REGULAR PAPERS

The electronic structure of the C₂H₃Cl···HX (X = Cl, CN, NC and CCH) vinylcloride complexes evaluated via topological parameters and DFT calculations

Boaz G. Oliveira

Departamento de Ciências Farmacêuticas, Universidade Federal de Pernambuco
50740-521, Recife – PE, Brazil
E-mail: boazgaldino@gmail.com

Received August 11, 2008.
In final form November 12, 2008.

Abstract
The optimized geometries of the C₂H₃Cl···HX vinylchloride complexes with X = Cl, CN, NC and CCH were obtained at B3LYP/6-311++G(d,p) level of theory. In a first analysis, the (Cl···HX) hydrogen bonds were examined by taking into account their distances, intermolecular interaction energies and CHELPG charge transfer, as well as charge densities obtained through the calculations of theory of Atoms In Molecules (AIM). Moreover, a (X···H) secondary interaction between the hydrogen atoms of vinylchloride and fluorine of HF, nitrogen of both HCN and HNC molecules, and p bond of HCCH was also a target of investigation. This secondary interaction was studied not only in terms of topological criteria or by results of structural and electronic parameters, but it was also analyzed the stretch modes in the infrared spectrum. At last, as far as the vibrational red-shifts of the HX molecules were characterized, the stretch frequencies and absorption intensities of the (X···H) secondary interactions were also identified, but only for the C₂H₃Cl···HCCH complex.

Resumen
Las geometrías del C₂H₃Cl···HX vinylchloride complejos con X = Cl, CN, NC y CCH fueron obtenidas en el nivel de teoría B3LYP/6-311++G(d,p). En un primer análisis, el ligaciones de hidrógeno (Cl···HX) fueron examinadas teniendo en cuenta sus distancias, energías de interacción intermoleculares y transferencia de carga CHELPG, así como las densidad de electróns obtenidas por los cálculos de la teoría de Atoms in Moleculres (AIM). Además, una interacción secundaria (X···H) entre los átomos de hidrógeno de vinylchloride y el flúor de HF, nitrógeno de HCN como de las moléculas de HNC, y la ligacion p de HCCH fueron también un objetivo de investigación. Esta interacción secundaria fue estudiada no sólo en términos de criterios topológicos o por resultados de parámetros estructurales y electrónicos, pero también fue analizado los modos de extensión en el espectro infrarrojo. Por fin, por lo que los cambios rojos vibrational de las moléculas HX fueron caracterizados, las frecuencias y intensidades de absorción del las interacciones secundarias (X•••H) también fueron identificadas, pero sólo para el complejo C₂H₃Cl ••• HCCH.

Introduction
Nowadays, it has been manifested a great interest by studies of non-covalent intermolecular phenomena, in which the hydrogen bonding is one of the most important types because there is a large number of biological, physical and chemical systems formed through the interaction between a proton donor and a rich charge density site. One important charge density center is the halide species, which in some situations interacts with hydrocarbons and produces the halide hydrocarbons. As example, vinylhalide or more specifically vinylchloride (C₂H₃Cl), which is a chloride hydrocarbon containing a carbon-carbon double bond formed by attack of hydrochloric acid to acetylene [1-2], properly the formation of C₂H₃Cl is ruled by the interaction of the hydrochloride acid aligned with p bond of acetylene, what leads at formation of an intermolecular system characterized by a typical (p···H) interaction [3]. After this, other hydrochloride acid molecule interacts with the n lone electron pair (Cl) of vinylchloride and thereby a (n···H) hydrogen bond is formed [4].
Some years ago, geometries and related parameters of p intermolecular systems formed by acetylene and proton donors have been detailed studied [3]. Recently, coexistence of theoretical and experimental observations about the electronic structures of the C₂H₃Cl···HCl and C₂H₃Cl···HF complexes has been reported by Herrebout and van der Veken [5-7]. Experimentally, by using the pulsed-nozzle Fourier Transform Microwave Spectroscopy (FTMS) [8], Legon and co-workers have documented several studies about the equilibrium geometry of hydrogen complexes constituted by vinylhalide and monoprotic acids [9-11]. From these works, it has been established that the interaction between vinylhalide (Y = Cl or F) and acid species (HX) are characterized by a distortion on its (Y···HX) hydrogen bonds, as already observed in other hydrogen-bonded species [12]. Specifically, the (Y···HX) hydrogen bond is non-linear because is supposed the formation of a secondary interaction between the halogen and hydrogen atom of vinylhalide. For C₂H₃Cl···HCl and C₂H₃F···HF complexes, in fact this secondary interaction is based on experimental evidences, which says that Cl and F interacts with the H atom (=CH₂ group) of the C₂H₃Cl and C₂H₃F molecules, respectively [11]. By taking into account the C₂H₃Cl···HX with X = Cl, CN, NC and CCH set of complexes, however, we alert the importance for studying the nature of the secondary interaction in these systems. In practice, we expect to obtain theoretical informations that corroborates with the FTMS experimental results, as well as lead us to predict new insights about this interaction phenomenon.

Computational strategy
However, by projecting a theoretical study of the C₂H₃Cl···HX vinylchloride complexes and their hydrogen bonds and secondary interactions, we should mention that a quantumchemical description of charge density and molecular topology seems to be essential. The objective of determination and evaluation of molecular surface parameters from charge density can be naturally associated to theory of Atoms in Molecules (AIM) [13] of Bader. In this work, the contribution of AIM calculations will be performed by localization of Bond Critical Points (BCP) between chloride of vinylchloride and hydrogen atom of acid species, as well as if possible between Cl, CN, NC and CCH groups and hydrogen atoms of the vinylchloride, what properly characterizes the (Cl···X) hydrogen bonds and (X···H) secondary interactions, respectively. In this insight, we would like to emphasize that the choice of computational method must be evaluated critically. As well-known, the addition studies of hydrogen halides to alkenes [14] have been effectuated successfully by using the Density Functional Theory (DFT) [15]. In terms of DFT calculations, the B3LYP [16] hybrid was chosen because a lot of hydrogen-bonded systems have been successfully studied through this popular functional [17-23]. For ab initio basis sets, during all these years the choice for split-valence and/or correlation consistent types still yields intense discussion among the theoreticians. Thereby, we admit some traditional concepts, i.e., the description of "heavy" (C, N and Cl) and "soft" (H) atoms will be developed through the application of "d" and "p" polarization functions within the 6-31G Pople's split-valence wave function. Fundamentally, the inclusion of diffuse functions (++) is also important, mainly for BSSE correction.

Theoretical procedure
The optimized geometries of the C₂H₃Cl···HX with X = Cl, CN, NC and CCH vinylchloride complexes were processed by using the GAUSSIAN 98W program [24] through the execution of the B3LYP/6-311++G(d,p) calculations. Through the GAUSSIAN 98W, it was calculated the CHELPG atomic charges [16]. The DQ^CHELPG quantities were determined by a balance of atomic charges on proton donor molecules. The topological analysis was performed by using the AIM 1.0 2000 program [25]. The results of DE interaction energies were determined through the application of the supermolecule approach, DE = E(AB) – [E(A) + E(B)] [26]. Furthermore, the DE values were corrected by the BSSE [27] scheme of Boys and Bernardi.

Results and discussion
Optimized geometrical parameters
From the B3LYP/6-311++G(d,p) calculations, the optimized geometries of the C₂H₃Cl···HCl (I), CC₂H₃Cl···HCN (II), C₂H₃Cl···HNC (III) and C₂H₃Cl···HCCH (IV) vinylchloride complexes are illustrated in Figure 1, whereas the results of the structural parameters are listed in Table 1. In this picture, the van der Waals surfaces are represented in background [28]. From a long time ago, more specifically since the first empirical studies of hydrogen complexes, the van der Waals fields have been taken as useful parameter to analyze intermolecular interactions and thereby some interesting conclusions were proposed [29-33]. For the vinylchloride complexes studied here, it was admitted that van der van Waals surface can contribute at least qualitatively with the study of the hydrogen bonds (Cl···X) and secondary interactions (X···H). Thus, the van der Waals surfaces depicted in Figure 1 shows that (X···H) secondary interactions are not formed, although almost all (Cl···H) hydrogen bonds were identified, excepting in the C₂H₃Cl···HCCH vinylchloride complex because the van der Waals surfaces of HCCH and vinylchloride does not overlaps. By assuming that van der Waals surface is an parameter of current interest in studies of molecular modeling and intermolecular interactions [34], in practice the van der Waals radii based on this surface are the only criteria to certify the formation of an intermolecular contact, although if we consider the R(Cl···HX) distances of 2.5471 Å, 2.7704 Å, 2.464 Å and 3.035 Å for (I), (II), (III) and (IV) vinylchloride complexes, as well as their R(X···H) secondary interactions values of 3.3599 Å, 3.8470 Å, 3.249 Å and 3.1589 Å, excepting the C₂H₃Cl···HCCH whose R(Cl···HX) and R(X···H) results are longer than sum of van der Waals radii [H (1.40), C (1.70), O (1.50), and Cl (1.76)], all remaining complexes have typical intermolecular distance values.

Fig. 1. Illustration of the van der Waals surfaces and optimized geometries of the C₂H₃Cl···HCl (I), C₂H₃Cl···HCN (II), C2H3Cl···HNC (III) and C₂H₃Cl···HCCH (IV) vinylchloride complexes using B3LYP/6-311++G(d,p) calculations.

Table 1. Main structural parameters of the C₂H₃Cl···HX vinylchloride complexes using B3LYP/6-311++G(d,p) calculations.

* Values of r and R are given in ångströms, Å;
* Values of q angles are given in degrees.

A natural consequence of secondary interactions for vinylchloride complexes is the non-linearity deviation (q) on the (Cl···X) hydrogen bonds (35-36). From B3LYP/6-311++G(d,p) calculations, it was found a large q value of 28.7 º for (IV), whereas smaller for (I), (II) and (III) complexes. Based on previous papers (37), the linearity deviation is observed when the distances of the secondary interactions are compatible to van der Waals radii. Although all R(X···H) values are longer than van der Waals radii, this distance criterion is not adequate for (I), (II), (III) and (IV) complexes. Regarding to molecular deformations, the slight DrHX value of 0.0014 Å for (IV) indicates how weakly bound is this intermolecular system. Moreover, for (I) and (III), we can observe by DrHX results of 0.006 Å and 0.0063 Å that the hydrochloride acid and hydroisocyanic acid properly provokes substantial deformations on the structure of the vinylchloride complexes.

Interaction energies and charge transfers
The values of uncorrected intermolecular energies (DE), corrected intermolecular energies (DE^C), and BSSE correction amounts for the (I), (II), (III) and (IV) vinylchloride complexes are presented in Table 2. All DE^C results obtained here corresponds to low energies, which can be associated to van der Waals interactions whose values are in range of 3.0-9.8 kJ mol-1 [38]. In this sense, we can emphasize that these DE^C results were obtained by small BSSE contributions, as in accord with data documented for p hydrogen-bonded complexes [39]. As debated here, the main structural changes (DrHX) which occurs due to formation of hydrogen complexes is related to proton donor molecules. Such geometric parameter suggests systematic tendencies about the interaction strength by means of a direct relationship between DrHX results and DE^C intermolecular energies, as shown by Figure 2. From this picture, a linear coefficient R² of 0.96 was computed, what in fact, is a demonstration that stronger vinylchloride bound complexes are formed by intense changes on their molecular structures (40). In fact, by the interaction between HOMO orbital of proton acceptor and LUMO orbital of proton donor (41), electronically we can interpret the charge transfer between these frontier orbitals by means of the intermolecular CHELPG quantities (DQ^CHELPG). From DQ^CHELPG values of -0.026e.u. and -0.036 e.u. gathered in Table 2, we can verify the (I) and (II) complexes as the strongest bound systems, what corroborates with DE^C Sanalysis already debated here. For (III) and mainly the (IV) complex, the DQ^CHELPG amounts of -0.014 e.u. and -0.012 e.u. indicates weak interaction strengths.

Fig. 2. Relationship between the values of the corrected intermolecular energies (DE^C) and increments of the proton donor bonds (DrHX) of the
C₂H₃Cl···HCl (I), C₂H₃Cl···HCN (II), C₂H₃Cl···HNC (III) and C₂H₃Cl···HCCH (IV) vinylchloride complexes using B3LYP/6-311++G(d,p) calculations.

Table 2. Values of uncorrected (DE) and corrected intermolecular energies (DE^C), BSSE amounts and CHELP charge transfer (DQ^CHELPG) of the C₂H₃Cl···HX vinylchloride complexes using B3LYP/6-311++G(d,p) calculations.

* Values of DE, BSSE and DE^C are given in kJ mol^-1.

Infrared spectra analysis
In terms of infrared spectrum parameters, the main vibrational modes of the (I), (II), (III) and (IV) vinylchloride complexes are presented in Table 3. As widely known, one of the most important vibrational phenomena upon the formation of hydrogen complexes is the red-shift effects on the proton donor [42], whose n(HX),m frequency signal of isolated monomer is re-localized to a lower n(HX),c region accompanied by a elevation on the absorption intensity, I(HX,c)/I(HX,m) (35). For the (I), (II), (III) and (IV) vinylchloride complexes, their Dn(HX) results were analyzed by DQ^CHELPG amount data, whose relationship between them is in very good agreement, as can be seen in Figure 3. By analyzing this graph, a R² linear correlation coefficient of 0.95 says that the red-shifts can be securely interpreted by quantification of the intermolecular charge transfer.

Table 3. Main vibrational modes of the C₂H₃Cl···HX vinylchloride complexes using B3LYP/6-311++G(d,p) calculations.

* Values of n and I are given in cm^-1 and km mol^-1, respectively;
* Dn(HX) = n(HX),c - n(HX),m.

Fig. 3. Relationship between red-shift effects of HX proton donating and CHELPG charge transfer on C₂H₃Cl···HCl (I), C₂H₃Cl···HCN (II), C₂H₃Cl···HNC (III) and C₂H₃Cl···HCCH (IV) vinylchloride complexes.

Well, the excellent relationship for charge transfer is because the CHELPG algorithm has been implemented to calculate electronic populations near of outside of the van der Waals surface [43-45], which is illustrate on Figure 1. However, it was also verified the existence of weak vibrational modes, which in essence are named as hydrogen bond stretch frequencies. So, we can verify by the n(Cl···HX) and I(Cl···HX) values that all vinylchloride complexes are weak bound, mainly for (IV) whose result of absorption intensity of 0.65 km mol^-1 is the lowest. However, it was found an interesting information for (IV) concerning to secondary interaction stretch frequency, whose results for n(X···H) and I(X···H) are 21.1 cm^-1 and 1.3 km mol^-1, respectively. In fact, the discovering of this secondary interactions is quite impressive, although we should notice that such observation was not verified on the (I), (II) and (III) complexes. In terms of the optimized geometric structure, the secondary interaction on (IV) was expected due the larger non-linearity deviation (q) computed.

Contribution of the AIM topology
Regarding to electronic parameters, we hope that an investigation of the molecular charge density can help us to understand the possibility to form the (Cl···H) hydrogen bonds and (X···H) secondary interactions. In this insight, the Table 4 presents the results of AIM calculations for the (I), (II), (III) and (IV) vinylchloride complexes, where the values of electronic densities (r) and Laplacian (Ѳr) are presented. According to inherent approaches of the AIM theory, Ѳr Laplacian is a topological parameter defined through the sum of the eigenvalues from diagonalization of Hessian matrix of r. Through the identification of Bond Critical Points (BCP) between two neighbouring atoms (46), Laplacian of r can be used to characterize the formation of hydrogen-bonded complexes when concentrations (Ѳr> 0) and depletions (Ѳr < 0) of the charge density are quantified. If take a look in our results, we can firstly perceive the high charge density concentration on HX bonds, whose values are defined in an average of 0.190 e/a₀³. Moreover, the negative Laplacian values also indicates an electronic accumulation on proton donor bonds, what in terms of AIM theory, such elevated lumps of r is named as shared interactions. In other words, the charge concentration is localized within the atomic pathway, more specifically on BCP.

Table 4. Values of electronic densities (n) and Laplacians (Ѳr) of the C₂H₃Cl···HX vinylchloride complexes using AIM calculations.

For the (Cl···HX) hydrogen bonds, however, the AIM result shows a slight concentration of charge density, consequence of an electronic separation on the atomic centers (Cl and H) revealed by negative values to Ѳr (47), as can be seen in relief maps of electronic density of the (I), (II), (III) and (IV) vinylchloride complexes pictured in Figure 4. Indeed, we can see a protuberance of charge density on Cl atom of vinylchloride and X (Cl, CN, NC and CCH) groups of the proton donors. Nevertheless, as previously debated about the possibility to form the secondary interaction between the hydrogen atoms of vinylchloride species and CN, NC and CCH groups of proton donors, as demonstrated in Table 4 the r(X···H) and Ѳr (X···H) values of 0.003 e/a₀³ and 0.008 e/a₀⁵ obtained from AIM integrations identified such secondary interactions, but only on the C₂H₃Cl···HCCH complex (IV), as demonstrated in Figure 5, where is illustrated their whole set of BCP.

Fig. 4. Relief maps of the electronic densities on the C₂H₃Cl···HCl (I), C₂H₃Cl···HCN (II), C₂H₃Cl···HNC (III) and C₂H₃Cl···HCCH (IV) vinylchloride complexes.

Fig. 5. BCP (in small black spheres) and molecular pathways on the C₂H₃Cl···HCl (I), C₂H₃Cl···HCN (II), C₂H₃Cl···HNC (III) and C₂H₃Cl···HCCH (IV) vinylchloride complexes.

However, we make evidence that the secondary interaction is not formed between the hydrogen atom of vinylchloride and r bond of acetylene, by contrary, it was found that the hydrogen of vinylchloride interacts directly with carbon of acetylene instead of unsaturated bond [11]. As discussed in the structural parameters that even though the CCH···H distance is longer than sum of van der Waals radii, but the AIM protocol was efficacious to identify a BCP between the C and H atoms, showing then the existence of the secondary interaction, which has been presumed by FTMS analysis [10]. By the way, it is not surprising that BCP are localized between near atoms, as in case of halogen interactions recently fond and reported by Grabowski [49]. So, a direct consequence about the identification of the secondary interaction in (IV) is that, undoubtedly its interaction energy of 2.28 kJ mol^-1 cannot be associated to Cl···H primary hydrogen bond, but it must be also related to CCH···H. Thereby, there is a limitation of the supermolecule approach for determination of the interaction energies, which cannot be performed by subtracting the energy of the complex (C₂H₃Cl···HCl, C₂H₃Cl···HCN, C₂H₃Cl···HNC or C₂H₃Cl···HCCH) minus of its isolated monomers (C₂H₃Cl and HCl, HCN, HNC or HCCH). This problem was recently debated in hydrogen-bonded complexes (alcohol···water and heteorcyclic···hydrofluoric-acid) [49-50] wherein multiple hydrogen bonds were characterized on these structures.

Concluding remarks
A theoretical study about the molecular structure of the C₂H₃Cl···HX vinylchloride complexes with X = Cl, CN, NC and CCH was proposed through the B3LYP/6-311++G(d,p) calculations and topological integrations of the atoms in molecules theory. Through the structural and electronic parameters, the vinylchloride complexes were considered weakly bound systems because it was computed large R(Cl···H) hydrogen bond distances and low DE^C interaction energies.
Based on experimental assays documented in literature, it has been observed a (X···H) secondary interaction formed between the halogen atom (H) of vinylchloride specie and X group of the HCl, HCN, HNC and HCCH monoprotic acids. From B3LYP/6-311++G(d,p) calculations, this secondary interaction unlikely cannot be formed because the R(X···H) distance is longer than sum of van der Waals radii. Still about this, it was showed by van der Waals surfaces that no secondary interactions might to exist. Indeed, by taking into account the van der Waals surface of the C₂H₃Cl···HX set of complexes, as far as the (X···H) secondary interactions is not observed, but for C₂H₃Cl···HCCH system, the structure of its optimized geometry suggests that the formation of the (Cl···H) primary hydrogen bonds also is not possible to be done.
By analyzing the infrared spectrum, however, we have observed that all n(Cl···H) stretch frequencies and I(Cl···H) absorption intensities were successfully identified, although the n(X···H) signal of the secondary interaction on C₂H₃Cl···HCCH complex was characterized and interpreted. In corroborating to that, AIM calculations also localized BCP between CCH group and vinyl hydrogen, although this contact is formed by a direct alignment of vinyl hydrogen to the carbon of acetylene instead of r bond.

Supplementary information
Cartesian coordinates of optimized geometries and the values of the molecular energies (E) of the C₂H₃Cl···HCl (I), C₂H₃Cl···HCN (II), C₂H₃Cl···HNC (III) and C₂H₃Cl···HCCH (IV) vinylchloride complexes using B3LYP/6-311++G(d,p) calculations.

Acknowledgements
The author would like to gratefully to the CAPES and CNPq Brazilian funding agencies, as well as to CENAPAD-SP (Centro Nacional de Processamento de Alto Desempenho-São Paulo) by computational facilities to complete this work.

References
1 Tang, T.-H.; Cui, Y.-P. Can. J. Chem. 1996, 74, 1162.         [ Links ]

2 Alkorta, I.; Rozas, I.; Elguero, J. J. Chem. Soc. Rev. 1998, 27, 163.         [ Links ]

3 Zhang, Y.-H.; Hao, J.-K.; Wang, X.; Zhou, W.; Tang, T.-H.; J. Mol. Struct. (THEOCHEM) 1998, 455, 85.         [ Links ]

4 Araújo, R. C. M. U.; Ramos, M. N.; J. Mol. Struct. (THEOCHEM) 1996, 366, 233.         [ Links ]

5 Herrebout, W. A.; van der Veken, B. J. ; J. Mol. Struct. 1995, 348, 481.         [ Links ]

6 Herrebout, W. A.; van der Veken, B.J. ; J. Phys. Chem. 1996, 100, 15695.         [ Links ]

7 Herrebout, W. A.; van der Veken, B.J. ; J. Mol. Struct. 2002, 642, 1.         [ Links ]

8 Read, W. G.; Flygare, W.H. ; J. Chem. Phys. 1982, 76, 2238.         [ Links ]

9 Kisiel, Z.; Fowler, P. W.; Legon, A.C. ; J. Chem. Phys. 1990, 93, 3054.         [ Links ]

10 Cole, G. C.; Legon, A. C.; Chem. Phys. Lett. 2003, 369, 31.         [ Links ]

11 Cole, G. C.; Legon, A. C. Chem. Phys. Lett. 2004, 400, 419.         [ Links ]

12 Oliveira, B. G.; Araújo, R. C. M. U.; Carvalho, A. B.; Lima, E. F.; Silva, W. L. V.; Ramos, M. N.; Tavares, A. M.; J. Mol. Struct. (THEOCHEM) 2006, 775, 39.         [ Links ]

13 Bader, R. F. W. Atoms in Molecules. A Quantum Theory; International Series of monographs on Chemistry, Oxford University Press, Oxford, 1990.         [ Links ]

14 Chandra, A. K.; Nguyen, M. T. ; Chem. Phys. 1998, 232, 299.         [ Links ]

15 Hohenberg, P.; Kohn, W. ; Phys. Rev. B 1964, 136, 864.         [ Links ]

16 Breneman, C. M.; Wiberg, K.B. ; J. Comp. Chem. 1990, 11, 361.         [ Links ]

17 Cho, Y. S.; Hwang, S.; Chem. Lett. 2006, 35, 1362.         [ Links ]

18 Kryachko, E .S.; Nguyen, M. T.; J. Chem. Phys. 2001, 115, 833.         [ Links ]

19 Zheng, Y. J.; Bruice, T. C.; Proc. Natl. Acad. Sci. USA 1997, 94, 4285.         [ Links ]

20 Zhao, Y.; Tishchenko, O.; Truhlar, D. G.; J. Phys. Chem. B 2005, 109, 19046.         [ Links ]

21 Vila, A.; Graña, A. M.; Mosquera, R. A.; Chem. Phys. 2002, 281, 11.         [ Links ]

22 van Erp, T. S.; Meijer, E. J.; J. Chem. Phys. 2003, 118, 8831         [ Links ]

23 Qu, Z.-W.; Zhu, H.; Zhang, X.-K.; Zhang, Q.-Y.; Chem. Phys. Lett. 2003, 367, 245.         [ Links ]

24 Frisch, M. J, Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery Jr., J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Rega, N.; Salvador, P.; Dannenberg, J. J.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; 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.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A., Gaussian, Inc., Pittsburgh PA, 2001 Gaussian 98W (Revision A.1), Gaussian, Inc., Pittsburgh PA, 1998.         [ Links ]

25 AIM 2000 1.0 program designed by F. Biegler-König, University of Applied Sciences, Bielefeld, Germany.         [ Links ]

26 van Duijneveldt, F. B.; Murrell, J. N.; J. Chem. Phys. 1967, 46, 1759.         [ Links ]

27 Boys, S. B.; Bernardi, F. Mol. Phys. 1970, 19, 553-566.         [ Links ]

28 Connolly, M. L. Science 1983, 221, 709.         [ Links ]

29 Bondi, A. ; J. Phys. Chem.1964, 68, 441.         [ Links ]

30 Sanner, M.; Olson, A.; Spehner, J. Biopolymers 1996, 38, 305.         [ Links ]

31 Liang, J.; Edelsbrunner, H.; Fu, P.; Sudhakar P.; Subramanian, S. Proteins 1998, 33, 1.         [ Links ]

32 Rocchia, W.; Sridharan, S.; Nicholls, A.; Alexov, E.; Chiabrera, A.; Honig, B. ;J. Comp. Chem. 2002, 23, 128.         [ Links ]

33 Alonso, J. A.; Mañanes, A. Theor. Chem. Acta 2007, 117, 467.         [ Links ]

34 McKinnon, J. J.; Mitchell, A. S.; Spackman, M. A.; Chem. Comm. 1998, 2071.         [ Links ]

35 Oliveira, B. G.; Santos, E. C. S.; Duarte, E. M.; Araújo, R. C. M. U.; Ramos, M. N.; Carvalho, A. B. Spectrochim. Acta A 2004, 60, 1883.         [ Links ]

36 Oliveira, B. G.; Duarte, E. M.; Araújo, R. C .M. U.; Ramos M. N.; Carvalho, A. B.; Spectrochim. Acta A 2005, 61, 491.         [ Links ]

37 Oliveira, B. G.; Araújo, R. C. M. U.; Ramos, M. N.; Carvalho, A. B.; Quim. Nova 2007, 30, 1167.         [ Links ]

38 Johnson, E. R.; Di Labio, G. A.; Chem. Phys. Lett. 2006, 419, 333.         [ Links ]

39 Rozas, I.; Alkorta, I.; Elguero, J. ; J. Phys. Chem. A 1997, 101, 9457.         [ Links ]

40 Araújo, R. C. M. U.; da Silva, J. B. P.; Ramos, M. N. Spectrochim. Acta A 1995, 51, 821.         [ Links ]

41 . Parnaíba-da Silva, A. J.; da Silva, J. B. P.; da Gama, A. A. S.; Ramos, M. N. Chem. Phys. Lett. 2002, 362, 159.         [ Links ]

42 Oliveira, B. G.; Araújo, R. C. M. U. Quim. Nova 2007, 30, 791.         [ Links ]

43 Hobza, P.; Zahradnik, R. Intermolecular Complexes, Elsevier Science, New York, 1997.         [ Links ]

44 Monany, F.; J. Phys. Chem. 1978, 82, 592.         [ Links ]

45 Cox, S.R.; Williams, D. E. J. Comp. Chem. 1981, 2, 304.         [ Links ]

46 Bader, R. F. W.; MacDougall, P. J.; Lau, C. D. H. ; J. Am. Chem. Soc. 1994, 106, 1594.         [ Links ]

47 Bader, R. F. W. Chem. Rev. 1991, 91, 893.         [ Links ]

48 Grabowski, S. J.; Struct. Chem. 2007, 19, 5.         [ Links ]

49 Oliveira, B. G.; Vasconcellos, M. L. A. A.; J. Mol. Struct. (THEOCHEM) 2006, 774, 83.         [ Links ]

50 Oliveira, B. G.; Araújo, R. C. M. U.; Carvalho, A. B.; Ramos, M. N.; J. Theor. Comp. Chem. 2007, 6, 647.         [ Links ]