibrational stretching and bending motions is seen at 13 µm (Gobrecht et al. 2022;Sloan et al. 2003).Additionally, previous studies (Gail & Sedlmayr 1999;Sloan et al. 2003) attribute emission features at 11, 20, 28, and 32 µm to the same carrier as the 13 µm feature.Despite this, monomeric forms of aluminum oxides like Al 2 O 3 have yet to be detected as their formation seems to be unfavorable due to many pathways hindered by endothermicities (Chang et al. 1998;Patzer et al. 2005;Gobrecht et al. 2022).Further, bulk-phase aluminum oxides exhibit high condensation temperatures that lead to reaction timescales that are too rapid to adequetly detect such clusters (Lodders 2003).The presence of Al 2 O 3 in chondritic meteorite studies suggests its existence in these stellar environments; without astronomical detection, though, their potential role in dust grain nucleation to formation cannot be confirmed (Nittler et al. 2008;Hutcheon et al. 1994).Thus, an investigation into an alternative Al-containing species that may not condense on timescales as quickly as Al 2 O 3 is warranted to elucidate long-sought-after dust formation pathways containing Al that have eluded astrochemists and astrophysicists to date.
While Al condensates show high refractory character (Lodders 2003), not all of its forms, in CSM, condense into large bulk solids early in stellar evolution and evade detection.Within the circumstellar envelope of IRC+10216, amongst other oxygen-rich sources, two Al-halide species have been observed in the form of AlCl and AlF (Cernicharo & Guélin 1987;Ziurys et al. 1994;Decin et al. 2017;Saberi et al. 2022).These Al-halides have also been observed within circumstellar envelopes with C/O ∼ 1 (Danilovich, T. et al. 2021).While these have been observed closer to the star, upon their ejection to the cooler regions of the stellar envelope, they are thought to deplete onto dust grains eluding any further detection.However, this is not the case for AlNC, which has been detected in larger concentrations within the cooler regions of the envelope and under the condensation temperature of the elusive Al 2 O 3 molecule and other aluminum oxide clusters (Ziurys et al. 2002).The presence of the Al-halides and AlNC suggests that Al-containing species are not solely locked up into aluminum oxide clusters or grains.Thus, O-deficient, Al-containing species can be formed within the warmer regions of the stellar envelope and persist long enough in the cooler, outer circumstellar dust clouds before depositing or aggregating and disappearing from rovibrational detection.
Additionally, a radioisotope of Al, 26 Al, was identified in its fluorinated form, 26 AlF, near the stellar merger of CK Vulpus (Kamiński et al. 2018). 26AlF is believed to have been introduced into the surrounding stellar region during the collision of the binary system yet persisted on a timescale long enough for detection (Kamiński 2015).Much like the elusive Al 2 O 3 , both the stable 27 Al and an extinct form of 26 Al, which later decayed into the 26 Mg isotope based on isotopic abundance studies, were found within the Murchison CM2 chondritic meteorite.An investigation of the ratio of 26 Al/ 27 Al suggests that the 26 Al present is in larger abundance in at least this meteorite compared to the ratio in the solar system at large.In any case, the presence of an aluminum nitride system within Murchison CM2 is suggested via a comparison of the SiC abundance and CN − /C − ratio and the Al and N present within.Such a correlation suggests that the Al in the meteorite condensed not as some form of aluminum oxide, like Al 2 O 3 , but rather as some form of aluminum nitride system (Zinner et al. 1991).As discussed previously, the Al−N moiety is not unheard of in CSM from the presence of AlNC.Previous computational studies have calculated an Al−N bond strength of −105.0 kcal mol −1 , which is stronger than the bond strength of the N−C bond at −77.8 kcal mol −1 (Doerksen & Fortenberry 2020).This larger bond strength of the Al−N bond, relative to the N−C bond in AlNC, suggests the stability of Al−N bonds in CSM and the ISM.
The study of the Murchison CM2 meteorite implies that the aluminum nitride systems present within play a key role in the nucleation of the graphite that composes the bulk of the carbonaceous material within the meteor by catalyzing the graphite's inhibited nucleation (Czyzak et al. 1982;Nuth 1985;Zinner et al. 1991).With that, these new Alcontaining species may be instrumental for the nucleation of aggregated material onto other solar system bodies, such as comets, asteroids, and other meteors.That being said, these conclusions justify an investigation into the presence of unreported aluminum nitride molecular systems in CSM and the ISM that may potentially assist in elucidating the processes of how Al-bearing species get from the gas phase into their bulk solid-phase dust grain counterparts.
As aluminum nitride systems have not been characterized in any stellar environment, no gas-phase observational or experimental spectroscopic data are available to begin the search for such species.Thus, the present quantum chemical study provides reference data for a proposed pathway of formation from the aluminum hydride, alane, (AlH 3 ) and ammonia (NH 3 ) into the first cyclic species along said pathway.Regardless of the AlH 3 molecule's lack of interstellar detection, the present study utilizes AlH 3 as the main source of aluminum given its simplicity as a metal hydride and its closed-shell configuration.The AlH 3 molecule is used in place of the more simple, and previously detected (Kamiński, T. et al. 2016), aluminum mono-hydride (AlH) as previous computational studies suggest that access to more hydrogen atoms assists the progress of the reaction pathway (Grosselin & Fortenberry 2022;Flint & Fortenberry 2023).The rovibrational spectroscopic data herein will be instrumental in supporting the currently available spectroscopic telescopes and observational technologies like the James Webb Space Telescope (JWST) for its efficiency in probing the near-to mid-IR spectrum with its Near-Infrared Spectrograph (NIRSpec) and Mid-Infrared Instrument (MIRI) instruments.Where available, the provided rotational data will assist microwave spectroscopic observatories like the Atacama Large Millimeter/sub-millimeter Array (ALMA).To that end, the rovibrational spectroscopic analysis provided should aid in the potential astrophysical identification of aluminum nitride species that have yet to be characterized and may contribute to the dust grain nucleation and formation processes present in CSM and the ISM.
Unless otherwise stated, all geometry optimizations, single-point energy (SPE) computations, and zero-point vibrational energy corrections for the reactants, intermediates, and products of the aluminum nitride reaction pathway are conducted utilizing coupled cluster theory at the singles, doubles, and perturbative triples level [CCSD(T)] (Raghavachari et al. 1989;Shavitt & Bartlett 2009;Crawford & Schaefer III 2000).For an additional gain in accuracy, the CCSD(T) level of theory is corrected within the explicitly correlated F12b formalism (Adler et al. 2007;Knizia et al. 2009) along with its corresponding cc-pVTZ-F12 basis set (Peterson et al. 2008;Yousaf & Peterson 2008).The aforementioned level of theory will henceforth be abbreviated as "F12-TZ."Geometry optimization and harmonic frequency computations for all transition states along the pathway are conducted with the B3LYP density functional (Yang et al. 1986;Lee et al. 1988) along with the aug-cc-pVTZ correlation consistent Dunning basis set (Kendall et al. 1992).After the transition states are optimized at the B3LYP/aug-cc-pVTZ level of theory, single-point energy computations are computed at the F12-TZ level (Ramal-Olmedo et al. 2021), and are subsequently corrected with B3LYP/aug-cc-pVTZ zero-point vibrational energies (ZPVEs).All minima along the reaction pathway are computed via the MOLPRO 2022.2 suite of quantum chemical packages (Werner et al. 2020).Finally, all transition state computations on the pathway are conducted via GAUSSIAN16 (Frisch et al. 2016).

Rovibrational Spectroscopic Methods
The highly accurate rovibrational spectroscopic constants are computed utilizing the quartic force field (QFF) approach.A QFF is a fourth-order Taylor series expansion of the potential energy portion of the internuclear Watson Hamiltonian (Fortenberry & Lee 2019).QFFs as employed herein have been able to produce rovibrational spectroscopic constants within 1% of experimental values for many molecular systems (Huang & Lee 2008, 2009;Huang et al. 2011;Zhao et al. 2014;Huang et al. 2013;Fortenberry et al. 2014Fortenberry et al. , 2015;;Kitchens & Fortenberry 2016;Fortenberry 2017;Fortenberry et al. 2018;Gardner et al. 2021).F12-TZ has been shown to produce accurate fundamental vibrational frequencies and rotational constants at far less computational cost compared to other QFF methods (Martin & Kesharwani 2014;Agbaglo et al. 2019;Agbaglo & Fortenberry 2019;Inostroza-Pino et al. 2020;Palmer & Fortenberry 2022).Additionally, the QFF implemented in this work is conducted within the recently developed automated PBQFF framework (Westbrook & Fortenberry 2023).The PBQFF procedure begins with a geometry optimzation utilizing MOLPRO (Werner et al. 2020) at the F12-TZ level of theory with tight convergence criteria.From there, the optimized Cartesian geometry is displaced by 0.005 Å respective of bond lengths or angles, to mimic a QFF but is truncated to the second-order yielding a Cartesian harmonic force field.SPE computations for every displacement are computed and used to generate a harmonic force constant (FC) matrix.The normal coordinates are then extracted from the resulting mass-weighted Hessian matrix for the given molecular species.The optimized molecular geometry is then displaced along these normal coordinates to compute the rest of the semi-diagonal QFF, and SPE computations are performed at each normal coordinate displacement.
Once the SPE computations are finished, the final normal FCs are computed directly utlizing a finite differences procedure.The normal coordinate FCs are then passed to a second-order vibrational and rotational perturbation theory (VPT2) (Mills 1972;Watson 1977;Papousek & Aliev 1982;Franke et al. 2021) algorithm within the PBQFF framework itself.From this, the harmonic frequencies, fundamental anharmonic vibrational frequencies, vibrationallyaveraged rotational constants, singly-vibrationally-excited rotational constants, quartic distortion constants, and sextic distortion constants are produced.Additionally, if present in the analysis, the type-1 and -2 Fermi resonances and Coriolis resonances are taken into account as it has been shown to increase the accuracy of the computed rovibrational spectroscopic constants (Martin & Taylor 1997;Martin et al. 1995).To further assist in potential astrophysical detection, dipole moments for AlNH 6 and AlNH 4 are computed at the F12-TZ level within MOLPRO 2022.2 (Werner et al. 2020).Finally, double-harmonic infrared intensities computed using GAUSSIAN16 (Frisch et al. 2016) at the MP2/cc-pVDZ (Møller & Plesset 1934;Dunning 1989) level of theory are included to assist in the detection of these species in the infrared (IR).Computed intensities at this level of theory have been show to produce semi-quantitative agreement with higher levels of theory for far less computational costs (Yu et al. 2015;Finney et al. 2016;Westbrook et al. 2021).
In addition to IR intensities, absorption cross sections, σ, are given for all applicable vibrational frequencies.The absorption cross sections are derived utilizing the formula in EQ. 1, where "N a " is Avogadro's number, and "ϵ" is the molar absorption coefficient.The molar absorption coefficients for each vibrational frequency are computed following the formula in EQ. 2 (Spanget-Larsen 2015), where "I IR " is the IR intensity computed above and "w" is the resolving power of the given observing telescope.
The resolution, "R," of the NIRSpec and MIRI on the JWST, at their respective operating wavelengths, are provided and are trivially converted to the resolving power in EQ. 3 (Labiano, A. et al. 2021;Jakobsen, P. et al. 2022).
3. RESULTS AND DISCUSSION

Reaction Pathway Analysis
The reaction coordinate profile shown in Figs. 1 and 2 along with their corresponding equilibrium geometries, and definitions and chemical formulae in Table 1, shows the continual addition of equivalents of AlH 3 and NH 3 .Additions of AlH 3 and NH 3 produce progressively larger datively-bonded structures but contain an initially raised transition barrier from I 1 to the P 1 .In order for the reaction to progress to larger aluminum nitride systems, I 1 must overcome the aforementioned barriered TS 1 that sits 1.9 kcal mol −1 higher than the reactants and lose an H 2 molecule to form P 1 .This is in stark contrast with previous computed reaction schemes (Grosselin & Fortenberry 2022;Gobrecht et al. 2022) on AlH 3 and water that produce aluminum oxides with submerged barriers of formation.These barrierless formation most likely govern the short timescales of leading to the underdetection of a suitable carrier of the Al−O features, like Al 2 O 3 in CSM or the ISM.Regardless, overcoming this barrier requires sufficiently high temperatures, ∼960 K, in the aluminum nitride species' formation environment from the surrounding stellar environments to begin forming larger clusters.
Obviously, the cold, diffuse ISM at ∼10−40 K is not a likely region for the formation of P 1 to occur.However, as stated earlier, the previous work on Murchison CM2 (Zinner et al. 1991) suggests that the theorized aluminum nitride systems present in the meteorite may have nucleated the meteorite's dust grain formation.If this is the case, then the aluminum nitride system would have been formed in some region warm enough for its own production and for dust grain formation to occur.The warm environments of inner protoplanetary disks can achieve a range of temperatures anywhere from 500−1500 K (Boss 1998) and contain ample material for molecular synthesis to begin that may potentially lead to seeding and nucleating processes of dust grain formation.Additionally, highly evolved asymptotic giant branch (AGB) stars are known to exhibit much higher temperatures within 1−2 stellar radii at 2000−3000 K compared to the warm inner protoplanetary disks (Maercker et al. 2022).AGB stars also contribute considerable dust forming material to their surrounding environment, and the ISM at large, given the stars substantial mass-loss rates (Höfner & Olofsson 2018;Ferrarotti & Gail 2006).If a region of CSM or the ISM contains sufficient temperatures and has the necessary material, the proper conditions toward formation the aluminum nitride species along the reaction pathway proposed herein will be satisfied.Once these aluminum nitrides have been formed, they may likely go on to contribute to dust grain nucleation and formation as suggested in the study of the Murchison CM2 meteorite.
Once the transitional barrier, shown in Fig. 1, is overcome there will be enough latent energy within the system to further progress through the now relatively submerged pathway of formation.Thus, the reaction pathway is no longer nearly as limited by the surrounding temperature and can further condense into larger and larger dust grains in both the warmer and cooler regions of the CSM or ISM.In any case, from the P 1 structure, additions of AlH 3 or NH 3 lead to either the N−I 2 or the Al−I 2 structure.The addition of the AlH 3 leads to a lower energy cyclic structure with a three-center two-electron bond commonly seen in trivalent species containing an empty p-orbital like aluminum and boron (Mayer 1989).Upon the loss of the H 2 molecule, seen in the N/Al−TS 2 species, both pathways lead to their respective products (P 2 ) of similar structure.Interestingly, if an equivalent of AlH 3 is added to N−P 2 , it stabilizes into N−I 3 , which is structurally similar to Al-I 2 with a three-center two-electron bond.The extra stability of the three-center two-electron bond in N−I 3 yields the lowest energy structure of the present reaction pathway.While N−I 3 is the lowest energy structure, the reaction pathway should still progress further not only due to the energy from the ambient temperature of its formation environments but also from collision with other molecular citizens present within the same regions.
Further departure of an H 2 molecule from (N or Al)−I 3 yields the cyclic Al−P 3 structure, whereas N−P 3 is an open chain structure.The open-chain N−P 3 structure must overcome a torsional barrier before it becomes the cyclic N−P 4 .At this point along the pathway, the paths of additions of AlH 3 and NH 3 converge to the same structure.After a final loss of and H 2 molecule in Al−TS 4 and N−TS 5 , the proposed reaction pathway concludes with the final cyclic structure of Al−P 4 and N−P 5 (Al 2 N 2 H 4 ).This Al 2 N 2 H 4 species may then go on to form larger aluminum nitride clusters that potentially contribute to the nucleation and formation of dust grains in the universe.Given that the above reaction pathway contains no carbon-or oxygen-containing species, the present reaction pathway may contribute to the aluminum dust grain nucleation pathways in regions where the C/O ratio is ∼ 1.However, in oxygen-rich environments it may compete with the aluminum-oxygen pathways described in previous studies (Gail & Sedlmayr 1998, 1999;Gobrecht et al. 2022).This may not be the case for carbon-dominated environments, C/O ≥ 1, given the lack of oxygen and the aluminum-carbon motif has yet to be characterized in CSM or the ISM in any form other than AlNC.Therefore, the reaction pathway investigated in this work may assist in the potential detection of aluminum-containing dust grain nucleation species that that have gone undetected, and understudied, in the literature for decades.

Rovibrational Spectroscopic Analysis
As stated previously, some of the aluminum nitride systems investigated in this work have little-to-no previous experimental or observational data of any type.Therefore, the computed rovibrational spectroscopic constants for R 1 (AlH 3 ), I 1 (AlNH 6 ), and P 1 (AlNH 4 ) as shown in Fig. 1 reported herein are reference data necessary for laboratory analysis and potential astrophysical detection.Presently, AlH 3 and AlNH 4 have Ar matrix spectroscopic data in the  a Experimental Ar matrix FTIR spectroscopy (Chertihin & Andrews 1993).
literature, and AlNH 4 and AlNH 6 have had previous theoretical studies conducted.Several of the previous theoretical studies (Davy & Jaffrey 1995;Leboeuf et al. 1995;Marsh et al. 1992) for AlNH 4 and AlNH 6 only provide an analysis of the harmonic frequencies and their structural character.However, The work herein provides anharmonic vibrational frequencies and rotational spectroscopic constants at a more rigorous level of theory.
In order to provide a full rovibrational profile for the aluminum nitride species investigated herein, the equilibrium, vibrationally averaged, and vibrationally excited rotational constants are reported in Table 2. Also, the quartic and sextic distortion constants from the A-and S-reduced Watson Hamiltonians are given in Tables 3 and 4, respectively.Additionally, the formation pathways to larger aluminum nitride species assume the presence of AlH 3 in the same regions.As AlH 3 has not yet been observed in CSM or the ISM, perhaps a consequence of its rapid reaction with ammonia or water, the present study also provides the reference data for this species for completeness.To that end, the vibrational profile for AlH 3 , AlNH 6 , and AlNH 4 are given in Tables 5, 6, and 7, respectively.
As stated above, previous Ar matrix spectroscopic data (Chertihin & Andrews 1993) exists for AlH 3 and characterizes three of the four vibrational frequencies available, shown in Table 5.The out-of-plane bending mode, ν 2 , differs the furthest from experiment at 10 cm −1 or 1.4%.The closest to experiment is ν 4 , the H−Al−H anti-symmetric bending motion, differing by 5.7 cm −1 or 0.7%.While the F12-TZ anharmonic vibrational frequencies exhibit relatively large differences compared to experiment, it should be noted that Ar matrix spectroscopy is known to cause a shift in the true vibrational frequency (Pimentel & Charles 1963).Thus, most of the discrepancy between the current high-level quantum chemical computations and experiment should be attributed to the Ar matrix shifts.Further, previous computational studies of Al-containing species utilizing the F12-TZ methodology have produced vibrational frequencies within 0.4% of the gas-phase experimental value (Fortenberry et al. 2020).Given the higher-order, D 3h symmetry exhibited by AlH 3 the permanent dipole of this molecule is zero, thus rendering it undetectable via rotational spectroscopy.For this reason, the anharmonic vibrational frequencies computed in this work are even more crucial for potential spaced-based IR spectroscopic telescopes.
Further, AlH 3 exhibits very intense vibrational transitions with the ν 2 , out-of-plane bend being the most intense at 387 km mol −1 .Compared to the anti-symmetric stretch of H 2 O at 70 km mol −1 and CO 2 at ∼475 km mol −1 , which are both considered to be intense transitions, the present ν 2 intensity should be considered intense enough for detection via IR spectroscopy even at low concentrations.Additionally, the other vibrational fundamentals of AlH 3 with intensities of 251 and 234 km mol −1 are also substantially greater than the aforementioned stretches in water and carbon dioxide.Looking at the spectral profile, ν 4 sits at 12.67 µm putting it around the 13 µm spectral feature that is typically used as an identifier for Al 2 O 3 .While this does not really question Al 2 O 3 's presence based on spectral feature, it does posit the existence of another carrier of said spectral feature in CSM or the ISM that may be attributed to the present aluminum nitride system.Nevertheless, the computed vibrational data herein should be especially important for the detection of AlH 3 that would be supportive for confirming the reaction pathway of formation proposed in this work and from previous computational reaction pathways (Grosselin & Fortenberry 2022;Flint & Fortenberry 2023).The first intermediate, AlNH 6 , exhibits the most notable vibrational transition intensities of the two formed structures studied herein, shown in Table 6.AlNH 6 's ν 8 frequency, the H−Al−N symmetric bending motion, at 515 km mol −1 is 30 km mol −1 larger than the CO 2 motion mentioned above.Further, AlNH 6 ν 4 , ν 6 , and ν 7 exhibit transition intensities of 331, 135, and 271 km mol −1 , respectively.While AlNH 6 exhibits multiple intense vibrational transitions, due to the nature of its synthesis, it may be a short-lived species as it will likely progress to AlNH 4 or regress back to the reactants.However, even with a relatively small concentration, its intense transitions may still be seen in the IR.Rotationally, AlNH 6 also exhibits the largest permanent dipole moment of the three molecules studied, at 5.40 D. Compared to the previously detected (Tenenbaum & Ziurys 2010) AlOH molecule with a permanent dipole of 1.11 D (Fortenberry et al. 2020), AlNH 6 may be a suitable candidate for potential radioastronomical observation, but may be limited by shorter lifetimes as discussed above.Regardless, like AlH 3 , AlNH 6 also exhibits spectral features in and around the 13 µm dust feature as well as the associated 11, 20 and 28 µm.Namely, the aformentioned ν 8 frequency, with the 515 km mol −1 intensity, sits directly at 13.23 µm, as shown in Table 6.It should be noted that the midto far-IR regions where these features are located are dominated by larger dust grains than present potential grain nucleating species.Regardless, a laboratory and observational study of AlNH 6 is warranted utilizing the novel reference data provided herein in order to assist in the astrophysical detection of the first intermediate along an alternative pathway for formation for dust grains in CSM or the ISM.
The AlNH 4 molecule has both previous Ar matrix spectroscopic data (Himmel et al. 2000) and theoretical vibrational frequency computations (Watrous et al. 2021).The previous vibrational frequency studies are computed at the F12-TZ level of theory much like the rovibrational spectroscopic data provided herein.While the present computational study utilizes a normal coordinate system to compute the QFF procedure, the previous study utilizes a symmetry  (Himmel et al. 2000).b Previous F12-TZ anharmonic vibrational data (Watrous et al. 2021).
internal coordinate system that is comparable to the present normal coordinate system.Any deviation between the two methods should be considered an effect of the difference between the construction of the two coordinate systems.In any case, while, AlNH 6 contains more intense vibration transitions, AlNH 4 still exhibits exceptionally intense transitions.Shown in Table 7, the AlNH 4 molecule's most intense transition is its anti-symmetric Al−H stretching motion, ν 3 , of 257 km mol −1 .Like AlNH 6 , AlNH 4 also contains multiple intense vibrational transitions such as ν 6 , ν 8 , ν 9 , and ν 11 at 217, 145, 165, and 236 km mol −1 , respectively.Again, while most of the these transitions are less intense than AlNH 6 , the above intensities are still relatively intense suggesting AlNH 4 is a strong candidate for potential astrophysical detection utilizing IR spectroscopy.Additionally, this species may be longer-lived in its formation environment in CSM making it an even stronger candidate for astronomical observational detection, perhaps, than AlNH 6 itself.
In terms of its dipole moment, the AlNH 4 molecule's is much smaller at 1.08 D. While AlNH 4 can still be observed rotationally given a high enough column density, with such a small dipole moment AlNH 4 may be better suited for detection via high resolution IR spectroscopy which can be achieved via the JWST.Also, AlNH 4 contains multiple spectral features that fall in or around the 13 µm feature and other associated spectral lines.Specifically, ν 7 and ν 8 have wavelengths at 13.39 and 13.94 µm, respectively, shown in Table 7. Again, this suggests that more than Al 2 O 3 or the other associated suspected carriers exhibit this spectral feature, but this does suggest that species containing aluminum may contribute to the features more than initially observed or speculated.To that end, the novel vibrational spectroscopic data provided herein are necessary for further laboratory and possible astronomical observational investigations into the proposed formation pathway that will potentially assist in characterizing another potential player in dust grain formation.

CONCLUSIONS
The reaction pathway of AlH 3 and NH 3 leads to the formation of larger aluminum nitride molecular systems.This pathway must first overcome a barrier of 1.9 kcal mol −1 which is fully achievable in high temperature environments (∼1000 K) such as warmer inner protoplanetary disks and circumstellar envelopes of AGB stars, but not necessary to begin the process of formation.The rest of the pathway is submerged compared to the reactants and is available given the latent energy present in the molecular system.The final step of the presently studied pathway involves the formation of a four-membered cyclic ring that is also the only step on the pathway to have a submerged product over its preceding intermediate.Even so, the present reaction pathway provides a novel, potential formation mechanism for Al-bearing dust grains containing nitrogen as suggested in the studies of the Murchison CM2 chondritic meteorite and gives a hint at where such nucleation can take place in protoplanetary disks.
The AlNH 4 molecule investigated herein is the most likely candidate for potential astronomical observation via current rovibrational spectroscopic technologies in order to support this proposed reaction pathway.AlNH 4 contains multiple vibrational transitions with exceptionally large intensities, notably the 1895.3cm −1 frequency with the 257 km mol −1 intensity and the 442.9 cm −1 frequency with the 236 km mol −1 intensity.While AlNH 4 has a smaller dipole moment of 1.08 D, if there is sufficient column density, this species should still be observable utilizing current radioastronomical telescopes.The rovibrational analysis of AlNH 6 suggests that the most intense vibrational transition studied here is the 515 km mol −1 intensity corresponding to the 755.7 cm −1 frequency.Additionally, the 5.40 D dipole moment feature calculated is the largest of the three studied.However, given the AlNH 6 molecule's likely shorter timescales within the reaction pathway, it may not be a suitable candidate for rovibrational detection in CSM or the ISM.The AlH 3 molecule also exhibits exceptionally intense vibrational transitions, especially the 707.8 cm −1 frequency with an intensity of 387 km mol −1 .Like the AlNH 6 molecule, the AlH 3 molecule may react too quickly, with ammonia, water, or other circumstellar or interstellar denizens before it can be detected.However, the spectral features give it a strong chance of observation with JWST.That being said, while all three species contain strong IR features and some strong rotational features, AlNH 4 may be the most likely candidate for potential astronomical observation.
The three Al-containing molecules studied in the present work contain vibrational frequencies that fall in or around the 13 µm spectral feature attributed to Al−O class of molecules.Additionally, the computed vibrational profile shows the presence of vibrational frequencies at the associated 11, 20, and 28 µm carrier features.The spectral features found in the present Al-containing species imply that dust containing some form of aluminum oxide may not be the only source of the 13 µm dust feature, and the aluminum nitride species studied herein may provide other alternative answers to the question of the origins of such features.These computed vibrational analyses warrant further laboratory, theoretical, and observational investigations into the present reaction profile and other, higher-order aluminum nitride clusters.These investigations will assist in the search for Al-containing species that may be present in CSM and the ISM, but have been uncharacterized and understudied in the present literature.

Figure 1 .
Figure 1.Reaction coordinate diagram from AlH3 and NH3 to N− and Al−P2.The arrowed lines indicate isomerization, the circular lines indicate H2 departure, the starred lines indicate NH3 addition, and the squared lines indicate AlH3 addition.Relative energies are in kcal mol −1 .White atoms indicate H, blue atoms indicate nitrogen, and grey beige indicate Al.

Figure 2 .
Figure 2. The continued reaction coordinate diagram from N− and Al−P2 to cyclic-Al2N2H4.The arrowed lines indicate isomerization, the circular lines indicate H2 departure, the starred lines indicate NH3 addition, and the squared lines indicate AlH3 addition.Relative energies are in kcal mol −1 .White atoms indicate H, blue atoms indicate nitrogen, and grey beige indicate Al.

Table 1 .
Symbol definitions and chemical formulae for the species in the present reaction pathway.

Table 3 .
Quartic and sextic distortion constants in the Watson A-reduced Hamiltonian for AlNH4 and AlNH6

Table 4 .
Quartic and sextic distortion constants in the Watson S-reduced Hamiltonian for AlH3, AlNH4, and AlNH6