Benco - Adsorption Hc Zeolite Dft Intestigation

JOURNAL OF CHEMICAL PHYSICS

VOLUME 114, NUMBER 14

8 APRIL 2001

Adsorption of linear hydrocarbons in zeolites: A density-functional investigation Lubomir Benco,a) Thomas Demuth, and Ju¨rgen Hafner Institut fu¨r Materialphysik and Center for Computational Materials Science, Universita¨t Wien, Sensengasse 8, A-1090 Wien, Austria

Franc¸ois Hutschka Total Raffinage Distribution, Centre Europe`en de Recherche et Technique, B. P. 27, F-76700 Harfleur, France

Herve Toulhoat Institut Franc¸ais du Pe´trole, F-92852, Rueil-Malmaison Cedex, France

共Received 11 October 2000; accepted 23 January 2001兲 An extensive first-principles periodical study of adsorption properties of linear hydrocarbons in zeolites is presented. The applicability of density-functional theory to weak interactions is inspected within both local-density 共LDA兲 and generalized-gradient 共GGA兲 approaches for C1 to C6 linear hydrocarbons. The LDA adsorption energies are due to the overbinding ⬃2.5 times larger than the GGA values. A compact diagram is constructed showing the increase of the adsorption energy with the length of the adsorbed molecule and with the concentration of acid sites in the zeolite support. The flow of the electron density induced by the adsorption indicates that the adsorption on the acid site is realized through the hydrogen bonding between the OH group and the CH3 group. The pattern of the reconstructed bonding, however, is more complex than that of the simple hydrogen bond. The regions of redistributed electron density within the adsorbed molecule are spread over the whole CH3 group and the adjacent C–C bond. The off-centering of the reconstructed regions from atomic positions is in good agreement with recent 13C measurements, showing only slight variation of chemical shifts with the hydrocarbon length for both proton-free and the protonated forms of zeolites. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1355769兴

I. INTRODUCTION

complex defect structures produced by the postsynthetic processing of zeolites causes the interaction energy to increase proportionally to the concentration of defects. Hydrocarbons 共HC兲 are raw materials for many technologically important products and their adsorption in zeolites is of continuous attention to both experimentalists and theoreticians. The adsorption isotherms of C5 –C10 normal alkanes in silicalite crystals are measured by Sun et al.3 The adsorption of C3 –C6 normal alkanes in acidic zeolites is studied by Eder et al.,4 and Denayer et al. have recently reported on the adsorption of n-alkanes at high temperatures.2 The experimental data indicate that adsorption energies of the HC are much smaller than those of small polar molecules such as ammonia and water. The adsorption of polar molecules is accomplished through relatively strong N–H¯O and O–H¯O hydrogen bonds 共HB兲 with typical adsorption energies of ⬃200 kJ/mol 共NH3 5兲 and ⬃100 kJ/mol (CH3OH, 6 H2O7兲. The strength of the adsorption forces acting on the HC is documented, e.g., by the adsorption energy of propane. For acidic ferrierite 共Si/Al⫽45兲 the measured value is 49 kJ/mol.4 For n-hexane Eder et al.4 deduced the dependence of the heat of adsorption on the zeolite framework density. Supposing that a similar dependence is valid also for other n-alkanes, the estimate for the adsorption of propane in acidic gmelinite is ⬃40 kJ/mol and a much lower adsorption energy is expected for the purely siliceous structure.

Zeolites are microporous materials widely used in technological processes as multipurpose materials.1 They are very good sorbents with a high internal surface. Their channel-like structures make the transport of molecules inside or outside the crystals an easy process. Because of the high stability and numerous imperfections such as Si/Al substitutions compensated with acid protons or with extraframework cations, zeolites perform well as heterogeneous catalysts. In a series of intrazeolite processes through which reactants are converted into products, the adsorption of molecules to the internal surface represents an important first step. The strength of the interaction depends on the composition of the zeolite being the weakest for the purely siliceous compounds and proportionally increased with the increased concentration of the acid sites. For different structure types different adsorption energies have been measured. In the more compact structures 共ZSM-22, MOR兲 the contact between the framework and the adsorbed molecule is tighter and leads to higher adsorption energies. On the contrary, adsorption energies for the more open structures with smaller framework densities 共Y,X兲 are smaller.2 A wide range of a兲

Electronic mail: [email protected]. Permanent address: Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, SK-84236 Bratislava, Slovakia.

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Theoretical ab initio works investigating a contact between the zeolitic framework and the HC include molecules of various complexity, starting with methane8 and ending with long linear hydrocarbon chains9 or unsaturated branched molecules like isobutene.10 The HC to zeolite interaction has been, however, inspected mostly by means of the molecular cluster approach, which uses a fragment of the zeolite containing the active site as a representative model of the zeolite. The fragment is cut out from the parent structure with the hydrogen atoms saturating terminal bonds. Two main disadvantages of this approach are 共i兲 a relaxation of the cluster resulting in the lost of resemblance to the environment of the active site, and 共ii兲 omitting of long-range electrostatic effects. Both relaxation producing the more tight contact between the adsorbent and the adsorbate and neglection of electrostatic repulsion lead to adsorption energies too high compared with experimental data. The former drawback is eliminated by usage of a constrained cluster. An influence of the long-range electrostatic interactions is taken into account via embedding techniques11,12 based on the combination of the quantum mechanics 共‘‘inner’’ region of interest兲 and the molecular mechanics 共less important outer region兲. Application of both corrections end with adsorption energies diminished to values compared reasonably with experimental data.10 The density-functional theory 共DFT兲13 and the generalized gradient approximation 共GGA兲 for the exchange functional14 have been used in numerous applications in which DFT compares well with experiment and with the most accurate ab initio calculations for properties such as structure and bond energy and are now in routine use for a number of fundamental properties of chemical and physical systems. Despite the successes, problems remain. The GGA considerably improves bond distances and bond energies for strong interactions of both covalent and ionic character compared to the uncorrected local density approach 共LDA兲. Applicability of GGA to weak intermolecular forces has been tested on rare-gas diatomic molecules.15 Though GGA functionals significantly improve the LDA values of bond lengths, binding energies, and vibrational frequencies, the agreement is still not quantitative. Interaction energy comprises a high percentage of dispersion energy 共more than 90% in He2 兲. Because dispersion energy scales with r ⫺6 , it is sensitive to interatomic distances. Undervaluation of bond lengths which often occurs in GGA, e.g., for Ar and Kr,15 then leads to too small GGA interaction energies. Investigation of alkali metal adsorption at the surface of MgO16 have shown that application of GGA functionals decreases interaction energies by a factor of ⬃1.6 共PBE9617兲 and by ⬃2.7 共BLYP18兲. We have performed an extensive study of properties of zeolite structures aiming at increasing knowledge of intrazeolite chemistry. Within the periodical approach the topology of the inner surface of zeolites is preserved and longrange electrostatic effects are taken into account. Both a model structure and a zeolite of technological importance are under study. Gmelinite as a model structure represents, due to its relatively high symmetry and the small number of atoms per cell, a framework convenient for numerical simula-

Benco et al.

tions of chemical processes. Subsequent comparative studies on technological zeolite are performed with mordenite. We have compared structural properties as well as energetics of protonation of the two structures19,20 complemented by calculations of the stretching frequencies of hydroxyl groups. A dynamical study of H2O adsorbed in Na-free gmelinite has demonstrated the existence of the spontaneous proton transfer 共PT兲 between O sites.21 A similar scenario of the PT is found for the Na zeolite.22 The present report describes the adsorption of linear hydrocarbons in zeolites. The periodical approach is used to preserve the surface structure of the zeolitic framework and to include the long-range electrostatic effects. Two basic DFT approaches, LDA and GGA, are used to calculate the adsorption energies. Weak interactions between the hydrocarbon molecules and the zeolite framework represent a probe for the applicability of commonly used functionals to adsorption phenomena in zeolites. II. STRUCTURE AND MODEL OF ADSORPTION

The simulation of the adsorption of hydrocarbons in a zeolite is modeled on the gmelinite structure. Gmelinite is a rather rare natural zeolite with the chemical composition Na8共AlO2兲8共SiO2 ) 16 . The primary building blocks 共SiO4 and AlO4 tetrahedra兲 are stacked into hexagonal prisms which are secondary building units isomorphous with those of the technologically important faujasites.23 Parallel linkage of hexagonal prisms leads to a hexagonal structure ( P6 3 mmc). The set of irreducible atomic positions contains only one tetrahedral site 共Si/Al兲 and four oxygen sites.24 The largest aperture is a ⬃7 Å channel circumscribed by a ring of 12 SiO4 tetrahedra 共12-membered ring: 12MR兲, which runs parallel to the c axis. From the main channel perpendicular to the c axis the smaller eight-membered rings 共8MR兲 lead to the gmelinite cages which is the only type of cage in the structure. Figure 1 presents the structure, the orientation of 12MR and 8MR, the situation of the gmelinite cage, and the positions of irreducible O atoms. The x-ray structure refinement performed on natural gmelinite with an Si/Al ratio of approximately 2 and containing the corresponding number of counterions and approximately 24 water molecules per cell yields cell dimensions of a⫽13.756 Å and c⫽10.048 Å. 24 The simulations of the adsorption of n-hydrocarbons are performed with the fixed volume and shape of the experimental unit cell of the hydrated zeolite.24 The experimental volume was shown to be only slightly larger than that obtained by the optimization within the GGA approach19 共cf. similar results for mordenite20 and chabazite25兲. Because the adsorption in a zeolite always leads to slight expansion of the crystal lattice, the cell volume determined on hydrated samples reasonably compares with the optimized unit cell of the zeolite. The hydrocarbons are placed in the 12MR. The most probable position of the adsorbed molecules, transported into the structure by the stream of gaseous or liquid hydrocarbons flowing along the main channels, is parallel to the main channel. The position of the hydrocarbon molecule is therefore chosen parallel to the c axis in which any energy loss due to the deformation of the the linear chain of the molecule is avoided. The acid proton is located at the O4

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J. Chem. Phys., Vol. 114, No. 14, 8 April 2001

FIG. 1. Hexagonal structure of gmelinite. Top view showing large 12MR channels 共a兲. Side view of the framework structure 共b兲 displaying the 8MR and the gmelinite cages. Short arrows indicate the four inequivalent O sites surrounding the tetrahedral site.

site, the OH group pointing to the center of the main channel.19 To facilitate a maximum contact of the adsorbed molecule with two acid sites 共AS兲, a second proton is placed at a relatively short distance from the first one located on another O4 atom. Two Al atoms corresponding to two AS are placed in second-neighbor positions, obeying the Lo¨wenstein rule for the distribution of the Al-sites. The fragment of the structure, the position of the adsorbed molecule, the location of the acid protons and of the Al atoms, respectively, are displayed in Fig. 2. III. COMPUTATIONAL DETAILS

Periodic first-principles calculations are performed within the density-functional theory 共DFT兲 using the Vienna ab initio simulation package VASP.26,27 The simulations use both the local-density 共LDA兲 and gradient-corrected 共GGA兲 density functionals in standard versions proposed by Ceperley and Alder and parametrized by Perdew and Zunger28 and by Perdew and Wang.29 The valence-electron wave functions are expanded in terms of plane waves,30,31 and the electron– ion interaction is described by Blo¨chl’s projector augmented wave 共PAW兲 technique32,33 applied to ultrasoft pseudopotentials.34,35 The calculations are performed with a plane wave cutoff energy of E pw⫽400 eV. Cutoff radii of r s ⫽r p ⫽r d ⫽1.9 a.u. for the pseudo-wave functions are used for aluminum and silicon, respectively. Cutoff radii of r s ⫽1.3 a.u. and r p ⫽r d ⫽1.5 a.u. are used for oxygen and car-

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FIG. 2. Fragment of the structure showing the location of the adsorbed hydrocarbon molecule, the Al atoms, and the acid protons, respectively. Top view 共a兲 and the side view 共b兲.

bon, and radii of r s ⫽r p ⫽1.1. a.u. are used for hydrogen. Brillouin-zone sampling is restricted to the ⌫ point. The total energy is converged to 10⫺5 eV; the convergence is improved using a modest smearing of the eigenvalues. The optimization of atomic positions within the unit cell is performed combining both the quasi-Newton and the conjugategradient algorithms. In relaxed positions the residual analytical Hellman–Feynman force acting on atoms is not larger than 0.1 eV Å⫺1. IV. RESULTS AND DISCUSSION A. Adsorption energies

The adsorption of HC in a purely siliceous zeolite is realized via the contact between the zeolite O sites and the hydrogen atoms of the HC. In a protonated structure the strongest interaction occurs between the Brønsted O–H group of the zeolite and one carbon atom of the HC. Figure 3 schematically compares these two types of bonding to the ordinary O–H¯O hydrogen bond and orders the bonding contacts according to a decreasing bond strength. All of them belong to the category of the hydrogen bonds.36 Compared to the typical O–H¯O interaction 关Fig. 3共a兲兴 the other two contacts, O–H¯C 关Fig. 3共b兲兴 and C–H¯O 关Fig. 3共c兲兴, are much weaker due to much lower electronegativity of carbon compared with oxygen. Adsorption energies are calculated using the expression E ads⫽E 共 zeo⫹HC兲 ⫺E 共 zeo兲 ⫺E 共 HC兲 ,

共1兲

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FIG. 3. Schematic illustration of different hydrogen bonds 共HBs兲 in zeolites. Ordinary O–H¯O HB for adsorbed water 共a兲, the O–H¯C contact between the acid site and a hydrocarbon 共b兲, and the C–H¯O contact between the purely siliceous zeolite and the hydrocarbon molecule.

where E(zeo⫹HC) is the energy of the relaxed zeolite structure containing the HC molecule adsorbed in the main channel, E(zeo) is the energy of the adsorbate-free zeolite structure, and E(HC) is the energy of the HC molecule optimized in vacuo. Geometries of both free HC molecules and adsorbed complexes are given below. No volume (p•⌬V) and entropy (T•⌬S) terms are considered in the calculation of adsorption energies. Figure 4 displays the adsorption energies as a function of the HC length for the purely siliceous structure 共a兲, for one acid site/cell 共b兲, and for two acid sites/cell located in the framework at the short distance of ⬃4.8 Å 共c兲. For a series of C1 –C6 molecules adsorbed in the purely siliceous structure, a quasilinear dependence is observed for both GGA and LDA. The values calculated using the GGA result from a tedious structure optimization often ending in numerous local minima of the potential energy surface. Figure 4共a兲 shows a slight increase between C1 and C2 . The adsorption energies for longer HC then oscillate around the value of ⫺4 kJ/mol and do not increase for longer HC. Within the LDA the corresponding adsorption energies are much higher than those obtained with GGA, e.g., for ethane the GGA and LDA values are ⫺4.7 and ⫺11.2 kJ/mol, respectively. A modest increase of the LDA adsorption energies between C1 and C2 is followed by a quasilinear increase for higher HC with an increment of ⬃⫺4.3 kJ/mol per C atom. The quasilinear behavior of LDA energies agrees reasonably with the experimental data obtained for adsorption of n-alkanes in acid zeolites2,4 as well as with the adsorption data for silicalite.3 The linearity is due to the homogeneous increase of the lateral interactions between adsorbed molecules and zeolite structure with every CH2 group of the HC. Much lower values of the GGA adsorption energies calculated for weak interactions are in agreement with the former results. The applications to rare-gas diatomic molecules15 and alkali metal adsorption at the surface of MgO16 have documented that when GGA functionals overvalue bond lengths the longrange van der Waals forces otherwise making substantial contributions to the adsorption energy vanish due to too large interatomic distances. Energies calculated for one acid site/cell 关Fig. 4共b兲兴 are quasilinear for GGA and LDA, both shifted to higher adsorption energies by an almost constant increment of about 28 kJ/mol 共LDA兲 and 8 kJ/mol 共GGA兲 compared with corresponding values for the purely siliceous structures. This proves that the strength of the O–H¯C interaction 关Fig. 3共b兲兴 is larger than that of the C–H¯O bond 关Fig. 3共c兲兴. Figure 4共c兲 shows that on structures with two acid sites the adsorption energies are further increased, displaying a

FIG. 4. Adsorption energies of linear alkanes. Adsorption of C1 to C6 in the purely siliceous structure 共a兲, C3 to C6 to one acid site 共b兲, and C3 to C6 to two acid sites 共c兲.

nonlinear increase between C4 and C5 . The reason for the step-like dependence is another contact of the adsorbed molecule to the second acid site. While C3 and C4 molecules make only one contact, the C5 and C6 molecules are long enough to make contacts to both acid sites. The gain in adsorption energy through the formation of this contact is ⬃⫺25 kJ/mol 共LDA兲 and ⬃⫺9 kJ/mol 共GGA兲, i.e., almost the same as for the first bond to the acid site. This increase of the adsorption energies is expected for protonated structures with high concentration of acid sites 共Si/Al⫽1兲 provided that the geometry of the adsorbed molecules and the distribution of the acid sites allow for a simultaneous formation of two unstrained bonds. No such data, however, are available to be compared with our calculated adsorption energies. Figure 5 comprehends the adsorption data as a function

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J. Chem. Phys., Vol. 114, No. 14, 8 April 2001

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TABLE I. Geometry parameters of a propane molecule in vacuo 共distances in Å, angles in deg, and deviation 共␦兲 in percent兲. Notation according to Fig. 6.

FIG. 5. Adsorption energies as a function of the hydrocarbon length and the concentration of acid sites.

of the acid site concentration for C3 –C6 molecules. It demonstrates that at all concentrations the GGA adsorption energies are approximately 2.5 times lower than those by LDA. More pronounced LDA-calculated adsorption energies demonstrate that the strength of the interaction between the HC and the zeolite framework is approximately doubled for the acid zeolite compared with the purely siliceous structure. With the increase of the acid site concentration the gain in energy is slowed down, probably due to steric constraints. In structures with a concentration of up to one acid site per adsorbed molecule the adsorption energy increases almost linearly with increased length of the HC. For higher acid site concentrations, however, a pronounced nonlinearity appears, distinguishing between molecules according to the number of contacts with framework acid sites 共C3 ,C4 —one contact; C5 ,C6 —two contacts兲. B. Structure of adsorption complexes

As a response to the interaction with the zeolite support structural changes are induced in an extent which depends on the interaction strength. This section reports details of the geometries of the adsorbate sorbent complex at the example of the propane molecule. 1. Molecule in vacuo

Geometry parameters of the propane molecule optimized in vacuo by means of PAW-projected pseudopotentials within both LDA and GGA are compiled in Table I together with experimental data.37 These values indicate that for interatomic distances the GGA performs slightly better than the LDA. All the LDA distances deviate by about 1% from the experimental value, the C–C bond length being underestimated and the C–H bonds overestimated by this amount. Within the GGA all distances are slightly overestimated and compare reasonably to experimental data. The angles calculated within both LDA and GGA are of acceptable quality.

C–C C2–H C1–Hs C1–Ha C1–H C–C–C H–C2–H Ha–C1–Ha Ha–C1–Hs H–C1–H C2–C1–Hs C2–C1–Ha a

Exp. 共Ref. 37兲

LDA

␦

GGA

␦

1.526共2兲 1.096共2兲 1.089共9兲 1.094 1.091共10兲a 112.4共2兲 106.1共2兲 107.3 108.1 107.7共10兲a 111.8共10兲 110.6

1.509 1.107 1.102 1.105 1.104a 111.9 105.5 107.0 107.7 107.5a 112.5 110.8

⫺1.11 ⫹1.00 ⫹1.19 ⫹1.01 ⫹1.19 ⫺0.44 ⫺0.57 ⫺0.28 ⫺0.37 ⫺0.19 ⫹0.63 ⫹0.18

1.528 1.102 1.099 1.101 1.100a 112.7 106.0 107.4 107.6 107.5a 111.9 111.1

⫹0.13 ⫹0.55 ⫹0.92 ⫹0.64 ⫹0.82 ⫹0.27 ⫺0.09 ⫹0.09 ⫺0.46 ⫺0.19 ⫹0.09 ⫹0.45

Average value.

siliceous structure does not induce any remarkable deformation of the adsorbed molecule. The distances and angles of the Ha atoms which are in contact with the zeolite are similar to those of the free molecule 共cf. Tables II and I兲. The O1¯Ha distances to the framework O sites, however, are considerably shorter within LDA. The adsorption to the acid site gives rise to changes which are observable in both LDA and GGA. These changes, however, are more pronounced within LDA. The OH-to-C1 contact, which represents the strongest interaction, keeps the adsorbed molecule at a distance shorter than that in the siliceous structure 共cf. averaged LDA values of 2.593 and 2.623 Å, respectively兲. The interaction leads to a widening of the Ha–C1–Ha angle and to the elongation of the C1–Ha bonds. On the side of the zeolite the O1–H bond is elongated, giving evidence for the formation of the O–H¯C hydrogen bond. The adsorption of the hydrocarbon induces a deformation of the zeolite structure as well. Table II reports the angle O1⬘ –O4–O1 characterizing the curvature of the inner surface of the zeolite 共cf. Fig. 6兲. The comparison of this angle with the values in parentheses, which correspond to the adsorbent-free zeolite structures, shows that both the siliceous and the acid zeolite are deformed in the same manner. The uniform decrease of this angle indicates that in response to the local adsorption, a global deformation of the framework occurs producing an ellipsoidal shape of the main channel. Different O1⬘ –O4–O1 angles observed for the acid

2. Adsorbed molecule

The geometrical arrangement of the contact site between the zeolite support and the hydrocarbon molecule is displayed in Fig. 6 and the geometry parameters are collected in Table II. The weak interaction between the molecule and the

FIG. 6. Geometry of the contact site between zeolite and the hydrocarbon molecule. Purely siliceous zeolite 共a兲, bonding at the acid site 共b兲. For the numerical values of bond-distances and angles, see Table II.

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J. Chem. Phys., Vol. 114, No. 14, 8 April 2001

TABLE II. Geometry parameters of the adsorbate/sorbent complex for propane adsorbed in gmelinite 共distances in Å and angles in deg兲. Notation according to Fig. 6. Purely siliceous zeolite Hydrocarbon C–C C2–H C1–Hs C1–Ha C–C–C H–C2–H Ha–C1–Ha Contact site O4共zeo兲¯C1 O4–H H¯C O1¯Ha O1⬘¯Ha O1¯Ha zeolite O1⬘ –O4–O1

Acid zeolite

GGA

LDA

GGA

LDA

1.527 1.103 1.099 1.101 112.4 105.9 107.2

1.508 1.107 1.103 1.106 112.4 105.8 106.9

1.529 1.101 1.098 1.107 113.3 106.4 111.7 共107.4兲a

1.509 1.105 1.102 1.115 112.3 106.1 113.1 共106.7兲a

3.514

3.150

2.908 2.994 2.951b

2.604 2.642 2.623b

158.6 共159.4兲c

156.3 共158.4兲c

3.085 0.996 2.090 2.781 2.672 2.727b 163.4 共164.2兲c

2.941 1.014 1.927 2.669 2.517 2.593b 162.1 共163.9兲c

a

Values in parentheses refer to the contact-free methyl group. Average value. c Sorbent-free zeolite structures. b

zeolite compared to the siliceous structure are due to the local deformation raised by the Al/Si substitution. C. Bonding to zeolite framework

The formation of a chemical bond between the zeolite support and the adsorbed molecule is accompanied by a redistribution of the electron density. The change of bonding is displayed by the differential charge density calculated as the difference between the electron density of the adsorbed complex and that of the adsorbent-free support and of the free nonadsorbed molecule, all systems preserving the relaxed atomic positions of the adsorbed complex.

FIG. 7. Difference electron densities of the propane molecule adsorbed in the purely siliceous zeolite. Spheres show atomic positions of the adsorbed molecule and the zeolite fragment adjacent to the contact site. Light gray regions indicate a gain and the dark regions a depletion of the electron density. LDA 共a兲 and GGA 共b兲 approaches 共isosurfaces of ⫹10 e/Å3 and ⫺7.5 e/Å3兲.

1. Purely siliceous zeolite

Figure 7 displays the difference electron densities of the propane molecule adsorbed in the purely siliceous structure. Only minor changes of the electron density are induced within both LDA 关Fig. 7共a兲兴 and GGA 关Fig. 7共b兲兴 as shown by the low-value isosurfaces of ⫹10 and ⫺7.5 e/Å3 共cf. isosurfaces of the acid zeolite displayed below兲. A different pattern of stabilizing interactions is obtained within LDA and GGA, none of them indicating a hydrogen bonding of the type O共zeo兲¯H–C. The GGA leads to a very small charge redistribution not localized on atoms. The LDA functional leads to a more pronounced charge flow in correspondence with higher LDA adsorption energies 共Figs. 4 and 5兲 and shorter O4共zeo兲¯C1 distances 共Table II兲. The bonding is of clear directional character localized between the O atoms of the zeolite and the CH3 group of the hydrocarbon molecule 关Fig. 7共a兲兴. The changes are of comparable extent on both the adsorbed molecule and on the zeolite framework. The shortest contact between C1 and O4 induces a slight

increase of the electron density between the two Ha atoms close to the C1 atom and a polarization of the framework O4 atom on which the charge density is withdrawn from the side of the zeolite and accumulated towards the CH3 group of the adsorbed molecule. The other end of the molecule makes another contact between the second C1 atom and the framework O3 atom of 3.343 Å. For this weaker contact Fig. 7共a兲 shows a charge redistribution of an extent comparable to that within the shortest contact between O4 and C1. The electron density is again accumulated on the framework O3 atom, but depleted from the C–H bond. 2. Acidic zeolite

The charge flow induced by the interaction of the propane molecule with the zeolite acid site is displayed in Fig. 8. A distinct redistribution of the charge density is obtained for both LDA 关Fig. 8共a兲兴 and GGA 关Fig. 8共b兲兴 functionals

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J. Chem. Phys., Vol. 114, No. 14, 8 April 2001

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nounced feature of the hydrogen-bonded hydrocarbon molecule is the large region of increased electron density between the two Ha atoms elongated towards the zeolite acid site. An increase of similar extent and shape is found for a benzene molecule adsorbed in acid mordenite, as well.39 This accumulation of the electron density weakens the C–H bonds and leads to an increased Ha–C1–Ha angle 共cf. Table II兲. The off-centered position of the two depleted regions indicates that the transferred electron density comes from nonbonding regions of the Ha atom 共Fig. 8, left兲 and of the Hs atom. The third depleted region is localized directly on the C–H bond. The depletion of the electron density within the CH3 group polarizes the C–C bond whose electron density is shifted towards the CH3 group. Figures 7 and 8 show that regions of substantial difference electron densities within hydrocarbons adsorbed in both purely siliceous and acid zeolites are typically not localized on atoms. Recently, adsorption properties of linear alkanes in ZK-5 zeolites were investigated by means of 13C NMR measurements.40 The NMR chemical shifts, which are very sensitive to the change of bonding on the measured atomic center, show only slight variation for hydrocarbons of different length in both the proton-free and protonated form of the zeolite. This agrees well with our results displaying the change of bonding within the terminal CH3 group which is localized close to the H atoms or within the C–C and C–H bonds but leaves the electron density around the carbon atoms unchanged. V. CONCLUSIONS

FIG. 8. Difference electron densities of the propane molecule adsorbed to the acid site. LDA 共a兲 and GGA 共b兲 approaches 共isosurfaces of ⫹40 e/Å3 and ⫺30 e/Å3兲.

which is slightly more pronounced for LDA. Both functionals provide the same pattern of bonding restricted to the OH group on one side and to the terminal CH3 group on the other side. A rather complex charge redistribution occurs in the hydroxyl group, showing features typical of hydrogenbonded OH groups.38 The area of the acid H atom is depleted of electron density which is transferred towards both the O–H bond and the CH3 group. A rather symmetrical redistribution on the O atom indicates a nonisotropic polarization directed along the OH group, leaving the two covalent O–Si and O–Al bonds unaffected by the hydrogen bonding. On the side of the hydrocarbon changes occur only in that part of the molecule which is involved in the contact with the zeolite. In contrast to the typical O–H¯O hydrogen bond where the contact is realized through a single O atom, the hydrocarbon molecule makes contact through the entire CH3 group. Figure 8 shows that the increase of the electron density here is not centered on a single atom, but reflects a polarization of the whole methyl group. The most pro-

A first-principles DFT study of the adsorption properties of linear hydrocarbons in zeolites is presented. The weak adsorbate–sorbent interaction energies are calculated within both LDA and GGA approaches. The LDA adsorption energies are ⬃2.5 times larger compared to the GGA values, which is in agreement with other applications of the DFT to weak interactions. There are no direct experimental data for the adsorption of the hydrocarbons in gmelinite. Adsorption experiments performed on different structures of zeolites 共mordenite, ZSM-5, ferrierite兲 show that adsorption energies are similar to the LDA interaction energies. Experiments, however, are performed on real crystals containing attractive centers for the adsorption like framework defects and nanoparticles of extra framework aluminum oxides. Our calculated GGA interaction energies indicate that much lower adsorption energies are expected for ideal crystal structures of zeolites. In the relaxed structures of adsorbed molecules obtained by GGA, the contact between the molecule and the support is looser compared with corresponding structures calculated using LDA. Proportionally to the decreased strength of the interaction, the adsorbed molecules are in the GGA much less deformed relative to geometries of the noninteracting molecules. The GGA adsorption energies are much smaller than the corresponding LDA energies due to longer interatomic distances and underestimation of long-range van der Waals forces in the GGA. For the adsorption on the acid sites the LDA/GGA ratio is ⬃2.6 and much larger differences are

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obtained for the adsorption of longer hydrocarbons in the purely siliceous structures. Bonding effects visualized through difference electron densities show that within the GGA almost no charge redistribution occurs in both the adsorbed molecule and in the siliceous framework—in contrast to the LDA. There is no hydrogen bonding of the type C–H¯O. Within the LDA the interaction of the framework with the adsorbed molecule is not realized through individual hydrogen atoms. Due to the contact with framework oxygen atoms, the entire terminal CH3 group of the hydrocarbon molecule is polarized and participates in the formation of the adsorbate/sorbent bond. The adsorption on the acid zeolite induces extensive charge redistribution. The bonding is realized here through the acid hydroxyl group. Again, the bonding leads to a redistribution of the electron density within the whole CH3 group and even to a polarization of the adjacent C–C bond. The regions of maximum charge flow are not centered at atomic positions and therefore not detectable by NMR measurements. ACKNOWLEDGMENTS

The work has been performed within the Groupement de Recherche Europe´en ‘‘Dynamique Mole´culaire Quantique Applique´e a` la Catalyse,’’ founded by the Council National de la Recherche Scientifique 共France兲, the Institut Franc¸ais du Pe´trole 共IFP兲, TOTAL Recherche et Development, and the Universita¨t Wien. Computing facilities at IDRIS 共France兲 are kindly acknowledged. 1

Benco et al.

J. Chem. Phys., Vol. 114, No. 14, 8 April 2001

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