J. Phys. Chem. B 2008, 112, 1765-1769
1765
Attractive Strain: The Disadvantages of Rigid Multiple H-Bond Donors and Acceptors. A Theoretical Analysis of the Hydrogen-Bonding Interactions in Complexes of Tetraazaanthracenedione with Pyridylureas Antonio Oliva,† Juan Bertran,† and J. J. Dannenberg*,‡,§ Departament de Quı´mica, Unitat de Quı´mica Fı´sica, UniVersitat Auto` noma de Barcelona, 08193 Bellaterra, Barcelona, Spain; Department of Chemistry, City UniVersity of New YorksHunter College and the Graduate School, 695 Park AVenue, New York, New York 10065; and Institute of Computational Chemistry and Department of Chemistry, UniVersity of Girona, 17071 Girona, Catalonia, Spain ReceiVed: September 21, 2007; In Final Form: NoVember 5, 2007
We report density functional theory calculations at the B3LYP/D95(d,p) level on the hydrogen-bonding complexes of tetraazaanthracenedione, 1, with N-(pyridin-2-yl)urea, 2H, or N-(6-aminopyridin-2-yl)urea, 2N. The interaction energy of the 1-2H complex exceeds that of 1-2N, despite the fact that 1-2N contains a strong N-H‚‚‚O interaction in place of a weak C-H‚‚‚O interaction in 1-2H. We show that the 1-2N interaction is weaker than the sum of the four normal individual H-bonding interactions because the steric constraints of the complex prevent the H-bonding donors and acceptors from optimally approaching each other to form the two central H-bonds. This steric phenomenon, which we call attractiVe strain, is likely present to some extent in most H-bonding systems that contain more than two H-bonds between rigid monomers. Attractive strain is unusually important in 1-2N. Attractive strain can be conceived of as an enthalpic cost for the entropic benefits of freezing the dihedral angles of the multiple H-bond donors and acceptors by designing rigid systems.
Both nature and man have used multiple H-bonds extensively in the formation of natural and synthetic self-assembling materials. As such materials are much too numerous to cite completely, we provide a few representative examples. Natural materials include DNA (base pairs), proteins (β-sheets and turns), and silk. Synthetic materials include complexes of cyanuric acid derivatives with melamine,1 various derivatized porphyrins,2 and tubules assembled from species such as HOOCCH2NHCOCH2NHCO(CH2)NCONHCH2CONHCH2COOH.3 Interactions with fixed complementary H-bonding sites (donors or acceptors) have an entropic advantage over those with conformational flexibility as fewer vibrations are frozen in the process of association (the rigidity of the monomers freezes these vibrations prior to the H-bonding interaction). However, the rigidity of the multiple H-bonding sites can become a steric, and thus enthalpic, obstacle when the molecules are too inflexible to allow for simultaneous optimal H-bonding interactions at each individual H-bonding site. For example, the cooperatiVe interactions in the guanine-cytosine (GC) base pair are not substantially greater than those in the adenine-thymine (AT) pair, despite the additional H-bond in GC, due to the inability of all three H-bonds in GC to achieve optimal local geometries at the same time.4 Optimizing the interaction of one of the exterior N-H‚‚‚O H-bonds causes the other to become less stable as the GC base pair tilts about the central N-H‚‚‚N interaction. An extreme example of this phenomenon has been recently described by Zimmerman5 based upon systems originally studied by Luining.6 Tetraazaanthracene, 1, forms a more stable complex * Corresponding author. E-mail:
[email protected]. † Universitat Autonoma de Barcelona. ‡ City University of New York. § University of Girona.
with an H-bonding partner, N-butyl-N′-(pyridin-2-yl)urea, which contains only three intermolecular H-bonds, than with a similar complementary pyridylurea containing an additional -NH2 partner that forms a fourth intermolecular N-H‚‚‚O H-bond. In this paper, we report molecular orbital calculations designed to probe the individual H-bonds and the interactions between them in complexes of tetraazaanthracene with two pyridylureas that contain the same H-bonding interactions as those described by Zimmerman. We simplified the molecules used in the experimental studies by removing the substituent groups not directly involved in the H-bonds or the major structural components. Thus, we considered underivatized tetraazaanthracene interacting with N-(pyridin-2-yl)urea, 2H, or N-(6-aminopyridin-2-yl)urea, 2N (see Figures 1 and 2). We use techniques similar to those previously applied to the AT and GC base pairs.4 To probe the energies of each H-bond individually, we calculated the interaction energies of each complex with the entities rotated so that the planes of the molecules are perpendicular to each other. In these structures all dihedrals and the two angles pertaining to the H-bond in question are fixed at their equilibrium values in the fully optimized system (see Figure 3 for a typical structure). To properly convert calculated H-bonding energies into enthalpies, corrections must be made for the basis set superposition error (BSSE) {Van Duijneveldt, 1997 #1801} and for vibrational levels and the proper Boltzmann distribution over them. One most usually corrects for BSSE using the counterpoise (CP) correction,8,9 typically as a single-point correction on the preoptimized geometry. However, CP modifies the potential energy surface (PES) which lowers the CP correction, generally lengthens H-bonds, and red-shifts the stretches associated with breaking the H-bonds. A general procedure for optimizing the geometry on the CP-corrected PES allows for properly accounting for BSSE with respect to energies, geom-
10.1021/jp077622s CCC: $40.75 © 2008 American Chemical Society Published on Web 01/23/2008
1766 J. Phys. Chem. B, Vol. 112, No. 6, 2008
Oliva et al. TABLE 1: Relative Energies and Enthalpies (kcal/mol) of the Monomers and Interaction Energies and Enthalpies for the Complexes 2H 2Ha 2N 2Na 1-2H 1-2N
Figure 1. Relevant structures for the formation of the 1-2H complex.
∆E
∆H
∆Ecp
∆Hcp
3.74 0.00 4.15 0.00 -17.80 -15.84
3.05 0.00 3.46 0.00 -16.91 -14.80
-14.69 -12.64
-13.78 -11.58
vibrational frequencies calculated on the CP-optimized PES10 using the harmonic approximation as programmed in GAUSSIAN 03. The enthalpies were calculated from the CP-corrected vibrations, which provide better vibrational frequencies than those on the normal (uncorrected) surface. Since the interactions of the individual H-bonds calculated from the structures with the planes of the two molecules perpendicular to each other are not stationary points on the potential surface, only energies on the normal (not CP-corrected) surfaces were calculated for the structures twisted about each H-bond. These are expressed as energies (rather than enthalpies). Although reports of problems with DFT have appeared,14 the validity of DFT calculations for normal H-bonds has been confirmed.15,16 Results and Discussion
Figure 2. Relevant structures for the formation of the 1-2N complex.
Figure 3. 1-2NHB1 Note 90 twist about H-bond 1 and intact intramolecular C-H‚‚‚O interaction.
etries, and vibrations as well as any other property that can be formulated as a derivative of the energy.10 Calculational Details The molecular orbital calculations were performed at the density functional theory (DFT) level using the Gaussian 03 program11 using B3LYP hybrid functional and the D95(d,p) basis set. This method combines Becke’s three-parameter functional,12with the nonlocal correlation provided by the correlation functional of Lee, Yang, and Parr.13 The complexes were completely optimized without any geometric restraints and
Monomers. The optimization of tetraazaanthracene constrained to be planar is not a true minimum on the potential energy surface (PES) as it has one small imaginary frequency. Both N-(pyridin-2-yl)urea, 2H, and N-(6-aminopyridin-2-yl)urea, 2N, can attain two reasonable conformations (see Figures 1 and 2). One of these conformations closely resembles the one each takes in the associated systems. This conformation includes a C-H‚‚‚OdC interaction (H‚‚‚O ) 2.222 Å) while the other (designated as “a” ) is twisted 180° about the exocyclic CNCO dihedral angle. In the second conformation the C-H‚‚‚OdC interaction is replaced with a N-H‚‚‚N interaction between the NH2 and the pyridyl nitrogen. For both pyridinylureas, the conformations containing the N-H‚‚‚N H-bond are lower in both energy and enthalpy (see Table 1). Three of these structures do not represent true minima on the PES as each has small imaginary frequencies involving the pyrimidalization of the NH2’s. The only structure that represents a true minimum on the PES is 2Ha where the NH2 H-bonds to the pyridyl N. This behavior is common for -NH2’s in ureas. For example the NH2’s of urea, itself, have been found to be pyrimidal at the PES minimum as calculated by several methods. However, the enthalpy minimum at 298 K corresponds to the planar geometry. When ureas H-bond, the planar structures become minima even on the PES.17 Similar behavior was reported in the DNA bases.4 We tested for this behavior in 2Na. The completely optimized structure, which contains one planar (that which H-bonds) and one pyrimidal NH2, is lower in energy by 0.51 kcal/mol than the completely planar structure. However, the latter has the lower enthalpy by 0.24 kcal/mol. This behavior is analogous to that reported for urea.17 In this study, we used the planar structures both for simplicity and since they provide reasonable models. The structures containing the N‚‚‚H interaction have lower enthalpies by 3.05 and 3.46 and lower energies by 3.74 and 4.15 kcal/mol for 2H and 2N, respectively (see Table 1). The lowest energy conformations of each monomer are taken as zero. The subscript “cp” denotes values optimized on the CP-corrected surfaces.
Attractive Strain
J. Phys. Chem. B, Vol. 112, No. 6, 2008 1767
TABLE 2: H-Bond Lengths (angstroms) and Energies (kcal/mol)a H-bond
CPcorrected uncorrected twisted
diff
∆E 1 HB
1 2 3 4 3 with CH-O broken cooperativity
2.042 2.219 1.789 2.423
1-2H 2.013 2.188 1.754 2.386 1.754
2.059 2.096 1.874 2.438 1.867
0.046 -0.092 0.120 0.052 0.113 -2.00
-7.69 -5.13 -6.18 -0.55 -6.80
1 2 3 4 3 with CH-O broken cooperativity
2.005 2.352 2.123 1.856
1-2N 1.969 2.308 2.077 1.827 2.077
2.118 2.136 1.902 1.987 1.889
0.149 -0.172 -0.175 0.160 -0.188
-7.10 -4.98 -5.02 -3.81 -5.70 0.92
Figure 4. 2H with intramolecular H-bond broken by 90° twist of N-C-N-C dihedral angle.
a Cooperativity is referenced to the interaction of 1 with 2H or 2N, which are not the lowest energy monomer conformations.
Complexes. The two complexes are depicted in Figures 1 and 2. The interaction enthalpy of the three and four H-bond systems are calculated to be -13.78 and -11.58 kcal/mol, respectively, as indicated in Table 1. These values use the lower energy structures for 2H and 2N that contain the N‚‚‚H internal interactions (which need to be broken to form the complexes). They agree qualitatively with Zimmerman’s report.5 1-2H. We first consider 1-2H. This structure contains three N-H‚‚‚N and one C-H‚‚‚O interaction. If we rotate 90° about each H-bond individually (see the numbering of the H-bonds in Figure 1), keeping the local valence angles at the values they have in the optimized system and freezing all the dihedral angles, we obtain estimates of each individual H-bond to the total interaction energy. Any further interaction beyond the sum of the individual H-bond contributions can be attributed to the cooperative interactions between the H-bonds. We designate the associated structures rotated about a single H-bond with “HBn” (where n is the number of the H-bond noted in the figure) appended to the structure name. Assuming cooperativity to occur, one would generally expect the H-bonding distance to lengthen upon rotation since the removal of the cooperative interaction with the other H-bonds should weaken (therefore lengthen) the remaining H-bond. We have reported this phenomenon in the AT base pair4 and the cyclic acetic acid dimer.18 Both are complexes that contain two cyclic H-bonds. In contrast, the GC base pair contains three H-bonds. Here, at least one of the H-bonds cannot achieve its most stable geometry in the planar complex. Consequently, this H-bond becomes stronger (therefore shortens) when the individual G and C bases of the pair are rotated 90° on the axis of this O‚‚‚H H-bond. The 1-2 complex resembles G-C as it contains multiple H-bonds. From Table 2, we see that three of the H-bonds weaken (lengthen) upon rotation about their respective H-bonding axes, while one (HB2, the central N-H‚‚‚H interaction) strengthens (shortens). From this data, we conclude that HB2 is constrained to a distorted local geometry, which has an N‚‚‚H distance longer than optimal for this particular H-bond. It relaxes when the other H-bonds are broken. The observations that we calculate this H-bond to be abnormally long (2.219 Å) for an N-H‚‚‚N interaction and that Zimmerman reported 2.298 Å from the crystal structure of his similar complex5 reinforces this conclusion. The difference refers to the change in H-bond lengths (angstroms) upon twisting about that H-bond. The ∆E refers to the energy of that specific H-bond. Cooperativity refers to the
Figure 5. 1-2HHB3 with intramolecular C-H‚‚‚O interaction broken. Note 90° twist about both H-bond 1 and N-C-N-H dihedral angle.
difference between the ∆E for the planar complex and the sum of the individual H-bonds. The CP-corrected H-bond lengths are included for reference. There are two C-H‚‚‚O interactions in this complex, one intramolecular and one intermolecular. The intermolecular C-H‚‚‚O interaction appears to be a true H-bond in this system. It becomes longer upon rotation about its H-bond axis, implying that its contribution to the planar complex be somewhat greater than the 0.55 kcal/mol calculated for the individual H-bond. Alternatively, the H-bond lengthening could possibly be due to release of strain in the form of a compression of the H‚‚‚O distance caused by the stronger N-H‚‚‚N interactions. Analysis of the other (intramolecular) C-H interaction is somewhat more complex. This interaction exists in the monomeric N-pyridylurea, 2H. Breaking this interaction by opening the cyclic H-bonding system via rotation 90° about the exocyclic C-N bond (see Figure 4) requires 3.7 kcal/mol (∆E). One cannot perform the same rotation in the planar 1-2H complex without disturbing the proximate HB1 and HB2 interactions. However, one can achieve a similar goal by performing this rotation on the structure that is already rotated about HB3, 1-2HHB3 (see Figure 5). Doing this has a ∆E barrier of 3.1 kcal/mol, or 0.6 kcal/mol less than for the monomer (see Table 3). In other words, the intramolecular interaction is weakened upon association. We conclude that no cooperativity exists, at least between this intramolecular C-H bond and HB3. The destabilization of this C-H‚‚‚O interaction appears to be due to compression in the complex as the O‚‚‚H distance decreases from 2.222 Å (short, but reasonable for a C-H‚‚‚O interaction) in the monomer to 2.138 Å in the complex (versus 2.197 Å for Zimmerman’s similar crystal structure5), which is quite short. This C-H‚‚‚O interaction also contributes to the weakening of the unusually long HB2 interaction as shortening the HB2 interaction would require flexibility to adjust one or more
1768 J. Phys. Chem. B, Vol. 112, No. 6, 2008
Oliva et al.
TABLE 3: Characteristics of the Intramolecular H-Bondsa species 2H 2Ha 2H90 1-2H-HB3 1-2H 2N 2Na 2N90 1-2N-HB3 1-2N
relative ∆E
relative ∆H
C-H‚‚‚O
3.74 0.00 15.56 11.19
3.05 0.00
2.222
4.15 0.00 15.46 -10.63
3.46 0.00
2.138 2.244
2.091
a
Energies and enthalpies in kcal/mol and C-H‚‚‚O distances in angstroms.
valence angles that are constrained by the cyclic C-H‚‚‚O interaction. Breaking the intramolecular C-H‚‚‚O bond by rotating the CONH2 group in 2N requires 11.82 kcal/mol, but only 11.19 kcal/mol in 1-2HB3. This accounts for almost the entire difference in energy for HB3 when the C-H‚‚‚O interaction is broken. The sum of the individual ∆E’s of interaction (-19.54 kcal/ mol) for the individual (twisted) H-bonds is 2.00 kcal/mol less than the ∆E for the total interaction of 1 and 2H, in accord with a small cooperative interaction between the H-bonds. 1-2N. When we consider the complex with the additional N-H·‚‚O H-bond in a manner analogous to that described above, we immediately notice several important differences (see Figure 2 for the numbering of the H-bonds). We have already mentioned that the interaction energy of this complex is less stabilizing than that of 1-2H, in accord with experiment.5 Upon consideration of the energies of individual H-bonds obtained by rotation about each H-bond as described above, we see (Table 2) that the sum of the individual H-bonding stabilizations is 0.92 kcal/mol greater than that for the complex. Thus, the small (-2.00 kcal/mol) cooperative interaction operative in 1-2H has become anticooperatiVe in 1-2N. The explanation for this behavior becomes apparent upon inspection of the H-bond lengths in the complex and in the structures with the monomers rotated about each H-bond. The two most central H-bonds (HB2 and HB3) are both significantly longer in 1-2N than in 1-2H, suggesting that these H-bonds are distorted from their optimal geometries in order to accommodate other interactions. This suggestion is reinforced by the observations that both of the H-bonds shorten upon rotation of the monomers about them. The shortening for these H-bonds is much more significant than for 1-2H. One should note that each of the individual H-bond energies is less stabilizing for 1-2N (except for HB4 which becomes N-H‚‚‚O rather than C-H‚‚‚O),suggesting that the addition of the NH2 provokes a substituent effect that destabilizes the H-bonds, in addition to the steric problems we discuss. The C-H‚‚‚O distance of the intramolecular H-bond decreases in 2N from 2.244 to 2.091 Å upon formation of the complex, 1-2N. The C-H‚‚‚O bonding interaction decreases from 11.31 in 2N to 10.63 kcal/mol in 1-2NHB3. These interaction energies are smaller than the corresponding values for 2H, by 0.5-0.6 kcal/mol. Despite the fact that the compression of the C-H‚‚‚O distance is considerably greater in 1-2N than in 1-2H (0.154 vs 0.084 Å, see Table 3), the difference in the change in ∆E for this H-bond is only about 0.1 kcal/mol upon association between 1-2HHB3 and 1-2NHB3. The C-H‚‚‚O intramolecular H-bonds are quite strong for interactions of this type. One reason may derive from the fact that the cyclic system containing the C-H‚‚‚O interaction contains six π-electrons, which is normally associated with
Figure 6. Morse curve for an individual attractive interaction. Both positions 1 and 2 correspond to distances that correspond to interactions for which the energies are less attractive than at the minimum. Yet, both interaction energies are attractive as both points 1 and 2 are well below the energy required to break the interaction.
aromaticity. We have previously observed that some cyclic H-bonding systems containing 4N + 2 p-electrons,19 including those with C-H‚‚‚O interactions,20 have enhanced H-bonding interactions. Another possible explanation might be the polarizability of the π-system. Alternating charges around the ring would enhance the positive charge on the H-bond donor and the negative charge on the acceptor. This argument could also be applied to the cyclic H-bond of 2Ha and 2Na, which have N-H‚‚‚O interactions and contain seven p-electrons in the ring. We have recently shown that polarizability can greatly enhance N-H‚‚‚OdC H-bonds.21,22 They can also be thought of as being resonance stabilized H-bonds.23-25 Attractive Strain. This study illustrates a type of steric strain that we do not believe has been formally discussed in the literature. The strain devolves from steric factors which preVent two mutually attractive centers from optimally approaching each other, yet contain no net repulsive interactions between the centers. This contrasts with the more common steric strain in which functional groups are constrained to too closely approach each other. The latter is clearly due to repulsions, the former to attenuated attractions. We propose this phenomenon be called attractiVe strain. The two inner H-bonds (HB2 and HB3) of 1-2N provide excellent examples of this phenomenon. Attractive strain, as we define it, differs from the strain on a C-C bond in a hexaalkylethane or hexaarylethane in that the C-C bond is elongated due to repulsions between the substituents. In the present cases of 1-2H and 1-2N, the interactions between the two monomers are all attractive. The strain derives from the inability to optimize all the attractive interactions simultaneously. Consider a morse curve for a bonding (in this case H-bonding) interaction, as in Figure 6. Attractive strains occurs when steric interactions prevent the attracting entities from approaching each other (point 2 of Figure 6) or approach slightly too closely (point 1 of Figure 6) so that the distance between them in the optimized geometry of the system remains different than it would be if the specific interaction between these entities could reach its equilibrium geometry. Nevertheless, the interactions (at either point 1 or 2) remain attractive as the energy of the system remains lower than it would be if the interaction did not occur. In the counterexample of a hexaarylethane, the interactions between aryls are completely repulsive since (1) there is no substantial (neglecting small van der Waals interactions) attraction between these groups at any distance and (2) relieving these repulsions by breaking the central C-C bond can actually lower the overall energy (as in hexaphenylethane which is unstable relative to a pair of triphenylmethyl radicals). In an example of “attractive strain”, such as 1-2N, we have two rigid molecules held together by multiple H-bonds. The
Attractive Strain formation of the outer H-bonds keeps the donors and acceptors of the inner H-bonds from approaching to their optimal H-bonding distances, which remain a bit longer than they would normally be. The outer H-bonds might be slightly compressed, but not sufficiently to render them repulsive (only slightly less attractiVe). There are no purely repulsiVe steric interactions. All the H-bonds are attractiVe. The problem remains that the geometries of the individual H-bonds prevent the complex from achieving all optimal H-bonding distances because some of the H-bonding distance are too long while others too short. Thus, the problem is not steric repulsion but the inability of the H-bond donors and acceptors to approach each other in the central H-bond’s and a slight compression in the outer H-bonds. The rigidity of the two H-bonding molecules places a strain upon the system without creating any repulsive interactions between the two molecules. This strain derives entirely from weakened attractiVe interactions (hence, “attractive strain”). While 1-2N may be an extreme example of a system containing sufficient attractive strain to render this complex less stable than 1-2H, attractive strain probably exists to a lesser degree in most systems containing multiple H-bonds between two entities. Attractive strain affects the enthalpic contribution to the free energy of interaction. Designed molecular interactions often contain rigid multiple H-bonding systems, as these systems have the entropic advantage of existing with relevant dihedral angles frozen in the desired conformation with respect to H-bonding interactions. Apparently, this entropic advantage can often provoke an enthalpic disadvantage such as attractive strain. This enthalpic disadvantage should be considered when designing self-assembling systems. Conclusion DFT calculations reproduce the experimental observation that the H-bonding interaction of 1-2H is greater than that of 1-2N, despite the fact that the former has three and the latter four H-bonds (excluding the intermolecular C-H‚‚‚O interaction in 1-2H). We attribute this behavior to attractiVe strain due to steric constraints that prevent 1-2N from forming four normal H-bonds. Forming strong outer H-bonds combined with the restricted conformational space dictated by the rigidity of the two H-bonding entities prevent the donors and acceptors of the two central H-bonds from approaching to normal H-bonding distances. Acknowledgment. We thank Prof Weston Thatcher Borden for several helpful comments. J.J.D. thanks DURSI of the Generalitat de Catalunya for a visiting professorship at the Universitat de Girona. A.O. thanks the Generalitat de Catalunya for a grant for a sabbatical stay at Hunter College.
J. Phys. Chem. B, Vol. 112, No. 6, 2008 1769 Supporting Information Available: Cartesian coordinates of all species involved in this study. This information is free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Mathias, J. P.; Seto, C. T.; Simanek, E. E.; Whitesides, G. M. J. Am. Chem. Soc. 1994, 116, 1725. (2) Shi, X.; Barkigia, K. M.; Fajer, J.; Drain, C. M. J. Org. Chem. 2001, 66, 6513. (3) Djalali, R.; Chen, Y.-f.; Matsui, H. J. Am. Chem. Soc. 2003, 125, 5873. (4) Asensio, A.; Kobko, N.; Dannenberg, J. J. J. Phys. Chem. A 2003, 107, 6441. (5) Quinn, J. R.; Zimmerman, S. C. Org. Lett. 2004, 6, 1649. (6) Brammer, S.; Lu¨ning, U.; Ku¨hl, C. Eur. J. Org. Chem. 2002, 2002, 4054. (7) Van Duijneveldt, F. B. Basis set superposition error. In Molecular Interactions; Scheiner, S., Ed.; Wiley: Chichester, UK, 1997; p 81. (8) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (9) Jansen, H. B.; Ros, P. Chem. Phys. Lett. 1969, 3, 140. (10) Simon, S.; Duran, M.; Dannenberg, J. J. J. Chem. Phys. 1996, 105, 11024. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J.; J. A.; 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, K.; 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.; 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; 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, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. GAUSSIAN 03; Gaussian, Inc.: Pittsburgh, PA, 2003. (12) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (13) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (14) Wodrich, M. D.; Corminboeuf, C.; Schreiner, P. R.; Fokin, A. A.; Schleyer, P. v. R. Org. Lett. 2007. (15) Ireta, J.; Neugebauer, J.; Scheffler, M. J. Phys. Chem. A 2004, 108, 5692. (16) Simon, S.; Duran, M.; Dannenberg, J. J. J. Phys. Chem. A 1999, 103, 1640. (17) Masunov, A.; Dannenberg, J. J. J. Phys. Chem. A 1999, 103, 178. (18) Turi, L.; Dannenberg, J. J. J. Phys. Chem. 1993, 97, 12197. (19) Dannenberg, J. J.; Rios, R. J. Phys.Chem 1994, 98, 6714. (20) Cardenas-Jiron, G. I.; Masunov, A.; Dannenberg, J. J. J. Phys. Chem. A 1999, 103, 7042. (21) Kobko, N.; Dannenberg, J. J. J. Phys. Chem. A 2003, 107, 10389. (22) Chen, Y.-f.; Dannenberg, J. J. J. Am. Chem. Soc. 2006, 128, 8100. (23) Bertolasi, V.; Gilli, P.; Ferretti, V.; Gilli, G. Acta Crystallogr., Sect. B: Struct. Sci. 1998, B54, 50. (24) Bertolasi, V.; Nanni, L.; Gilli, P.; Ferretti, V.; Gilli, G.; Issa, Y. M.; Sherif, O. E. New J. Chem. 1994, 18, 251. (25) Gilli, G.; Bellucci, F.; Ferretti, V.; Bertolasi, V. J. Am. Chem. Soc. 1989, 111, 1023.
