[2+2] Cycloaddition Reactions of Ethylene Derivatives with the Si(100

Possible mechanisms of the [2+2] cycloaddition reactions of ethylene (1), propylene (2), vinyl chloride (3), and styrene (4) with the Si(100)-2 × 1 s...
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J. Phys. Chem. B 2005, 109, 5199-5206

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[2+2] Cycloaddition Reactions of Ethylene Derivatives with the Si(100)-2 × 1 Surface: A Theoretical Study Yong Wang,† Jing Ma,*,† Satoshi Inagaki,‡ and Yong Pei† Department of Chemistry, Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of MOE, Nanjing UniVersity, Nanjing, 210093, P. R. China, and Department of Chemistry, Gifu UniVersity, Gifu, 501-1193, Japan ReceiVed: NoVember 2, 2004; In Final Form: December 27, 2004

Possible mechanisms of the [2+2] cycloaddition reactions of ethylene (1), propylene (2), vinyl chloride (3), and styrene (4) with the Si(100)-2 × 1 surface have been investigated by theoretical calculations with the unrestricted density functional theory (DFT) and the second-order Møller-Plesset perturbation theory (MP2). Facile occurrence of the studied reactions is supported by the low activation energies (2.45∼5.76 kcal/mol) in the rate-determining steps. The buckled Si(100) surface facilitates the reactions via the low-symmetric pathways. The reactions follow the diradical mechanism of thermal [2+2] cycloaddition reactions between π-electron donors (the ethylene derivatives) and acceptors (the Si surface) through a π-complex precursor and a singlet diradical intermediate. The influence of substitutents on the relative reactivity takes a qualitative sequence of 1 < 2 < 3 < 4. The natural bond orbital (NBO) analysis and the released heat of some model reactions suggest that the relative reactivity might be partially understood by the π-electron-donating abilities of the substituent to stabilize the radical centers at the transition states of the rate-determining steps.

1. Introduction In recent years, the surface-tethered organic molecules have been of increasing interest. An active silicon surface is likely to undergo relaxation and reconstruction to gain stability.1-3 The chemistry of the silicon (100) surface has attracted both experimental and theoretical interests because it is the starting point for designs of the silicon-based microelectronics.4 With the development of new experimental techniques and quantum mechanical methods, the cycloaddition reactions of some unsaturated organic compounds,4-20 such as ethylene,18 acetylene,19 cyclopentene,4 and benzene,20 with the Si(100) surface have been investigated, offering useful information for the potential usages in microelectronics, nonlinear optical materials, sensors, and biologically active surfaces.21 The introduction of various function groups in those unsaturated reactants is thus anticipated to be able to tune the chemical and physical activities of the silicon surfaces. However, the substituent effect on the cycloaddition reactivities of various unsaturated molecules with the Si(100) surface was less known until now. The present work makes an effort to investigate the effects of substitutions on the cycloaddition reactions of CH2dCHR (1: R) H, 2: R) CH3, 3: R) Cl, and 4: R) C6H5) with the Si(100) surface (cf. Scheme 1) through our theoretical calculations. On the native Si(100) surface, each Si dimer has two dangling bonds with each Si atom having a single unpaired electron as shown in Figure 1a. So, the surface atoms on thermally reconstructed Si surface can easily pair into dimers connected by a strong σ bond and a weak π bond.1-17,22-24 In other words, it can be thought of as a silicon double bond analogous to alkenes (cf. Figure 1a), which has been revealed by the scanning tunneling microscope images of Si(100). 25 It has been suggested * Author to whom correspondence should be addressed. † Nanjing University. ‡ Gifu University.

SCHEME 1. [2+2] Cycloaddition on the Si(100)-2 × 1 Surface with Ethylene Derivatives

that the SidSi bonds of the Si(100) surface could undergo the cycloaddition reactions with the unsaturated organic compounds such as those CdC bonds of the alkenes. On the other hand, the π bonds of Si(100) are very weak, implying that these dimers might be better thought of as a diradical with each Si atom having a single unpaired electron.1,4,26 In practical theoretical studies, the truncated cluster model Si(100)-2 × 1 (Figure 1b) has been employed. The good agreement between the calculation results and experimental observations1,22,27,28 encourages us to extend the theoretical treatments to the cycloaddition reactions of the substituted alkenes with the Si(100)-2 × 1 surface. The cycloaddition reactions are widely known in organic chemistry as the Diels-Alder ([4+2]) reaction between a conjugated diene and an alkene. The [2+2] cycloaddition reactions are important processes from both the synthetic and mechanistic viewpoints. It is well-known that the concerted [2+2] cycloaddition reactions are symmetry-forbidden according to the Woodward-Hoffmann rules. However, on the Si(100) surface, evidences have shown the minor but significant [2+2] cycloaddition products of the conjugated diene exist,23,24,29-31 although the [4+2] products are more thermodynamically favorable because of the smaller strain energies in the sixmembered rings. In addition, the [2+2] cycloaddition reaction of ethylene with the Si(100) surface has been observed recently,18e-18g which agrees well with the theoretical predictions.1-4,9,12,13a,18h,23,32 The calculations of [2+2] and [4+2] pathways for the carbonyl compounds adding to the Si(100) surface have also suggested that both reactions proceed with negligible activation barriers.32,33 So, both the experimental

10.1021/jp0450080 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/25/2005

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Figure 1. (a) Top and side views of the native and reconstructed Si(100) surface. (b) A Si9H12 cluster is adopted as a model of the Si(100) surface consisting of four layers of silicon atoms in our calculations.

and theoretical studies indicate that the analogous [2+2] reactions between alkenes and the Si(100) surface are very facile, and they can even take place at room temperature. In addition to the above-mentioned achievements, exploration of the substituent effects on the [2+2] cycloaddition reaction mechanisms and reactivities may serve as guides in understanding the general trends in reactions of various organic molecules with Si surfaces. In this paper, we hope to gain new insights into the [2+2] cycloaddition reactions with the Si(100)-2 × 1 surface through the study of the [2+2] reactions by changing the substituent group, R (1: R ) H, 2: R ) CH3, 3: R ) Cl, and 4: R ) C6H5) of CH2dCHR (Scheme 1). This study enables us (1) to observe the changes in electronic structures of the reactants, intermediates, transition states, and products caused by the substituents and (2) to understand the substituent effects on the reactivity of olefins in the [2+2] cycloadditions with the Si surfaces. 2. Models and Computational Details In our quantum chemical calculations, a Si9H12 cluster (as shown in Figure 1b) is adopted as a model of the Si(100) surface consisting of four layers of silicon atoms, with two Si atoms in the top layer comprising the surface dimer, four second-layer silicon atoms, two third-layer silicon atoms, and one fourthlayer silicon atom. Similar to the other theoretical works,33 no geometry constraint on either atomic positions or overall symmetry has been applied in studies of reaction path. All calculations are performed with the help of the Gaussian0334 programs on SGI3000 and SGI3800 workstations. The density functional theory with the three-parameter hybrid functional (B3LYP)35 was employed in most of the previous works.10,11,15-17,20f,23,26,28,30-33 In our present work, all reactants, intermediates (M1 and M2), transition states (TS1 and TS2), and products (Pr) of the cycloaddition reactions of ethylene derivatives 1-4 with the Si9H12 cluster model are also fully optimized at the UB3LYP/6-31G* level (with the optimized geometries displayed in Figure 2), since the singlet diradical intermediate and transition states are involved in the reaction process.36 However, the small activation energy barriers in those reactions and the relatively large spin contaminations in the broken-symmetry unrestricted calculation results of intermediates and transition states require the further references from the other electron correlation methods. In fact, Choi and Gordon37 have carried out extensive calculations to test the performance of the single-configurational methods (including the HartreeFock, DFT(B3LYP), the second-order Møller-Plesset perturbation theory (MP2)38), the multi-configurational complete active space self-consistent field (CASSCF), and the multireference MP2 theory on the cycloaddition reactions of acrylonitrile with

the Si(100)-2 × 1 surface. Although the use of multiconfigurational methods has been demonstrated to be necessary to obtain the quantitatively accurate predictions on the entire potential energy surface,37 the more economical singleconfigurational methods are employed in the present work, since we are mainly interested in the qualitative trends in relative reactivities of various ethylene derivatives. To include electron correlation contributions on the dispersion energies, the singlepoint calculations using MP2 with a basis set of 6-31G* are performed at the UB3LYP/6-31G* optimized structures. Such a strategy is designated by the standard notation of UMP2/631G*//UB3LYP/6-31G*. We also carry out some validation calculations on the reaction paths of 1 by using the more timeconsuming UMP2 full optimizations with effective core potential of LANL2DZ.39 The UMP2 fully optimized geometries of reactants, intermediates, transition states, and products along the reaction paths for 1 are shown in Figure S1 of Supporting Information. It can be found that all the UMP2/LANL2DZ optimized geometries along the [2+2] cycloaddition reaction paths for ethylene with the Si(100)-2 × 1 surface are very close to those optimized by the UB3LYP/6-31G* level (cf. Figure 2 and Figure S1). Although the activation energy barriers are underestimated by UB3LYP/6-31G* because of the limitation of functionals in describing the dispersion energy, the UB3LYP/ 6-31G* energy profiles are in qualitative agreement with the UMP2/LANL2DZ curves (cf. Figure S1). As addressed above, we pay attention to the changes in the activation barriers with different substituents; thus, we only adopt the UB3LYP/6-31G* results (supplemented with UMP2/6-31G*//UB3LYP/6-31G* energies in Table 1) throughout this paper to qualitatively discuss the substituent effects on the [2+2] cycloaddition reactions of ethylene derivatives with the Si(100) surface. Furthermore, to understand the trend in the reactivities of ethylene derivatives in the cycloadditions with the Si(100) surface, the natural bond orbital (NBO) analyses for all species are carried out with the UB3LYP/6-31G* wave functions. The charges calculated by the natural population analysis (NPA) and the energies of orbital interactions are obtained by using the NBO program40 as implemented in Gaussian 03. 3. Results and Discussion Low-Symmetric Pathways. Without constraints on the motion of subsurface atoms, a UB3LYP/6-31G* calculation of the symmetric dimer in Si9H12 produces a structure with C2V symmetry and a silicon double bond with a length of 2.239 Å (Figure 1b). As mentioned in the Introduction, a concerted [2+2] cycloaddition reaction of a symmetric dimer with an alkene is formally symmetry-forbidden according to the WoodwardHoffmann rules. However, the reaction might proceed via a low-

Cycloaddition Reactions of Ethylene Derivatives

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Figure 2. The optimized geometries of the intermediates (M1 and M2), the transition states (TS1 and TS2), and the products (Pr) for the [2+2] cycloaddition of CH2dCHR, 1 (R ) H), 2 (R ) CH3), 3 (R ) Cl), and 4 (R ) C6H5) with Si9H12 cluster model (UB3LYP/6-31G*).

symmetric pathway. Figure 2 depicts the predicted intermediates (M1, M2), transition states (TS1, TS2), and products (Pr) for the [2+2] cycloaddition of 1 (R ) H: ethylene), 2 (R ) CH3: propylene), 3 (R ) Cl: vinyl chloride), and 4 (R ) C6H5: styrene) with the SidSi double bond of the Si9H12 cluster model at the UB3LYP/6-31G* level. The potential energy profiles of these reaction paths are drawn in Figure 3 with the relative energies (∆E) and the Gibbs free energies (∆G) listed in Table 1. It can be found that all reactions proceed in a similar way. The reaction is initiated by the formation of the intermediate M1, releasing the small amount of the association energy (0.414.71 kcal/mol). The transition-state TS1 is then reached by overcoming the small activation barrier of around 2.45-5.76 kcal/mol. The formation of the first Si-C bond between CH2d CHR and the SidSi bond leading to the intermediate M2 releases relatively a larger amount of the energy (around 4.399.98 kcal/mol). Finally, the cycloaddition product Pr is generated by the second Si-C bond formation through the transitionstate TS2, whose activation barrier is negligible (less than 1 kcal/mol). For the parent species 1 (R) H), we obtain similar results to those in previous works.1,32 In addition to the abovementioned intradimer [2+2] cycloaddition, it was recently

reported that the interdimer [2+2] process of ethylene as well as the parallel end-bridge adsorption mode may play an important role.32c The similar mechanism of the [2+2] cycloaddition for 1, 3-cyclohexadiene has also been investigated by Choi and Gordon.41 It is probable that once the [2+2] cycloaddition of the alkene portion of the molecule has occurred, the cyclopropyl fragment is held in close proximity, enabling the reaction to take place with ease. For the propylene (2) addition, there is another potential competing reaction, the so-called “ene” reaction, in which the H-migration from the methyl group to the Si(100) surface takes place. Such ene reactions have been studied in the cycloadditions of the cyclohexadiene on Si surfaces.23 For styrene (4) cycloaddition reaction with the Si(100) surface, the [4+2] cycloaddition can also occur easily on the (100) surface in addition to the [2+2] process.42 The essence of the occurrence of the [2+2] cycloadditions of 1-4 with the SidSi dimers in contrast with that from the hydrocarbon chemistry is the reconstructed Si surface with a low-symmetric structure in the initial intermediate M1, which will be discussed as follows. The geometrical feature of M1 is a three-centered interaction between the two carbon atoms of the CdC bond and one Si

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TABLE 1. The Relative Energies (∆E, kcal/mol) at the Levels of UB3LYP/6-31G* and UMP2/6-31G* Relative to M1 and the Gibbs Free Energies (∆G, kcal/mol) Obtained at the UB3LYP/6-31G* Level ∆E (kcal/mol) species

UB3LYP/6-31G*a

CH2dCH2 + Si(100)-2 × 1 2.36 1a(M1) 0.00(0.00) 1b(TS1) 5.76(0.45) 1c(M2) -1.76(1.01) 1d(TS2) -1.46(0.95) 1e(Pr) -40.78(0.00) CH2dCHCH3 + Si(100)-2 × 1 3.30 2a(M1) 0.00(0.00) 2b(TS1) 3.78(0.40) 2c(M2) -0.61(1.00) 2d(TS2) -0.28(0.97) 2e(Pr) -36.01(0.00) CH2dCHCl + Si(100)-2 × 1 0.41 3a(M1) 0.00(0.00) 3b(TS1) 3.17(0.31) 3c(M2) -5.23(1.01) 3d(TS2) -4.62(0.92) 3e(Pr) -41.52(0.00) CH2dCHC6H5 + Si(100)-2 × 1 4.71 4a(M1) 0.00(0.00) 4b(TS1) 2.45(0.00) 4c(M2) -7.53(1.02) 4d(TS2) -6.54(0.87) 4e(Pr) -32.67(0.00) a The 〈S2〉 values are given in the parentheses. b UMP2/6-31G*//UB3LYP/6-31G*.

Figure 3. Potential energy profiles of [2+2] cycloaddition reactions of CH2dCHR (1-4) with the Si(100)-2 × 1 surface at the level of UB3LYP/6-31G*.

atom of the SidSi bond. According to qualitative thoughts using the orbital interaction theory, the interaction of two centers of a donor and one center of an acceptor is a peculiar feature of the initial stage of thermal [2+2] cycloaddition reactions between the electron donors and electron acceptors, which favors the interactions between the HOMO of the donor and the LUMO of the acceptor to the greatest extent.43 The geometry of M1 is unstable and readily collapses. The corresponding species was called a quasi-intermediate for its negligible barrier in the [2+2] cycloaddition reaction between olefins (electron donors) and singlet oxygen (an electron acceptor).43d Scheme 2 gives us a simple picture of orbital interactions between the π-electron donor and acceptor to illustrate a possible mechanism of [2+2] cycloaddition reaction. The HOMO (d) of the CdC bond (the

∆G (kcal/mol) UMP2/6-31G*b 0.00 21.03 2.90 3.83 -42.23 0.00 11.07 4.19 4.68 -43.37 0.00 4.23 -16.29 -15.18 -63.35 0.00 4.31 19.78 21.10 -42.11

UB3LYP/6-31G* -7.77 0.00 5.74 -1.59 -0.54 -39.33 -7.73 0.00 4.12 -0.82 0.73 -33.81 -7.76 0.00 6.19 -1.91 -0.54 -36.44 -7.23 0.00 3.98 -6.73 -4.70 -30.71

donor, denoted by “D”) is allowed by the orbital symmetry in M1 to interact with not only the LUMO (a*) but also HOMO (a) of the SidSi bond (an acceptor, denoted by “A”). The d-a* interaction mixes the transferred configuration (T) into the ground (G) configuration. Concurrent d-a interaction allowed in M1 shifts an electron from the HOMO of the acceptor (a) to the hole in the HOMO of the donor (d) left by the preceding d-a* electron shift. The d-a* interaction followed by the d-a interaction gives rise to a significant mixing of the locally excited (HOMOfLUMO) electron configuration (EA) of the acceptor (i.e., the SidSi bond in this case) to prepare for the reactions characteristic to excited states or for the [2+2] cycloadditions in this case.43 In M1, the orbital symmetry forbids mixing-in of the locally excited configuration, ED, of the donor, since the interaction between a* and d* (denoted by a*-d*) required for an electron shift from a* in T to d* is forbidden by the orbital symmetry. However, the symmetry is broken at TS1, where the mixing-in of ED occurs. The mixing of T and EA increases as the decrease occurs in the HOMO-LUMO (da*) energy gap between the π-electron donor and the acceptor and the HOMO-LUMO (a-a*) energy gap of the acceptor, respectively. The thermal [2+2] cycloaddition is expected to be facilitated by the remarkable π-electron donor-acceptor relationship and by the polarizabilities of the reacting bonds, especially of the acceptor. Electronic Structures. To understand the general trend in the [2+2] cycloadditions of 1-4 with the Si(100) surface, we take a closer look at the changes in geometries and relative energies of the intermediates (M1, M2), the transition states (TS1, TS2), and the products (Pr). The intermediate M1 for the reactants 1-4 are denoted as 1a, 2a, 3a, and 4a, respectively. The shortest surface Si1-Si2 bond length of 2.257 Å is found in 3a (R ) Cl), which is almost identical to that of the bare Si9H12 cluster model (2.239 Å). To qualitatively understand this phenomenon, we resort to the HOMO and LUMO energies of reactants 1-4 and Si surface, which have been shown in Table 2. From Table 2, it can be found that ethylene derivatives 1-4 may play the role of

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SCHEME 2a

a

When the reactant is acrylonitrile, >Si)Si< is donor, while CH2)CH-CN is acceptor.

TABLE 2. The HOMOs and LUMOs (in Units of au) for the Reactants, and the Energy Gaps between the HOMO Orbital and the LUMO Orbital (d-a*, a*-d*, and a-d) energy gaps 1 (R ) H) 2 (R ) CH3) 3 (R ) Cl) 4 (R ) C6H5)

Si9H12a R ) CNa

HOMO (d)

LUMO (d*)

d-a*

a*-d*

a-d

-0.267 -0.250 -0.262 -0.221

0.019 0.028 -0.001 -0.031

0.148 0.131 0.143 0.102

0.138 0.147 0.118 0.088

0.061 0.044 0.056 0.015

HOMO (a)

LUMO (a*)

-0.206 -0.289

-0.119 -0.056

0.150

0.063

0.083

a

When the reactant is acrylonitrile, Si9H12 is donor (d), while CH2dCHCN is acceptor (a).

π-electron donors whereas the SidSi bond is an acceptor, because of the smaller gap between the HOMO of CH2dCHR and the LUMO of the Si(100) surface than that between the HOMO of the Si(100) surface and the LUMO of CH2dCHR. The π-electron-donating abilities of the ethylene derivatives usually increase with the HOMO (πCdC) energy: 3 (-0.262 au) < 2 (-0.250 au) < 4 (-0.221 au). Then, the energy gap between the HOMO of donors (ethylene derivatives) and the LUMO of the acceptor (Si surface) takes a reverse order, that is, 3 (0.143 au) > 2 (0.131 au) > 4 (0.102 au). So, the strong

SidSi bond in 3a relative to the other intermediates is understood by the weakest interactions between vinyl chloride and the SidSi bond because of the largest HOMO-LUMO energy gap, supported by the largest distance of 3.343 Å between Si1 and C3 in 3a (about 1.0 Å longer than those in 1a, 2a, and 4a) and by the little energy change (0.41 kcal/mol) from the isolated reactants to the intermediate M1 (Table 1). For the other intermediates (1a, 2a, and 4a), the surface SidSi dimers are significantly weakened because 2 and 4 have HOMOs at higher energy levels and donate electrons more to the SidSi bonds (cf. Table 2). The HOMO energy of 1 is -0.267 au; it is lower than those of the other three for there is no extra stabilization by the interaction with the substituents in 1. The electron population of the LUMO or the π* antibonding orbital increases and elongates the surface Si1-Si2 bond to around 2.35 Å. On the other hand, the calculated C3-C4 bond lengths of M1 are 1.363 Å (1a), 1.360 Å (2a), 1.333 Å (3a), and 1.370 Å (4a), respectively, which are close to the normal CdC bond length of 1.35 Å. In addition, the relative order of the C3-C4 bond lengths in M1, 3a < 1a ≈ 2a < 4a, is parallel to that of the CdC bond lengths in the isolated reactants, 3 (1.327 Å) < 1 (1.331 Å) ≈ 2 (1.333 Å) < 4 (1.339 Å) (cf. Figure S2). Here, the weak HOMO-LUMO interaction of vinyl chloride with the SidSi dimer is reflected again by a very small change of 0.006 Å in the CdC distance from the reactant 3 to the intermediate

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SCHEME 3. A Possible Pathway for the Attachment of Ethylene Derivatives with the Si(100)-2 × 1 Surface

3a, which is in contrast with the larger differences of around 0.030 Å in the CdC bond lengths upon the formation of the intermediate M1 for systems 1 (0.032 Å), 2 (0.027 Å), and 4 (0.031 Å). From these results, M1 can be approximately taken as a π-complex precursor. It can be found in Figure 2 that the SidSi dimers in M1 are in fact buckled, which enables the occurrence of the low-symmetric pathway as addressed above. The low-symmetric structure of the surface SidSi dimers in M1 may lead to a gradient in the electronic density. The calculated NBO charges presented in Table S1 of Supporting Information do exhibit the picture with a nucleophilic “buckledup” Si and electrophilic “buckled-down” Si as suggested by Liu and Hoffmann.1 The transition-states TS1 for the reactants 1-4 are denoted as 1b, 2b, 3b, and 4b, respectively, which connect the stable M1 precursor state to another intermediate M2. The lengths of the surface Si1-Si2 bond in 1b-4b are changed to 2.324 Å, 2.343 Å, 2.317 Å, and 2.413 Å, respectively. The Si1...C3 distances in the transition-states TS1 are shortened to 2.292 Å (1b), 2.177 Å (2b), 2.344 Å (3b), and 2.110Å (4b), respectively. Thus, the surface Si-Si bond length is the shortest and the interaction between the addition reactants is the weakest for 3b with the chloro-substituent, as in the M1 precursor state. On the contrary, the Si1...C3 distance in 4b (2.110 Å) with the phenyl-substituent is the shortest. This is also the case with that in the intermediate 4a with the shortest distance of 2.300 Å and the largest association energy of 4.71 kcal/mol. There is no remarkable difference in the geometries of the intermediate M2 (1c, 2c, 3c, and 4c). In M2, the CH2dCHR moiety is mono-σ bonded onto a Si atom with the Si1-C3 bond length of 1.944 Å (1c), 1.954 Å (2c), 1.947 Å (3c), and 1.949 Å (4c). The surface Si1-Si2 bond length is about 2.393 Å, which is considerably longer than that of the Si-Si bonds of the known disiliranes (2.27∼2.33 Å)44. The nonbonded Si2...C4 distance increases in the order of 1c (3.967 Å) < 2c (4.023 Å) < 3c (4.028 Å) < 4c (4.049 Å). There is also little difference in the geometries of transitionstates TS2 (1d-4d) of diradical character connecting the intermediates M2 to the [2+2] cycloaddition products. The surface Si1-Si2 bond lengths are 2.390 Å (1d), 2.393 Å (2d), 2.389 Å (3d), and 2.388 Å (4d), respectively. The Si1-C3 bonds in 1d-4d have similar bond lengths of around 1.944 Å. Our calculations reveal that the [2+2] cycloaddition products (Pr) of CH2dCHR with the Si(100)-2 × 1, 1e-4e, are more stable than the reactants by 43.14 (1e), 39.31 (2e), 41.93 (3e), and 37.38 kcal/mol (4e), respectively (at the UB3LYP/6-31G* level of theory). The Gibbs free energies at the 298.15 K and 1 atm (with the inclusion of ZPE corrections) for the products of 1-4 in the proposed mechanism are 31.56, 26.08, 28.68, and 23.48 kcal/mol with respect to the reactants. Although the small four-membered rings are formed with the Si2-Si1-C3 bond angles of around 78°, the [2+2] products (Pr) are stabilized by the formation of two strong Si-C bonds. The calculations predict that the activation barriers are low, indicating

TABLE 3. The Stabilization of the Radical Center with Different Substituents Can Be Verified by the Reaction Energies of RCH3 + CH3• f RCH2• + CH4 (R ) CH3, Cl, and C6H5) R

∆E (kcal/mol)

CH3 Cl C6H5

-4.85 -6.20 -16.67

the facile [2+2] cycloaddition of CH2dCHR (1-4) with the Si(100) surface. In addition, the acrylonitrile, CH2)CH-CN, is also selected to study [2+2]CC cycloaddition reaction with the Si(100)-2 × 1 surface. We reproduced the results previously reported by other groups.37 In the intermediate M2, the length of the surface Si1-Si2 bond is significantly increased to be larger than 4 Å, suggesting the surface Si-Si bond is broken. In this case, the donor-acceptor relationship is reversed. The surface SidSi bond is a π-electron donor while acrylonitrile is an acceptor: the energy gap (0.150 au) between the HOMO of the surface SidSi bond and the LUMO of acrylonitrile is smaller than that (0.170 au) between the HOMO of acrylonitrile and the LUMO of the surface SidSi bond. The Si atoms are more positively charged (0.27) and the nitrogen atom is negatively charged (-0.33) to a significant degree. The polarizability of the acceptor was suggested to facilitate the thermal [2+2] cycloaddition reactions. The HOMO-LUMO gap (0.233 au) of acrylonitrile is larger than that (0.087 au) of the SidSi bond or the acceptor in the reactions with 1-4. The lower polarizability of the acceptor or acrylonitrile may account for the slightly more reluctant [2+2] cycloaddition with the predicted activation energy barrier of 16.7 kcal/mol at the level of MRMP2.37 The electron-accepting property of acrylonitrile makes it different from ethylene (1), propylene (2), vinyl chloride (3), and styrene (4) in the [2+2] reactions with the Si(100)-2 × 1 surface. The Singlet Diradical Mechanisms. The cycloaddition reactions of 1-4 with Si(100) surfaces follow the similar singlet diradical mechanism as shown in Scheme 3, in which the intermediate M2 and the transition-states TS1 and TS2 have diradical characters to different extents. The 〈S2〉 values have been applied to evaluate the extent of spin contaminations in the unrestricted wave functions. They can also reflect to some extent the diradical characters. For the closed-shell systems, such as the reactants (CH2dCHR, 1-4), the intermediates M1 (1a4a), and the products Pr (1e-4e), all the electrons are paired with 〈S2〉 ) 0.00, displaying the “pure” singlet ground states. An “ideal” singlet diradical corresponds to a model with the unpaired electrons completely localized on the distal atoms without any through-space interactions. The real singlet diradicals lie between these two extremes with weak through-space interactions such as M2 (〈S2〉 ∼ 1.0) and TS2 (〈S2〉 ) 0.87∼0.97). Therefore, the nonbonded distance of Si2...C4 can provide a gross evaluation of the diradical character. This picture is in agreement with the other theoretical studies on the [2+2] cycloaddition of simple alkenes and alkynes with the Si(100)-2

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TABLE 4. The Stabilization Energies (in Units of kcal/mol) Obtained by the NBO Analysis of the Transition-state TS1 of the Rate-determining Step in the [2+2] Reactions at the UB3LYP/6-31G* Level of Theory

× 1 surface, which also follows the singlet diradical mechanism.1,9,13b,15,32 To summarize, the high π-electron-accepting capability (or the low LUMO (πsi-si*)) and the high polarizability (or the small HOMO-LUMO energy gap) of the SidSi π bond resulting from the weakness of SidSi facilitate the formation of radicallike intermediates such as M2 (1c, 2c, 3c, and 4c), which is different from the analogous alkenes. Thus, the [2+2] cycloaddition reactions can easily take place with the Si(100) surface through the singlet diradical mechanism. Trend in Reactivity. Although the cycloaddition reactions of 1-4 with Si(100) surfaces proceed by the similar mechanism, the relative activation barriers are different among the ethylene derivatives studied. From Figure 3 and Table 1, we find that the process from M1 to TS1 is the rate-determining step and its activation barrier takes the sequence of 1 (5.76 kcal/mol) > 2 (3.78 kcal/mol) > 3 (3.17 kcal/mol) > 4 (2.45 kcal/mol). In other words, the effect of substitutions on relative reactivity follows the order of 1 (R ) H) < 2 (R ) CH3) < 3 (R ) Cl) < 4 (R ) C6H5). One should be aware that this predicted reactivity trend is rather qualitative, because the calculation results obtained by the unrestricted methods may suffer from the strong spin contaminations for some stationary points. Since the process from M1 to M2 through TS1 is the ratedetermining step, the relative stability of TS1 is crucial for rationalizing the substituent effect. For the parent reactant 1 (R ) H), there is no extra stabilization by the interaction with the substituent. However, methyl-, chloro-, and phenyl substituents in the reactants 2-4 are anticipated to stabilize TS1 by the interactions between the p orbital of C4 and σ or π bonding orbitals of the substituents. The substituent effects on the stabilization were evaluated by the released heat of some model reactions, RCH3 + CH3• f RCH2• + CH4. The results of the calculations (Table 3) show a sequence of R ) CH3 (-4.85 kcal/mol) < R ) Cl (-6.20 kcal/mol) < R ) C6H5 (-16.67 kcal/mol), in agreement with the order of cycloaddition reactivities. The natural bond orbital (NBO) analysis of the transition-state TS1 (1b-4b) has also been carried out at the UB3LYP/6-31G* level to analyze such stabilization effects on the radical centers. The selected donor-acceptor interactions in Table 4 are the most significant ones with appreciable stabilization energies, which can partly account for the differences in relative stabilities of TS1. As expected, the NBO results show the relatively weak orbital interaction of 3.32 kcal/mol in 2b between the σC-H bonding orbital of the methyl group and the p orbital of C4, while in 4b a strong orbital interaction of 38.54 kcal/mol was found between the π bonding orbital of the phenyl group and the p orbital. The interaction of the lone pair orbital n on the chlorine atom with the vacant antibonding π*C-C orbital of the ethylene segment is demonstrated with the

stabilization energy of 10.57 kcal/mol (3b). Therefore, the stabilization of TS1 by the substituents have the trend of 1b < 2b < 3b < 4b, which is the same as the above-mentioned sequence of the reactivity, 1 (R ) H) < 2 (R ) CH3) < 3 (R ) Cl) < 4 (R ) C6H5). 4. Conclusions The mechanisms for [2+2] cycloaddition reactions of the ethylene derivatives CH2dCHR (1: R ) H, 2: R ) CH3, 3: R ) Cl, and 4: R ) C6H5) with the Si(100)-2 × 1 surface have been investigated through our DFT and MP2 calculations. Unlike the ordinary [2+2] cycloaddition in the hydrocarbon chemistry, the existence of the Si(100)-2 × 1 surface-enhanced low-symmetric pathway leading to the [2+2] products is demonstrated. The reaction barriers of the rate-determining steps for systems 1-4 are predicted to be 2.45-5.76 kal/mol, which indicates that the [2+2] reactions can easily occur with the Si(100)-2 × 1 surface. The cycloaddition reactions of the ethylene derivatives 1-4 are shown to follow the similar singlet diradical mechanism, proceeding via a π-complex precursor (M1) and a singlet diradical intermediate (M2). The order of 1 (R ) H) < 2 (R ) CH3) < 3 (R ) Cl) < 4 (R ) C6H5) in the relative reactivity has been predicted. The substituent effects on the stabilities of TS1 are suggested to rationalize the relative reactivity through the studies on some model reactions as well as the NBO analysis on the transition states. Our results may provide further insights into the understanding of the [2+2] cycloaddition reactions with the Si(100)-2× 1 surface. The unusually interesting chemistry of the Si(100) surface may be ascribed largely to the high π-electron accepting capability (the low LUMO (π*)) and the high polarizability (the small HOMO-LUMO energy gap) of the very weak π bond of the surface SidSi dimers. The mechanism of the [2+2] cycloaddition reactions can be qualitatively understood by the simple picture of orbital interactions between the π-electron donors (HOMO) from ethylene derivatives (R ) H, CH3, Cl, and C6H5) and the acceptor (LUMO) from the Si(100) surface, followed by the HOMO-HOMO and LUMO-LUMO interactions. Further investigations on more surface reactions on the Si surfaces are still underway in our group. Acknowledgment. The authors thank two reviewers for their constructive and pertinent comments. This work is supported by the China NSF (No. 90303020, No. 20103004, No. 20433020, and No. 20420150034). Supporting Information Available: Figures S1 depicts the reaction pathway obtained by UMP2/LANL2DZ optimizations for the [2+2] cycloaddition of ethylene with the Si9H12 cluster model in comparison with UB3LYP/6-31G* results. The

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