Gas-phase Synthesis of Silaformaldehyde (H₂SiO) and Hydroxysilylene (HSiOH) in Outflows of Oxygen-rich Asymptotic Giant Branch Stars

The gas-phase reaction of the D1-silylidyne radical (SiD; X²Π) with D2-water (D₂O; X¹ A₁) was studied under single-collision conditions in a crossed molecular beam machine (Yang et al. 2021). Considering the natural isotope abundances of silicon (²⁸Si: 92.23%; ²⁹Si: 4.67%; ³⁰Si: 3.10%), the reactive scattering signal was collected at a mass-to-charge (m/z) of m/z = 48 and 46, which are related to the potential products upon the emission of atomic (²⁸SiD₂O⁺: m/z = 48; reaction (1)) and molecular deuterium (²⁸SiDO⁺: m/z = 46; ³⁰SiDO⁺: m/z = 48; reaction (2)) and fragments generated via dissociative electron impact ionization of the parent molecule leading to ²⁸SiDO⁺ (m/z = 46). Time-of-flight (TOF) spectra were accumulated for up to 96 hr at each angle with ion counts at m/z = 46 emerging at a level of 50% ± 3% compared to m/z = 48. These TOF spectra are superimposable after scaling (Figure A1); along with the isotopic substitution pattern, this finding suggests the existence of a single reaction channel, i.e., the reaction of the D1-silylidyne radical (SiD; X²Π) with D₂O forming SiD₂O isomer(s)—predominantly via the reaction of ²⁸SiD—along with the emission of atomic deuterium (D; 2 amu), yielding the signal at m/z = 48 (²⁸SiD₂O, hereafter SiD₂O). The signal at m/z = 46 originates from dissociative electron impact ionization of the parent molecules. Consequently, the laboratory data suggest that the reaction of the D1-silylidyne radical (SiD; X²Π) with D₂O involves the formation of SiD₂O isomer(s) via the atomic deuterium emission. The resulting TOF spectra and the full laboratory angular distributions were collected at the best signal-to-noise ratio at m/z = 48 (SiD₂O⁺; Figure 2). This distribution is almost forward–backward symmetric around the center-of-mass (CM) angle of 433 (Table A1) and spans a scattering angular range from 283 to 583. These results indicate that the reaction proceeds via indirect scattering dynamics involving the existence of SiD₃O intermediate(s) that ultimately dissociate to SiD₂O via atomic deuterium emission (Levine 2005). Note that, accounting for distinct recoil circles for the atomic and molecular deuterium loss channels (Figure A2), the ratio of the ion counts at m/z = 48 (reaction (1)) versus 46 (reaction (2)) is determined to be 1 (m/z = 48):0.04 ± 0.01 (m/z = 46). This may explain that the products of reaction (2) cannot be detected under our experimental conditions compared with the already weak scattering signal for reaction (1):

$$\begin{eqnarray}&&\begin{array}{c}\begin{array}{l}{}^{28}{\rm{S}}{\rm{i}}{\rm{D}}(30\,{\rm{a}}{\rm{m}}{\rm{u}})+{{\rm{D}}}_{2}{\rm{O}}(20{\rm{a}}{\rm{m}}{\rm{u}})\\ \,\,\to \,{}^{28}{{\rm{S}}{\rm{i}}{\rm{D}}}_{3}{\rm{O}}(50{\rm{a}}{\rm{m}}{\rm{u}})\to {}^{28}{{\rm{S}}{\rm{i}}{\rm{D}}}_{2}{\rm{O}}\\ \,\,\\ (48{\rm{a}}{\rm{m}}{\rm{u}})+{\rm{D}}(2{\rm{a}}{\rm{m}}{\rm{u}}),\end{array}\end{array}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\begin{array}{l}{}^{28}{\rm{S}}{\rm{i}}{\rm{D}}(30{\rm{a}}{\rm{m}}{\rm{u}})+{{\rm{D}}}_{2}{\rm{O}}(20{\rm{a}}{\rm{m}}{\rm{u}})\\ \,\,\to \,{}^{28}{{\rm{S}}{\rm{i}}{\rm{D}}}_{3}{\rm{O}}(50{\rm{a}}{\rm{m}}{\rm{u}})\to {}^{28}{\rm{S}}{\rm{i}}{\rm{D}}{\rm{O}}(46{\rm{a}}{\rm{m}}{\rm{u}})\\ \,\,+\hspace{0.15cm}{{\rm{D}}}_{2}(4{\rm{a}}{\rm{m}}{\rm{u}}).\end{array}\end{eqnarray} \tag{ 2 }$$

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Our primary objective is to explore the nature of the SiD₂O isomer(s) along with the underlying reaction mechanism(s) on the pertinent SiD₃O potential energy surface(s) (PESs) accessed through the bimolecular reaction of the D1-silylidyne radical (SiD; X²Π) with D₂O. To reach these goals, a forward convolution of the laboratory data into the CM reference frame generates the CM translational energy P(E_T ) and angular T(θ) flux distributions (Figure 3; Yang et al. 2021) via a transformation of the laboratory data to the CM frame. Within our error limits, the resulting best-fit CM functions (Figure 3) were achieved using a single channel of the product mass combination of 48 amu (SiD₂O) plus 2 amu (D). The resulting CM translational energy distribution P(E_T ) reveals a maximum translational energy release (E_max) of 37 ± 10 kJ mol⁻¹. Considering the energy conservation, the maximum translational energy (E_max), collision energy (E_C ), and reaction energy (Δ_r G) are connected via E_max = E_C – Δ_r G with regard to the molecules born without rovibrational excitation. Therefore, the reaction energy is calculated to be −10 ± 10 kJ mol⁻¹. Furthermore, the P(E_T ) distribution peaked away from zero translational energy at 19 ± 5 kJ mol⁻¹, suggesting a tight exit transition state leading to SiD₂O molecules from the SiD₃O intermediates (Levine 2005). Further, the average translational energy of the products was derived to be 18 ± 5 kJ mol⁻¹, suggesting that 49% ± 13% of the available energy is transformed into the translational degrees of freedom of the products. Finally, the resulting CM angular distribution T(θ) depicts nonzero intensity over the complete scattering range from 0° to 180°, proposing indirect scattering dynamics via the formation of SiD₃O complex(es); the forward–backward symmetry of T(θ) implies that the lifetime of the decomposing SiD₃O complex is longer than the rotational period(s) (Miller et al. 1967).

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The electronic structure calculations identified the existence of two distinct SiDO isomers (p1–p2) that may be produced via molecular deuterium loss; further, four SiD₂O isomers (p3–p6) were identified that can be accessed through atomic deuterium emission (Figure 4). Our computations suggest that the reaction is initiated by the barrierless formation of a complex i1, which is stabilized by 50 kJ mol⁻¹ with respect to the separated reactants and bound through a dative bond formed by donation of the lone oxygen atom to the empty p orbital of Si. This complex isomerizes via deuterium migration from the oxygen atom of the water to the SiD moiety, leading to the hydroxy-d3-silyl radical (D₂SiOD, i2, X¹A') with an inherent barrier of 32 ± 5 kJ mol⁻¹. The hydroxy-d3-silyl radical represents the global minimum of the SiD₃O PES. Our calculations also identified that a molecular deuterium loss from i1 yields the product hydroxy-d-silylidyne (SiOD, p1, X¹A', Δ_r G = −131 ± 5 kJ mol⁻¹) with an inherent barrier of 27 ± 5 kJ mol⁻¹. Intermediate i1 can emit atomic deuterium from the silicon atom, forming a van der Waals complex silicon-D2-water (SiOD₂, p6, ³A'', Δ_r G = 256 ±5 kJ mol⁻¹) in an overall endoergic reaction. The products trans-d2-hydroxysilylene (t-DSiOD, p4, X¹A', Δ_r G = −5 ± 5 kJ mol⁻¹) and cis-d2-hydroxysilylene (c-DSiOD, p5, X¹A', Δ_r G = −5 ± 5 kJ mol⁻¹) can also be produced via atomic deuterium loss from i1 with transition states located 79 and 86 kJ mol⁻¹ above the separated products, respectively. Note that the pathways i1 → p4/p5 are not competitive due to the transition states ranging well above our collision energy of 27.3 ± 0.5 kJ mol⁻¹, which cannot be overcome under our experimental conditions. Intermediate i2 can isomerize via a deuterium shift from the oxygen atom to the silicon atom, yielding the d3-silyloxy intermediate (D₃SiO, i3, ¹A') via a barrier of 188 kJ mol⁻¹ above intermediate i2. The product hydroxy-d-silylidyne (SiOD, p1, X¹A') can be accessed via molecular deuterium loss from i2 via a tight exit transition barrier lying 100 kJ mol⁻¹ above the separated products, while the products d2-silaformaldehyde (D₂SiO, p3, X¹A', Δ_r G = −8 ± 5 kJ mol⁻¹), trans-d2-hydroxysilylene (t-DSiOD, p4, X¹A', Δ_r G = −5 ± 5 kJ mol⁻¹), and cis-d2-hydroxysilylene (c-DSiOD, p5, X¹A', Δ_r G = −5 ± 5 kJ mol⁻¹) can be formed via atomic deuterium loss from i2. Here the formation of d2-silaformaldehyde (D₂SiO, p3) occurs via an exit barrier of 18 kJ mol⁻¹, whereas p4 and p5 are produced via loose transition states without distinct exit barriers. The decomposition of i3 yields the product oxo-silyl-d (DSiO, p2, ¹A', Δ_r G = −95 ± 5 kJ mol⁻¹) via a molecular deuterium loss from i3 via a tight exit transition state lying 96 kJ mol⁻¹ above the separated products. The product d2-silaformaldehyde (D₂SiO; p3) can be formed via atomic deuterium emission from i3 via a loose transition state.

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We are now merging our experimental findings with the results from the ab initio calculations to propose the underlying reaction mechanism(s) along with the chemical dynamics of the reaction. The experimentally derived reaction energy of −10 ± 10 kJ mol⁻¹ is in good agreement with our computed value for an exoergic reaction of −8 ± 5 and −5 ± 5 kJ mol⁻¹ to synthesize the d2-silaformaldehyde (D₂SiO, p3, Δ_r G = −8 ± 5 kJ mol⁻¹), trans-d2-hydroxysilylene (t-DSiOD, p4, Δ_r G = −5 ± 5 kJ mol⁻¹), and/or cis-d2-hydroxysilylene (c-DSiOD, p5, Δ_r G = −5 ± 5 kJ mol⁻¹) along with atomic deuterium. The silicon-D2-water complex (SiOD₂, p6, Δ_r G = 256 ± 5 kJ mol⁻¹) is energetically not available considering the collision energy (E_C ) of 27.3 kJ mol⁻¹. Consequently, we deduce that the d2-silaformaldehyde (D₂SiO; p3), trans-d2-hydroxysilylene (t-DSiOD; p4), and/or cis-d2-hydroxysilylene (c-DSiOD; p5) are formed in the crossed molecular beam reaction of the D1-silylidyne radical (SiD; X²Π) with D₂O. The reaction of the D1-silylidyne radical (SiD; X²Π) with D₂O proceeds via indirect scattering dynamics (complex forming reaction) and is initiated with the formation of a bound dative complex i1. The collision complex i1 undergoes atomic deuterium migration to i2, with the latter ejecting a deuterium atom to form the products d2-silaformaldehyde (D₂SiO, p3, X¹A', Δ_r G = −8 ± 5 kJ mol⁻¹), trans-d2-hydroxysilylene (t-DSiOD, p4, X¹A', Δ_r G = −5 ± 5 kJ mol⁻¹), and/or cis-d2-hydroxysilylene (c-DSiOD, p5, X¹A', Δ_r G = −5 ± 5 kJ mol⁻¹). The product d2-silaformaldehyde (D₂SiO, p3, X¹A', Δ_r G = −8 ± 5 kJ mol⁻¹) can also be formed via the atomic deuterium emission from intermediate i3, which stems from the deuterium shift from the OD group to SiD₂ moiety in i2. It is instructive to compare the present results of the electronic structure calculations on the SiH₃O PES with those reported by Zachariah & Tsang (1995), who explored the thermochemistry, energetics, and kinetics of high-temperature Si_xH_yO_z reactions at the BAC-MP4 level of theory including, in particular, unimolecular decomposition of H₂SiOH and H₃SiO and its reverse reactions, although the SiH + H₂O channel was not considered in either direction. The agreement appears to be rather close, as the average unsigned difference in the relative energies of various species and barrier heights is only 6 kJ mol⁻¹, and the maximal deviation is 14 kJ mol⁻¹.

To assess to what extent p3–p5 could be formed in this experiment, we calculated the statistical yields of products p1–p6 using Rice–Ramsperger–Kassel–Marcus (RRKM) theory (Table A3). These studies reveal that d2-silaformaldehyde (D₂SiO, p3), trans-d2-hydroxysilylene (t-DSiOD, p4), and cis-d2-hydroxysilylene (c-DSiOD, p5) contribute 25%, 26%, and 49%, respectively, at E_C = 27.3 kJ mol⁻¹. For the product d2-silaformaldehyde (D₂SiO, p3), dissociation from i2 and i3 supplies 2% and 23%, respectively. Since the isomerization of i1 to i2 is a key link to form the products d2-silaformaldehyde (D₂SiO, p3), trans-d2-hydroxysilylene (t-DSiOD, p4), and cis-d2-hydroxysilylene (c-DSiOD, p5) along with the atomic deuterium, it is critical to recall that a fit of the experimental data had to be obtained via the combination of a reaction threshold of 27–32 kJ mol⁻¹ with the fitting routine. In the fitting program, the collision energy (E_C) and velocity distribution of each supersonic beam f(v_i ), with i being the primary SiD and secondary D₂O beam, are defined by

$$\begin{eqnarray}&&{E}_{C}=\ \displaystyle \frac{1}{2}\mu {\nu }_{r}^{2},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\mu =\displaystyle \frac{{m}_{\mathrm{SiD}}\ast \ {m}_{{{\rm{D}}}_{2}{\rm{O}}}}{{m}_{\mathrm{SiD}}+{m}_{{{\rm{D}}}_{2}{\rm{O}}}},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{\nu }_{r}^{2}={v}_{\mathrm{SiD}}^{2}+{v}_{{{\rm{D}}}_{2}{\rm{O}}}^{2},\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&f\left({v}_{\mathrm{SiD}}\right)\propto \ {v}_{\mathrm{SiD}}^{2}\exp \left(-{\left(\displaystyle \frac{{v}_{\mathrm{SiD}}}{{\alpha }_{\mathrm{SiD}}}-{S}_{\mathrm{SiD}}\right)}^{2}\right)\ ,\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&f\left({v}_{{{\rm{D}}}_{2}{\rm{O}}}\right)\propto \ {v}_{{{\rm{D}}}_{2}{\rm{O}}}^{2}\exp \left(-{\left(\displaystyle \frac{{v}_{{{\rm{D}}}_{2}{\rm{O}}}}{{\alpha }_{{{\rm{D}}}_{2}{\rm{O}}}}-{S}_{{{\rm{D}}}_{2}{\rm{O}}}\right)}^{2}\right)\ ,\end{eqnarray} \tag{ 7 }$$

with the relative velocity ν_r , velocity v_i , reduced mass μ, mass of the reactant m, velocity v_i , speed ratio S_i , α_i = (2kT/m_i)^1/2, temperature of the beam T, and Boltzmann's constant k. The fitting program convolutes over the apparatus functions including the velocity distributions and the velocity spreads. The corresponding relative velocity peaked at 2133 m s⁻¹, yielding a peak collision energy of E_C = 27.3 ± 3.4 kJ mol⁻¹. Considering the computed barrier of the reaction connecting i1 and i2 of 32 ± 5 kJ mol⁻¹, around 50% of the collisions are sufficiently high to overcome this isomerization barrier. The resulting reaction cross section (σ) increases as the collision energy increases (Equation (8)), with E₀ denoting the inherent barrier to the reaction as derived from the line-of-center model (Kaiser et al. 1996; Alagia et al. 2000):

$$\begin{eqnarray}&&\sigma \propto 1-\displaystyle \frac{{E}_{0}}{{E}_{C}}.\end{eqnarray} \tag{ 8 }$$

Laboratory investigations of these products are rare. Bogey et al. determined the structure of H₂SiO by rotational submillimeter-wave spectra (Bogey et al. 1996). The experimental results suggest that the bond lengths and angles were Si = O 1.515 Å, Si–H 1.472 Å, and <H–Si–H 1120. The Si = O stretching frequency was identified as 1202 cm⁻¹ via infrared spectroscopy of H₂SiO in an argon (Ar) matrix (Withnall & Andrews 1985). A frequency of 697 cm⁻¹ is also obtained, which is assigned to the SiH₂ wag or SiH₂ rock. Our calculations reveal that, for the H₂SiO molecule, the bond lengths of Si = O and Si–H are 1.528 and 1.483 Å (Figure 1), respectively, along with the <H–Si–H of 1114, and the Si = O stretching frequency in H₂SiO is 1217 cm⁻¹ (Table A7). These experimental identified structure parameters of the H₂SiO molecule are well reproduced in our calculation. Margrave and coworkers performed the reaction of silicon atoms with water in a solid argon matrix at a low temperature of 15 K (Ismail et al. 1982). The final products are confirmed as trans- and cis-HSiOH via the infrared spectrum. The trans-HSiOH carries Si–O, Si–H, and O–H bond lengths of 1.591 ± 0.100, 1.521 ± 0.030, and 0.958 ± 0.005 Å and <H–Si–O and <Si–O–H of 966 ± 40 and 1145 ± 6°, respectively. The frequencies of the H–O bond stretch, H–Si bond stretch, HSiO bending, Si–O bond stretch, SiOH bending mode, and out-of-plane torsion mode of trans-HSiOH are 3650.0, 1872.3, 937.0, 850.6, 722.6, and 659.1 cm⁻¹, respectively. Furthermore, the observed frequencies (cm⁻¹) of HSiOD, DSiOD, HSi¹⁸OH, HSi¹⁸OD, and DSi¹⁸OD are also included in this study. Our best computed geometry for HSiOH (Figure 1, Table A7) agrees within these experimental errors.

The gas-phase reaction of the D1-silylidyne radical (SiD; X²Π) with D2-water (D₂O; X¹ A₁) was studied under single-collision conditions using a universal crossed molecular beam machine at the University of Hawai'i at Manoa (Kaiser et al. 2010; Yang et al. 2018). In the primary source chamber, a pulsed supersonic D1-silylidyne beam was produced in situ by laser ablation of a rotating silicon rod at 266 nm, 4 ± 1 mJ pulses (Spectra-Physics Quanta-Ray Pro 270 Nd:YAG laser; 30 Hz), and seeding the ablated species in a gas mixture of deuterium gas (D₂, 99.7%; Icon Isotopes, Inc.) and neon (Ne, 99.999%; Specialty Gases of America) with a ratio of 1:1 and a total pressure of 4 atm. Since the silicon atom has natural isotope abundances (²⁸Si, 92.23%; ²⁹Si, 4.67%; ³⁰Si, 3.10%), the intensity optimization of the D1-silylidyne beam was conducted at m/z = 31, and no higher molecular weight silicon-/deuterium-bearing species were detected. Although the supersonic beam carries some ground-state silicon atoms (Si(³P)), these silicon atoms (Si(³P)) were found not to react with D2-water under our experimental conditions. The D1-silylidyne beam passed through a skimmer and was velocity-selected by a four-slit chopper wheel, resulting in a well-defined peak velocity (v_p ) and speed ratio (S) of 1235 ± 30 m s⁻¹ and 8.2 ± 2.0 (Table A1), respectively. In the secondary source chamber, the pulsed supersonic beam of D₂-water (D₂O, 99.9%; Sigma-Aldrich) seeded in helium (99.9999%; Airgas) at a fraction of 5% at 550 torr with a peak velocity of v_p = 1738 ± 5 m s⁻¹ and a speed ratio of S = 18.8 ± 0.5 crossed perpendicularly with the primary D1-silylidyne beam in the main chamber. This resulted in a collision energy (E_C) of 27.3 ± 0.5 kJ mol⁻¹ and a CM angle (Θ_CM) of 432 ± 07 (Table A1). Each supersonic beam was released by a piezoelectric pulsed valve that was operated at 60 Hz, a pulse width of 80 μs, and a peak voltage of −400 V. Note that even if D1-silylidyne radicals in the A²Δ state are formed initially, taking into account the short lifetime of around 500 ns (Bauer et al. 1984), they will decay to the ground-state X²Π during a travel time of about 18 μs to the interaction region in the main chamber.

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The neutral reaction products (Figure A1 and Figure A2) entering the detector were ionized by an electron impact ionizer (80 eV; Yang et al. 2018), then filtered according to the mass-to-charge ratio (m/z) utilizing a quadrupole mass spectrometer (Extrel, QC 150) and eventually recorded by a Daly-type ion counter (Yang et al. 2018). The detector is housed within a triply differentially pumped and rotatable chamber that allows the collection of angularly resolved TOF spectra in the plane defined by both reactant beams. To obtain the information on the reaction dynamics, a forward-convolution method was used to transform the laboratory frame data into the CM frame (Yang et al. 2018), which represents an iterative method whereby user-defined CM translational energy P(E_T ) and angular T(θ) flux distributions are varied iteratively until a best fit of the laboratory frame TOF spectra and angular distributions is achieved. These functions comprise the reactive differential cross section I(θ, u), which is taken to be separable into its CM scattering angle θ and CM velocity u components, I(u, θ) ∼ P(u) × T(θ). The error ranges of the P(E_T ) and T(θ) functions are determined within the 1σ limits of the corresponding laboratory angular distribution and beam parameters (beam spreads, velocities) while maintaining a good fit to the laboratory TOF spectra.

Geometries of the reactants, products, intermediates, and transition states involved in the silylidyne reaction with water were optimized using the hybrid B3LYP (Becke 1993) density functional theory (DFT) method with the 6-311G(d,p) basis set (Table A7). Vibrational frequencies of all species were computed at the same B3LYP/6-311G(d,p) level of theory, taking into account the particular isotopic composition of the ²⁸Si¹⁶OD₃/²⁸Si¹⁶OH₃ species involved in the SiD + D₂O/SiH + H₂O reactions, respectively. For the reactants and critical transition states involved in the pathways for molecular hydrogen loss from the dative complex i1 (i1 → p1) and H atom migration in this complex (i1 → i2), geometry optimization was also carried out at the doubly hybrid DFT B2PLYPD3/6-311G(d,p) level of theory (Goerigk & Grimme 2011) incorporating a dispersion correction (Grimme et al. 2011) and at the coupled clusters CCSD/6-311G(d,p) level (Scuseria & Schaefer 1989). For the B2PLYPD3/6-311G(d,p) optimized structures, the vibrational frequencies were recalculated using the same method. Single-point energies were subsequently improved at the explicitly correlated coupled cluster CCSD(T)-F12 level (Knizia et al. 2009) with single and double excitations and perturbative treatment of triple excitations. The CCSD(T)-F12 calculations were carried out with the cc-pVQZ-f12 basis set (Dunning 1989) for most structures, whereas for the critical transition states i1 → p1 and i1 → i2, additional CCSD(T)-F12/cc-pVTZ-f12 calculations were also performed, and the energies were then extrapolated to the complete basis set (CBS) limit using the two-point formula, E_CBS = E_cc-pVQZ-f12 + (E_cc-pVQZ-f12 – E_cc-pVTZ-f12) × 0.69377 (Martin & Uzan 1998). For the reactants and the two critical transition states, the CCSD(T)-F12/CBS energies were calculated not only for B3LYP but also for B2PLYPD3 and CCSD optimized geometries. For these species, the energies were further refined by taking into account the core electron correlation effects via CCSD(full,T)-F12 calculations with the cc-pCVTZ-f12 and cc-pCVQZ-f12 basis sets (Hill et al. 2010) extrapolated to the CBS limit, which included all core electrons except 1 s of Si atoms in the correlation treatment. Finally, anharmonicity corrections to zero-point vibrational energies were evaluated through calculations of anharmonic frequencies at the B3LYP/6-311G(d,p) level of theory using vibrational perturbation theory to the second order (VPT2) (Barone 2005). The B3LYP and B2PLYPD3 calculations, CCSD geometry optimizations, and VPT2 computations of anharmonic frequencies were performed using the GAUSSIAN 09 package (Frisch et al. 2009), whereas the CCSD(T)-F12 calculations were carried out employing MOLPRO 2010 (Werner et al. 2010). It should be noted that the relative CCSD(T)-F12/CBS energies of the i1 → p1 and i1 → i2 transition states including the core correlation and anharmonic ZPE corrections with their geometries optimized using B3LYP, B2PLYPD3, and CCSD agreed with the CCSD(T)-F12/cc-pVQZ-f12//B3LYP/6-311G(d,p) + harmonic ZPE(B3LYP/6-311G(d,p)) energies within 1 kJ mol⁻¹.

Product branching ratios in the SiD + D₂O reaction under single-collision conditions and at the experimental collision energy of 27.3 kJ mol⁻¹ were evaluated using RRKM calculations (Steinfeld et al. 1982) of unimolecular rate constants for the reaction steps beginning with the i2 intermediate. Here the rate constants were evaluated as functions of the available internal energy of each intermediate or transition state within the harmonic approximation using B3LYP/6-311G(d,p) frequencies, with the internal energy assumed to be equal to the chemical activation energy, that is, negative of the relative energy of a species with respect to the reactants, plus the collision energy. Only one energy level was considered throughout at a zero-pressure limit reproducing the conditions in crossed molecular beams. For the H elimination reaction steps occurring via loose transition states without distinct exit barriers (i2 → p4/p5 and i3 → p3), variational RRKM theory (Steinfeld et al. 1982) was employed. Here the minimal energy reaction paths (MEPs) were scanned at the B3LYP/6-311G(d,p) level along the bond distances for the breaking Si–H bonds with all other geometric parameters being optimized. Vibrational frequencies for the optimized structures were then computed at the same level of theory, with the normal mode corresponding to the reaction coordinate projected out. Single-point energies of these MEP structures were recomputed at CCSD(T)-F12/cc-pVQZ-f12. These structures were then considered as transition-state candidates, and rate constants for the H losses from i2 and i3 were evaluated with these candidates. In each case, the minimal rate constant was selected as the true rate constant corresponding to a particular collision energy. The conventional and variational RRKM rate constants were used to evaluate product branching ratios by solving first-order kinetic equations within steady-state approximation (Kislov et al. 2004). It should be noted that from the dative complex i1, the reaction flux can branch not only to i2 but also to p1, thus increasing the yield of this product. However, since the predicted energies of the i1 → p1 and i1 → i2 transition states are within our expected error bars of ±5 kJ mol⁻¹ from the experimental collision energy and the D₂ loss product could not be experimentally detected, we did not consider the i1 → p1 pathway in the present calculations, keeping in mind that the computed yield of p1 (Table A3) is likely underestimated.

Additionally, RRKM master equation (ME) calculations (Fernández-Ramos et al. 2006) were carried out to evaluate temperature-dependent total and individual product channel rate constants for the SiH + H₂O reaction in the temperature range from 300 to 3000 K in the limit of zero pressure (Table A2 and Table A4). The MESS program package (Georgievskii et al. 2013; Georgievskii & Klippenstein 2015) was used for the calculations where the rigid rotor-harmonic oscillator approximation was employed in the evaluation of partition functions. All channels on the PES depicted in Figure 4 were included in the RRKM ME calculations, excluding only the highly unfavorable p6 + H route. Rate constants for the barrierless H elimination channels were assessed using variational RRKM theory as described above. For the astrochemical modeling, the initial fractional abundances of parent molecules and radial column densities for our models are reflected in Tables A5 and A6, respectively.