Negative Dissociation Energy Phenomenon of Metastable H-Bonds As

Dec 10, 2009 - as a high-energy node in a DNA wire which modulates migration of a hole into ... could result in HO H-bonds a negative dissociation ene...
0 downloads 0 Views 799KB Size
Download PDF
1144

J. Phys. Chem. B 2010, 114, 1144–1147

Negative Dissociation Energy Phenomenon of Metastable H-Bonds As Revealed in Triplex DNA Hole Migration Jun Wang, Lixiang Sun, and Yuxiang Bu* The Center for Modeling and Simulation Chemistry, Institute of Theoretical Chemistry, Shandong UniVersity, Jinan, 250100, P.R. China ReceiVed: October 21, 2009; ReVised Manuscript ReceiVed: NoVember 17, 2009

Ab initio calculations reveal an unknown energetic phenomenon for H-bonds in the hole-trapping triplex Cp•GoC motif observed experimentally in hole migration which can explain the lower but really available oxidization possibility in Cp•GoC site. Hole trapping can considerably destabilize the Cp•GoC unit and lead to an unexpected barrier-hindered channel with a negative dissociation energy. This channel is governed by a balance between electrostatic repulsion and H-bonding attraction in the two associated moieties and different attenuations of two opposite interactions with respect to the H-bond distance. This Cp•GoC unit can be viewed as a high-energy node in a DNA wire which modulates migration of a hole into or through it via its unusual energetics. It provides useful information for understanding of an unknown type of the complicated intermolecular interactions, a novel type of “high-energy” bond, and can be applied further to interpret the hidden transport properties and the energy conversion/transfer mechanisms in the related fields. Introduction Hydrogen bonds (H-bonds) play an important role not only in the secondary structures of proteins but also in the duplexes and triplexes of DNA. In the DNA-associated functional processes, such as transcription, duplication, etc., the enzymatic activity is highly specific and involves H-bonding interactions among cofactors and nucleotide bases. Life on earth thus depends strongly on the functionality of H-bonds in biological molecules. The role of H-bonds for the structure and function of the normal duplex or triplex DNA is nowadays well understood, but that in the oxidative lesions/damages is still not fully explored. In general, one-electron oxidation1-7 of DNA can cause guanine (G) damage selectively through a π-stackmediated hole migration.6-9 Although base sequences, base stacking, and accessibility of water and/or oxygen to the hole are believed to be the principal factors in affecting position and efficiency of hole trapping, the H-bonds among bases and cofactors are also extremely important, not only in conserving the DNA helical structures that carries genetic information and has specific functions in vivo10 but also in regulating hole migration along the DNA wire.11 Thus, knowledge about the H-bonding properties for DNA in the oxidative lesion or hole migration/trapping is therefore of fundamental importance. In general, hole trapping is preferentially at sequences of Gs, especially the G sites stacked by two or more Gs, and competes with hole migration through DNA. Inhibition of hole trapping at the G sites may be favorable for hole migration. An effective way to inhibit hole trapping is residing of a positively charged species through the counterion (Na+) penetration or the proton bonding in base pairing.12,13 In the latter, a protonated cytosine (Cp) in the third strand of Cp•GoC (“•” and “o” represent Hoogsteen (HO) and Watson-Crick (WC) H-bonds, respectively) triplex effectively inhibits hole trapping at G and even GG (runs) sites, forcing hole migration, as evidenced experimentally by a lower oxidization possibility in the triplex zone * To whom correspondence should be addressed. E-mail: byx@ sdu.edu.cn.

Figure 1. Geometrical character and the corresponding H-bonding length changes (Å) induced by hole trapping. The red values denote the increments and the blue negative values denote the decrements. The WC H-bond zone includes two (pu)N-H · · · N/O(py) and one (pu)N/O · · · H-N(py) sub-H-bonds for CpGC, or a (pu)N/O · · · H-N(py) and a (pu)N-H · · · N/O(py) sub-H-bonds for TAT, while the HO H-bond zone includes two (pu)N/O · · · H-N(py) for CpGC, or a (pu)N · · · H-N(py) and a (pu)N-H · · · N/O(py) for TAT, where pu denotes the purine units and py the pyrimidine units.

than that in the duplex zone.13 An intuitionistic understanding for the G site oxidization with a lower possibility in the triplex region is that the C protonation raises the ionization potentials of those G sites, thus inhibiting hole trapping. Actually, the holetrapping-induced energetics is also extremely exceptional for the H-bonds (HO vs WC) in the triplex motifs. We herein report a novel calculational finding for the H-bonds in triplex DNA containing pyrimidine•purineopyrimidine (py•puopy: Cp•GoC or T•AoT) motifs. That is, hole trapping could result in HO H-bonds a negative dissociation energy, an energy-reserved one. Thus, the hole-trapping possibility could be understood from a new aspect. Results and Discussion The geometries of Cp•GoC and T•AoT motifs (Figure 1) and their mono-oxidized derivatives were determined at the B3LYP/ 6-31+G* level of theory, and the energy quantities were refined at the B3LYP/6-311++G**//B3LYP/6-31+G* level14 with the

10.1021/jp9100637  2010 American Chemical Society Published on Web 12/10/2009

Negative Dissociation Energy of Metastable H-Bonds

Figure 2. Schematic profiles of PES along WC and Hoogsteen H-bond dissociation coordinates of trimer complex units in their initial (T•AoT or Cp•GoC), oxidized (T•A+oT or Cp•G+oC) and possibly protontransferred (T•A+oT or Cp•G-HoCp) states where Cp is the protonated C and G-H is the dehydrogenated G in the DNA triple helixes. The corresponding dissociation energies are also shown. The PESs are shifted upward (by 3.84 kcal/mol for Cp•G-HoCp) and downward (by 223.57 kcal/mol for Cp•G+oC and 171.90 kcal/mol for T•A+oT), respectively, to make them an unified zero point for comparison.

basis set superposition error corrections if necessary using the counterpoise correction method of Boys and Bernardi.15 The potential energy surfaces (PES) were also scanned along their H-bond vectors for four motifs. To characterize H-bonds in different situations, Laplacians of electron density at their bond critical points (BCP, ∇2FBCP) were determined using the AIM method. All calculations were performed with Gaussian 03 program package.16 PES with respect to WC and HO H-bonds of two triplex motifs and their corresponding radical cations are shown in Figure 2. In the normal states (not oxidized), the triplexes are located at the minima of their PESs, and their dissociation energies (∆ED) along two H-bond dissociation channels are 42.44 (WC), 26.75 (HO) kcal/mol for Cp•GoC and 11.44 (WC), 10.72 (HO) kcal/mol for T•AoT, respectively. Upon hole trapping, PES for the produced [T•AoT]+ has similar feature to that of T•AoT but with a slightly deep well. The ∆EDs of HO H-bond and WC H-bond increase to be 18.14 and 17.07 kcal/ mol, respectively. However, for [Cp•GoC]+, a different change on PES was observed with an unexpected character. Although well depth of the WC H-bond dissociation channel increases (by ca. 20 kcal/mol), the HO H-bond dissociation channel sinks and falls, and the channel exit is even far below the PES well bottom (by ca. 21 kcal/mol), but separated by a barrier of ∼7 kcal/mol (Figure 2). That is to say, [Cp•GoC]+ has a negative ∆ED for HO H-bond. Clearly, this is an unexpected variation upon hole migration through Cp•GoC, which is certainly associated with some properties of hole transport, and also implies a character distinctly different from T•AoT. As shown in Figure 1, either WC or HO H-bonds consist of the multiple sub-H-bonds with different donor-acceptor modes. Geometrical inspection indicates that hole trapping can considerably change lengths of all sub-H-bonds by elongating (pu)N/ O · · · H-N(py) and shortening (pu)N-H · · · N/O(py) in both WC and HO H-bond zones of two triplex motifs. Clearly, these variations imply weakening of all (pu)N/O · · · H-N(py) H-bonds (but not ruptured!) and strengthening of all (pu)N-H · · · N/O(py) ones, and can be accounted for by acidity-basicity changes of the associated H-bond donor/acceptor induced by hole trapping. Undoubtedly, these H-bond changes should stem from either increase of the donor (pu)N-H acidity or decrease of the acceptor (pu)N/O basicity, suggesting that the hole must be trapped at the purine part of the triple. These geometrical changes are closely associated with the holetrapping-induced ∆ED changes. As mentioned above, for either of WC or HO H-bonds in T•AoT, hole trapping weakens its (pu)N · · · H-N(py) sub-H-bonds, but strengthens its (pu)N-H · · · O(py) ones. As an overall result, ∆ED of WC and HO H-bonds in

J. Phys. Chem. B, Vol. 114, No. 2, 2010 1145

Figure 3. Variation of electrostatic potential (ESP) surfaces of Cp•GoC unit upon hole trapping (molecular total electron density ) 4 × 10-4 au) and proton transfer. Here, ESP surfaces were generated by mapping the 6-31+G* potentials onto surfaces of the molecular total electron density. Hole trapping can considerably increase ESP around the HO H-bond zone, thus leading to its exceptional energetics. Further proton transfer may expand the exceptional energy zone.

T•AoT slightly increase. However, for Cp•GoC, a distinctly different situation was observed because of its different H-bond pattern from that in T•AoT. For WC H-bonds in Cp•GoC, since two (pu)N-H · · · N/O(py) sub-H-bonds are strengthened while only one (pu)O · · · H-N(py) is weakened after hole trapping, ∆ED of WC H-bond is considerably increased. But, for its HO H-bond, both two (pu)N/O · · · H-N(py) sub-H-bonds are weakened, leading to a sinking of the product PES even with a considerably negative ∆ED (Figure 2). Examination of the spin density distribution confirms the above suggestion that a hole is almost trapped at the purine fragment for [Cp•GoC]+ or [T•AoT]+. Such a localization of a hole implies there occurs considerable electrostatic interaction among the composite bases in addition to their normal H-bonds. Clearly, hole trapping at purine could increase the electrostatic attractions for all (pu)N-H · · · N/O(py) sub-H-bonds, but the electrostatic repulsions for all (pu)N/O · · · H-N(py) in both T•AoT and Cp•GoC. The increased electrostatic attraction in (pu)N-H · · · N/O(py) can compensate the hole-trapping-induced weakening of (pu)N/O · · · H-N(py) with an excess, thus leading to increase of ∆ED. More particular is the HO H-bond in Cp•GoC in which the increased is only the repulsion and the increment is drastic because of an explicit positive charge of Cp. Hole trapping significantly increases the electrostatic repulsion, thus largely raising total energy of Cp•GoC and leading the triplex to a metastable state and the separated state to the most stable one. Actually, energy decomposition analysis indicates that the electrostatic interaction mainly contributes to the ∆ED changes of the H-bonds, as supported by their BCP properties. ∇2FBCP of all WC and HO H-bonds in both Cp•GoC and T•AoT are positive17 and hole trapping may result in their different variations. In general, for the (pu)N-H · · · N/O(py) sub-H-bonds, ∇2FBCP and FBCP increase, while those of the (pu)N/O · · · H-N(py) sub-H-bonds decrease upon hole trapping, indicating increase of the electrostatic interaction for the former but decrease for the latter. However, an exception was observed in the (pu)N · · · H-N(py) HO H-bond of Cp•GoC. Although hole trapping decreases FBCP, similar to the above rule, ∇2FBCP inversely increases, indicating a considerable increase of the electrostatic interaction in this zone. Overall, these changes further suggest that additional electrostatic interaction upon hole trapping becomes a dominant contribution to the energetic changes of these WC and HO H-bonds. Figure 3 shows the electrostatic potential (ESP) of Cp•GoC, a good indicator of this dissociation channel sink, in an attempt to characterize the hole-trapping-induced ∆ED changes. In general, the red zone with small ESP value denotes a weaker electrostatic interaction there corresponding to a normal dissociation channel with positive ∆ED, while the blue zone with

1146

J. Phys. Chem. B, Vol. 114, No. 2, 2010

Figure 4. Schematic profile for the interaction modes between two H-bonded bases. There may occur up to three types of interactions between two H-bonded bases: (pu)Y-H · · · X(py), (pu)X · · · H-Y(py), and electrostatic repulsion. The former two are the H-bonding attractions, while the latter is a repulsion between the positive charge from protonation and a π-hole produced by hole trapping.

large ESP value denotes stronger electrostatic interaction there corresponding to an anormal dissociation channel with negative ∆ED. Hole trapping can result in a considerable increase of ESP only around HO H-bond zone of Cp•GoC, implying larger electrostatic repulsion there. In other words, hole trapping promotes HO H-bond zone of Cp•GoC to be a “high-energy” one, but WC H-bond zone of Cp•GoC and all of H-bond zones of T•AoT hardly changed, still as “low-energy” zones. The remaining is to further clarify essence why hole trapping can lead to an abnormal PES for Cp•GoC HO H-bond. Actually, this observation can be easily understood from relative attenuation of two types of different electrostatic interactions (Hbonding attraction vs electrostatic repulsion) in each H-bond zone along its dissociation channel and the repulsion property. There are two types of interactions in each H-bond unit (Figure 4): attraction between Hδ+ and the in-plane lone-pair electrons; repulsion between Hδ+ and the π-hole localized at the H-bond acceptor (especially the acceptor atom N/O(pu)). As known, H-bond is a short-range interaction with large attenuation rate with respect to its length, but electrostatic attraction/repulsion has a relative small attenuation rate and can still exhibit considerable interaction even at a large separation. Upon hole trapping at G of Cp•GoC, drastically increased electrostatic repulsion between the newly created π-hole at G and Cp in its HO H-bond zone is not so large enough to break the original H-bond, but only weakening it. As a result, HO H-bond in this zone is still available, keeping the system at a stable state (a local minimum on PES). However, as the H-bond elongates, its strength decreases drastically, while electrostatic repulsion decreases with a relatively small attenuation rate. So, the H-bond attraction is dominant, and the dissociation curve goes up along with elongation of H-bond in a short-range of H-bond distance. But, at a certain distance, two interactions may become comparable and the system reaches a dissociation transition state. After that, the electrostatic repulsion becomes dominant and gradually attenuates with a small magnitude, while the H-bonding attraction drastically disappears (Supporting Information). So the dissociation curve goes down until an infinite separation of two moieties (the global minimum). Overall, the HO H-bond PES of [Cp•GoC]+ behaves with a “sinking” feature at the dissociated state with negative ∆ED. However, for other H-bonds in Cp•GoC, T•AoT, [T•AoT]+, and even G•GoC, A•AoT, and their cations, since electrostatic repulsions are small and H-bonding attractions are always dominant, the dissociation PES exhibits the normal shape with positive ∆EDs. To further examine effect of trimer structures on this special negative dissociation energy phenomenon and to explore its

Wang et al. properties, some base pairs (Cp•G, GoC, T•A, and AoT) associated with the triplex motifs and the proton-transferred isomer of Cp•GoC were also considered because one-electron oxidation of GoC may lead to a proton transfer from G to C. Similar to that in the triple motifs, one-electron ionization can increase ∆ED for GoC, T•A, and AoT, but decrease ∆ED to a considerably negative value (∼25 kcal/mol) for Cp•G, exhibiting the termed negative dissociation energy phenomenon. Interestingly, for Cp•GoC, hole-trapping-induced proton transfer from G to C in WC H-bond unit not only stabilizes the [Cp•GoC]+ unit (by 3.84 kcal/mol), but also significantly changes ∆EDs of its WC and HO H-bonds. As a result, ∆EDs of both H-bonds become as -15.3 kcal/mol, reduced by ca. 63.4 (WC) and 5.1 (HO) kcal/mol, respectively. That is to say, proton transfer leads to a significant falling of the product PES along the WC H-bond vector, changing the dissociation channel a double-well pathway with a negative ∆ED. In addition, a three-layer TAT/CpGC/TAT and a four-layer TAT/CpGC/CpGC/TAT structure were also checked for the stacking effect, and all relevant results are given in the Supporting Information. Results indicate that the stacking could have considerable effect on the values of dissociation energies but their signs. That is, for the Cp•GoC sandwiched by 2(T•AoT), the Hoogsteen H-bond dissociation energy goes down from ca. -20 kcal/mol (in Cp•GoC) to about -5.7 kcal/mol (see [TAT/ CpGC/TAT]+ in Table S11, Supporting Information). But, for the Cp•GoC sandwiched by T•AoT/Cp•GoC and a T•AoT (see [TAT/CpGC/CpGC/TAT]+), the Hoogsteen H-bond dissociation energy does increase considerably from ca. -20 kcal/mol to ca. -40 kcal/mol. These observations may be attributed to the fact that Cp•GoC stacking could increase the electrostatic repulsion, but TAT stacking may decrease the electrostatic repulsion through hole delocalization. However, it is noteworthy that, for the four-layer TAT/CpGC/CpGC/TAT (not oxidized), the dissociation energy by removing a Cp is still positive (11.2 kcal/mol), although there is repulsion between two adjacent CpGC triplexes. Clearly, this observation may be due to the stacking effect originating from two TAT layers which scatters the Cp-concentrated positive charge via charge transfer. Overall, stacking can change the energy values but cannot disappear this negative ∆ED phenomenon. Clearly, the above findings may be also understood from a balance between two different electrostatic interactions (the attractive H-bonding versus the electrostatic repulsion originating from hole trapping). For Cp•G, GoC, T•A, and AoT, although their ∆EDs have been changed with little magnitudes compared with those of the corresponding H-bonds in the triplet, properties of their dissociation PESs and energetics are basically unchanged. These observed changes can be attributed to the base pairing effect because localization of a hole and the explicit positive charge unchanged, still at the purine fragments. However, for the proton-transferred Cp•G-HoCp, compared with [Cp•GoC]+, although the electron hole is still resided at the purine fragment, the explicit positive charge has shifted from the middle G (delocalized over G) to the WC H-bonded complementary base, C (localized at the protonated N). This shift considerably decreases the electrostatic repulsion between two explicit positive charges. As a result, the potential well on the HO H-bond PES becomes shallow. At the same time, this shift also expands the electrostatic repulsion zone to cover the WC H-bond one (Figure 3), thus changing property of WC H-bond into what similar to HO H-bond, making WC H-bond a negative ∆ED.

Negative Dissociation Energy of Metastable H-Bonds These findings further indicate that, although hole-trapping significantly increases electrostatic repulsion between the positively charged sites separated at the H-bonded moieties, it does not break their existing H-bonds and thus a balance between the H-bonding attraction and the pure electrostatic repulsion governs the metastable geometries of these kinds of the charged species. A series of the modeling complexes have confirmed this special energetics phenomenon. In addition, it is noteworthy that the HO H-bonding energy of Cp•GoC is ca. 42 kcal/mol, not larger enough to compensate the energy loss caused by hole-trapping-induced electrostatic repulsion energy increase (ca. 63 kcal/mol, extracted by comparing IPs of Cp•GoC and GoC). Thus, this observation implies that hole trapping forces Cp•GoC HO H-bond to reserve some of energy which can be released by H-bond cleavage or hole delocalization or migration. Finally, in order to clarify if this special energetics phenomenon exists in other DNA triplex motifs, two other triplexes CGG and TAA, that is, CoG•G and ToA•A or G•GoC and A•AoT in which the purines (G or A) in the third strands are HoogsteenH-bonded with the corresponding natural base pairs as the efficient hole-trapping sites,18 were also examined at the same level of theory, and all results are given in the Supporting Information. The main point in this examination is that the negative dissociation energy phenomenon does not exist in all these purine•purineopyrimidine (pu•puopy) triplex DNA motifs, very similar to the T•AoT situation. Since the hole-trapping efficiency at a DNA site inversely depends on its ionization energy, these different observations for G•GoC, A•AoT, and even T•AoT from that for Cp•GoC reveals a dependence of the holetrapping efficiency of the triplex DNA motifs on the oxidizability of a base in the third strand and also on the hole-trappinginduced dissociation energetics changes of their Hoogsteen H-bonds. Speaking simply, a positively charged base in the third strand has very large ionization potential, and thus its formed triplex DNA motif with a base pair exhibits a low hole-trapping efficiency and a large Hoogsteen H-bond dissociation energy decrease upon hole trapping, leading to the negative dissociation energy phenomenon. An easily oxidized base (e.g., guanine) in the third strand can effectively increase the hole-trapping efficiency of the DNA motif and also increase the Hoogsteen H-bond dissociation energy upon hole trapping. Conclusion In summary, the present ab initio calculations reveal an unknown energetic phenomenon for H-bonds in the hole-trapped triplex Cp•GoC motif observed experimentally in hole migration which can explain the lower but really available oxidization possibility in Cp•GoC site. Hole trapping can considerably destabilize the unit and lead to an unexpected barrier-hindered channel with a negative dissociation energy. This channel is governed by a balance between electrostatic repulsion and H-bonding attraction in the two associated moieties and different attenuations of two opposite interactions with respect to the H-bond distance. This Cp•GoC unit can be viewed as a highenergy node in a DNA wire which modulates migration of a hole into or through it via its unusual energetics. Although this phenomenon originates from hole-trapped Cp•GoC, it may apply into many other H-bonded complexes, such as the cation (Na+ or -NH3+)-bound GoC, and RsArgH+ · · · H+Arg-R in proteins, TTF+ · · · TTF+ in conductive materials, and etc. Thus, it provides useful information for understanding of an unknown type of the complicated intermolecular interactions, a novel type of

J. Phys. Chem. B, Vol. 114, No. 2, 2010 1147 “high-energy” metastable bond with negative dissociation energy, and motivates continued theoretical explorations. Acknowledgment. Y.B. sincerely thanks Prof. Borden for being host and Dr. Hrovat at UNT for helpful discussions on this work while Y.B. was on sabbatical there. This work is supported by NSFC (20633060, 20973101) and NCET. Supporting Information Available: Molecular geometries, spin densities, interaction analyses, relevant energy quantities, ESP surfaces, BCP parameters, and others. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) For reviews, see: (a) Grinstaff, M. W. Angew. Chem., Int. Ed. Engl. 1999, 38, 3629–3635. (b) Holmlin, R. L.; Dandliker, P. J.; Barton, J. K. Angew. Chem., Int. Ed. Engl. 1997, 36, 2714–2730. (2) (a) Giese, B.; Amaudrut, J.; Ko¨ hler, A. K.; Spormann, M.; Wessely, S. Nature 2001, 412, 318–320. (b) Giese, B.; Spichty, M. Chem. Phys. Chem. 2000, 1, 195–198. (c) Giese, B. Acc. Chem. Res. 2000, 33, 631–636. (3) Lewis, F. D.; Letsinger, R. L.; Wasielewski, M. R. Acc. Chem. Res. 2001, 34, 159–170. (4) Schuster, G. B. Acc. Chem. Res. 2000, 33, 253–260. (5) (a) Nakatani, K.; Dohno, C.; Saito, I. J. Am. Chem. Soc. 2000, 122, 5893–5894. (b) Nakatani, K.; Dohno, C.; Saito, I. J. Am. Chem. Soc. 1999, 121, 10854–10855. (6) Hall, D. B.; Holmlin, R. E.; Barton, J. K. Nature 1996, 382, 731–734. (7) (a) Melvin, T.; Botchway, S.; Parker, A. W.; O’Neill, P. J. Chem. Soc., Chem. Commun. 1995, 653–654. (b) Becker, D.; Sevilla, M. D. AdV. Radiat. Biol. 1993, 17, 121–180. (8) (a) Jortner, J.; Bixon, M.; Langenbacher, T.; Michael-Beyerle, M. E. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 12759–12765. (b) Berlin, Y. A.; Burin, A. L.; Ratner, M. A. J. Am. Chem. Soc. 2000, 122, 10903–10909. (9) (a) Arkin, M. R.; Stemp, E. D.; Pulver, S. C.; Barton, J. K. Chem. Biol. 1997, 4, 389–400. (b) Gasper, S. M.; Schuster, G. B. J. Am. Chem. Soc. 1997, 119, 12762–12771. (c) Nunez, M.; Hall, D. B.; Barton, J. K. Chem. Biol. 1999, 6, 85–97. (d) Meggers, E.; Michel-Beyerle, M. E.; Giese, B. J. Am. Chem. Soc. 1998, 120, 12950–12955. (10) (a) Frankkamenetskii, M. D.; Mirkin, S. M. Annu. ReV. Biochem. 1995, 64, 65. (b) Soyfer, V. N.; Potaman, V. N., Triple-Helical Nucleic Acid; Springer Verlag: New York, 1996. (11) Gervasio, F. L.; Boero, M.; Parrinello, M. Angew. Chem., Int. Ed. 2006, 45, 5606–5609. (12) Barnett, R. N.; Cleveland, C. L.; Joy, A.; Landman, U.; Schuster, G. B. Science 2001, 294, 567–571. (13) Kan, Y.; Schuster, G. B. J. Am. Chem. Soc. 1999, 121, 11607– 11614, also see Supporting Information. (14) This method has been proved to be applicable. See: (a) Peters, M.; Rozas, I.; Alkorta, I.; Elguero, J. J. Phys. Chem. B. 2003, 107, 323–330. (b) Sy¨poner, J.; Jurecka, P.; Hobza, P. J. Am. Chem. Soc. 2004, 126, 10142– 10151. (15) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (16) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., 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, 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, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, ReVision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (17) In general, sign of ∇2FBCP is considered to relate with whether the atomic interaction possesses a dominant character of the covalent interaction (∇2FBCP < 0) or the electrostatic or H-bond interaction (∇2FBCP > 0). Bader, R. F. W. Atoms in Molecules: A Quantum Theory: Oxford University Press: Oxford, UK, 1990. Popelier, P. Atoms in Molecules, An Introduction; Prentice-Hall, Pearson Education Ltd.: Upper Saddle River, NJ, 2000. (18) Dohno, C.; Nakatani, K.; Saito, I. J. Am. Chem. Soc. 2002, 124, 14580–14585.

JP9100637