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Introduction

The chemistry of hybrid structures composed of organic molecules and semi-conductor surfaces is opening up exciting new avenues of development in molecular electronics, nanoscale devices, and surface lithography. The possibility of engineering such novel structures requires a detailed understanding of how organic molecules react with the semiconductor substrate. In order to realize the covalent attachment of nanoscale objects to the surface, controlled functionalization of the latter is required. Although the chemical vapour deposition technique is the currently used tool in this atomic level fabrication process, novel ‘carrier’ STM tips capable of holding reactive organic agents could open up an entirely new field of mechanistically selective surface functionalization¹.

Joint theoretical and experimental studies of conjugated dienes on a Si(100)-2x1 surface² identified an analog version of one of the most important products of organic reactions, the Diels-Alder [4+2] adduct. The latter is a six-membered ring containing two silicon atoms of a dimer at the (100)-2x1 surface and the four carbon atoms of the reactant diene. Very recent scanning tunneling microscopic (STM) experiments³ of 1,3-cyclohexadiene addition to the surface show that, in addition to the DA [4+2] adduct, other products are possible, specifically, [4+2]-like adducts that bridge two dimers within a row or across adjacent rows, and two intra-dimer [2+2] adducts. Finally, a sixth species was also reported, although it was not possible to determine its identity conclusively.

The later examples demonstrate that the complex chemistry of conjugated dienes on semiconductor surfaces has exciting potential as a method for controlled synthesis of organic/semiconductor interfaces. Additionally, while this chemistry could, in principle, be used as a starting point for lithographic patterning schemes if appropriate methods can be found to remove unmodified adducts from the surface, it was shown for the [4+2] adduct that the retro-Diels-Alder process is not observed on Si(100)-2x1. Instead, thermal decomposition was found to be the major reaction pathway upon heating⁴.

Despite the novelty of these results, neither experiments nor static ab initio calculations can identify specific mechanisms by which the observed addition products form. For the DA [4+2] adduct, an outstanding and controversial question of whether the reaction mechanism involves a concerted (symmetric or asymmetric) or stepwise formation of the two Si-C bonds remains unanswered; one might expect that similar questions arise for the other adducts. Furthermore, investigation of the energetic and mechanistic details of the DA [4+2] adduct formation on Si(100) could explain its heating induced thermal decomposition. One explanation for this experimental finding might be the presence of large activation barriers along the retro-Diels-Alder pathway. Assuming that energetic considerations play a major role, additional questions arise: For example, is there any derivative of chemically substituted dienes, which would favor a retro-Diels-Alder reaction over thermal decomposition? It seems reasonable to expect that such derivative compounds could be devised, since a spontaneous retro-Diels-Alder reaction has already been reported on Ge(100)⁴ and one might, therefore, expect that similar results would be obtained on Si(100) by a proper choice of the diene.

In order to address the aforementioned issues, we have undertaken a finite temperature ab initio molecular dynamics (AIMD) study, using forces obtained “on the fly” from electronic structure calculations, in order to investigate the addition product distribution as well as the underlying mechanistic aspects of the chemical adsorbtion of cis-1,3-butadiene to the Si(100)-2x1 surface. The trajectories generated show that the reaction occurs in a non-concerted manner via the formation of an intermediate zwitterionic state containing a carbocation. In addition, the free energy profile along the reaction pathway leading to the Diels-Alder [4+2] adduct is obtained, lending further support to the non-concerted mechanistic picture. Finally, the effect on the free-energy profile caused by mono-fluorinating the diene was investigated. The latter provides valuable insight into efficient and reliable lithographic pattering schemes.

Methods

AIMD calculations were performed using the PINY_MD code⁶ on a system of four silicon layers composed of 32 atoms (four surface dimers), a passivating bottom layer of hydrogens, and one cis 1,3-butadiene at a temperature of 300 K. The electronic similarity between 1,3-butadiene and the 1,3-cyclohexadiene of Ref. 2 allows direct comparison between theory and experiment. The electronic structure was represented within the generalized gradient⁷ formulation of Kohn-Sham density functional theory (DFT). The orbitals were expanded in a plane-wave basis at the Γ-point, with atomic pseudopotentials⁸, up to a cutoff of 35 Ry, which is sufficient to converge the geometry of the butadiene and reproduce the change in energy per surface dimer upon reconstruction⁹. For the monofluorinated butadiene, a cutoff of 80 Ry was employed. Rigorous treatment of the surface boundary conditions¹⁰ allowed a box with periodic dimensions 15.34 Å, 7.67 Å and nonperiodic dimension 22.53Å to be used. The dynamics of the system was generated using a new formulation⁹ of the Car-Parrinello algorithm developed by us¹¹ for treating reactive systems.

Results

Since the geometry and charge distribution of the neat Si (100)-2x1 surface can influence the reaction mechanism, it is necessary to review our current understanding of the surface. The present theoretical approach, in agreement with recent experiments¹², indicates that the room-temperature structure is the c(4x2) buckled dimer structure, which persists to temperatures as low as 10 K¹³. The average geometry of the dimers was found to be in good agreement with static ab initio calculations¹⁴. Consequently, the charge distribution within each dimer is asymmetric, with an excess positive and negative charge on the lower and upper atoms, respectively.

In order to have a meaningful product distribution, forty trajectories, each of length 2-3 ps, were initiated from an unbiased distribution of initial configurations of the butadiene above the surface. In total, nearly 110 ps of trajectory data were generated. Table 1 shows the percentages of the addition products¹⁵ (see Scheme 1 and Ref. 15) together with the experimental³ values for 1,3-cyclohexadiene. It can be seen that the yields of all products analogous to those of Ref. 3, i.e. A-D(+E), agree with experiment within the error bars. Some slight differences between the 1,3-butadiene and 1,3-cyclohexadiene products are (1) for the former, the B adduct forms diagonally across two intrarow dimers, and (2) the [2+2] adduct is an interdimer adduct within a row.

Table 1. Distribution of the final addition products¹⁵.

Product Theory (%) Exp. (%)	Product Theory (%) Exp. (%)
A 15 11 ± 3	D(+E) 30 22 ± 15
B 30 31 ± 6	H 10 21 ± 5
C 15 16 ± 7

The movies below show the formation of the DA adduct and the inter-row [4+2]-like adduct.

Despite the variety of addition products, a detailed electronic structure analysis of the trajectories reveals that a common mechanism underlies their formation (see Scheme 1).

Scheme 1. Mechanism of addition product formation.

The scheme presented is supported by electron localization function (ELF)¹⁶ isosurfaces, which use a conditional probability to locate spatial regions of high electron density (Fig. 1). Fig. 1 also shows the centers of maximally localized periodic Boys-Wannier orbitals, also known as Wannier functions.¹⁷.

The common mechanism (Scheme 1) begins with a nucleophilic attack of the C=C double bond on the positive member of a Si-Si surface dimer, suggesting a predominantly stepwise mechanism. The subsequent migration of the local positive charge from the Si atom, now neutralized by formation of the Si-C bond, dictates the subsequent fate of the reaction. In all cases, the next step involves the migration of the positive charge into the butadiene, leading to a carbocation (Scheme 1 (R)). Carbocation formation has also been observed in STM measurements of ethylene on the Si(100)2x1 surface¹⁸. Evidence of the carbocation intermediate can be gleaned from the ELF as well as the center of the Wannier functions. The carbocation, which can exist for up to 1-2 ps, is stabilized by resonance, as illustrated by the three ELF lobes and three Wannier centers around the positive carbon atoms (indicated by red spheres (Fig. 1(R)). The Wannier center of the delocalized orbital is located below the middle carbon atom, indicating that it is shared by two bonds. Since the carbocation bonds to a Si atom of a surface dimer, and the other dimer member has a net negative charge, an intermediate zwitterionic state ensues. In one of the resonant structures, the positive charge is “localized” on the end of the butadiene (Scheme 1 (R-right)), which allows the carbon to attack the negatively charged Si atom, leading to the final DA [4+2] adduct (Fig. 1(A) , Scheme 1 (A)).

Figure 1. Snapshots of the addition products obtained. The lettering corresponds to that of Scheme 1. Blue, green and white spheres denote Si, C and H atoms, respectively, and grey spheres indicate the location of Wannier centers. Red spheres locate atoms with positive full or partial charge. Full positive charge is defined to be an atom surrounded by three Wannier centers. The purple surface is the ELF 0.95 isosurface.

If the double bond is localized on the end of the butadiene (Scheme 1 (R-right)), then the positive carbon can attack the negatively charged Si of a neighboring dimer, leading to an inter-row [2+2] adduct (Fig. 1(D), Scheme 1(D)). The trajectories indicate a further reaction that occurs when the butadiene is oriented so as to allow a second nucleophilic attack on the positively charged Si of this dimer. The reaction involves an intermediate “fluxional” species (Fig. 1(F), Scheme 1(F)), that rapidly converts into a stable [4+2]-like inter-dimer adduct (Fig. 1(B), Scheme 1(B)) via an electron-pair reorganization. The existence of such a “fluxional” species was also suggested in Ref. 3. The [2+2] adduct, D, is stabilized if the double bond at the end of the butadiene is oriented between the rows. Finally, the inter-row adduct formation is initiated by a second nucleophilic attack of the C=C double bond in the zwitterion on the positively charged Si atom in a neighboring row. Here, a nine-membered ring finally forms, leading to a migration of positive charge into a bulk layer, as seen in the ELF (Fig. 1(C), Scheme 1(C)).

Further evidence for the stepwise mechanism is provided by the time evolution of the Si-C and C-C bond lengths. In Figure 2, a representative trajectory leading to the [4+2] DA adduct is shown. There is a brief time window in which the two Si-C distances become distinctly different, as only one Si-C bond is formed. Moreover, Fig. 2 clearly shows the interchange of CC single and double bonds as the DA adduct is formed. Furthermore, at its maximum value, d[C₃-C₄] = d(s) (d(s) is the single bond length) and d[C₁-C₂] = d[C₂-C₃] = d(s-d) (d(s) < d(s- d) < d(d)) suggesting a possible resonant structure (see Scheme 1) that could help stabilize the carbocation.

Figure 2. Si-C and C-C bond lengths vs. simulation time for a representative trajectory leading to the [4+2] Diels-Alder adduct. From left to right the three snapshots depict: i) butadiene above the Si(100)-2x1 surface; ii) carbocation formation; iii) final [4+2] DA adduct. Blue, green and white spheres denote Si, C and H atoms, respectively, and grey spheres indicate the location of Wannier centers. Red spheres locate positively charged atoms.

It has been suggested that a diradical mechanism is also possible. In order explore this possibility, spin-unrestricted ab initio molecular dynamics calculations were carried out in order to generate a small ensemble of reactive trajectories forming the DA [4+2] adduct. Figure 3 shows the analog time evolution of C-C bond lengths for the representative trajectory of figure 2. The bond length changes in the figures indicate that there is no significant difference between them leading to the same qualitative conclusion. Interestingly, the lifetime of the carbocation species is even more extended in the spin-unrestricted trajectory. Additionally spin polarization was quantitatively measured along representative trajectories by monitoring the electronic gradients for the spin-up and spin-down orbitals. The nearly identical electronic gradients obtained in the 0-300 fs time window exclude the presence of any radical mechanism along the [4+2] DA adduct formation. Finally, analysis of the spin-up and spin-down ELFs showed that the up and down ELFs were similar to each other as well as to the spin-restricted ELF. In addition, the Wannier centers obtained matched closely those of the spin-restricted calculation. Hence, we can conclude that the diradical mechanism is not favored for this reaction.

Figure 3. (Top) C-C bond lengths (see Fig. 2 for numbering scheme) vs. simulation time for a representative trajectory leading to the [4+2]-DA adduct generated using spin unrestricted density functional theory within the ab initio molecular dynamics protocol. (Bottom) Electronic gradients for the spin-up (black) and spin-down orbitals (green) vs. simulation time.

In order to characterize the reaction mechanism from a thermodynamic point of view, free energy calculations were carried out. The main objective of this study is to verify the conclusions obtained in our previous investigation, namely that the various adduct formations are governed by a stepwise zwitterionic mechanism. For this reason the free energy profile along the reaction pathway leading to the [4+2] Diels-Alder adduct is computed. Free energy profiles for the other adducts were not calculated due to high computational overhead. The choice of this particular adduct was twofold: (i) [4+2] DA is the final product of one of the most important reactions (Diels-Alder) in organic chemistry; (ii) the mechanism of this particular reaction has been a long standing problem^19-22.

Scheme 2. The possible reaction mechanisms between butadiene and the Si(100)-2x1 surface leading to the DA [4+2] adduct. In a concerted one-step mechanism, the Si-C bonds form simultaneously in either a synchronous or an asynchronous pathway. The former implies either non-buckled surface dimers or an approach to a buckled surface dimer by the butadiene at the buckling angle. A non-concerted stepwise mechanism involving a zwitterionic intermediate is also depicted. This type of path involves formation of a positively charged carbocation bonded to a negatively charged Si-Si dimer.

For this adduct, the reaction can proceed via a concerted or non-concerted stepwise mechanism. While the former proceeds via a simultaneous electronic structure rearrangement passing through a symmetric or anti-symmetric transition state, the stepwise mechanism could follow a zwitterionic or a diradical pathway. Since it has already been argued that a diradical mechanism is not favored, the two alternatives, shown in Scheme 2, illustrate the symmetric concerted and zwitterionic non-concerted mechanisms only. One can expect that a concerted mechanism would imply a free-energy profile with a single minimum, whereas a reaction intermediate of a zwitterionic pathway would correspond to a separate minimum or an inflexion point.

In order to investigate this question, the thermodynamic free energy profile ΔG(ξ) along the DA [4+2] reaction path is determined. Here, ξ is taken to be the relative coordinate between the mass centers of the two outer carbons of the 1,3-butadiene and the two Si atoms in the dimer forming the adduct,=ξ(r)=½ |(r_{Si_1}+r_{Si_2})-(r_{C_1}+r_{C_4})|. ξ decreases from 3.90 Å to 1.96 Å as the butadiene approaches the surface and forms the DA adduct. The free energy profile is then computed via thermodynamic integration via

(1)

where is the Hamiltonian of the system, and <…>_cond is a conditional average over an equilibrium ensemble at a fixed value of ²³ . In order to enhance sampling along the path, the average in Eq. (1) was performed using the blue moon ensemble method²⁴, which reformulates Eq. (1) in terms of constraints ξ(r) = ξ′ and . In order to compute the profile, thirteen separate systems were set up with values equidistantly distributed along the [1.97 Å, 3.90 Å] interval, and productions run of 8 ps in length were carried out after a 1.0 ps equilibration period at each point, for a total of 117 ps.

The profile in Fig. 4 is clearly more characteristic of a non-concerted mechanism involving a well-defined reaction intermediate. The fact that the free energy barrier is relatively low (3-4 kcal/mol) suggests that the reaction can occur at room temperature. The occurrence of the reverse reaction on a potential retro-Diels Alder pathway is very unlikely since the activation barrier is high (~10-20 kcal/mol). This may explain the experimental finding, that the main reaction pathway, upon heating of the adduct, is thermal decomposition⁴. Interestingly, on the analog Ge(100) surface, the retro-Diels Alder is more favored, implying that a similar result could be obtained on Si(100) by appropriate chemical modifications on either the surface or the diene.

Figure 4. Free energy along the reaction pathway leading to a Diels-Alder [4+2] adduct. The blue and red triangles indicate the product (EQ) and intermediate states (IS), respectively. The inset shows the buckling angle (a) distribution of the Si dimer for both the IS (red line) and the EQ configurations (blue line). The snapshots include configurations representing the IS and EQ geometries. Blue, green and white spheres denote Si, C and H atoms, respectively, and grey spheres indicate the location of Wannier centers. Red spheres locate positively charged atoms. The purple surface is the ELF 0.95 isosurface.

It is known in organic chemistry that Diels-Alder reaction rates increase when a strong electron donating group occurs on the conjugated diene. Based on this fact, it would be natural to assume that electron withdrawing groups on the diene have an opposite effect. Furthermore, it is expected that electron withdrawing groups destabilize the DA [4+2] adduct, so that it is more likely to undergo a retro-Diels-Alder reaction upon heating. In order for a substituted diene to be of utility for lithographic applications, the candidate molecule should have the following properties: i) it should participate in a spontaneous DA [4+2] reaction on the room temperature surface, and ii) the [4+2] adduct should undergo a retro-Diels-Alder reaction upon heating. To accommodate both of these requirements, the candidate substituent must have moderate electron withdrawing ability in order to favor the retro-Diels-Alder pathway, while at the same time, it should spontaneously react producing the DA [4+2] adduct at a sufficient rate. Based on qualitative arguments, fluorine was chosen as a test substituent because it has a high electronegativity, yet it is not considered to be a highly effective electron withdrawing substituent, i.e., it is less effective than, for example, groups such as –CF₃ or –SO₃H. In order to investigate this idea, the free energy profile of Fig. 4 was recomputed for a fluorinated cis 1,3-butadiene (see Figure 5).

Figure 5. Comparison of free energy profiles along the reaction pathway leading to a Diels-Alder [4+2] adduct for cis-1,3-butadiene and its fluorinated substituent.

The free energy profile for the fluorinated substituent was obtained using the same methods and protocols discussed above, with run lengths of 4 ps..

Figure 5 indicates that, similar to ordinary 1,3-butadiene, F-butadiene has negligible activation barrier (4-5 kcal/mol) for formation of the DA [4+2] adduct, so that a spontaneous reaction is expected at room temperature. The complex shape of the free energy profile implies the presence of a reaction intermediate similar to that obtained for ordinary 1,3-butadiene, suggesting a similar reaction path. The key difference between the two profiles is a 6-8 kcal/mol decrease in the activation free energy for the retro-Diels-Alder pathway for the F-butadiene. The activation energy is still too high to expect a spontaneous retro-Diels-Alder reaction upon heating, but we view this result as an important illustration of the potential power of computer-based “reverse engineering” applied to the design functionalizing agents with a set of desired chemical characteristics and thermodynamic properties.

Conclusion

In this paper a comprehensive study of the mechanistic and energetic details of the functionalization of the Si(100)-2x1 surface were presented. For simplicity, the smallest diene, cis 1,3-butadiene, was used as the functionalizing agent. Based on both free energy calculations and an extensive ensemble of non-equilibrium trajectories, a dominant zwitterionic stepwise mechanism was found. The latter arguments were further supported by detailed analysis of the electronic structure, which identified a common intermediate carbocation for all the products obtained. Furthermore both the identity and the distribution of the virtual products were shown to be in excellent agreement with the experimental STM measurement³. Finally, the idea of using reverse chemical engineering was investigated as a means of designing a novel substituted diene derivative with a specified property (lower activation free energy along the retro Diels-Alder pathway), thereby leading to a better functionalizing agent for lithographic purposes.

Acknowledgment

This work was supported by NSF CHE-9875824, CHE-0310107 and the Camille and Henry Dreyfus Foundation, Inc.

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