Ab initio and AIM studies on intramolecular dihydrogen bonds

Journal of Molecular Structure 645 (2003) 287–294 www.elsevier.com/locate/molstruc

Ab initio and AIM studies on intramolecular dihydrogen bonds Sławomir Wojtulewskia, Sławomir J. Grabowskia,b,* a

Institute of Chemistry, University of Białystok Al. J. Piłsudskiego 11/4, 15-443 Białystok, Poland Department of Crystallography and Crystallochemistry, University of Ło´dz´, ul. Pomorska 149/153, 90-236 Ło´dz´, Poland

b

Received 5 August 2002; revised 8 November 2002; accepted 8 November 2002

Abstract Ab inito calculations on molecules with intramolecular dihydrogen bonds have been performed at MP2/6-311þþ G(d,p) level of theory. The O – H bond for these systems is the proton donator and the H– B bond of BH2 3 group is the acceptor within B– H· · ·H – O H-bridge. Different geometrical, energetic and topological parameters derived from the theory of Bader have been studied. The correlation analysis shows that there is no the meaningful delocalization of electrons within the ring formed by the intramolecular H-bridge. The properties of the bond critical points of Hþd· · ·2dH contacts and the properties of the ring critical points are useful parameters for the description of the unconventional H-bond analysed in this study. q 2003 Elsevier Science B.V. All rights reserved. Keywords: Dihydrogen intramolecular bonds; The Bader theory; Ab initio calculations; Bond critical points; Ring critical points

1. Introduction There has been considerable interest recently in various types of weak and unconventional hydrogen bonds in the context of supramolecular chemistry, crystal engineering and a wide range of chemical and biological processes [1 – 3]. Among these interactions the H2d· · ·þdH or dihydrogen bond is often the subject of investigations [3]. The concept of dihydrogen bond has been introduced few years ago [4] to name the interaction occurring between a conventional hydrogen bond donor such as N – H or O – H bond as the weak acid component and an element-hydride bond as the weak * Corresponding author. Address: Department of Crystallography and Crystallochemistry, University of Ło´dz´, ul. Pomorska 149/153, 90-236 Ło´dz´, Poland. E-mail address: [email protected] (S.J. Grabowski).

base component, where the element in question can be transition metal or boron. Dihydrogen bonds with B – H2d bond as a proton acceptor have been investigated both experimentally [4 –7] as well as theoretically [5,8 –17]. For example, a comparison of the melting points of H3CCH3 (2 181 8C) and of the isoelectronic species H3BNH3 (þ 104 8C) suggests that unusually strong interactions are present in H3BNH3. Because of the lack of lone pairs it cannot be conventional hydrogen bonds but rather H2d· · ·þdH bonds [5]. The B – H· · ·H – N bond within [H3BNH3]2 dimer has been investigated theoretically [5] by PCI-80/B3LYP theoretical studies, an empirically parametrized density functional theory [18,19]. The interaction energy of H· · ·H bond for such system amounts to 6.1 kcal/mol [5]. It has been pointed out that the dihydrogen bond corresponds to the predissociative protonation [20]; it

0022-2860/03/$ - see front matter q 2003 Elsevier Science B.V. All rights reserved. doi: S0022-2860(02)00581-1

288

Sł. Wojtulewski, Sł.J. Grabowski / Journal of Molecular Structure 645 (2003) 287–294

has been investigated using the Bader theory [21] and analysing the ELF function (the electron localization function) gradient field [22]. The more detailed insight into crystalline intermolecular and intramolecular dihydrogen bonded complexes was done showing the existence of short H· · ·H distances within H-bridges [23,24]. The Cambridge Structural Database (CSD) [25] was also searched for specific close intermolecular DHBs—B – H· · ·H – N systems of which 26 were ˚ in amine-boranes [4]. found in the range 1.7 – 2.2 A Intramolecular B –H· · ·H –N hydrogen bonds have been also found in boronated heterocycles as for example N-1-(cyanoboryl)cytosine [26]. The similar intramolecular B –H· · ·H –O interactions have been investigated recently using different levels of theory up to MP2/6-311þ þ G(3d,3p) [17]. The calculations have been performed for a (1Z)-2-borylethen-1-ol molecule and its derivatives [17] to show that in this case the similar effect may be detected as for the intramolecular O –H· · ·O bonds known as resonance assisted hydrogen bonds (RAHBs) [27 –32]. The aim of the present work is to study intramolecular H-bonded B – H· · ·H – O systems where B –H2d proton accepting bond derives from 2 BH2 3 group. The ionic systems investigated here are similar to the studied previously (1Z)-2-borylethen-1ol molecule and its derivatives [17]. The systems studied here may form stronger intramolecular dihydrogen bonds because of their ionicity. The intermolecular ionic H-bonds with BH2 4 proton accepting moiety were studied previously [12] up to MP2/6-31G** level of theory with BSSE correction. The stronger ionic H-bonds than for the other non-ionic related systems [12] were detected; for example the binding energy for BH2 4 · · ·HCN complex amounts to 18.03 kcal/mol for the mentioned above MP2/6-31G** level of theory. The atoms in molecules theory of Bader (AIM) [21] is also applied here to study the properties of the bond critical point of H2d· · ·þdH contact and of the ring critical point and to analyse dependencies between topological, energetic and geometrical parameters. The possibility of the estimation of the H-bond energy of the intramolecular H-bridge are also analysed.

2. Computational details The calculations were carried out at the ab initio level, using GAUSSIAN 98 program [33]. The MP2/6-311þ þ G** level of theory was used to optimise the geometry of molecules. Additionally the AIM theory of Bader [21] was used to localize bond critical points and to calculate their properties: electron densities at bond critical points (rBCPs) and electron densities at ring critical points (rRCPs). The Laplacians of these densities were also calculated: Laplacians of electronic densities at bond critical points—72rBCPs and Laplacians of electronic densities at ring critical points—72rRCPs. All AIM calculations [34,35] were performed using AIM2000 program [36].

3. Results and discussion The calculations on (1Z)-2-borylethen-1-ol (BH2 – CH – CH – OH) have been performed previously [17]; the similar systems are the subject of the present study—the BH2 group is replaced by BH2 3 . In such case we may expect the formation of the stronger intramolecular dihydrogen bonds. Hence BH2 3 –CH – CH – OH and its fluoro derivatives are investigated. Two configurations of each compound investigated here were optimized within MP2/6-311þ þ G** level of theory: the first one called later as ‘the open configuration’ and the second one—‘the closed configuration’ (Scheme 1). The calculations on the open configuration were performed in the following way. For the closed optimized configuration the O –H bond was rotated 1808 around C –O bond. Afterwards the obtained moiety was optimized at the same level of theory as it was previously done for the closed configuration. The difference between energies of both configurations corresponds approximately to H-bond energy. Such procedure of the estimation of the intramolecular H-bond energy was applied earlier [37,38] but it was also pointed out that the other effects due to the rotation should be taken into account [37]. In other words the mentioned above difference only roughly corresponds to the H-bond energy. Table 1 presents the calculated energies and the geometrical parameters of the molecules investigated

Sł. Wojtulewski, Sł.J. Grabowski / Journal of Molecular Structure 645 (2003) 287–294

289

Scheme 1.

here; the results of both configurations are included. EHB being the difference in energy described above do not correlate with the other parameters. For example, the linear correlation coefficients for the dependencies EHB vs rH· · ·H and EHB vs rOH amount to 0.315 and 0.249, respectively. rH· · ·H and rOH are the distances corresponding to the H· · ·H contact and to the O –H bond, respectively. The similar dependencies for intermolecular conventional H-bonds are often well correlated [39,40]. Even for intramolecular H-bonds

existing within malonaldehyde and its derivatives there are well correlations—EHB vs rOH and EHB vs r H· · ·O (H· · ·O is the contact within O – H· · ·O intramolecular H-bond) [38]. What may be the reason of the lack of such correlations for the sample of species investigated here? The first reason may be that the difference in energy between open and closed configurations do not correspond to the H-bond energy. The second reason of the lack of the mentioned above correlations is

Table 1 ˚ ), for closed and open configurations. H· · ·H distances (in A ˚) The geometrical parameters—C–O, O– H, CyC, C– B and B–H bond lengths (in A and energies—EHB and EpHB (in kcal/mol) are also given; R1 –R4 substituents correspond to those presented in Scheme 1 R1, R2, R3, R4

C –O

O –H

CyC

C –B

B –H

H· · ·H

EHB

EpHB

Closed configuration H, H, H, H F, F, H, H H, H, F, F F, H, H, H H, F, H, H F, H, F, H H, F, F, H H, F, F, F F, H, F, F

1.387 1.363 1.384 1.359 1.389 1.355 1.384 1.384 1.355

0.976 0.976 0.972 0.980 0.972 0.980 0.972 0.970 0.977

1.348 1.341 1.345 1.335 1.346 1.336 1.346 1.344 1.334

1.625 1.610 1.619 1.628 1.607 1.623 1.613 1.621 1.618

1.247 1.244 1.249 1.251 1.242 1.258 1.247 1.247 1.257

1.704 1.708 1.758 1.641 1.762 1.627 1.756 1.780 1.653

213.9 211.3 211.9 212.5 212.2 210.8 214.0 210.8 211.0

24.79 24.70 24.19 25.70 24.06 26.00 24.16 23.91 25.57

Open configuration H, H, H, H F, F, H, H H, H, F, F F, H, H, H H, F, H, H F, H, F, H H, F, F, H H, F, F, F F, H, F, F

1.406 1.372 1.399 1.371 1.402 1.365 1.400 1.395 1.366

0.958 0.960 0.958 0.960 0.958 0.963 0.957 0.957 0.961

1.343 1.340 1.339 1.328 1.345 1.328 1.343 1.343 1.326

1.626 1.608 1.627 1.631 1.606 1.630 1.637 1.630 1.629

1.226 1.223 1.223 1.226 1.223 1.228 1.231 1.222 1.224

290

Sł. Wojtulewski, Sł.J. Grabowski / Journal of Molecular Structure 645 (2003) 287–294

Fig. 1. The relationship between the EpHB energy (kcal/mol) and the ˚ ). H· · ·H distance (in A

probably connected with the characteristic of the sample, ionic systems ( –BH2 3 group) and the greater strain effects than for the intramolecular H-bonded systems investigated earlier [17,38]. In other words EHB energy defined as the difference between two configurations presented in Scheme 1 does not correspond to the H-bond energy for the sample of species investigated here. Another approach is based on the consideration of the isodesmic reactions [41,42]. Again this way does not guarantee to obtain the proper H-bond energies. The H-bond energies may be also estimated from the properties of bond critical points. Hydrogen bonded X – H· · ·O (X ¼ C, N, O) systems taken from accurate X-ray measurements were analysed [43] and from the experimental electron densities the topological parameters were obtained. The simple relationship between H-bond energy and the potential energy density V(rCP) at the critical point

corresponding to H· · ·O contact was proposed [43] EpHB ¼ 1/2 V(rCP). EpHB designates here the real Hbond energy in opposite to the designation EHB corresponding to the mentioned earlier energy difference between two conformations (Scheme 1). EpHB energies calculated from the potential energy densities of H· · ·H contacts are included in Table 1. There is no correlation between EHB and EpHB; the linear correlation coefficient amounts to 0.266. However, EpHB correlates with the geometrical parameters which are usually assumed to be good descriptors of the H-bond strength. It is well known that for the related systems the stronger is H-bond the greater is the elongation of the proton donating bond and the shorter is H· · ·Y (Y is the proton acceptor) contact. Such situation is observed for the species studied here. There is the correlation between EpHB and H· · ·H distance (Fig. 1); the linear correlation coefficient R amounts to 0.995. The linear dependence is also observable between EpHB and O – H bond length 2 R is equal to 0.957. It means that EpHB is a good description of the H-bond strength and probably corresponds to H-bond energy according to the findings of Espinosa et al. [43]. The more detailed insight into the results of Table 1 show that there is no the delocalization of electrons which may be observed for the resonance assisted Hbonds (RAHBs) [27 – 32]. For such systems (Scheme 2) we can observe the equalization of CyC and C – C bonds and the same effect of the equalization for C – O and CyO bonds. This effect is observable for both open and closed configurations being stronger for the second

Scheme 2.

Sł. Wojtulewski, Sł.J. Grabowski / Journal of Molecular Structure 645 (2003) 287–294

(of O – H bond), it means the loss of the electron charge. There is a slight decrease of the electron charge for O-atom of the system with R1 ¼ F, R2 ¼ H, R3 ¼ F, R4 ¼ H and a slight decrease for H-atom (an accepting centre) for the case with R1 ¼ H, R2 ¼ R3 ¼ F, R4 ¼ H. For the last two cases such decrease of the electron charge is probably connected with the fractional transfer of the electron charge to electronegative fluorine atoms. The insight into the results of Table 1 shows the relationships between geometrical parameters. For example, the linear correlation coefficient for the dependence between the O – H proton donating bond length and the H· · ·H distance is equal to 0.986. Table 3 presents the topological parameters of the closed configurations of the species investigated here. The electron densities at B – H2d; O –Hþd; H2d· · ·þdH bond critical points are given. The corresponding values of Laplacians are also collected. Figure 2 presents the contour map of the intramolecular Hbonded conformation of BH2 3 –CH –CH –OH molecule. The circles of Fig. 3 correspond to atoms (attractors), triangles correspond to the bond critical points and the square within the ring formed due to the intramolecular H-bond designates the existence of the ring critical point. The topological parameters similarly as the geometrical ones do not correlate with EHB energy. However, we observe the correlations between topological parameters. For example, the correlation coefficient between rO – H and rH· · ·H amounts to 0.981 (Fig. 3). rO – H corresponds to the electron density at the O – H bond critical points and rH· · ·H corresponds to the electron density at the H· · ·H bond critical point.

Table 2 Change in natural population atomic charge (me) of atoms in Hbonded system O –Hþd· · ·2d H relative to the open configuration R1,R2, R3, R4

DqO

DqH( – O)

DqH(acceptor)

H, H, H, H F, F, H, H H, H, F, F F, H, H, H H, F, H, H F, H, F, H H, F, F, H H, F, F, F F, H, F, F

55.7 17.5 59.4 15.2 47.1 21.6 38.6 51.2 30.6

20.6 27.4 1.2 28.6 6.7 26.6 13.8 8.8 23.9

27.3 7.7 7.7 30.0 2.5 13.8 24.3 7.7 23.5

291

one where the intramolecular O – H· · ·O hydrogen bridge exists [38]. The delocalization of p-electrons leading to the equalization of the corresponding bonds is much weaker for the similar systems with intramolecular dihydrogen bonds [17]. This effect of the equalization of bonds does not exist for the species investigated here (Table 1). However, we see the slight elongation of CyC bond for the closed configurations in comparison with the open ones. It is connected with the loss of electron charge within the CyC bond region and its transfer to the proton donating bond and to the acceptor. Table 2 shows the change of atomic charges for atoms within O – Hþd· · ·2dH dihydrogen bonds of the species investigated here. Comparing the closed configurations with the open ones we see an increase of the electron density for all atoms except of a slight loss for few cases. There are the following exceptions; for R1 ¼ R2 ¼ R3 ¼ R4 ¼ H we observe a slight increase of the positive charge density for H-atom

Table 3 The topological parameters for the closed configurations: electron densities rH· · ·H, rO – H, rH – B, rRCP (e/a30) and their Laplacians 72rH· · ·H, 72rO – H, 72rH – B, 72rRCP (e/a50) R1, R2, R3, R4

rH· · ·H

rOH

rH – B

rRCP

72rH· · ·H

72rO – H

72rH – B

72rRCP

H, H, H, H F, F, H, H H, H, F, F F, H, H, H H, F, H, H F, H, F, H H, F, F, H H, F, F, F F, H, F, F

0.024 0.024 0.021 0.028 0.021 0.028 0.022 0.020 0.027

0.346 0.344 0.351 0.340 0.350 0.340 0.351 0.353 0.343

0.139 0.140 0.151 0.137 0.141 0.141 0.146 0.152 0.147

0.018 0.018 0.016 0.019 0.017 0.019 0.016 0.015 0.018

0.060 0.059 0.058 0.063 0.055 0.065 0.056 0.055 0.065

22.412 22.420 22.462 22.379 22.443 22.381 22.452 22.474 22.409

0.027 0.034 20.102 0.038 0.024 20.028 20.044 20.107 20.088

0.079 0.078 0.075 0.085 0.073 0.088 0.074 0.071 0.086

292

Sł. Wojtulewski, Sł.J. Grabowski / Journal of Molecular Structure 645 (2003) 287–294

Fig. 2. The contour map of the electron density of the closed configuration; the circles correspond to the positions of atoms, the triangles represent the positions of the bond critical points and the square correspond to the position of the ring critical point.

The second value is the electron density at the critical point of the H· · ·Y contact within X – H· · ·Y hydrogen bridge. In this case it is the H· · ·H contact within the intramolecular dihydogen bond. It is well known that such parameter (rH· · ·Y) often correlates with H-bond energy for conventional H-bonds [44,45] and for unconventional ones as for example dihydrogen bonds [12,15]. The correlation between EHB and

Fig. 3. The relationship between the electron density at the H· · ·H bond critical point—rH· · ·H (e/a30) and the electron density at the O– H bond critical point—rO – H (e/a30).

rH· · ·Y was found even for intramolecular H-bonds [38] but not for the systems with the intramolecular dihydrogen bonds investigated here. As it was mentioned earlier in this study the reason of the lack of such correlation is rather connected with EHB parameter which does not correspond to H-bond energy. In the case of EpHB energy the correlations with topological parameters are observed here. The linear correlation coefficient for the relationship EpHB vs rH· · ·H amounts to 0.988 (Fig. 4). Similarly there is the correlation for EpHB vs rOH; the linear correlation coefficient is equal to 0.954. From the analysis of topological parameters we see that the EpHB energy obtained from the potential energy density at H· · ·H BCP may correspond to H-bond energy. Another topic analysed here is the existence of the ring critical point for closed configurations. It has been pointed out very recently [46] that for intramolecular H-bonds there is the correlation between the electron density at the bond critical point corresponding to the contact within H-bridge and the electron density at the ring critical point rRCP. The excellent linear correlation was detected for two different samples with intramolecular H-bonds: the derivatives of malonaldehyde and the derivatives of o-hydroxybenzaldehyde [46]. For the sample investigated here there is also a good polynomial correlation (the polynomial of the second degree) between these parameters (rRCP and rH· · ·H) with the correlation coefficient of 0.973 (Fig. 5). It means that the properties of the ring critical point which exists due to the hydrogen bonding formation may be very useful to estimate the strength of the intramolecular H-bond. Additionally the R-value for

Fig. 4. The dependence between the EpHB energy (kcal/mol) and the electron density at the H· · ·H bond critical point—rH· · ·H (e/a30).

Sł. Wojtulewski, Sł.J. Grabowski / Journal of Molecular Structure 645 (2003) 287–294

Fig. 5. The relationship between the electron density at the H· · ·H bond critical point—rH· · ·H (e/a30) and the electron density at the ring critical point—rRCP (e/a30).

the second order polynomial regression—EpHB vs rRCP is equal to 0.922. The molecules investigated in this paper are the modelled systems chosen because of their simplicity and convenient for higher level ab initio calculations; MP2/6-311þ þ G(d,p) in this study. However, the similar, but usually much more complicated and complex molecules exist in the liquid or in the solid state. For example, for the crystals of 2,2,2-tris((Boranato(diphenyl)phosphonio)methyl)ethanol (YIBTAE refcode in the Cambridge Crystal Structural

293

Database [25]) the intramolecular B – H2d· · ·þdH – O hydrogen bonds exist (BH2 3 group as a proton ˚ acceptor) with the H· · ·H distance of 2.230 A (Fig. 6); close to the corresponding sum of the van der Waals radii. Such results taken from the experimental measurements suggest the existence of the hydrogen bonding. The single point ab initio calculations on the moiety of 2,2,2-tris((Boranato(diphenyl)phosphonio)methyl)ethanol taken from the crystal structure have been performed in this study. Because of the complexity and the large size of the moiety the HF/3-21G* level of theory was chosen. The AIM calculations on the corresponding wave function gave the value of the electron density of the H2d· · ·þdH bond critical point—rH· · ·H ¼ 0.0060 a.u. and the value of the electron density at the ring critical point—rRCP ¼ 0.0055 a.u. The corresponding Laplacian values, 72rH· · ·H and 72rRCP, amount to 0.0340 and 0.0282 a.u., respectively. These results also suggest that for the crystal structure presented here the intramolecular dihydrogen bonds may exist since the topological criteria of the existence H-bond have been given [47]. According to these criteria we say that H-bond exists if the electron density at H· · ·Y bond critical point is in the range 0.002 – 0.035 au and the range of the corresponding Laplacian (72rH· · ·Y) is from 0.024 to 0.139 a.u. The rH· · ·H and 72rH· · ·H values for the H· · ·H bond critical point of 2,2,2tris((Boranato(diphenyl)phosphonio)methyl)ethanol amount to 0.006 and 0.034 a.u., respectively; they are within the ranges described above.

4. Conclusions

Fig. 6. The fragment of the 2,2,2-tris((Boranato(diphenyl)phosphonio)methyl)ethanol moiety taken from CSD.

The intramolecular dihydrogen bonds for the simple modeled systems (BH2 3 – CH –CH –OH and its fluoro derivatives) have been investigated here using MP2/6-311þ þ G** level of theory. The ab initio results and the topological parameters derived from the Bader theory suggest that the systems are characterized by the existence of H-bonds of the medium strength, however, some of correlations are problematic. There is no correlations between EHB energy (which usually roughly corresponds to H-bond energy) and the other parameters. However, EpHB energy calculated from the topological parameters may be treated as the H-bond energy and it well

294

Sł. Wojtulewski, Sł.J. Grabowski / Journal of Molecular Structure 645 (2003) 287–294

correlates with the other values which are usually assumed to be the descriptors of H-bond strength. Additionally it seems that some of data may be treated as measures of H-bond strength; H· · ·H distance, O –H bond length, the electronic densities at the critical points: the H· · ·H bond critical point—rH· · ·H, the O – H bond critical point—rOH and the ring critical point—rRCP.

[26]

[27] [28] [29]

References

[30]

[1] G.A. Jeffrey, W. Saenger, Hydrogen Bonding in Biological Structures, Springer, Berlin, 1991. [2] G.R. Desiraju, T. Steiner, The Weak Hydrogen Bond in Structural Chemistry and Biology, Oxford University Press, New York, 1999. [3] I. Alkorta, I. Rozas, J. Elguero, Chem. Soc. Rev. 27 (1998) 163. [4] T.B. Richardson, S. deGala, R.H. Crabtree, P.E.M. Siegbahn, J. Am. Chem. Soc. 117 (1995) 12875. [5] R.H. Crabtree, P.E.M. Siegbahn, O. Eisenstein, A.L. Rheingold, T.F. Koetzle, Acc. Chem. Res. 29 (1996) 348. [6] J. Wessel, J.C. Lee, E. Peris, G.P.A. Yap, J.B. Fortin, J.S. Ricci, G. Sini, A. Albinati, T.F. Koetzle, O. Eisenstein, A.L. Rheingold, R.H. Crabtree, Angew. Chem. Int. Ed. Engl. 34 (1995) 2507. [7] T.B. Richardson, T.F. Koetzle, R.H. Crabtree, Inorg. Chim. Acta 250 (1996) 69. [8] Q. Liu, R. Hoffman, J. Am. Chem. Soc. 117 (1995) 10108. [9] G. Orlowa, S. Scheiner, J. Phys. Chem. A 102 (1998) 260. [10] G. Orlowa, S. Scheiner, J. Phys. Chem. A 102 (1998) 4813. [11] G. Orlowa, S. Scheiner, T. Kar, J. Phys. Chem. A 103 (1999) 514. [12] I. Alkorta, J. Elguero, C. Foces-Foces, Chem. Commun. (1996) 1633. [13] P.L.A. Popelier, J. Phys. Chem. A 102 (1998) 1873. [14] S.J. Grabowski, Chem. Phys. Lett. 312 (1999) 542. [15] S.J. Grabowski, J. Phys. Chem. A 104 (2000) 5551. [16] S.J. Grabowski, J. Mol. Struct. 553 (2000) 151. [17] S.J. Grabowski, Chem. Phys. Lett. 327 (2000) 203. [18] P.E.M. Siegbahn, M.R.A. Blomberg, M. Svensson, Chem. Phys. Lett. 223 (1994) 35. [19] P.E.M. Siegbahn, M. Svensson, P.J.E. Boussard, J. Chem. Phys. 102 (1995) 5377. [20] F. Fuster, B. Silvi, S. Berski, Z. Latajka, J. Mol. Struct. 555 (2000) 75. [21] R.F.W. Bader, Atoms in Molecules. A Quantum Theory, Oxford University Press, New York, 1990. [22] A.D. Becke, K.E. Edgecombe, J. Chem. Phys. 92 (1990) 5397. [23] D. Braga, P.D. Leonardis, F. Grepioni, E. Tedesco, M.J. Calhorda, Inorg. Chem. 37 (1998) 3337. [24] D. Braga, F. Grepioni, E. Tedesco, M.J. Calhorda, P.E.M. Lopes, New J. Chem. (1999) 219. [25] F.H. Allen, J.E. Davies, J.E. Galloy, J.J. Johnson, O. Kennard,

[31] [32] [33]

[34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47]

C.F. Macrave, E.M. Mitchel, J.M. Smith, D.G. Watson, J. Chem. Inf. Comput. Sci. 31 (1991) 187. M.A. Zottola, P. Pedersen, P. Singh, B. Ramsay-Shaw, in: D.A. Smith (Ed.), Modeling the Hydrogen Bond, ACS Symposium Series, vol. 569, American Chemical Society, Washington, DC, 1994. G. Gilli, F. Bellucci, V. Ferretti, V. Bertolasi, J. Am. Chem. Soc. 111 (1989) 1023. V. Bertolasi, P. Gilli, V. Ferretti, G. Gilli, J. Am. Chem. Soc. 113 (1991) 4917. G. Gilli, V. Bertolasi, P. Gilli, V. Ferretti, J. Am. Chem. Soc. 49 (1993) 564. P. Gilli, V. Bertolasi, V. Ferretti, G. Gilli, J. Am. Chem. Soc. 116 (1994) 909. G. Gilli, V. Bertolasi, in: Z. Rappaport (Ed.), The Chemistry of Enols, Wiley, New York, 1990, Chapter 13. G.K.H. Madsen, B.B. Iversen, F.K. Larsen, M. Kapon, G.M. Reisner, F.H. Herbstein, J. Am. Chem. Soc. 120 (1998) 10040. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, L.R. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, G. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, GAUSSIAN 98; Revision A.6, Gaussian, Inc., Pittsburgh, PA, 1998. F.W. Biegler-Ko¨nig, R.F.W. Bader, Y.H. Tang, J. Comput. Chem. 3 (1982) 317. R.F.W. Bader, Y.H. Tang, Y. Tal, F.W. Biegler-Ko¨nig, J. Am. Chem. Soc. 104 (1984) 946. AIM2000 designed by Friedrich Biegler-Ko¨nig, University of Applied Sciences, Bielefeld, Germany. M. Cuma, S. Scheiner, T. Kar, J. Mol. Struct. (Theochem) 467 (1999) 37. S.J. Grabowski, J. Mol. Struct. 562 (2001) 137. M. Ichikawa, Acta Crystallogr. B34 (1978) 2074. S.J. Grabowski, T.M. Krygowski, Tetrahedron 54 (1998) 5683 and references cited therein. W.J. Hehre, L. Radom, P.v.R. Schleyer, J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986. I. Rozas, I. Alkorta, J. Elguero, J. Phys. Chem. A 105 (2001) 10462. E. Espinosa, E. Molins, C. Lecomte, Chem. Phys. Lett. 285 (1998) 1703. L. Gonza´lez, O. Mo´, M. Ya´n˜ez, J. Phys. Chem. A 101 (1997) 9710. E. Espinosa, M. Souhassou, H. Lachekar, C. Lecomte, Acta Crystallogr. B55 (1999) 563. S.J. Grabowski, Monatsh. Chem. 133 (2002) 1373. U. Koch, P.L.A. Popelier, J. Phys. Chem. A 99 (1995) 9747.