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The topology of the charge distribution of the silanol–thiophene van der Waals complex: ab initio and DFT study
Journal of Molecular Structure (Theochem) 531 (2000) 315±321
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The topology of the charge distribution of the silanol±thiophene van der Waals complex: ab initio and DFT study H. SoscuÂn*, O. Castellano, J. HernaÂndez SeccioÂn de Teoria CuaÂntica y DisenÄo Molecular, Laboratorio de QuõÂmica InorgaÂnica TeoÂrica, Departmento de QuõÂmica, Facultad de Ciencias, La Universidad del Zulia, AP 526, MoÂdulo No. 2, Grano de Oro, Maracaibo, Venezuela Received 24 August 1999; received in revised form 18 February 2000; accepted 29 February 2000
Abstract This work reports a quantum-chemistry SCF-MO ab initio study of the topology of charge distribution of the silanol± thiophene van der Waals molecular complex, by using the Hatree±Fock method, perturbation theory at the second level MP2, and density functional theory at the BLYP level. The geometry of the isolated species and the corresponding complexes were fully optimized at each level of theory by using the standard STO/6-311G(d,p) basis set. Cs symmetry was used for the molecular geometry of silanol and the complex, and C2v for thiophene. The geometric, electronic and vibrational results are compared with previous calculations for the silanol±H2S molecular complex. The nature of the chemical interactions that lead to the formation of the silanol±thiophene complex is analyzed in terms of the topologic properties of the linear conformation. This model reproduces the experimental prediction from the FT-IR adsorption spectra of thiophene in H-ZSM5 zeolites. q 2000 Published by Elsevier Science B.V. Keywords: Silanol; Thiophene; Infrared spectra; van der Waals interaction
1. Introduction Thiophene is a polar molecule that can be chemically adsorbed in zeolites leading to the formation of van der Waals complexes [1]. The nature of these complexes has been experimentally studied from the adsorption of the thiophene molecule into ZSM5 zeolites, and the interaction process followed by FTIR and gravimetric determinations at different pressures of thiophene gas [1]. From the analysis of the IR spectra of these experiments, it was proposed that at equilibrium a stable (1:1) van der Waals molecular complex between thiophene and the OH hydroxyl * Corresponding author. Tel.: 1 58-61-598098; fax: 1 58-6159809981. E-mail address: [email protected] (H. SoscuÂn).
groups of the zeolites is formed, where the formation of the complex occurs through the hydrogen bonding between the S atom of thiophene and the H atom of the acidic hydroxyl OH groups of the zeolites [1]. The acid behavior of these sites, the OH bridged (BroÈnsted site) and the OH terminal, have been rationalized in terms of their structural, electronic and vibrational properties [2]. According to the experimental IR spectra of the thiophene adsorption, these OH groups are able to give similar thiophene±OH complexes, where the main features of the S±H bond are of the same nature. In fact, one complex is formed between the OH bridged and the S atom of thiophene, and the second one occurs between the OH terminal and the S atom of thiophene. In particular, the IR frequency corresponding to the OH stretching mode of the terminal complex appears at a higher frequency than the
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H. SoscuÂn et al. / Journal of Molecular Structure (Theochem) 531 (2000) 315±321
bridged ones [1]. These ®ndings are due to the higher acidity of the OH bridged group than the terminal one, i.e. the terminal molecular complexes are weaker than that formed with the BroÈnsted group. Recently, the acid sites of zeolites have been characterized by using the topologic properties of the charge distribution r (r) of small clusters of Si and Al, including silanol [2]. The topologic properties of r (r) are based on the theory of atoms in molecules proposed by Bader et al. [3,4]. This approach is able to provide a reliable electronic picture about the nature of acid sites in zeolites. The aim of this paper was to investigate by quantum-chemistry methods, at the Hartree±Fock and post-Hartree±Fock levels, the structural, vibrational and the topologic properties that characterize the charge distribution of the chemical interaction between thiophene (C4H4S) and zeolite, using silanol (H3SiOH) as the model for the OH terminal groups. The post-Hartree±Fock (HF) methods used are perturbation theory at the second level of correlation MP2 [5] and density functional theory methods with the BLYP hybrid level [6]. The results are analyzed in terms of the available experimental data, and are compared with previous calculations for the H2S±silanol complex [7].
2. Theory and computational methods 2.1. Theory of atoms in molecules The quantum mechanic description of the topologic properties of the charge distribution r (r) of a molecular system was developed by Bader et al. and is known as the Theory of Atoms in Molecules [3,4]. This approach is based on the properties of the associated ®elds of r (r), the gradient vector 7r (r) and the Laplacian ®eld 7 2r (r). The points where the 7r (r) vanishes 7r r 0 are the extremes of r (r) and are referred to as critical points, which are classi®ed according to the three eigenvalues (l 1, l 2 and l 3) of the diagonalized Hessian matrix of r r; H ij 2 2 r r=2xi 2xj : Each critical point is labeled by the (D,S) pair of numbers, where D is the number of nonzero l i eigenvalues of Hij, and S the difference between the nonzero and the negative l i eigenvalues. The (D,S) set de®nes the label or signature of the
extreme. For a maxima critical point, the label is (3, 23) because all the three eigenvalues of H are nonzero and negative, being S 3 and D 23; while for a minima, the label is (3, 13). In a molecular system, the maxima, minima and saddle points in r (r) are de®ned as attractors, cage and either, bond (3, 21) or ring points (3, 11), respectively. The molecular regions where the 7r (r) is zero, lead to the existence of a zero-¯ux surface that splits the molecule in fragments linked by bond paths characterized as (3, 21). These regions, demarcated by the zero-¯ux surfaces are named the basins. Attractors of basins, are often located at the position of the nuclei, while bond critical points are located between two bonded atoms and correspond to a local maxima in two directions and a local minima in the third direction. The set of (3, 21) critical points de®ne the network of bond paths and describe the molecular structure by the characterization of all their atomic interactions. Along each of this bond path, the charge density is a maximum with respect to the any neighboring link. The value of the electron density at the bond critical point (r c(r)) has been referred as a useful index for representing the corresponding bond order [3,4]. This property accounts for the degree of charge concentration on the bond path. At these (3, 21) bond paths, the charge density attains its minimum value at the critical point and the associated l 3 eigenvalue is positive. On the other hand, the charge density in an interatomic surface attains its maximum value at the bond critical point and the two associated curvatures l 1 and l 2 are thus negative. If l 2 is the smallest eigenvalue, the ratio between l 1 and l 2 measure the bond deviation of cylindrical symmetry in the bond path, and the bond ellipticity is de®ned as e l 1 =l2 2 1: This property provides a measure of the extent to which the charge is preferentially accumulated within a molecule according to the orientation determined by l 2. The characterization of how the electronic density is rearranged according to the concentrations and depletions of the charge is described by the properties of the Laplacian of r (r), 7 2r (r). In particular, the sign of 7 2r (r) determines the regions where the charge density is locally concentrated 7 2 r r , 0 or locally depleted 7 2 r r . 0 [3,4]. These regions identify the chemical reactivity of a molecule. For instance, if the Laplacian is calculated at the position of a bond
H. SoscuÂn et al. / Journal of Molecular Structure (Theochem) 531 (2000) 315±321
Fig. 1. Thiophene±silanol structure and geometric parameters.
critical point, 7 2r c(r), positive values are indicative of ionic interactions, while negative values are associated with covalent bonds. In the present study, we have performed an ab initio study and applied the Bader theory of atoms in molecules as implemented by Cioslowsky and coworkers [8,9], to characterize the topologic properties of the electronic charge distribution of the interaction between silanol and thiophene that lead to the formation of the silanol±thiophene van der Waals complex. 2.2. Methods Calculations of topologic properties of r (r) were performed at the HF and Moller±Plesset (MP2) [5] methods by using the standard STO/6-311G(d,p) basis set [10]. Molecular geometries of silanol and thiophene were fully optimized at the Cs and C2v symmetries, respectively. The silanol-complex structure was calculated at Cs symmetry. The Gaussian 94 [11] quantum-chemistry system was employed for the calculations. 3. Results and discussion 3.1. Stability and geometric structures The fully optimized geometric parameters as shown in Fig. 1, the bond distances in Angstroms and the
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bond angles in degrees of thiophene, silanol and silanol±thiophene complex are reported in Table 1. Cs symmetry was used for the molecular geometry of silanol and the complex, and C2v for thiophene molecule. These geometry optimizations were carried out at the HF, MP2, and BLYP levels of theory and the STO/6-311G(d,p) standard basis set. Total energies ET in atomic units and the interaction energies EB in kcal/mol for the silanol±thiophene complex are also reported in Table 1. The stability of the van der Waals silanol±thiophene complex can be analyzed by the slightly negative values of the EB interaction energies at the different levels of theory: HF (20.904 kcal/mol), MP2 (21.977 kcal/mol) and BLYP (20.841 kcal/mol), indicating that the dominant interaction for the formation of these complexes is weakly attractive. These energy values show the differences in evaluating only the main correlation contribution (MP2), and the determination of the exchange and correlation together (BLYP), showing that the use of electronic correlation is necessary when we handle van der Waals complexes. Fig. 1 shows the structural conformations of the species, indicating the corresponding geometric parameters. Table 1 shows that the results of the geometry optimization for silanol [7] and thiophene [12] are in agreement with previous calculations at similar levels of theory. The ®nal structure for the silanol±thiophene complex (see Fig. 1) was obtained by interacting the S atom of thiophene with the H atom of the OH group of silanol in the plane of both molecules. This interaction leads to the formation of a stable van der Waals molecular complex with a structure of linear conformation with Cs symmetry. This structure corresponds to a con®guration of local minima of second order, with two negative frequencies. In the present work, we only report the OH frequencies for silanol and the corresponding frequencies for the complex (see Table 1). The geometric results in Table 1 show that at the HF level the stability of the silanol±thiophene complex is reached at the S±HO interaction distance Ê . This value con®rms the fact that the interof 3.011 A action between thiophene and silanol occurs through a weak hydrogen bond, whose length lies in the expected range for the van der Waals complexes. For comparison, Table 1 also reports the HF/631G pp calculations for the H2S±silanol molecular
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Thiophene HF a b c d q r t u y z ab qr bq n (OH) 2 ET 2 EB a b c
Silanol MP2
BLYP
HF
MP2 1.655 0.941
1.724 1.349 1.072 1.436 1.074
1.716 1.380 1.078 1.417 1.081
1.754 1.382 1.088 1.434 1.092
551.30389
551.96893
552.92746
Silanol±thiophene
120.8 4233 366.14701
1.685 0.963
117.7 3953 366.43750
HF/6-31G pp and MP2/6-31G pp [7]. Exp: terminal SiOH groups of zeolites [1]. Exp: interaction of terminal SiOH groups of zeolites with thiophene [1].
BLYP 1.692 0.973
117.6 3751, 3745 b 367.11059
HF
MP2
BLYP
1.647 0.942 1.469 1.477 3.011, 3.031 a 1.725 1.348 1.074 1.438 1.071 121.8 125.0 166.9 4225 917.45234 0.904
1.677 0.964 1.467 1.477 2.960, 2.740 a 1.717 1.379 1.081 1.437 1.078 117.3 126.8 136.8 3934 918.40958 1.977
1.689 0.975 1.488 1.498 2.763 1.754 1.381 1.091 1.439 1.088 117.7 141.3 171.0 3712, 3628 c, 3595 c 920.03939 0.841
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Table 1 Structural properties, OH vibrational frequencies (n (OH) in cm 21, total energy ET in hartree and interaction energy EB in kcal/mol, of thiophene, silanol, and the silanol±thiophene complex, with the STO/6-31 1 G(d,p) basis set
H. SoscuÂn et al. / Journal of Molecular Structure (Theochem) 531 (2000) 315±321
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Table 2 Topological properties of the charge density at the critical points of thiophene, silanol and the silanol±thiophene complex: total density r (r), laplacian density 7 2r (r) and ellipticity E, with the STO/6-31 1 G(d,p) basis set Molecule
r (r)
Thiophene Silanol Silanol±thiophene
7 2r (r)
Thiophene Silanol Silanol±thiophene
E
Thiophene Silanol Silanol±thiophene
a HF MP2 HF MP2 HF MP2 HF MP2 HF MP2 HF MP2 HF MP2 HF MP2 HF MP2
0.126 0.117 0.126 0.119
1.102 0.836 1.032 0.868
0.067 0.074 0.066 0.073
complex [7]. The value of the S±HO interaction distance in the thiophene±silanol complex Ê ) is shorter than in the H2S±silanol (3.011 A complex (3.031 AÊ), indicating that the S±HO interaction is relatively stronger in thiophene than in hydrogen sul®de. The results in Table 1 additionally show that the effect of electronic correlation increases the strength of the interaction between the S atom and the OH group in the Ê ) , MP2 (2.960 A Ê ) levels order of BLYP (2.763 A of theory. This tendency of MP2 distance is similarly observed for the H 2S±silanol complex Ê ) [7]. These results are in concordance (2.740 A with the relative stability of these complexes. Analysis of the rest of the geometric parameters displayed in Table 1, at the different levels of theory for the isolated molecules and the silanol±thiophene complex, shows that no signi®cant changes are observed in the structural properties of these species by effect of the interaction. These results show that the dominant interactions are of local nature and only the atoms that are involved in the chemical area in the van der Waals interaction are affected.
b
q
0.382 0.356 0.381 0.355
22.460 22.033 22.459 22.022
0.007 0.008 0.007 0.008
r 0.221 0.214
0.298 0.286
0.221 0.214
0.299 0.286
20.530 20.440
21.184 21.062
20.524 20.436
21.186 21.068
0.233 0.237
0.028 0.035
0.230 0.235
0.029 0.035
0.004 0.005
0.015 0.020
z
0.129 0.060
3.2. OH vibrational frequencies The chemisorption of thiophene in HZSM5 zeolites has been investigated experimentally by quantitative FT-IR spectroscopy [1]. These studies have proposed that thiophene interacts weakly with the OH bridged and with the OH terminal of zeolites as well, leading to the formation of stable 1:1 molecular van der Waals complexes. When these complexes are formed by the interaction between the S atom and the OH hydroxyl groups of zeolites, the OH vibrational modes are perturbed. These perturbations are re¯ected in the IR spectra. Table 1 displays the harmonic frequencies of the OH group for silanol and the silanol±thiophene complex, calculated at the HF, MP2 and BLYP levels of theory. These results show that the OH frequency decreases by effect of the interaction between S and the OH groups. At HF, MP2 and BLYP, the corresponding vibrational shifts are 28, 219 and 239 cm 21, respectively. Experimental observations [1] indicate that the OH frequency for silanol is 3745 cm 21 and decreases due to the effect of interaction to a band that is located between 3698 and 3595 cm 21 re¯ecting that there is an average shift of
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Fig. 2. A relief map of the distribution of the Laplacian of electron density for the silanol±thiophene complex. The map has been orientated taking as reference the plane of the complex.
298.5 cm 21 due to the effect of the interaction. Our theoretical results are consistent with these experimental observations, showing that the adsorption of thiophene into terminal OH groups of zeolites produces a negative shift in the OH vibrational band. It is important to mention that at the DFT level, these OH frequency shifts are ampli®ed, giving a best representation with respect to the experimental reports. 3.3. Topological properties The topological properties of the charge distribution of thiophene, silanol and the thiophene±silanol complex, calculated at the HF and MP2 levels are reported in Table 2. The table reports the values of the total density (r (r)), the Laplacian density (7 2r (r)) and the ellipticity E, calculated at the position of the critical points of the bond paths, as displayed in the bond network of Fig. 1. 3.4. Density of charge The results of total charge density r (r) are given in Table 2. The very low value of r (r) (0.004) at the critical point of the q bond path determines that the interaction for the formation of the silanol±thiophene complex is very weak. No signi®cant changes in the r (r) values are observed in the rest of bond paths of the involved species. The correlation MP2 does not introduce determinant effects in these properties. 3.4.1. Laplacian of the charge density The Laplacian of the charge density is determined
by the signs of 7 2r (r) at each point of the space, determining the regions where the charge density is locally concentrated 7 2 r r , 0 or locally depleted 7 2 r r . 0: These charge concentrations determine the nature of the bonding interactions, either ionic or covalent ones. Also, the locally depleted regions in a molecule are associated to sites of electrophilic attack. Table 2 reports the values of the Laplacian density 7 2r (r), calculated at the position of the bond critical points of thiophene, silanol and the thiophene±silanol complex. Silanol is characterized by two bonds, one with a negative value of 7 2r (r) (22.443 at HF) at the position of the critical point of the O±H bond (b) which is dominated by covalent interactions, while the other one has a positive value of 7 2r (r) (11.102 at HF) at the position of critical point of the Si±O (a) being dominated by ionic interaction. From the values in Table 2, the 7 2r (r) of the Si±O and the OH bonds are changed by effects of the interaction, 11.032 and 22.459 being the corresponding HF values for the Laplacians of these bonds in the complex, respectively. In the region of the interaction, q bond path (S±HO), the value of 7 2r (r) (10.0015) is positive, giving a weakly ionic feature to this bond. MP2 results show that electronic correlation affect the values of the Laplacian, being signi®cant for the S±HO interaction, by increasing the weakly ionic property of this bond. In Fig. 2 is depicted the distribution of the Laplacian of r (r) for the silanol±thiophene complex as performed with the MOLDEN software [13], where the positive and negative regions are shown. The positive regions are located around the Si and O atoms of
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the silanol fragment, and around the C and S atoms of the thiophene species, while the negative regions are concentrated around the H atoms and around the S± OH bond. The low concentration of charge observed in the S±OH segment is indicative of the weak interactions that dominate the complex. 3.4.2. Ellipticity The ellipticity (E) of a bond is associated to the measure of the extent to which the charge is preferentially accumulated within a bond in a molecule. This tendency of the charge is determined by the orientation of the smallest eigenvalue of the diagonalized Hessian matrix of r (r). The E values for thiophene, silanol and silanol±thiophene structures as reported in Table 2 indicate that this property in the bonds is not affected by the formation of the complex. However, the value of E at the position of the critical point of the hydrogen bond between S and the HO group of silanol reveals that a considerable deformation of the charge E 0:129 occurs in the interaction bond. This effect is higher than the corresponding to the C±H and Si±H bond paths of the isolated species. This electronic picture is reduced at the MP2 level. 4. Conclusions The van der Waals complex between thiophene and silanol has been studied at different levels of ab initio SCF-MO and DFT theory. We have found that a Cs linear conformation for this complex is able to model the experimental adsorption of thiophene in zeolites ZSM5. In fact, we show that this conformation reproduce reasonably the experimental shifts of the OH frequency of the terminal OH by effect of the perturbation with thiophene in the complex. These shifts are negative because these OH bands decrease due to the interaction. The weak nature of the silanol±thiophene complex is revealed by the topologic properties of the charge density as re¯ected by the total density, the Laplacian and the ellipticity at the critical point of the S±OH hydrogen bond. These properties de®ne a pattern of values for the silanol±thiophene complex.
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The complex is stabilized by electron correlation, which affect signi®cantly the laplacian and the ellipticities. We have also shown that the interaction between thiophene and OH groups of silanol, and between H2S and silanol, lead to van der Waals molecular complex of a similar nature.
Acknowledgements The authors would like to thank to CONICIT for the ®nancial support under contract number S195001617, CONDES-LUZ for partial support and CeCalcula of ULA for time computing.
References [1] C.L. GarcõÂa, J.A. Lercher, J. Mol. Struct. 293 (1993) 235. [2] H. SoscuÂn, J. HernaÂndez, O. Castellano, G. DõÂaz, A. Hinchliffe, Int. J. Quantum Chem. 70 (4/5) (1998) 951. [3] R.F. Bader, Atoms in MoleculesÐa Quantum Theory, Claderon Press, Oxford, 1990. [4] R.F.W. Bader, P.J. MacDougall, J. Am. Chem. Soc. 107 (1995) 6788. [5] C. Mùller, M.S. Plesset, Phys. Rev. 46 (1984) 3265. [6] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [7] H. SoscuÂn, P.O. Malley, A. Hinchliffe, J. Mol. Struct. (Theochem) 341 (1995) 237. [8] J. Cioslowsky, T.S. Mixon, J. Am. Chem. Soc. 113 (1991) 4142. [9] J. Cioslowsky, P.R. SurjaÂn, J. Mol. Struct. (Theochem) 255 (1992) 9. [10] M.J. Frisch, J.A. Pople, J.S. Binkley, J. Phys. Chem. 80 (1984) 3265. [11] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Lahan, V.G. Zakrzewsky, J.V. Ortiz, J.B. Foresman, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Steward, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian 94, Revision B.2, Gaussian Inc., Pittsburgh, PA, 1995. [12] A. Hinchliffe, H. SoscuÂn, J. Mol. Struct. (Theochem) 331 (1995) 109±125. [13] G. Schaftenaar, CAOS/CAMN Center, University of Nijmegen, The Netherlands, http/www.caos.kun.nl/staff/ schaft.html.
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The topology of the charge distribution of the silanol±thiophene van der Waals complex: ab initio and DFT study H. SoscuÂn*, O. Castellano, J. HernaÂndez SeccioÂn de Teoria CuaÂntica y DisenÄo Molecular, Laboratorio de QuõÂmica InorgaÂnica TeoÂrica, Departmento de QuõÂmica, Facultad de Ciencias, La Universidad del Zulia, AP 526, MoÂdulo No. 2, Grano de Oro, Maracaibo, Venezuela Received 24 August 1999; received in revised form 18 February 2000; accepted 29 February 2000
Abstract This work reports a quantum-chemistry SCF-MO ab initio study of the topology of charge distribution of the silanol± thiophene van der Waals molecular complex, by using the Hatree±Fock method, perturbation theory at the second level MP2, and density functional theory at the BLYP level. The geometry of the isolated species and the corresponding complexes were fully optimized at each level of theory by using the standard STO/6-311G(d,p) basis set. Cs symmetry was used for the molecular geometry of silanol and the complex, and C2v for thiophene. The geometric, electronic and vibrational results are compared with previous calculations for the silanol±H2S molecular complex. The nature of the chemical interactions that lead to the formation of the silanol±thiophene complex is analyzed in terms of the topologic properties of the linear conformation. This model reproduces the experimental prediction from the FT-IR adsorption spectra of thiophene in H-ZSM5 zeolites. q 2000 Published by Elsevier Science B.V. Keywords: Silanol; Thiophene; Infrared spectra; van der Waals interaction
1. Introduction Thiophene is a polar molecule that can be chemically adsorbed in zeolites leading to the formation of van der Waals complexes [1]. The nature of these complexes has been experimentally studied from the adsorption of the thiophene molecule into ZSM5 zeolites, and the interaction process followed by FTIR and gravimetric determinations at different pressures of thiophene gas [1]. From the analysis of the IR spectra of these experiments, it was proposed that at equilibrium a stable (1:1) van der Waals molecular complex between thiophene and the OH hydroxyl * Corresponding author. Tel.: 1 58-61-598098; fax: 1 58-6159809981. E-mail address: [email protected] (H. SoscuÂn).
groups of the zeolites is formed, where the formation of the complex occurs through the hydrogen bonding between the S atom of thiophene and the H atom of the acidic hydroxyl OH groups of the zeolites [1]. The acid behavior of these sites, the OH bridged (BroÈnsted site) and the OH terminal, have been rationalized in terms of their structural, electronic and vibrational properties [2]. According to the experimental IR spectra of the thiophene adsorption, these OH groups are able to give similar thiophene±OH complexes, where the main features of the S±H bond are of the same nature. In fact, one complex is formed between the OH bridged and the S atom of thiophene, and the second one occurs between the OH terminal and the S atom of thiophene. In particular, the IR frequency corresponding to the OH stretching mode of the terminal complex appears at a higher frequency than the
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bridged ones [1]. These ®ndings are due to the higher acidity of the OH bridged group than the terminal one, i.e. the terminal molecular complexes are weaker than that formed with the BroÈnsted group. Recently, the acid sites of zeolites have been characterized by using the topologic properties of the charge distribution r (r) of small clusters of Si and Al, including silanol [2]. The topologic properties of r (r) are based on the theory of atoms in molecules proposed by Bader et al. [3,4]. This approach is able to provide a reliable electronic picture about the nature of acid sites in zeolites. The aim of this paper was to investigate by quantum-chemistry methods, at the Hartree±Fock and post-Hartree±Fock levels, the structural, vibrational and the topologic properties that characterize the charge distribution of the chemical interaction between thiophene (C4H4S) and zeolite, using silanol (H3SiOH) as the model for the OH terminal groups. The post-Hartree±Fock (HF) methods used are perturbation theory at the second level of correlation MP2 [5] and density functional theory methods with the BLYP hybrid level [6]. The results are analyzed in terms of the available experimental data, and are compared with previous calculations for the H2S±silanol complex [7].
2. Theory and computational methods 2.1. Theory of atoms in molecules The quantum mechanic description of the topologic properties of the charge distribution r (r) of a molecular system was developed by Bader et al. and is known as the Theory of Atoms in Molecules [3,4]. This approach is based on the properties of the associated ®elds of r (r), the gradient vector 7r (r) and the Laplacian ®eld 7 2r (r). The points where the 7r (r) vanishes 7r r 0 are the extremes of r (r) and are referred to as critical points, which are classi®ed according to the three eigenvalues (l 1, l 2 and l 3) of the diagonalized Hessian matrix of r r; H ij 2 2 r r=2xi 2xj : Each critical point is labeled by the (D,S) pair of numbers, where D is the number of nonzero l i eigenvalues of Hij, and S the difference between the nonzero and the negative l i eigenvalues. The (D,S) set de®nes the label or signature of the
extreme. For a maxima critical point, the label is (3, 23) because all the three eigenvalues of H are nonzero and negative, being S 3 and D 23; while for a minima, the label is (3, 13). In a molecular system, the maxima, minima and saddle points in r (r) are de®ned as attractors, cage and either, bond (3, 21) or ring points (3, 11), respectively. The molecular regions where the 7r (r) is zero, lead to the existence of a zero-¯ux surface that splits the molecule in fragments linked by bond paths characterized as (3, 21). These regions, demarcated by the zero-¯ux surfaces are named the basins. Attractors of basins, are often located at the position of the nuclei, while bond critical points are located between two bonded atoms and correspond to a local maxima in two directions and a local minima in the third direction. The set of (3, 21) critical points de®ne the network of bond paths and describe the molecular structure by the characterization of all their atomic interactions. Along each of this bond path, the charge density is a maximum with respect to the any neighboring link. The value of the electron density at the bond critical point (r c(r)) has been referred as a useful index for representing the corresponding bond order [3,4]. This property accounts for the degree of charge concentration on the bond path. At these (3, 21) bond paths, the charge density attains its minimum value at the critical point and the associated l 3 eigenvalue is positive. On the other hand, the charge density in an interatomic surface attains its maximum value at the bond critical point and the two associated curvatures l 1 and l 2 are thus negative. If l 2 is the smallest eigenvalue, the ratio between l 1 and l 2 measure the bond deviation of cylindrical symmetry in the bond path, and the bond ellipticity is de®ned as e l 1 =l2 2 1: This property provides a measure of the extent to which the charge is preferentially accumulated within a molecule according to the orientation determined by l 2. The characterization of how the electronic density is rearranged according to the concentrations and depletions of the charge is described by the properties of the Laplacian of r (r), 7 2r (r). In particular, the sign of 7 2r (r) determines the regions where the charge density is locally concentrated 7 2 r r , 0 or locally depleted 7 2 r r . 0 [3,4]. These regions identify the chemical reactivity of a molecule. For instance, if the Laplacian is calculated at the position of a bond
H. SoscuÂn et al. / Journal of Molecular Structure (Theochem) 531 (2000) 315±321
Fig. 1. Thiophene±silanol structure and geometric parameters.
critical point, 7 2r c(r), positive values are indicative of ionic interactions, while negative values are associated with covalent bonds. In the present study, we have performed an ab initio study and applied the Bader theory of atoms in molecules as implemented by Cioslowsky and coworkers [8,9], to characterize the topologic properties of the electronic charge distribution of the interaction between silanol and thiophene that lead to the formation of the silanol±thiophene van der Waals complex. 2.2. Methods Calculations of topologic properties of r (r) were performed at the HF and Moller±Plesset (MP2) [5] methods by using the standard STO/6-311G(d,p) basis set [10]. Molecular geometries of silanol and thiophene were fully optimized at the Cs and C2v symmetries, respectively. The silanol-complex structure was calculated at Cs symmetry. The Gaussian 94 [11] quantum-chemistry system was employed for the calculations. 3. Results and discussion 3.1. Stability and geometric structures The fully optimized geometric parameters as shown in Fig. 1, the bond distances in Angstroms and the
317
bond angles in degrees of thiophene, silanol and silanol±thiophene complex are reported in Table 1. Cs symmetry was used for the molecular geometry of silanol and the complex, and C2v for thiophene molecule. These geometry optimizations were carried out at the HF, MP2, and BLYP levels of theory and the STO/6-311G(d,p) standard basis set. Total energies ET in atomic units and the interaction energies EB in kcal/mol for the silanol±thiophene complex are also reported in Table 1. The stability of the van der Waals silanol±thiophene complex can be analyzed by the slightly negative values of the EB interaction energies at the different levels of theory: HF (20.904 kcal/mol), MP2 (21.977 kcal/mol) and BLYP (20.841 kcal/mol), indicating that the dominant interaction for the formation of these complexes is weakly attractive. These energy values show the differences in evaluating only the main correlation contribution (MP2), and the determination of the exchange and correlation together (BLYP), showing that the use of electronic correlation is necessary when we handle van der Waals complexes. Fig. 1 shows the structural conformations of the species, indicating the corresponding geometric parameters. Table 1 shows that the results of the geometry optimization for silanol [7] and thiophene [12] are in agreement with previous calculations at similar levels of theory. The ®nal structure for the silanol±thiophene complex (see Fig. 1) was obtained by interacting the S atom of thiophene with the H atom of the OH group of silanol in the plane of both molecules. This interaction leads to the formation of a stable van der Waals molecular complex with a structure of linear conformation with Cs symmetry. This structure corresponds to a con®guration of local minima of second order, with two negative frequencies. In the present work, we only report the OH frequencies for silanol and the corresponding frequencies for the complex (see Table 1). The geometric results in Table 1 show that at the HF level the stability of the silanol±thiophene complex is reached at the S±HO interaction distance Ê . This value con®rms the fact that the interof 3.011 A action between thiophene and silanol occurs through a weak hydrogen bond, whose length lies in the expected range for the van der Waals complexes. For comparison, Table 1 also reports the HF/631G pp calculations for the H2S±silanol molecular
318
Thiophene HF a b c d q r t u y z ab qr bq n (OH) 2 ET 2 EB a b c
Silanol MP2
BLYP
HF
MP2 1.655 0.941
1.724 1.349 1.072 1.436 1.074
1.716 1.380 1.078 1.417 1.081
1.754 1.382 1.088 1.434 1.092
551.30389
551.96893
552.92746
Silanol±thiophene
120.8 4233 366.14701
1.685 0.963
117.7 3953 366.43750
HF/6-31G pp and MP2/6-31G pp [7]. Exp: terminal SiOH groups of zeolites [1]. Exp: interaction of terminal SiOH groups of zeolites with thiophene [1].
BLYP 1.692 0.973
117.6 3751, 3745 b 367.11059
HF
MP2
BLYP
1.647 0.942 1.469 1.477 3.011, 3.031 a 1.725 1.348 1.074 1.438 1.071 121.8 125.0 166.9 4225 917.45234 0.904
1.677 0.964 1.467 1.477 2.960, 2.740 a 1.717 1.379 1.081 1.437 1.078 117.3 126.8 136.8 3934 918.40958 1.977
1.689 0.975 1.488 1.498 2.763 1.754 1.381 1.091 1.439 1.088 117.7 141.3 171.0 3712, 3628 c, 3595 c 920.03939 0.841
H. SoscuÂn et al. / Journal of Molecular Structure (Theochem) 531 (2000) 315±321
Table 1 Structural properties, OH vibrational frequencies (n (OH) in cm 21, total energy ET in hartree and interaction energy EB in kcal/mol, of thiophene, silanol, and the silanol±thiophene complex, with the STO/6-31 1 G(d,p) basis set
H. SoscuÂn et al. / Journal of Molecular Structure (Theochem) 531 (2000) 315±321
319
Table 2 Topological properties of the charge density at the critical points of thiophene, silanol and the silanol±thiophene complex: total density r (r), laplacian density 7 2r (r) and ellipticity E, with the STO/6-31 1 G(d,p) basis set Molecule
r (r)
Thiophene Silanol Silanol±thiophene
7 2r (r)
Thiophene Silanol Silanol±thiophene
E
Thiophene Silanol Silanol±thiophene
a HF MP2 HF MP2 HF MP2 HF MP2 HF MP2 HF MP2 HF MP2 HF MP2 HF MP2
0.126 0.117 0.126 0.119
1.102 0.836 1.032 0.868
0.067 0.074 0.066 0.073
complex [7]. The value of the S±HO interaction distance in the thiophene±silanol complex Ê ) is shorter than in the H2S±silanol (3.011 A complex (3.031 AÊ), indicating that the S±HO interaction is relatively stronger in thiophene than in hydrogen sul®de. The results in Table 1 additionally show that the effect of electronic correlation increases the strength of the interaction between the S atom and the OH group in the Ê ) , MP2 (2.960 A Ê ) levels order of BLYP (2.763 A of theory. This tendency of MP2 distance is similarly observed for the H 2S±silanol complex Ê ) [7]. These results are in concordance (2.740 A with the relative stability of these complexes. Analysis of the rest of the geometric parameters displayed in Table 1, at the different levels of theory for the isolated molecules and the silanol±thiophene complex, shows that no signi®cant changes are observed in the structural properties of these species by effect of the interaction. These results show that the dominant interactions are of local nature and only the atoms that are involved in the chemical area in the van der Waals interaction are affected.
b
q
0.382 0.356 0.381 0.355
22.460 22.033 22.459 22.022
0.007 0.008 0.007 0.008
r 0.221 0.214
0.298 0.286
0.221 0.214
0.299 0.286
20.530 20.440
21.184 21.062
20.524 20.436
21.186 21.068
0.233 0.237
0.028 0.035
0.230 0.235
0.029 0.035
0.004 0.005
0.015 0.020
z
0.129 0.060
3.2. OH vibrational frequencies The chemisorption of thiophene in HZSM5 zeolites has been investigated experimentally by quantitative FT-IR spectroscopy [1]. These studies have proposed that thiophene interacts weakly with the OH bridged and with the OH terminal of zeolites as well, leading to the formation of stable 1:1 molecular van der Waals complexes. When these complexes are formed by the interaction between the S atom and the OH hydroxyl groups of zeolites, the OH vibrational modes are perturbed. These perturbations are re¯ected in the IR spectra. Table 1 displays the harmonic frequencies of the OH group for silanol and the silanol±thiophene complex, calculated at the HF, MP2 and BLYP levels of theory. These results show that the OH frequency decreases by effect of the interaction between S and the OH groups. At HF, MP2 and BLYP, the corresponding vibrational shifts are 28, 219 and 239 cm 21, respectively. Experimental observations [1] indicate that the OH frequency for silanol is 3745 cm 21 and decreases due to the effect of interaction to a band that is located between 3698 and 3595 cm 21 re¯ecting that there is an average shift of
320
H. SoscuÂn et al. / Journal of Molecular Structure (Theochem) 531 (2000) 315±321
Fig. 2. A relief map of the distribution of the Laplacian of electron density for the silanol±thiophene complex. The map has been orientated taking as reference the plane of the complex.
298.5 cm 21 due to the effect of the interaction. Our theoretical results are consistent with these experimental observations, showing that the adsorption of thiophene into terminal OH groups of zeolites produces a negative shift in the OH vibrational band. It is important to mention that at the DFT level, these OH frequency shifts are ampli®ed, giving a best representation with respect to the experimental reports. 3.3. Topological properties The topological properties of the charge distribution of thiophene, silanol and the thiophene±silanol complex, calculated at the HF and MP2 levels are reported in Table 2. The table reports the values of the total density (r (r)), the Laplacian density (7 2r (r)) and the ellipticity E, calculated at the position of the critical points of the bond paths, as displayed in the bond network of Fig. 1. 3.4. Density of charge The results of total charge density r (r) are given in Table 2. The very low value of r (r) (0.004) at the critical point of the q bond path determines that the interaction for the formation of the silanol±thiophene complex is very weak. No signi®cant changes in the r (r) values are observed in the rest of bond paths of the involved species. The correlation MP2 does not introduce determinant effects in these properties. 3.4.1. Laplacian of the charge density The Laplacian of the charge density is determined
by the signs of 7 2r (r) at each point of the space, determining the regions where the charge density is locally concentrated 7 2 r r , 0 or locally depleted 7 2 r r . 0: These charge concentrations determine the nature of the bonding interactions, either ionic or covalent ones. Also, the locally depleted regions in a molecule are associated to sites of electrophilic attack. Table 2 reports the values of the Laplacian density 7 2r (r), calculated at the position of the bond critical points of thiophene, silanol and the thiophene±silanol complex. Silanol is characterized by two bonds, one with a negative value of 7 2r (r) (22.443 at HF) at the position of the critical point of the O±H bond (b) which is dominated by covalent interactions, while the other one has a positive value of 7 2r (r) (11.102 at HF) at the position of critical point of the Si±O (a) being dominated by ionic interaction. From the values in Table 2, the 7 2r (r) of the Si±O and the OH bonds are changed by effects of the interaction, 11.032 and 22.459 being the corresponding HF values for the Laplacians of these bonds in the complex, respectively. In the region of the interaction, q bond path (S±HO), the value of 7 2r (r) (10.0015) is positive, giving a weakly ionic feature to this bond. MP2 results show that electronic correlation affect the values of the Laplacian, being signi®cant for the S±HO interaction, by increasing the weakly ionic property of this bond. In Fig. 2 is depicted the distribution of the Laplacian of r (r) for the silanol±thiophene complex as performed with the MOLDEN software [13], where the positive and negative regions are shown. The positive regions are located around the Si and O atoms of
H. SoscuÂn et al. / Journal of Molecular Structure (Theochem) 531 (2000) 315±321
the silanol fragment, and around the C and S atoms of the thiophene species, while the negative regions are concentrated around the H atoms and around the S± OH bond. The low concentration of charge observed in the S±OH segment is indicative of the weak interactions that dominate the complex. 3.4.2. Ellipticity The ellipticity (E) of a bond is associated to the measure of the extent to which the charge is preferentially accumulated within a bond in a molecule. This tendency of the charge is determined by the orientation of the smallest eigenvalue of the diagonalized Hessian matrix of r (r). The E values for thiophene, silanol and silanol±thiophene structures as reported in Table 2 indicate that this property in the bonds is not affected by the formation of the complex. However, the value of E at the position of the critical point of the hydrogen bond between S and the HO group of silanol reveals that a considerable deformation of the charge E 0:129 occurs in the interaction bond. This effect is higher than the corresponding to the C±H and Si±H bond paths of the isolated species. This electronic picture is reduced at the MP2 level. 4. Conclusions The van der Waals complex between thiophene and silanol has been studied at different levels of ab initio SCF-MO and DFT theory. We have found that a Cs linear conformation for this complex is able to model the experimental adsorption of thiophene in zeolites ZSM5. In fact, we show that this conformation reproduce reasonably the experimental shifts of the OH frequency of the terminal OH by effect of the perturbation with thiophene in the complex. These shifts are negative because these OH bands decrease due to the interaction. The weak nature of the silanol±thiophene complex is revealed by the topologic properties of the charge density as re¯ected by the total density, the Laplacian and the ellipticity at the critical point of the S±OH hydrogen bond. These properties de®ne a pattern of values for the silanol±thiophene complex.
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The complex is stabilized by electron correlation, which affect signi®cantly the laplacian and the ellipticities. We have also shown that the interaction between thiophene and OH groups of silanol, and between H2S and silanol, lead to van der Waals molecular complex of a similar nature.
Acknowledgements The authors would like to thank to CONICIT for the ®nancial support under contract number S195001617, CONDES-LUZ for partial support and CeCalcula of ULA for time computing.
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