J. Phys. Chem. A 2010, 114, 2855–2863
2855
Bifunctional Hydrogen Bonds in Monohydrated Cycloether Complexes Margarita M. Vallejos,† Emilio L. Angelina,† and Ne´lida M. Peruchena*,†,‡ Laboratorio de Estructura Molecular y Propiedades, A´rea de Quı´mica Fı´sica, Departamento de Quı´mica, Facultad de Ciencias Exactas y Naturales y Agrimensura, UniVersidad Nacional del Nordeste, AVenida Libertad 5460, (3400) Corrientes, Argentina, and Facultad Regional Resistancia, UniVersidad Tecnolo´gica Nacional, French 414, (3500) Resistancia, Chaco, Argentina ReceiVed: July 6, 2009; ReVised Manuscript ReceiVed: December 29, 2009
In this work, the cooperative effects implicated in bifunctional hydrogen bonds (H-bonds) were studied (in monohydrated six-membered cycloether) within the framework of the atoms in molecules (AIM) theory and of the natural bond orbitals (NBO) analysis. The study was carried out in complexes formed by six-membered cycloether compounds (tetrahydropyrane, 1,4-dioxane, and 1,3-dioxane) and a water molecule. These compounds were used as model systems instead of more complicated molecules of biological importance. All the results were obtained at the second-order Møller-Plesset (MP2) level theory using a 6-311++G(d,p) basis set. Attention was focused on the indicators of the cooperative effects that arise when a water molecule interacts simultaneously with a polar and a nonpolar portion of a six-membered cycloether (via bifunctional hydrogen bonds) and compared with conventional H-bonds where the water molecule only interacts with the polar portion of the cycloether. Different indicators of H-bonds strength, such as structural and spectroscopic data, electron charge density, population analysis, hyperconjugation energy and charge transference, consistently showed significant cooperative effects in bifunctional H-bonds. From the AIM, as well as from the NBO analysis, the obtained results allowed us to state that in the monohydrated six-membered cycloether, where the water molecule plays a dual role, as proton acceptor and proton donor, a mutual reinforcement of the two interactions occurs. Because of this feature, the complexes engaged by bifunctional hydrogen bonds are more stabilized than the complexes linked by conventional hydrogen bonds. Introduction Hydrogen bonding (H-bond) is one of the most studied phenomena in chemistry. It was discovered approximately 100 years ago. However its understanding is far from being completed.1-9 Conventional H-bonds are usually defined as X-H · · · Y interactions, where X-H is a typical covalent bond, being the proton-donating moiety, and Y the proton-accepting center (i.e., lone pairs of an electronegative atom or a region of electron density excess like a π-electron system). Conventional H-bonds, also named proper H-bonds, are characterized by the elongation of the X-H proton donor bond and a concomitant decrease of the X-H stretch frequency (red shift). This effect is usually accompanied by an increase in the IR intensity of the X-H stretch vibration upon formation of the complex. On the basis of these indicators, the red shift in the X-H stretching vibration is usually considered to be the most important and easily detectable manifestation of the formation of H-bonds.3 In contrast, the improper H-bonds, also named blue-shifted hydrogen bonds, have been reported by a lot of experimental and theoretical investigations as C-H · · · Y.10,11 These H-bonds are characterized by a contraction of the X-H bond and a concomitant increase of the X-H stretch frequency (blue shift) upon complexation. Generally, the frequency of stretching vibration, for a C-H bond, involved in H-bonds, has been found * To whom correspondence should be addressed. E-mail: arabeshai@ yahoo.com.ar. † Universidad Nacional del Nordeste. ‡ Universidad Tecnolo´gica Nacional.
to shift to the blue. However, it is necessary to note that this indicator is far from universality.8 A lot of works12-14 have been reported in which the hydration of soluble molecules shows an increase of the stretch frequency, ν(C-H) (i.e., ethanol/water). In these mentioned cases the water molecule interacts simultaneously with the hydroxyl group and with the hydrogen atoms of the methyl group of the ethanol. In the same context, Mizuno et al.15 carried out 1H NMR and IR studies for 1,4-dioxane/water mixtures over the whole range of concentrations to determine the influence of the polar group on the H-bond formation at the hydrophilic and hydrophobic groups, respectively. They found out that when the water concentration increases the ν(C-H) stretching modes blue shifts and the absorption intensities of the same modes decrease. Additionally, they have found a slight increase in the chemical shifts of NMR (δCH) with the XH2O increase. Although molecular interactions in aqueous solutions are much more complex than those in gas phase, Mizuno et al.12,13,15-17 have associated the blue shifts in the ν(C-H)s, observed for the aqueous solutions, with the same blue shifting H-bonds formed between a proton donor and a water molecule in the gas-phase calculations. They proposed the formation of a “bifunctional hydrogen-bonding hydration complex”, in which the water molecule plays the role of a proton donor, in conventional O-H · · · O H-bonds, and a proton acceptor, in blueshifting C-H · · · OH2 H-bonds, simultaneously. In addition, experimental evidence of C-H · · · Ow interactions has been obtained by Chang et al. They have investigated the effect of the pressure versus C-H · · · Ow interactions in aqueous 1,4-dioxane18 and 1,3-dioxane19 by infrared spectrum. Their study demonstrated that although the C-H · · · Ow interactions
10.1021/jp906372t 2010 American Chemical Society Published on Web 02/08/2010
2856
J. Phys. Chem. A, Vol. 114, No. 8, 2010
are weak “high pressure can be used to give evidence of hydrogen bond-like C-H · · · O interactions”. Experimental and theoretical studies demonstrated that in the (1:1) tetrahydrofurane and water complex the most stable structure is formed only by one H-bond O · · · Hw-Ow interaction and that this is due to the contribution of the steroelectronic effect.20,21 However, in the (1:2) tetrahydrofurane and water complex, a bifunctional H-bond was found. In this case, a water-water interaction is involved. In these studies,21 the authors proposed that the formation of this type of cooperative H-bonds is responsible for the hydrophobic hydration of the tetrahydropyran. All these previous studies have conducted us to an attempt of the quantification of the effect of the polar group (where the O · · · Hw-Ow H-bond is formed) on the hydration of the hydrophobic portion of the six-membered cycloether, in the base of the electronic charge density and natural bond orbital (NBO) analysis. Additionally, the reverse, the evaluation of the strength augment of the O · · · Hw-Ow H-bond (in the hydrophilic portion), as a consequence of C-H · · · O interactions at the hydrophobic portion of the cycloether, has also been considered. In previous works, we have analyzed the topology of the charge density distribution in other weak and moderate interactions produced in several chemistry fields.22 This methodology is appropriate to analyze the characteristics of all types of bonds as well as the cooperatives effects. Generally, the cooperative effects are investigated in a one-dimensional network of intermolecular H-bonds and involve more than two monomers. Wang and Balbuena23 described the cooperative effect as “the enhancement of the first H-bond between a donor and an acceptor once a second H-bond is formed between the third molecule and one of the first two molecules”. However, this effect can also be seen in dimers, for example, in complexes engaged by bifunctional H-bonds as the ones studied here. According to our knowledge and in contrast to the large number of experimental and theoretical investigations aimed to understand the cooperative effect in lineal chains,24,25 the cooperative effect in dimers engaged by bifunctional H-bonds has received scarce or null attention, especially from the theoretical point of view. In this work and in order to gain insight about the significance of the additional stabilization due to bifunctional H-bonds, we have carried out an analysis of the local topological properties of the electronic charge density distribution within the framework of the atoms in molecules (AIM) theory26 and a study of the charge transference through the NBO analysis.27 Six simple complexes (1a, 2a, 3a, 1b, 2b, and 3b) were selected (Figure 1). These complexes correspond to the tetrahydropyrane, the 1,4-dioxane, and the 1,3-dioxane (1:1) in water. They were linked, by bifunctional H-bonds, to the hydrophobic and to the hydrophilic portions of the six-membered cycloether in complexes a and linked only to the hydrophilic portion by conventional H-bonds in complexes b. We have also provided a detailed analysis of several cooperative effects indicators in complexes a. Finally, one of the key reasons for studying the strength and the topological characteristic of the bifunctional H-bonds is the understanding of the contribution that these types of interactions can make to hydration of hydrophobic moieties in biological molecules,28 with proton acceptors and proton donors, simultaneously.
Vallejos et al.
Figure 1. Optimized structure of cycloether/water complexes. Letter a denotes the complexes linked by bifuncional H-bond and b the complexes linked by proper H-bond. The tetrahydropyrane/H2O, 1,4dioxane/H2O, and 1,3-dioxane/H2O complexes are denoted 1, 2, and 3, respectively.
2.0 program29 was used.30 These hydration structures were used as an initial guess for a full geometry optimization for all the complexes (1:1) in gas phase, at the B3LYP/6-31G(d,p) level.31 Afterward, the geometries corresponding to the more stable complexes were reoptimized at the MP2/6-31+G(d,p) level of calculation.32 This theory level and basis set have been successfully used to describe intermolecular interactions, especially weak interactions such as C-H · · · O contacts.8,28,33 In all complexes, the nature of the stationary points was characterized by calculation of the Hessian matrix. The structures were confirmed as true minima over the potential energy surface by the presence of real harmonic frequencies. The interaction energies (∆E) were calculated as the difference between the total energy of the complex and the sum of total energies of the two isolated monomers, at the MP2/6-311++G(d,p) level. The basis set superposition error (BSSE) was taken into account using the counterpoise method.34 The calculations of local topological properties of the electron charge density at critical point and the average atomic properties, as well as the molecular graphs display were performed with the AIM2000 package,35 with the wave functions obtained at the same level. Also, the natural bond orbital analysis was performed with the NBO 3.136 program as implemented in the Gaussian 03 programs. All calculations were carried out using the Gaussian 03 suite of programs.37
Methods and Calculation Details To explore the hydration structures of the six-membered cycloethers (which are simply denoted as cycloethers hereafter) using their molecular electrostatic potential (MEP), the AGOA
Results and Discussion Geometric, Energetic, and Vibrational Analysis. In Figure 1, the optimized geometries of complexes tetrahydropyrane/H2O,
Bifunctional Hydrogen Bonds
J. Phys. Chem. A, Vol. 114, No. 8, 2010 2857
TABLE 1: Energetic, Geometrical, and Vibrational Parameters of the H-bonded Complexesa-d parameters corr
∆E rO1 · · · Hw rOw · · · H ∆rOw-Hw ∆rC-H ∠O1HwOw ∠OwHC ∆νOw-Hw Ic/Im
1a
1b
2a
2b
3a
3b
-5.29 1.897 2.599e 0.009 -0.001e 164.5 128.0e -53.1 2.4
-4.76 1.917
-4.83 1.906 2.612e 0.008 -0.002e 161.2 128.1e -50.1 2.6
-4.29 1.935
-4.26 1.963 2.560 0.007 -0.001 155.3 127.0 -45.4 2.7
-3.60 1.963
0.008 159.5 -45.4 2.8
0.007 155.1 -42.9 2.9
0.006 151.8 -41.9 3.0
a ∆Ecorr in kcal/mol at the MP2/6-311++G**//MP2/6-31+G**; bond distances are given in angstroms (Å) and angles in degrees. r(O1 · · · H) and r(Ow · · · H) binding distances, ∆r, the difference between proton donor bond length in the complex compared with those in the monomer. c ∆ν (O-H) asymmetric stretch in the complex compared with those in the monomer, in cm-1. d Ic and Im are the intensity in the complex and in the monomer, respectively. e Correspond to two parameters equal due to symmetry reasons.
b
1, 1,4-dioxane/H2O, 2, and 1,3-dioxane/H2O, 3, are shown. In this figure two different configurations of each complex can be seen. In one of them (denoted by a), the water molecule plays a dual role, as a proton acceptor and as a proton donor; in the other one, (denoted by b), the water molecule simply acts as a proton donor. Because of their molecular symmetry, the tetrahydropyrane and the 1,4-dioxane interact with water in a similar manner. Consequently, in the complexes 1a and 2a the water oxygen atom (Ow) is oriented toward the hydrogen atoms of the C(3,5)-Hax bonds, with the resulting formation of a bifurcated H-bond, (or three-center H-bond). In the 1,3-dioxane molecule, particularly the complex 3a, the Ow atom is oriented toward the hydrogen atom of the C5-Hax bond, forming a single interaction (i.e., C5-Hax · · · Ow). In contraposition, in complexes b the formation of an O1 · · · Hw-Ow H-bond (which is present in all complexes) is simply observed. These structural data were analyzed considering a topological point of view. Table 1 shows MP2 results obtained with the 6-311++G(d,p) basis set for interaction energy corrected by BSSE (∆Ecorr). This table also reports relevant geometrical parameters, bond distances rO1 · · · Hw and rOw · · · H along with the angle bonds and the variations in proton donor bond distances upon complexation, ∆rOw-Hw and ∆rC-H. In addition, the variation of the vibrational frequency corresponding to the stretching asymmetry mode and the relationship of the absorption intensity are given. The difference in selected energetic, geometrical, and vibrational parameters between complexes a and b are given in Table S1 of the Supporting Information. As it can be seen in Table 1, the calculated ∆Ecorr energies lie between -5.29 to -4.26 kcal/mol for complexes a and are lower (from -4.76 to -3.60 kcal/mol) for complexes b. These interaction energies increase in the order 3 < 2 < 1. The complexes associated with bifunctional H-bond, 1a, 2a, and 3a result more stabilized than complexes 1b, 2b, and 3b by 11, 13, and 18% of the total interaction energy, respectively. From the data in Table 1, it can be seen that the intermolecular distances r(O1 · · · Hw) lie between 1.90-1.96 Å and the ∠O1HwOw bond angles lie in the152-165° range. These values are in agreement with the proposed range for moderate H-bonds (where the r(O · · · H) distances vary from 1.5 to 2.2 Å).1 The r(O1 · · · Hw) distances in complexes a are slightly shorter than in complexes b and follow the tendency 1 < 2 < 3, in both types of complexes, consistent with the energy values. Also, in complexes a the ∠O1HwOw bond angles displayed lower deviation from linearity, when compared to the same angles in complexes b. In the same sense, the intermolecular distances r(Hax · · · Ow) are longer than r(O1 · · · Hw), where the first one varies from 2.56 to 2.61 Å. It was found that the complex 3a
has the shorter distance of all. Additionally, in all complexes, the ∠OwHC bond angle showed a significant deviation from linearity. As a result of the formation of the Ow-Hw · · · O1 H-bond, a lengthening in the proton donor bond was found. This lengthening correlated well with the interaction distance and with the strength of the interaction in the differents complexes. As expected, the increase was foremost in complexes a. This increase in the Ow-Hw bond length is mirrored by the red shift of the vibration frequency, corresponding to the stretching mode of these (Ow-Hw) bonds. Besides, an increase of the absorption intensity, with respect to the isolated monomer, is always observed. In the same sense and as a consequence of the formation of complexes bonded by bifunctional H-bonds, the proton donor bond (i.e., C-Hax bond) localized in the cycloether hydrophobic portion experimented with a contraction in its length, which is a characteristic feature of the C-H · · · O H-bonds,10 (more noticeable in the complex 2a). Our results, for the complexes a, indicate that Cβ-Hax bonds are the more favorable site for an interaction with a water molecule. In contraposition, Chang et al. have studied, using high pressure IR and Raman spectroscopy and theoretical calculations, the 1,3-dioxane/(water)n clusters, (with n ) 1-6).19 In their work they have established that the equatorial CR-H groups are more favorable sites for hydrogen bonding than axial CR-H groups. Comparison among our structural results and the obtained by other authors demonstrate to be in agreement; i.e., 1,4-dioxane/H2O38 and tetrahydropyrane/H2O,39 show that the water molecule lies in the same plane of symmetry than the cycloether and that the water hydrogen involved in the H-bond is axial with respect to the ring, while the hydrogen not involved in the H-bond is entgegen to the ring (complexes 1a and 2a). Also, these authors have proposed a structure, similar to those of 1b and 2b, as a possible geometry for 1,4-dioxane/H2O and tetrahydropyrane/H2O complexes respectively. From the structural and spectroscopic data, it can be said that, as a consequence of the secondary interactions present in complexes a and absent in complexes b, the Ow-Hw · · · O1 H-bond resulted to be stronger in the first complexes. In addition, it was clear that the formation of bifunctional H-bonds that connects (through a water molecule) the hydrophilic and the hydrophobic portion of the cycloether, forming a cyclic hydration structure, generated an additional stability of these compounds. Local Topological Properties. In Figure 2, the molecular graphs, formed by a network of bond paths (BP), corresponding to the complexes a and b are displayed. In the same figure, big circles correspond to attractors or (3, -3) critical points
2858
J. Phys. Chem. A, Vol. 114, No. 8, 2010
Vallejos et al.
Figure 2. Molecular graphs for monohydrated complexes. Big circles correspond to attractors or nuclear critical point (3, -3), attributed to nuclei, lines connecting the nuclei are the bond paths and the small circles on them are the BCPs or (3, -1) critical points.
TABLE 2: Local Topological Properties of the Electronic Charge Density Calculated at the BCP of the H-bond and Bond Proton Donor of the H-bonded Complexesa,b complex
PC (3, -1)
Fb
∇ 2 Fb
|λ1|/λ3
|Vb|/Gb
1a
O1 · · · Hw Ow · · · H(3,5)axb Ow-Hw O1 · · · Hw Ow-Hw O1 · · · Hw Ow · · · H(3,5)axb Ow-Hw O1 · · · Hw Ow-Hw O1 · · · Hw Ow · · · H5ax Ow-Hw O1 · · · Hw Ow-Hw
0.0285 0.0073 0.3487 0.0266 0.3514 0.0280 0.0071 0.3499 0.0252 0.3528 0.0246 0.0080 0.3524 0.0236 0.3542
0.1001 0.0268 -2.4489 0.0982 -2.4694 0.0992 0.0260 -2.4567 0.0956 -2.4777 0.0889 0.0295 -2.4750 0.0907 -2.4865
0.0268 0.6304 0.0230 0.0256 0.0225 0.0271 0.4452 0.0232 0.0271 0.0226 0.0264 0.4612 0.0227 0.0463 0.0227
0.2217 0.1658 1.6608 0.2121 1.6721 0.2194 0.1610 1.6634 0.2061 1.6789 0.2106 0.1643 1.6773 0.2027 1.6850
0.9674 0.8334 9.8613 0.9463 9.9112 0.9614 0.8373 9.8520 0.9311 9.9202 0.9382 0.8366 9.9253 0.9189 9.9234
1b 2a 2b 3a 3b
a The values of the properties are in au.; ε, |λ1|/λ3 and Vb|/Gb are dimensionless. All symbols are explained in the text. b Correspond to two BCPs equal due to symmetry reasons. c Topological properties at the Ow-Hw BCP of the isolated water molecule: Fb ) 0.3624 au.; ∇2Fb ) -2.4940 au.; ) 0.0254; |λ1|/λ3 ) 1.7240; |Vb|/Gb ) 9.4888.
(attributed to the positions of the atomic nuclei), lines connecting the nuclei are the BPs, and the small circles are the bond critical points (BCP) or (3, -1) critical points, obtained from topological analysis of the electronic density. The presence of a BP path and its associated virial path provides a universal indicator of bonding between the atoms so linked.40 In this figure the presence of a BP between the oxygen atom of the cycloether (O1) and the water hydrogen atom (Hw) is clearly visualized in all complexes. Additionally, in complexes a, BPs between the water oxygen atom (Ow) and the H3ax and H5ax atoms of the cycloether (in 1a and 2a) and between the Ow and the H5ax (in 3a) can also be seen. The observation of the topological structures of the complexes, some linked by more than one trajectory, gives an idea of the increased stability of complexes a with respect to those presented by the respective complexes b. The most significant local topological properties (electron density Fb, Laplacian of electron density ∇2Fb, the ellipticity, , relationship between the perpendicular and parallel curvature |λ1|/λ3, and relationship between the potential and kinetic energy
densities |Vb|/Gb,) at the BCP for intermolecular interactions, for all complexes, are shown in Table 2. In addition, the properties at the BCP on the proton donor bonds are included. The Fb values at O1 · · · Hw BCPs are low, ranging between 0.024 and 0.029 au. Moreover, the values of the Laplacian at some BCPs lie between 0.089 and 0.100 au. In all cases ∇2Fb > 0; this indicates that the BCPs were localized in an electron charge density depletion zone. In consequence, these indicators show that the intermolecular interactions present all the characteristics of the closed shell interactions. (The values lie in the classic or typical quantity for H-bond, from 0.002 to 0.040 au. in Fb and 0.020 to 0.150 au. in ∇2Fb.)41 Commonly, it has been observed that the electron charge density and its Laplacian at the H-bond BCP gives an easy indication of H-bond strength.42 Also, in several previous works43-46 it was found that the topological properties at the intermolecular interactions BCP reflect the strength of the interaction, in an improved mode, over other parameters (i.e., geometrical parameters).
Bifunctional Hydrogen Bonds By comparison of the values of Fb at the same O1 · · · Hw BCP, it can be seen that the density increases following the order 1 > 2 > 3 in both complexes a and b, in agreement with the tendency followed by the interaction energy in these complexes (see Table 1). In addition, the Fb values at the Ow · · · Hax BCP lie between 0.007 and 0.008 au. Obviously, these values are significantly lower than those calculated for the interactions between the O1 and the Hw. These values show how weak the strength of the C-Hax · · · Ow secondary interactions is. Our results are in accordance with those obtained by other authors14d for ethanol/water system, whereas the F value at the BCP, found between the oxygen atom of the water molecule and the hydrogen atom of the methyl group of the alcohol, lies between 0.011 and 0.008 au. (values obtained at the B3LYP/cc-pVDZ level). Furthermore, the Fb values at the O1 · · · Hw BCP are also comparable. In Table 2, it can be seen that the values of Fb at the O1 · · · Hw BCP show a little increase in the complexes a with respect to those in complexes b, resulting in a slight strengthening of the Ow-Hw · · · O1 H-bond in the first case. This observation is in agreement with the diminished distance between O1 and Hw in complexes a, relative to the same distance in complexes b. Note that no difference was found in this distance between complexes 3a and 3b, but the value of Fb at the O1 · · · Hw BCP reflected a slight strengthening of the interaction in the first complex. In addition, all the BCPs that correspond to intermolecular interactions |λ1|/λ3 and |Vb|/Gb are always less than one. This last indicator reveals that the kinetic energy contribution is greater than the potential energy at the BCP. In contraposition, at the BCP of the proton donor bond, the relationship |λ1|/λ3 is >1, and |Vb|/Gb is > > 1. This is a characteristic of shared interactions or covalent interactions. In summary, the most important topological changes observed by formation of the complexes a and b are: a new BCP on the Hw · · · O1 BP and the decrease of the electronic charge density at the Ow-Hw BCPs. These results are in accordance with the lengthening of the Ow-Hw bond lengths and the red shift of ν(O-H) (see Table 1). The decrease of Fb at the Ow-Hw BCPs is major in complexes a with respect to complexes b. In addition, two new BCPs on the H(3,5)ax · · · Ow BP were found in complexes 1a and 2a and another one on the H5ax · · · Ow BP in the complex 3a. Clearly, in complexes a, the bifunctional H-bond is involved with the ringlike structure of the monohydrated complexes, whereas the proton donor unit acts simultaneously as a proton acceptor unit, and it corresponds to the most stable configuration. We attribute this stabilization to cooperative effects. Generally, an indication of these effects is a bigger bond stretch and an enhanced frequency shift of the proton donor bond. Both indicators were found in the complexes studied here. In addition, in these singular systems another indicator of the cooperativity is the increase of Fb values at the Hw · · · O1 BCP in complexes engaged by bifunctional H-bonds. Atomic Properties. To identify the effects that occur due to the formation of different types of H-bonds in the monohydrated cycloethers and to detect the specificity of bifunctional H-bonds, involved in the more stable complexes, we performed an analysis of the atomic properties changes in all atoms of the complexes studied here. In addition, atomic properties, defined by AIM as integrations over the atomic volume, can be computed from experimental electron density.47 In the present work, the atomic properties of significance were the electronic population, N(Ω), the atomic energy, E(Ω), the atomic volume, V(Ω), and the atomic net charge, q(Ω). In Table 3, the atomic property changes (calculated as the difference between the
J. Phys. Chem. A, Vol. 114, No. 8, 2010 2859 TABLE 3: Average Atomic Charge and Change in the Average Atomic Properties on the Atoms Participating in Ow-Hw · · · O and C-H · · · Ow Interactiona,b,c atoms
complex
q(Ω)
∆E(Ω)
∆V(Ω)
H(3,5)axd
1a 1b 2a 2b 3a 3b 1a 1b 2a 2b 3a 3b 1a
0.0261 0.0240 0.0248 0.0224 0.0227 0.0204 -0.0129 -0.0059 -0.0256 -0.0168 -0.0191 -0.0145 0.0094
-9.30 -8.79 -8.94 -8.35 -8.08 -7.86 -0.45 1.06 -0.23 0.039 -1.49 -0.71 -5.07
H(3,5)axd
2a
H5ax
3a
O1
C(3,5)d
1a 1b 2a 2b 3a 3b 1a
C(3,5)d
2a
C5
3a
+0.610 +0.610 +0.609 +0.607 +0.606 +0.604 -1.197 -1.067 -1.197 -1.179 -1.182 -1.172 +0.028 (-0.005) +0.038 (+0.005) +0.049 (-0.015) -1.060 -1.067 -1.054 -1.064 -1.070 -1.076 +0.024 (+0.030) +0.490 (+0.496) +0.017 (+0.022)
Hw
Ow
0.0089
-4.96
0.0103
-4.81
0.0009 -0.0073 0.0014 -0.0070 0.0049 -0.0008 -0.0044
-9.84 -8.01 -9.90 -7.44 -7.96 -6.77 0.07
-0.0033
0.12
-0.0023
-0.13
a The values of the properties are in au. All symbols are explained in the text. b The values of the q(Ω) corresponding to the monomers isolated are given between parentheses. c ∆ refers to change in indicated quantity as a result of formation of the complex. d Correspond to two different atoms, equal due to symmetry reasons. e For the water molecule q(Ow) ) -1.132 and q(Hw) ) +0.566.
monohydrated complex and the isolated monomers) on selected atoms involved in intermolecular H-bonds (i.e., Ow-Hw · · · O1 and C-H · · · Ow) are shown. All the integrated atomic properties were obtained with values of |L(Ω)| less than 4 × 10-4 for the carbon and oxygen atoms and less than 10-5 for the hydrogen atom, such as is specified in the literature.48 The results in Table 3 show that the hydrogen atoms involved in H-bonds verify the following characteristics: (i) decrease of the electronic population, (∆N(Ω) < 0), (ii) energetic destabilization, (∆E(Ω) > 0), and (iii) volume contraction, (∆V(Ω) < 0).49 For comparison, the electronic population change in all atoms of the six complexes is represented in Figure 3. In all complexes the largest changes occurred in the atoms corresponding to the proton donor bond of the Ow-Hw · · · O1 interaction, in which the Hw atom loses and the Ow atom gains electronic population. This is indicative of the polarization of the O-H bond. In consequence, the hydroxyl group of the water molecule merges as a better proton donor and at the same time the Ow atom is transformed in the most important proton acceptor. On the other hand, in complexes a the atoms of the proton donor bonds (i.e., C-Hax) exhibit similar changes but of lesser magnitude. The atoms whose populations were significantly affected when passing from the isolated state to the complex formation (i.e., the absolute difference is greater than 0.02 e) were the Hw, which lost electrons (from -0.044 e (in 1a) to -0.038 e
2860
J. Phys. Chem. A, Vol. 114, No. 8, 2010
Vallejos et al.
Figure 3. Variation of atomic populations for all atoms of the complexes 1a, 2a, 3a, 1b, 2b, and 3b with respect to isolated molecules calculated at the MP2/6-311+G**//MP2/6-31+G** level.
(in 3b)), and the Ow, which gained electrons (from 0.065 e (in 1a) to 0.040 e (in 3b)), after sharing hydrogen atoms with the oxygen atom of the cycloether. In the same sense, the H(3,5)ax in 1a and 2a and H5ax in 3a and their bonded carbon atoms also show loss and gain of electrons. However, the most important topological changes observed by the formation of complexes a and b are not detected on the hydrogen atom bridged between both oxygen atoms in the Ow-Hw · · · O1 interaction. It can be seen in Figure 3 that the loss of electron population at the Hw atom is of similar magnitude in both types of complexes. The difference clearly comes out from the comparison of the electron population of the Ow atom, between both types of complexes. The gain of electronic population at the Ow atom is high in complexes a (26% in 1a, 38% in 2a, and 24% in 3a). Because of this feature, in complexes a assisted by the bifunctional H-bond, the Ow atom is converted into a better proton acceptor. This is a direct consequence of the role played by the oxygen of the water molecule in bifunctional H-bonded complexes. The O1 gains electronic population as well but differently from the previous observation; the increase is more evident in complexes b than in complexes a. Additionally, it is interesting to highlight that the O1 atom results stabilized in complexes b. This must be a consequence of the σ-electronic delocalization in all bonds of the cyclic hydrated complexes; in other words, it must be a consequence of the electron density rearrangement in the whole complex. In Table 3, it can also be observed that the stabilization of the Ow atom in complexes 1a, 2a, and 3a related to complexes 1b, 2b, and 3b increased by 119, 52, and 32%, respectively. This enhancement is accompanied with a diminution in the atomic volume in the complexes 1a and 2a. In both complexes 3a and 3b, the volume decreases, and this reduction is greater in the first complex. As a consequence of the strong Ow-Hw · · · O1 interaction, the O1 and Hw atoms experiences a greater decrease in volume. In the same sense, the H(3,5)ax and H5ax, atoms involved in the C-Hax · · · Ow interactions show energetic destabilization and volume decrease (similar to the Hw atom, but of lower magnitude).
The same findings were obtained by the observation of the atomic charge values. In all complexes positive/negative charges of the Hw/Ow atoms augment with respect to the water molecule. Additionally, the charge on Ow in complexes a was greater in magnitude than in complexes b. This additional charge makes possible the Ow atom interaction with the Hax atoms localized in the hydrophobic part of the cycloethers. Note that the Hax atoms involved in the C-Hax · · · Ow interactions also become more positive. In this regard, a change of sign upon the H(3,5)ax atoms in the tetrahydropyrane molecule can be observed to enable the interaction with the Ow atom. In summary, in complexes a the interactions between the water molecule and either the hydrophilic or the hydrophobic portion of the cycloether molecule are granted by the additional gain of negative charge supported by the Ow atom. Consequently, this fact can explain their ability to interact with the C-Hax bonds of the hydrophobic portion of the cycloether. NBO Analysis. To deepen the knowledge of the effects of the formation of bifunctional H-bonds, we have performed a detailed investigation of the individual H-bond interactions trough natural population and hyperconjugation energies analysis.27 The data in Table 4 reveals the existence of two main hyperconjugative interactions between two lone pairs localized on the O1 atom and the antibonding orbital of the proton donor bond, n(1,2)O1fσ*Ow-Hw, in both complexes a and b. These interactions show high hyperconjugative energies E(2), and they are involved in the Ow-Hw · · · O1 H-bonds. The sum of these interactions indicates that H-bonds are stronger in complexes 1a, 2a, and 3a, when compared to the corresponding complexes b, and by 1.61, 2.38, and 1.09 kcal/mol, respectively. These interactions are responsible for the evident increase in the σ*Ow-H orbital population. In complexes 1a, 2a, and 3a, the gain in electronic population is higher than in complexes b and by 31, 44, and 28%, respectively. These key gains are accompanied by the drop in the electronic population at nOw and nO1 orbitals (this is more significant in a complexes).
Bifunctional Hydrogen Bonds
J. Phys. Chem. A, Vol. 114, No. 8, 2010 2861
TABLE 4: Calculated NBO Atomic Charges (q/e) and Charge Transfer (∆Q/me) at the MP2/6-311++G** Level and Occupancy and Second-Order Interaction Energies (E(2)/kcal/mol) at the HF/6-311++G** Levela parameters
1a
E (nO1fσ*Hw-Ow) E(2)(nOwfσ*C-Hax) ∆σ*Ow-Hw ∆nOw ∆σ*C-H ∆nO1 ∆Q q(Hw) q(Ow) q(H)ax
9.08 0.44b +16.37 -2.10 -0.69 -4.18 -21 +0.4672 -0.9344 +0.2109 (+0.1904) -0.6119 (-0.5905) -0.4142 (-0.0090)
(2)
q(O1) q(C)
1b 7.47 +12.51 -1.33 -2.49 -15 +0.4691 -0.9262 -0.6151
2a
2b
3a
3b
8.57 0.45b +15.28 -2.05 -1.83 -3.17 -20 +0.4662 -0.9342 +0.1790 (+0.1540) -0.6064 (-0.5845) -0.0541 (-0.0430)
6.41
6.07 0.45 +11.42 -1.50 -0.61 -0.40 -13 +0.4672 -0.9252 +0.2224 (+0.1999) -0.6104 (-0.5851) -0.4454 (-0.4324)
4.99
+10.62 -1.57 -0.42 -11 +0.4688 -0.9236 -0.6114
+8.90 -0.74 +1.72 -8 +0.4680 -0.9189 -0.6164
a
Data in parentheses correspond to monomers. b Data corresponds to two equal interactions, only one is reported. c For the isolated water molecule q(Ow) ) -0.8957 and q(Hw) ) +0.4476.
In complexes a, hyperconjugative interactions among the two lone pairs of the Ow atoms and the σ*C-Hax antibonding orbitals were also found. In complexes 1a and 2a these interactions were n(1,2)Owfσ*C(3,5)-Hax, and in 3a was n(1,2)Owfσ*C5-Hax, each one related with the formation of the C-Hax · · · Ow H-bond. The hyperconjugative energies, due to these interactions, are smaller than the ones corresponding to the Ow-Hw · · · O1 H-bonds. However, these weaker interactions act in a concerted form with the n(1,2)O1fσ*Ow-Hw interactions forming a “cyclic donor and acceptor” pattern, causing an enhancement on the main interactions. Also, the favorable position of the lone pair orbital nOw allows a better overlapping between both orbitals. In Figure 4 the main orbitals involved in the H-bonds of complexes 1a and 1b, are represented. As it can be observed, both complexes share a similar pattern of nO1fσ*Ow-Hw interactions, where the two orbitals are oriented face-to-face, providing a strong overlap. Moreover, in the complex 1a the water oxygen atom behaves as a double H-bond acceptor, and the position of the nOw orbital is directly facing each σ*C(3,5)-Hax antibonding orbital (the lone pair of the Ow atom is almost perpendicular to both orbitals σ*C(3,5)-Hax of the tetrahydropyrane). The orientation of the two orbitals provides less overlapping, as compared to the nO1fσ*Ow-Hw interaction. In addition, as nOw donates charge density into two separated antibonding orbitals, the stabilization energy of each of these interactions becomes weaker. Furthermore, the charge transfer between the two monomers was also obtained (Table 4). Taking into account that the charge for each isolated monomer is zero, this magnitude in the complex represents an estimation of the net charge transfer (∆Q) from cycloether to water. The values in Table 4 demonstrate an electron density increase over the water molecule. The ∆Q values for complexes 1a, 2a, and 3a are larger by 40, 82, and 63%, respectively, when compared to complexes b. In summary, complexes engaged by bifunctional H-bond show a good space alignment of these orbitals for cooperative charge transfer through a water molecule. In addition, we have found that the results of the NBO charges are in agreement with those obtained with the AIM analysis. This is to say, the water hydrogen/ oxygen atoms are more positive/negative upon the complexation. In the isolated cycloethers, the intramolecular hyperconjugations are important. These interactions are affected by the intermolecular interactions upon the formation of the complexes. To understand how intermolecular interactions influence in these kind of systems and to find out a particular characteristic of the
Figure 4. Differents view of the complex 1a illustrating the interaction (a) nO1fσ*Ow-Hw related with the formation of the Ow-Hw · · · O1 H-bond and (b) nOwfσ*C(3,5)-Hax related with the formation of the C-H · · · Ow H-bonds. (c) represents the primary interaction nO1fσ*Ow-Hw related with the formation of Ow-Hw · · · O1 H-bond in complex 1b. The lone pair of the oxygen atom is represented by a meshed isosurface and the antibonding orbital by a solid isosurface. Note in (b) the reduced orbitals overlap relative to (a) and (c) cases.
2862
J. Phys. Chem. A, Vol. 114, No. 8, 2010
Vallejos et al.
TABLE 5: NBO Charge-Transfer Intramolecular Analysisa,b parameters ∆E(2){nO1fσ*Za} ∆E(2){σZbfσ*C-H} ∆σ*Za ∆σZb
1a
1a
2a
2b
3a
3b
-6.03 -5.22 -6.31 -4.28 -4.74 -3.83 -1.04c -1.13c -0.49 -8.64 -7.35 -7.64 -6.62 -8.00 -7.94 +1.74c +3.86c +0.55
a ∆E(2) variation of the second-order perturbation energy calculated as the difference between E(2) in the complex and in the isolated monomers, in kcal/mol. b Idem, population variation, ∆σ in milielectrons, me. c Correspond to the single interaction.
complexes engaged by bifunctional H-bond, the intramolecular interactions nO1fσ*Za and σZbfσ*C-Hax, (where σ*Za denotes the antibonding orbitals that interact with the lone pairs of O1 atom and σZb denotes the bonding orbitals that interact with the antibonding orbitals σ*C-Hax) were also investigated. In Table 5, the results related to total hyperconjugation energy change involved in all the intramolecular interactions, and the increase or decrease in the orbital populations involved in these interactions, are summarized. The hyperconjugative energies of the nO1fσ*Za intramolecular interactions exhibited a weakening subsequent to the formation of the complexes. The decrease of the E(2) was slightly larger in complexes a than in complexes b. This fact caused the decrease in the electronic population of the σ*Za antibonding orbitals. We have recognized that the majority of the charge lost on σ*Za was retransferred via nO1 to the σ*Ow-Hw. In the case of the σZbfσ*C-Hax interaction, E(2) also decreases due to the secondary intermolecular interaction (i.e., n(1,2)Owfσ*C(3,5)-Hax), but this reduction is smaller than in the nO1fσ*Za interaction. Because of competitive effects between intra- and intermolecular interactions, the population of the σZb orbitals increased because these orbitals either diminish their charge transfer or fail to transfer charge density to σ*C-Hax. Conclusions A theoretical study about cooperative effects produced by bifunctional H-bonds, at the MP2 level, is accomplished in this work within the framework of the AIM and the NBO theories. We have found that different indicators of H-bond strength such as (i) O1 · · · Hw and Ow-Hw bond distances, (ii) vibrational frequencies at proton donor bonds, (iii) F at the O1 · · · Hw BCPs, (iv) electronic population of the atoms, (v) electronic population of bonding and antibonding orbitals, (vi) stabilization energies due to hyperconjugative interactions (two orbitals-two electrons), and (vii) charge transfer consistently show significant cooperative effects in the bifunctional H-bonds. From the AIM, as well as from the NBO analysis, we conclude that in the monohydrated six-membered cycloether, where the water molecule plays a dual role as proton acceptor and proton donor, remarkable charge density redistribution is produced and this σ-electron delocalization makes the formation of bifunctional H-bond possible. Because of this feature, complexes a are more stable than complexes b. We believe that this study, although it was done in the gas phase and on small model systems, can contribute to the interpretation of the concept of the hydrophobic hydration of solutes with polar groups. In other words, we consider that the molecular electronic distribution undergoes significant changes due to the main interaction on the polar group and its effect on the rest of the molecule can assist to the formation of H-bonds between the C-H bonds and the water molecules.
Finally, studies of the cycloether microhydration (with n ) 2, 3, and 4 water molecules) are under investigation in our laboratory and the results will be published in the near future. Acknowledgment. The authors acknowledge to SECYTUNNE for financial support. M.M.V. is a fellow researcher of SECYT-UNNE; E.L.A. is a fellow researcher of CONICET, and N.M.P. is career researcher of CONICET, Argentina. This work was supported by the PICTO-UNNE 089 grant. Supporting Information Available: A table containing the differences in selected energetic, geometrical, and vibrational parameters between complexes a and b. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Jeffery, G. A. An Introduction to hydrogen bonding; Oxford University Press: New York, 1997. (2) Sheiner, S. Hydrogen Bonding, Oxford University Press: New York, 1997. (3) Desiraju, R. G.; Steiner T. The weak hydrogen bond; Oxford University Press: Oxford, 1999. (4) Grabowski, S. J.; Sokalski, W. A.; Dyguda, E.; Leszczynski, J. J. Phys. Chem. B 2006, 110, 6444. (5) Grabowski, S. J. J. Phys. Chem. A 2007, 111, 3387. (6) Thar, J.; Kirchner, B. J. Phys. Chem. A 2006, 110, 4229. (7) Lamsabhi, A. M. J. Phys. Chem. A 2008, 112, 1791. (8) Scheiner, S.; Kar, T. J. Phys. Chem. A 2008, 112, 11854. (9) Sedlak, R.; Hobza, P.; Patwari, G. N. J. Phys. Chem. A 2009, 113, 6620. (10) Hobza, P.; Havlas, Z. Chem. ReV. 2000, 100, 4253. (11) Reimann, B.; Buchhold, K.; Vaupel, S.; Brutschy, B.; Havlas, Z.; Hobza, P. J. Phys. Chem. A 2001, 105, 5560. (12) Mizuno, K.; Miyashita, Y.; Shindo, Y.; Ogawa, H. J. Phys. Chem. 1995, 99, 3225. (13) Mizuno, K.; Kimura, Y.; Morichika, H.; Nishimura, Y.; Shimada, S.; Maeda, S.; Imafuji, S.; Ochi, T. J. Mol. Liq. 2000, 85, 139. (14) (a) Li, Q.; An, X.; Gong, B.; Cheng, J. Spectrochim. Acta A 2008, 69, 211. (b) Gojło, E.; Gampe, T.; Krakowiak, J.; Stangret, J. J. Phys. Chem. A 2007, 111, 1827. (c) Li, Q.; Wang, N.; Zhiwu, Y. J. Mol. Struct. (THEOCHEM) 2007, 847, 68. (d) Oliveira, B. G.; Vasconcellos, M. L. A. A. J. Mol. Struct. (THEOCHEM) 2006, 774, 83. (15) Mizuno, K.; Imafuji, S.; Fujiwara, T.; Ohta, T.; Tamiya, Y. J. Phys. Chem. B 2003, 107, 3972. (16) Mizuno, K.; Ochi, T.; Shindo, Y. J. Chem. Phys. 1998, 109, 9502. (17) Mizuno, K.; Imafuji, S.; Ochi, T.; Ohta, T.; Maeda, S. J. Phys. Chem. B 2000, 104, 11001. (18) Chang, H.-C.; Jiang, J.-C.; Chuang, C.-W.; Lin, S. H. Chem. Phys. Lett. 2004, 397, 205. (19) Chang, H.-C.; Jiang, J.-C.; Chuang, C.-W.; Lin, J.-S.; Lai, W.-W.; Yang, Y.-C.; Lin, S. H. Chem. Phys. Lett. 2005, 410, 42. (20) Sahu, P. K.; Lee, S.-L. J. Chem. Phys. 2005, 123, 044308. (21) Mizuno, K.; Masuda, Y.; Yamamura, T.; Kitamura, J.; Ogata, I. B.; Tamai, Y.; Yagasaki, T. J. Phys. Chem. B 2009, 113, 906. (22) (a) Sosa, G. L.; Peruchena, N. M.; Contreras, R. H.; Castro, E. A. J. Mol. Struct. (THEOCHEM) 2002, 577, 219. (b) Okulik, N.; Sosa, G. L.; Esteves, P.; Mota, C.; Jubert, A. H.; Peruchena, N. M. J. Phys. Chem. A 2002, 106, 1584. (c) Fidanza, N. G.; Sosa, G. L.; Lobayan, R.; Peruchena, N. M. J. Mol. Struct. (THEOCHEM) 2005, 722, 65. (d) Chamorro, E.; Sequeira, A.; Zalazar, M. F.; Peruchena, N. M. J. Bioorg. Med. Chem. 2008, 16, 8535. (23) Wang, Y.; Balbuena, P. B. J. Phys. Chem. A 2001, 105, 9972. (24) (a) Scheiner, S. J. Phys. Chem. B 2006, 110, 18670. (b) Kar, T.; Scheiner, S. J. Phys. Chem. A 2004, 108, 9161. (25) (a) Parthasarathi, R.; Elango, M.; Subramanian, V.; Sathyamurthy, N. J Phys. Chem. A 2009, 113, 3744. (b) Chen, Y.; Viswanathan, R.; Dannenberg, J. J. J. Phys. Chem. B 2007, 111, 8329. (c) Li, Q.; An, X.; Gong, B.; Cheng, J. J. Phys. Chem. A 2007, 111, 10166. (d) Grabowski, S. J.; Bilewicz, E. Chem. Phys. Lett. 2006, 427, 51. (e) Ziolkowski, M.; Grabowski, S. J.; Leszczynski, J. J. Phys. Chem. A 2006, 110, 6514. Kobko, N.; Dannemberg, J. J. Phys. Chem. A 2003, 48, 10389. (26) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Oxford Science Publications, Clarendon Press: London, 1990. (27) (a) Reed, A. E.; Curtis, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. (b) Weinhold, F. A. J. J. Mol. Struct. (THEOCHEM) 1997, 398, 181. (28) (a) Kim, S.; Schaefer, H. F. J. Phys. Chem. A 2007, 111, 10381. (b) Scheiner, S.; Kar, T. J. Phys. Chem. B 2005, 109, 3681.
Bifunctional Hydrogen Bonds (29) Hernandes, M. Z. AGOA Program, version 2.0 2003. Depto. de Cieˆncias Farmaceˆuticas (UFPE) Available from: http://www.ufpe.br/ farmacia/zaldini/agoa.html/. (30) Oliveira, B. G.; Arau´jo, R. C. M. U.; Carvalho, A. B.; Ramos, M. N.; Hernandes, M. Z.; Cavalcante, K. R. J. Mol. Struct. (THEOCHEM) 2007, 802, 91. (31) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B. 1988, 37, 785. (32) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618. (33) Joseph, J.; Jemmis, E. D. J. Am. Chem. Soc. 2007, 129, 4620. (34) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (35) Blieger-Ko¨nig, F.; Scho¨nbohn, J. AIM 2000 program package, version 2.0; Bader, R. F. W., chemical adviser; Bu¨ro fu¨r Innovative Software Streibel Blieger-Ko¨nig: Bielefeld, Germany, 2002. (36) Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. NBO, Version 3.1; University of Wisconsin: Madison, WI. (37) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; 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.;
J. Phys. Chem. A, Vol. 114, No. 8, 2010 2863 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 D.01; Gaussian, Inc.: Wallingford, CT, 2004. (38) Caminati, W.; Dell` Erba, A.; Melandr, S.; Favero, P. G. J. Am. Chem. Soc. 1988, 120, 5555. (39) Spoerel, U.; Stahl, W.; Caminati, W.; Favero, P. G. Chem.-Eur. J. 1988, 4, 1974. (40) Bader, R. F. W. J. Phys. Chem. A 1998, 102, 7314. (41) Popelier, P. L. A. Atoms in Molecules. An Introduction; Pearson Education: Harlow, U.K., 2000. (42) Boyd, R. J.; Choi, S. C. Chem. Phys. Lett. 1985, 120, 80. (43) Oliveira, B. G.; Pereira, F. S.; de Araujo, R. C. M. U.; Ramos, M. N. Chem. Phys. Lett. 2006, 427, 181. (44) Grabowski, S. J. Chem. Phys. Lett. 2001, 338, 361. (45) Wojtulewski, S.; Grabowski, S. J. J. Mol. Struct. 2002, 605, 235. (46) Grabowski, S. J. J. Phys. Org. Chem. 2004, 17, 18. (47) Koritsanszky, T.; Flaig, R.; Zobel, D.; Krane, H. G.; Morgenroth, W.; Luger, P. Science 1998, 279, 356. (48) Blieger-Ko¨nig, F. J. Comput. Chem. 2000, 21, 1040. (49) (a) Koch, U.; Popelier, P. L. A. J. Phys. Chem. 1995, 99, 9747. (b) Popelier, P. L. A. J. Phys. Chem. A 1998, 102, 1873.
JP906372T
