Computational Thermochemistry of Mono- and Dinuclear Tin Alkyls

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Computational Thermochemistry of Mono- and Dinuclear Tin Alkyls Used in Vapor Deposition Processes Robin P. Harkins, Christopher J. Cramer,* and Wayne L. Gladfelter* Department of Chemistry, University of MinnesotaTwin Cities, Minneapolis, Minnesota 55455, United States

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S Supporting Information *

ABSTRACT: Hexamethylditin has been reported to be a more effective precursor compared to monotin analogs in hybrid molecular beam epitaxy depositions of perovskite oxides. To understand the differences, a library of 68 monotin- and ditincontaining molecules bearing hydrido and/or carbon-based ligands was generated, and their structures were optimized using density functional theory. On the basis of a modified W1-F12 composite thermochemical method, thermochemical data (enthalpy of formation, entropy, and heat capacity) were calculated for each structure over a range of temperatures (298− 5000 K). The application of the modified W1-F12 method to heavy element compounds was benchmarked against existing experimental and computational studies of mononuclear hydrido, alkyl, and mixed hydridoalkyl complexes of silicon, germanium, and tin. The library of thermodynamic data was used in partial equilibrium calculations from 300 to 1500 K to determine gas phase compositions resulting from the pyrolysis of tetramethyltin and hexamethylditin at 10−6 and 760 Torr.

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INTRODUCTION

Monotin alkyls have been studied for their role in SnO2 chemical vapor deposition (CVD) mechanisms.18,19 Early pyrolysis experiments on Me4Sn led to suggested mechanisms involving either an initial loss of a methyl group resulting in Me3Sn and a methyl radical or a reductive elimination of ethane and formation of Me2Sn.20−22 In studies of the atmospheric pressure deposition of SnO2 starting from Me4Sn and O2, Gordon and co-workers found that the loss of a methyl group initiated radical chain reactions ultimately leading to SnO2 deposition.18 Studies by Allendorf and coworkers showed similar results for related tin alkyl chloride precursors.23 They reported that in the CVD of SnO2 using the precursors dimethyltin dichloride and monobutyltin trichloride, both mechanisms include an alkyltin bond-breaking initiation step followed by formation of an important tin hydroxide intermediate. The publications by the Gordon and Allendorf groups emphasize that accurate enthalpies of formation and bond dissociation energies are important in understanding the kinetic pathways that describe these deposition reactions. In the absence of experimental thermochemical data for alkyltin molecules and fragments, such quantities can be calculated using computational chemistry methods.24 Several multilevel wave function theory based methods have been developed specifically for the accurate calculation of molecular

Volatile tin compounds have been widely used as precursors to deposit films of tin oxide for diverse applications including coatings of architectural glass,1 glass containers,2 electrooptical devices,3,4 and sensors.5,6 Tin tetrachloride7 and mixed alkyl chlorides8,9 including monobutyltin trichloride10 are among the precursors widely used in chemical vapor deposition processes for such applications. Many of the above precursors have also been demonstrated effective for depositing thin tin oxide films using atomic layer deposition methods.11,12 In a more recent, related application, Jalan and co-workers used tin organometallics in a hybrid molecular beam epitaxy process to deposit single crystal perovskite films of barium and strontium stannates.13,14 Like SnO2, BaSnO3 and SrSnO3 are transparent semiconductors that when doped exhibit high carrier mobilities.15−17 The substitution of a molecular precursor as a tin source in place of a traditional Knudsen cell provided improved beam stability, but the choice of precursor played a critical role in achieving the ideal film stoichiometry.13 Even with an excess flux of tetraethyltin, a 1:1 Sn to Ba ratio could not be achieved. Films comprising Sn to Ba ratios exceeding unity, however, were formed using hexamethylditin (Me6Sn2). Even more importantly, use of Me6Sn2 led to depositions in which the ideal Sn to Sr (or Ba) ratio was self-regulating. These observations prompted us to consider a more detailed study of the species contributing to the deposition process using computational methods. © XXXX American Chemical Society

Received: December 15, 2018 Revised: January 26, 2019

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DOI: 10.1021/acs.jpca.8b12072 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A enthalpies of formation.25−31 Many of these methods make use of basis set extrapolation in which in addition to the HF energy, separate contributions to the correlation energy (e.g., at the coupled cluster level of theory including contributions from all single and double excitations (CCSD) as well as a perturbative estimate for the effect of triple excitations (T)) are extrapolated to the complete basis set (CBS) limit using known extrapolation schemes.32 Additional calculations account for contributions to the electronic energy associated with core−electron correlation, scalar relativistic effects, and spin−orbit coupling, all of which must be addressed in order to predict enthalpies of formation with near quantitative accuracy.31 An alternative approach that has been used to compute enthalpies of formation for alkyltin molecules is the bond additivity correction (BAC) method.33−35 In a BAC calculation, the electronic energy is obtained at some reasonably well correlated level of electronic structure theory (e.g., fourth-order perturbation theory (MP4)), and corrections to the ultimate enthalpy of formation are made for each bond present in the molecule based on parameters and functional forms optimized against experimental data; additional parameters are included to address spin contamination in unrestricted Hartree−Fock calculations. The BAC approach thus assumes there is a systematic and transferable error in the electronic energy associated with each type of bond in the molecule. Allendorf has shown this approach to lead to predictions of enthalpies of formation accurate to ±2−5 kcal/ mol for a range of mononuclear organotin molecules.36 As an empirical model, the BAC method relies on well-characterized reference compounds from which the individual bond corrections are derived. In this study, we adopt a method that significantly reduces the impact of empirical parameters in order to avoid complications associated with uncertainties in available experimental data for alkyltin molecules. We chose the W1F12 method based on its documented ability to calculate enthalpies of formation accurate to within ∼1 kcal/mol for molecules containing first and second row atoms.37 Importantly, this method reduces the number of empirical parameters found in standard W1 calculations, and indeed W1-F12 calculations only contain molecule-independent empirical factors used in the basis set extrapolation schemes.38 Because the W1-F12 method was originally designed for molecules containing first and second row atoms, application of this method to heavier elements requires additional definition of the model. Peterson et al. developed pseudopotential-based basis sets for the heavy main group elements for use in explicitly correlated calculations where all electron basis sets would become too computationally costly.39 We used this basis set for Sn and included experimental atomic spin−orbit coupling values for the W1-F12 calculations in lieu of explicit calculation of relativistic effects and spin−orbit coupling from the W1-F12 protocol. In the following we show this approach to deliver good accuracy against benchmark data. We additionally compute structures and thermochemical data for 68 mono- and ditin species bearing hydride and carbon-based ligands and use them to determine equilibrium concentrations of these species in the gas phase as a function of temperature and pressure.

functional41 and an ultrafine grid (the method defined for use in W1 and W2 theory38). For all optimizations, the cc-pVTZ basis set42 was used for H and C atoms and the cc-pVTZ-PP basis set for tin.43,44 Stationary points were confirmed as minima based on analytical frequency calculations having zero imaginary frequencies. For structures with no methyl groups, thermodynamic properties were obtained using the default ideal-gas/rigid-rotator/harmonic-oscillator approximation. For structures containing methyl groups, thermodynamic properties were obtained using the multistructural approximation with torsional anharmonicity.45,46 Explicitly correlated calculations47,48 were performed with the Molpro electronic structure package49 using density fitting50,51 to increase computational efficiency. Thermochemical calculations on all fragments were based on the explicitly correlated W1-F12 method as detailed by Karton and Martin37 with some modifications. In particular, relativistic effects and second order spin−orbit coupling terms were not explicitly included in calculation of the atomization energies. Rather, scalar relativistic effects were accounted for in the Sn pseudopotential43 and the spin-orbit correction used for Sn was the experimental value of 0.42 eV.52 In the W1-F12 calculations, the cc-pVnZ-F12 basis sets of Peterson et al. were used for carbon and hydrogen, while the cc-pVnZ-PP-F12 basis sets were used for tin, where PP indicates the small-core relativistic pseudopotential (28 electrons).39,43,53 The cc-pwCVnZ and cc-pwCVnZ-PP basis sets were used for carbon and tin, respectively, in calculations accounting for core−valence contributions.54,55 The values for the geminal Slater exponents for the VDZ-F12 and VTZ-F12 basis sets were 0.9 and 1.0, respectively. As done in the original W1 and W2 theories, as well as the subsequent W1w and W2w methods, electronic energies were extrapolated to the complete basis set (CBS) limit using a two point extrapolation procedure with the general formula ECBS = E(L) + [E(L) − E(L − 1)]/ {[L/(L − 1)]α − 1} where L = S max (maximum angular momentum present in the basis set).27 The values of α were taken from Karton and Martin. 37 HF energies were extrapolated using the cc-pVDZ-F12 and cc-pVTZ-F12 (PP version for Sn) basis sets with α = 5.0. CCSD energies were extrapolated with the cc-pVDZ-F12 and cc-pVTZ-F12 (PP version for Sn) basis sets with α = 3.67. The quasi-perturbative triples were extrapolated from the standard aug-cc-pVDZ and aug-cc-pVTZ (PP version for Sn) basis sets with α = 3.22. The core-correlation energy was calculated from a single coupled cluster calculation using the cc-pwCVTZ basis set (ccpwCVTZ-PP for Sn), scaling the CCSD contribution by 1.1. For the open-shell ditin complex, Me5Sn2, the enthalpy was calculated using the following isogyric reaction (eq 1). Me3Sn−SnMe3 + CH3 F Me3Sn−SnMe2 + H3C−CH3 (1)

Heats of formation were calculated from atomization energies using the CCSD(T)-F12/CBS energies with core correlation and atomic spin−orbit corrections. Atomic heats of formation and heat capacities were taken from the NIST WebBook56 and Gurvich et al.57 Zero point energies and vibrational frequencies were calculated at the B3LYP/cc-pVTZ level and scaled by the anharmonic correction factor 0.985 as suggested by Martin and de Oliveira.38 Thermodynamic quantities for each tin fragment containing methyl groups (Cp(T), S(T), and H(T) − H(298)) over a temperature range of 298−5000 K were calculated using a multistructural method

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COMPUTATION DETAILS Geometry optimizations were accomplished with the Gaussian 09 electronic structure package40 using the B3LYP density B

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be compared to that reported by Allendorf and Melius, −66.9 (kJ/mol)/methyl.59 For disilane, Walsh reported a ΔH°f of 80 ± 1.5 kJ/mol,63 which was the same number used by Ho et al.66 More recent theoretical studies60 have indicated preference for the value obtained by Green and Gunn, 71.5 ± 1.3 kJ/mol,61 which is also close to our value of 70.1 kJ/mol. A wide range of experimental values have been reported for the enthalpy of formation of Me6Si2; Pilcher et al. recently addressed this issue and determined a value of −303.7 ± 5.5 kJ/mol.67 Our calculated value of −296.2 kJ/mol is reasonably close to this value. Germane Benchmarks. Fewer experimental results are available for alkylgermane compounds. As reviewed by Simoes et al., enthalpies of formation for germanium obtained through static-bomb combustion calorimetry can suffer from errors due to the assumed state of germanium oxide after combustion (amorphous, hexagonal, or tetragonal). 68 We used a combination of experimental and computational results to benchmark the accuracy of our calculated enthalpy of formation for four alkyl germanium compounds. For germane, H4Ge, Simoes et al.68 listed the enthalpy of formation as 90.8 ± 2.1 kJ/mol which is nearly identical to the value obtained by Green and Gunn of 90.4 ± 2.1 kJ/mol through combustion measurements.61 Baer and co-workers calculated the enthalpy of formation of H4Ge through a CCSD(T)/CBS method that included corrections for core valence and scalar relativistic effects.69 Their calculated enthalpy of formation of 82 kJ/mol matches well with our value of 80.4 kJ/mol. This value was further supported by Rayne and Forest,70 who calculated a value of 81.5 kJ/mol using the G4 method developed by Curtiss et al.25 Experimental values for Me4Ge are less consistent than those for H4Ge. The review of Simoes et al. gives three different values ranging from −71.0 ± 9.4 to −103.8 ± 8.3 kJ/mol.68 Lappert et al. used a value of −134 ± 13 kJ/mol which was based on the enthalpy of formation of Et4Ge and corrected for methyl vs ethyl group contributions.71 Baer et al. calculated a value of −123 kJ/mol.69 The reported value at the G4 level is −121.3 kJ/mol.70 Our calculated value of −117.9 kJ/mol is similar to these two calculated values. Calculated vs experimental values for digermane follow a similar trend. Simoes et al.68 and Green and Gunn61 list experimental heats of formation of 162.3 ± 1.3 and 161.9 ± 1.3 kJ/mol, respectively. Our calculated value of 144.7 kJ/mol is much closer to the G4 value of 142.5 kJ/mol 70 than to either of the experimental values. Dávalos et al. recently studied Me6Ge2 using threshold photoelectron−photoion coincidence spectroscopy in which they suggest −153.1 ± 6.3 kJ/mol, obtained through an isodesmic reaction, for the enthalpy of formation.72 The isodesmic equation used experimental values of 90.8 ± 2.1 kJ/mol and 162.3 ± 1.3 kJ/mol for H4Ge and H6Ge2 (see above). Our calculated value of −144.2 kJ/mol is reasonably close to this value but only because of offsetting differences in the reference heats. Clearly further attention to the acquisition of reliable experimental enthalpies of formation for alkylgermanium compounds is warranted. Stannane Benchmarks. Simoes et al. assert that static bomb combustion calorimetry, the source for most experimental heats of formation for organotin compounds, is more accurate than in the case of organogermanium compounds68 and cite a value of 162.8 ± 2.1 kJ/mol for the enthalpy of formation of stannane (determined by Green and Gunn61). Allendorf et al. used this value as a reference to establish a

with torsional anharmonicity (MS-T) using the MSTor code developed by Truhlar and co-workers.45,46 Calculated thermodynamic quantities were converted to the NASA polynomial form through the Fitdat utility within the CHEMKIN program.58 CHEMKIN was then used to perform partial equilibrium calculations with the library of tin fragments over the temperature range 298−1500 K.

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RESULTS AND DISCUSSION Because the CCSD(T)-F12 framework was originally developed for molecules with first and second row atoms alone, suitable benchmarks were assessed to evaluate its potential accuracy for the tin compounds studied here. In particular, comparisons were made to both experimental values and previous computational studies for heats of formation of compounds H4−xMexM, where x = 0−4 and M = Si, Ge, and Sn. We note that experimental data derived from reactions involving solids can have larger uncertainties owing to incomplete combustion or the formation of different phases of the solid product, e.g., amorphous vs crystalline. In the case of the tin compounds, some degree of benchmarking is also desirable to assess the utility of the pseudopotential basis set used for Sn. We now proceed to examine such benchmarks. For simplicity, we note that unless otherwise specified, discussed heats of formation are at 298 K. Silane Benchmarks. Silane and methylsilane have been used as reference compounds by Allendorf et al. to establish bond additivity corrections (BACs) for Si−H and Si−C bonds.59 The ΔH°f for H4Si is given by NIST as 34.31 kJ/ mol.56 According to Feller and Dixon,60 however, this result may be due to a revision of the original experimental value,61 and they proposed a value of 39.7 ± 2.5 kJ/mol at 0 °C which corresponds to a value of 30.2 kJ/mol at 298 K. Our calculated value of 29.2 kJ/mol agreed well with Feller and Dixon’s value.60 The standard enthalpy of formation for Me4Si is generally accepted as −233.2 ± 3.2 kJ/mol as determined experimentally by Steele62 and often cited.63,64 This value is in agreement with another study by Szepes and Baer who determined a heat of formation of −226.2 ± 4.5 kJ/mol.65 Our calculated value of −225.1 kJ/mol is closer to the latter value. Figure 1 depicts the trend in ΔH°f for the H4−xMexSi series where x = 0−4. The slope, −63.7 ± 0.7 (kJ/mol)/methyl, may

Figure 1. Trends in enthalpies of formation as a function of methyl substitution in the homologous series H4−xMexM where x = 0−4 and M = Si, Ge, and Sn, using W1-F12 values calculated in this work. Table S1 lists the data shown on the graph. C

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Table 1. Bond Dissociation Enthalpies (298 K, kJ/mol) Calculated for Selected Group 14 Molecules Calculated with the W1F12 Methoda M C Si Ge Sn

Me3M−H 405.5 396.0 361.9 323.7

(403.8 ± 1.7) (377.8,40 397 ± 2 57) (364,58 345.6 ± 2.1) (309.5 ± 10.7 52)

Me3M−Me 367.8 389.4 341.8 297.5

(366.1 ± 1.7) (394 ± 8 41) (340.5 ± 9.8,59 339 ± 13) (284.1 ± 9.9 52)

Me3M−MMe3 330.9 334.2 301.0 261.3

(328.9 ± 2.9) (332 ± 12 41) (294.7 ± 14.1 59) (252.6 ± 14.8 52)

a

Experimental values are shown in parentheses.

bond additivity correction for Sn−H bonds.33 Our calculated value of 169.1 kJ/mol is reasonably close to this value. There are several studies related to the enthalpy of formation of Me4Sn,71,73,74 although according to Dávalos et al.,73 they rely on the enthalpy of formation of liquid tetramethyltin (ΔH°f = −52.3 ± 1.9 kJ/mol) established by Davies et al. in 1963.74 Dávalos et al. recently corrected this liquid value to −49.2 ± 1.9 kJ/mol.73 Lappert et al. assign the gaseous enthalpy of formation as −20.1 ± 3.8 kJ/mol.71 Our value of −8.3 kJ/mol is slightly less negative as we computed also for stannane. Presumably due to its instability, there are no experimental measurements of the enthalpy of formation for distannane. Our calculated value is 287.3 kJ/mol. For hexamethyldistannane, Lappert et al. cited a gaseous enthalpy of formation of −26.8 ± 10.0 kJ/mol.71 Dávalos et al. corrected this value to −19.4 ± 5.7 kJ/mol using updated values for the heat of vaporization of Me6Sn2 and the heat of formation of liquid Me6Sn2.73 Our calculated value of 26.3 kJ/mol differs significantly from this latter value. On the basis of the relatively small differences with experiment for our calculated enthalpies of formation for Me6Si2 and Me6Ge2, we suggest that the experimental enthalpy of formation for Me6Sn2 should be reevaluated. Allendorf and van Mol have suggested that theoretical methods used to calculate enthalpies of formation can be further evaluated using trends in ΔH°f vs the number of a particular type of ligand.36 Reproduction of this trend by the computational method is an indication that the chosen approach is reasonable. To evaluate the CCSD(T)-W1-F12 approach for calculating enthalpies of formation of species containing heavy main group elements, we looked at the homologous series of compounds H4−xMexM where M = Si, Ge, and Sn and x = 0−4. Figure 1 depicts the linear trends in ΔH°f vs number of methyl groups, which have been attributed to localized bonding between the ligand and the central atom.36 For the stannane series, we predict −44.3 kJ/mol change in ΔH°f per substituting methyl group, which may be compared to −46.0 kJ/mol calculated by Allendorf and van Mol.36 Allendorf and Melius also used the MP4-BAC method to calculate the gas phase thermochemistry of a large number of tin-containing molecules. We include 17 of the same molecules here, and a comparison reveals that on average we compute ΔH°f (298 K) values to be higher than the MP4-BAC values by 14 ± 6 kJ/mol. As the W1-F12 model includes a more complete accounting for electron correlation and does not rely on relatively uncertain experimental values to derive bond additivity corrections, we suggest that our new values are likely to be more reliable than prior ones. Bond Dissociation Enthalpies. On the basis of the benchmarking assessment above for the germanium and tin compounds, the W1-F12 method is well suited for the prediction of enthalpies of formation for molecules containing the heavier main group elements. As a further test of the

computational approach, however, we also compared experimental and computed BDE values for three types of bonds, Me3M−H, Me3M−CH3, and Me3M−MMe3 where M = Si, Ge, and Sn (Table 1). Examining BDEs ensures that open-shell species are treated with accuracies equivalent to closed-shell ones. The calculated BDEs for the silicon compounds are all within experimental error of the measured values. The calculated BDEs for the Ge and Sn compounds are also mostly within experimental error. The largest inconsistencies are found in the Sn compounds, although the reported experimental values exhibit a large spread and large error bars, making a critical evaluation difficult. Both Me4Sn and Me6Sn2 have been used as precursors in vapor phase depositions of SnO2 or other tin-containing films. At 297.5 kJ/mol, the Sn−C BDE in Me4Sn is substantially weaker than the C−H bonds in the molecule. In contrast, the Sn−Sn bond is the weakest in Me6Sn2 (261.3 kJ/mol) and would be expected to break more readily than a Sn−C bond in the gas phase at a given temperature. In each instance, however, cleavage of the weakest bond will lead to the same tin-containing product, Me3Sn·. From this intermediate, each of the subsequent Sn−Me dissociation reactions requires less energy than that needed to form Me3Sn·. The average Sn−C BDE values for Me4Sn and Me6Sn2 are 223 and 218 kJ/mol, respectively, but especially in Me4Sn, there is substantial variation in the individual BDEs (Table 2). Most notably, in the stepwise removal of the four methyl groups, the BDE of the second methyl (i.e., converting Me3Sn· to Me2Sn:) is 166.6 kJ/ mol, which is only slightly more than half that for dissociation of the first methyl from Me4Sn. This is consistent with the known stability of divalent tin. Dissociation of the third and Table 2. Bond Dissociation Enthalpies (298 K, kJ/mol) for Me4Sn and Me6Sn2

D

reactant

tin product

BDE (kJ/mol)

Me4Sn Me3Sn Me2Sn MeSn Me6Sn2 Me6Sn2 Me3Sn−SnMe2 Me3Sn−SnMe2 Me3Sn−SnMe Me3Sn−SnMe Me2Sn−SnMe2 Me3Sn−Sn Me2Sn−SnMe Me2Sn−Sn MeSn−SnMe MeSn−Sn

Me3Sn Me2Sn MeSn Sn Me3Sn Me3Sn−SnMe2 Me3Sn−SnMe Me2Sn−SnMe2 Me2Sn−SnMe Me3Sn−Sn Me2Sn−SnMe Me2Sn−Sn MeSn−SnMe MeSn−Sn MeSn−Sn Sn−Sn

297.5 166.6 242.1 184.9 261.3 287.5 181.3 195.4 233 234.4 218.9 203.5 273.7 220.7 151.9 212.5

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Table 3. Calculated Standard Thermochemical Quantities (298 K, 1 atm) for All Tin Species Included in Partial Gas-Phase Equilibrium Calculationsa species

ΔH°f (kJ/mol)

Me4Sn SnH4 Me6Sn2 Me3SnSnMe2H Me3SnSnMeH2 Me2HSnSnMe2H Me2HSnSnMeH2 Me3SnSnH3 MeH2SnSnMeH2 Me2HSnSnH3 MeH2SnSnH3 H6Sn2 Me3SnSnMe2 Me2SnSnMe2 Me3SnSnMe Me2SnSnMe Me3SnSn MeSnSnMe Me2SnSn MeSnSn Sn2 Me3SnSnMe2(CH2) Me3SnSnMe(CH2) Me2SnSn(CH2) MeSnSn(CH2) SnSn(CH2) SnCSn H3Sn H3SnC H3Sn(CH) H3Sn(CH2) H3Sn(σ-CHCH2) H2Sn H2SnC H2Sn(CH) H2Sn(CH2) H2Sn(η2-C2H4) H2Sn(σ2-C2H2) HSn HSnC HSn(CH) HSn(CH2) HSn(σ-CHCH2) Me2Sn Me2SnH Me2Sn(CH) Me2Sn(CH2) Me3Sn2(CH2) MeSn MeSnH MeSnH2 MeSn(CH2) MeSnH(CH2) MeSnH(η2-C2H4) Sn SnC Sn(CH) Sn(CH2) Sn(CH2)2 Sn(σ2-C2)

−8.3 (−17.1 ± 2.1) 169.1 (162.8 ± 2.1) 68 26.3 (−19.4 ± 5.7) 73 85.6 113.8 115.6 159.2 155.0 202.5 200.6 244.8 287.3 168.4 218.4 204.3 291.9 293.3 420.2 351.4 426.7 493.8 239.2 268.7 371.9 510.1 560.7 606.3 271.0 775.5 558.7 339.7 247.8 255.6 783.6 579.3 338.9 294.9 458.1 307.6 793.2 603.5 402.9 320.2 165.0 (123.0 ± 16.5) 73 187.3 489.3 256.4 306.2 261.7 212.2 229.7 356.0 296.5 253.9 301.2 57 859.4 541.0 342.4 512.7 641.4 73

E

S° (J/mol)

Cp° (J mol−1 K−1)

408.7 228.8 609.9 568.0 522.1 525.4 486.2 477.7 435.7 432.5 387.3 336.7 569.7 506.7 524.1 465.8 452.4 384.5 395.2 353.4 261.2 616.3 558.6 368.9 413.0 338.1 306.9 240.2 285.4 301.8 314.0 316.3 229.6 283.8 288.0 278.1 298.9 289.0 213.1 273.3 278.1 282.5 303.5 325.1 336.3 379.9 389.8 483.3 273.7 283.1 290.1 334.9 331.0 303.8 168.5 233.1 245.9 255.0 299.4 274.1

145.1 50.9 239.9 210.7 187.3 186.7 162.6 164.1 138.5 139.5 115.7 92.8 206.8 173.4 175.1 139.3 137.7 115.6 102.5 69.2 36.9 244.0 203.6 135.8 106.8 70.1 48.9 44.7 60.8 73.5 78.0 85.1 36.5 56.3 65.5 66.3 85.3 76.1 29.3 44.1 54.3 59.9 70.9 81.9 89.0 109.9 114.0 163.3 51.3 59.2 66.2 86.0 87.7 108.7 21.3 33.5 44.3 47.5 77.4 46.2 DOI: 10.1021/acs.jpca.8b12072 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Table 3. continued species MeSnH3 Me2SnH2 Me3SnH Me3Sn Me3Sn(CH2) Sn(CH2)4 Me2Sn(CH2)2 Me2Sn(CH)2 Sn2H2

ΔH°f (kJ/mol)

S° (J/mol)

Cp° (J mol−1 K−1)

126.5 82.8 38.1 143.8 (116.6 ± 9.7) 73 203.3 468.0 214.0 370.7 354.5

294.6 333.8 384.7 382.7 444.0 354.7 334.9 277.1 288.9

73.1 96.3 120.2 113.0 149.6 115.0 133.4 120.1 50.5

a

Known experimental values are shown in parentheses. The value for atomic tin is the experimental number.

fourth methyl groups requires a larger amount of energy (242.1 and 184.9 kJ/mol, respectively). There are alternative bimolecular reactions that could lead to further demethylation. For example, based on the enthalpy values in Table 3, one can calculate a favorable enthalpic change of −130.9 kJ resulting from disproportionation of 2 mol of Me3Sn to form Me4Sn and Me2Sn. Although no kinetic information is as yet available, reactions such as this disproportionation could contribute to an energetically favorable pathway for loss of methyl ligands. Reactive Intermediates. The W1-F12 method was used to calculate thermochemical quantities for a large number of species that could form during the pyrolysis of Me4Sn and Me6Sn2. The 298 K, 1 atm enthalpies of formation, standard entropies of formation, and heat capacities of all tin-containing fragments are compiled in Table 3. Fragment species were generated based on known and predicted paths from experimental and theoretical studies of the decomposition of alkyltin molecules,20,22,75 as well as from related studies of silicon compounds.76,77 The molecules include saturated tin species in which hydrogen replaces methyl groups, e.g., Me3SnH, and unsaturated compounds such as stannylenes (R2Sn),78,79 distannenes (R2SnSnR2),80,81 stannynes, H2Sn2,82 and radical species such R3Sn·. The thermochemical quantities for saturated (CH4 and C2H6) and unsaturated (C2H4 and C2H2) hydrocarbons, methyl radical (CH3·), hydrogen, and atomic and diatomic tin were also calculated and are listed in the Supporting Information. For molecules with structures known from experimental measurements or previous computational studies, good agreement was observed with the computed structures reported here (the Supporting Information includes structural data as .xyz files for all compounds). Gas-phase equilibrium calculations were used to determine the mole fraction of individual species during thermal decomposition for both Me4Sn and Me6Sn2 in the absence of additional reactive or inert gas components; i.e., the elemental composition of the gas mixture is determined by the precursor stoichiometry. In addition, these partial gas phase equilibria were calculated without including condensed phases such as liquid tin or solid carbon in contact with the gases. As described by others, inclusion of condensed phases would dominate the equilibrium and obfuscate the appearance of potentially less stable intermediates35 (this indeed proved to be the case when both condensed phases were included in the calculation). Under high vacuum conditions (10−6 Torr) the equilibrium diagrams for Me4Sn and Me6Sn2 are nearly superimposable. Figure 2 shows the mole fractions of the more abundant species between 298 and 1500 K. Methylditin (MeSn2) is the

Figure 2. Partial equilibrium diagram for Me6Sn2 at initial pressure of 10−6 Torr.

only organotin compound to appear at non-negligible concentration, and its mole fraction is ∼10−5 at 298 K. In this temperature range, other stable tin species include Sn2C, Sn2, Sn, and SnC2, with atomic tin dominating at temperatures of >500 K. With an initial pressure of 1 atm, 23 species have mole fractions of >10−5 at some point between 298 and 1200 K for both Me4Sn (Figure 3) and Me6Sn2 (Figure 4). Notable similarities between the two precursors are the initial rise in methyltin fragments from 298 to ∼550 K followed by a falloff above this temperature. Ditin species (indicated by the solid lines in both figures) dominate at temperatures of