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A Mechanistic Investigation of Thermal and Photoreactions between B and Silane Jiwon Moon, Heehyun Baek, and Joonghan Kim J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b03202 • Publication Date (Web): 15 Aug 2017 Downloaded from http://pubs.acs.org on August 16, 2017

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The Journal of Physical Chemistry

A Mechanistic Investigation of Thermal and Photoreactions between B and Silane

Jiwon Moon, Heehyun Baek, and Joonghan Kim* Department of Chemistry, The Catholic University of Korea, Bucheon 14662, Republic of Korea

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT Density functional theory and high-level ab initio calculations were performed to elucidate the detailed reaction mechanism from B and SiH4 to a structure with two bridging H atoms (Si(µ–H2)BH2, silicon tetrahydroborate). On the basis of the calculated results, this reaction mechanism includes both thermal and photochemical reactions. Especially, thermal conversion of silylene dihydroborate (H2B=SiH2) to Si(µ–H2)BH2 is not feasible because two high energetic barriers must be overcome. In contrast, the reverse reaction is feasible because it is effectively only necessary to overcome a single barrier. The characteristics of the excited states of H2B=SiH2 and Si(µ–H2)BH2 have been identified. Two successive conical intersections (CIs) are involved in the photochemical reaction. The BSiH4 bending coordinate is almost parallel to the reaction coordinate near the regions from the second CI to Si(µ– H2)BH2. The activated BSiH4 bending mode lift the degeneracy of the second CI, thereby the reaction readily proceeds to Si(µ–H2)BH2. All calculated results in this work reasonably well describe the recent experimental observations.


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1. INTRODUCTION Compounds containing B−Si bonds have attracted much attention due to their various intriguing properties.1 For example, the B−Si bond exhibits chemoselective activation due to the electronegativity difference between B and Si. Studies have shown the reaction of B atoms prepared by laser-ablation with CH4 to form B−C bonds, which has allowed several organoborane species to be generated.2-3 Although the activation of the Si−H bond by B is expected to occur readily when compared with C−H activation due to weaker strength of the Si−H bond, both experimental and theoretical investigations of the reaction of B with silane (SiH4) are still limited. A recent experimental study showed that B atoms readily react with SiH4 to form a planar silylene dihydroborate (H2B=SiH2) structure.4 Upon photolysis of H2B=SiH2 at 300−350 nm, an unusual structure with two H atoms being bridged between B and Si was formed (Si(µ–H2)BH2, silicon tetrahydroborate). These two reaction intermediates (IMs) were characterized by infrared (IR) spectroscopy in a matrix environment.4 On annealing, Si(µ–H2)BH2 reformed H2B=SiH2, however, the reverse thermal reaction from H2B=SiH2 to Si(µ–H2)BH2 did not take place. Although the reaction between B and SiH4 showed rich chemistry, a detailed reaction mechanism including both thermal and photoreactions has not yet been elucidated. In addition, no information is available regarding the characteristics of the excited states of H2B=SiH2 and Si(µ–H2)BH2. A detailed reaction mechanism as well as the characteristics of the excited states as clarified by high-level ab initio methods are necessary to gain an insight into the reactivity of the B−Si bond-containing compound. In this work, a detailed mechanism for the reaction of B with SiH4 to form a bridged structure containing two H atoms (Si(µ–H2)BH2) is elucidated using density functional theory (DFT) and high-level ab initio methods such as coupled cluster singles and doubles with perturbative

triples (CCSD(T)) and multi-state

multiconfigurational second-order perturbation theory (MS-CASPT2). This reaction mechanism involves both thermal and photoreactions. Two successive conical intersections (CIs) where two potential energy surfaces (PESs) with the same spin multiplicity are degenerate play an important role in the photochemical reaction of B and SiH4. To the best of our knowledge, this work is the first time the involvement of CIs in photochemical reactions of B- and Si-containing compounds has been revealed.



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2. COMPUTATIONAL DETAILS The molecular structures of the IMs and transition states (TSs) in the reaction between B and SiH4 were optimized using DFT.5-6 A hybrid exchange-correlation functional, PBE0,7 was used with the aug-cc-pVTZ basis sets in the DFT calculations. Subsequent harmonic vibrational frequency calculations were performed to identify the minimum energy structures and TSs. The ‘superfine grid’ option in the Gaussian09 program was used to ensure the accuracy of the DFT calculations. In addition, the ‘tight’ option in the Gaussian09 program was used to ensure that the convergence criteria for the geometry optimizations were stringent. All TSs were identified by one imaginary frequency and confirmed by the intrinsic reaction coordinate (IRC) method.8-9 Single-point energy calculations using CCSD(T)10 with aug-cc-pVQZ basis sets were performed on the optimized structures by PBE0/aug-ccpVTZ (CCSD(T)/aug-cc-pVQZ//PBE0/aug-cc-pVTZ) to obtain more accurate energetics. All DFT and CCSD(T) calculations were performed using the Gaussian09 program.11 However, the molecular structures of two important IMs (H2B=SiH2: IM2 and Si(µ–H2)BH2: IM4) were optimized at the CCSD(T)12/aug-cc-pVTZ level of theory using the Molpro2015 program.13 Subsequent vibrational frequency calculations for these two IMs were performed at the same level. The complete active space self-consistent field (CASSCF) method14 was used to consider multireference character and calculate the excited states. The active orbitals consist of the 2s and 2p orbitals of B, the 3s and 3p orbitals of Si, and the 1s orbital of H. Thus, full valence orbitals were considered as the active orbitals. In other words, the eleven electrons were distributed in twelve active orbitals. Hereafter, this is denoted as CAS(11,12). The active orbitals of IM2 and IM4 are shown in Figs. S1 and S2 in the SI, respectively. The state-averaged (SA)-CASSCF method was used to examine the ground and excited states simultaneously. The three states were averaged in the SA-CASSCF calculations, denoted SA3-CAS(11,12). The minimum energy paths (MEPs) were calculated at the SA3-CAS(11,12)/aug-cc-pVTZ level. The MSCASPT2 method15 with aug-cc-pVQZ basis sets along the MEPs was used to account for the dynamic electron correlation effect. In all SA3-CAS(11,12) and MS-CASPT2 calculations, the symmetry was not imposed. Two IMs (IM2 and IM4) were also optimized using MS-CASPT2/aug-cc-pVTZ to compare the results with those from PBE0 and CCSD(T). The Cholesky decomposition of two-electron integrals 4 ACS Paragon Plus Environment

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(threshold of 10−4)16 was used in all MS-CASPT2 calculations. All SA-CAS(11,12) and MS-CASPT2 calculations were performed using the Molcas8.0 program.17 All molecular structures of the two CIs were optimized using SA-CAS(11,12) with the 6-311++G(2d,p) basis sets instead of aug-cc-pVTZ due to the unavailability of a general contracted basis set. The geometry optimizations of the CIs were performed using the GAMESS-US program.18

3. RESULTS AND DISCUSSION 3. 1. Thermal Reaction. The calculated reaction potential energy surface (PES) of B and SiH4 and the related molecular structures optimized by PBE0/aug-cc-pVTZ are shown in Figures 1 and 2, respectively. The relative energies of all IMs and TSs as calculated by PBE0/aug-cc-pVTZ and CCSD(T)/aug-cc-pVQZ//PBE0/aug-cc-pVTZ including zero-point energy (ZPE) corrections are also summarized in Table S1 in the supporting information (SI). Hereafter, we focus on the energetics calculated by CCSD(T)/aug-cc-pVQZ//PBE0/aug-cc-pVTZ unless otherwise stated. When the B atom approaches SiH4, the activation of the Si−H bond takes place readily without a barrier, thereby forming IM1. This result is in contrast to the reaction of Al and Ga with SiH4. In those cases, an initial adduct between M (M = Al and Ga) and SiH4 forms as an IM.19-20 The reaction proceeds to the more thermodynamically favorable IM2 via TS1-2, which has a small barrier height (5.7 kcal/mol), with one H atom from the SiH3 unit migrating to B. As shown in Figure 2, PBE0, CCSD(T), and MSCASPT2 give very similar structural parameters for IM2. In particular, the structural parameters as optimized by PBE0 are almost identical to those obtained using MSCASPT2, indicating that PBE0 works well for predicting the molecular structures of both B- and Si-containing compounds. IM2 has C2v symmetry and its electronic state is the 2B1 state. The major electronic configuration (92.5%) of IM2 as calculated by MS-CASPT2/aug-ccpVQZ//MS-CASPT2/aug-cc-pVTZ is 222000α 02200

(where “α” represents the

alpha spin electron and the order of the molecular orbitals is the same as shown in Figure S1 in the SI). This electronic configuration is the exactly same as that of both PBE0 and the reference wave function of CCSD(T). In addition, the contributions of other minor electronic configurations are less than 1% each, indicating that single reference based methods also work well for calculating the molecular properties of the 5 ACS Paragon Plus Environment


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2

B1 state of IM2. The vibrational frequencies of IM2 calculated by PBE0 and

CCSD(T) are listed in Table S2 in the SI. The vibrational frequencies of IM2 calculated by both PBE0 and CCSD(T) are in good agreement with the experimental values.4 In TS2-3, one H from the SiH2 moiety migrates to the BH2 moiety, leading to IM3 where one H is bridged between B and Si. It is noted that IM3 was not observed in the previous study4 and thus it is proposed for the first time in this work. Another H (H4) from the SiH moiety then migrates to the middle point between B and Si bond in TS3-4, such that eventually two H atoms are bridged between B and Si in IM4. We also performed geometry optimizations of IM4 using CCSD(T) and MS-CASPT2 with aug-cc-pVTZ basis sets. PBE0, CCSD(T), and MS-CASPT2 all give similar structural parameters, as seen for IM2. PBE0, CCSD(T), and MS-CASPT2 all predict that IM4 has C2v symmetry and its electronic state is also the 2B1 state. The major electronic configuration (92.0%) of IM4 as calculated by MS-CASPT2/aug-cc-pVQZ//MS-CASPT2/aug-cc-pVTZ is

2220002α 0200 , where the order of the molecular orbitals is the same as in Figure S2 in the SI. This electronic configuration is the same as those of both PBE0 and the reference wave function of CCSD(T). The following minor electronic configuration (1.2%) is 2200002α 0220 . Therefore, single reference based methods also work well for calculating the molecular properties of the 2B1 state of IM4, as seen for IM2. IM4 was also detected in the recent IR spectroscopic experiment.4 The vibrational frequencies of IM4 as calculated by PBE0 and CCSD(T) are listed in Table S2 in the SI. As in the case of the IM2, the vibrational frequencies of IM4 calculated using PBE0 and CCSD(T) are in good agreement with the experimental values.4 As mentioned above, IM4 cannot be generated via thermal reaction from IM2. This is readily understandable from the calculated results, because two barriers must be overcome to reach to IM4, such that 27.3 kcal/mol is required to proceed from IM2 to IM4 (see Figure 1). Thus, irradiation at an appropriate wavelength is required in order to circumvent this barrier and reach IM4. However, the reverse reaction from IM4 to IM2 was shown to be achievable by continuous annealing in the recent experiment.4 This can be rationalized based on the PES calculated in this work. As shown in Figure 1, it is effectively only necessary to overcome one barrier between IM4 and TS3-4 (16.8 kcal/mol, see Figure 1) to proceed to IM2. Once this has been


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overcome, reaching IM2 is trivial as the second barrier is very low (4.3 kcal/mol between IM3 and TS2-3). However, although the barrier from IM4 to TS3-4 is not particularly large, it is substantial enough to limit conversion to IM3. Indeed, in the recent experiment only a small portion of IM4 disappeared (i.e., proceeded to IM3 by overcoming the barrier to TS3-4) via continuous annealing.4 The calculated results are consistent with the experimental observation. It is noted that the relative energies calculated by PBE0/aug-cc-pVTZ are very close to those calculated using CCSD(T)/aug-cc-pVQZ//PBE0/aug-cc-pVTZ, with the exception of the reaction of the B atom with SiH4 (B + SiH4). These results indicate that PBE0 shows good performance for calculating energetics. However, PBE0 overestimated the relative energy of B + SiH4 compared with that yielded using CCSD(T) (see Table S1 in the SI). This overestimation can be attributed to a wellknown problem concerning B atoms in DFT calculations, which is that the density associated with the p0 orbital differs from that of the p±1 orbital.21-23 In a previous study, B3LYP/aug-cc-pVTZ was also shown to suffer from this problem.4 In addition, the relative energy between IM2 and IM4 as calculated by B3LYP/aug-cc-pVTZ was 15.1 kcal/mol in the previous study,4 which is an overestimate compared with the values provided by PBE0/aug-cc-pVTZ (9.6 kcal/mol, see Table S2 in the SI) and CCSD(T)/aug-cc-pVQZ (10.5 kcal/mol). We can conclude that PBE0 is superior to B3LYP and that the performance of PBE0 for calculating the structural and energetic parameters of both B- and Si-containing compounds (excluding individual B atoms) is remarkable.

3. 2. Photo Reaction. The vertical excitation energies of IM2 were calculated using MS-CASPT2/aug-cc-pVQZ optimized by MS-CASPT2/aug-cc-pVTZ, and the results are summarized in Table 1. The major (87.7%) and subsequent minor (3.5%) electronic configurations of the D1 state of IM2 are

22α 000202200

and

22α 000022200 , respectively (the order of the molecular orbitals is the same as that shown in Figure S1 in the SI). Therefore, the characteristic of the D1 state is σB−Si (a1(3)) → π (b1(1)) with respect to the D0 state. The major (89.7%) and subsequent minor (2.0%) electronic configurations of the D2 state of IM2 in the same calculation are 2220000α 2200

and 22αβ 00α 02200 , respectively (where “β” represents a



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beta spin electron). The characteristic of the D2 state of IM2 is π (b1(1)) → π* (b1(2)) with respect to the D0 state. As shown in Table 1, the D2 state is optically available according to its large oscillator strength. In the recent experiment, 300−350 nm irradiation induced a photochemical reaction to proceed from IM2 to IM4.4 Because the vertical excitation energy of the D2 state falls into this energy range, occurring at 3.69 eV (336 nm), the D2 state will be populated by this irradiation. The vertical excitation energies of IM4 were also calculated using MSCASPT2/aug-cc-pVQZ//MS-CASPT2/aug-cc-pVTZ, and the results are summarized in Table 1. The major (92.2%) and subsequent minor (1.8%) electronic configurations of the D1 state of IM4 are 2220002002α 0

and 2200002202α 0 , respectively

(the order of the molecular orbitals is the same as that shown in Figure S2 in the SI). Therefore, the characteristic of the D1 state is nsi (b1(2), px orbital of Si) → nsi (b2(2), mainly py orbital of Si) with respect to the D0 state. In contrast to the D1 state, two electronic configurations are equally contributed to the D2 state; the first (46.2%) and second

(44.5%)

22α 000220200

electronic and

configurations

of

the

D2

state

of

IM4

are

222α 00200200 , respectively. Thus, multireference

character is significant in the D2 state of IM4. The excitation properties of the D2 state of IM4 are a mixture of σB−H (a1(3)) → nsi (b1(2)) and nsi (b1(2)) → σ*Si−H (a1(4)) with respect to the D0 state. In contrast to the case of IM2, the D1 and D2 states are dark and almost dark, respectively, according to their oscillator strengths. Therefore, the reverse photochemical reaction from IM4 to IM2 is not feasible. To clarify the photochemical reaction mechanism, MEP calculations were performed using SA3-CAS(11,12)/aug-cc-pVTZ from the Franck-Condon (FC) region, and the results are shown in Figure 3a. Single-point energy calculations were performed along the MEP using SA-CAS(11,12) and MS-CASPT2 with the aug-ccpVQZ basis sets to obtain more accurate energetic values, and the results are shown in Figure 3b. As shown in Figure 3, both SA3-CAS(11,12) and MS-CASPT2 show similar shapes for the reaction PESs. Since the D2 state is populated, the MEP calculations were performed for the D2 state. As shown in Figure 3, CI1 between the D2 and D1 states is located near the FC region. The optimized molecular structure of CI1 is shown in Figures 4a and 4b. The migration of one H atom from Si to B can be clearly seen in the CI1 structure. MEP calculations were performed on the D1 state


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after passing through CI1. The energy gap between the D1 and D0 states gradually decreases along the MEP on the D1 state. Eventually, the reaction reached CI2, where the energies of the D1 and D0 states are degenerate. The optimized molecular structure of CI2 is shown in Figures 4c and 4d. As shown in Figure 4c, one H atom is located between B and Si in CI2. The MEP of the D0 state proceeds from CI2 to IM3. After reaching to IM3, the barrier to IM2 is 4.3 kcal/mol (Figure 1) which is much smaller than that to IM4 (14.9 kcal/mol), indicating that the reaction proceeds to IM2 rather than IM4. This result contradicts to the experimental results. Since the PES of the quartet state lies much higher in energy than doublet one (over 50 kcal/mol) according to the results of PBE0/aug-cc-pVTZ calculations, the reaction does not involve the intersystem crossing from doublet to quartet state. The re-excitation can occur on IM3 via the initial irradiation (300−350 nm). However, the excitation energies of the D1 and D2 states on IM3 are 2.36 and 2.78 eV (MS-CASPT2/aug-ccpVQZ), respectively; they do not fall within 300−350 nm energy range. Even their oscillator strengths are small (~0.010). These results indicate that the repopulations to the D1 and D2 states on IM3 unlikely occur. If the excitation to the D1 state on IM3 takes place, the reaction on the D1 state proceeds to CI2 according to the MEP calculations. But these results give an insight on the PES near this region. The reaction coordinate from IM3 to IM4 through TS3-4 significantly correlates to the BSiH4 bending coordinate according to the results of IRC calculations (Figure S3 in the SI). The BSiH4 bond angles of IM3, CI2, and TS3-4 are 114.7°, 90.7°, and 68.8°, respectively. Therefore, the location of CI2 (1.87 eV and 43.1 kcal/mol at MSCASPT2/aug-cc-pVQZ) may lie between IM3 and TS3-4 in respect of the BSiH4 bending coordinate. As can be seen from Figure 4c, the derivative coupling vector of CI2 involves the BSiH4 bending coordinate. In order to explore the nature of PES near this

region,

we

performed

single-point

energy

calculations

using

SA3-

CAS(11,12)/aug-cc-pVQZ along the derivative coupling vector of CI2 and IRC coordinate of TS3-4; these PESs are shown in Figures S4a and b in the SI, respectively. As shown in Figure S4a, the degeneracy of CI2 is lifted according to the derivative coupling vector of CI2. The negative direction (opposite direction of the arrows shown in Figure 4c) of the derivative coupling vector of CI2 points toward IM3 according to the BSiH4 bond angle. The decrease of energy of D0 near CI2 is steeper along the negative direction than the positive direction (Figure S4a in the SI). 9 ACS Paragon Plus Environment


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These results are consistent with those of two MEP calculations; the first one is of the D0 state on CI2 proceeding to IM3 and the second one is of the D1 state on IM3 proceeding to CI2. The last part of PESs of the positive direction of the derivative coupling vector of CI2 is similar to that of near TS3-4 shown in Figure S4b in the SI; increasing of energy of the D0 state and closing energies between the D1 and D2 states. As mentioned above, the region near TS3-4 is closely related to the BSiH4 bending coordinate. Another single-point calculations using SA3-CAS(11,12)/aug-cc-pVQZ via decreasing the BSiH4 bond angle were performed to identify it. These single-point calculations started from the end point of the positive direction of the derivative coupling vector of CI2 and the calculated PESs are shown in Figure S5 in the SI. The PESs are very similar to those along the IRC coordinate of TS3-4 towards IM4; decreasing energies of the D0 and D1 states and a peak of energy of the D2 state. Therefore, both the positive direction of the derivative coupling vector of CI2 and the IRC coordinate of TS3-4 are indeed almost parallel to the BSiH4 bending coordinate. These results indicate that when the BSiH4 bending mode is activated, the degeneracy on CI2 is readily lifted, thereby the reaction proceeds along with the BSiH4 bending coordinate on the D0 PES. Indeed, the MEP calculation from the shifted molecular structure of CI2 along the BSiH4 bending coordinate converges to IM4 (Figure S6 in the SI). In summary, the reaction proceeds from CI1 along the MEP to CI2. The BSiH4 bending mode is readily activated due to the excessive energy of the photochemical reaction from the FC region. The degeneracy of CI2 is lifted because the BSiH4 bending coordinate is almost parallel to the derivative coupling vector of CI2. Thereby, the reaction readily proceeds to IM4. This reaction mechanism clearly elucidates the details of the experimentally observed photoisomerization reaction from IM2 to IM4 upon irradiation at 300–350 nm.4

4. CONCLUSIONS We investigated the mechanism of the conversion of B and SiH4 to a structure with two H atoms bridged between the units (Si(µ–H2)BH2, IM4) using DFT and highlevel ab initio methods. The relative energies of the thermal reaction calculated using the PBE0/aug-cc-pVTZ are in good agreement with those obtained using 10 ACS Paragon Plus Environment

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CCSD(T)/aug-cc-pVQZ//PBE0/aug-cc-pVTZ. The vibrational frequencies calculated using PBE0 and CCSD(T) are in good agreement with the experimental values. Therefore, PBE0 describes the molecular structures, vibrational frequencies, and relative energies well. Thermal conversion of IM2 to IM4 is not feasible because two high energetic barriers must be overcome. In contrast, the reverse thermal reaction from IM4 to IM2 is feasible as effectively only one barrier must be overcome. On the basis of the vertical excitation energies calculated by MS-CASPT2, the D2 state of IM2 (H2B=SiH2) is an optically available state as shown by its large oscillator strength. In addition, the excitation energy of the D2 state (3.69 eV and 336 nm) falls within the energy range (300–350 nm) used for photoconversion in the recent experimental study, and the D2 state would be populated from this irradiation. The MEP calculations show that two successive CIs are involved in the photochemical reaction from IM2. The reaction proceeds to IM4 through lifting the degeneracy of CI2 by the activated BSiH4 bending mode. All calculated results in this work reasonably well describe the recent experimental observations. We hope that this work will stimulate further theoretical and experimental investigations of reaction mechanisms involving B- and Si-containing compounds.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: XX.XXXX/XXXX The active orbitals of IM2 and IM4 calculated using SA3-CAS(11,12), relative energies of all species calculated using PBE0 and CCSD(T), vibrational frequencies of IM2 and IM4 calculated using PBE0 and CCSD(T), IRC pathway from TS3-4 to IM4, PESs calculated by single-point calculations using SA3-CAS(11,12)/aug-ccpVQZ along the derivative coupling vector of CI2 and IRC coordinate of TS3-4, PESs calculated by single-point calculations using SA3-CAS(11,12)/aug-cc-pVQZ along via decreasing the BSiH4 bond angle, MEP calculation from the shifted structure of CI2 structure along the BSiH4 bending coordinate, and xyz coordinates of IM, TS, and CI.



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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Tel: +82-2-2164-4338. Fax: +82-2-2164-4764.

ACKNOWLEDGMENTS This work was supported by the Catholic University of Korea, Research Fund, 2017. This research was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT

&

Future

Planning

(NRF-2014R1A1A1007188

and

NRF-

2016R1D1A1B03933120). This work was supported by the National Institute of Supercomputing and Network/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC-2016-C1-0002).

REFERENCES (1) Oestreich, M.; Hartmann, E.; Mewald, M. Activation of the Si–B Interelement Bond: Mechanism, Catalysis, and Synthesis. Chem. Rev. 2012, 113, 402-441. (2) Hassanzadeh, P.; Andrews, L. Reactions of Pulsed Laser Evaporated Boron Atoms with Methane. 1. Synthesis and Characterization of a Novel Molecule with CarbonBoron Double Bonds: HBCBH. J. Am. Chem. Soc. 1992, 114, 9239-9240. (3) Hassanzadeh, P.; Hannachi, Y.; Andrews, L. Pulsed Laser Evaporated Boron Atom Reactions with Methane. II: Infrared Spectra of H2CBH2, H2CBH, HCBH, and HBCBH in Solid Argon. J. Phys. Chem. 1993, 97, 6418-6424. (4) Zhao, J.; Xu, B.; Yu, W.; Wang, X. Silicon Tetrahydroborate and Silylene Dihydroborate with Interelement B–H–Si and B–Si Bonds. Organometallics 2016, 35, 3272-3280. (5) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. B 1964, 136, 864-871. (6) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. A 1965, 140, 1133-1138.


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(7) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158-6170. (8) Gonzalez, C.; Schlegel, H. B. An Improved Algorithm for Reaction Path Following. J. Chem. Phys. 1989, 90, 2154-2161. (9) Gonzalez, C.; Schlegel, H. B. Reaction Path Following in Mass-Weighted Internal Coordinates. J. Phys. Chem. 1990, 94, 5523-5527. (10) Raghavachari, K., Trucks, G. W., Pople, J. A., Head-Gordon, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479-483. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision D.01; Gaussian, Inc.:Wallingford, CT, 2009. (12) Watts, J. D.; Gauss, J.; Bartlett, R. J. Coupled- Cluster Methods with Noniterative Triple Excitations for Restricted Open- Shell Hartree–Fock and Other General Single Determinant Reference Functions. Energies and Analytical Gradients. J. Chem. Phys. 1993, 98, 8718-8733. (13) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schutz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; et al. MOLPRO, version 2015.1, a package of ab initio programs, 2015; http://www.molpro.net (accessed Aug 12, 2016). (14) Roos, B. Advances in Chemical Physics; Ab Initio Methods in Quantum Chemistry II. Wiley, Chichester: 1987. (15) Finley, J.; Malmqvist, P.-Å.; Roos, B. O.; Serrano-Andrés, L. The Multi-State CASPT2 Method. Chem. Phys. Lett. 1998, 288, 299-306. (16) Aquilante, F.; Boman, L.; Boström, J.; Koch, H.; Lindh, R.; de Merás, A. S.; Pedersen, T. B. Cholesky Decomposition Techniques in Electronic Structure Theory. In Linear-Scaling Techniques in Computational Chemistry and Physics, Springer: 2011; pp 301-343. (17) Aquilante, F.; Autschbach, J.; Carlson, R. K.; Chibotaru, L. F.; Delcey, M. G.; De Vico, L.; Ferré, N.; Frutos, L. M.; Gagliardi, L.; Garavelli, M. Molcas 8: New Capabilities for Multiconfigurational Quantum Chemical Calculations across the Periodic Table. J. Comput. Chem. 2016, 37, 506-541.



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(18) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347-1363. (19) Gaertner, B.; Himmel, H. J. Characterization and Photochemistry of the Silane– Aluminum Complex Al⋅ SiH4 and Its Photoproducts HAlSiH3 and AlSiH3 in a Solid Argon Matrix. Angew. Chem. Int. Ed. 2002, 41, 1538-1541. (20) Gaertner, B.; Himmel, H. J.; Macrae, V. A.; Downs, A. J.; Greene, T. M. Matrix Reactivity of Al and Ga Atoms (M) in the Presence of Silane: Generation and Characterization of the η2- Coordinated Complex M⋅ SiH4, the Insertion Product HMSiH3, and the MI Species MSiH3 in a Solid Argon Matrix. Chem. Eur. J. 2004, 10, 3430-3443. (21) Becke, A. D. Current Density in Exchange-Correlation Functionals: Application to Atomic States. J. Chem. Phys. 2002, 117, 6935-6938. (22) Maximoff, S. N.; Ernzerhof, M.; Scuseria, G. E. Current-Dependent Extension of the Perdew–Burke–Ernzerhof Exchange-Correlation Functional. J. Chem. Phys. 2004, 120, 2105-2109. (23) Jensen, F. Introduction to Computational Chemistry. John Wiley & Sons: 2013.


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Table 1. Vertical excitation energies (in eV) and their characteristics for IM2 and IM4 optimized by MS-CASPT2/aug-cc-pVTZ with C1 symmetry MS-CASPT2/aug- MS-CASPT2/augcc-pVTZ

cc-pVQZ

3.13 (0.003)a

3.14 (0.004)a

3.74 (0.167)a

3.69 (0.166)a

1.36 (0.000)a

1.35 (0.000)a

3.74 (0.004)a

4.43 (0.004)a

D1 (2A1) σB−Si → π IM2

D2 (2B1)

π → π* D1 (2B2) nsi → nsi IM4

D2 (2A1) σB−H → nsi and nsi → σ*Si−H

a

Values in parentheses are the oscillator strength.



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Figure 1. Reaction PES (in kcal/mol [in eV]) for B + SiH4 (doublet) calculated using CCSD(T)/aug-cc-pVQZ//PBE0/aug-cc-pVTZ including ZPE correction calculated by PBE0/aug-cc-pVTZ. 16 ACS Paragon Plus Environment

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Figure 2. Optimized molecular structures (bond lengths in Å and bond angles in °) of IMs and TSs during the reaction of B and SiH4 along with their relative energies (in kcal/mol [in eV], including ZPE correction), as calculated using PBE0/aug-cc-pVTZ. Values in parentheses and in bold are optimized using CCSD(T)/aug-cc-pVTZ and MS-CASPT2/aug-cc-pVTZ, respectively. 17 ACS Paragon Plus Environment


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Figure 3. Potential energy curves calculated using (a) SA3-CAS(11,12)/aug-cc-pVQZ and (b) MS-CASPT2/aug-cc-pVQZ along the MEP calculated by SA3-CAS(11,12)/aug-cc-pVTZ. The grey arrows in (a) indicate the progress direction of the MEP.


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Figure 4. (a) Derivative coupling and (b) gradient difference vectors for CI1 (bond lengths Å in and bond angles in °) optimized by SA3CAS(11,12)/6-311++G(2d,p). (c) Derivative coupling and (d) gradient difference vectors for CI2 optimized by SA2-CAS(11,12)/6311++G(2d,p).



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