New Orbital Symmetry Allowed Route for Cycloreversion of

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

New Orbital Symmetry Allowed Route for Cycloreversion of Silacyclobutane and Its Methyl Derivatives Ismail Badran, Arvi Rauk, and Yujun Shi J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08071 • Publication Date (Web): 08 Feb 2019 Downloaded from http://pubs.acs.org on February 10, 2019

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The Journal of Physical Chemistry

New Orbital Symmetry Allowed Route for Cycloreversion of Silacyclobutane and Its Methyl Derivatives

Ismail Badran, Arvi Rauk, Yujun Shi*

Department of Chemistry, University of Calgary, Calgary, Alberta, T2N 1N4, Canada

* Corresponding author, email: [email protected]; Tel: 1-403-2108674

1 ACS Paragon Plus Environment

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Abstract The [2+2] cycloreversion of silacyclobutane (SCB) and its two methyl-substituted derivatives, namely 1-methyl-1-silacyclobutane (MSCB) and 1,1-dimethyl-1-silacyclobutane (DMSCB), were studied using ab-initio quantum chemistry calculations. The second-order Møller-Plesset (MP2) perturbation theory, complete active space self-consistent field (CASSCF), and coupled clusters methods were used to explore both the concerted and stepwise cycloreversions of the three molecules. In addition to the orbital-symmetry-forbidden supra-supra [2s+2s] transition state, a new orbital-symmetry-allowed supra-antara [2s+2a] transition state was discovered for the concerted route for all three molecules. Both methyl substitution and temperature play a role in the kinetic competition between the [2s+2s] and [2s+2a] routes. At 0 K and 298 K, the concerted [2s+2a] cycloreversion is kinetically more favorable than the [2s+2s] cycloreversion for SCB, but the opposite is true for MSCB and DMSCB. With increasing temperatures to above 600 K and 1800 K, the [2s+2a] cycloreversion becomes more favorable for MSCB and DMSCB, respectively. The methyl substitutions on Si atoms also affect the stability of the diradical intermediate formed by Si-C bond rupture, leading to a less stable diradical with increasing methyl groups.


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Introduction [2+2] cycloreversion of four-membered rings has gained extensive interest due to its importance in orbital symmetry theory,1,2 organic synthesis,3,4 material science,5,6 and DNA repair.7 [2+2] cycloreversion of cyclobutane and its derivatives has been extensively studied both experimentally8-10 and theoretically.11-14 There is a long-time debate on whether this reaction occurs by a concerted or a two-step mechanism. According to the Woodward-Hoffmann rules,1 the concerted supra-supra [2s+2s] process is orbital symmetry forbidden, while the supra-antara [2s+2a] is orbital symmetry allowed for a thermal cycloaddition/cycloreversion reaction. The latter involves a twisted transition state accompanied with a 180° methylene rotation. If the symmetry allowed [2s+2a] process is considered, the stereochemical relationships at three of the four carbons of cyclobutane will be retained in the product.1 This fact has been proven true experimentally for cyclobutane analogues.15,16 Using the self-consistent field (SCF) method, Wright et al. calculated the potential barrier of 156 kcal/mol for [2s+2s] decomposition of cyclobutane to two ethylene molecules using a minimum basis set of Slater-type orbitals.11 In 1985, Bernardi et al. used MC-SCF methods to estimate the potential barrier for the concerted [2s+2s] and [2s+2a] path for the cycloaddition of two ethylene molecules to form cyclobutane.13 The π and π* orbitals of each ethylene molecule for the valence space were used to construct the molecular orbitals, involving a total of 4 electrons. No true transition state was found for the “forbidden” [2s+2s] path, but two saddle points existed, each with two negative eigenvalues. A transition state for the “allowed” [2s+2a] path was located at 87.9 kcal/mol relative to the two ethylene molecules at the MC-SCF/STO-3G level.13 In another study by Bernardi et al.,14 they discussed the head-to-tail dimerization of two ethylenes leading to the tetramethylene diradical using the MC-SCF method with an active space of four electrons in four orbitals (i.e., the π and



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π* orbitals of the two reactant molecules). This type of dimerization was also discussed in our recent work for 1,3-disilacyclobutane (1,3-DSCB).17 In a study by Carr et al., the activation barrier for the thermal decomposition of cyclobutane into two ethylene molecules was experimentally determined to be 62.5 ± 0.4 kcal/mol.8 This discrepancy in the activation energy values has led to the hypothesis that cycloreversion of cyclobutane is more likely to proceed via a stepwise mechanism rather than the single-step concerted one. The stepwise mechanism involves a tetramethylene diradical intermediate, which has been theoretically determined to be a thermodynamically stable species.12,13,18 The investigation of the concerted and stepwise mechanism at the same theoretical level has shown that the activation barrier via the diradical intermediate is lower than the concerted route.13,14 In 1994, Zewail and his coworkers showed evidence for the existence of tetramethylene diradical in their experiment using the femtosecond pump-probe techniques with mass spectrometry,19 thereby providing unequivocal support for the stepwise cycloreversion of cyclobutane via a diradical intermediates. Recently, Liese et al. used radical scavengers and electron paramagnetic resonance (EPR) experiments to directly prove the existence of a diradical indeterminate in the thermal cycloreversion of two stereoisomers containing a cyclobutane moiety.20 In addition to the extensively studied cyclobutane molecule, cycloreversion of silacyclobutanes (SCBs), a group of heterocyclobutane molecules containing a silicon atom, has also been studied.3,5, 21-24 Also, the ring opening of the silacyclobutene ring either as a substituent or fused to an annulene ring has been theoretically studied.25 In their work on non-polar vs. polar cycloadditions, Bernardi et al. reported that the concerted cycloaddition can be stabilized in polar π-bonds containing C=Si and C=O.14 In addition, for [2+2] cycloaddition, the polarization in the double bond in the reactants is known to lead to a relaxation of the Woodward-Hoffman


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rules.26,27 This relaxation of the Woodward-Hoffman rules has been demonstrated in the theoretical study of the dimerization of silene by Seidl et al.28 It is therefore interesting to study the cycloreversion of SCBs. The ring opening of the SCB molecule has been theoretically investigated by Gordon and coworkers.21 The authors have located the transition state for the symmetry forbidden [2s+2s] concerted route and found it to lie 62.1 kcal/mol above SCB at the MRMP/6-311G(d,p)//CASSCF(8,8)/6-31G(d) level of theory. This value is higher than the ones for the transition state of stepwise process initiated by a C-C bond rupture (51.5 kcal/mol) or by a Si-C bond cleavage (57.3 kcal/mol). Both concerted [2s+2s] and stepwise cycloreversion mechanisms of SCBs and other heterocyclobutanes have been a subject of research by Gusel'nikov and coworkers,22,23 who also found that the stepwise mechanism was energetically more favorable for SCB and its dimethyl-substituted derivative, i.e., 1,1-dimethyl-1silacyclobutane (DMSCB). In Gusel'nikov’s work, the stepwise cycloreversion in SCB initiated by a C-C bond rupture was shown to have a lower activation barrier than the one initiated by a Si-C bond breakage, in good agreement with Gordon’s study. This theoretical prediction was experimentally proven by a study from our group,29 where deuterium labeling of the two methyl substituents in DMSCB was utilized to provide evidence of stepwise ring-opening processes initiated by both ring Si-C and C-C bond cleavage and also of the preference of an initial C-C bond cleavage. In our recent kinetic study of 1-methyl-1-silacyclobutane (MSCB) in a hot-wire chemical vapor deposition process,30 the activation energies for three individual decomposition pathways, including cycloreversion, ring opening initiated by 1,2-H shift, and exocyclic Si-CH3 cleavage, were determined both experimentally and theoretically. The much lower experimental values lent strong support that the decomposition in the presence of a metal wire is catalytic in nature. Furthermore, in the process of ab initio calculations of the cycloreversion of MSCB,30 a



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new transition state for the concerted cycloreversion (64.0 kcal/mol relative to MSCB) was reported, in addition to the well-known symmetry forbidden one (62.9 kcal/mol relative to MSCB). The new transition state reported in the concerted cycloreversion of MSCB30 is believed to correspond to the orbital-symmetry-allowed [2s+2a] route, which has escaped being located so far, to our best knowledge. In this work, we present a systematic study for the concerted and stepwise cycloreversion of SCB and its two methyl-substituted derivatives (MSCB and DMSCB) using ab initio calculations. For each molecule, its cyclorversion via concerted [2s+2s], concerted [2s+2a], and stepwise diradical mechanism initiated by a Si-C or a C-C bond cleavage was investigated. The newly discovered symmetry allowed [2s+2a] transition states were reported for the three molecules, along with the energetic comparison to other cycloreversion routes. The second-order Møller-Plesset (MP2) perturbation theory, complete active space self-consistent field (CASSCF), and high-level coupled clusters calculation methods were used to optimize and validate the transition states and the corresponding diradical intermediates. Theoretical Methods The theoretical calculation methods used in this work were described in detail previously.17,30 Briefly, geometry optimization and vibration frequency calculations of the reactants, products, and diradical intermediates were performed using MP231,32 with the 6311++G(d,p) basis set. All intermediates involved in this work were optimized in their singlet state unless stated otherwise. Transition states were located by exploring the potential energy surface (PES) along the expected reaction coordinate, followed by a transition state optimization for the highest point in the PES and vibration frequency calculation. All transition states were confirmed to have a single imaginary frequency. Intrinsic reaction coordinate (IRC) was used to


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confirm that each TS connects the two desired minima. Final single point energies were calculated using the coupled cluster method with single, double, and perturbative triple excitations (CCSD(T))33,34 with the 6-311++G(3d,2p) basis set. Therefore, the full notation for the calculation method used in this work is referred herein by CCSD(T)/6-311++G(3d,2p)// MP2/6-311++G(d,p). To validate the use of MP2 calculations for the stepwise cycloreversion via diradical intermediates, we have used the stepwise route initiated by a Si-C bond cleavage as a benchmark system. For this, the CASSCF35 method with the 6-311++G(d,p) basis set was used to optimize the geometry of all species involved in this route, followed by single point energy calculation with CCSD(T)/6-311++G(3d,2p). A CASSCF(8,8) active space was used, which included eight C-C and ring Si-C bonding and virtual orbitals and eight electrons in the two C-C and two Si-C bonding orbitals. The results were then compared with those obtained at the CCSD(T)/6-311++G(3d,2p)// MP2/6-311++G(d,p) level. In addition, CAS + MP2 single point energy calculations with the basis set of 6-311++G(3d,2p) were also performed on the CASSCF geometry. This was done by adding the keyword MP2 in the route section to the CAS calculations in Gaussian. The results were compared with those obtained at both CCSD(T)//CASSCF and CCSD(T)//MP2 levels. As CAS is not a size consistent method, i.e., EA+EB ≠ EA+B, one needs to be careful when using CASSCF or CASMP2 for the optimization and single-point energy calculations of two separate product species. The two separate species were placed in the same input file and kept at a fixed distance of approximately 8 Å. Zero-point energies (ZPE) were scaled by a factor of 0.9748 for those obtained by MP2 calculations as suggested by Scott and Radom,36 but they were not scaled for those calculated by CASSCF. Enthalpies (H298), Gibbs free energies (G298), and entropies (S298) at room temperature (298 K) and higher temperatures were computed as described in our earlier work.17 All calculations were



performed using the Gaussian 09 program.37 Natural atomic charges were obtained by performing the natural bond orbital (NBO) analysis using NBO 6.0,38 accompanying Gaussian. Results and discussions The [2+2] cycloreversion of SCB and its methyl-substituted derivatives (MSCB and DMSCB) to ethylene and (methyl-substituted)silenes via either a concerted or a stepwise mechanism is described in Scheme 1. The stepwise cycloreversion of SCBs can be initiated by a ring Si-C bond rupture through the diradical intermediate, ·Si(R1R2)CH2CH2CH2·, denoted as I. Another route for the stepwise cycloreversion is initiated by a C-C bond rupture proceeding through the diradical intermediate, ·CH2CH2Si(R1R2)CH2·, denoted as II. Here R1 and R2 can be H or CH3. Stepwise TS1-CR-S-SiC C

H

H2C

SiR1R2

I

Si

H

TS 2CR SSiC

SiR1R2

H R1

H

Concerted

Cycloreversion

Si

H2C

TS-CR-C1 TS-CR-C2

H

CH2

R2

H

S C C

(SCB: R1

H2C

=R =H 2

MSCB:R1=CH3, R2=H DMSCB: R1=R2=CH3)

Stepwise

R 1R 2 Si

H2C

C

TS1-CR-S-CC C

C

TS 2CR

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

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II

Scheme 1. Stepwise and concerted [2+2] cycloreversion processes of silacyclobutanes We successfully located the transition states of both [2s+2s] symmetry-forbidden (labeled as TS-CR-C1) and [2s+2a] symmetry-allowed (labeled as TS-CR-C2) routes for the three compounds, i.e., SCB, MSCB, and DMSCB. The optimized geometries for the six transition states are shown in Figure 1. Note here that the terms “allowed” and “forbidden” refer to orbital-


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symmetry-allowed and -forbidden processes. The geometry for TS-CR-C1-SCB agrees well with the one reported by Gordon et al.,21 and the one for TS-CR-C1-MSCB is in agreement with that obtained recently by Shiroudi et al.24 using the density functional theory (DFT) methods (shown in parentheses in Figure 1). The imaginary frequencies for transition states TS-CR-C1 correspond to synchronized vibration between the two olefins. This is not surprising since the transition state for the cycloreversion can be thought as the same for the cycloaddition process, as stated in the principle of microscopic reversibility.22

Figure 1. Optimized structures of the transition states involved in the concerted [2+2] cycloreversion of (a,d) SCB, (b,e) MSCB, and (c,f) DMSCB at the MP2/6-311++G(d,p) level of theory. The values in parentheses for TS-CR-C1-SCB are obtained from Ref. 2121 at the CASSCF(8,8)/6-31G(d) level of theory, and those for TS-CR-C1-MSCB are from Ref. 2424 at the B3LYP/6-311G** level of theory. All numbers shown are for bond distances between the heavy atoms.



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A [2s + 2a] approach with atoms solely from main group elements involves an allowed Zimmerman-Möbius orbital topology in contrast to the forbidden [2s +2s] Hückel topology. Recently, Mauksch et al. have shown that the Craig-Möbius [2s + 2s] transition state becomes allowed and competes with the Zimmerman-Möbius [2s + 2a] transition states in the olefin metathesis when a transition metal is involved.39,40 Although the symmetry-allowed [2s+2a] transition state, TS-CR-C2, was discussed for the cyclobutane molecule,12,13 this type of transition state has never been reported for silacyclobutanes. As Figure 2 shows, the fundamental difference between the two concerted transition states, TS-CR-C1 and TS-CR-C2, is the orientation at which ethene is approaching (methyl-substituted)silene to complete the cycloaddition. In TS-CR-C1 for SCB, ethene is mostly parallel to silene, i.e., the dihedral angle ∠Si1C2C3C4 is 0.0° (Figure 1a), but it is 63.0° in TS-CR-C2 (Figure 1d). The values for the same dihedral angles for MSCB and DMSCB are also shown in Figure 1. In addition, the imaginary vibrational frequency for TS-CR-C2 involves a full 180° methylene rotation in order to flip the p-orbital and achieve the antara attack required for this type of transition state. H

C

Si

H

CH3

H H

C

Si

CH3

H H

H

C

C

H

H

H

H

H

TS-CR-C-1

C

C

H H

TS-CR-C-2

Figure 2. p-orbital overlap for the [2+2] cycloaddition of methyl-substituted silene to ethene 10 ACS Paragon Plus Environment

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Examining the structure of TS-CR-C2 for the concerted [2s+2a] symmetry-allowed route and the associated IRC allowed us to reclassify it as an asynchronous transition state. Looking at TS-CR-C2 for SCB shown in Figure 1d, the C2-C3 bond distance (2.810 Å) is longer than the Si1-C4 distance (2.141 Å). This is also observed for MSCB and DMSCB. This indicates that TSCR-C2 is an asynchronous transition state, where a C-C rupture precedes the Si-C bond rupture. The progress of the intrinsic reaction coordinate for this transition state unambiguously confirms this finding. For the stepwise [2+2] cycloreversion via a Si-C bond rupture, the transition states, labeled TS1-CR-S-SiC and TS2-CR-S-SiC in Scheme 1, connecting the silacyclobutane molecules to the diradical intermediates I, and then to the final olefin products, respectively, have been found for the three compounds of SCB, MSCB, and DMSCB at the MP2/6311++G(d,p) level of theory. Optimized geometries for the three diradicals (I) for SCB, MSCB and DMSCB and the associated transition states are all shown in Figure 3. The transition state, TS1-CR-S-SiC, represents the head-to-tail dimerization of the two olefins, in accordance with our recent work on 1,3-DSCB.17 The geometries for the diradical and transition states of SCB are close to the ones reported by Gordon et al.21 The imaginary vibrational frequency for TS1-CR-SSiC corresponds to an Si1-C4 bond stretching accompanied with methylene and silene rotation. As for the imaginary vibrational frequency for TS2-CR-S-SiC, it represents a C2-C3 bond stretching as expected, in order to complete the C-C rupture to form the two olefins. Both TS1CR-S-SiC and TS2-CR-S-SiC have been confirmed to connect their respective diradicals with SCBs and the olefin products, respectively, by following their intrinsic reaction coordinates (IRC).



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Figure 3. Optimized structures of the transition states involved in the [2+2] stepwise cycloreversion via an initial ring Si-C bond cleavage of (a, d, g) SCB, (b, e, h) MSCB, and (c, f, i) DMSCB at the MP2/6-311++ G(d,p) level of theory. The values in parentheses for SCB diradical and transition states are obtained from Ref. 2121 at the CASSCF(8,8)/6-31G(d) level of theory. Values in red for the three diradicals represent natural atomic charges computed using natural bond analysis (NBO) at the MP2/6-311++G(d,p) level of theory. All numbers shown are for bond distances between the heavy atoms.

At the MP2/6-311++G(d,p) level of theory, all attempts to locate the transition states for the stepwise cycloreversion of SCB, MSCB, and DMSCB initiated by a C-C bond rupture have failed. Gordon et al. were able to locate the transition states for this reaction pathway at the CASSCF(8,8) level and suggested that this transition state was not likely to exist at higher levels 12 ACS Paragon Plus Environment

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of theory such as the MP2 methods used here.21 Since MP2 is based on a single-determinantal UHF wavefunction, it is not entirely appropriate for application to diradicals. Accordingly, the geometries for all species in the entire stepwise routes via diradical intermediates were also optimized at the CASSCF(8,8)/6-311++G(d,p) level of theory. The single point energies were then obtained at the CCSD(T)/6-311++G(3d,2p) level with the CASSCF-optimized geometries. The results obtained for the stepwise route initiated by a Si-C bond cleavage via diradical I were compared with those at the CCSD(T)/6-311++G(3d,2p)//MP2/6-311++G(d,p) level. The geometry data for diradical I and the two transitions states involved in this route, i.e., TS1-CR-SSiC and TS2-CR-S-SiC, optimized at the CASSCF(8,8)/6-311++G(d,p) level is shown in square brackets in Figure 3 for comparison. It can be seen that, for diradical I, the central C2-C3 bond is slightly shorter in the CASSCF geometry as compared to the MP2 one, whereas the two terminal bonds (Si1-C2 and C3-C4) are slightly longer in the CASSCF geometry. A comparison of the relative energy values at 0 K of various species involved in this route to the reactant obtained at different levels of theory is listed in Table 1. The CCSD(T) energies of the diradical I and the two transition states on the CASSCF geometry were slightly lower than those with the MP2 geometry, with the difference in the range of 0.4 - 5.3 kcal/mol. In addition, single point energies were also calculated at the CASMP2(8,8)/6-311++G(3d,2p) level on the CASSCF geometry as described in the Theoretical Methods section. The CASMP2 approach, which builds on a better MC-SCF wavefunction but does not capture as much electron correlation, is then compared with the CCSD(T) approach, which builds on the UHF wavefunction. As Table 1 shows, the differences between the energy values at the CASMP2//CASSCF and the CCSD(T)//CASSCF levels were in the range of 0.2 – 7.4 kcal/mol. The comparison of the calculation results at



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different level of theories for the stepwise route via diradical I showed that CCSD(T)//MP2 level provided results in reasonable agreement with the CCSD(T)//CASSCF methods. We also successfully located the transition states for the stepwise route through diradical II using the CASSCF(8,8) approach with the 6-311++G(d,p) basis set. Optimized structures of the transition states labelled as TS1-CR-S-CC and TS2-CR-S-CC, and diradical II at the CASSCF/6-311++G(d,p) level of theory are shown in Figure S1 in the Supporting Information. The comparison of the relative energy values at 0 K of all species involved in this route relative to the reactant at the CCSD(T)//CASSCF and CASMP2(8.8)//CASSCF can be found in Table S1 in the Supporting Information. The same comparison of calculations using the three different levels of theory for the concerted cycloreversion routes via both TS-CR-C1 (2s+2s) and TS-CRC2 (2s+2a) was also made. The results are shown in Table S1. It is noticed that the energies of TS-CR-C1 for the (2s+2s) cycloreversion route obtained at the CCSD(T)//CASSCF level are lower than those obtained at the CCSD(T)//MP2 level, but with much smaller difference. All the comparisons described above suggested that calculations at the CCSD(T)/6-311++G(3d,2p)// MP2/6-311++G(d,p) can capture the energetics reasonably well for both the concerted and stepwise cycloreversion of the three silacyclobutane molecules studied in this work. Therefore, only the results using CCSD(T)/6-311++G(3d,2p)//MP2/6-311++G(d,p) are presented below.


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Table 1. Relative energy values at 0 K to the reactant (in kcal/mol) of all species involved in the stepwise cycloreversion route by a SiC bond cleavage for the three silacyclobutane molecules SCB

MSCB

TS1a

Ia

TS2a

CCSD(T)//MP2

59.9

57.5

64.9

CCSD(T)//CASSCF

54.6

54.0

CASMP2//CASSCF

52.3

50.8

Productsb

TS1a

Ia

40.2

62.9

64.2

40.6

65.3

35.3

DMSCB

TS2a Productsb

TS1a

Ia

TS2a

Productsb

58.8

66.5

41.7

63.2

59.4

67.5

43.0

59.6

56.8

66.1

42.1

62.0

58.8

67.0

43.9

58.9

56.3

73.5

38.9

57.3

59.3

66.8

47.0

a

TS1 and TS2 are both for the stepwise cycloreversion route initiated by a Si-C bond cleavage. The full names as appeared in previous sections are TS1-CR-S-SiC and TS2-CR-S-SiC. I represents diradical I, ·Si(R1R2)CH2CH2CH2·. b Products represent the two species produced from cycloreversion of the three silacyclobutane molecules. Specifically, they are silene + ethylene, methylsilene + ethylene, and dimethylsilene + ethylene, respectively for SCB, MSCB, and DMSCB.



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Figure 4 shows the relative enthalpies at 0 K for all the transition states and products involved in the [2+2] cycloreversion to that of the reactant (i.e., SCB, MSCB, and DMSCB) calculated at the CCSD(T)/6-311++G(3d,2p)//MP2/6-311++G(d,p) level of theory. Since no transition states can be located for the stepwise route via an initial C-C bond cleavage at the same level of theory, it is not included in Figure 4, but the results from the CCSD(T)/6311++G(3d,2p)//CASSCF/6-311++G(d,p) level are shown separately in the Supporting Information in Figure S2 (a –c) for the three silacyclobutane molecules, along with those for the stepwise route via an initial Si-C bond cleavage. It was previously shown that the stepwise [2+2] cycloreversion was favored over the concerted one for SCB21 and 1,3-DSCB.17 Our calculations in this work agree well with the finding for SCB, as shown in Figure 4a, where the energy of TSCR-C1-SCB (64.6 kcal/mol) is higher than that of the stepwise transition state TS1-CR-S-SiCSCB (59.9 kcal/mol). Interestingly, the difference between TS-CR-C1-MSCB and TS1-CR-SSiC-MSCB is zero, and TS-CR-C1-DMSCB is lower in energy than TS1-CR-S-SiC-DMSCB by 2.0 kcal/mol. This can be rationalized by the fact that the imaginary frequency of TS1-CR-S-SiC involves a rotation of the silene and ethylene moieties about the central C-C bond. Adding one methyl group (MSCB) or two (DMSCB) hinders this rotation, and therefore raises the TS1-CRS-SiC energy. Similar observation is obtained for the newly found TS-CR-C2 transition states. There is a gradual increase in their energies from SCB, to MSCB, and to DMSCB. Since the imaginary frequency for this type of transition state involves a methyl-substituted silene rotation, the increase in energy is attributed to the same reason. On the other hand, it is noted that the methyl substitution also affects the stability of diradical I, the intermediate formed in the stepwise cycloreversion via an initial Si-C bond rupture. Adding methyl substitutions to the Si atom in diradical I increases the natural atomic charge on Si, as shown in Figure 3 (a-c).


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Figure 4. Energy level diagrams for the concerted and stepwise cycloreversion of (a) 1,1dihydrio-1-silacyclobutane (SCB), (b) 1-methyl-1-silacyclobutane (MSCB), and (c) 1,1dimethyl-1-silacyclobutane (DMSCB). Values obtained for 0 K at CCSD(T)/6311++G(3d,2p)//MP2/6-311++G(d,p) level of theory (ZPE correction included).



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According to the NBO analysis, the charges on Si are +0.984, +1.175, and +1.372 in diradical I for SCB, MSCB, and DMSCB, respectively. This is because adding more methyl groups to the positively charged silicon causes more electron density withdrawn by the more electronegative methyl groups. Due to this positive charge increase in Si atoms, the diradical I becomes less stable with increasing methyl substitution, as Figure 4 shows. The new surprising fact is that the symmetry allowed TS-CR-C2-SCB, which involves a rotation of methylene in the silene moiety, is more favorable than TS-CR-C1-SCB by 1 kcal/mol at the CCSD(T)/6-311++G(3d,2p)//MP2/6-311++G(d,p) level of theory. This discovery motivated us to optimize and compare the energies for the symmetry forbidden and allowed transition states for the [2+2] cycloreversion of cyclobutane (CB) under the same level of theory. We successfully located TS-CR-C1-CB at the MP2/6-311++G(d,p) level and found it to be highly energetically unfavorable at 96.4 kcal/mol above cyclobutane. This value is much lower than the potential barrier of 156 kcal/mol determined theoretically by Wright and Salem.11 This is due to the fact that the 156 kcal/mol barrier was computed from the potential energy surface using primitive Slater-type orbitals, without eventually optimizing the transition state. Unfortunately, we were not able to optimize TS-CR-C2 for cyclobutane using MP2/6311++G(d,p). Hence, we used simple Hartree-Fock method to optimize its structure, and then computed its energy at the CCSD(T)/6-311++G(3d,2p) level. We found that TS-CR-C2-CB is 71.8 kcal/mol above cyclobutane at CCSD(T)/6-311++G(3d,2p) //HF/6-311++G(d,p) level of theory. At this same level, TS-CR-C1-CB was 98.2 kcal/mol higher than cyclobutane. This suggests that the symmetry-allowed transition state for cyclobutane is lower in energy than the symmetry-forbidden one, in agreement with our results for SCB. The fact that TS-CR-C2-CB can be optimized only at the HF level does, however, questions its authenticity as a true


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transition state for cyclobutane. Optimized structures for the two concerted transition states for cyclobutane are shown in Figure 5.

Figure 5. Optimized structure of the transition states involved in the [2+2] concerted cycloreversion of cyclobutane . TS-CR-C1-CB is obtained at MP2/6-311++G(d,p) level of theory. TS-CR-C2-CB is obtained at HF/6-311++G(d,p) level of theory. The values in parentheses for TS-CR-C1-CB and TS-CRC2-CB are obtained from Ref. 1313 at MC-SCF/STO-3G level of theory. All numbers shown are for bond distances between the heavy atoms.

In the previous section, we discussed the [2+2] cycloreversion of SCB, MSCB, and DMSCB in terms of the activation enthalpies computed at 0 K at the CCSD(T)/6311++G(3d,2p)//MP2/6-311++G(d,p) level, which are listed in Table 2. The activation enthalpy values at 0 K in Table 2 show that the relative stability of TS-CR-C1 increases as more methyl substitution replaces H on the Si atom, i.e., going from SCB to DMSCB. In order to know the effect of temperature on the cycloreversion reactions, we computed the activation parameters, ≠ ≠ ≠ including ∆𝐻𝐻298 , ∆𝐺𝐺298 , and ∆𝑆𝑆298 at room temperature (298 K) and they are also listed in Table

2. The thermochemical parameters at 298 K, including ∆H298, ∆G298, and ∆S298 are shown in

Table 3. Similar to the temperature of 0 K, SCB cycloreversion through the symmetry-allowed transition state (TS-CR-C2-SCB) is more kinetically favorable than the symmetry-forbidden one ≠ ≠ (TS-CR-C1-SCB) at the room temperature, both in terms of ∆𝐻𝐻298 and ∆𝐺𝐺298 . This is not the

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case for MSCB or DMSCB at both 0 K and 298 K, as Table 2 shows. However, the entropic term ≠ 𝑇𝑇∆𝑆𝑆298 for the symmetry-allowed transition state, TS-CR-C2, is higher than the one for the TS-

CR-C1 for MSCB and DMSCB. This is due to the loose nature of the TS-CR-C2 transition state. ≠ ≠ Because a high value of ∆𝑆𝑆298 will affect the growth of ∆𝐺𝐺298 as a function of temperature, we ≠ for TS-CR-C2 to surpass the one for TS-CR-C1 at one point with expect that the ∆𝐺𝐺298

increasing temperatures, and become more kinetically favorable for these two molecules. Therefore, we computed the Gibbs free energy of activation, ∆G≠, for both concerted cycloreversion transition states at temperatures ranging from 298 – 2000 K at 200 K intervals. The results are plotted in Figure 6. While SCB cycloreversion through the symmetry allowed TS-CR-C2-SCB is more favorable than the TS-CR-C1-SCB at all temperatures, it also becomes kinetically favored for MSCB and DMSCB at temperatures higher than 600 K and 1800 K, respectively. Table 3 lists the thermochemical parameters at 298 K for the cycloreversion processes of SCB, MSCB, and DMSCB. The increase in the energy of diradical I as the number of methyl substitution in Si increases has been explained previously in terms of the increase in the natural atomic charges in the terminal Si atoms. The cycloreversion reactions of three molecules become less endergonic with increasing temperature due to the large entropic terms as is shown in Table 3.


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Table 2. Enthalpies, entropies, and Gibbs free energies of activation for the concerted and stepwise [2+2] cycloreversion of three silacyclobutane molecules along with the imaginary frequencies for the corresponding transition states (TS) calculated at the CCSD(T)/6-311++G(3d,2p)//MP2/6-311++G(d,p) level Molecule

SCB

MSCB

Route

[2s+2s] [2s+2a]

TS

TS-C1

TS-C2 TS1-SiC TS2-SiC

TS-C1

TS-C2 TS1-SiC TS2-SiC

TS-C1 TS-C2 TS1-SiC TS2-SiC

Imaginary Frequency (cm-1)

-372.6i

-382.7i

-185.9i

-604.9i

-326.2i

-358.1i

-176.6i

-612.0i

-290.1i

-341.4i

-100.5i

-602.7i

64.6

63.7

59.9

64.9

62.9

64.0

62.9

66.5

61.2

64.7

63.2

67.5

65.1

64.2

60.7

65.8

63.4

64.6

63.1

67.3

61.6

65.3

63.5

68.3

64.2

63.2

59.0

63.6

62.6

63.2

62.7

65.0

60.9

63.9

62.5

65.8

1.0

1.0

1.6

2.2

0.8

1.4

0.4

2.2

0.8

1.3

0.9

2.5

∆𝐻𝐻0≠ (kcal/mol) ≠ ∆𝐻𝐻298 (kcal/mol) ≠ ∆𝐺𝐺298 (kcal/mol) ≠ 𝑇𝑇∆𝑆𝑆298 (kcal/mol)

Stepwise via I

[2s+2s] [2s+2a]

DMSCB

Stepwise via I

[2s+2s] [2s+2a]

Stepwise via I



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Figure 6. Gibbs free energies of activation (∆G≠) for the cycloreversion of (a) 1,1-dihydrio-1silacyclobutane (SCB), (b) 1-methyl-1-silacyclobutane (MSCB), and (c) 1,1-dimethyl-1silacyclobutane (DMSCB). Values obtained at CCSD(T)/6-311++G(3d,2p)//MP2/6-311++G(d,p) level of theory (ZPE correction included).


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Table 3. Reaction enthalpies, entropies, and Gibbs free energies for the cycloreversion of three silacyclobutane molecules calculated at the CCSD(T)/6-311++G(3d,2p)//MP2/6-311++G(d,p) level Reactant

SCB

Products

I

∆H0 (kcal/mol)

57.5

∆H298 (kcal/mol)

MSCB

two olefins

DMSCB

I

two olefins

I

two olefins

40.2

58.8

41.7

59.4

43.0

58.4

42.1

59.5

43.3

59.7

44.5

∆G298 (kcal/mol)

56.0

29.5

57.7

29.9

58.9

31.1

T∆S298 (kcal/mol)

2.4

12.6

1.8

13.5

0.8

13.4

Conclusions A theoretical study for the concerted and stepwise [2+2] cycloreversion of silacyclobutane (SCB) and its methyl-substituted derivatives (MSCB and DMSCB) was performed. In addition to the known symmetry-forbidden concerted [2s+2s] cycloreversion transition state, a new symmetry-allowed [2s+2a] transition state was located for all three molecules at the MP2/6-311++G(d,p) level of theory. It has been found that the concerted [2s+2a] cycloreversion is kinetically more favorable than the [2s+2s] cycloreversion for SCB at all temperatures. The opposite was true for MSCB and DMSCB at 0 K and room temperature, where the [2s+2s] route was favored. However, because of the loose nature of the [2s+2a] transition state, an analysis for the Gibbs free energy of activation (∆G≠) as a function of temperature shows that ∆G≠ for the symmetry-allowed [2s+2a] cycloreversion becomes lower than the one for [2s+2s] at temperatures above 600 K and 1800 K, respectively, for MSCB and DMSCB. The transition states for stepwise cycloreversion via a ring Si-C and a C-C bond cleavages were located using MP2/6-311++G(d,p) and CASCSCF/6-311++G(d,p) level, respectively. For SCB, the stepwise pathway through the Si-C bond cleavage is more 23 ACS Paragon Plus Environment


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energetically favorable than the concerted reaction. However, the diradical intermediate I, represented by ·Si(R1R2)CH2CH2CH2· becomes less stable with increasing methyl substitutions on Si atoms, which leads to a more favorable concerted cycloreversion for DMSCB. This work provides new theoretical insights into the [2+2] cycloreversion process in SCB and its methyl-substituted derivatives. The existence of the new symmetry-allowed [2s+2a] transition state can be examined experimentally by studying the thermal decomposition of SCB molecules with different substituents on the Si atom as the route taking place through the [2s+2a] transition state should involve a change in the stereochemistry of the substituents on the Si atom. Supporting Information The optimized structures of the transition states involved in the stepwise cycloreversion of three silacyclobutane molecules through a C-C bond rupture and the energy-level diagrams can be found in the Supporting Information. Acknowledgments The financial support for this work by the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. Access to Gaussian 09 was provided by Compute Canada. Special thanks are due to Yilin Zhao for performing some of the calculations in this work.


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New Orbital Symmetry Allowed Route for Cycloreversion of

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