Doping Effects on Structural and Electronic Properties of Ladderanes

ARTICLE pubs.acs.org/JPCA

Doping Effects on Structural and Electronic Properties of Ladderanes and Ladder Polysilanes: A Density Functional Theory Investigation Xin Wang† and Kai-Chung Lau* Department of Biology and Chemistry, City University of Hong Kong, Kowloon, Hong Kong, China

Wai-Kee Li Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China

bS Supporting Information ABSTRACT: Doping effects on the structural and electronic properties of ladderanes and ladder polysilanes have been studied using density functional theory. Two types of doping: substitution with isoelectronic atoms or heteroatoms (or radicals), have been used to design low band gap ladderanes. It is found that the B-doped [n]-ladderanes and 1,2 P-doped [n]-silaladderanes exhibit a very noticeable bent conformation, whereas the 1, 2 and 1,3 N-doped ladderanes, P-doped ladderanes, and silaladderanes keep the relatively straight ladder shapes. The isoelectronic atom doping reduces the HOMO
LUMO (H-L) gaps of [n]-ladderanes but increases those of [n]-silaladderanes with n > 5. The present results show that isoelectronic atom doping is not an effective way to decrease the H-L gaps of ladderanes and silaladderanes. Heteroatom doping has a more pronounced effect than the isoelectronic atom doping. The HOMOs of heteroatom-doped ladderanes and silaladderanes are destabilized and LUMOs are stabilized, leading to significant reduction of H-L gaps. Most of the B-, N-, and P-doped [n]-silaladderanes we designed have H-L gaps below 1.5 eV. Therefore, it is expected that these silaladderanes are promising candidates of conductive or semiconductive materials. The heteroatom doping is a viable approach to reduce H-L gaps for the silaladderanes. In addition, it is found that nine different density functionals, including B3LYP, SVWN LDA, four pure GGAs, and three hybrid GGAs, as well as the time-dependent B3LYP method, all lead to the same predictions on the H-L gaps of ladderanes, silaladderanes, as well as their doped derivatives.

1. INTRODUCTION In recent years, the search and design of novel polymers with low HOMO
LUMO (H-L) gaps has attracted great interest among chemists and physicists.1
6 Many conducting or semiconducting polymers with low H-L gaps have been synthesized.1
4 These polymers usually have H-L gaps, or band gaps, less than 1.5 eV. The H-L gap is a significant criterion affecting the electronic and conducting properties of the polymers. To design and synthesize new conductive polymers, we can often tune the H-L gaps through appropriate composition modification such as doping.4 Ladderanes form an interesting family of molecules with highly strained fused polycyclobutane rings. (See Scheme 1.)7,8 These compounds have important applications in materials science7
12 and biology7,13,14 because of their unique structural and electronic properties. Although ladderanes are considered to be promising building blocks in optoelectronics,10,12 the electron transfer properties of long ladderanes have not been demonstrated experimentally.7 Hence, the electronic properties of ladderanes and related derivatives with considerable lengths are of interest to chemists and materials scientists alike. Ladder polysilanes, or laddersilanes, are the silicon analogs of ladderanes with highly σ-conjugated characteristics and strong r 2011 American Chemical Society

electron-donating properties.15
17 Laddersilanes are composed of two polysilane chains connected to each other by bridging Si
Si bonds. (See Scheme 1.) The single-chain polysilanes have highly flexible backbones, but ladder polysilanes have strained and rigid conformations.17 Polysilane chains have been demonstrated to function as 1D nanowires.18 Many ladderanes7,9
11 and ladder polysilanes,15,16,19,20 with various lengths have been synthesized. Some theoretical studies on their structural and electronic properties have also been carried out.17,21
27 To our knowledge, the doped ladderanes or ladder polysilanes have not been investigated either theoretically or experimentally. In this light, studying the electronic and structural properties of ladder polysilanes made up of two polysilane chains, in particular with doped atoms in the chains, may yield potential conductive or semiconductive materials. It has been demonstrated that the heteroatom substitution of silicon in polysilanes is an effective technique to obtain polarized conjugated polymers with small H-L gaps.28
30 Selective doping Received: January 3, 2011 Revised: April 21, 2011 Published: June 14, 2011 7656

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Scheme 1. Structures of [n]-Ladderanes, [n]-Silaladderanes, and Various Isoelectronic Atom-Doped and X-Doped Derivatives

with boron or phosphorus has been successfully used to modify the electronic properties of silicon nanowires (SiNWs).28 Quite recently, oligoacenes with nitrogens replacing CH moieties have been designed for n-channel organic semiconductors; they have also been realized experimentally and studied computationally.31 In the present study, we have designed a series of doped [n]-ladderanes and [n]-silaladderanes, where n is the number of the cyclobutane rings in the oligomer ranging from 3 to 16. The size-dependent effect on the H-L gaps of doped [n]-ladderanes and [n]-silaladderanes is examined. In addition, we examine how doping with isoelectronic atoms or heteroatoms affects the structures, the HOMO and LUMO wave functions, as well as the H-L gaps of doped [n]-ladderanes and [n]-silaladderanes. We will also aim at rationalizing the criterion for which the ladderanes and silaladderanes with H-L gap in the semiconductive and conductive ranges can be formed.

2. COMPUTATIONAL METHODS As shown in Scheme 1, we have designed derivatives of [n]-ladderanes and [n]-silaladderanes doped with isoelectronic atoms or with heteroatoms (X). In the former, we replace CH moieties with N atoms for ladderanes and SiH with P atoms for silaladderanes. Because 1,2- and 1,3-diazetidine derivatives with N-doped cyclobutanes have been synthesized,32,33 we replace the two CH groups in 1,2 and 1,3 positions in each cyclobutane fragment of ladderanes with two nitrogen atoms. These substituted ladderanes are named 1,2 and 1,3 N-doped [n]-ladderanes, respectively. The same procedure has also been used to design 1,2 and 1,3 P-doped [n]-silaladderanes. In recent experimental studies on doped polysilanes, boron and phosphorus atoms have been successfully introduced to the SiNWs to increase their conductivity.28 Experimental measurements have shown that these two types of doped SiNWs behave as p-type and n-type materials. Because only limited boron and phosphorus atoms were introduced in SiNWs, in the present study, we simply substitute one carbon or one silicon atom in the center ring of [n]-ladderanes or [n]-silaladderanes with a heteroatom such as boron, nitrogen, or

phosphorus (X = B, N, or P). It is noted that the heteroatomdoped ladderanes and silaladderanes are radicals. All calculations were performed with the Gaussian 03 package of programs.34 The geometries of all species were optimized using the B3LYP functional with the 6-31þG(d) basis set. Vibrational frequency calculations at the same level were done to ensure that the optimized structures are minima on the corresponding potential energy surfaces (PESs). Besides the B3LYP functional, several other exchange and correlation functionals were also used to study the effect on the H-L gaps of [n]-ladderanes, [n]-silaladderanes (n = 3, 10 and 16), and selected doped derivatives. The selected molecules were optimized, and their H-L gaps were calculated with the BHandH,35 M05-2X,36 MPW1PW91,37 SVWN,38 PBE,39 BPW91,40 and BP8641 functionals. Compared with the B3LYP (20%) functional, a different degree of exact exchange terms is implemented in BHandH (50%), M05-2X (56%), and MPW1PW91 (25%) functionals, whereas the different correlation terms are used in the SVWN, PBE, BPW91, and BP86 functionals. To examine further the reliability of B3LYP method, additional time-dependent B3LYP predictions were done on the H-L gaps of [n]-silaladderanes and N-doped [n]-silaladderanes (n = 3
8, 12, 16) at the TD-B3LYP/ 6-311þþG(d,p)//B3LYP/6-31þG(d) level and the calculated results were compared with ultraviolet (UV) absorption peak of the isopropyl substituted [n]-silaladderanes (n = 3
8).15,16,20

3. RESULTS AND DISCUSSIONS 3.1. Doped [n]-Ladderanes (n = 3
16). On the basis of the optimized structures of [n]-ladderanes with n = 3
16, selected CH groups are replaced with isoelectronic nitrogen atoms and heteroatoms to yield 28 N-doped and 42 X-doped [n]-ladderanes, with X being B, N, or P. The structures of these 70 species have all real vibrational frequencies and represent minima on the PES. All of these doped molecules are reported for the first time here. Our optimized structures are consistent with those obtained in previous studies,21,25 which were mostly concerned with the structures and ring strain energies of [n]-ladderanes. In 7657

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Figure 1. Optimized structures of the [16]-ladderane and its doped derivatives.

the present study, we focus on the doping effects on the H-L gaps of the ladderanes. The optimized structures of [16]-ladderanes and doped [16]ladderanes are shown in Figure 1. Their HOMO and LUMO wave functions are illustrated pictorially in Figure 2. The variations of H-L gaps of doped [n]-ladderanes with respect to n are shown in Figure 3. As shown in Figure 1, the 1,2- and 1,3-doped [16]-ladderanes retain the relative straight ladder shapes in their skeleton, whereas the structures of three X-doped [16]-ladderanes have bent ladder conformations, especially for the B-doped oligomer. The extent of bending can be better seen from the side views also displayed in Figure 1: now the bending of B-doped [16]-ladderane is particularly noticeable. Compared with the parent [16]-ladderane, the C
C bond distances of the five doped derivatives do not differ much, but for the three X-doped structures, the “central” C
X bond is broken and a six-membered ring is formed at the center of the molecule. The physical properties of a polymer depend strongly on the size or length of the polymer chain.42 To investigate the doping effect on the length of the [n]-ladderane, we have also estimated the length, which is defined as the distance between the two carbon atoms at the head and the end of the molecules, for each of the six ladderanes. The length of [16]-ladderanes is 20.7 Å, whereas 1,2 and 1,3 N-doped [16]-ladderanes are shorter by 1.3 and 0.9 Å, respectively. For the three X-doped molecules, lengths of N- and P-doped [16]-ladderanes decrease slightly (by 0.4 and 0.2 Å, respectively), whereas the B-doped [16]-ladderane contracts by 0.9 Å. The [16]ladderane is a highly symmetrical molecule with C2v symmetry. After substitution with isoelectronic atoms or heteroatoms, the doped structures naturally have lower symmetries: the 1,2 and 1,3 N-doped [16]-ladderanes have C2 and Cs symmetry, respectively, and the three X-doped molecules have only C1 symmetry.

Figure 2 shows that the HOMO and LUMO of ladderane derivatives, whose H-L gaps are significantly reduced upon doping with isoelectronic atoms or heteroatoms. For example, [16]-ladderane has an H-L gap of 6.30 eV; its HOMO consists of a chain of σ C
C bonding orbitals, and the LUMO is a π MO localized in the middle of the molecule. For 1,2 N-doped [16]ladderane, the doping changes both HOMO and LUMO significantly: now the HOMO becomes a combination of σ bonding orbitals localized at the two ends of the molecule and the nodal plane of the π orbital disappears. Compared with [16]-ladderane, the 1,2 N-doped [16]-ladderane has an H-L gap of 5.59 eV; the doping has stabilized the LUMO by 0.98 eV. The 1,3 N-doped [16]-ladderane has a less stable HOMO, but its LUMO is stabilized; it has an even smaller gap, 5.85 eV. More importantly, the heteroatom doping has a more pronounced effect than the isoelectronic atom doping: the B-, N-, and P-doped [16]-ladderanes have substantially smaller H-L gaps of 3.24, 3.55, and 3.37 eV, respectively. The HOMO and LUMO of X-doped [16]-ladderanes, much different from those of the parent molecule, are mainly localized around the heteroatom and its nearby carbon atoms. As mentioned above, the “central” C
X bond in X-doped [16]-ladderanes is broken; then, a dangling bond on the “central” carbon atom is formed, which results in two defective sites on the chain of the molecules. Both HOMO and LUMO are localized defect orbitals, which lead to a significant decrease in H-L gaps. Figure 3 shows the H-L gaps of [n]-ladderanes and the doped derivatives exhibit distinct size dependence with numbers of cyclobutane rings (n). When n becomes larger, the H-L gap of [n]-ladderanes decreases. The present theoretical results indicate that [n]-ladderanes with increasing n retain the rigid ladder structures, and their H-L gaps are still very large. In passing, it 7658

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Figure 2. Plots of the HOMO and LUMO of [16]-ladderane and its doped derivatives.

Figure 3. HOMO
LUMO energy gaps (eV) of [n]-ladderanes, N-doped [n]-ladderanes, and X-doped [n]-ladderanes (n = 3
16).

is noted that the largest ladderane that has been synthesized so far is [13]-ladderane.10 The H-L gap curves of doped [n]-ladderanes shown in Figure 3 are all below that of [n]-ladderanes, indicating that doping does decrease the H-L gap. Quantitatively, the doping effect is not enhanced to a large extent as n increases. For [3]-ladderane, the 1,2 and 1,3 N-doping lead to a lowering of 1.39 and 1.41 eV,

respectively. As n increases, the changes in H-L gaps remain relatively constant. The isoelectronic atom doping leads to a drop of 0.6 to 1.4 eV in H-L gaps when n increases from 3 to 16. Analogous nitrogen replacement of CH moieties in oligoacenes in fact results in larger H-L gaps.31 These results indicate that the introduction of nitrogen atoms on different molecules could have opposite effects on the H-L gaps. The B-, N-, and P-doping of [n]-ladderanes will yield more pronounced reductions of the H-L gaps, as shown in Figure 3. For n > 7, the gaps remain essentially constant, which implies that X-doped [n]-ladderanes do not have size dependence on H-L gaps. Comparing the three types of X-doped [n]-ladderanes, we see that the H-L gaps are in the order of N > P > B. The H-L gaps of these heteroatom-doped ladderanes fall in a narrow range of 3.2 to 3.9 eV, which are ∼3 eV lower than those of the parent ladderanes; they are also much smaller than those of the previously reported closed ladderanes.22
24,26 Our results strongly suggest that the heteroatom doping has a remarkable effect on the H-L gaps and the HOMO/LUMO wave functions of [n]-ladderanes. 3.2. Doped [n]-Silaladderanes (n = 3
16). Karni and Apeloig17 have carried out a theoretical study on [n]-silaladderanes with n = 1
8 and found that the H-L gaps in silicon ladderanes are much smaller than those in the corresponding carbon ladderanes. The largest calculated [n]-silaladderanes in their study is [8]-silaladderanes, which has a gap of 3.4 eV. In addition, their results indicate that chain elongation destabilizes HOMO and stabilizes LUMO, leading to a reduced H-L gap. To 7659

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Figure 4. Optimized structures of the [16]-silaladderane and its doped derivatives.

search for narrow band gap molecules, we have extended their study on [n]-silaladderanes to n = 9
16 and to the related doped [n]-silaladderanes (n = 3
16). The optimized structures of [16]-silaladderane and related doped derivatives are displayed in Figure 4. Their HOMO and LUMO are shown in Figure 5. The variations of H-L gaps with n of doped [n]-silaladderanes are presented in Figure 6. In Figure 4, we can see that the doping effects on the structures of five types of doped silaladderanes are quite different. The ladder structure of 1,2 P-doped [16]-silaladderane appears almost arch-like, whereas the bending in the structures of B-, N-, and P-doped [16]-silaladderanes is much less pronounced. At the same time, the 1,3 P-doped [16]-silaladderane has a very straight ladder structure. The Si
Si bond distances in the five doped derivatives are about 2.3 to 2.4 Å, quite close to those in [16]silaladderanes. It is interesting to note that the “central” Si
X bonds in the three X-doped structures are not broken; in the corresponding X-doped carbon analogs, the C
X bonds are cleaved, and a six-membered ring is formed. The molecular length of [16]-silaladderanes is 31.5 Å, whereas those of 1,2 and 1,3 P-doped [16]-silaladderanes are considerably shorter, at 23.2 and 28.3 Å, respectively. The noticeable contraction of the 1,2 P-doped structure is mainly due to its strongly bent structure. The [16]-ladderane has a symmetrical structure with C2v symmetry, whereas its silicon analog, [16]-silaladderane, has only C2 symmetry. The 1,3 P-doped and P-doped [16]-silaladderanes have Cs symmetry. The 1,2 P-doped and the remaining two X-doped molecules have only C1 symmetry. Comparing Figures 2 and 5, it can be seen that the HOMO of [16]-silaladderane is similar to that of its carbon analog, which is composed of a chain of Si
Si σ bonding orbitals. The LUMO consists of many localized π orbitals, which is obviously different

from that of [16]-ladderane. As a result, [16]-silaladderane has H-L gap of 2.84 eV, which is 3.46 eV lower than that of [16]ladderane. The HOMOs of isoelectronic 1,2 and 1,3 P-doped [16]-silaladderanes have their σ bonding orbitals reorganized. But their LUMOs are similar to those of the parent silaladderane. Compared with [16]-silaladderane, both the HOMO and LUMO of the P-doped derivatives are stabilized, with the HOMO being stabilized to a larger extent. As a result, the H-L gaps become larger, at 3.35 eV for both isomers. To sum up at this point: [16]silaladderane doped with isoelectronic atoms has an H-L gap similar to its parent compound. Heteroatom doping significantly reduces the H-L gaps of silaladderane. The B-, N-, and P-doped [16]-silaladderanes have H-L gaps of 1.18, 0.88, and 0.98 eV, respectively, which are smaller than the typical H-L gap range of 2.3 to 2.7 eV for semiconductor17 and below 1.5 eV for the low band gap polymers.5 The HOMOs and LUMOs of B-, N-, and P-doped [16]silaladderanes have undergone drastic reorganization: they are mainly localized in the center portion of the ladder chains. Compared with the corresponding carbon analog, the HOMO and LUMO of X-doped [n]-silaladderanes show different localization behavior. In X-doped [n]-ladderanes, both HOMO and LUMO of are defect orbitals, but in X-doped [n]-silaladderanes, HOMO is a defect orbital only when X is N or P, whereas LUMO is defective only when X is B. Such a difference may be due to X-doped [n]-ladderanes that have a dangling bond on the “central” carbon atom. The “central” Si
X bonds in X-doped [n]-silaladderanes are not broken. Figure 6 shows the doping effects on H-L gaps of [n]silaladderanes as a function of n. The H-L gaps of [n]-silaladderanes and 1,2 and 1,3 P-doped derivatives exhibit obvious size dependence. Their H-L gaps decrease with increasing n. The 1,2 7660

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Figure 5. Plots of the HOMO and LUMO of [16]-silaladderane and its doped derivatives.

Figure 6. HOMO
LUMO energy gaps (eV) of [n]-silaladderanes, P-doped [n]-silaladderanes, and X-doped [n]-silaladderanes (n = 3
16).

and 1,3 P-doped [n]-silaladderanes have quite different structures, but their H-L gaps are very close to each other. For n = 3 and 4, the P-doped [n]-silaladderanes have smaller gaps than those of the corresponding silaladderanes. For n = 5, the gap of P-doped and parent silaladderanes are almost the same. Compared with the P-doped derivatives, the [n]-silaladderanes have smaller gaps at n > 5. Although isoelectronic atom doping has been used for oligoacenes to design the n-channel organic semiconductors successfully,31 the present results show that this kind of doping is not an effective way for silaladderanes.

The largest silaladderane, which has been reported theoretically, is [8]-silaladderanes with an H-L gap of 3.4 eV.17 In the present work, we have extended the theoretical study to [n]-silaladderanes for n = 9
16. From n = 3
8, the H-L gaps of silaladderanes decrease by 1.46 eV, but for n = 9
16, the decrease is only 0.45 eV. It appears to be a challenge to synthesize large size silaladderanes because the longest one that has been prepared so far is a [8]-silaladderane derivative.15,16 Thus, increasing the chain length is neither an easy nor an effective way to reduce the H-L gaps of silaladderane. The H-L gaps of X-doped [n]-silaladderanes are much smaller than the parent silaladderanes, which shows that the heteroatom doping strongly affects the electronic properties of silaladderanes. Figure 6 shows that the H-L gaps of the three X-doped [n]silaladderanes decrease when n = 3
7. For n > 8, the H-L gaps remain fairly constant and reach a plateau with larger n. For n = 9, the H-L gaps of N- and P-doped [n]-silaladderanes are ∼1 eV; this implies that low band gap silaladderanes are readily obtainable with a relatively shorter chain. Comparing the three X-doped [n]-silaladderanes, the B-doped molecules have a larger H-L gap than those of N- and P-doped molecules. For most X-doped [n]silaladderanes, their H-L gaps are 7. For [n]-silaladderanes, only the 1,3 P-doped derivative remains a straight ladder skeleton. All other doped [n]-silaladderanes have bent structures. The two aforementioned modes of doping have different effects on the H-L gaps of [n]-silaladderanes. The isoelectronic atom doping increases H-L gaps as n > 5, whereas the heteroatom doping yields silaladderanes with very smaller H-L gaps in the range of 1 to 2 eV. The [n]-silaladderanes as well as 1,2 and 1,3 P-doped derivatives exhibit size dependence on H-L gaps, and the H-L gaps are still above 3 eV for n = 16. The heteroatom X-doped [n]-silaladderanes are found to have much smaller H-L gaps and in a narrower gap range in comparison with the parent silaladderanes. The heteroatom doping effectively yields silaladderanes with H-L gap in the semiconductive range. Therefore, the B-, N-, and P-doped [n]-silaladderanes are promising candidates for conductive or semiconductive materials. Also, nine different density functionals, including B3LYP, SVWN LDA, four pure GGA, and three hybrid GGA, as well as the timedependent B3LYP method, have been employed to calculate the H-L gaps of selected ladderanes, silaladderanes, and their doped derivatives and very similar results have been obtained.

’ ASSOCIATED CONTENT

bS

Supporting Information. Doping effects on H-L gaps of the selected [n]-ladderanes and [n]-silaladderanes (n = 3, 10, and 16) using different DFT functionals and absolute H-L gaps (in electronvolts) of selected [n]-ladderanes (n = 3, 10 and 16) and their doped derivatives using different DFT functionals. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Present Addresses †

College of Chemistry, Sichuan University, Chengdu 610064, People’s Republic of China.

’ ACKNOWLEDGMENT X.W. is grateful for the support of National Science Foundation of China under grant no. 20503018. The work described in this Article was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. CityU 101308 K.C.L.). We thank the reviewers for very helpful comments. ’ REFERENCES (1) Roncali, J. Chem. Rev. 1997, 97, 173. (2) Kitamura, C.; Tanaka, S.; Yamashita, Y. Chem. Mater. 1996, 8, 570. 7662

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