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A Comparative Study of Aromaticity in Substituted Tetracyclic and Hexacyclic Thiophenes S. Thomas and Y. A. Pati* Solid state and Structural Chemistry Unit, Indian Institute of Science, Bangalore, India -560 012 ReceiVed: March 7, 2010; ReVised Manuscript ReceiVed: April 7, 2010
We have studied the nature of aromaticity in expanded porphyrinic analogues of thiophenes formed by four and six thiophenes. Using density functional theory (DFT) we have analyzed the aromaticity of both the macrocycle and individual molecular fragments. We find paramagnetic annulenic ring currents in the case of tetracyclic molecules and diamagnetic annulenic ring currents for hexacyclic molecules. We have also studied the effect of substitution of benzene rings within the macrocycle. We find that as the number of benzene rings is increased the aromaticity increases for tetracyclic systems and decreases for hexacyclic systems. All the results have been analyzed with various microscopic parameters, including geometry, excitation gap, and NMR criteria. Introduction Aromaticity, even though an old concept, is still an interesting area of research.1-5 The concept, which was originally introduced for organic molecules, has been extended to inorganic molecules,6-9 metallic clusters,10-15 and three-dimensional systems.6,11 Now aromaticity is described not only by contributions from π- electrons, but also from σ-electrons and d-orbital electrons. Involvement of s, p, and d atomic orbitals lead to σ, π, and δ aromaticity/antiaromaticity in molecules.16 This concept has been used to predict the structure and stability of a large classes of systems. Generally, conjugated organic molecules are either π-aromatic or antiaromatic, whereas main group compounds can show σ- and π-aromaticity (antiaromaticity). In the case of transition metal clusters, due to the presence of d-orbital electrons, there is the possibility of δ-aromaticity/antiaromaticity.16 Besides, systems can show multiple aromaticity/ antiaromaticity wherein they show σ, π, and δ aromaticity simultaneously or conflicting aromaticity in which one of these is aromatic and the other is antiaromatic.17,18 Interestingly, aromaticity is not a directly measurable quantity. Several criteria, such as structural index,19 magnetic based index, and, the most recent one, the electronic based index, are used to classify the molecule as aromatic/antiaromatic. Among structure-based methods, Bird’s indices and the harmonic oscillator model of aromaticity (HOMA) indices are widely used.20,21 This is based on the bond length/order alternation, and the advantage of this method is that it can be used even for crystalline structures. The energy-based indices use different types of energies such as resonance energy, stabilization energy, σ-π separation energy, and so forth.19-22 The most widely used magnetic-based method is nucleus independent chemical shift (NICS) values.23 In this method, magnetic shieldings can be computed at any spatial point in the three-dimensional space. The sign and magnitude of the shielding indicates the aromaticity/antiaromaticity of the molecule. The other methods in this class include aromatic ring current shielding (ARCS),24 NICS scan,25 and the ring current model.26 Furthermore, electron localization functions have also been used as an estimation of aromaticity.27,28 Recently, based on the atoms in molecule (AIM) * To whom correspondence should be addressed. E-mail: anusooya@ sscu.iisc.ernet.in.
theory of Bader et al.,29 the electron delocalization index, which gives the measure of number of electrons shared between two atoms, has been used to quantify aromaticity.30 σ-π separation analysis has also been used to study the aromaticity of metal clusters.22,31,32 Porphyrins and their analogues have been studied extensively for their optical as well as magnetic properties. Local and global aromaticity of porphyrins have been studied by Cyranski et al. using both geometry criteria (HOMA indices) and magnetic criteria.33 The effect of deconjugation on aromaticity of porphyrin molecules is studied by Juselius and Sundholm using the ARCS method.34 Stepien and Latos have synthesized an expanded porphyrin, a Mo¨bius system, A,D-di-p-benzi[28]hexaphyrin(1.1.1.1.1.1).35 They found that, the system changes from a Mo¨bius aromatic to a Hu¨ckel antiaromatic system as the temperature is varied. Pyrrole inversion in sapphyrin, an expanded porphyrin with five pyrrole units, has been studied using the NICS method.36 They have also studied the effect of substitution of N by S, O, and Se atoms. Cuesta et al. have studied aromaticity in linear oligo-thiophenes and oligothienoacenes by analyzing current density maps and magnetic susceptibility.37 Porphyrin analogues of four- and sixmembered cyclic thiophenes containing benzenes have been synthesized, and the aromaticity of these molecules is studied using 1H NMR spectra.38,39 In this article, we report the theoretical study of the nature of aromaticity in tetra- and hexacyclic thiophenes. We have used geometry based methods and NMR shielding tensors to study these systems. The effect of replacing the thiophene units by benzene on aromaticity is also analyzed. We have interpreted the aromaticity/antiaromaticity of these molecules in terms of energy criteria, bond length alternation, 1H NMR shielding and NICS and NICS scan methods. In the next section, computational details are given, followed by results and discussion, and finally we conclude the paper with a summary of all our results. Computational Details We optimized the geometries of molecules shown in Figure 1 using the Amsterdam density functional (ADF) package.40 For calculating the NICSs, we used the gauge including atomic orbital (GIAO) formalism as developed in the ADF package.41 Ghost atoms are placed at the center of the macromolecule as
10.1021/jp102065g 2010 American Chemical Society Published on Web 04/19/2010
Aromaticity in Tetracyclic and Hexacyclic Thiophenes
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Figure 1. Optimized structures of cyclic thiophenes and benzene-substituted cyclic thiophenes: (a) tetracyclic thiophene (TCTh) (b) singly substituted TCTh (TCTh1B) (c) doubly substituted TCTh (TCTh2B) (d) hexacyclic thiophene (HCTh) and (e) doubly substituted HCTh (HCTh2B).
well as at centers of individual rings for calculating NICS. We also obtained NICSs at different distances, NICS(x), up to 4 Å above the plane of the molecule. The in-plane and out-of plane contributions to paramagnetic and diamagnetic shieldings are obtained by eigenvalues of the magnetic shielding tensor matrix. To verify our results, we performed calculations at different levels of theory using different basis sets. We used the double-ζ (DZ) basis set, without and with polarization (DZP) functions using both BLYP and PW91 exchange functionals.42,43 Since we did not observe any major differences in the magnitude of shielding constants between different methods, we report all our results based on BLYP functionals with the DZ basis set, unless stated otherwise. We also compared our results obtained from ADF, with those obtained from the Gaussian ’03 suite of programs at similar level of basis set and exchange functionals.44
We find that the isotropic shielding constants differ by a maximum of 3 ppm. Results and Discussion Optimized geometries of all the systems are shown in Figure 1. For clarity, we have shown only unique bondlengths of carbon-carbon and carbon-sulfur bonds. The CH bond is almost the same in all molecules (1.1 and 1.0 Å). Only H atoms have been labeled, because we are interested only in 1H NMR shielding constants. Upon geometry optimization, we find that all molecules adopt nearly planar structure. We refer to tetracyclic thiophenes as TCTh and hexacyclic thiophenes as HCTh in all subsequent discussions. The substituted analogue
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of these molecules are represented by TCThnB and HCThnB, where n represents the number of benzene units in the macrocycle. TCTh, as shown in Figure 1a, is a 4n π (28 electrons: 6 from each thiophene unit and 4 from meso-carbons) system with C2h symmetry and has two different thiophenic units. In one of the thiophenes, the Cβ-Cβ bond is shorter than the Cβ-CR bond, and it is vice versa in the other ring (R and β positions are shown in Figure 1a), although the magnitude of this difference is small (∼0.08 and ∼0.02 Å, respectively). C-S bonds in the two units are almost similar (1.75 and 1.77 Å), and the value is similar to that in an isolated thiophene ring (1.74 Å). Interestingly, the two diagonally opposite thiophene units retain the isolated thiophene structures. (See Figure SI1 in the Supporting Information.) Bond lengths nearly alternate at the periphery of the macrocycle, indicating antiaromatic nature of the molecule. From our calculations, we find that, upon replacement of the thiophene unit by a benzene unit, the geometry of the thiophenes remains almost the same, except for C-S bonds (see Figure 1b,c). The peripheral benzene C-C bonds are longer compared to the interior C-C bonds. Interestingly, however, the mesobonds become longer and retain the bond alternation characteristics. Bond lengths are alternating along the periphery of the macrocycle except at benzene units. This structure is similar to one of the resonant structures reported earlier.38 We have given in the Supporting Information possible resonance structures for this molecule based upon our calculations. (see Figure SI2). HCTh, as shown in Figure 1d, is a (4n + 2) π-system (42 π-electrons) with all six thiophenes having almost the same bond length. Compared to the isolated thiophene, the Cβ-Cβ bond is shorter (1.39/1.38 Å), and the Cβ-CR bond is longer (1.42 Å). However, all meso-bonds have same bond length of 1.40 Å. Thus, the HCTh molecule has almost equal bondlengths (1.40 ( 0.02 Å) along the periphery, making it a good candidate as an aromatic molecule. As we replace two thiophenes by benzene rings (HCTh2B, Figure 1e), there occurs a slight rearrangement of bond lengths in the remaining thiophene rings. Interestingly, the doubly and triply replaced HCTh molecules become C4 and C3 symmetric, respectively, and the replaced benzenes have almost quinonoid structures with alternating bond lengths (1.38 Å and 1.44 Å) (see Supporting Information Figure SI3). Note that our optimized structure is planar, and the effect of substitution of benzene is local, i.e., only bondlengths of the nearest meso-bonds connected to benzene are changed by 0.02 Å, and the rest of the geometry remains almost the same. Mesobonds have a very small bond alternation and the magnitude of bond alternation increases with proximity to the benzene ring (see Supporting Information, Figure SI3). Along the macrocyclic periphery, there is a small bond length alternation. Interestingly, it was found that, at high temperature (T ) 178K), one of the benzene rings shows benzenoid structure, while the other one remains quinonoid.38 This could possibly be due to the crystal packing effect. The HOMA index has been used previously as a good measure of aromaticity.21 We calculated the HOMA index using the equation
HOMA ) 1 -
R n
∑ (Ropt - Rk)2
(1)
k
where R is an empirical constant and Ropt is the optimal bond length. n is total number of bonds taken into summation. We
TABLE 1: HOMA Values for Tetracyclic and Hexacyclic Systemsa HOMA molecule benzene thiophene TCTh4 TCTh1B TCTh2B HCTh HCTh1B HCTh2B HCTh3B
macromolecule
thiophene I
0.375(0.297) -0.049(-0.165) -0.429(-0.450) 0.592(0.439) 0.592(0.483) 0.613(0.551) 0.570(0.538)
0.712 0.702 0.023 -0.145 0.444 0.417 0.454 0.321
thiophene II
benzene 0.960
0.143 0.494
0.269 0.307
0.446 0.468
0.671 0.619 0.723
a Thiophene I is nearest to benzene, followed by thiophene II in substituted systems. Numbers in the bracket indicate HOMA for the internal cross, without considering the outer vinyl bridge, for thiophene and benzene molecules.
TABLE 2: HOMO-LUMO Gap (∆) for Tetra- and Hexacyclic Molecules molecule
∆ in eV
molecule
∆ in eV
TCTh TCTh1B TCTh2B
0.48 0.71 0.97
HCTh HCTh1B HCTh2B HCTh3B
1.30 1.16 1.01 1.43
used the TZP basis set for geometry optimization. We used the R and Ropt values reported earlier21 and obtained the HOMA index, which is given in Table 1. In Table 1 we also give the HOMA values for isolated benzene and thiophene, which are 0.960 and 0.712 respectively. The value of HOMA for cyclic butadiene, which is an antiaromatic system, -3.936. In tetracyclic series, there are two types of thiophenes with HOMA ) 0.702 and 0.143, resembling two pyrroles in porphyrin.33 In contrast with the TCTh molecule, the HCTh molecule has all similar thiophenes (HOMA is 0.444 and 0.446). HOMA indices also indicate a lesser degree of aromaticity for individual thiophene as well as benzene rings in hexacyclic systems. We have also given the HOMA for the internal cross, i.e., without the exocyclic bridge, for the macrocycle. The HOMA of the internal cross is less than that of the actual macromolecule in all cases. This indicates that the internal cross is less aromatic in contrast with the porphyrin molecule.19 In the case of hexacyclic series, contribution of exocyclic bridges to aromaticity decreases with the substitution of benzene. To understand the stability associated with these molecules, we have calculated the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, ∆, for all these systems. The TCTh molecule has the smallest gap, ∆ ) 0.48 eV (see Table 2). In accordance with the analysis of the HOMO-LUMO gap by earlier studies, TCTh is thus likely to be antiaromatic.45,46 According to the maximum hardness principle, the greater the hardness, η, the more stabilized is the molecule.47,48 Absolute hardness, η, is half of the HOMO-LUMO gap.49 As we replace thiophene rings by benzene rings, the absolute hardness increases, indicating the onset of aromaticity. The opposite trend is observed, i.e., absolute hardness decreases in the case of the hexacyclic molecule except for triply substituted benzenes. The value of HOMO-LUMO gaps for hexacyclic molecules are similar in magnitude to those found in the case of fused heaxcyclic porphyrin systems (1.74 eV).50 Note, however, that the magnitude of aromaticity in these molecules is small, when compared with the ∆ of benzene (5.2 eV) and thiophene (4.5 eV). Moreover, we find that the total bonding energy, which is the algebraic sum of electrostatic,
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Figure 2. Proton chemical shift of tetra- and hexacyclic thiophenes and their substituted analogues: (a) TCTh, (b) TCTh1B, (c) TCTh2B, (d) HCTh, and (e) HCTh2B.
Coulomb, exchange and kinetic energy,40 stabilizes while going from TCTh to TCTh2B (from -207.78 to -244.10 eV) and from HCTh to HCTh3B (from -315.99 to -378.97 eV, respectively). Since 1H NMR chemical shift is the measure of aromaticity, we computed the 1H NMR shielding tensor for all the systems studied. For direct comparison of the 1H shielding values, we calculated the same for H atoms of tetramethyl silane (TMS) at the same level of theory. For TMS protons, NMR shielding appears at 32.8 ppm. TCTh being a 4n π-electron system, shows paramagnetic shielding. The 1H shieldings are 35.1 and 34.9 ppm for protons of two different thiophene rings (see Figure 2a). Both of these are upfield shifted with respect to the TMS value and are thus indicators of antiaromaticity. In contrast, 1H NMR shielding of an isolated thiophene is 25.6 and 26.0 ppm for the two types of protons and is thus likely to be aromatic. This clearly indicates that the macrocyclic ringcurrent dominates in thiophene (microcycle) when it is part of TCTh molecule and is paratropic in nature. As we replace thiophene units by
benzene units, the magnitude of shielding reduces from ∼35 ppm to ∼28 ppm for the thiophene protons (Figure 2a,c). The interesting point to note is that the inner protons of benzene are downfield shifted with respect to the outer protons of benzene (1.3 and 30.1 ppm for TCTh1B and 11.11 and 27.89 ppm for TCTH2B), indicating the annulenic ring current in the molecule. This, in fact, indicates a paratropic ring current since the inner protons are downfield shifted with respect to outer protons,51 and this result is similar to the earlier experimental results on porphyrinic system tetraphenyl-p-benziporphyrin (TPB).52 TPB is aromatic and shows up- and downfield shift for the inner and outer protons, respectively. The overall nature of shielding for protons is σH(benzene) < σH(thiophene). In the case of hexacyclic systems, the 1H shielding values are ∼19 ( 2 ppm, which is less than that of TMS values, indicating that the molecules are aromatic. When thiophene units are replaced by benzene units, we observe downfield shift for outer protons and upfield shift for inner protons. This implies a diamagnetic annulenic ring current in the hexacyclic molecules.
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Thomas and Pati TABLE 3: ZZ-Component of NICS at the Center of Individual Rings and at the Center of the Macromoleculea molecule
thiophene
TCTh TCTh1B TCTh2B HCTh HCTh1B HCTh2B HCTh3B
107.39 68.74 48.65 -38.04 -32.12 -36.44 -15.04
benzene 16.18 8.44 -14.87 -5.48 -5.48
center
NICSiso
χzz
χaniso
143.28 81.29 51.23 -35.39 -31.24 -33.66 -16.39
43.45 23.06 13.89 -12.84 -11.48 -12.45 -6.59
1248.66 560.16 338.24 -2637.86 -2251.53 -2535.41 -1358.20
1354.68 663.42 437.30 -2496.82 -2107.06 -2392.16 -1213.17
a σiso is the isotropic sheilding tensor at the center of the macromolecule. χzz is ZZ-component of magnetic susceptibility and χaniso ) χzz -(1/2){χxx + χyy} is the anisotropic susceptibility.
Figure 3. NICS scan at the center of the macromolecule as well as at the center of individual rings: (a) TCTh, (b) HCTh, (c) TCTh1B, (d) TCTH2B, (e) HCTh1B, and (f) HCTH2B. Note that NICS at distance ) 0 represents the value at the plane of the molecule.
In the case of HCTh2B, the inner proton shielding of benzene is 42.1 ppm, while that of the outer protons is 20.4 ppm, clearly indicating the annulenic nature of the macrocycle. However, high-temperature (178 K) experimental findings reveal a singlet peak for benzene protons in the case of HCTh2B.38 We believe that it could be due to the fact that, at higher temperature, the benzene molecule can rotate and thereby one finds an average quantity. However, a similar system studied at a lower temperature shows annulenic nature.52 We have further analyzed the nature of aromaticity in these molecules through NICS and NICS spatial scan. TCTh has a positive NICS at the center of the molecule as well as at the centers of individual thiophene rings, indicating a paramagnetic ring current (see Figure 3a). NICS at the center of the molecule (∼43 ppm) is nearly twice that at the center of the thiophenic unit (∼22 ppm). NICS scan also confirms the paramagnetic shielding both at the center of the molecule and at individual rings (see Figure 3a).25 In the case of substituted molecules, at benzene ring centers, NICS scan shows diamagnetic ring current, which is indicated by negative shielding values as well as a minimum at 0.8 Å in both TCTh1B and TCTh2B molecules (see Figure 3c,d). The magnitude of the NICS at the minimum is larger for TCTh2B compared to TCTh1B (-6.2 ppm against -4.5 ppm), again indicating the reduced degree of antiaromaticity in the case of TCTh2B molecules. In the isolated benzene molecule, the NICS scan shows a minimum at 0.8 Å but with
a larger peak height. As the distance is increased, the benzene unit shows slight paramagnetic shielding and is nearly equal to that of thiophene. This trend has also been observed in earlier studies.25 The thiophene molecule shows paramagnetic ring current in both of the substituted molecules with the magnitude decreasing from the unsubstituted molecule to the substituted molecules (∼20 to 10 to 5 ppm). The hexacyclic ring shows diamagnetic ring current as indicated by the negative NICS at the center and also at all individual thiophenes (Figure 3b). The NICS at the center of the molecule is half of that of the individual ring (-12.8 and -24.4 ppm). The NICS scan shows that the individual thiophenic units are indeed aromatic with a minimum at 0.4 Å (-25.2 ppm). The NICS scan at the center of the molecule remains negative at all distances without passing through a minimum. HCTh1B has negative shielding at the center of the molecule, and the NICS scan remains negative and does not show any minimum (Figure 3e). The NICS scan is similar to that of HCTh molecule both in magnitude and in shape. The thiophenic unit is more aromatic than the benzenic unit. The benzenic unit has a minimum at 1 Å and the thiophenic unit has a minimum at 0.5 Å. An earlier calculation of the NICS scan suggests a minimum at the same distance.25 For HCTh2B, the NICS scan is similar to that of HCTh molecule. The NICSs at the center of benzene and thiophene are also negative, indicating the aromatic nature of rings (Figure 3f). Thus, the NICS scan value further confirms the diamagnetic shieldings at both the individual rings and macrocycle and hence the aromatic nature of rings. In the case of the HCTh3B molecule, aromaticity at the center of the macrocycle as well as at the center of thiophene ring reduces drastically, while that of the benzene ring remains same. To further verify our observation of the aromaticity/antiaromaticity of these molecules, we calculated the magnetic susceptibility. We have taken the optimized geometry from ADF and using the 6-31+G* basis and B3LYP functional in the Gaussian suite of programs,44 we obtained the magnetic susceptibility. We report values obtained from continuous set of gauge transformation (CSGT) method.53 In Table 3, we give values of the ZZ-component of NICS at different centers of molecules, isotropic NICS at the center of the molecule, and the ZZ-component of magnetic susceptibility and anisotropic susceptibility. All values of NICS and χ are positive for the tetracyclic series and negative for the hexacyclic series of molecules. The magnitude of reduction in values of both NICSzz and NICSiso are in the same proportion upon substitution by benzene (also see Figure SI4). This implies that it is the outof-plane component that is mainly responsible for the aromaticity/antiaromaticity of molecules, confirming the earlier report.3 As can be seen from the table, in the case of tetracyclic systems, paramagnetic susceptibility decreases upon insertion of a benzene molecule, and diamagnetic susceptibility decreases in
Aromaticity in Tetracyclic and Hexacyclic Thiophenes the hexacyclic series except for HCTh2B. Even the HOMA values show a similar trend for the hexacyclic series (see Table 1). In the case of triply substituted benzene molecules, both χzz and NICSzz values decrease by nearly half of that of the HCTh molecule. Conclusion In summary, we have studied tetra- and hexacyclic thiophene molecules and also their substituted analogues. The aromaticity and antiaromaticity have been probed by three different quantities, namely geometry, NMR shielding tensors, and NICS scan. Bond-length alternation indicates that all the tetracyclic molecules have paramagnetic ring current, while the hexacyclic molecules have diamagnetic ring current. The HOMO-LUMO gaps and stabilization energies of these molecules also reveal the same trend. Up-field NMR 1H shielding with respect to the TMS value for TCTh supports this conclusion. In the case of the singly substituted TCTh1B molecule, the inner protons of benzene shift downfield, while the outer protons shift upfield, which is characteristic of paramagnetic annulenic shielding. This is in contrast to the shielding trend found for HCTh2B, which is an aromatic molecule and hence shows diamagnetic annulenic shielding. HCTh being a 4n+2 π-electron system, shows downfield shift. These trends are further confirmed by magnetic susceptibility data. Acknowledgment. We thank Prof. S. Ramasesha and Prof. S.K. Pati for fruitful discussions. Supporting Information Available: Optimized geometries of thiophene, benzene, possible resonance structures of TCTh1B, bondlengths and NMR shielding values for HCTh1B and HCTh2B, and ZZ-components of NICS for all the molecules. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) (a) Kekule, A. Bull. Soc. Chim. 1865, 3, 98. (b) Pauling, L. J. Chem. Phys. 1936, 4, 673. (c) London, F. J. Phys. Radium 1937, 8, 397. (2) Cyranski, M.; Krygowski, T. M.; Katrizky, A. R.; Schleyer, P. von. R. J. Org. Chem. 2002, 67, 1333. (3) Lazzeretti, P. Phys. Chem. Chem. Phys. 2004, 6, 217. (4) Stanger, A. Chem. Commun. 2009, 1939. (5) Minkin, V. I.; Glukhovtsev, M. N.; Simkin, B. Y. Aromaticity and Antiaromaticity: Electronic and Structural Aspects; J. Wiley and Sons: New York, 1994. (6) (a) King, R. B. Chem. ReV. 2001, 101, 1119. (b) Chen, Z.; King, R. B. Chem. ReV. 2005, 105, 3613. (7) Katritzky, A. R.; Jug, K.; Oniciu, D. C. Chem. ReV. , 101, 1421. (8) Minkin, V. I.; Minyaev, R. M. Chem. ReV. 2001, 101, 1247. (9) Chattaraj, P. K.; Roy, D. R. J. Phys. Chem. A 2007, 111, 4684. (10) Li, X.-W.; Pennington, W. T.; Robinson, G. H. J. Am. Chem. Soc. 1995, 117, 7578. (11) Lu, X.; Chen, Z. Chem. ReV. 2005, 105, 3643. (12) Fowler, P. W.; Havenith, R. W. A.; Steiner, E. Chem. Phys. Lett. 2002, 359, 530. (13) Tsipis, C. A. Coord. Chem. ReV. 2005, 249, 2740. (14) Boldyrev, A. I.; Wang, L.-S. Chem. ReV. 2005, 105, 3716. (15) (a) Datta, A.; Pati, S. K. Chem. Commun. 2005, 5032. (b) Datta, A.; Pati, S. K. J. Am. Chem. Soc. 2005, 127, 3496. (c) Mallajosyula, S. S.; Datta, A.; Pati, S. K. J. Phys. Chem. B 2006, 110, 20098. (16) (a) Zhai, H.-J.; Averkiev, B. A.; Zubarev, D. Y.; Wang, L.-S.; Boldyrev, A. I. Angew. Chem., Int. Ed. 2007, 46, 4277. (b) Averkiev, B. A.; Boldyrev, A. I. J. Phys. Chem. A 2007, 111, 12864. (c) Zubarev, D. Y.; Averkiev, B. B.; Zhai, H.-J.; Wang, L.-S.; Boldyrev, A. I. Phys. Chem. Chem. Phys. 2008, 10, 257. (17) Monaco, G.; Scott, L. T.; Zanasi, R. J. Phys. Chem. A 2008, 112, 8136. (18) Buhl, M.; Hirsch, A. Chem. ReV. 2001, 101, 1153, and references therein. (19) Krygowski, R. M.; Cyranksi, M. K. Chem. ReV. 2001, 101, 1385.
J. Phys. Chem. A, Vol. 114, No. 18, 2010 5945 (20) (a) Bird, C. W. Tetrahedron 1985, 41, 1414. (b) Bird, C. W. Tetrahedron 1993, 49, 8441, and references therein. (21) (a) Kruszewski, J.; Krygowski, T. M. Tetrahedron Lett. 1972, 3839. (b) Krygowski, T. M. J. Chem. Inf. Comput. Sci. 1993, 33, 70. (22) Jug, K.; Hiberty, P. C.; Shaik, S. Chem. ReV. 2001, 101, 1477, and references therein. (23) (a) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; Hommes, N. J. R. v. E. J. Am. Chem. Soc. 1996, 118, 6317. (b) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Chem. ReV. 2005, 105, 3842. (c) Chen, Z.; Corminboeuf, C.; Heine, T.; Bohmann, J.; Schleyer, P. v. R. J. Am. Chem. Soc. 2003, 125, 13930. (24) Juselius, J.; Sundholm, D. Phys. Chem. Chem. Phys. 1999, 1, 3429. (25) (a) Stanger, A. J. Org. Chem. 2006, 71, 883. (b) Stanger, A. Chem.sEur. J. 2006, 12, 2745. (26) Faglioni, F.; Ligabue, A.; Pelloni, S.; Soncini, A.; Viglione, R. G.; Ferraro, M. B.; Zanasi, R.; Lazzeretti, P. Org. Lett. 2005, 7, 3457. (27) Poater, J.; Duran, M.; Sola, M.; Silvi, B. Chem. ReV. 2005, 105, 3911, and references therein. (28) Santos, J. C.; Andres, J.; Aizman, A.; Fuentealba, P. J. Chem. Theory Comput. 2005, 1, 83. (29) (a) Bader, R. W. F. Atoms in Molecules: A Quantam Theory; International Series of Monographs on Chemistry; Oxford Science publication, U.K., 1990. (b) Nasertayoob, P.; Shahbazian, Sh. Int. J. Quantum Chem. 2008, 108, 1477. (c) Nasertayoob, P.; Shahbazian, Sh. Int. J. Quantum Chem. 2009, 109, 726. (d) Nasertayoob, P.; Shahbazian, Sh. Int. J. Quantum Chem. 2010, 110, 1188. (30) (a) Bader, R. F. W.; Streitwieser, A.; Neuhaus, A.; Laidig, K. E.; Speers, P. J. Am. Chem. Soc. 1996, 118, 4959. (b) Poater, J.; Fradera, X.; Duran, M.; Sola, M. Chem.sEur. J. 2003, 9, 400. (c) Bultinck, P.; Rafat, M.; Ponec, R.; Ghelum, B. V.; Carbo-Dorca, R.; Popelier, P. J. Phys. Chem. A 2006, 110, 7642. (31) (a) Datta, A.; Pati, S. K. J. Chem. Theory Comput. 2005, 1, 824. (b) Rehaman, A.; Datta, A.; Mallajosyula, S. S.; Pati, S. K. J. Chem. Theory Comput. 2006, 2, 30. (32) Datta, A.; Mallajosyula, S. S.; Pati, S. K. Acc. Chem. Res. 2007, 40, 213. (33) Cyranski, M. K.; Krygowski, T. M.; Wisiorowski, M.; Hommes, N. J. R. v. E.; Schleyer, P. v. R. Angew. Chem., Int. Ed. 1998, 37, 177. (34) Juselius, J.; Sundholm, D. Phys. Chem. Chem. Phys. 2000, 2, 2145. (35) (a) Stepien, M.; Latos-Grazynski, L.; Sprutta, N.; Chwalisz, P.; Szterenberg, L. Angew. Chem., Int. Ed. 2006, 46, 7869. (b) Stepien, M.; Latos-Grazynski, L. Chem.sEur. J. 2001, 7, 5113. (36) Cardenas-Jiron, G. I.; Venegas, C.; Lopez, R.; Menendez, M. I. J. Phys. Chem. A 2008, 112, 8100. (37) Cuesta, I. G.; Arago, J.; Orti, E.; Lazzeretti, P. J. Chem. Theory Comput. 2009, 5, 1767. (38) Reddy, J. S.; Anand, V. G. Chem. Commun. 2008, 1326. (39) Reddy, J. S.; Anand, V. G. J. Am. Chem. Soc. 2009, 131, 15433. (40) (a) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca, G., C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931. (b) Baerends, E. J.; Autschbach, J. A.; Ba˜l’rces, A.; Bo, C.; Boerrigter, P. M.; Cavallo, L.; Chong, D. P.; Deng, L.; Dickson, R. M.; Ellis, D. E.; Fan, L.; Fischer, T. H.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Groeneveld, J. A.; Gritsenko, O. V.; Gra˜ijning, M.; Harris, F. E.; van den Hoek, P.; Jacobsen, H.; van Kessel, G.; Kootstra, F.; van Lenthe, E.; Osinga, V. P.; Patchkovskii, S.; Philipsen, P. H. T.; Post, D.; Pye, C. C.; Ravenek, W.; Ros, P.; Schipper, P. R. T.; Schreckenbach, G.; Snijders, J. G.; Sola, M.; Swart, M.; Swerhone, D.; Te Velde, G.; Vernooijs, P.; Versluis, L.; Visser, O.; van Wezenbeek, E.; Wiesenekker, G.; Wolff, S. K.; Woo, T. K.; Ziegler, T. ADF, version 2002.0; SCM: Amsterdam, 2002. (41) (a) Schreckenbach, G.; Ziegler, T. J. Phys. Chem. 1995, 99, 606. (b) Schreckenbach, G.; Ziegler, T. Int. J. Quantum Chem. 1997, 61, 899. (c) Wolff, S. K.; Ziegler, T. J. Chem. Phys. 1998, 109, 895. (d) Schreckenbach, G.; Ziegler, T. J. Am. Chem. Soc. 2001, 123, 3341. (42) (a) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (43) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Sing, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (44) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, 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.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, 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, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,
5946
J. Phys. Chem. A, Vol. 114, No. 18, 2010
B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision B.03; Gaussian, Inc.: Pittsburgh, PA, 2003. (45) Krygowski, T. M.; Cyranski, M. K.; Czarnocki, Z.; Ha¨felinger, G.; Katritzky, A. R. Tetrahedron 2000, 56, 1783. (46) Aihara, J. Phys. Chem. Chem. Phys. 1999, 1, 3193. (47) (a) Parr, R. G.; Chattaraj, P. K. J. Am. Chem. Soc. 1991, 113, 1854. (b) Chattaraj, P. K.; Roy, D. R.; Elango, M.; Subramanian, V. J. Phys. Chem. A 2005, 109, 9590. (48) De Proft, F.; Geerlings, P. Chem. ReV. 2001, 101, 1451. (49) Zhou, Z.; Parr, R. G. J. Am. Chem. Soc. 1989, 111, 7371.
Thomas and Pati (50) Tokuji, S.; Shin, J.-Y.; Kim, K. S.; Lim, J. M.; Youfu, K.; Saito, S.; Kim, D.; Osuka, A. J. Am. Chem. Soc. 2009, 131, 7240. (51) Pople, J. A.; Untch, K. G. J. Am. Chem. Soc. 1966, 88, 4811. (52) Stepien, M.; Latos-Grazynski, L. J. Am. Chem. Soc. 2002, 124, 3838. (53) (a) Keith, T. A.; Bader, R. F. W. Chem. Phys. Lett. 1992, 194, 1. (b) Keith, T. A.; Bader, R. F. W. Chem. Phys. Lett. 1993, 210, 223.
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