10706
J. Phys. Chem. A 2010, 114, 10706–10711
Theoretical Investigations on the Reaction of Monosubstituted Tertiary-Benzylamine Selenols with Hydrogen Peroxide Gavin S. Heverly-Coulson and Russell J. Boyd* Department of Chemistry, Dalhousie UniVersity, Halifax, NoVa Scotia, Canada B3H 4J3 ReceiVed: June 18, 2010; ReVised Manuscript ReceiVed: August 22, 2010
The effects of introducing electron-donating (NH2, OCH3, CH3) and electron-withdrawing (NO2, CF3, CN, F) groups to N,N-dimethylbenzylamine-2-selenol are studied to determine the effect of the selenium electron density on the efficiency of the reduction of hydrogen peroxide. Introducing substituents in the meta and para positions decreases or increases the energy barrier of the reaction in the expected way, due to changes in the electronic environment of the reacting selenium center. Ortho substituents are found to have a greater effect on the electronic environment of the selenium center, which is mitigated by changing the steric environment. Insight into the origins of the substituent effects is obtained through quantum theory of atoms in molecules (QTAIM) and electrostatic potential analysis. Introduction
SCHEME 1: Catalytic Cycle of GPx 1
The glutathione peroxidase (GPx) family of selenoenzymes is a part of the human body’s antioxidant system, protecting against oxidative stress by reducing hydroperoxides. It has been established that the selenium moiety, incorporated into the enzyme as the amino acid selenocysteine, is the active group in these enzymes.2–4 Both experiment3 and computer modeling5 suggest that the active form of the selenium, that is the one that reacts with peroxides, is not the selenol found in selenocysteine, but is instead the deprotonated selenolate anion. On the basis of their observations, Epp et al.3 proposed a catalytic cycle for GPx, shown in Scheme 1, with their crystal structure of bovine GPx. Deficiencies in the GPx system can lead to oxidative stress, which has negative effects on proteins, lipids, DNA, and cell membranes. These effects have been linked to a number of degenerative conditions, particularly inflammation, atherosclerosis, and some cancers,6,7 and therefore for the past 25 years, there have been many attempts to design small organoselenium compounds that counteract these effects. The first compound proposed as a GPx mimic was ebselen (2-phenyl-1,2-benzisoselenazol-3(2H)-one),8,9 which has been studied extensively as an antioxidant10–16 and has been observed as a substrate for thioredoxin reductase.17 Since then, many other organoselenium compounds have been proposed as antioxidants.18–28 Of the compounds proposed, some of the most successful GPx mimics are those that contain a selenium-nitrogen interaction, which closely resembles the enzyme active site, which has an arginine residue near the selenocysteine,29 and therefore has been demonstrated to be important for GPx-like activity.18,21,30 Another important factor for the activity of organoselenium compounds as GPx mimics is the selenol group, or rather the selenolate. Many studies have either observed an anionic selenium experimentally3,21,31 or predicted it computationally to have greater activity than the neutral selenol as a reducing agent.5,15 We have recently found32 that the mechanism for reduction of hydrogen peroxide by N,N-dimethylbenzylamine* To whom correspondence should be addressed. E-mail: russell.boyd@ dal.ca.
2-selenol (DMBS), a GPx mimic originally proposed by Wilson, et al.,19 in its neutral selenol form is a two-step process with large energy barriers for each step. Conversely, the zwitterionic form shows a one-step mechanism with a significantly lower barrier. Therefore, it seems likely that altering the electron density on the selenium atom, by introducing electron withdrawing or donating groups to the phenyl ring, would affect the barrier for peroxide reduction of these compounds. In 1989,33 it was observed that introducing a nitro group ortho to the selenium in ebselen increased its GPx-like activity by a factor of 9. More recently, Bhabak and Mugesh34 have shown that introducing a methoxy group ortho to the selenol in DMBS increases the GPx-like activity by an order of magnitude, an effect they attribute to a combination of steric and electronic effects. On the other hand, Pearson and Boyd16 have reported that introducing a methoxy group ortho to the selenium in ebselen increases the energy barrier for hydrogen peroxide reduction by about 21 kJ/mol. In the same study, a t-butyl group in the same position also increased the energy barrier, indicating a primarily steric effect. In this work, we introduce seven functional groups, ranging from strongly electron withdrawing to strongly electron donating, in the ortho, meta, and para positions relative to the selenol in N,N-dimethylbenzylamine-2-selenol. By modeling these compounds using the peroxide reduction mechanism we previously reported,32 we can study the purely electronic effects of these substituents in the meta and para positions and compare to substitutions in the ortho position, where both electronic and steric effects can influence the reaction. The two reactions
10.1021/jp105651x 2010 American Chemical Society Published on Web 09/13/2010
Selenium Electron Density and the Reduction of H2O2 SCHEME 2: The Reactions Studied in This Worka
J. Phys. Chem. A, Vol. 114, No. 39, 2010 10707 TABLE 1: Gibbs Energies for Formation of the Zwitterion from the Selenol of DMBSa ∆Grxn substitution NH2 OCH3 CH3 F CN CF3 NO2
a The monosubstituted derivatives of DMBS, with NH2, OCH3, CH3, F, CN, CF3, or NO2 placed in the ortho, meta, or para positions relative to the selenol, were also studied.
Computational Methods Calculations were performed with the Gaussian 0935 suite of programs. Geometry optimizations were performed with the B3PW91 hybrid DFT functional, composed of Becke’s threeparameter exchange functional (B3)36 and the correlation functional proposed by Perdew and Wang (PW91)37 with the 6-31+G(d,p) Pople basis set, as suggested by Pearson, et al.38 Transition states were found with Schlegel’s synchronous transitguided quasi-Newton (STQN) method,39,40 and the reaction path was followed using intrinsic reaction coordinate (IRC)41,42 calculations. Frequency calculations were performed on all optimized structures at the same level of theory to confirm whether the structure is a local minimum or first-order saddle point and to obtain thermochemical corrections. Accurate energies were obtained for all systems at the B3PW91/6311++G(3df,3pd) level. Solvent effects for an aqueous environment (dielectric constant of 78.39) were included in singlepoint calculations using the conductor-like polarizable continuum model (CPCM). The topology of the electron density was studied using the quantum theory of atoms in molecules (QTAIM) calculations43,44 performed using AIMAll (Version 10.03.25).45 Results and Discussion Zwitterion Formation. Experimental evidence suggests that the zwitterionic form of N,N-dimethylbenzylamine-2-selenol is the predominant form in water at room temperature21 and therefore is likely the form that reacts with peroxides. To determine the relative stability of the zwitterion, we have modeled both the selenol and zwitterion forms. A transition state search was also performed to connect the selenol to the zwitterion, which found a transition state lower in energy than the selenol for all systems, indicating a direct conversion from the selenol to the zwitterion, rather than passing through a transition state. In all systems studied, the zwitterion is more stable than the selenol and the conversion from the selenol to the zwitterion is energetically downhill, from the transition states identified. These results are summarized in Table 1. The zwitterion of unsubstituted DMBS is 23.1 kJ/mol more stable than the selenol. In the substituted systems, the zwitterions are 20-30 kJ/mol more stable than the selenols. Previous work by Bhabak and Mugesh,34 determined that the zwitterionic form of DMBS is about 21 kJ/mol more stable than the selenol, which is in qualitative agreement with our results. They also found that
meta
para
-30.5 -19.1 -22.0 -25.9 -30.3 -25.6 -20.5
-24.1 -24.3 -28.5 -26.2 -26.6 -34.9 -27.1
-19.5 -20.8 -22.4 -22.5 -27.3 -26.6 -28.7
-23.1
unsubstituted a
studied in this work, outlined in Scheme 2, are the selenium to nitrogen proton transfer in the selenol to form the zwitterion and the reaction of the zwitterion with hydrogen peroxide.
ortho
Energies relative to the selenol form in kJ/mol.
TABLE 2: QTAIM Charges for the Selenium Atom in DMBS (au) ortho substitution NH2 OCH3 CH3 F CN CF3 NO2 unsubstituted
meta
para
qselenol
qzwitterion
qselenol
qzwitterion
qselenol
qzwitterion
0.082 0.188 0.102 0.186 0.163 0.181 0.298
-0.351 -0.262 -0.317 -0.254 -0.232 -0.229 -0.162
0.118 0.131 0.127 0.131 0.136 0.135 0.144
-0.325 -0.312 -0.316 -0.296 -0.279 -0.286 -0.271
0.145 0.143 0.132 0.138 0.111 0.124 0.074
-0.326 -0.320 -0.316 -0.308 -0.265 -0.280 -0.244
0.129
-0.311
ortho-methoxy substituted DMBS has a zwitterionic form about 38 kJ/mol more stable than the selenol, which is significantly more stable than we are reporting. Using atoms in molecules (QTAIM) analysis, the electron density changes during the proton transfer can the followed. It is observed that in the selenol the Se-H bond critical point Se-H (BCP) density (FBCP ) has an average value of 0.170 au and N· · ·H FjBCP ) 0.045 au. In the zwitterion, after the proton transfer has been completed, FjBCP is 0.071 and 0.238 au for Se · · · H and N-H, respectively, demonstrating that the N-H bond is stronger in the zwitterion than the Se-H bond in the selenol, with FBCP 0.07 au higher. The Se · · · H interaction in the zwitterion is also stronger than the N · · · H interaction in the selenol, with FBCP 0.025 au higher. This combination of two stronger interactions provides an explanation for the increased stability of the zwitterion relative to the selenol. Looking at the atomic charges of the selenol and the zwitterionic forms, Table 2, provides an explanation for the reactivity of these two species with hydrogen peroxide that we previously found.32 The number of electrons in the selenium atomic basin (N(ΩSe)), for the unsubstituted species, is 33.871 and 34.311 au for the selenol and zwitterion, respectively, giving atomic charges (qSe) of 0.129 and -0.311 au, respectively. The zwitterion has gained nearly half an electron compared to the selenol, which makes it a stronger nucleophile toward hydrogen peroxide, allowing it to react more efficiently. The positive charge in the selenol, combined with its valency of two, makes a poor nucleophile compared with the zwitterion, which has an anionic selenium with a valency of one. These two factors lead to the two-step reaction found for the selenol with hydrogen peroxide, but allow the zwitterion to react via a one-step process. By studying the electron density on the atoms nearby the selenium, it is possible to identify where the additional charge comes from during the selenol to zwitterion conversion. In the selenol, the hydrogen bonded to the selenium atom has 0.961
10708
J. Phys. Chem. A, Vol. 114, No. 39, 2010
Heverly-Coulson and Boyd
TABLE 3: Gibbs Energies for Reaction of Zwitterionic DMBS with Hydrogen Peroxide (in kJ/mol) ortho substitution NH2 OCH3 CH3 F CN CF3 NO2 unsubstituted
meta
para
∆G‡
∆Grxn
∆G‡
∆Grxn
∆G‡
∆Grxn
86.3 84.2 88.2 87.4 90.7 91.2 89.3
-174.4 -183.8 -175.2 -173.4 -163.8 -165.5 -168.8
84.3 84.9 85.8 87.9 90.2 91.7 90.7
-175.6 -174.6 -177.1 -170.6 -169.1 -167.9 -168.9
82.0 83.0 83.0 86.3 91.5 91.3 94.4
-191.7 -186.5 -179.6 -179.0 -160.8 -165.3 -154.6
84.5
-176.2
au of charge in its basin (N(ΩH)). After it is transferred to the nitrogen, N(ΩH) ) 0.582 au, meaning that the hydrogen has lost an average of 0.379 au of charge. Over the course of the proton transfer, the nitrogen gains an average of 0.026 au of charge, whereas the selenium gains 0.426 au, implying that the majority of the charge lost by the hydrogen is transferred to the selenium atom. Peroxide Reduction. To determine the effects of changing the electron density on the selenium atom in DMBS, the reaction of substituted systems with hydrogen peroxide was modeled using the same mechanism found in our previous study.32 The reaction energies are outlined in Table 3 and Figure 1, with all energies relative to the infinitely separated reactants. The energy barriers for the substituted DMBSs range from 82.0 to 94.4 kJ/mol, with the unsubstituted DMBS showing a barrier of 84.5 kJ/mol. It is interesting to note that while substitution with electron donating groups (NH2, OCH3, and CH3) did decrease the energy barrier compared to the unsubstituted system, it was a very minor effect, with the largest change being only 2.5 kJ/mol, or less. On the other hand, substitution with electron withdrawing groups (F, CN, CF3, and NO2) had a much larger effect, increasing the barrier by as much as 10 kJ/mol. Within the meta and para substitution patterns, following the series from strongly electron donating to strongly electron withdrawing substituents shows that the energy barrier increases and the stability of the products relative to reactants decreases. In the ortho substitutions, there is no clear trend in energies going from electron donating to electron withdrawing groups, however substitution with electron donating groups generally results in lower barriers than substitution with electron withdrawing groups.
Figure 1. Energy barriers for peroxide reduction reaction with substituted DMBS. Heavy black line indicates barrier of the reaction with the unsubstituted compound.
Figure 2. Charge on selenium atom in the zwitterionic form of DMBS vs Gibbs energy barrier for peroxide reduction reaction.
By comparing the energy barrier for the peroxide reduction reaction to the atomic charge on the selenium atom in the zwitterionic form, calculated using QTAIM, shown in Figure 2, the effect of the charge on the energy barrier can be determined. It is seen that the meta and para substituted systems, as well as the unsubstituted system, follow a linear trend, with an R2 correlation coefficient of 0.91. However, the ortho substitutions are more scattered, with no clear trend. Previous work,34 has shown that ortho substituents can greatly increase the GPx-like activity of benzylamine selenols and attributed this change in activity to a combination of electronic and steric effects. Para substitutions are expected to have similar electronic effects to ortho substitution, but have no contributions from other effects, like sterics. Therefore, comparing the para and ortho substitutions allows one to examine electronic effects in this reaction only and to determine what arises from other effects. The largest and smallest energy barriers observed were for p-NO2 and p-NH2 (the strongest electron withdrawing and electron donating groups included in this study), respectively, indicating that the contribution of electronic effects to this reaction is significant. These same two substituents had the highest and lowest charge on the selenium atom, in the ortho substituted systems, with o-NH2 showing an atomic charge on selenium more than twice that of o-NO2. However, the difference in energy barrier for these two systems is only 3.0 kJ/ mol. This demonstrates that a strongly electron withdrawing or donating substituent adjacent to the selenium moiety has a large effect on the electron density of the selenium atom. However, it is mediated by other effects, such as sterics or polarization of charge induced by a group in close proximity to the reacting center. Some of these effects can be seen in the QTAIM analysis as bond paths between the selenium atom and the substituent, which are found for the o-NH2, o-NO2, and o-CF3 systems. At the Se-substituent BCP, FBCP in the amino and nitro-substituted systems is 0.017 au. The trifluoro-methyl system shows two Se-F bond paths with FBCP of 0.010 and 0.009 au. The presence of these bond paths indicate an interaction between the selenium and the substituent, which will contribute to both electronic and steric effects. The electrostatic potential can provide additional insight into the changes in the electronic environment around the selenium center introduced by ortho substitution. Electrostatic potential diagrams for the zwitterionic form of unsubstituted DMBS and the othro nitro and amino substituted compounds
Selenium Electron Density and the Reduction of H2O2
J. Phys. Chem. A, Vol. 114, No. 39, 2010 10709
Figure 3. Electrostatic potential maps of various systems. Blue isosurface corresponds to an electrostatic potential of 0.2 au and the red isosurface corresponds to -0.04 au. Negative isosurfaces have been faded to show positive regions underneath.
TABLE 4: The Volume of the Selenium Atom in the Zwitterionic Form of Each Molecule, Calculated at the 0.001 au Density Cutoff (in au3) substitution NH2 OCH3 CH3 F CN CF3 NO2 unsubstituted
ortho
meta
para
282.2 278.1 280.4 280.0 276.6 267.6 263.3
288.4 287.1 287.6 286.0 284.4 284.9 283.8
288.2 287.7 287.6 286.6 283.8 284.8 282.5
286.9
are shown in Figure 3. In the unsubstituted system, a large region of negative potential is observed around the selenium atom, in the same area where the hydrogen peroxide interacts with the selenium atom to form the reacting complex. In the other three systems, this region is extended onto the adjacent functional group. Pearson and Boyd,16 have also found an extended region of negative electrostatic potential for o-NO2 substituted ebselen. Although this would not prevent the peroxide from associating with the selenium center, it does present a much larger surface to the peroxide, which makes it less likely that the peroxide would interact with the selenium preferentially. The steric effects arising from ortho substituents can be studied by calculating the atomic volume of the selenium atom, using QTAIM. The meta and para substitutions show only minor changes in atomic volume compared to the unsubstituted DMBS, summarized in Table 4, which arise from the expected contraction or expansion of the atom due
to decreased or increased charge. In the ortho series however, the changes in atomic volume are much more pronounced, showing that functional group proximity has an effect on the volume beyond the small electronic one observed for the other substitutions. The largest decrease in volume is observed for o-NO2 substitution, with an 8% change. The contraction due decreased charge for the other nitro-substituted compounds is about 1.5%, indicating that the change due to steric effects is about 4 times greater than electronic effects. By visualizing the atomic basin of the selenium atom, shown in Figure 4, it is apparent the selenium’s basin is cut off on the edge facing the ortho substituent, resulting in a smaller selenium surface presented to an incoming peroxide. Conclusions Experimental evidence suggests that introducing substituents in the ortho position of tertiary-benzylamine-2-selenol compounds increases their GPx activity, in some cases by as much as an order of magnitude. The introduction of substituents in the ortho, meta, or para positions had little effect on the stability of the zwitterion relative to the selenol form of these compounds. Figure 1 shows that none of the ortho substituents included in this study significantly reduced the energy barrier for the peroxide reduction reaction, although including an amino group, a strongly electron donating group, in the para position does reduce the barrier for this reaction. Atoms in molecules analysis and electrostatic potential maps show that some ortho substituents change the environment around selenium in such a way that it becomes less favorable for the peroxide molecule to form a close association with the selenium center in the molecule.
10710
J. Phys. Chem. A, Vol. 114, No. 39, 2010
Heverly-Coulson and Boyd
Figure 4. Atomic basin of Se at the 0.001 au isodensity envelope.
The increased reactivity observed experimentally for ortho substituted systems likely comes from an increased rate of reaction during regeneration of the oxidized organoselenium compound through hindrance of thiol exchange reactions in the selenylsulfide intermediate.14 In this case, it is expected that ortho substituents provide needed steric bulk, which has only a minor effect on the peroxide reduction reaction, which blocks the thiol exchange reaction by making the sulfur more accessible. Acknowledgment. Hugo Boho´rquez and Jason Pearson are thanked for helpful suggestions and discussions. We gratefully acknowledge the Killam Trusts and the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support. Computational facilities are provided by ACEnet, the regional high performance computing consortium for universities in Atlantic Canada. ACEnet is funded by the Canada Foundation for Innovation (CFI), the Atlantic Canada Opportunities Agency (ACOA), and the provinces of Newfoundland & Labrador, Nova Scotia, and New Brunswick. Supporting Information Available: Transition state energies from zwitterion formation section; bond critical point densities for Se-H and N-H bonds; and atomic charges for Se, H, and N, in the selenol, transition state, and zwitterion discussed in Zwitterion Formation section, additional elec-
trostatic potentials maps (see Figure 3) and Se atomic basin plots (see Figure 4), and Cartesian coordinates for all systems studied are available as Supporting Information. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Rotruck, J. T.; Pope, A. L.; Ganther, H. E.; Swanson, A. B.; Hafeman, D. G.; Hoekstra, W. G. Science 1973, 179, 588–590. (2) Forstrom, J. W.; Zakowski, J. J.; Tappel, A. L. Biochemistry 1978, 17, 2639–2644. (3) Epp, O.; Ladenstein, R.; Wendel, A. Eur. J. Biochem. 1983, 133, 51–69. (4) Rocher, C.; Lalanne, J.; Chaudie´re, J. Eur. J. Biochem. 1992, 205, 955–960. (5) Prabhakar, R.; Vreven, T.; Morokuma, K.; Musaev, D. G. Biochemistry 2005, 35, 11864–11871. (6) Rayman, M. P. The Lancet 2000, 356, 233–241. (7) Nordberg, J.; Arne´r, E. S. J. Free Radical Biol. Med. 2001, 31, 1281–1312. (8) Mu¨ller, A.; Cadenas, A.; Graf, P.; Sies, H. Biochem. Pharmacol. 1984, 33, 3235–3239. (9) Wendel, A.; Fausel, M.; Safayhi, H.; Tiegs, G. Biochem. Pharmacol. 1984, 33, 3241–3245. (10) Engman, L.; Stern, D.; Cotgreave, I. A.; Andersson, C. M. J. Am. Chem. Soc. 1992, 114, 9737–9743. (11) Schewe, T. Gen. Pharmacol. Vasc. Syst. 1995, 26, 1153–1169. (12) Sies, H.; Masumoto, H. AdV. Pharmacol. 1996, 38, 229–246. (13) Mareque, A. M.-M.; Faez, J. M.; Chistiaens, L.; Kohnen, S.; Deby, C.; Hoebeke, M.; Lamy, M.; Deby-Dupont, G. Redox Report 2004, 9, 81– 87.
Selenium Electron Density and the Reduction of H2O2 (14) Sarma, B. K.; Mugesh, G. J. Am. Chem. Soc. 2005, 127, 11477– 11485. (15) Pearson, J. K.; Boyd, R. J. J. Phys. Chem. A 2007, 111, 3152– 3160. (16) Pearson, J. K.; Boyd, R. J. J. Phys. Chem. A 2008, 112, 1013– 1017. (17) Zhao, R.; Masayasu, H.; Holmgren, A. Biochemistry 2002, 99, 8579–8584. (18) Reich, H. J.; Jasperse, C. P. J. Am. Chem. Soc. 1987, 109, 5549– 5551. (19) Wilson, S. R.; Zucker, P. A.; Huang, R.-R. C.; Spector, A. J. Am. Chem. Soc. 1989, 111, 5936–5939. (20) Jacquemin, P. V.; Christiaens, L. E.; Renson, M. J. Tetrahedron Lett. 1992, 33, 3863–3866. (21) Iwaoka, M.; Tomoda, S. J. Am. Chem. Soc. 1994, 116, 2557–2561. (22) Galet, V.; Bernier, J.-L.; Henichart, J.-P.; Lesieur, D.; Abadie, C.; Rochette, L.; Lindenbaum, A.; Chalas, J.; de la Faverie, J.-F. R. J. Med. Chem. 1994, 37, 2903–2911. (23) Back, T. G.; Dyck, B. P. J. Am. Chem. Soc. 1997, 119, 2079– 2083. (24) Mugesh, G.; Panda, A.; Singh, H. B.; Punekar, N. S.; Butcher, R. J. Chem. Commun. 1998, 2227–2228. (25) Wirth, T. Molecules 1998, 3, 164–166. (26) Erdelmeier, I.; Tailhan-Lomont, C.; Yadan, J.-C. J. Org. Chem. 2000, 65, 8152–8157. (27) Mugesh, G.; Panda, A.; Singh, H. B.; Punekar, N. S.; Butcher, R. J. J. Am. Chem. Soc. 2001, 123, 839–850. (28) Back, T. G.; Moussa, Z. J. Am. Chem. Soc. 2003, 125, 13455– 13460. (29) Ren, B.; Huang, W.; Åkesson, B.; Ladenstein, R. J. Mol. Biol. 1997, 268, 869–885. (30) Mugesh, G.; du Mont, W.-W. Chem.sEur. J. 2001, 7, 1365–1370. (31) Reich, H. J.; Cohen, M. L. J. Org. Chem. 1979, 44, 3148?3151. (32) Heverly-Coulson, G. S.; Boyd, R. J. J. Phys. Chem. A 2010, 114, 1996–2000.
J. Phys. Chem. A, Vol. 114, No. 39, 2010 10711 (33) Parnham, M. J.; Biedermann, J.; Bittner, C.; Dereu, N.; Leyck, S.; Wetzig, H. Agents Actions 1989, 27, 306–308. (34) Bhabak, K. P.; Mugesh, G. Chem.sEur. J. 2008, 14, 8640–8651. (35) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; 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.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (36) Becke, A. D. J. Chem. Phys. 1993, 98, 1372–1377. (37) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244?13249. (38) Pearson, J. K.; Ban, F.; Boyd, R. J. J. Phys. Chem. A 2005, 109, 10373–10379. (39) Peng, C.; Schlegel, H. B. Isr. J. Chem. 1993, 33, 449–454. (40) Peng, C.; Ayala, P.; Schlegel, H. B.; Frisch, M. J. Comput. Chem. 1996, 17, 49–56. (41) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154–2161. (42) Gonzalez, C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523–5527. (43) Bader, R. F. W. Atoms in Molecules - A Quantum Theory; Oxford University Press: Oxford, 1990. (44) Matta, C. F.; Boyd, R. J., Eds.; The Quantum Theory of Atoms in Molecules; WILEY-VCH: Weinheim, 2007. (45) Keith,T.A.AIMAll,Version10.03.25;2010(http://aim.tkgristmill.com).
JP105651X
