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J. Phys. Chem. A 2010, 114, 9388–9393
A Computational Study of the Potential Energy Surface of Peroxyformic Acid Dimers Mohammad Solimannejad* and Fatemeh Shahbazi Quantum Chemistry Group, Department of Chemistry, Faculty of Sciences, Arak UniVersity, Arak 38156-8-8349, Iran
Ibon Alkorta* Instituto de Quı´mica Me´dica (CSIC), Juan de la CierVa, 3; 28006-Madrid, Spain ReceiVed: June 18, 2010; ReVised Manuscript ReceiVed: July 15, 2010
MP2 and M05-2x calculations with aug-cc-pVDZ basis sets were used to analyze intermolecular interactions in peroxyformic acid dimers. A total of 18 and 16 minima were located on the potential energy surface of HOOCHO dimer complexes at M05-2x and MP2 computational levels, respectively. The BSSE corrected interaction energies are in a range between 9 and 34 kJ mol-1 at the MP2/aug-cc-pVDZ computational level. The atoms-in-molecules (AIM) theory was also applied to explain the nature of the complexes. The interaction energies have been partitioned with the natural energy decomposition analysis (NEDA) showing that the most important attractive term corresponds to the charge transfer. Introduction The importance of noncovalent intermolecular interactions in many areas of contemporary chemical physics has been demonstrated in numerous studies of such systems.1 Among all noncovalent interactions, H-bonding types are particularly significant.2-4 H-bonded complexes involving peracids have become the focus of recent work because of some fascinating chemistry.5-18Peracids play a vital role in several chemically important reactions such as oxidizing agents in the epoxidation type of reactions where a carbon-carbon double bond in alkenes undergoes oxidation to generate epoxides (oxiranes), like a reagent in Baeyer-Villiger oxidation type of reactions, and so forth. Peroxyformic acid (PFA) is the simplest form of this type of molecule. However, there are no theoretical or experimental data currently available concerning a systematic study of the dimer structures of PFA. Only previous studies have considered a limited number of possibilities.19 Given the rapidly growing importance of title system, in conjunction with the absence of experimental information about the structures or energetics of such complexes, a theoretical analysis of their properties would appear to be in order. The present work thus reports a detailed examination of the stabilities, electronic structure, and vibrational frequencies of the title complexes for the first time. Computational Details Calculations were performed by using the Gaussian 03 system of codes.20 The geometries of the isolated PFA molecule and its dimer complexes were fully optimized at the MP221 and M052x levels22 by using aug-cc-pVDZ basis set. Harmonic-vibrationalfrequency calculations have been performed at the same computational level to confirm that the structures are energetic minima and to evaluate the vibrational frequencies. The interaction energy has been calculated as the difference of the total energy of the complexes and the isolated monomers in its minimum configuration. The deformation energy is * Corresponding authors. E-mail:
[email protected] and
[email protected].
calculated as the difference of energy of the monomers in the geometry of the dimers minus the isolated monomer in its minimum configuration. The full counterpoise (CP) method23,24 was used to correct the interaction energy from the inherent basis set superposition error (BSSE). The atoms-in-molecules (AIM) methodology25 has been used to analyze the electron density of the systems considered at the M05-2x/aug-cc-pVDZ computational level. The topological analysis has been carried out with the AIM2000 program,26 and the atomic integration within the atomic basins has been performed with the AIMAll27 and Morphy98 programs.28 The integrated Laplacian has been taken as an initial measure of the quality of the integration. Ideally, the Laplacian as integrated over any atomic basins of a system should result in a null value; however, values smaller than 1 × 10-3 have been shown to provide only negligible errors in energy and charge results.29 Thus, the conditions of the integration have been adjusted when this requirement was not satisfied. The natural energy decomposition analysis (NEDA)30,31 within the natural bond orbital methodology32 has been performed to obtain insight of the source of the interaction energy. This methodology divides the interaction energy in several attractive components as orbital charge transfer that arises from the delocalization of electron from one monomer to the other, electrostatic interaction of the monomers, polarization and exchange-correlation terms. Finally, a repulsive component is considered which takes into account the electronic deformation due to the complex formation in each monomer. These calculations have been performed at the M05-2x/aug-cc-pVDZ computational level with the NBO-5G33 on the GAMESS program.34 Results and Discussion Monomer. The potential-energy surface of the PFA has been already discussed in the literature by using RHF/STO-3G and RHF/4-31G computational methods35 and at MP2 level with different range of basis sets,5 and the results have been compared to the experimental data available for the peroxyformic acid.36 In the present case, we have calculated four stationary points that corresponds to the rotation of two dihedral angles
10.1021/jp1056539 2010 American Chemical Society Published on Web 08/10/2010
Computational Study of the PES of Peroxyformic Acid Dimers
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SCHEME 1
TABLE 1: Relative Energy (kJ/mol) of the Conformers Calculated of PFA conformer
R1
R2
M05-2x/ aug-cc-pVDZ
MP2/ aug-cc-pVDZ
I II III IV
0 0 180 180
0 180 180 0
0.00 17.07 20.08 48.80
0.00 13.54 16.57 46.18
(Scheme 1). At the two computational levels considered (Table 1), the conformer I is the most stable one. Only the two most stable ones are minima, whereas the other two are true transition state (only one imaginary frequency). The molecular electrostatic potential of the most stable conformer presents minima regions associated with the three oxygen atoms but with very different minima values (Figure. 1). Thus, the O2 present a small minimum with a value of -0.020 au, the hydroxyl group, O1, shows two minima regions associated to each lone pair with minima values of -0.042 au, and the carbonyl group, O4, presents the deepest minima with a value of -0.048 au. Positive regions are found surrounding the two hydrogen, H1 and H3, atoms and the carbon atom, C3, of the molecule. The analysis of the electron density of the most stable conformer, I, shows the presence of an intramolecular HB (Figure 2). The integrated atomic charges calculated within the AIM methodology show that the most negative atom is O4 and the most positive one is C3. Dimers. On the basis of the energetic difference between the conformations of the PFA, only the most stable one has been
Figure 1. Molecular electrostatic potential of the most stable conformer of PFA. The solid regions represent the (0.04 au isosurface. The countour lines correspond to (2 × 10n, 4 × 10n, 8 × 10n, where n is 0, -1, -2, and -3. The values of the minima are indicated.
considered in order to generate the dimers, even though complete freedom has been allowed in the optimization process reaching in some cases geometries very different of those of the isolated monomer. A systematic way to generate all the possible structures of dimers due to association of two PFA has been used. First of all, we started with two PFA monomers with internal HOOCHO H-bond that are closed together to form CH · · · O and OH · · · O intermolecular interactions; however, oxygen-oxygen interactions are observed in some of the structures (S5, S6, S8, S9, S12, S13, S15, S17, and S18). In the second step, one PFA monomer with internal HOOCHO H-bond is pairing to another PFA monomer breaking the internal HOOCHO H-bond in order to form intermolecular OH · · · O and CH · · · O interactions (S3, S4, S7, S10, S11, and S14). Finally, two PFA monomers breaking the internal HOOCHO H-bond are approached together to form two strong OH · · · O interactions (S1, S2, and S16). The complexes have been numbered on the basis of the interaction energy calculated at the M05-2X computational level. A total of 18 minima complexes have been obtained with the M05-2x computational method, of which two are not minima at MP2 level (Figure 3). The missing minima at the MP2 level (S15 and S18) are two of the less stable dimers found at the M05-2X level. A similar trend is observed in the BSSE corrected interaction energies of the complexes calculated with the two methods considered here. Thus, a linear correlation can be obtained with a square correlation coefficient of 0.94. However, the values obtained at the M05-2X level are larger than those
Figure 2. Electron-density map of the most stable conformer of the PFA. The bond and ring critical points are represented with square and triangles, respectively. The bond paths are depicted, and the AIM atomic charges are shown.
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Figure 3. Optimized structures at the M05-2x/aug-cc-pVDZ computational level with indication of the position of the bond and ring electron density critical points (small purple and white spheres, respectively) and bond paths.
Computational Study of the PES of Peroxyformic Acid Dimers TABLE 2: Stabilization Energies (kJ mol-1) of PFA Dimers at MP2 and M05-2x Computational Levels Obtained by Using aug-cc-pVDZ Basis Set M05-2x/aug-cc-pVDZ
MP2/aug-cc-pVDZ
complex
EI
EI+BSSE
Edef
EI
EI+BSSE
Edef
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15a S16 S17 S18a
-44.79 -29.31 -28.01 -27.69 -23.37 -21.75 -20.07 -19.36 -18.76 -18.67 -18.10 -18.03 -17.97 -15.07 -15.01 -13.68 -13.34 -12.6
-40.93 -25.96 -25.57 -25.29 -20.01 -19.77 -16.89 -17.33 -16.43 -15.57 -15.01 -16.32 -16.01 -12.53 -13.12 -10.56 -11.87 -11.2
31.04 34.23 2.63 11.95 1.02 0.74 12.97 1.24 0.79 14.59 17.15 0.69 0.83 7.05 0.57 28.3 0.48 0.27
-48.4 -34.23 -27.63 -29.6 -25.49 -22.16 -24.97 -20.94 -23.42 -27.83 -27.27 -19.78 -19.74 -18.92
-33.46 -21.78 -19.92 -20.43 -14.42 -16.15 -11.97 -12.12 -14.2 -14.52 -14.52 -14.37 -13.77 -9.42
26.49 27.86 2.18 12.27 9.83 0.44 11.78 11.69 0.69 13.11 14.21 0.4 0.51 9.78
-22.86 -16.82
-8.6 -12.05
24.07 0.33
a One imaginary frequency at MP2/aug-cc-pVDZ computational level.
at the MP2, in average 20%. This difference between the two methods can be associated to the larger values of the BSSE correction at the MP2 level than those at the M05-2X level. (See Supporting Information for the geometric parameters, stretching frequency, and Cartesian coordinates of the optimized structures of all studied complexes at M05-2x/aug-cc-pVDZ computational level.) The energetic values of the calculated dimers are gathered in Table 2. The two most stable complexes are those in which both molecules used O4 as HB acceptor and H1 as HB donor (S1 and S2). These two complexes in addition present the largest deformation energies. The replacement of the H1 by a H3 atom in one of the molecules (S3 and S4) provides interaction energies only slightly smaller than those of S2. The replacement of the O4 HB acceptor by O2 (S5) has an effect of approximately 5 kJ when compared to S2, whereas the replacement by O1 (S16) reduce even more the interaction energy. Among the weaker complexes obtained, most of them correspond to cases where the C3 atom acts as electron acceptor (S7, S9, S10, S11, and S12). S1 is clearly the most strongly bound of the various complexes, with a binding energy of 34 kJ/mol at MP2/augcc-pVDZ computational level after correction of BSSE. The OH · · · O hydrogen bonds are both about 1.8 Å in length. Perhaps more importantly, there is little strain in these bonds, with both (O1H1 · · · O4) angles within 20° of linearity, as reported in the last rows of Table 3. Such linearity has been shown to be an important component in the strength of such H-bonds.18,37-39 The two covalent O-H bonds that are involved in the H-bonds are both stretched, one by nearly 27 mÅ. The geometric results (Table 3 and S1) obtained for the two computational methods considered here present very similar intermolecular distances; with a few exception, the differences are never larger than 0.1 Å. The average unsigned difference in the distances is 0.018 Å. Something similar is found in the bond angles where the average unsigned difference is 2.6°. Also reported in Table 3 are the frequency shifts of the two O-H covalent bonds, resulting from the complexation at the MP2 computational level. Both shifts are to the red, as normally anticipated for O-H bonds. They are rather large, around 500 cm-1, reiterating the strength of these two H-bonds. Another important result of the need to break the internal HOOCHO H-bond in order to form complex S1 is that the
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9391 TABLE 3: H-Bond Angles and Distances, Bond Stretches, Stretching Frequency Shifts for Complexes Containing Intermolecular and Intramolecular OH · · · O and CH · · · O H-Bonds Calculated at the MP2/aug-cc-pVDZ Computational Level PFA(1)
PFA(2)
R(Å)
θ
∆r
∆ν
O1-H1 O4 C3-O4 O2-O1
O4 H1-O1 O4 O1
S1 1.813 1.813 3.204 2.911
161.4 161.4 82.6 116.8
33.3 33.3 33.6 64.9
-502.4 -502.4 -205.1 -105.2
O1-H1 O4 O2-O1
O4 H1-O1 O1
S2 1.892 1.891 3.055
142.1 142.3 96.5
28.4 28.4 65.0
-419.3 -419.3 -105.2
H1-O1 O4
S3 1.897 1.980 2.378
122.2 143.3 114.6
31.7 33.1 17.7
-435.6 -452.2 -150.3
H1-O1 O4
S4 1.899 1.833 2.299
121.8 169.2 122.7
31.1 29.6 17.8
-421.2 -421.2 -148.3
O1-H1 · · · O4 H1 O1-O2 O4-C3
S5 1.915 2.374 1.858 3.852 2.158
120.7 96.1 98.8 117.1 130.2
38.0 30.8 71.0 67.1 30.1
-530.8 -437.5 -126.0 -119.7 -188.2
C3-H3 O4
O1-H1 · · · O4 O4 H3-C3
S6 1.894 1.895 2.416 2.416
122.5 122.5 122.1 122.1
31.8 31.8 18.8 18.8
-439.8 -439.8 -163.3 -163.3
O1-H1 O4 H3-C3
O1-H1 · · · O4 O4 C3-H3 O1
S7 1.904 1.939 2.872 3.080
121.4 159.8 95.4 82.0
32.3 23.9 18.2 22.9
-306.6 -444.1 -160.6 -220.1
O1-H1 · · · O4 O4 H1
S8 1.882 2.563 2.321 1.955
123.1 84.4 129.1 110.4
33.3 24.6 17.9 69.3
-462.7 -320.3 -146.5 -126.5
O1 H3-C3
O1-H1 · · · O4 H3-C3 O4
S9 1.874 1.892 2.403 2.880
123.0 122.7 139.8 76.4
34.2 31.9 19.6 18.1
-479.6 -442.2 -173.9 -161.5
O1-H1 · · · O4
O1-H1 · · · O4 O1 C3-H3
S10 1.854 1.88 2.821
123.2 168.6 85.4
36.8 27.3 17.9
-524.4 -381.7 -157.5
H1-O1 O4
S11 1.853 1.901 2.862
123.3 161.6 66.6
37.4 26.5 17.3
-530.9 -368.7 -149.7
O1-H1 · · · O4 O4 H3-C3 O4
S12 1.884 1.899 2.415 2.501 3.058
123.1 122.4 127.8 111.2 166.2
33.0 31.6 18.4 19.0 68.6
-461.1 -436.1 -156.6 -166.9 -121.2
C3-O4
O1-H1 · · · O4 H1
S13 1.898 1.929 2.131
122.3 120.3 106.9
31.8 34.0 37.8
-437.5 -467.5 -218.4
O1-H1 O1
O1-H1 · · · O4 O4 H3-C3
S14 1.903 1.997 2.765
121.9 141.9 97.7
31.5 27.9 19.2
-430.5 -371.9 -169.2
O1-H1 O2
O4 H1-O1
S16 1.853 1.905
161.4 116.7
30.4 25.6
-426.5 -343.3
O1-H1 · · · O4 O2 H3-C3 O2-O1
S17 1.886 1.886 2.911 2.534 2.534
123.0 123.0 159.8 119.2 117.4
33.0 33.0 68.4 18.6 68.4
-459.5 -459.5 -123.3 -160.3 -123.3
O1-H1 · · · O4 O4 C3-H3 · · · O1-H1 · · · O4 O4 C3-H3 O1-H1 · · · O4 O2-O1 O4 H1 O1-H1 · · · O4
O1-H1 · · · O4 C3-H3 O1-O2 · · · O1-H1 · · · O4
O1-H1 · · · O4 O1 H3-C3 O1-H1 · · · O4 C3-H3 O2 O1-O2 O1-H1 · · · O4
O1-H1 · · · O4 O1-O2 O2 H3
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TABLE 4: NEDA Partition of the Interaction Energy (kJ mol-1) in the Calculated Dimers at the M05-2x/aug-cc-pVDZ Computational Level complex
charge transfer
electrostatic
polarization
exchange correlation
deformation monomer1
deformation monomer2
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18
-192.59 -133.05 -68.58 -92.97 -54.18 -30.75 -73.81 -47.66 -37.03 -77.53 -73.01 -29.41 -38.49 -40.00 -33.43 -113.09 -25.90 -24.39
-108.37 -87.74 -42.13 -57.07 -35.06 -26.82 -43.51 -26.23 -23.60 -43.85 -46.23 -22.22 -24.18 -28.91 -17.28 -58.37 -16.07 -14.18
-96.23 -81.55 -53.89 -63.47 -33.43 -37.70 -60.96 -33.76 -41.71 -51.09 -53.64 -27.15 -31.63 -34.18 -23.30 -59.96 -15.44 -20.38
-59.41 -48.16 -32.38 -35.19 -37.74 -22.64 -42.43 -22.84 -29.12 -37.20 -38.74 -18.79 -22.05 -30.04 -20.50 -42.09 -14.77 -14.90
192.34 145.10 84.94 108.37 73.01 48.66 102.42 51.59 61.59 86.27 88.12 36.02 49.33 68.66 44.22 118.03 29.92 31.13
192.34 145.18 83.85 103.05 66.48 48.70 88.41 60.42 52.76 93.26 91.50 44.60 50.29 45.02 36.61 116.73 29.92 31.30
binding energy reported represents an underestimate of the true interaction energy. More precisely, the binding energy is defined relative to the fully optimized, isolated monomers and may thus be thought of as a two-stage process. In order to form the complex, the planar HOOCHO molecule must first distort itself by rotating its OH group, breaking the internal H-bond, and raising its energy. It is the second step, wherein the two (predistorted) molecules come together, that accounts for the true interaction energy. In order to provide an estimate of the former quantity, it was found that the energy of the HOOCHO molecule, when in its geometry within the S1 complex, is higher than the energy of the fully optimized planar HOOCHO subunit. (The magnitude of this quantity is consistent with the notion that it is largely due to the breaking of an internal OH · · · O H-bond.) Thus, the true binding energy of the S1 complex can be considered as higher than the 34 kJ/mol listed in Table 3 by roughly this amount. The NEDA analysis (Table 4) provides some clues of the important term in the dimer formation. In all the complexes, the charge transfer is the most important stabilization term except for the S6 and S9 complexes where the polarization become more important. In general, the electrostatic and exchange-correlation term are the less important attractive terms. Those complexes that show large deformation energies due to the change of the geometry are the ones with the larger electronic deformation as calculated with the NEDA method. The topological analysis of the electron density (Figure 3) shows the presence of intermolecular-bond critical points between oxygen atoms of one molecule and the hydrogen, carbon, and oxygen atoms of the other one. The presence of O · · · H and O · · · C bcp’s are expected because of the opposite charge found for the interacting atoms whereas the presence of O · · · O bcp’s is not straightforward. However, several previous reports have shown the presence of similar interactions,40,41 and in addition, they have been considered to present stabilizing characteristics. The values of the electron density at the bcp and its Laplacian for all the O · · · H contact has been represented versus the interatomic distances in Figures 4 and 5. The values are clearly divided in intramolecular and intermolecular interactions. Recently, we have shown that, for a set of O · · · H interactions in glyoxal dimers and trimers, the values are clustered on the basis of the size of the rings formed.42 In the present case, all the intramolecular interactions generate a five-membered ring.
For each of these sets, exponential relationships are established between the interatomic-distance- and the electron-density-based parameters as have been shown for other hydrogen bonds.43,44
Figure 4. Electron density (au) vs the O · · · H distance (Å). The adjusted curve corresponds to exponential relationships with r2 of 0.988 and 0.981 for the intramolecular and intermolecular Fbcp, respectively.
Figure 5. Laplacian (au) vs the O · · · H distance (Å). The adjusted curve corresponds to exponential relationships with r2 of 0.980 and 0.976 for the intramolecular and intermolecular ∇2F bcp, respectively.
Computational Study of the PES of Peroxyformic Acid Dimers The results of the present study first confirm the nature of the intermolecular interaction as a hydrogen bond. The data further indicate that these H-bonded complexes ought to be experimentally observable in the gas phase. It is our hope that the present study may motivate experimentalists to search for the studied complexes, perhaps by matrix isolation study. Conclusions A theoretical study of the PFA has been carried out by using DFT (M05-2x) and MP2 computational methods. The stationary points of the monomer have been characterized, showing that the most stable conformer present an intramolecular hydrogen bond. The MEP of this conformer shows the possibility that the three oxygen present in this molecule could act as electron donors. A total of 18 dimers have been found to be minima at M052x/aug-cc-pVDZ computational level and 16 at MP2/aug-ccpVDZ. The stabilization energy due to the complex formation ranges between 8.6 and 33.5 kJ/mol at MP2 level. The NEDA partition shows that the most important stabilization term corresponds, in general, to the charge transfer followed by the polarization, the electrostatic and exchange-correlation term being the less important ones. The analysis of the electron-density properties of the hydrogen bond formed in the dimers shows a clear difference between those that correspond to intramolecular interactions and those that are intermolecular. Acknowledgment. This work was carried out with financial support from the Spanish Ministerio de Ciencia e Innovacion (Project No. CTQ2009-13129-C02-02), Comunidad Auto´noma de Madrid (Project MADRISOLAR2, S2009/PPQ-1533). Thanks are given to the CTI (CSIC) for allocation of computer time. Supporting Information Available: Geometric parameters, stretching frequency, and Cartesian coordinates of the optimized structures of all studied complexes at M05-2x/aug-cc-pVDZ computational level. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Muller-Dethlefs, K.; Hobza, P. Chem. ReV. 2000, 100, 143. (2) Jeffrey, G. A. An Introduction to Hydrogen Bonding; Oxford University Press: New York, 1997. (3) Scheiner, S. Hydrogen Bonding; Oxford University Press: New York, 1997. (4) Desiraju, G. R.; Steiner, T. The Weak Hydrogen Bond; Oxford University Press: Oxford, U.K., 1999. (5) Langley, C. H.; Noe, E. A. THEOCHEM 2004, 682, 215. (6) Andersen, A.; Carter, E. A. J. Phys. Chem. A 2003, 107, 9463. (7) Okovytyy, S.; Gorb, L.; Leszczynski, J. Tetrahedron Lett. 2002, 43, 4215.
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9393 (8) Yamabe, S.; Kondou, C.; Minato, T. J. Org. Chem. 1996, 61, 616. (9) Freccero, M.; Gandolfi, R.; Sarzi-Amade, M.; Rastelli, A. J. Org. Chem. 2002, 67, 8519. (10) Bach, R. D.; Canepa, C.; Winter, J. E.; Blanchette, P. E. J. Org. Chem. 1997, 62, 5191. (11) Bach, R. D.; Estevez, C. M.; Winter, J. E.; Glukhovtsev, M. N. J. Am. Chem. Soc. 1998, 120, 680. (12) Cardenas, R.; Cetina, R.; Lagunez-Otero, J.; Reyes, L. J. Phys.Chem. A 1997, 101, 192. (13) Carlo, P. Chem. Phys. 1977, 26, 243. (14) Bach, R. D.; Willis, C. L.; Lang, T. J. Tetrahedron 1979, 35, 1239. (15) Bach, R. D.; Dmitrenko, O. J. Phys. Chem. A 2003, 107, 4300. (16) Bock, C. W.; Trachtman, M.; George, P. Chem. Phys. 1981, 62, 303. (17) Kulkarni, A. D.; Rai, D.; Bartolotti, L. J.; Pathak, R. K. J. Phys.Chem. A 2006, 110, 11855. (18) Solimannejad, M.; Shirazi, S. G.; Scheiner, S. J. Phys. Chem. A 2007, 111, 10717. (19) Alkorta, I.; Elguero, J.; Elguero, J. Chem. Phys. 2003, 117, 6463. (20) Frisch, M. J.; Gaussian 03, revision B02; Gaussian, Inc.: Pittsburgh, PA, 2003. (21) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618. (22) Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Theory Comput. 2006, 2, 364. (23) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (24) Latajka, Z.; Scheiner, S. J. Chem. Phys. 1987, 87, 1194. (25) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, U.K., 1990. (26) Biegler-Konig, F.; Schonbohm, J. AIM2000 Program Package, Ver. 2.0; University of Applied Sciences: Bielefield, Germany, 2002. (27) AIMAll (Version 08.11.29), Todd A. Keith, 2008 (aim. tkgristmill.com). (28) Morphy98: Popelier, P. L. A. with a contribution from Bone, R. G. A. MORPHY98, a topological analysis program, 0.2 ed.; University of Manchester Institute of Science and Technology: Manchester, England, 1999. (29) Alkorta, I.; Picazo, O. ARKIVOC 2005, ix, 305. (30) Glendening, E. D. J. Am. Chem. Soc. 1996, 118, 2473. (31) Glendening, E. D. J. Phys. Chem. A 2005, 109, 11936. (32) Weinhold, F.; Landis, C. R. Valency and Bonding. A Natural Bond Orbital Donor-Acceptor PerspectiVe; Cambridge Press: Cambridge, 2005. (33) NBO5 Glendening, G. E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M. Weinhold, F. (Theoretical Chemistry Institute: University of Wisconsin, Madison, WI, 2004. (34) GAMESS Version 11 Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347. (35) Petrongolo, C. Chem. Phys. 1977, 26, 243. (36) Domanskaya, A. V.; Ermilov, A.; Andrijchenko, N.; Khriachtchev, L. Mol. Phys., in press, DOI: 10.1080/00268976.2010.496375. (37) Gu, Y.; Kar, T.; Scheiner, S. J. Am. Chem. Soc. 1999, 121, 9411. (38) Scheiner, S.; Duan, X. Biophys. J. 1991, 60, 874. (39) Duan, X.; Scheiner, S. J. Mol. Struct. 1992, 270, 173. (40) Bofill, J. M.; Olivella, S.; Sole, A.; Anglada, J. M. J. Am. Chem. Soc. 1999, 121, 1337. (41) Solimannejad, M.; Alkorta, I.; Elguero, J. Chem. Phys. Lett. 2009, 474, 253. (42) Solimannejad, M.; Massahi, S.; Alkorta, I. Int. J. Quantum. Chem. In press: DOI 10.1002/qua.22652. (43) Mata, I.; Alkorta, I.; Molins, E.; Espinosa, E. Chem.sEur. J. 2010, 16, 2442. (44) Picazo, O.; Alkorta, I.; Elguero, J. J. Org. Chem. 2003, 68, 7485.
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