Novel Beltlike and Tubular Structures of Boron and Carbon Clusters

Dec 22, 2007 - Congjie Zhang , Dongxia Ma , Shaoni Yang , and Jinxia Liang. ACS Omega ... Congjie Zhang , Wenhong Jia and Zexing Cao. The Journal of ...
0 downloads 0 Views 593KB Size
Download PDF
J. Phys. Chem. C 2008, 112, 351-357

351

Novel Beltlike and Tubular Structures of Boron and Carbon Clusters Containing the Planar Tetracoordinate Carbon: A Theoretical Study of (C3B2)nH4 (n ) 2-6) and (C3B2)n (n ) 4-8) Wenxiu Sun and Congjie Zhang* School of Chemistry & Materials Science, Shaanxi Normal UniVersity, Xi’an, 710062, China

Zexing Cao* Department of Chemistry and State Key Laboratory for Physical Chemistry of Solid Surface, Xiamen UniVersity, Xiamen, 361005, China ReceiVed: September 6, 2007; In Final Form: October 19, 2007

By use of the most stable structure of C3B2H4 as a basic block, we construct two types of novel compounds containing the planar tetracoordinate carbon (ptC), beltlike compounds (C3B2)nH4 (n ) 2-6) and tubular compounds (C3B2)n (n ) 4-8). Equilibrium geometries, vibrational frequencies, and electronic spectra of both series of compounds have been determined by the density functional theory. The results reveal that the same direction arrangement of C2CB2 units with ptC will result in the most stable isomers of (C3B2)nH4 (n ) 2-6). Predicted nucleus-independent chemical shift values show that the three-membered rings have aromaticity, whereas the six-membered rings have antiaromaticity. Calculations show that these compounds containing ptC atoms exhibit remarkable size dependence of their highest-occupied molecular orbital-lowestunoccupied molecular orbital energy gaps and the first excitation energies.

Introduction Since Hoffmann and co-workers first proposed the presence of species containing the planar tetracoordinate carbon,1 there has been a sharp growth of interest in such molecules recently,2-34 both theoretically and experimentally. In particular, many stable structures containing two or more ptC arrangements within the molecule have been predicted to be stable theoretically.35-41 For example, Merino and co-workers theoretically proposed the smallest carbon cluster C52- containing a ptC, which was stabilized by alkaline metals.18,19 Subsequently, Pancharatna et al. predicted the existence of multi-C52- units in an extended structure theoretically.35 The carbon lithium compounds with two ptC atoms36 and starlike perlithioannulenes CnLin (n ) 3-6) containing multi-ptC atoms are stable theoretically.37 More recently, a few novel sandwichlike compounds composed of two CAl42- units with ptC were investigated theoretically,38 which are different from previous dimeric structure ((Na+)2[CAl42-])2 proposed by Geske and Boldyrev in 2002.39 In 2005, Li et al. proposed hydrometal complexes containing two ptC atoms;40 meanwhile, multi-ptC centers in organoboron compounds were verified to be stable by Minyaev et al.,41 which are constructed by assembling three basic building blocks and carbon rings. Such an assembly strategy provides an effective route to construct novel structures with the ptC arrangements. By use of the stable isomer A1 of C3B2H4 with the ptC atom (see Figure 1) as a basic block, we have designed a series of beltlike structures containing ptC atoms. Furthermore, another series of tubular structures have been constructed by curling up the beltlike framework (C3B2)n. Their structures, stabilities, aromaticities, electronic spectra, and dependences of properties on configuration and size have been studied theoretically. * To whom correspondence should be addressed. E-mail: zxcao@ xmu.edu.cn (Z.C.); [email protected] (C.Z.).

Figure 1. Optimized geometries of the isomers A1 and A2.

Computational Methods The geometry optimization and vibrational frequency evaluation of beltlike compounds (C3B2)nH4 (n ) 2-6) containing two, three, four, five, and six basic building blocks with ptC were carried out by the hybrid B3LYP functional at the 6-311+G** basis set level.42-45 Similarly, optimization and frequency calculations of the tubular compounds (C3B2)n (n ) 4-8) with multi-quasi-ptC atoms were performed at the same level of theory. The convergence thresholds of the maximum force, root-mean-square (rms) force, maximum displacement, and rms displacement of the optimized structures between two iterations are default in Gaussian 03 program,46 which are 0.00045, 0.0003, 0.0018, and 0.0012, respectively. In addition, the self-consistent field convergence criterion is equal to 10-8. The nucleus-independent chemical shifts (NICS) of the most stable structure of (C3B2)nH4 (n ) 2-4) were determined by the gauge-independent atomic orbital (GIAO) approach. The electronic spectra of the most stable structures of (C3B2)nH4 (n ) 2-6) were estimated by the TD-B3LYP/6-311+G** method.

10.1021/jp0771522 CCC: $40.75 © 2008 American Chemical Society Published on Web 12/22/2007

352 J. Phys. Chem. C, Vol. 112, No. 2, 2008

Sun et al.

Figure 3. Selected molecular orbitals of the isomer B1.

Figure 2. Optimized geometries of the isomers B1-B3.

TABLE 1: Electronic States, Total Energies (in au.), Relative Energies (in kcal/mol), ZPEs (in kcal/mol), and HOMO-LUMO Energy Gaps (Gap, in eV) of Each Isomer isomer state A1 A2 B1 B2 B3 C1 C2 C3 C4 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 E1 F1

1A 1 1A 1 1A 1 1A g 1A g 1A 1 1A 1 1A 1 1A 1 1A 1 1A g 1A 1 1A 1 1A 1 1A g 1A 1 1A 1 1A g 1A g 1A 1 1A 1

energies

relative energies

ZPE

-166.36359 -166.29479 -330.35188 -330.34414 -330.30923 -494.33152 -494.32338 -494.28414 -494.27948 -658.31471 -658.30841 -658.30559 -658.26778 -658.26617 -658.26110 -658.25908 -658.25630 -658.25096 -658.22362 -822.29791 -986.28126

0.0 43.2 0.0 4.9 26.8 0.0 5.1 29.7 32.7 0.0 4.0 5.7 29.4 30.5 33.6 34.9 36.7 40.0 57.2 0.0 0.0

37.61 36.56 52.70 54.48 50.71 67.83 69.40 66.03 67.55 82.94 84.50 84.53 81.12 82.64 81.24 82.71 82.80 84.34 80.78 98.03 113.05

EHOMO ELUMO

gap

Figure 4. Optimized geometries of the isomers C1-C4.

-0.24 -0.23 -0.22 -0.23 -0.21 -0.21 -0.22 -0.20 -0.21 -0.21 -0.22 -0.21 -0.19 -0.21 -0.19 -0.20 -0.20 -0.21 -0.20 -0.20 -0.20

5.73 4.78 4.03 3.95 3.73 3.23 3.30 2.97 3.08 2.77 2.99 2.78 2.51 2.81 2.53 2.53 2.63 2.73 2.64 2.46 2.24

TABLE 2: Electronic State, Total Energies (in au.), ZPEs (in kcal/mol), and HOMO-LUMO Energy Gaps (in eV) of Each Tubular Compound

-0.03 -0.05 -0.08 -0.09 -0.08 -0.09 -0.10 -0.09 -0.10 -0.10 -0.11 -0.11 -0.10 -0.11 -0.10 -0.11 -0.10 -0.11 -0.10 -0.11 -0.12

All calculations in the present work have been performed by Gaussian03 program.46 Results and Discussion A. Structures and Stabilities of Beltlike structures (C3B2)nH4 (n ) 2-6) Containing ptC Atoms. Optimized geometries and relative energies of isomers of C3B2H4 with the ptC atom are displayed in Figure 1 and Table 1, respectively. As Table 1 shows, the isomer A1 is more stable than A2 by 43.2 kcal/mol. The bond lengths of ptC-B, ptC-C, and C-B in A1 are 1.615, 1.401, and 1.403 Å, respectively, which are consistent with the previous studies.41 Such atomic arrangement of A1 was denoted

structures T1 T2 T3 T4 T5

state 1

Ag A 1 Ag 1 A 1 Ag 1

energy

ZPE

EHOMO

ELUMO

gap

-655.71100 -819.75256 -983.76644 -1147.77418 -1311.77377

58.51 74.38 89.66 104.88 120.35

-0.22 -0.23 -0.21 -0.22 -0.20

-0.10 -0.10 -0.12 -0.11 -0.12

3.09 3.50 2.50 2.91 2.30

as H2C2CB2H2. By use of the isomer A1 as a basic block, we design a series of beltlike compounds (C3B2)nH4 (n ) 2-6) containing the ptC atoms. The isomer A1 has C2V symmetry, and the different linking ways will result in various isomers. For example, (C3B2)2H4 has three isomers as shown in Figure 2. Moreover, the number of the isomers will increase prominently with the increase of building units n. The optimized geometries of the three conformations of (C3B2)2H4, denoted as B1, B2, and B3, are displayed in Figure 2. Their electronic states, total energies, relative energies, and zero point energies (ZPE) are collected in Table 1. The vibrational analyses of these structures have also been performed at the same theoretical level and the frequency results reveal that all structures in Figure 2 are stable. As seen from Table 1, the order of energy of (C3B2)2H4 is B1 < B2 < B3. To describe the relationship between the stability and the arrangement of C2CB2 units in (C3B2)2H4, we denote the six-membered rings formed by B-C, B-B, and C-C connection as S1, S2, and S3 ring, respectively. For example, as Figure 2 displays, the six-membered rings in isomers B1, B2, and B3 are S1, S2, and S3, respectively. Relative energies

Structures of Boron and Carbon Clusters

J. Phys. Chem. C, Vol. 112, No. 2, 2008 353

Figure 6. Optimized geometries of the isomers E1 and F1.

Figure 5. Optimized geometries of the isomers D1-D10.

TABLE 3: WBIs of ptC-B Bonds (WBIC-B) and Total WBIs of the pt-Cs (WBIC) of (C3B2)nH4 (n ) 2-6) and (C3B2)n(n ) 4-8) isomer

WBIC-Ba

WBICa

A1 B1 B2 B3 C1 C2 C3 C4 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 E1

0.656 0.646, 0.651 0.639 0.652 0.639, 0.646, 0.648 0.641, 0.640, 0.634 0.650, 0.648, 0.649 0.632, 0.643, 0.650 0.639, 0.641, 0.643, 0.646 0.643, 0.636 0.640, 0.641, 0.636, 0.637 0.651, 0.642, 0.644, 0.647 0.643, 0.636, 0.634, 0.649 0.649, 0.646 0.632, 0.638, 0.643, 0.650 0.629, 0.641, 0.646, 0.648 0.630, 0.641 0.650, 0.633 0.638, 0.640, 0.638, 0.642, 0.645 0.637, 0.639, 0.611, 0.635, 0.639, 0.643 0.574 0.594 0.604 0.610 0.614

3.918 3.900, 3.823 3.901 3.815 3.888, 3.837, 3.836 3.888, 3.843, 3.882 3.820, 3.831, 3.840 3.880, 3.839, 3.820 3.889, 3.832, 3.846, 3.834 3.892, 3.835 3.890, 3.833, 3.849, 3.886 3.821, 3.827, 3.850, 3.834 3.892, 3.834, 3.833, 3.819 3.840, 3.834 3.887, 3.855, 3.827, 3.820 3.881, 3.841, 3.834, 3.840 3.881, 3.840 3.819, 3.833 3.889, 3.833, 3.840, 3.845, 3.833 3.887, 3.833, 3.824, 3.848, 3.845, 3.832 3.873 3.862 3.856 3.852 3.849

F1 T1 T2 T3 T4 T5

a The order of WBI values of (C B ) H (n ) 2-6) corresponds to 3 2 n 4 the order from left to right of compounds (C3B2)nH4 (n ) 2-6).

in Table 1 indicate that the S1 units in structure will cause energy decreases, while the S3 units will result in energy increases. As can be seen from Figure 2, the bond lengths and bond angles of the left C2CB2 unit are less changed, while the bond length of C-C increases about 0.04 Å, and the bond angle

of B-ptC-B increases by about 30° in the right C2CB2 unit relative to the isomer A1. The geometries of C2CB2 unit in the isomer B2 are very close to those in the isomer A1. The sixmembered ring in the isomer B3 is close to a regular hexagon. To detect the electronic properties of isomer B1, we depict the lowest-unoccupied molecular orbital (LUMO) and all of occupied π orbitals of isomer B1 in Figure 3. Figure 3 shows that there are four occupied π orbitals, which are highestoccupied molecular orbital (HOMO), HOMO-1, HOMO-6, and HOMO-7. These π orbitals play an important role in the delocalization of lone-pair electrons at the ptC atoms. The optimized geometries and symmetries of all possible combinations of beltlike compounds (C3B2)nH4 (n ) 3 and 4), isomers C1-C4 and D1-D10, are displayed in Figures 4 and 5, respectively. Their energies, relative energies and energy gaps are incorporated into Table 1. As seen from Table 1, the energies of isomers C1 and D1 are the lowest for (C3B2)nH4 (n ) 3, 4). The energy order of (C3B2)nH4 (n ) 3, 4) is C1 < C2 < C3 < C4 and D1 < D2 < D3 < D4 < D5 < D6 < D7 < D8 < D9 < D10, respectively. As Figure 4 displays, the arrangement orders of six-membered rings in isomers C1, C2, C3, and C4 are S1S1, S1S2, S3S1, and S2S3, respectively. As discussed above, the more the S1 units in structure, the more stable the compounds. Similarly, the isomer D1 with the six-membered ring arrangement of S1S1S1 has the lowest energy, whereas the D10 with S3S2S3 in Figure 5 is higher in energy. Predicted relative energies in Table 1 indicate that such stability rule is general for (C3B2)nH4 (n ) 2, 3 and 4). Therefore, the S1S1‚‚‚S1 structure of six-membered rings in (C3B2)nH4 (n ) 2-4) will have relatively high stability, i.e., the structure with the same direction arrangement of C2CB2 is the lowestenergy isomer, such structure is denoted as H2(C2CB2)nH2. The bond distances of C-C and B-C in the left C2CB2 are almost unchanged for (C3B2)nH4 (n ) 3, 4), which are about 1.416 (C-C), 1.404 (B-C), and 1.637 (B-ptC) Å, respectively. In addition, the bond lengths of C-C and B-C in the right C2CB2 are independent of the sizes, which are about 1.444 (CC), 1.402 (B-C), and 1.600 (B-ptC) Å, respectively. On the basis of the stability rule of (C3B2)nH4 (n ) 2-4), two structures of (C3B2)nH4 (n ) 5, 6) with the S1S1‚‚‚S1 arrangement of the six-membered rings, E1 and F1, are optimized. Their vibrational frequencies are calculated at the B3LYP/6-311+G** level, and both structures have no imaginary frequencies. The geometries of E1 and F1 are shown in Figure 6, and the energies are also incorporated into Table 1. Figure 6 displays that the bond distances of C-C and B-C in

354 J. Phys. Chem. C, Vol. 112, No. 2, 2008

Sun et al.

Figure 7. IR vibrational spectra of isomer B1, C1, D1, E1, and F1.

the left and right C2CB2 unit are close to those of (C3B2)nH4 (n ) 3, 4). The bond lengths of C-C of the middle C2CB2 units in structures C1, D1, E1, and F1 vary from 1.428 to 1.439 Å. The bond lengths of B-ptC are between 1.571 and 1.594 Å, and the bond lengths of other two kinds of C-C are about 1.522 and 1.422 Å, respectively. Furthermore, Wiberg Bond Indices (WBI) of (C3B2)nH4 (n ) 1-6) are calculated at the B3LYP/6-311+G** level and listed in Table 3. As seen from Table 3, the WBI of all of ptC-B bonds in the (C3B2)nH4 (n ) 1-6) structures vary between 0.611 and 0.656, and the total WBI values of ptC centers vary between 3.815 and 3.918, indicating that the ptCs follow the octet rule. The HOMO-LUMO energy gaps of the lowest-energy beltlike isomers B1, C1, D1, E1, and F1 in Table 1 are 5.73, 4.03, 3.23, 2.77, 2.46, and 2.24 eV, respectively, indicating that the HOMO-LUMO energy gaps of beltlike isomers decrease exponentially as the increase of the number of the building blocks.

Predicted IR spectra of isomers B1, C1, D1, E1, and F1 are shown in Figure 7. As seen from Figure 7, the spectra of the five kinds of systems are very similar, and the strong IR spectra mainly appear at about 600, 1000, 1700, and 2800 cm-1. Among these strong absorptions, the strongest IR peaks of the five isomers situate at about 1700 cm-1, and they correspond to the symmetrical stretching vibrations (a1) of all of the B-C bonds from the adjoining (C2CB2)n units. The strong vibrational frequencies at about 600 cm-1 arise from the in- and out-ofplane bending vibrations of C-B-C bonds. The IR bands at about 1000 cm-1 are from the stretching vibrations of C-C bonds, and the stretching frequencies of B-H bonds occur at about 2800 cm-1. However, the IR absorptions from the C-H bond stretching at about 3270 cm-1 are very weak. B. Aromaticity of H2(C2CB2)nH2 (n ) 2-4). The NICS values at the central position of each ring of the most stable isomers B1, C1, and D1 were listed in Figure 8. As Figure 8 displays, all of three-membered rings have strong diatropic

Structures of Boron and Carbon Clusters

J. Phys. Chem. C, Vol. 112, No. 2, 2008 355

Figure 8. NICS values (in ppm) of the isomers B1, C1, and D1.

Figure 10. Optimized geometries of the tubulars T1, T2, T3, T4, and T5.

Figure 9. Plot of the wavelength of the origin band of the electronic transition of the isomers B1, C1, D1, E1, and F1 vs n.

contribution and correspond to negative NICS values, while each six-membered ring presents paratropic contribution and corresponds to positive NICS values. This indicates that the threemembered rings have strong aromatic character, while the sixmembered rings have antiaromaticity, which is consistent with the previous results.6 C. Electronic Spectra of H2(C2CB2)nH2 (n ) 2-6). The electronic spectra of isomers B1, C1, D1, E1, and F1 are calculated by the TD-B3LYP/6-311+G** method. The configuration of the frontier and near-frontier orbitals of B1, C1, D1, E1, and F1 is a22a22b10b10, and their first electronic transitions are a22a22b10b10 f a22a21b11b10 for B1 and a22a22b10b10 f a21a22b11b10 for C1, D1, E1, and F1, in which a2 and b1 belong to π and π* orbitals, respectively. As a consequence, the first transitions in isomers B1, C1, D1, E1, and F1 are X1A1 f 11B2, and the corresponding excitation energies and oscillator strengths are 251.09 (f ) 0.0195), 307.09 (f ) 0.0106), 366.78 (f ) 0.0099), 424.67 (f ) 0.0072), and 478.68 nm (f ) 0.0051), respectively. The plot of the wavelength of the origin band of the electronic transition of (C3B2)nH4 (n ) 2-6) is displayed in Figure 9. As Figure 9 shows, there is a linear dependence of the first excitation energies of (C3B2)nH4 (n ) 2-6) upon the size of n, i.e., the excitation energies linearly decrease with the increase of the building block. D. Tubular Compounds of (C2CB2)n (n ) 4-8) Containing Quasi-ptC Atoms. As mentioned above, the beltlike structures D1, E1, and F1 are the most stable isomers. By curling up the H-deleted framework of beltlike structures (C3B2)nH4 (n ) 4-6), the tubular compounds (C3B2)n (n ) 4-6) can be constructed. In addition, another two tubular compounds (C3B2)n (n ) 7, 8) are also constructed. These five tubular compounds (C3B2)n (n

) 4-8), denoted as T1, T2, T3, T4, and T5, are considered here. The optimized geometries and symmetries of structures T1, T2, T3, T4, and T5 are shown in Figure 10, and the total energies and HOMO-LUMO energy gaps are listed in Table 2. Predicted IR spectra of T1, T2, T3, T4, and T5 are displayed in Figure 11. The vibrational frequencies indicate these structures have no imaginary frequencies, and they are stable isomers. In contrast to (C3B2)nH4 (n ) 4-8), Table 2 shows that the HOMO-LUMO energy gaps of the tubular compounds T1, T2, T3, T4, and T5 are 3.09, 3.50, 2.50, 2.91, and 2.30 eV, respectively, exhibiting an obvious odd-even alternation character. The HOMO-LUMO energy gaps decrease as the increase of the size of the tubular compounds. Moreover, the tetracoordinate carbon has a near-planar configuration in the tubular compounds T1, T2, T3, T4, and T5. The sums of the four bond angles associated with ptC atoms in T1, T2, T3, T4, and T5 are 347.7, 350.6, 352.5, 353.9, and 355.0°, respectively, which are close to 360°. Therefore, the tubular compounds (C2CB2)n contain n quasi-ptC centers. Moreover, the quasi-tetracoordinate carbon atom approaches the ptC with the increase of the C2CB2 unit. As Figure 10 displays, there is only one kind of C-C bond and three types of B-C bonds in these tubular compounds. The bond lengths of C-C in the five tubular compounds increase from 1.4283 to 1.4353 Å. The bond distances of B-ptC in C3B2 units decrease from 1.6563 to 1.6144 Å. The bond distances of the other two B-C bonds have no significant changes for the five kinds of tubular compounds. The WBIs of tubular compounds (C3B2)n (n ) 4-8) are also calculated at the B3LYP/6-311+G** level and displayed in Table 3. Table 3 shows that the WBI of all of ptC-B bonds in the tubular compounds (C3B2)n (n ) 4-8) vary between 0.574 and 0.614 and that the total WBI values of ptC centers vary between 3.873 and 3.849. Then the WBI values indicate that the ptCs in the tubular compounds (C3B2)n (n ) 4-8) follow the octet rule, which is consistent with the beltlike compounds (C3B2)nH4 (n ) 1-6).

356 J. Phys. Chem. C, Vol. 112, No. 2, 2008

Sun et al.

Figure 11. IR vibrational spectra of tubulars T1, T2, T3, T4, and T5.

The IR spectra of T1, T2, T3, T4, and T5 are shown in Figure 11, and they are quite similar. The strong IR bands appear at 500, 600, 1000, 1200, and 1600 cm-1, and the peak of 1600 cm-1 is the strongest IR absorption among them. The vibrational frequencies at about 500 cm-1 arise from the in-tube bending vibrations of C-B-C on the top and bottom of tubulars. The vibrational frequencies at about 600 cm-1 correspond to the out-of-tube bending vibrations of C-B-C on the top and bottom of the tubes and the breathing vibration of the ptCs, in which the latter is greater than the former for each system. The vibrational frequencies of the symmetrical and unsymmetrical stretching vibrations of ptC-C are about 1000 and 1200 cm-1, respectively. The strongest IR frequencies of (C3B2)n (n ) 4-8) are 1518(eu), 1610(e1′), 1653(e1u), 1679(e), and 1692(e), respectively, corresponding to the symmetrical stretching vibrations of all of the B-C bonds from the adjoining (C3B2)n units. Summary and Conclusions In the present work, two types of compounds containing ptC or quasi-ptC atoms, beltlike compounds (C3B2)nH4 (n ) 2-6) and tubular compounds (C3B2)n (n ) 4-8), have been con-

structed with the most stable structure of H2C2CB2H2 as a basic building block. At the B3LYP/6-311+G** level, structures, stabilities, clustering rules, and vibrational frequencies of beltlike compounds (C3B2)nH4 (n ) 2-6) have been investigated. The results indicate that the most stable structures of (C3B2)nH4 (n ) 2-6) have atomic arrangement H2(C2CB2)nH2, in which the C2CB2 units are assembled in the same direction. The calculated NICS values show that the three-membered rings have aromatic character, whereas the six-membered rings have antiaromaticity. The electronic spectra from the first excitation in the most stable isomers H2(C2CB2)nH2 (n ) 2-6) have been calculated, and predicted first excitation energies linearly depend upon n. Structures and stabilities of the tubular compounds of (C3B2)n (n ) 4-8) constructed by (C2CB2)n units have been discussed. Generally, the low-energy stable isomers of tubular structures (C2CB2)n (n ) 4-8) contain four, five, six, seven, and eight quasi-ptC, respectively, and their HOMO-LUMO energy gaps have odd-even alternation character. Acknowledgment. This work was financially supported from the start-up fund of Shaanxi Normal University, the State Key Laboratory of Physical Chemistry of Solid Surfaces (Xiamen

Structures of Boron and Carbon Clusters University) (200504), the scientific research foundation of the graduate school of Shaanxi Normal University, the National Science Foundation of China (20673087 and 20473062), and the Ministry of Science and Technology (2004CB719902). References and Notes (1) Hoffmann, R.; Alder, R. W.; Wilcox, C. F., Jr. J. Am. Chem. Soc. 1970, 92, 4992. (2) Li, X.; Wang, L. S.; Boldyrev, A. I.; Simons, J. J. Am. Chem. Soc. 1999, 121, 6033. (3) Li, X.; Zhang, H. F.; Wang, L. S.; Geske, G. D.; Boldyrev, A. I. Angew. Chem., Int. Ed. 2000, 39, 3630. (4) Boldyrev, A. I.; Simons, J. J. Am. Chem. Soc. 1998, 120, 7967. (5) Wang, L. S.; Boldyrev, A. I.; Li, X.; Simons, J. J. Am. Chem. Soc. 2000, 122, 7681. (6) Perez, N.; Heine, T.; Barthel, R.; Seifert, G.; Vela, A.; MendezRojas, M. A.; Merino, G. Org. Lett. 2005, 7, 1509. (7) Esteves, P. M.; Ferreira, N. B. P.; Correˆa, R. J. J. Am. Chem. Soc. 2005, 127, 8680. (8) McGrath, M. P.; Radom, L. J. Am. Chem. Soc. 1993, 115, 3320. (9) Merino, G.; Me´ndez-Rojas, M. A.; Vela, A.; Heine, T. J. Comput. Chem. 2007, 28, 362. (10) Sateesh, B.; Reddy, A. S.; Sastry, G. N. J. Comput. Chem. 2007, 28, 335. (11) Rasmussen, D. R.; Radom, L. Angew. Chem., Int. Ed. 1999, 38, 2876. (12) Wang, Z. X.; Schleyer, P. v. R. J. Am. Chem. Soc. 2001, 123, 994. (13) Wang, Z. X.; Schleyer, P. v. R. J. Am. Chem. Soc. 2002, 124, 11979. (14) Roy, D.; Corminboeuf, C.; Wannere, C. S.; King, R. B.; Schleyer, P. v. R. Inorg. Chem. 2006, 45, 8902. (15) Sorger, K.; Schleyer, P. v. R. THEOCHEM 1995, 338, 317. (16) Boldyrev, A. I.; Wang, L. S. J. Phys. Chem. A 2001, 105, 10759. (17) Keese, R. Chem. ReV. 2006, 106, 4787. (18) Merino, G.; Mendez-Rojas, M. A.; Vela, A. J. Am. Chem. Soc. 2003, 125, 6026. (19) Merino, G.; Mendez-Rojas, M. A.; Beltran, H. I.; Corminboeuf, C.; Heine, T.; Vela, A. J. Am. Chem. Soc. 2004, 126, 16160. (20) Xie, H. B.; Ding, Y. H. J. Chem. Phys. 2007, 126, 184302. (21) Collins, J. B.; Dill, J. D.; Jemmis, E. D.; Apeloig, Y.; Schleyer, P. v. R.; Seeger, R.; Pople, J. A. J. Am. Chem. Soc. 1976, 98, 5419. (22) Krogh-Jesperson, K.; Cremer, D.; Poppinger, D.; Pople, J. A.; Schleyer, P. v. R.; Chandrasekhar, J. J. Am. Chem. Soc. 1979, 101, 4843. (23) Schleyer, P. v. R.; Boldyrev, A. I. J. Chem. Soc., Chem. Commun. 1991, 1536. (24) Boldyrev, A. I.; Schleyer, P. v. R. J. Am. Chem. Soc. 1991, 113, 9045. (25) Zakrzewski, V. G.; von Niessen, W.; Boldyrev, A. I.; Schleyer, P. v. R. Chem. Phys. 1993, 174, 167. (26) Poumbga, C. N.; Benard, M.; Hyla-Kryspin, I. J. Am. Chem. Soc. 1994, 116, 8259.

J. Phys. Chem. C, Vol. 112, No. 2, 2008 357 (27) Rottger, D.; Erker, G.; Frohlich, R.; Grehl, M.; Silverio, S. J.; HylaKryspin, I.; Gleiter, R. J. Am. Chem. Soc. 1995, 117, 10503. (28) Crans, D. C.; Snyder, J. P. J. Am. Chem. Soc. 1980, 102, 7152. (29) Wiberg, K. B.; Wendoloski, J. J. J. Am. Chem. Soc. 1982, 104, 5679. (30) Schulman, J. M.; Sabio, M. L.; Disch, R. L. J. Am. Chem. Soc. 1983, 105, 743. (31) McGrath, M. P.; Schaefer, H. F.; Radom, L. J. Org. Chem. 1992, 57, 4847. (32) Li, S. D.; Ren, G. M.; Miao, C. Q.; Jin, Z. H. Angew. Chem., Int. Ed. 2004, 43, 1371. (33) Dodziuk, H. J. Mol. Struct. 1990, 239, 167. (34) Luef, W.; Keese, R. THEOCHEM 1992, 257, 353. (35) Pancharatna, P. D.; Mendez-Rojas, M. A.; Merino, G.; Vela, A.; Hoffmann, R. J. Am. Chem. Soc. 2004, 126, 15309. (36) Wang, Z. X; Manojkumar, T. K.; Wannere, C.; Schleyer, P. v. R. Org. Lett. 2001, 3, 1249. (37) Minkin, V. I.; Minyaev, R. M.; Starikov, A. G.; Gribanova, T. N. Russ. J. Org. Chem. 2005, 41, 1289. (38) Yang, L. M.; Ding, L. H.; Sun, C. C. J. Am. Chem. Soc. 2007, 129, 658. (39) Geske, G. D.; Boldyrev, A. I. Inorg. Chem. 2002, 41, 2795. (40) Li, S. D.; Ren, G, M.; Miao, C. Q. J. Phys. Chem. A 2005, 109, 259. (41) Minyaev, R. M.; Gribanova, T. N.; Minkin, V. I.; Starikov, A. G.; Hoffmann, R. J. Org. Chem. 2005, 70, 6693. (42) Becke, A. D. J. Chem. Phys. 1992, 96. 2155. (43) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (44) Frisch, M. J.; People, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (45) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. (46) Frisch, M. J.; Trucks, G. A.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheseman, J. R.; Montgomery, J. A., Jr.; Vreeven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennuci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochtersky, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, L.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004.