fulltext

First-principles molecular dynamics investigations of the stability

of zeolite offretite under various Si

_O(Al

, H

_{) substitutions (*)}

L. CAMPANA(1)(2), A. SELLONI(1), J. WEBER(1) and A. GOURSOT(3) (1_{) Department of Physical Chemistry, University of Geneva}

30 quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland

(2_{) Institute IRRMA, Swiss Federal Institute of Technology, PHB-Ecublens} CH-1015 Lausanne, Switzerland

(3_{) National School of Chemistry, URA 418}

8 rue de L’Ecole Normale, F-34053 Montpellier, France (ricevuto il 28 Febbraio 1997; approvato l’8 Maggio 1997)

Summary. — A local density functional study of Si4 1_{O( Al}3 1_{, H}1_{)-substituted} offretites is presented. Proton siting and dynamical properties are investigated within the First-Principles Molecular Dynamics method, using a periodically repeated unit cell. Results for monoaluminated offretites, e.g., with one Al per unit cell, show that the proton is located inside the channel of the zeolite, where it is accessible to incoming molecules for reaction. Calculated vibrational spectra of the framework, extracted from a dynamical simulation, reproduce experimental data well. The determined OH stretching frequencies show a rather weak dependence on the H1 _{position. A comparison of these frequencies with those of offretites} containing three Al per unit cell does not indicate a significative change.

PACS 31.15.Qj – Molecular dynamics and other numerical methods. PACS 82.30 – Specific chemical reactions; reaction mechanisms. PACS 01.30.Cc – Conference proceedings.

1. – Introduction

Knowledge of the cation distribution in zeolites is extremely important for under-standing their activity. The most widely used neutralizing counterions are protons, which are known to be firmly bonded to the lone pairs of the bridging oxygen species. These acidic hydroxyl groups play a crucial role in the catalytic activity of zeolites.

We have used local density functional theory, within the framework of the Car-Parri-nello [1] approach, to study the proton siting in zeolite offretite (54 atoms/unit cell), for an Al/Si ratio corresponding to 1 Al per unit cell. Unlike most previous quantum

(*) Paper presented at the “First International Workshop on Reactivity of Oxide Materials. Theory and Experiment”, Como, 8, 9 November 1996.

chemical studies on zeolites, which were typically based on cluster models of rather limited size, our study takes the full periodicity of the lattice into account. Moreover, all atomic positions are fully relaxed, without constraining some atoms at their experimental geometry, as it is often the case in cluster calculations.

Since IR spectroscopy is widely used to characterize the structure and acidity of zeolites, we have also studied the vibrational properties of offretite by means of first-principles molecular dynamics simulations. The vibrational spectra of the zeolite framework that we obtain are in good agreement with experimental data. Calculated OH stretching frequencies show a rather weak dependence on the H1 _{position, more}

“open” positions (e.g. in the channel) having however slightly higher frequencies than sites within cages or rings.

2. – Calculations

Offretite comprises a cancrinite and a gmenilite cage with a hexagonal-prism structure (fig. 1). The unit cell of Al-free offretite is hexagonal [2] with dimensions a 4

b 413.291 Å and c47.582 Å, and it contains 18 silicon and 36 oxygen atoms. There are

two distinct tetrahedral (T) sites, namely 12 T1sites belonging to the hexagonal prisms,

and 6 T2sites, in the six-fold rings of the gmenilite cages. The substitution of silicon by

Al at either T1 or T2 is studied using the same periodically repeated unit cell of the

Al-free structure.

The electronic valence wave functions are expanded in a plane-wave basis set, and they are calculated only at the G point of the Brillouin zone. For Si and Al, electron-core interactions are described by norm-conserving pseudopotentials in a Kleinman and Bylander [3] form whereas for oxygen an “ultrasoft” pseudopotential was generated according to the scheme proposed by Vanderbilt [4], using a cut-off radius of 1.5 a.u. for the valence wave functions. For Na (K), 2s and 2p (3s and 3p) shells have been treated as valence states in order to improve the transferability, and the

O O O O O O O 1 2 3 4 5 6 7 T T 2 1 T' T'1 2

corresponding pseudopotentials have been also generated using Vanderbilt’s scheme, with cut-off radii of 1.6 and 1.8 a.u. for Na and K, respectively. The parametrization of Perdew-Zunger has been used for the functional of local exchange correlation. Calculations were performed with a kinetic energy cut-off Ecut , 14 24 Ry for the wave

functions and Ecut , 24 200 Ry was used for the augmented electron density.

The electrostatic potential

(

)

Theory according to VMEP_{(R) 42}



!

where r(r) is the electron density of the sytem at r and ZIis the charge of I-th nucleus

located at RI.

3. – Proton siting in Al-substituted offretite

In order to study the acidic properties of offretite, we substituted a Si in either T1or

T2 with an Al, and added a proton to each non-equivalent oxygen. This gives seven

different structures: four in the case of a T1aluminated site and three for T2, which are

referred to as T1OjH and T2OjH ( j 41 to 7). A full geometry relaxation was performed

and substitution energies were calculated using the formula:

Esubs4 [Etot( TiOjH ) 1Eat( Si ) ] 2 [Etot( Al-free ) 1Eat( Al ) 1Eat( H ) ] ,

(2)

Etot( TiOjH ) is the total energy of an offretite Ti substituted with a proton on oxygen

Oj, Eat(X) is the energy of atom X calculated within the local density approximation, Etot(Al-free) is the total energy of the aluminum-free offretite.

The results are listed in table I. We remark some differences with respect to the energy values we reported previously [5]. These are due to a different (lower) cut-off used in our previous work. The present results which employ higher cut-off (larger basis) are much better converged. This allows us to estimate the error bar on the energies reported as 6 1 mHartree (0.6 kcal/mol). Table I shows that two structures

TABLE I. – Energies of different proton sites. Values in parentheses are substitution energies relative to the most stable site. Estimated errors on relative energies are of 1 mHartree (1 mH=0.6 kcal/mol).

Site Substitution energy

(kcal/mol) Proton affinity (kcal/mol) offretite Al(T1) T1O1H T1O2H T1O3H T1O4H 2 37.7 (6.0) 2 38.9 (4.8) 2 37.3 (6.3) 2 37.8 (5.9) 303.5 304.6 303.1 303.5 Al(T2) T2O5H T2O6H T2O7H 2 36.6 (7.1) 2 42.7 (1.0) 2 43.7 (0.0) 294.7 300.8 301.8

Fig. 2. – a) Isovalue contours (2 0.159 u.a.) of the electrostatic potential calculated within the Car-Parrinello scheme for an offretite with an aluminum in T2 (black) without proton. The grey lobes correspond to the proton position of the lowest energy structure of protonated offretite T2O7H. b) Isovalue contours at 2 0.145 u.a. along the Z-axis of offretite. A second lobe appears, corresponding to the proton position in the second most stable structure T2O6H.

which are energetically very close, namely T2O6H and T2O7H, are more stable by about

5–7 kcal/mol than the other ones. As these two configurations are T2 aluminated, we

conclude that a T2site is more stable than a T1site by about 6 kcal/mole. This result is in

agreement with the experimental finding that dealumination is easier in T1than in T2[6].

Proton affinities have been calculated according to PA 4E

(

)

(3)

E

(

)

counterion, but with a + 1 charge delocalized throughout the unit cell. E( TiOjH ) is the

total energy of an offretite with an aluminum in Tiand a proton in position Oj.

The results show that T2O5H is the most acidic site and T1O2H the most basic one.

T2O6H and T2O7H, which according to our calculations should be the only sites occupied

at room temperature, exhibit intermediate proton affinities. The first structure corresponds to a proton located inside the six-fold ring of the gmenilite cage which

is thus accessible to molecules of intermediate size, whereas O7H is located in the pore

and it is accessible to relatively large molecules for reactions.

Isovalue surfaces of the electrostatic potential of a monoaluminated offretite, with Al in T2and without counterion are represented in fig. 2. The minima of VMEP(R) are

depicted by the grey lobes and they correspond actually to the most stable positions reported above for the proton, T2O7H and T2O6H. This suggests that the electrostatic

potential can help localizing proton siting within the zeolite framework. 4. – Dynamical properties and infrared vibrational spectra of offretite

A short (A 0.9 ps.) molecular dynamics simulation for the T2O7H structure at 480 K

has been carried out. Table II presents the average atomic displacements. As expected, the proton moves the most during the simulation. Displacements as large as 1 Å take place. Despite these relatively important displacements, the proton remains basically localized on the same oxygen. Indeed experimental estimates of the energy barrier required for the proton to hop from one site to the other are relatively large (A 10–14 kcal/mole) [7].

This simulation has also been used to calculate the vibrational spectrum of offretite (fig. 3). This can be carried out by taking the Fourier transform of the atomic velocity autocorrelation function [8]. As the simulation is short, only a qualitative analysis is possible. The characteristic bands of zeolites are well reproduced by the calculations [9]. At 1156 and 1040 cm21 _{the bands of the asymmetric stretchings can be}

seen, while the bands at 578 and 751 cm21 _{correspond to the symmetric stretching}

modes. The three peaks at 173, 300 and 405 cm21 _{arise from the TOT bending}

modes.

To evaluate the influence of the proton position in the framework on the OH stretching frequencies, we have calculated the vibrational frequencies for offretite with a proton in three different positions: T1O3H, T2O6H and T2O7H. These frequencies were

obtained by performing three independent short simulations of (0.1 ps). The results, which are presented in table III, show that the differences between the three sites are about 20 cm21_{, that is smaller than the experimental differences and of the order of the}

accuracy of our calculations.

To check whether the Al/Si ratio could influence the OH stretching frequencies, we performed the same analysis for an offretite containing three Al atoms per unit cell. In this case, finding the most stable structure is much more difficult than previously. Actually, there are many possibilities to accommodate the three aluminum atoms, and for each of them there are many different proton localizations. Thus a systematic study similar to the one performed in the case of a monoaluminated offretite has not been carried out. As T2has been found to be more stable than T1, two Al’s were subtituted in

a T2site and one in T1. Protons were located on the same oxygens as in our study of OH

stretching frequencies in monoaluminated offretite (O3, O6, O7). The results displayed

TABLEII. – Average atomic displacements arb (in Å) during the simulation at 480 K (a_).

Atoms H O Al Si

arb 0.54160.032 0.19260.001 0.13060.024 0.13260.005

Fig. 3. – Vibrational spectrum at 480 K of T2O7H substituted offretite. Due to the short simulation, the positions of the bands only, and not their intensities, are meaningful.

TABLEIII. – OH stretching frequencies calculated for three different cation sitings of substituted offretites containing one Al and three Al’s per unit cell.

Site Frequency cm21_{(0.1 ps)} 1 Al/cell 3 Al’s/cell T1O3H T2O6H T2O7H 3503 3490 3525 3494 3509 3529

in table III show that there is not much difference between monoaluminated and trialuminated offretite. In both cases the stretching frequency of the proton at O7,

which is located in the channel, is slightly larger than that of the other protons, which are located in cages. This can be rationalized by noting that for O3 and O6 the

neighboring oxygens weaken the OH bond, thus decreasing their frequencies. Such a mechanism has been proposed to elucidate the infrared frequencies of NAHY zeolite [10].

5. – Conclusion

In this work we have presented a first-principles molecular dynamics study of the stucture and acidic properties of offretite. Our approach uses a periodically repeated unit cell, which allows to take into account long-range electrostatic effects. It has been shown that the protons siting at room temperature make them accessible to molecules of intermediate and large size. The simulated IR spectra indicate that OH stretching frequencies show a rather weak dependence on the H1_{position, more “open” positions}

(e.g., in the channel) having, however, slightly higher frequencies than sites within cages or rings.

* * *

Financial support by the Swiss National Science Foundation is gratefully acknowledged. Calculations were performed on the NEC-SX3 at CSCS Manno (Switzerland), and the Cray YMP at EPFL-Lausanne; the authors are grateful to these computer centers for generous grants of CPU time.

R E F E R E N C E S

[1] CARR. and PARRINELLOM., Phys. Rev. Lett., 55 (1985) 2471. [2] GARDJ. A. and TAITJ. M., Acta Cryst. B, 28 (1972) 825.

[3] KLEINMANNL. and BYLANDERD. M., Phys., Rev. Lett., 48 (1982) 1425. [4] VANDERBILTD., Phys. Rev. B, 41 (1990) 7892.

[5] CAMPANAL., SELLONIA., WEBERJ., PASQUARELLOA., PAPAII. and GOURSOTA., Chem. Phys. Lett., 226 (1994) 245.

[6] FERNANDEZC., AUROUXA., VEDRINEJ. C., GROSMANGINJ. and SZABOG., Proceedings of the VII International Zeolite Conference (Kodansha Elsevier, Tokyo) 1986, p. 345.

[7] SARV P., TUHERM T., LIPPMAA E., KESKINEN K. and ROOT A., J. Phys. Chem., 99 (1995) 13763.

[8] CHANDLER D., Introduction to Modern Statistical Mechanics (Oxford University Press, New York) 1987.

[9] R. A. VAN SANTEN and VO¨GEL D. L., Lattice Dynamics of Zeolites, in Adv. Solid-State Chemistry, 1 (1989) 151.