Feasibility of Benzene Dissociation on the Singlet and Triplet

ARTICLE pubs.acs.org/JPCC

Feasibility of Benzene Dissociation on the Singlet and Triplet Electronic States of Selected Cluster Models for the Si(100) Surface Qing Zhu and Nicholas F. Materer* Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078-3071, United States ABSTRACT: Density functional theory was used to investigate possible adsorption and dissociation processes for benzene on the Si(100) surface using Si-dimer clusters. On this surface, benzene can react across a Si-dimer in a 1,2 manner across a double bond or in a 1,4 route across the benzene molecule to form a di-σ chemisorbed product. At this level, the transition state geometry from the gas phase into either of these di-σ products is activated and suggests a diradial adsorption mechanism. The activation energy to form the 1,4 bond product (a butterfly configuration) is significantly less than other possible chemisorbed products. After adsorption, the 1,2 bond product (a tilted configuration) can undergo C
H bond cleavage to form lower-energy products. However, a previously reported one-step C
H cleavage pathway to form a doubly dissociative product is not possible,and more complex processes involving spin-crossing must be considered. After a spin-crossing process, a triplet 1,2 bond product can follow two possible dissociative pathways. One reaction pathway forms a product consisting of an absorbed phenyl group and hydrogen. The other product requires two C
H bonds to break and two H
Si bonds to form and is absorbed to the surface via two C
Si bonds. Both processes require a spin-crossing of the initial 1,2 bond product and a transition state with large activation barriers with respect to desorption or further reactions of remaining double bonds with an adjacent Si-dimer (a titledbridge structure). Thus, these dissociation pathways are unlikely to occur under typical experimental conditions.

’ INTRODUCTION The adsorption of organic molecules to fine-tune the chemical and physical properties of group IV semiconductor surfaces has applications in chemical sensors, biological recognition, and molecular and optical electronics.1
3 Toward this end, a recent review addresses the experimental and theoretical understanding of chemical manipulations of organic molecules on the silicon surfaces.4 In the past two decades, the adsorption and reaction of unsaturated aromatic organic molecules on the Si(100) surface have received significant attention. Benzene is a simple cyclic aromatic compound, and its adsorption on the Si(100) surface has been studied both experimentally and theoretically.5
27 A good summary of the experimental and computational literature can be found in refs 5 and 9, of which a majority discuss benzene adsorption and not dissociation. There are six possible adsorption configurations of benzene on the Si(100) surface that are commonly recognized. The di-σ Tilted and standard Butterfly configurations contain two σ-bonds to both Si atoms on the same Si-dimer (see Figure 1). The Diagonal-Bridge Butterfly is similar to the Butterfly configuration but bonded to two Si atoms on adjacent Si-dimers. The tetra-σ configurations have one σ-bond to each of the four Si atoms on two different adjacent dimers. These include the Pedestal, TwistedBridge, and the Tilted-Bridge configurations. The experimental observation of surface species resulting from benzene adsorption is complicated due to the possible mixture of products and the nonequilibrium nature of many experiments. A recent photoelectron diffraction investigation, conducted at room temperature, finds that at saturation coverage both the standard Butterfly and Tilted-Bridge configurations are present on the surface r 2011 American Chemical Society

at approximately equal concentrations.5 Given the time scale of this experiment and the belief that equilibrium can be achieved, a free energy difference between the Tilted-Bridge and Butterfly is estimated to be between
0.5 and 4.5 kJ/mol. However, Nisbet et al. acknowledge that kinetic factors and steric effects may influence the relative concentrations.5 A detailed high-level computational study concludes that the standard Butterfly is the lowest energy structure,9 with the energy difference between this geometry and the less favorable Tilted bridge being 9.6 kJ/mol. However, DFT studies have come to the opposite conclusion, with the Tilted-Bridge being strongly favored by at least 60 kJ/mol depending on the study. Jung and Gordon argue that DFT cannot describe silicon dimer models correctly due to strong multiconfigurational character within the Butterfly configuration.9 Given the presence of a dangling bond, this assessment seems reasonable. However, it is not clear if the same argument can be made for the double-dimer Tilted-Bridge model, which contains no dangling bonds. In addition to the equilibrium structures, other adsorption possibilities may lead to metastable surface species. This paper focuses on possible dissociation pathways starting from the di-σ Tilted structure. Jung and Gordon9 have shown that the Butterfly and Tilted-Bridge geometries can be obtained by first forming the Tilted species on the surface. Thus, additional pathways that start at the Tilted species and lead to stable structures are of interest. In particular, Nunzi et al. proposed a dissociation pathway involving Received: April 9, 2011 Revised: May 30, 2011 Published: June 07, 2011 13377

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Figure 1. Chemisorbed benzene adsorption structures: (a) Tilted, (b) Butterfly, and (c) Upright.

the abstraction of two H atoms by the Si-dimer atoms on the adjacent dimer with an activation barrier of 92.0 kJ/mol.6 Notwithstanding the reported activation energy of 66.5 kJ/mol for benzene desorption from this configuration, it is surprising that no such dissociation product is observed experimentally. In this paper, we show that this pathway is more complex and must involve a change in the spin state.

’ COMPUTATIONAL DETAILS The double dimer cluster model (Si15H16) is used to model the Si(100) surface for most of our calculations. For comparison, the single dimer cluster model (Si9H12) is used for those adsorption configurations that require only one Si-dimer bond. Finally, the triplet dimer cluster model (Si21H20) is used for larger adsorption configurations that require at least three dimer rows. Except when explicitly noted, single point energy calculation, geometry optimization, and frequency analysis are performed using the hybrid density functional method that includes Becke’s 3-parameter nonlocal-exchange functional28 with the correlation functional of Lee
Yang
Parr, B3LYP.29 If not specified, the 6-31G(d) all-electron split-valence basis set,30 which includes the polarization d-function on non-hydrogen atoms, was employed for calculations. The Gaussian 03 software package31 is utilized to perform the geometry optimization and frequency calculations. Unless explicitly stated, all geometries are fully optimized with no constraints. The reported adsorption energy is defined as the difference between the electronic energy of the adsorption model and the isolated molecule plus the bare Si cluster. All energies are reported without zero-point corrections. Unless explicitly stated, frequency calculations have confirmed that all the stable geometries have no imaginary vibrational frequencies, and all the transition states have only one imaginary mode. All connections between stable structures and their transition states are confirmed by internal reaction coordinate (IRC) calculations. The natural orbital occupation numbers (NOON) were calculated for the DFT optimized Tilted and Butterfly configurations using a 6-31G(d) basis. For the double-dimer cluster, the complete active space calculations, consisting of 10 active electrons and 10 active orbitals, were utilized. This CASSCF(10,10) computation includes the four active electrons in the dangling bonds on the two silicon dimers and the six active electrons in the six delocalized π orbitals on the benzene molecule. For the single-dimer cluster, CASSCF(8,8), corresponding to eight active electrons and eight active orbitals, including the two active electrons and two dangling bonds in the silicon dimers plus the six active electrons and six delocalized π orbitals from the benzene molecule, was employed. For spin-crossing processes, the search for the minimum energy crossing point (MECP) was performed, and the spin

orbital coupling (SOC) coefficients at this point were calculated to determine the spin crossing probability. Required MECP geometries were obtained from the code provided by Harvey et al.32 based upon the algorithm proposed by Bearpark et al.33 using DFT at the B3LYP level. In previous work by Zhu and Materer, MECPs determined from B3LYP were just as reliable as second-order Møller
Plesset perturbation theory (MP2) and coupled cluster (CCSD) methods for the silicon dimer cluster.34 The spin
orbit coupling coefficient (SOC) at the obtained MECP geometries was computed by GAMESS (US)35 using the same 6-31G(d) Gaussian-type basis set as found in Gaussian 03. The procedure starts with the determination of the optimized molecular orbital (MO) coefficients at the MECP geometry using the largest configuration interaction (CI) calculation possible given our resources. Once the optimized MO coefficients were determined, they were utilized to compute the SOC using an active space consisting of six orbitals from benzene and four from each Si-dimer.

’ RESULTS AND DISCUSSION Initial Adsorption Products. Figure 1a and 1b shows the conventional di-σ Tilted and Butterfly configurations. An additional di-σ Upright adsorption geometry (Figure 1c), which has the two bottom hydrogen atoms of benzene located on the two different sides of the benzene ring, was also considered. On a single-dimer cluster, the adsorption energy for this species is 12.0 kJ/mol. Since any potential dissociation process that passes through the Upright configuration requires, at a minimum, one Si-dimer on each side, an adsoption energy of 22.8 kJ/mol was also calculated using a triple-dimer cluster. The large cluster size effect is observed for the Upright configuration, with the calculated adsorption energy from the single-dimer cluster being about 50% of that found for the triple-dimer cluster. Unfortunately, the Upright configuration is predicted to have large positive adsorption energy on both clusters and was not explored further. The adsorption energies of the Tilted and Butterfly configurations are listed in Table 1. Single- and double-dimer clusters were used to model these species. For both the Tilted and Butterfly configurations, the adsorption energy difference between the single-dimer and the corresponding larger clusters is very small, less than 6%. The calculated adsorption energies on the double-dimer cluster for the Tilted and Butterfly configurations are
20.6 and
88.0 kJ/mol, respectively, consistent with the
20.5 and
85.8 kJ/mol values calculated by Nunzi et al.6 These calculations consistently predicted that the Butterfly adsorption configuration has the lowest energy of the three adsorption configurations selected for this study. 13378

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For the Tilted and Butterfly configurations, Jung and Gordon9 have performed a MRMP2//CASCF(10,10) calculation using the Dunning
Hay double-ζ valence basis set plus d polarization functions DZV(d) basis set under the surface integrated molecular orbital mechanics (SIMOMM) model and predict the same energy ordering of these geometries. However, they find more negative adsorption energies of
26.4 and
121.3 kJ/mol, respectively. Jung and Gordon9 have pointed out that there exists strong multiconfigurational character for chemisorbed benzene molecules on the silicon dimer clusters. However, previous work by Zhu and Materer has shown that the single reference CCSD and B3LYP methods can be more reliable than the multireference CASSCF method in the search for the minimum energy crossing point (MECP) for the silicon dimer cluster.34 Thus, for benzene chemisorbed on silicon dimer clusters, it is necessary to clarify whether the multiconfigurational character comes from the interaction between the benzene molecule and the Si-dimer atoms to which it is bonded or from the dangling bonds on the spectating neighbor Si-dimer, before a conclusion of whether the multireference method is required to accurately compute the energy profiles can be made. The calculated NOON for the two adsorption configurations on the two different Si-dimer cluster models is listed in Table 2. As previously discussed, the single-dimer NOON were determined using CASSCF(8,8), while the double-dimer required Table 1. Calculated B3LYP/6-31G(d) Adsorption Energies (kJ/mol) for the Transition States for the Initial Absorption, The Chemisorbed Benzene Molecules, And the Dissociative Chemisorbed Benzene Moleculesa Transition States

Tilted-TS0

Butterfly-TS0

Single-Dimer

56.5

7.0

Double-Dimer

41.6

1.2

Chemisorbed

Tilted

Butterfly

Single-Dimer Double-Dimer


19.6
20.6


90.0
88.0

Dissociated

Single

Double

Butterfly-Double

Double Dimer


187.1


272.8

47.7

a

See Figures 1 and 2 for the relevant geometries and transition states. The single-dimer and double-dimer refer to the Si9H12 and the Si15H16 clusters, respectively. Geometries are fully optimized and have no imaginary frequencies, except for the transition states which have only one. IRC calculations have been performed to confirm that the transition states connect the reactant with the product.

CASSCF(10,10) to describe the active electrons for the extra Sidimer. Taking into account the different methods used to model the Si(100) surface and the different basis sets, the results are in reasonable agreement with the values from Jung and Gordon’s paper9 and suggest a strong multiconfigurational character for the benzene on double dimer cluster. However, the NOON for the corresponding single dimer cluster models shows nearly full occupation numbers in the bonding orbitals, and all the antibonding orbitals have natural occupation numbers smaller than 0.1. According to the standard suggested by Pulay,36
38 which states that a multiconfigurational description is required if the NOON is equal to or is larger than 0.1 for the antibonding orbitals, benzene adsorbed on a single Si-dimer cluster should not require a multiconfigurational description. Since the major difference between the double-dimer and single-dimer cluster is the addition of a neighbor Si dimer, it is the dangling bonds located on this neighbor Si-dimer, and not the Si-dimer bounded to the benzene, that causes the multiconfigurational character. Thus, the single reference DFT methodology that recovers dynamical correlations should be a reliable method for obtaining reaction pathways. Chemisorption Transition States. Table 1 contains the energies, and Figure 2 shows the geometries of the two transition states found from these species. The formation of the Tilted adsorption configuration can occur through the [2 + 2] cycloaddition process, a concerted process which is formally symmetry forbidden on these clusters. However, Boland and co-workers39 have discussed symmetry allowed pathways for the [2 + 2] cycloaddition reaction on the p(2  1) and c(4  2) reconstruction Si(100) surface. At the DFT level, the transition state (Tilted-TS0, Figure 2a) has a configuration in which the benzene molecule leans toward one side of the Si(100) surface, resulting in one C
Si bond being longer than the other. This geometry is analogous to that suggested for the diradical mechanism to form a [2 + 2]-type product during the adsorption of ethylene40 or 1,3cyclohexadiene41 on the Si(100) surface. The energy of this transition state is 41.6 kJ/mol at the B3LYP/6-31G(d) level, which is consistent with the value of 48.1 kJ/mol at the B3LYP/ MIX level calculated by Jung and Gordon.9 IRC calculations were also performed to confirm that this transition state connects the free reactants and the adsorbed product. An additional weakly bound but stable intermediate, such as the van der Waals complex proposed by Jung and Gordon,9 was not found to be directly connected to the transition state. At the optimized Tilted-TS0 geometry, the single point energy difference between the MRMP2 method and the B3LYP method using the 6-31G(d) basis set is very small. The B3LYP and MRMP2 methods are

Table 2. Calculated NOON for the Tilted and Butterfly Configurations of the Intact Chemisorbed Benzene Molecules on the Si(100) Surfacea Model Double-Dimer Single-Dimer Jung and Gordonb

NOON Tilted Butterfly

1.79(0.21) 1.84(0.15)

1.91(0.09) 1.96(0.03)

1.97(0.03) 1.98(0.02)

1.97(0.03) 2.00(0.01)

1.98(0.02) 2.00(0.00)

Tilted

1.91(0.09)

1.97(0.03)

1.98(0.02)

2.00(0.01)

;

Butterfly

1.91(0.08)

1.92(0.08)

1.98(0.02)

2.00(0.00)

;

Tilted

1.69(0.31)

1.88(0.12)

1.93(0.07)

1.97(0.03)

1.98(0.02)

Butterfly

1.69(0.31)

1.91(0.09)

1.92(0.08)

1.98(0.02)

1.98(0.02)

a

The single-dimer and double-dimer refers to the Si9H12 and the Si15H16 clusters, respectively. The numbers listed in the parentheses are the NOON for the corresponding anti-bonding orbitals. The NOON computation for the Si single-dimer and double-dimer cluster model included four or five active bonding orbitals and the corresponding anti-bonding orbitals, respectively. b Adapted from ref 9. 13379

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Figure 2. Transition states that lead to the formation of an intact chemisorbed benzene molecule on the Si15H16 double-dimer cluster: (a) transition state that leads to Tilted configuration (Titled-TS0) and (b) transition state that leads to Butterfly configuration (Butterfly-TS0). C
Si bond lengths are shown to illustrate the unsymmetrical nature of these transition states.

both considered to be able to recover the dynamical correlations, except the latter can also recover the static correlations in the selected active space. Benzene can also react with the Si(100) surface to form the Butterfly specie in a symmetry allowed [4 + 2] cycloaddition fashion. IRC computations performed here imply that the transition state (Butterfly-TS0, Figure 2b) that leads to the Butterfly structure also has an asymmetrical configuration similar to that found for the Tilted adsorption, suggesting a diradical mechanism. Again, the geometry is analogous to the suggested diradical mechanism to form a [4 + 2]-type product during the adsorption of 1,3-cyclohexadiene41 or butadiene42 on the Si(100) surface. In addition, the 1.2 kJ/mol activation barrier implies that this reaction is essentially barrierless. At the CASSCF(10,10)/MIX level, Jung and Gordon9 obtained an abnormally high energy barrier of 74.1 kJ/mol for this transition state. However, MRMP2 single point energies at several geometries along a symmetric [4 + 2] IRC pathway calculated at the CASSCF(10,10) level suggest that there is no reaction barrier, consistent with the low energy barrier determined by DFT. The contrast between these methods further supports the discussion above that dynamical correlations are much more important than the static correlations in the calculation of benzene adsorption on silicon dimer cluster models. In addition, values are in disagreement with the 17 kJ/mol value determined by Alavis et al.17 for a symmetric [4 + 2] intermediate from a physisorbed state. However, independent of a symmetrical or asymmetrical transition state, all results support a relatively small activation barrier for the formation of the Butterfly product. Finally, cluster size effects are observed for both transition states. As shown in Table 1, the activation energy decreases by 26% and 83% for the Tilted-TS0 and Butterfly-TS0 configurations, respectively, when the silicon dimer cluster size increases from single- to double-dimer cluster. These cluster size effects further support a diradical adsorption mechanism, in which each unpaired electron in the transition state is stabilized by delocalization into the larger clusters. Dissociation Products. As shown in Figure 3, three different dissociation products starting from the Tilted and Butterfly adsorption configurations were considered. The adsorption energies are listed in Table 3. The reaction pathways that connect these products are considered in the next section. C
H bond cleavage can lead to two dissociation products from the Tilted

configuration. There is only one possible dissociation product from the Butterfly. Since we are focused only on pathways that lead to dissociation products, other pathways that lead to the Tilted-Bridge or Butterfly configurations are not considered except when necessary. These nondissociative pathways have been well discussed computationally by Jung and Gordon.9 The first product from the Tilted adsorption configuration consists of breaking one of the C
Si single bonds and abstracting the H atom from the other adsorbing C atom. In this product, the abstracted hydrogen atom forms a new bond on the Si-dimer atom to which the first carbon atom was connected. Since only one C
H bond is broken, this geometry is referred to as a single dissociation adsorption product or just Single. The other product from the Tilted adsorption configuration involves the breaking of both C
H single bonds from the two Si-bonded C atoms of the benzene ring and the formation of the new Si
H bonds with the Si-dimer atoms on the nearest neighbor. Since two C
H bonds are broken, this complex is referred to as double dissociation adsorption product or just Double. Dissociation products resulting from the Tilted structure have 167 kJ/mol (Single) and 252 kJ/mol (Double) greater adsorption energy than their precursor. The gain of adsorption energy for these species can be explained by the resumption of the aromaticity for the phenyl group in both products. The dissociation product from the Butterfly structure is similar to that of the double dissociation product discussed above. This configuration also involves the breaking of both C
H single bonds from the two Si-bonded C atoms of the benzene ring and the formation of the new Si
H bonds with the Si-dimer atoms on the nearest neighbor. The result indicates that the Butterfly dissociative adsorption product has 47.7 kJ/mol of adsorption energy, consistent with the 50.2 kJ/mol value obtained from the previous study.6 The positive adsorption energy suggests that this dissociative product is energetically unfavorable. By removing the two hydrogen atoms from the benzene ring, the C atoms can regain sp2 hybridization. However, the C
Si bonds are almost vertical to the benzene ring, the bond angle between the Si atom, the Si-bonded C atom, and the neighbor C in the ring is to be 88.6
, not 180
as expected for an ideal benzene ring. This smaller angle results in severe ring strain and breaks the symmetry requirement for aromaticity. Thus, the dissociative product from the Butterfly adsorption configuration is much less stable than its precursor and is not considered further. 13380

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Figure 3. Benzene dissociation products on the Si15H16 silicon double-dimer cluster: (a) single dissociation product (Single), (b) double dissociation product (Double), and the (c) butterfly dissociation product (Butterfly-Double).

Table 3. Calculated B3LYP/6-31G(d) Adsorption Energies (kJ/mol) with Respect to Singlet Benzene and the Singlet Double-Dimer (Si15H16) Clustera Common

Tilted

TS1

Singlet


20.6

91.5

Triplet

7.3 (
51.0)

127.2 (69.0)

Inter0
32.0 (
90.2)

Single Dissociation

TS2

Inter1

TS3

Inter2

TS4

Single

Singlet Triplet

;
27.8 (
86.0)


119.1
163.2 (
221.4)

4.6 5.7 (
52.5)


93.0
163.4 (
221.6)

57.9 72.9 (14.7)b


187.1b
158.1 (
216.3)

b

Double Dissociation

TS5

Double

Singlet


42.2


272.8

Triplet

153.2 (95.0)


122.9 (
181.2)

a

Energies in parentheses are the adsorption energies relative to singlet benzene and the triplet cluster. See Figures 3
5 for illustrations of the stable structures and selected transition states. Geometries are fully optimized, except as noted, and have no imaginary frequencies, except for the transition states, which have only one. IRC calculations have been performed to confirm that the transition states connect the reactant with the product. b Partially optimized by fixing the bottom two Si layers of the cluster.

Dissociation Pathways. Since the hydrogen dissociation process is not energetically favorable for the Butterfly configuration, only dissociation pathways for the Tilted adsorption configuration will be examined. After the formation of the Tilted species, two C
H bonds need to break, and two new Si
H bonds need to form to obtain the double dissociation product (Double), the energetic minimum. Nunzi et al. have addressed this reaction as a one-step cleavage process.6 They reported a transition state that directly connects between the intact Tilted chemisorbed structure and the double dissociation product, with an activation barrier of 92.0 kJ/mol.6 We found a transition state (TS1) with similar geometry and calculated energy barrier (91.5 kJ/mol). However, IRC calculation shows that this transition state does not connect the initial product to the expected final product but rather to an intermediate structure with one abstracted H atom. In addition, the geometry optimization of this potential intermediate structure failed due to a strong force vector that breaks one C
Si bond in the optimization. Even though the singlet intermediate structure could not be optimized, this intermediate state can be optimized as a triplet. The invocation of a triplet state is not uncommon. For example, Naumkin and Polanyi et al.43 have found that triplet spin states are necessary for several structures that are involved in the dissociation process for chlorinated benzene on the Si(100) surface. An adsorption energy of
32.0 kJ/mol is found for this triplet intermediate with respect to the singlet benzene molecule and the bare cluster. At the optimized triplet geometry, the single

point energy calculation for a singlet gives an adsorption energy of
7.0 kJ/mol, or 25 kJ/mol less than that of the triplet. Thus, the potential dissociation reaction pathways are approached in two steps. First, the pathways are described in this section assuming that spin-crossing can occur, after which the spincrossing probabilities at the critical steps are discussed within the Landau
Zener44
46 and transition state theory47 frameworks. For the pathways discussed below, the intermediates and selected transition states are shown in Figures 4 and 5. In Figure 4, the bond lengths for the C
H and Si
H bonds are shown to illustrate the single H atom transfer, in contrast to the one-step process suggested by Nunzi et al.6 The energies for both the singlet and triplet states, if available, are summarized in Table 3. Figure 6 illustrates the potential energy surface connecting the various stable species. In this figure, solid lines represent sections of the pathway on the singlet surface, while the dotted lines represent sections of the pathway on the triplet surface. The nondissociative Tilted-Bridge pathway is included to aid the discussion in the next section. The initial transition state (TiltedTS0), which results in the chemisorbed Tilted species, cannot be optimized as a triplet. If the Si-dimer was initially in a triplet state, benzene adsorption would not occur. Thus, all potential dissociation pathways need to start with the adsorbed single Tilted structure, which then must cross over to the triplet state. Even though the triplet Tilted species has a positive adsorption energy with respect to that of singlet reactants, the adsorption energy referenced to the triplet cluster plus singlet benzene molecule is 13381

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Figure 4. Transition state and intermediate that connect the intact chemisorbed Tilted and the common intermediate: (a) triplet TS1 and (b) triplet Inter0. Bond lengths for the C
H and Si
H bonds are shown to illustrate the H atom transfer.

Figure 5. Intermediates that connect between the common triplet Inter0 intermediate and the single dissociation product (Single): (a) triplet Inter1 and (b) triplet Inter2.


50.9 kJ/mol. Direct desorption of benzene from the triplet configurations is energetically unfavorable. NOON were computed to address the suitability of the DFT computation with respect to the possible multiconfigurational nature of these configurations. For comparison with the NOON computed for the singlet Titled and Butterfly (Table 2), NOON were obtained (Table 4) using CASSCF(10,10) for the triplet configurations of these species optimized at the B3LYP level using the double-dimer cluster. In Table 2, the NOON implies that the singlet geometries on the double-dimer clusters have noticeable multiconfigurational character. In contrast, the NOON for the triplet geometries on the double-dimer show that these structures are well described by a single-reference computation. For the triplet state, the opposite spins of the unpaired electrons located on the neighbor Si-dimer diminish the majority of the multiconfigurational character found in the singlet; the state loses all double bond character and becomes a simple diradical. This result further supports the supposition that the multiconfigurational character of the singlet Tilted and Butterfly structure on the Si single-dimer mainly comes from the spectator bare Si-dimer. Since a multiconfigurational description is only required if the NOON is larger than 0.1 for the antibonding orbitals,36
38 the single reference DFT computations are acceptable for the stable triplet configurations.

Once a triplet state has formed (triplet Tilted), the reaction can proceed through a 120 kJ/mol barrier (TS1) to transfer one of its H atoms to the neighbor Si-dimer to form an intermediate state (triplet Inter0), which has an adsorption energy of
32.0 kJ/ mol relative to the free singlet reactants. As seen in Figure 6, there are two potential reactions pathways starting from Inter0. One will lead to the single (Single) and the other to the double (Double) dissociative product. In the first pathway, the triplet Inter0 state can react over a small 4.2 kJ/mol barrier (TS3) to form the triplet Inter1 configuration. This resultant structure (triplet Inter1) has a phenyl group bonded to one Si-dimer atom and a H atom bonded to the neighboring Si-dimer. However, in the optimization of the singlet configuration the Si-atoms on adjacent Si-dimers attempt to pair. This results in unrealistic distortions of the framework of the cluster. In the triplet, the repulsive interaction between the two different Sidimers, which can be modeled as having two unpaired electrons with the same spin, keep Si-dimer atoms away from pulling together and distorting the framework of the cluster. For the singlet, partial optimization, obtained by freezing just the Si atoms in the bottom two layers of the cluster, resulted in a final geometry that contained one imaginary normal mode corresponding to the distortion of the Si atoms in the fixed layers and resulted in an adsorption energy of
119 kJ/mol, 44.1 kJ/mol less than that of the triplet. Thus, the triplet Inter1 is the ground state for this configuration. 13382

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Figure 6. Adsorption energy profile for the two possible dissociation pathways for benzene on Si(100) cluster models. Also included for comparison is the nondissociation Tilted-Bridge pathway, which has the lowest activation energy of possible nondissociation products. Solid lines and bolded text represent sections of the pathway on the singlet surface and the singlet species, respectively. Dotted lines and italic text represent sections of the pathway on the triplet surface and the triplet species, respectively.

Table 4. Calculated NOON for the Triplet Tilted and Butterfly Configurations of the Intact Chemisorbed Benzene Molecules on the Si15H16 Double-Dimer Clustersa Model

NOON

Tilted

1.00/1.00

1.91(0.09)

1.97(0.03)

1.97(0.03)

1.98(0.02)

Butterfly

1.00/1.00

1.91(0.08)

1.92(0.08)

2.00(0.00)

2.00(0.00)

The first column contains the NOON for the nonbonding HOMO and HOMO-1, separated by a slash. The other columns contain the NOON for the bonding orbitals, and the numbers in the parentheses correspond to the respective anti-bonding orbitals. a

Although the triplet Inter1 is the ground state on the triplet surface, one can obtain the energy minimum under configuration (singlet Single) by two H migrations. The relatively high migration barriers imply that the triplet Inter1 species is the kinetic product for the single dissociation pathway. For completeness, the H bonded to the Si-dimer can migrate to the other Si atom on the same Si-dimer to form another intermediate (Inter2) with an adsorption energy of
163.4 kJ/mol. Again, the triplet state is more stable than the singlet. The activation barrier (TS4) for this process on the triplet surface is 169 kJ/mol. Next, the H atom can migrate across the two Si-dimers through another large activation barrier (TS5) of 236 kJ/mol to obtain the single dissociation product (triplet Single). Since the fully optimized TS5 state is severely distorted both in singlet and triplet states, a partial optimization by freezing the Si atoms of the two bottom layers of the cluster was utilized. The resulting transition state has one imaginary normal mode that corresponds to the H migration for both multiplicities. Finally, a spin crossing process from the triplet to the singlet state is required to reach the minimum (singlet Single). The second pathway involves the abstraction of a second H atom, which has an activation barrier of 185 kJ/mol (triplet TS2). After the second H atom migrates to the neighbor Si-dimer, the triplet state of the double dissociation product (triplet Double) has an adsorption energy that is 150 kJ/mol less than that of the

singlet ground state. Thus, the triplet state can relax to the singlet through another spin crossing process to form the singlet double dissociation product (singlet Double), which is the energy minimum on the second dissociation pathway. DFT calculations show that the dissociative Tilted double adsorption product (Double) is energetically more favorable than the single adsorption product (Single). As discussed above, the primary difference between the single and the double dissociation pathways occurs after the dissociation of one H from the benzene ring to form the triplet Inter0 species. Given the significantly lower barrier to form the single dissociation product with respect to the double dissociation product, 4.2 kJ/mol vs 185 kJ/mol, the single dissociation pathway to form the triplet Inter1 species is kinetically preferred over the double dissociation pathway. Formation of the Common Intermediate. The formation of the common intermediate (Inter0) is required for both dissociation pathways. The creation of this species not only requires a spin-crossing of the Tilted species but also needs to pass over a 120 kJ/mol barrier (TS1). In addition, the formation of this species also competes with tetra-σ product formation and benzene desorption. Starting with the spin crossing, a search, using code by Harvey et al.,32 based on an algorithm by Bearpark et al.33 combined with DFT energy optimization from Gaussian 03 at the B3LYP level, finds the MECP for the Tilted configuration 28.2 kJ/mol above the singlet ground state. The norm of the multidimensional vector (ΔF), the gradient difference between the singlet and triplet potential energy surfaces at the MECP, was determined to be 2.38 eV/Å. Subsequent computations determined the spin
orbit coupling (SOC) coefficient at this point to be 16.23 cm
1. Using the Landau
Zener formula44
46 rffiffiffiffiffi! 2
4π2 HSOC μ Psh ðEÞ ¼ 1
exp 2E hΔF a spin crossing probability of 2.2  10
3 is found. In this equation, h is Planck’s constant; HSOC is the SOC coefficient; ΔF is the norm of the gradient difference between the two adiabatic energy surfaces at the MECP; μ is the reduced mass of 13383

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The Journal of Physical Chemistry C the system as it moves along the crossing coordinate; and E is the kinetic energy available to pass through the MECP. After combining transition state theory (TST) with the spin crossing probability47 one obtains   kB T
ΔG exp kðTÞ  ÆPsh æ  h RT In this equation, is spin crossing probability; h is Planck’s constant; kB is Boltzmann’s constant; R is the ideal gas constant; T is the absolute temperature; and ΔG is the activation free energy for the reaction. By expressing the free energy in terms of enthalpy and entropy and collecting the temperature-dependent and -independent terms, one finds that plays the role of an additional contribution to the activation entropy.47 For the formation of the common intermediate, we find that that the spin-crossing process adds an additional 50.9 J 3 mol
1 3 K
1 of activation entropy. At 298 K, this activation entropy is equivalent to adding 15.2 kJ/mol activation energy to the singlet to triplet crossing, giving a total activation barrier of 43.4 kJ/mol. Of the tetra-σ products that can be formed from the singlet Titled species, the Titled-Bridge has the lowest activation energy. Referring to Figure 6, this pathway starts at the singlet Titled configuration and proceeds to the product over TS6. For this process, Jung and Gordon9 find an activation barrier of 47.3 kJ/mol at the MRMP2//CASSCF(10,10)/Mixed level. At the B3LYP/6-31G* level, an activation barrier of 71.6 kJ/mol (TS6) was found for a partially optimized transition state with the Si atoms of the bottom two layers of the double-dimer cluster frozen to prevent unrealistic distortions of the framework of the cluster. Using the DFT activation energy, the spin-crossing is not rate limiting at 298 K, and a nonnegligible concentration of the triplet Tilted species could be present. However, the spin-crossing barrier will be larger than the activation energy required to form the Titled-Bridge at 853 K or about 580
C. Thus, the concentration of the triplet Tilted species, which is the precursor for benzene dissociation, will be depleted at elevated temperature. The next step along the dissociation pathways requires crossing a large 120 kJ/mol activation barrier (TS1) to form triplet Inter0. For this barrier to be compatible with the formation of the Titled-Bridge, for example, this transition state would have to be at least 60% lower or about 50 kJ/mol in energy. Although we have not addressed the multiconfigurational character of this transition state, it is unlikely that a change of this amount would occur. Thus, even though the triplet Tilted precursor is expected to be present at low temperatures, the TS1 barrier is too high to surmount. At the high temperatures required to surmount this barrier, the increasing spin-crossing activation energy will make the formation of the triplet Tilted precursor less likely with respect to the Titled-Bridge or even benzene desorption. Thus, either desorption or creation of the Titled-Bridge species is more favorable than the formation of the triplet intermediate (triplet Tilted) and the following transition state (TS1) required for benzene dissociation. This result is consistent with the experimental literature as discussed in refs 5 and 9. Even if both the spin-crossing and TS1 activation barriers could be surmounted, the single dissociation route is not likely to proceed to the final product. The large activation barrier for the H
Si migrations indicates that the dissociation will likely halt at the triplet Inter1 configuration. For the energetically unfavorable double dissociation route, the ground state (Double) is a singlet. For this species, the MECP is located 5.5 kJ/mol above the triplet

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state, and the equivalent activation entropy increment from the spin crossing process is found to be 99.2 J 3 mol
1 3 K
1. At 298.15 K, the overall activation barrier for this spin crossing process is 35.1 kJ/mol. Thus, the energy barrier for the formation of the singlet ground state product (singlet Double) is relatively small and will not be the rate-limiting step at any reasonable temperature. Finally, the SOC coefficients are based upon an incomplete full CI calculation due to the computational limitations. Zhu and Materer have previously found that the SOC coefficient for a Si9H12 single dimer cluster in complete full CI calculation is approximately 25 cm
1.34 Thus, it is possible that the SOC coefficient for the Tilted configuration could be as large as 25 cm
1 in a full CI calculation. With this value, the crossing probability for Tilted configuration increases to 5.2  10
3. However, the equivalent activation entropy only changes from 50.9 J 3 mol
1 3 K
1 to 44.1 J 3 mol
1 3 K
1, and the total activation barrier decreases slightly from 43.4 to 41.3 kJ/mol. On the other hand, the spin crossing probability is also temperature dependent. Upon increasing the temperature from 298 K to the silicon melting point of 1687 K, the calculated spin crossing probability for both the Tilted and Double configuration decreases by approximately 2.4 times, while the spin-crossing activation barrier increases by less than 11% and 7%, respectively. Overall, the results discussed previously will not qualitatively change.

’ CONCLUSIONS This paper investigated possible dissociation pathways of benzene on cluster models of the Si(100) surface starting from the Butterfly and Titled configurations. The transition states leading to both chemisorbed Titled and Butterfly species from gas-phase benzene support a diradial adsorption mechanism using DFT. The chemisorbed Butterfly configuration is energetically stable against C
H dissociation. However, the Tilted configuration can go through a C
H bond cleavage process to form lower-energy products. A dissociate pathway was originally proposed by Nunzi et al.6 and involves the abstraction of two H atoms by the Si-dimer atoms on the adjacent dimer. Using internal reaction coordinate calculations, we find that the transition state proposed by Nunzi et al.6 does not connect the proposed precursor with the final product. Instead, the pathway is more complex and must involve a change in the spin state of the Si-dimer. Similar considerations were made by Naumkin and Polanyi et al.,43 who found that the triplet spin state is necessary for several structures that are involved in the dissociation process for chlorinated benzene on the Si(100) surface. Once a spin-crossing occurs, there are two possible dissociation pathways. One forms an adsorption product in which one C
H bond breaks and one H
Si bond forms. The other involves a two-step process in which two C
H bonds are cleaved and two H
Si bonds are created. Although this double dissociated product is energetically more stable than the single dissociated product, the single dissociation route is kinetically favored. The kinetic product for the single dissociation pathway is a metastable triplet state with a phenyl group on one Si-dimer and a H atom on the adjacent one. Both dissociation pathways start at a common intermediate which can be formed from triplet Tilted species. The resulting spin-crossing probabilities and rates for the Tilted adsorbate, addressed within the Landau
Zener and transition state theory models, show that the spin-crossing is not a limiting factor. Unfortunately, there is a large activation barrier to form the common intermediate from the triplet Tilted 13384

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The Journal of Physical Chemistry C species. Thus, the formation of this common intermediate is unfavorable with respect to the creation of the Titled-Bridge or the desorption of benzene. Computationally, the dissociation of benzene is kinetically limited on the Si(100) surface, consistent with the experimental literature as discussed in refs 5 and 9.

’ AUTHOR INFORMATION Corresponding Author

*107 Physical Science, Stillwater, OK 74078. Phone: (405) 744-8671. Fax: (405) 744-6007. E-mail: [email protected].

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