Olefin Epoxidation by Molybdenum Peroxo Compound: Molecular

Topological analysis of ELF and electron density analysis reveals that all Mo−O bonds in MoO(η2-O2)2OPH3 and MoO2(η2-O2)OPH3 belong to closed-shel...
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514

J. Phys. Chem. A 2011, 115, 514–522

Olefin Epoxidation by Molybdenum Peroxo Compound: Molecular Mechanism Characterized by the Electron Localization Function and Catastrophe Theory Slawomir Berski,*,† Fabrı´cio R. Sensato,*,‡ Victor Polo,§,| Juan Andre´s,⊥ and V. S. Safont⊥ Faculty of Chemistry, UniVersity of Wroclaw, F. Joliot-Curie 14, 50-383 Wroclaw, Poland; Departamento de Cieˆncias Exatas e da Terra, UniVersidade Federal de Sa˜o Paulo, UNIFESP, R. Artur Riedel 275, 09972-270, Diadema, Brazil; Departamento de Quı´mica Fı´sica, UniVersidad de Zaragoza, c/Pedro Cerbuna s/n, 50009 Zaragoza, Spain; Instituto de Biocomputacio´n y Fı´sica de los Sistemas Complejos (BIFI), Edificio CerVantes, Corona de Arago´n 42, Zaragoza 50009, Spain; and Departament de Cie`ncies Experimentals, UniVersitat Jaume I, Apartat 224, 12080, Castello´, Spain ReceiVed: September 4, 2010; ReVised Manuscript ReceiVed: NoVember 23, 2010

The oxygen atom transfer reaction from the Mimoun-type complex MoO(η2-O2)2OPH3 to ethylene C2H4 affording oxirane C2H4O has been investigated within the framework of the Bonding Evolution Theory in which the corresponding molecular mechanism is characterized by the topological analysis of the electron localization function (ELF) and Thom’s catastrophe theory (CT). Topological analysis of ELF and electron density analysis reveals that all Mo-O bonds in MoO(η2-O2)2OPH3 and MoO2(η2-O2)OPH3 belong to closedshell type interactions though negative values of total energy densities Ee(rBCP) imply some covalent contribution. The peroxo OisOj bonds are characterized as charge-shift or protocovalent species in which pairs of monosynaptic basins V3(Oi), V3(Oj) with a small electron population of ∼0.25e each, are localized between core basins C(Oi), C(Oj). The oxygen transfer reaction from molybdenum diperoxo complex MoO(η2O2)2OPH3 to C2H4 system can be described by the following consecutive chemical events: (a) protocovalent peroxo O2-O1 bond breaking, (b) reduction of the double C1dC2 bond to single C1-C2 bond in ethylene, (c) displacement of oxygen O1 with two nonbonding basins, Vi)1,2(O1), (d) increase of a number of the nonbonding basins to three (Vi)1,2,4(O1)); (e) reorganization and reduction in the number of nonbonding basis to two basins (Vi)1,4(O1)) resembling the ELF-topology of the nonbonding electron density in oxirane, (e) formation of the first O1-C2 bond in oxirane, (f) C2-O1sC2 ring closure, (g) formation of singular nonbonding basin V(O2) in new ModO2 bond. The oxygen atom is transferred as an anionic moiety carrying a rather small electronic charge ranging from 0.5 to 0.7e. 1. Introduction Oxygen atom transfer reactions, OAT, belong to an important class of chemical processes in organic chemistry.1 Epoxidation of olefinssoxygenation of alkenes to form cyclic epoxide groupssis a very outstanding OAT reaction in organic synthesis inasmuch as the epoxy compounds are widely used as intermediates in the large-scale synthesis of a wide variety of highdemand commodity chemicals. In particular, the annual production capacity of propylene oxide is reported to be approximately 7.2 million tons.1 Catalytic epoxidation of olefins affords an interesting production technology and transition metal complexes play an important role in these processes.2,3 The use of Mo(VI) complexes came to prominence after the discovery in 1969 by Mimoun and co-workers of stable oxo-diperoxo metal complexes [MO(η2-O2)2Ln] (M ) Mo, W; L ) HMPA, DMF, pyridine, etc., and n ) 1,2)4-6 capable of epoxiding olefins. Since then, there has been some variation of the Mimoun molybdenum complex in order to optimize its epoxidizing power * To whom correspondence should be addressed. E-mail: sberski@ wchuwr.chem.uni.wroc.pl; [email protected]. † Faculty of Chemistry, University of Wroclaw. ‡ Departamento de Cieˆncias Exatas e da Terra, Universidade Federal de Sa˜o Paulo. § Departamento de Quı´mica Fı´sica, Universidad de Zaragoza. | Instituto de Biocomputacio´n y Fı´sica de los Sistemas Complejos (BIFI), Edificio Cervantes. ⊥ Departament de Cie`ncies Experimentals, Universitat Jaume I.

(for review and prominent examples, see refs 7-15). Indeed, molybdenum peroxo complexes have been widely used as either stoichiometric reactants or as catalysts (nearly always formed in situ) in conjunction with terminal oxidants such as H2O2 or organic peroxides or dioxygen, via homogeneous as well as heterogeneous routes. In addition to oxidizing olefins,2,10,16-19 Mimoun compounds are rather strong oxidants of a large variety of organic substrates, such as alkyl benzenes,16,20 amines,21,22 alcohols,17,23 sulfides,24-30 and other chalcogenides,31 as well as isomerization of allylic alcohol,32 etc. In this regard, the use of molybdenum peroxo complexes can be considered as one of the most inexpensive, environmentally benign, and industrially feasible methods of oxidizing olefins. Even stoichiometric oxidation can be considered ecologically benign inasmuch as the complex can be stoichiometrically recovered in the presence of hydrogen peroxide and reused to oxidize a new batch of substrates, showing catalytic efficiency and yielding water as a byproduct.10,28 Furthermore, the rigid “butterfly” geometry of the MoO(O2)2 moiety indicates a potential for storing stereochemical information and the asymmetric epoxidation of prochiral olefins can be achieved with Mimoun-type complexes bearing a chiral ligand.33 As far as the mechanism of stoichiometric olefin epoxidation mediated by Mimoum-type complexes is concerned, two limiting hypotheses have dominated the discussion. The first is due to Mimoun,5 who suggested that the olefin coordinates to the metal center before subsequent insertion into the Mo-O bond

10.1021/jp108440f  2011 American Chemical Society Published on Web 12/29/2010

Olefin Epoxidation by Molybdenum Peroxo Compound to form a five-member metallacycle which in turn decomposes into the epoxide and an oxo complex and, therefore, a stepwise mechanism takes place (stepwise reaction course). Sharpless34 however suggested a reaction mechanism involving a direct attack by the olefin on the peroxo oxygen atom along with a three member ring intermediate (concerted reaction course). Recent computational studies35-37 have found the Sharpless mechanism to be favored in this reaction: the direct attack of the nucleophilic olefin on an electrophilic peroxo oxygen center via a transition state of spiro structure requires a lower activation energy than the stepwise insertion mechanism. From a frontier molecular orbital standpoint, the process has been described as the interaction of the π(C-C) HOMO of ethylene and the unoccupied O-O antibonding orbital σ*(O-O) of the peroxo complex.35,37 Furthermore, the corresponding TS is reputed to be coarctate (e.g., refs 35 and 36) in which the reaction proceeds by breaking and making two bonds at one or more atoms at a time. Within the framework of our ongoing work on OAT reactions mediated by peroxo metal complexes, we previously investigated, using density functional calculations, the structural and electronic aspects of Mimoun-related peroxo complexes11,38 and their reactivity toward the oxidation of both simple39 and unsaturated sulfides.40 In order to obtain a deeper understanding on OAT reactions related to the oxygen transfer from molybdenum peroxo complexes to olefins, we have, in this work, characterized each elementary chemical process (i.e., bond forming/breaking processes, electron density rearrangements, creation/annihilation of lone pairs, among others) occurring along the channel connecting reactants with products, and the corresponding energetic supply for each elementary process was also determined. For this purpose, we based our work on the framework of the bonding evolution theory, BET, developed by Krokidis et al.41 This approach combines the topological analysis of the electron localization function, ELF (η(r)),42-44 and Thom’s catastrophe theory, CT.45 The topological analysis of ELF provides a partition of the molecular space in different localizations (basins) which are consistent with chemically meaningful entities as atomic cores, bonds, and lone pairs. Thom’s catastrophe theory, in turn, renders how the equilibrium of a gradient system changes as the control parameters, e.g., the set of nuclear coordinates, change. Indeed, in BET approach each elementary chemical event along the stationary points on the IRC path is characterized through ELF analysis and the corresponding changes occurring in its topology are classified via Thom’s catastrophe theory. In fact, we have successfully mapped out some organic reactions using this methodology46-53 and in the present work, we report the first BET study on a chemical reaction involving a transition metal complex. 2. Model and Computational Details In our theoretical approach, the model complex MoO(η2-O2)2OPH3 was taken for representing the Mimoun-type compound, whereas the olefin molecule was described by the ethylene model, C2H4. In such OAT reaction, the oxo-diperoxo complex MoO(η2-O2)2OPH3 transfers an oxygen atom to the C2H4 molecule yielding the corresponding oxo-monoperoxo complex MoO2(η2-O2)OPH3 and ethylene epoxide. All quantum chemical calculations were performed within the framework of density functional theory at B3LYP54,55 level as implemented in the Gaussian0356 program. The H, C, O, and P atoms were described using standard 6-311G(d,p) basis set57 and the Mo atom with the triple-ζ basis set of Ahlrichs58 (TZVPalls2; (19s14p9d)/[8s6p5d]) augmented with single set

J. Phys. Chem. A, Vol. 115, No. 4, 2011 515 of f- polarization functions. We have chosen an all-electron basis set for Mo to achieve clear description of electron localization in the core region. The molecular structure of all compounds was fully optimized. The transition state was characterized to have the correct type of vibrational eigenvalues. Starting with TS geometries, calculations of the Intrinsic Reaction Coordinates (IRC)59 were carried out to identify the related reactants and products. The points on the IRC path were calculated with steps of 0.1 [amu1/2bohr] and due to convergence problems only a range from -1.2 to 2.7 amu1/2bohr has been analyzed. A topological analysis of the electron density and electron localization function have been performed by means of the EXT94b program of the AIMPAC60 suite and TopMod.61,62 The calculations of the basin populations for ELF were carried out for a rectangular parallelepipedic grid and the step size of about 0.1 bohr. All molecular pictures were constructed with Molekel63 and ChemCraft.64 3. Results and Discussion 3.1. Energetic and Geometrical Parameters. A common characteristic in this kind of Mimoun complexes is that the molybdenum atom is surrounded by six atoms in a nearly pentagonal-bipyramidal geometry with the bidentate peroxo moieties and the -OPH3 ligand lying within the distorted pentagonal plane while the doubly bonded oxo group occupy the axial position. The two peroxo ligands are asymmetrically side-bound to the Mo center in an η2 fashion. For the sake of clarity, the oxygen atoms nearest to the equatorial ligand are sometimes referred to as cis oxygen atoms, Ocis, while the other oxygen atom of the same peroxo moiety (trans to the -OPH3 ligand) is called the trans oxygen atom, Otrans. The optimized structures of isolated MoO(η2-O2)2OPH3, MoO2(η2-O)OPH3, C2H4, C2H4O, and transition state (TS) for the studied reaction are presented in Figure 1. In MoO(η2-O2)2OPH3, the calculated bond distances are as follows: d(O1-O2) ) d(O5-O6) ) 1.45 Å; d(Mo-O3) ) 1.69 Å; d(Mo-OPH3) ) 2.18 Å; d(Mo-O2) ) d(Mo-O5) ) 1.90 Å and d(Mo-O1) ) d(Mo-O6) ) 1.93 Å. As far as the transition state characterization is concerned, we have assumed that the reaction involves a direct attack of the olefin on a peroxo oxygen atom trans to the -OPH3 ligand (i.e., O1 oxygen atom) via Sharpless’ mechanism (see Figure 1) as has been shown to be the case for this process.35,37 In TS, the O1 atom that is to be transferred to the ethylene molecule is 2.08 Å away from the C2 and 2.20 Å from the C1. The main structural features of the OAT process are as follows: the C-C olefin double bond is lengthened by 0.04 Å, whereas the attacked peroxo bond O1-O2 is significantly lengthened by 0.35 Å. The Mo-O1 bond is elongated by 0.07 Å, while the Mo-O2 is shortened by 0.06 Å on the way to an Mo-O double bond. The calculated structure reproduces the predicted one in previous studies in whichthesamemolybdenumperoxocomplexwasconsidered.35,39,40 The reaction energy, ∆E, for this reaction was calculated to be -35.2 kcal/mol, while a value of 13.4 kcal/mol was obtained for the corresponding energy barrier, ∆E‡. After transferring an oxygen atom to the olefin molecule, the oxo-diperoxo molybdenum complex converts into a dioxomonoperoxo complex and the corresponding calculated bond lengths are as follows: d(O5-O6) ) 1.45 Å; d(Mo-O3) ) 1.73 Å; d(Mo-O2′) ) 1.70 Å; d(Mo-O5) ) 1.97 Å; and d(Mo-O6) ) 1.91 Å. 3.2. Topological Analysis of Stationary Points. To the best of our knowledge, there is only one report on the topological characterization of the metal-peroxo function, which is due to

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Figure 1. Calculated structures of reactants, TS, and products corresponding to the investigated OAT reaction (MoO(η2-O2)2OPH3 + C2H4 f MoO2(η2-O2)OPH3 + C2H4O).

Figure 2. Critical points of index 0 (valence and core attractors) localized by topological analysis of the Electron Localization Function η(r) field for MoO(η2-O2)OPH3, MoO2(η2-O2)OPH3 C2H4, C2H4O, and TS.

Macchi and co-workers9 who investigated the chemical bonding properties in MoO(O2)(HMPA)(dipic) and some related prototype transition metal complexes, molecules, and ions. In their study, chemical bonding properties were rationalized within the framework of the quantum theory of atoms in molecules (QTAM),65 through topological analysis of theoretical and experimental electron densities (ED). The corresponding topological ED analysis revealed that the Mo-Operoxo bond contains considerable covalent character with a short Mo-O distance, a large electron density along the bond path, and a negative energy density at the bond critical point (bcp). In this work, valence and core attractors localized in the ELF field for the reactants, products, and TS are shown in Figure 2. The peroxo moieties (O1-O2; O5-O6) are characterized by pairs of monosynaptic nonbonding basins V3(Oi)1,2) and V3(Oi)5,6) localized between oxygen cores C(Oi) approximately on lines joining oxygen nuclei. Previously, similar ELF-topology has been recognized in F2,66 the O2-2 anion, NbO5- 67 and classified as “charge-shift” bonds68 or “protocovalent bond”. All corre-

sponding localization basins in MoO(η2-O2)2OPH3 are depicted at Figure 3 and the basin populations are included in Table 1. Each peroxo bond “contains” about 0.5e (2 × 0.25e) and most of the valence electron density is concentrated in the lone electron pairs V1(Oi) and V2(Oi) with a total population ∼6.2e. In the valence region of the oxygen O4 bound to the PH3 group, there are four ELF-localization basins: two lone electron pairs Vi)2,3(O4) with a total population of 4.88e, a single bonding basin V(P,O4) corresponding to the P-O4 bond with 1.74e and a single basin V1(O4) with 1.06e localized approximately on a line joining Mo and O4 nuclei. In the case of the O3 atom, a single nonbonding basin V(O3) corresponds to three (formal) lone electron pairs with 7.0e. Topological charges based on the j ) yield: +3.4e (Mo), -1.1e (O3), -1.79e basin populations (N (O4) (assuming that the V(P,O4) basin is formed only by electrons from the O4 atom) and -0.56 (O2, O5) and -0.62e (O1, O6) for the peroxo oxygen atoms. Interestingly, there are not any valence bonding attractors of the disynaptic type V(Mo,Oi)1,6) in regions of formal Mo-Oi)1,6 bonds and thus

Olefin Epoxidation by Molybdenum Peroxo Compound

J. Phys. Chem. A, Vol. 115, No. 4, 2011 517 In both molecules, the peroxo bonds Oi)2,5-Oi)1,6 are described with CPs of index 1 (bond critical point, BCP), large values of the electron density at BCP (1.912 e/Å3 and 1.858 e/Å3 for di- and monoperoxo complexes, respectively) which are the largest among all BCPs analyzed and positive values of the electron density Laplacian 32FBCP (2.987e/Å5; 3.478, 2.987e/ Å5, respectively). The computed values of FBCP are similar to those calculated by Macchi et al.9 for O-O single bonds in the monoperoxo complex MoO(O2)(HMPA)(dipic) (∼1.9 e/Å3), which is found to be comparable to those for C-C single bonds. High values of F(rBCP) are accompanied by relatively large values (0.707, 0.698) of ELF η(F(rBCP)). The energy densities EeBCP are negative (-1.51 hartree/Å3 ave) with prevailing potential energy contributions. Positive values of 32FBCP suggest “closed-shell” interactions between the peroxo oxygen atoms, whereas EeBCP and η(F(rBCP) values are typical for “shared” interactions. Therefore, the peroxo bonds Oi)2,5-Oi)1,6 may be classified as intermediate between both types. In MoO2(η2O2)OPH3 with only one peroxo bond, the value of F(rBCP) is smaller than that found in MoO(η2-O2)2OPH3 and such difference is reflected by the ELF analysis. All Mo-Oi bond paths that reflect the chemical bonds in the sense of Bader65 exhibit F(rBCP) values in the range from 0.922 e/Å3 (Mo-Oi)1;5) to 1.830 e/Å3 (ModO3). The smallest values of F(rBCP) and η(F(rBCP)) are calculated for the Mo-O4 bonds (0.51 e/Å3 ave and 0.17 ave) where O4 is bound to the atoms P and Mo with positive and small values of 32FBCP (8.0 e/Å5 ave) in agreement with values for ionic interactions, e.g., for LiCl (F(rBCP) ) 0.311 e/Å3, 32FBCP ) 6.403 e/Å5).69 This conclusion supports our interpretation of the V1(Mo,O4) basin as being rather of the monosynaptic type V1(O4). A small deviation from ionic characteristics stems from very small but negative values of total energy density EeBCP (-0.59 hartree/Å3, ave) which would imply small contribution of covalency. In the case of the Mo-Oi)1,6, Mo-Oi)2,5 bonds the F(rBCP) values are larger than for the Mo-O4 bonds, namely, 0.944 e/Å3

Figure 3. Plot of Electron Localization Function (ELF) for MoO(η2O2)2OPH3.

on the basis of the chemical bond classification derived from the topological analysis of ELF,43 all Mo-Oi)1,6 bonds belong to the closed-shell type of interactions. We emphasize that all valence attractors of oxygen atoms are localized outside formal Mo-Oi)1,6 bonds that can be explained by the large Pauli repulsion between electrons of Mo and six Oi atoms. Furthermore, it explains why the basin populations of Vi(Oi) are larger that formal values of lone electron pairs (2.0e)sthe electron density is “repelled” from regions of the Mo-Oi)1,6 bonds to the lone electron pairs. Similar ELF-topology is observed for MoO2(η2-O2)OPH3 and all Mo-Oi)1,6 are of the donor-acceptor type with valence attractors “outside” formal bonds. A complementary analysis has been carried out for the electron density F(r) field within the AIM formalism and all critical points (CP) localized in MoO(η2-O2)2OPH3 and MoO2(η2O2)OPH3 are shown at Figure 4. The topological data are reported in Table 2.

j ) in e for Different Points on the IRC Patha TABLE 1: Basin Populations (N basin/distance

MoO6PH3 + C2H4

sd ) -1.2

s ) -0.5

TS

s ) 1.0

s ) 1.2

s ) 1.8

r(O1 · · · O2)[Å] r(O1 · · · C2)[Å] r(O1 · · · C1)[Å] V1(C1,C2) V2(C1,C2) V(C1,O1) V(C2,O1) V1(O1) V2(O1) V3(O1) V4(O1) C(Mo) V1(O2) V2(O2) V3(O2) V(O3) V1(O4) V2(O4) + V3(O4) V(P,O4) V1(O5) V2(O5) V3(O5) V1(O6) V2(O6) V3(O6)

1.439

1.598b 2.391 2.281 1.56 1.82

1.681 2.307 2.194

1.789 2.199 2.083

1.961 2.021 1.896

1.987 1.993 1.866

2.065 1.907 1.778

1.69 1.69

}3.24

}2.96

}2.87

}2.89

MoO5PH3 + C2H4O 2.732c 1.566 1.446

1.428 1.428

}2.66

}2.04

}1.90

0.14

0.74 1.10 2.93

0.99 0.99 2.66

3.14 3.08 0.23

3.23 3.21

3.20 3.28

3.33 3.15

3.35 1.69

4.93

3.89

38.59 3.14 3.08 0.26 7.00 1.06 4.88 1.74 3.16 3.09 0.26 3.14 3.08 0.23

38.79 3.37 3.28

38.74 3.40 3.32

38.53 3.48 3.35

1.54 38.72 3.60 3.33

1.63 38.72 3.64 3.36

2.66 38.77 3.67 3.34

2.53 38.76

2.66 38.54

}6.98

}7.01

6.80 1.06 4.89 1.77 3.16 3.03 0.25 3.12 3.11 0.24

6.82 1.12 4.88 1.77 3.17 3.04 0.25 3.10 3.11 0.26

6.97 1.23 4.72 1.75 3.15 3.09 0.25 3.13 3.13 0.25

6.84 1.33 4.67 1.78 3.14 3.06 0.24 3.11 3.11 0.26

6.83 1.39 4.65 1.79 3.11 3.06 0.24 3.11 3.09 0.26

6.84 1.46 4.54 1.75 3.10 3.08 0.24 3.12 3.14 0.27

6.84 1.35 4.63 1.83 3.11 3.11 0.25 3.13 3.11 0.27

7.05 1.10 4.84 1.73 3.16 3.13 0.21 3.16 3.10 0.25

a The protonated basins V(Ci)1,2-Hj) and core basins C(X), X ) C, O, and P have been omitted for clarity. b First point on the IRC path. Point localized scanning r(O2-O1) distance and optimizing other geometrical parameters. d The variable s ) steps in amu1/2 bohr along the reaction path.

c

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Figure 4. Critical points of index 0 (nuclear attractors), 1 and 2 localized in the electron density F(r) field for MoO(η2-O2)2OPH3 and MoO2(η2O2)OPH3.

TABLE 2: Topological Data for the Bond Critical Points of Index 1 (BCP) for the Mn-O and O-O Bonds in the MoO(η2-O2)2OPH3 and MoO2(η2-O2)OPH3 Moleculesa,b,c,d,e,f bond

F(rBCP) 32F(rBCP) Ee(rBCP) G(rBCP) G/F [e/Å3] η(rBCP) [e/Å5] [hartree/Å3] [hartree/Å3] [hartree/e]

O1-O2 O5-O6 Mo-O1 Mo-O2 Mo-O5 Mo-O6 ModO3 Mo-O4

1.912 1.912 0.944 1.012 1.012 0.944 1.830 0.478

0.707 0.707 0.305 0.322 0.322 0.305 0.448 0.145

O5-O6 Mo-O5 Mo-O6 ModO2 ModO3 Mo-O4

1.858 0.881 1.030 1.795 1.657 0.537

0.698 0.283 0.324 0.433 0.414 0.197

MoO(O2)2OPH3 2.987 -1.523 2.987 -1.523 11.42 -1.100 11.94 -1.190 11.94 -1.190 11.42 -1.100 17.05 -2.444 7.70 -0.553 MoO2(O2)OPH3 3.478 -1.485 11.16 -1.037 12.12 -1.228 17.56 -2.434 17.03 -2.216 8.31 -0.626

1.314 1.314 0.301 0.355 0.355 0.301 1.251 0.030

0.68 0.68 0.32 0.35 0.35 0.32 0.68 0.06

1.242 0.255 0.359 1.206 1.025 0.043

0.67 0.29 0.37 0.67 0.62 0.08

a F(rBCP), the electron density at rBCP. b η(rBCP), the electron localization function value at rBCP. c 32F(rBCP), the trace of the Hessian of the electron density at rBCP. d Ee(rBCP), the energy density at rBCP. e G(rBCP), the Hamiltonian kinetic energy density at rBCP. f G/F ≡ G(rBCP)/ F(rBCP), the kinetic energy per electron at rBCP.

and 1.012 e/Å3 for Mo-Oi)1,6 and Mo-Oi)2,5, respectively, in (MoO(η2-O2)2OPH3) and 0.881 e/Å3 and 1.030 e/Å3 for Mo-O5 and Mo-O6, respectively, in (MoO2(η2-O2)OPH3). The Laplacian 32F(rBCP) values are positive (11.66 e/Å5 ave) revealing that the electron density is lower than the average electron density in the vicinity but the total energy density is negative (EeBCP ) -1.14 hartree/Å3 ave) suggesting that Mo-Oi bonds involved in the interaction with peroxo groups, similar to Mo-O4, are intermediate between ionic and covalent types. The calculated values are in line with those calculated by Macchi et al.9 for the Mo-Operoxo bonds in MoO(O2)(HMPA)(dipic), namely, F(rBCP) ) 0.95 e/Å3 (ave) and 32F(rBCP)) ∼12 e/Å5 (ave). Furthermore, a comparison with the Mo-O4 bonds reveals that Mo-Oi)1;2, Mo-Oi)5;6 exhibit “closed-shell” type but shifted toward the “shared” interactions. The F(rBCP) values for ModOoxo bonds in MoO(η2-O2)2OPH3 (ModO3) and MoO2(η2-O2)OPH3 (ModO2 and ModO3) are large (1.830 and 1.76 e/Å3, respectively) and the corresponding values of η(F(rBCP)) are larger than those computed for others

Mo-Oi bonds. Since the Laplacian 32F(rBCP) is large (17.21 e/Å5 ave) and positive, they belong to “closed-shell” interactions but the electronic energy density EeBCP, which is large and negative (-2.36 hartree/Å3 ave), implies that the ModOoxo bonds have the largest contribution of covalency among all studied Mo-Oi bonds and may be considered as dative bonds. 3.3. Topological Analysis of the Reaction Path. The oxygen transfer reaction from MoO(η2-O2)2OPH3 to C2H4 consists of several well-defined steps as denoted on the IRC path (see Figure 5). The calculated reaction path (s) ranges from -1.1 to 2.7 amu1/2bohr. At the beginning of the reaction, when the r(O1-O2) distance gradually increases and system evolves toward the TS, the peroxo O1-O2 bond is broken and two monosynaptic basins, V3(O1) and V3(O2), localized “inside” the bond, disappear. The electron densities from V3(O1) and V3(O2) basins are redistributed to the oxygen lone pairs Vi)1,2(O1) and Vi)1,2(O2) “outside” the peroxo bond. At the first point (s ) -1.1 amu1/2bohr) corresponding to r(O1 · · · O2) ) 1.598 Å, r(O1 · · · C1) ) 2.281 Å and r(O1 · · · C2) ) 2.391 Å the basin populations of Vi)1,2(O1) and Vi)1,2(O2) are 3.23e and 3.21e, respectively, and the atomic charge of O1 is -0.47e. Assuming that reorganization mechanism of the valence basins is similar to that identified by Llusar and co-workers66 for the F-F protocovalent bond dissociation, one can expect two subsequent fold catastrophes. It is interesting to note that the double C1dC2 bond in ethylene molecule is described with two disynaptic basins Vi)1,2(C1,C2) and the other peroxo bond (O5-O6) are not perturbed and their ELF-topology correspond to that of the isolated molecules. At s ≈ -0.5 amu1/2bohr, r(O1 · · · O2) ) 1.681 Å, r(O1 · · · C1)) 2.194 Å, and r(O1 · · · C2)) 2.307 Å, the two valence basins V1(C1,C2), V2(C1,C2) of C2H4 are joined into a single basin V1∪2(C1,C2) with 3.24e. From a topological point of view, the double C1dC2 bond in ethylene is “reduced” to single type bond C1-C2. However, the value of N, which is much larger than 2e, suggests that the C1-C2 bond still has properties of a double bond. Such a chemical event is related to a cusp-type catastrophe in which two critical points of index 0 and one of index 1 yield a new critical point of index 0. In comparison to the point at s ) -1.1 amu1/2bohr, one observes an electron depletion in the C1dC2 bond by 0.14e. A maximum of ELF in the region of the C1-C2 bond is found outside the approximate σh symmetry

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Figure 5. A fragment of the IRC path with marked domains of the structural stability (steps) and the points on the total energy curve achieved by means of a relaxed scan of the O2 · · · O1 distance. The points on the IRC path are interpolated with second order polynomial (R2 ) 1.014).

Figure 6. Plot of Electron Localization Function (ELF) for the transition state of the MoO(η2-O2)2OPH3 + C2H4 f MoO2(η2-O2)OPH3 + C2H4O reaction.

plane of C2H4 (Figure 6) which suggests an increase of the Pauli repulsion between electron density of C2H4 and that of O1 atom. The valence electron density of O1 is characterized by two nonbonding basins Vi)1,2(O1) with the ELF-topology similar to that in isolated MoO(η2-O2)2OPH3. Their basin populations are 3.20 and 3.28e while the corresponding atomic charge is -0.49e. In this step, the peroxo bond is broken, the C2dC1 bond is “reduced” and the electron density is continuously concentrated in the O1 · · · C2 and O1 · · · C1 regions but a new O1-C2 bond is not yet formed. Since the same ELF-topology is observed for the transition state (Figure 2) one may conclude that the oxygen transfer reaction is a nonconcerted process inasmuch as the O1-O2 bond breaking and O1-C1 bond formation do not occur simultanelously. This step has been identified for 15 points on the IRC path (Figure 5) and Etot initially increases by 1.38 kcal/ mol to get TS and decreases by ∼5.06 kcal/mol to reach the next catastrophe. The basin population of the C1dC2 bond decreases to 2.96e. It is worth noting that from the ELF point of view, the corresponding TS for this reaction is not coarctate, as has been claimed,35 inasmuch as the reaction does not proceed by breaking and making of two bonds at one or more atoms at time. The nonbonding electron density and electron pairing in the valence shell of oxygen O1 changes qualitatively at s ≈ 1.0 amu1/2bohr for r(O1 · · · O2) ) 1.961 Å, r(O1 · · · C1) ) 1.896 Å, and r(O1 · · · C2) ) 2.021 Å, where a new monosynaptic nonbonding basin V4(O1) appears in the valence shell of O1.

An ELF-topology of the oxygen atom being transferred is now characterized with three nonbonding basins V1(O1), V2(O1), and V4(O1), as shown at Figure 7 with the basin populations 3.35, 1.69, and 1.54e, respectively. It is a maximal perturbation of the oxygen valence shell observed on the IRC path. The atomic charge corresponds to -0.61e and the V4(O1) basin is localized approximately between C(Mo) and C(C1) core basins. The presence of a new V4(O1) basin suggests that the electronic structure of O1 resembles that in the C2H4O molecule because the position of the V4(O1) attractor is very similar to the position of V1(O1) in isolated C2H4O. From a chemical point of view, one may state that O1 is effectively polarized both by MoO(η2O2)OPH3 and C2H4 molecules. This step is very short with only one point on the IRC path. At s ≈ 1.2 amu1/2bohr, which corresponds to the following bond lengths: r(O1 · · · O2)) 1.987 Å, r(O1 · · · C1) ) 1.866 Å, and r(O1 · · · C2) ) 1.993 Å, the nonbonding monosynaptic basin V2(O1) disappears in a fold catastrophe. The electron density of V2(O1) is now distributed in two basins V1(O1) and V4(O1) with values of the basin population of 4.93 and 1.63e, respectively. The atomic charge of O1 equals -0.57e. The location of both nonbonding basins resembles the positions of the lone electron pairs in oxirane. An observed reorganization (Figure 7) of the electron density and electron localization in both the previous step and this step is required to form the donor-acceptor bonds between O1 and C1, C2 atoms. The first chemical bond between C2H4 and O1 atom is formed at s ≈ 1.8 amu1/2bohr corresponding to r(O1 · · · O2) ) 2.065 Å, r(O1-C1) ) 1.778 Å, and r(O1 · · · C2)) 1.907 Å. The disynaptic bonding basin V(C1,O1) is formed between C(C1) and C(O1) core basins with the corresponding attractor localized at 1.06 Å from C(O1) and 0.72 Å from C(C1). The basin population of V(C1,O1) equals 0.14e. In comparison to the previous step, one observes an “equilibration process” between the V1(O1) and V4(O1) basins since the electron density flows (∼1e) from V1(O1) j is 3.89 and 2.66e, respectively. The to V4(O1) for which N second bond O1-C1 is not yet established what can be associated with larger interatomic distance r(O · · · C2) ) 1.91 Å. The covalent bond C1-C2 is characterized by a single disynaptic basin V(C1,C2) with the basin population reduced to 2.66e. In the next steps (s > 2.7 amu1/2bohr), the second covalent bond (O1-C1) between C2H4 and O1 atom is established. Because we were unable to locate its position on the IRC path,

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Figure 7. ELF profile along the IRC path related to the OAT reaction from MoO(η2-O2)2OPH3 to ethylene molecule.

a relaxed scan of the potential energy scan has been performed for the r(O2-O1) distance. The corresponding change of the total energy is presented in Figure 5. The IRC and energy scan paths differ when the system evolves toward TS. However, at larger distances, the pseudoreaction coordinate description seems to be reliable. A formation of the O1-C2 bond with the bonding disynaptic basin V(O1,C2) is observed when r(O1-C1) and r(O1-C2) correspond to 1.446 Å and 1.566 Å, respectively, with an O2 · · · O1 separation of 2.732 Å. In the most probable mechanism, the Vj(O1) basin changes from monosynaptic V(O1) to disynaptic V(O1,C1). From a chemical point of view, the reaction has finished and both chemical bonds O1-C1 and O1-C2 in oxirane are established. Inasmuch as the ELF-topology of the isolated MoO2(η2-O)OPH3 molecule reveals only one monosynaptic nonbonding basin V(O2), an additional cusp catastrophe is expected to occur in which two basins, V1(O2) and V2(O2), are joined into a single basin,V(O2). In oxirane (Figure 2) one can distinguish six valence ELFbasins: V1∪2(C1,C2) with 1.9e corresponding to classical single C1-C2 bond, V(C1,O1), V(C2,O1) with 0.99e characterizing two covalent-polarized Ci)1,2-O1 bonds, two nonbonding monosynaptic basins V1(O1), V4(O1) of oxygen lone electron pairs with 2.66e and four protonated basins V(Ci)1,2-Hj) with 2.12e (C-H bonds). The small basin populations of the Ci)1,2-O1 bonds reflect the oxygen polarization effect since valence electrons are “repelled” from the bonds and concentrated in the lone electron pairs Vi)1,4(O1). In comparison to ethylene, the basin population of the C1-C2 bond in oxirane is reduced by 1.48e. It is interesting to note that an ELF-representation of the bonding in C2H4 and C2H4O corresponds to classical Lewis representation, i.e., single valence V(X,Y) basin corresponds to single Lewis X-Y bond. When the reaction is terminated, the populations of ELFbasins (Table 1) calculated for MoO2(η2-O2)OPH3 are similar to those in MoO(η2-O2)2OPH3. An exception is the O2 atom, which after oxygen transfer accepts 0.79e and three nonbonding basins Vi)1,2,3(O2) are joined into a single basin V(O2) with

7.01e. The ELF-topology of valence electrons in O2 is reorganized throughout the reaction and when the ModO2 bond is formed, its ELF-topology is similar to that of the ModO3 moiety. In both MoO(η2-O2)2OPH3 and MoO2(η2-O2)OPH3 the ELF-topological description of the chemical bonds differs from classical Lewis representations. 4. Conclusions During the oxygen transfer reaction from molybdenum diperoxo complex MoO((η2-O2)2OPH3 to C2H4 the electron density undergoes large redistribution through inter- and intramolecular channels. In C2H4, the C2dC1 bond is gradually electron depleted and its basin population decreases from 3.38e to 1.90e in C2H4O. Electron charge flows from CdC to O1-C1 and O1-C2 bonds, while the corresponding basin population increases from 0.14e (V(C1,O1)) to 0.99e. The oxygen atom is transferred from MoO(η2-O2)2OPH3 to C2H4 as an anionic moiety carrying a small electronic charge ranging from 0.5 to 0.7e. In isolated MoO(η2-O2)2OPH3, the atomic charge on the oxygen atom is 0.56e (including the V1(Oi), V1(Oj) basins of the peroxo OisOj bonds). At the beginning of the IRC path (r(O1 · · · O2) ) 1.598 Å) δ ) -0.47e, at TS -0.58e, at the point of maximum distortion of the oxygen O1 valence shell reflected by three Vi)1,2,4(O1) basins (r(O1 · · · O2) ) 1.961 Å) -0.61e, after reorganization of Vi)1,2,4(O1) to two V1(O1), V4(O1) basins (r(O1 · · · O2)) 1.987 Å) -0.57e and at the last point (r(O1 · · · O2)) 2.052 Å, r(O1 · · · C2) ) 1.792 Å) before formation of the V(O1,C2) basin -0.57e. An interesting step observed on the IRC path is the reorganization of the nonbonding basins Vi(O1) from an arrangement in MoO(η2-O2)2OPH3sbeing the consequence of the peroxo O2 · · · O1 bondingsto that suitable for formation of donor-acceptor bonds O1-C1, O1-C2 in oxirane. A picture of ELF-basins achieved for the reacting system and their reorganization along the IRC path reveals the mechanism which supports the proposal by Sharpless and co-workers34

Olefin Epoxidation by Molybdenum Peroxo Compound where one of the peroxo oxygens is transferred to the olefin. However, from an ELF standpoint, the transition state was not found to be coarctate inasmuch as the corresponding reaction does not involve atoms at which two bonds are made and broken simultaneously. Indeed, the transition state has the ELFtopology, which is also recognized for all points on the IRC path between s ≈ -0.5 and 1.0 amu1/2bohr where the peroxo O1-O2 bond is already broken but new C1-O1, C2-O1 bonds are not yet formed. Acknowledgment. F.R.S. acknowledges FAPESP and CNPQ funding agencies. J.A. and V.S.S. thanks support by the Ministerio de Ciencia y Tecnologia (MCyT), DGICyT (Project CTQ2009-14541-C02-01), Generalitat Valenciana (Project PROMETEO/2009/053) and the Universitat Jaume I-Fundacio´n Bancaixa (P1.1B2007-25 and P1.1B2008-37). The authors thank the Wroclaw Centre and the Servei d’Informatica, Universitat Jaume I, for Networking and Supercomputing for generous allocation of computer time. References and Notes (1) Weissermel, K.; Arpe, H.-J. Industrial Organic Chemistry; Wiley: New York, 2003. (2) Jorgensen, K. A. Chem. ReV. 1989, 89, 431–458. (3) Adam, W.; Malisch, W.; Roschmann, K. J.; Saha-Moller, C. R.; Schenk, W. A. J. Organomet. Chem. 2002, 661, 3–16. (4) Mimoun, H.; Deroch, I. S.; Sajus, L. Bull. Soc. Chim. Fr. 1969, 1481–1492. (5) Mimoun, H.; Roch, I. S. D.; Sajus, L. Tetrahedron 1970, 26, 37– 50. (6) Mimoun, H. Angew. Chem., Int. Ed. Engl. 1982, 21, 734–750. (7) Bayse, C. A.; Jimtaisong, A.; Kandalam, A. K.; Luck, R. L.; Pandey, R.; Stevens, M. J. J. Mol. Struct. 2005, 754, 96–99. (8) Dickman, M. H.; Pope, M. T. Chem. ReV. 1994, 94, 569–584. (9) Macchi, P.; Schultz, A. J.; Larsen, F. K.; Iversen, B. B. J. Phys. Chem. A 2001, 105, 9231–9242. (10) Piquemal, J.-Y.; Halut, S.; Bregeault, J.-M. Angew. Chem., Int. Ed. Engl. 1998, 37, 1146–1149. (11) Sensato, F. R.; Cass, Q. B.; Longo, E.; Zukerman-Schpector, J.; Custodio, R.; Andre´s, J.; Zaldini-Hernandes, M.; Longo, R. L. Inorg. Chem. 2001, 40, 6022–6025. (12) Sergienko, V. S. Crystallogr. Rep. 2008, 53, 18–46. (13) Sundermeyer, J. Angew. Chem., Int. Ed. Engl. 1993, 32, 1144– 1146. (14) Wahl, G.; Kleinhenz, D.; Schorm, A.; Sundermeyer, J.; Stowasser, R.; Rummey, C.; Bringmann, G.; Fickert, C.; Kiefer, W. Chem.sEur. J. 1999, 5, 3237–3251. (15) Zhao, Z.-H.; Hou, S.-Y.; Wan, H.-L. Dalton Trans. 2004, 1393– 1399. (16) Das, S.; Bhowmick, T.; Punniyamurthy, T.; Dey, D.; Nath, J.; Chaudhuri, M. K. Tetrahedron Lett. 2003, 44, 4915–4917. (17) Maiti, S. K.; Molik, K. M. A.; Gupta, S.; Chakraborty, S.; Ganguli, A. K.; Mukherjee, A. K.; Bhattacharyya, R. Inorg. Chem. 2006, 45, 9843– 8857. (18) Salles, L.; Piquemal, J. I.; Thouvenot, R.; Minot, C.; Bregeault, J. M. J. Mol. Catal. A: Chem. 1997, 117, 375–387. (19) Wang, G.; Chen, G.; Luck, R. L.; Wang, Z.; Mu, Z.; Evans, D. G.; Duan, X. Inorg. Chim. Acta 2004, 357, 3223–3229. (20) Bandyopadhyay, R.; Biswas, S.; Guha, S.; Mukherjee, A. K.; Bhattacharyya, R. Chem. Commun. 1999, 1627–1628. (21) Ballistreri, F. P.; Barbuzzi, E. G. M.; Tomaselli, G. A.; Toscano, R. M. J. Org. Chem. 1996, 61, 6381–6387. (22) Biradar, A. V.; Kotbagi, T. V.; Dongare, M. K.; Umbarkar, S. B. Tetrahedron Lett. 2008, 49, 3316–3319. (23) Luan, Y.; Wang, G.; Luck, R. L.; Yang, M.; Han, X. Chem. Lett. 2007, 36, 1236–1237. (24) Ballistreri, F. P.; Tomaselli, G. A.; Toscano, R. M.; Conte, V.; Di Furia, F. J. Am. Chem. Soc. 1991, 113, 6209–6212. (25) Basak, A.; Barlan, A. U.; Yamamoto, H. Tetrahedron: Asymmetry 2006, 17, 508–511. (26) Batigalhia, F.; Zaldini-Hernandes, M.; Ferreira, A. G.; Malvestiti, I.; Cass, Q. B. Tetrahedron 2001, 57, 9669–9676. (27) Bonchio, M.; Conte, V.; De Conciliis, M. A.; Di Furia, F.; Ballistreri, F. P.; Tomaselli, G. A.; Toscano, R. M. J. Org. Chem. 1995, 60, 4475–4480. (28) Bortolini, O.; Di Furia, F.; Modena, G.; Seraglia, R. J. Org. Chem. 1985, 50, 2688–2690.

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