Adsorption energies of NH3 and NH4+ in zeolites. An embedded cluster model including electron correlation

CHEMICAL

10 March 1995

PHYSICS LETTERS ELSEVIER

Chemical Physics Letters 234 (1995) 367-372

Adsorption energies of N H 3 and NH4 in zeolites. An embedded cluster model including electron correlation Stephen P. Greatbanks a, Paul Sherwood b Ian H. Hillier Neil A. Burton c Ian R. Gould a

a

Richard J. Hall

a

a Chemistry Department, University of Manchester, Manchester M13 9PL, UK b Daresbury Laboratory (DRAL), Warrington WA4 4AD, UK c Manchester Computing Centre, University of Manchester, Manchester M13 9PL, UK Received 13 December 1994

Abstract

An embedded cluster model, including both the electrostatic potential of the infinite crystal and electron correlation, is used to predict the adsorption energies of NH 3 and NH~- in zeolites. The importance of both effects is shown by comparison of the calculated difference of the zeolite proton affinity and the intra-zeolite ion pairing energy with the experimental quantity, as suggested by Parrillo, Gorte and Farneth.

1. Introduction Zeolites are of considerable industrial importance as catalysts for processes such as hydrocarbon cracking [1] and the conversion of methanol to gasoline [2], due largely to their Brcnsted acid sites. A central problem is to place zeolite acidity and the associated acid-catalyzed reactivity on a firm quantitative basis, In an attempt to achieve this end, there have been many experimental [3-7] and theoretical studies [8] probing the interaction of simple bases with the Br0nsted sites. A widely used theoretical approach is to model zeolites by means of electronic structure calculations of finite clusters in which the dangling bonds are terminated by hydrogen atoms [9]. This approach has been used to study the interaction of ammonia, water and methanol with the acid site and has been used to predict experimental quantities such as binding energies and vibrational frequencies [10-

12]. However, the degree of realism achieved by such bare cluster models, which do not explicitly include the effect of the remainder of the infinite lattice, is unclear. The importance of allowing for this effect has been recognized by a number of workers, who have embedded the cluster in a field of point charges, the magnitude of which have been determined using different procedures [13,14]. Allavena et al. [13] have used an electronegativity equalization method and corrections for the effect of the dangling bond hydrogen atoms to arrive at formal atomic charges. On the basis of their model, a study of ammonia adsorption found that the ionic form (NH~-) was preferentially stabilized by the Madelung field, compared to NH 3, by 197 kJ m o l - l . In a more quantitative approach, we have developed an embedded cluster model for studying zeolite-substrate interactions [15]. To model the environment of the cluster and to correct for cluster termination

0009-2614/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 0 0 9 - 2 6 1 4 ( 9 5 ) 0 0 0 5 2 - 6

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S.P. Greatbanks et al. / Chemical Physics Letters 234 (1995) 367-372

effects, a set of formal point charges is derived which correctly reproduce the electrostatic potential of the infinite 3D lattice calculated at the HartreeFock level. Such an approach reproduces adsorption energies to within = 5 kJ moi-1 of the periodic results. We here use this model to study the interaction of ammonia with the Bmnsted site of a representative zeolite. Such interactions have been extensively studied both experimentally and using bare cluster models [10,16-18].

2. Computational method The basis of our embedded cluster model and its computational implementation has been described [15]. A bare cluster, suitably terminated, is embedded in an array of point charges chosen so that the total electrostatic potential, due to both the quantum mechanical cluster and the point charges, reproduces that from the ab initio calculation on the infinite periodic system. We have chosen to model zeolite Y [19] 1, in view of the number of experimental studies involving its interaction with small substrate molecules. For the purpose of the periodic calculation, the aluminium sites were replaced by silicon, allowing the sodium counterions to be neglected and generating a purely siliceous framework with 144 atoms per primitive unit cell. From this structure, a T3 cluster (where T is Si or AI) was excised from the framework and used as the basis for the fitting procedure. The terminal oxygen atoms were replaced with hydrogen atoms 1.48 A from the terminal silicon atoms, to give a cluster S i 3 0 4 H 8. The fitting procedure to determine the appropriate potential-derived charges (PDC) via the electrostatic potential calculated at the Hartree-Fock level for the infinite periodic system using the code CRYSTAL [20], has been described previously [15]. Here we use a periodic potential calculated at the 3-21G level. These PDC were then used in cluster calculations in which the central silicon had been replaced by aluminium. The cluster calculations employed a 6-31G * * basis and were carried out both at the Hartree-Fock and at

i This work benefited from the Chemical Database Service at the Daresbury Laboratory.

a correlated level. To model electron correlation effects we use both a perturbative correction at the MP2 level and a density functional theory (DFT) method employing the Becke [21] exchange, and Lee-Yang-Parr [22] correlation functionals as implemented by us [23]. Thus, using our previous nomenclature [15], the calculations described here are labelled as follows: (a) S i - H / 6 - 3 1 G * * ( H F ) / N O N E , (b) S i - H / 6 - 3 1 G * * (B-LYP)/NONE, (c) S i - H / 6 - 3 1 G * *(MP2)/NONE, (d) S i - H / 6 - 3 1 G * *(HF)/3-21G, (e) S i - H / 6 - 3 1 G * *(B-LYP)/3-21G, (f) S i - H / 6 - 3 1 G * * (MP2)/3-21G, where, for example, (e) denotes a calculation on a H-terminated cluster, at the 6-31G* * level, employing the B-LYP functional, with PDC derived from a periodic calculation using a 3-21G basis. The Hartree-Fock cluster calculations were carried out using GAMESS-UK 2. The correlation calculations employed GAUSSIAN 92 [25] and included our implementation of the B-LYP functional. The periodic calculations were carried out using the Fujitsu VPX 240/10 at the Manchester Computing Centre. The cluster calculations were carried out on the Intel iPSC/860 at the Daresbury Laboratory and on Hewlett-Packard 9000/700 series workstation clusters.

3. Computational results The structures calculated at the 6-31G* * level are given in Tables 1 and 2. For the acidic cluster, without substrate, the structures with and without the point charges are both similar to those widely employed in bare cluster studies, with the more important bond lengths ( O - H , Si-O, Al3-O6)being close to those suggested by Sauer for Brcnsted acid sites

2 GAMESS-UK is a package of ab initio programs written by M.F. Guest, J.H. van Lenthe, J. Kendrick, K. Schoffel, P. Sherwood and R.J. Harrison, with contributions from R.D. Amos, R.J. Buenker, M. Dupuis, N.C. Handy, I.H. Hillier, P.J. Knowles, V. Bonacic-Koutecky, W. von Niessen, V.R. Saunders and A.J. Stone. The package is derived from the original GAMESS code due to Dupuis et al. [24].

S.P. Greatbanks et al. / Chemical Physics Letters 234 (1995) 367-372 Table 1 Calculated geometries adsorbate Cluster Sil-O 2 AI3-O 2 ml3-O

4

1.614 1.716 1.716 1.694 1.948 0.949 1.683

Cluster + NH 3

Cluster + NH 3 -1-PDC

1.632 1.745 1.733 1.739 1.932 0.952 1.697

1.606 1.727 1.721 1.704 1.900 0.992 1.664 1.685 1.002

1.619 1.750 1.741 1.747 1.882 1.018 1.674 1.615 1.004

1.001 1.004 2.344

1.005 1.003

AI3-O5 AI3-O 6 06 - H s Si 7-O 6 Ng-H s Ng-HIo N~-H~ Nq-H12 H~2-O z a See Fig. 1 for atom labelling,

3.046

[26]. Our calculated structures are also close to that obtained from a Car-Parrinello molecular dynamics simulation of the structure of a bulk zeolite [27]. Constrained energy minimization, in which the positions of the terminal silicon atoms (Sil, Si 7) and the hydrogens were kept fixed, led to structures (assumed to be minima) corresponding to NH 3 and NH~ bound to the neutral and anionic zeolite, both in the absence and in the presence of the point charge field, As far as binding of ammonia to the acidic cluster (Table 1) is concerned, there is a short nitrogen-

Table 2 Calculated geometries (.~) a of cluster with NH~- adsorbate Cluster Cluster +NH +

+NH~- + P D C

AI ~-Os A13-O6 O6 - H s

1.613 1.768 1.791 1.722 1.768 2.133

1.616 1.801 1.761 1.750 1.797 1.601

Si 7 -06 N,~-H 8 Ng-H,o N9 -H I I N9 -H 12 Hi2 - O 2

1.612 1.011 1.039 1.002 1.020 1.910

1.631 1.053 1.007 1.008 1.007 2.388

Si 1 - 0 2 A13-O2 AI 3 -0

4

II H -i j r Ht° H12 N9

(~)a of acidic cluster and with NH 3 Cluster + PDC

See Fig. 2 for atom labelling.

369

"\H8 |10

.

H ~

.~6~ , , ' ) Si,• .AI \3 H'"/ .._-" • H 4005

H J Si\'.. k'"H H

~ 7

/

\

H H Fig. 1. Atom labelling of cluster-NH 3 adsorbate system.

acidic proton distance ( N 9 - H 8 ) , indicative of strong hydrogen bonding, and a longer hydrogen bond ( H 1 2 - O 2) involving an oxygen atom of the zeolite framework and an ammonia proton. As judged from these calculated structures, both in the absence and presence of the point charge field the interaction with the acidic site of the zeolite is the more dominant, this dominance being more pronounced in the presence of the point charge field. The calculated binding energy of NH 3 is significantly increased by the presence of the point charge field, which is reflected in the shorter N9 . . - H 8 hydrogen bond compared to that of the bare cluster. The effect of electron correlation at both the MP2 and density functional levels is quite similar (Table 3), with the binding energy being increased by some 2 0 - 3 0 kJ mol-1 both in the absence and presence of the point charges. Thus, the six calculations of neutral NH 3 binding to the acidic site yield binding energies ranging from 68-126 kJ mol-1, with both the models including correlation yielding values of = 125 kJ mol- 1. The results for the binding of NH ~ to the anionic 11121H I o

/

H~N~ , H8 I i J, ', s i / O ~ .'2. ~ A I / ~ 6'

H ,.,;

~'"/ H

1

..

/ 40 / H

3

~ (~5 \ H

H Si/ 7

c,,

~'"H H

Fig. 2. Atom labelling of cluster-NH~- adsorbate system.

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S.P. Greatbanks et al. / Chemical Physics Letters 234 (1995) 367-372

Table 3

Calculated energies (kJ mol- J) for cluster-substrate complcxes Substrate NH 3 NH 3 NH 3 NH 3 NH 3 NH 3 NH] NH ~ NH ~ NH ~ NH 4 NH+

Model a Si-H/6-31G * *(HF)/NONE Si-H/6-31G * *(MP2)/NONE Si-H/6-31G * *(B-LYP)/NONE Si-H/6-31G * *(HF)/3-21G Si-H/6-31G * *(MP2)/3-21G Si-H/6-31G * *(B-LYP)/3-21G Si-H/6-31G * *(HF)/NONE Si-H/6-31G * *(MP2)/NONE Si-H/6-31 G* *(B-LYP)/NONE Si-H/6-31 G* *(HF)/3-21G Si-H/6-31G * *(MP2)/3-21G Si-H/6-31G * *(B-LYP)/3-21G

AEbinding b - 68.2 92.9 - 90.5 - 98.0 - 124.5 - 125.9 - 71.8 - 115.5 - 106.7 - 110.2 - 144.9 - 138.2

AEinteraction _ PAzo

847 804 805 809 775 773

a Structures optimized at the 6-31G * *(HF) level. b Energies are relative to free N H 3 and acidic cluster.

cluster generally parallel those described for NH 3. However, the structures calculated (Table 2) in the presence and absence of the point charge field differ somewhat. In the presence of the point charges, NH~ interacts via two hydrogen bonds (O 6 - - - H s, 0 2 . . . H12) to the framework oxygen atoms, with one hydrogen bond ( 0 6 . . . H 8) being quite short, similar to the case of binding of neutral NH 3. In the absence of the point charges, this short hydrogen bond is considerably lengthened, and there is a third hydrogen bond (O 4 . . . Hlo) involving one of the terminal oxygen atoms. Such doubly and triply hydrogen bonded structures have been previously reported for the interaction of NH~- with AI(OH)2H 2 and A I ( O H ) 3 H - clusters, respectively [17]. For the different levels of theory the binding energy of NH~follows the trend noted for binding of NH 3. Thus, the binding energy is considerably increased by inclusion of the point charge field and of correlation effects. It is to be noted that at all levels of theory, the binding of NH]- is favoured over that of NH 3. However, at the H a r t r e e - F o c k level, in the absence of the point charge field, this difference is quite small ( 3 - 4 kJ mol 1), whereas when correlation effects are included, the preference for NH~- binding is definite, both with and without the PDC. The calculated binding energies including both the electrostatic field and electron correlation, 145 and 1 3 8 kJ mol ~ for the MP2 and B-LYP calculations, respectively, are very close to the value measured by Parrillo et al. for the binding enthalpy of ammonia to

H-ZSM-5 (145 kJ mo1-1) [18]. Corresponding values for HY are given in the range 1 0 0 - 1 3 0 kJ mol - I [28]. Correction for the basis set superposition errors (BSSE) will naturally reduce our calculated binding energies. We have estimated BSSE using the traditional counterpoise method [29] for the four models in the absence of correlation effects. The corrections obtained are in the range 6 - 1 0 kJ mol - I . W e have not included zero-point effects in our calculated binding energies due to the problems in obtaining vibrational frequencies for our constrained structures. However, in view of the non-covalent nature of the interactions, the zero-point contribution to the binding energy is expected to be small. Parrillo et al. [18] have noted an interesting relationship arising from their measurements of the adsorption enthalpies of a number of bases with HZSM-5. A linear relationship with slope of unity, between the heat of adsorption (AHbinding) and the proton affinity of the base was noted. On the basis of their hypothetical thermodynamic cycle for picturing adsorption on H-ZSM-5 (ZOH), A Hbinding

B~g) + ZOH /_Pnzo

~ BH ÷ . - - Z O - , TAHi

-

/ PAB

B~g) + H ÷ + Z O -

~ BH(g) + Z O - ,

ion

S.P. Greatbanks et al. / Chemical Physics Letters 234 (1995) 367-372

it is clear that A Hbinding = - - P A z o _

371

the NH~- . . . O - structure relative to the structure + pA B + A Hint. . . .

tion"

Hence the intercept of their plot is I = - P A z o - + A n int. . . . tion, where PAzo is the proton affinity of the anionic zeolite. Parrillo et al. [18] have suggested that this value should be extremely useful for calibrating quantum mechanical treatments of zeolite acidity. In terms of the calculations carried out, this intercept ( I ) is given as EBH +ZO -- EZOH -- EBH~g; This quantity is shown in Table 3, where again the closest agreement with the experimental intercept (712 + 10 kJ mol 1) is given by the calculations including both the point charge field and electron correlation effects,

4. Conclusions All the models used here to describe the interaction of ammonia with the zeolite acid site favour proton transfer to the base, in agreement with previous bare cluster calculations [10,16,17]. The calculated binding energies of NH 3 and NH~ increase both upon the inclusion of the point charge field and of electron correlation calculated at either MP2 or using the B-LYP functional. Our value for the binding energy at the highest level of theory used is (probably somewhat fortuitously) extremely close to the experimental value recently reported. At the SCF level, the inclusion of the PDC increases the stability

having physisorbed ammonia, is somewhat different at the correlated (MP2 and DFT) and Hartree-Fock levels. Using both correlation treatments, the PDC reduces the preferential stabilization of the ionic structure by a small amount, 2 - 4 kJ mol-~ cornpared to an increased stabilization of the ionic structure at the Hartree-Fock level of = 10 kJ tool -1. We have shown that this effect is due to the enhanced correlation energy of the zwitterionic structure having three hydrogen bonds, found in the absence of the PDC (Table 2). Geometry optimization in the presence of the PDC leads to a structure having only two hydrogen bonds, also described in Table 2. In order to consider the individual effects of correlation and the PDC we have compared this structure with the corresponding one for physisorbed ammonia. Calculations at the MP2 level, using these two structures, with and without the PDC show that the effects of the PDC and electron correlation are indeed additive. Thus, the electrostatic field of the infinite lattice, and electron correlation favour the zwitterionic form and must both be properly considered in realistic procedures for modelling Br0nsted acid catalysis in zeolites.

Acknowledgement We thank EPSRC for support of this research.

References

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