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PCCP

Interaction between probe molecules and zeolites.
Part II:yInterpretation of the IR spectra of CO and N2 adsorbed in NaY and NaRbY
A. V. Larin,a D. P. Vercauteren,*b C. Lamberti,c S. Bordigac and A. Zecchinac
a

b

c

Laboratory of Molecular Beams, Department of Chemistry, Moscow State University, Leninskie Gory, Moscow, B-234, 119899, Russia Institute for Studies in Interface Sciences, Laboratoire de Physico-Chimie Informatique, ? Facultes Universitaires Notre Dame de la Paix, Rue de Bruxelles 61, B-5000 Namur, Belgium Dipartimento di Chimica Fisica, Chimica Inorganica e Chimica dei Materiali, via P. Giuria 7, 10125 Torino, Italy

Received 9th August 2001, Accepted 29th January 2002 First published as an Advance Article on the web 29th April 2002

The interaction energy and band shift values of the fundamental vibrational modes of CO and N2 adsorbed within the NaY and NaRbY zeolite forms are calculated using a pair-wise addition scheme. A clear difference between the most stable positions of CO and N2 in NaY and NaRbY is observed. While, for NaY, both diatomic probes are close to the alkali-metal ion, this is not the case for NaRbY. For CO, the isolated Rb+-CO pair-wise interaction cannot describe the system, because the Rb-CO and O-CO distances are comparable whereas for N2 within NaRbY, the molecule is closer to the framework oxygens than to the Rb. The influence of both molecular and zeolite framework parameters (ionic charges, polarizabilities, and radius) on the interaction energy and band shift values is definitively proven.

I. Introduction
Zeolites are crystalline aluminosilicates whose applications in the areas of chemical synthesis and separation processes are continually increasing. Therefore, IR studies of small probe molecules like carbon monoxide, nitrogen, and hydrogen adsorbed within zeolite frameworks have become a popular and powerful method for understanding the adsorbed state of the guest molecule and the host system. At the same time, numerous theoretical attempts1 have helped to provide a deeper insight into the influence of the zeolite structure on the spectra of the adsorbed molecules. For example, for CO, the band shift (BS) of the fundamental vibrational transition of adsorbed CO has been correlated not only to the type of cation directly involved in the adsorption process1 but also to the electrostatic influence of the framework. In relation to this, it is worth recalling that appreciable variations of the BS values for adsorbed H22,3 and CO3 within the sodium exchanged form of different zeolites (ZSM-5, MOR, X, Y, A) have indicated a strong influence on the interaction energy (IE) of the whole zeolite framework. These findings indicate that the total BS cannot be interpreted only on the basis of the isolated Me+- CO pair approach (Me ? Li, Na, K, Rb, Cs).4 For example, the framework influence on the adsorption of methane was partially mimicked by constructing a cluster around the cation, i.e., Me[HAl(OH)3].5,6 Similarly, the BS values of CO adsorbed within ZSM-5 and the main channel sites of mordenite (MOR)7 have been interpreted on the basis of a simple model including only the electrostatic field induced by Me+, the two closest oxygen atoms, and an additional field component generated by the remaining zeolite framework polarized
y For part I see ref. 19.

by the presence of the cation, but neglecting the effects of the adjacent cations. This crude approximation is acceptable for low cation populated zeolites only (e.g., ZSM-5 or the main channel sites of MOR) but cannot be extended to frameworks with lower Si/Al ratios such as zeolites Y, X or A. This trend in the development of models4-7 clearly underlines the necessity of treating, as accurately as possible, the IE between the probe and zeolite structure represented via a more general spatial model including explicitly the influence of all the framework and extraframework atoms. This approach is even more necessary if the influence of the cationic nature of Y type zeolites on their activity is considered, as has been already demonstrated for the aldol condensation reaction of acetone,8 the disproportionation of alkylsilanes,9 etc. On this basis, it is evident that variation of the cation location can change strongly both the ratio between the IE components and the total IE value. Theoretical investigations are thus necessary to clarify the influence of this ratio on the reaction mechanisms. They surely will help in the experimental assignments of the cation positions proposed for the Zn,10 Cd,11,12 La,13,14 Cu,15 Rb,16 and other forms of Y zeolite. In our previous study,16 IR spectra of CO and N2 probes in the adsorbed state were also recorded. Calculations of the probe position inside a zeolite should take into account all components of the IE, e.g., electrostatic, inductive, dispersive, charge transfer, exchange-overlap or repulsive.17 Similarly, the effect of all contributions to the BS value coming from the different IE components should be considered. This is possible using either ab initio approaches or through simplified pair-wise addition schemes. The second method does not allow us to estimate the charge transfer contribution, but this drawback is of minor importance (this is practically true when dealing with alkali-metal cations). The DOI: 10.1039/b107242k

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small magnitude of the charge transfer has indeed been demonstrated by energy decomposition procedures like the constrained space orbital variation (CSOV).1,18 In this work, we will use the pair-wise addition scheme to evaluate the IE and BS. The BS values can be computed provided that the dependences of all multipole moments and polarizabilities of the probe molecule, as well as the dispersive and repulsive coefficients for all `` host-guest '' atom pairs are known with respect to the probe internuclear distance r. Within the pair-wise scheme, it has been shown that the r dependence of the repulsive coefficients can be determined from the routine condition of the equilibrium position of the adsorbed molecule relative to all ions of the adsorbent. If such an equilibrium does not exist for the Ozeol-CO pair (owing to the negative charge on C), a possible approximation of the repulsive coefficients with r could be achieved allowing a stable Ozeol-CO configuration for the higher vibrational states of CO within the Na4Ca4A zeolite.19 Therefore, we have calculated the IE and BS values for CO and N2 adsorbed within the Na and Rb forms of Y zeolite in the same way as for Na4Ca4A.19 As all theoretical bases as well as all necessary CO and N2 molecular properties are presented in the preceding paper,19 we start with the ionicity determination for the Y model and with an additional intercombination rule for the dispersive coefficients used in this paper as compared to ref. 19. In section III, we will illustrate the main characteristics of the zeolite models. In section IV, all results for the CO/NaY and CO/NaRbY models based on the comparison between the calculated and experimental BS values will be discussed. In section V, we will present the problem of the BS calculations for the N2 case within the various chosen zeolite models. Finally, a comparison of the electrostatic field values with available experimental estimations is made in section VI.

all interaction terms. As has been widely shown,25 the neglect of a part of the electrons for example related to the framework Al or Si atoms provides zeolite models with different electron redistributions at different q0 . Such a difference obviously leads to errors in the dispersive term which vary with the ionicity. This is particularly important because of the intercombination rule for the van der Waals (vdW) coefficients Cij . A common expression can be used on the basis of both the Kirkwood-Muller (KM) and Slater-Kirkwood (SK) rules. If we Å express the diamagnetic susceptibility via ai and ni ,26 e.g., in pffiffiffiffiffiffiffiffi atomic units:wi ? ni ai =ð4c2 Þ, c being the velocity of light, then the Cij values can be given by: C ij ? 3=2 ai aj =?ðai =ni Þ
1=2

þðaj =nAB Þ1=2

ð2Þ

where ai and ni are the static polarizability and number of electrons of the framework ion i, aj and nAB are the static polarizability and number of electrons of the AB diatomic probe (j corresponding to the parallel and perpendicular ion-molecule orientations without difference between the i-AB and i-BA geometries). In formula (2), the number of electrons is calculated as ni ? n0i À q(i), n0i being the electron number of the respective ion i. For the KM case, n0i is the total number of electrons, i.e., nCO ? nN2 ? 14, while for the SK rule, n0i is the number of valence electrons, i.e., nCO ? nN2 ? 10.

III. Zeolite Y models
We considered all 156 framework atoms21 belonging to the central unit cell of NaY with the lattice constant (a ? b ? c) œ of 24.767 A and the F23 spatial group. For N2 interacting with NaY, we here show that a fragment containing 19 cells is large enough to give accurate IE and BS values. For the NaRbY form, we have assumed that all atoms have the same coordinates as in NaY, the Rb substituting Na at position II within the supercage.21 The four NaI ions within the hexagonal prisms are assumed to remain in their positions. The same charge ratio q(Al)/q(Si) ? 0.844721 was used for all zeolite models considered below. Two different O atom types are present in NaY or NaRbY, i.e., those belonging to the Si-O-Si moieties (crystallographically independent O2 , O4 , O5 , O7 atoms, see Table 7 of ref. 27) and those of the Si-O-Al (O1 , O3 , O6 , O8) ones. Even though the O atoms of each type of Si-O-T moiety (T ? Si or Al) in zeolite Y have very similar average T-O bond distances (R) and Si-O-T angles (W) (which together determine the O charge value27) within each of the two groups, they will be considered as separate ones. For Si-O-Si, our results based on the ps-21G*(Si)/6-21G*(O) basis set periodic Hartree- Fock (PHF) computations28 showed that the charge ratios q(O4)/q(Oi) are 1.003, 1.003, and 1.004, for i ? 7, 5, 2, respectively. One should mention that this level of basis set corresponds to nearly `` convergent '' atomic charges in the series STO-3G ! 88-51G(Si)/6-21G(O) ! ps-21G*(Si)/6-21G(O) ! 6-21G*(Si, O) for all-siliceous systems.28 Previously, the applied atomic charges were calculated with split-valence basis sets which were indeed overestimated as compared to the other basis sets of this series. In order to determine the ratio between the charges of the oxygens of the Si-O-Al and Si-O-Si types, a simple analytical approximation, fitted with respect to R and W for 79 crystallographically independent oxygens of all-siliceous zeolites27-29 was applied to 63 oxygens of the Si-O-Al type within the five H-form zeolites.30 The O charges of Si-O-Al type are higher by about 1.1 e with respect to those of Si-O- Si for similar internal coordinates (R, W). Hence, we have adopted a model (called below the CRY model) based on the charge ratio 1.1 for all Si-O-Al oxygens and 1.0 for all Si-O-Si oxygens. Let us note that an alternative O charge distribution with more pronounced differences between charges, Phys. Chem. Chem. Phys., 2002, 4, 2424-2433 2425

II. Ionicity of Y zeolite models and intercombination rules
The total interaction energy (IE) Utot between the adsorbed molecule and the zeolite framework can be evaluated as the sum of the electrostatic Uelec , inductive Uind , dispersive Udisp , and repulsive Urep interaction contributions. All necessary expressions are given in detail in ref. 19. The total charge of each cationic (or anionic) zeolite subunit has been determined through the ionicity parameter q0 .20 For zeolite Y with Si/Al ? 3, corresponding to the total formula NaSi3AlO821 the relation is: q0 ? qðNaÞþ 3qðSiÞþ qðAlÞ ?
8 X k?1

jqðOk Þj

ð1 Þ

It is worth mentioning that such q0 computation leads to a larger ionicity by a factor of 2 as compared to the value used for the A type zeolites.19,20 The charge dependences of the ionic polarizabilities and radius (Table 1 for Rb and Table 3 in ref. 19 for Na, O, Si, and Al) require the consideration of all framework atoms in
Table 1 Polarizability a and radius r functions expressed as linear X(q) ? X(0) À Aq forms (a03 and a0) for Rb (see ref. 19 for Na, O, Si, and Al) X(q) a R
a

q-Dependence Linear Linear

X(0) 43.9 2.48
a c

A 42.2b 1.814d

Ref. 22. b Estimated A value considering a(Rb+) ? 1.7 a0322 (a03 ? 0.148 Â 10À30 m3). c Ref. 23. d Estimated A value considering r(Rb+) ? 1.52 a024 (a0 ? 0.5292 Â 10À10 m).


i.e., charge ratio between 0.89 and 1.12 (called below the UDM model), was obtained by Uytterhoeven et al.21 For both CRY and UDM models, the charge values estimated on the basis of the electronegativity equalization method (EEM)21 were used, which led to an ionicity of q0 ? 6.584 e for zeolite NaY. The usual O charges, obtained via PHF calculations performed with the STO-3G basis, range between À0.6 and À0.8 e, which leads to q0 ? 4.8 and 6.4 e. The ionicity q0 ? 6.584 e could thus be considered as a lower bound. As an upper estimate of q0 , we could consider values provided by PHF computations with a basis of 6-21G quality.27 Then, O charges range between À1.1 and À1.2 e and q0 is between 8.8 and 9.6 e, respectively. In this work, we will limit the q0 range for zeolite Y to between 6.584 and 9.5 e.

IV. Co-adsorption
IV.1. Spatial models of the CO molecule The determination of the molecular semi-axes of CO on the basis of a fitting procedure of the frequency of the experimentally observed two main bands of the fundamental vibrational transition of CO adsorbed in NaCaA has already been discussed.19 The two peaks correspond to two different orientations of CO relative to the zeolite: Ca+2-CO and Ca+2-OC. In order to determine the three CO semi-axis values, the experimental IE obtained at small coverages is used as a third reference point. By the fitting procedure, we obtained four different models for CO, all corresponding to nearly the same molecular volume (cf. Table 7 in ref. 19). In this way, we have CO relevant parameters and IE expressions (eqn. (2)-(11) all given in ref. 19), which are needed to calculate the BS and IE values for NaRbY. The results are very close for all spatial CO models (Table 2). For this reason, in the following, we will consider the A model only which is in accordance with a conventional r?/rk 1 relation (with the exception of section IV.3). We next calculated the IE and BS values for both CRY and UDM oxygen charge distribution models considering various q(Me) parameters (Me ? Na, Rb) for both zeolites (Table 3). Compared to the experimental BS data,16 the UDM model provides (by using a higher Me charge) rather underestimated BS values for NaY and overestimated ones for NaRbY or (by using a lower Me charge) underestimated BS values for both Y forms. As the BS values calculated with the CRY model are in agreement with the experimental ones (Table 3), it will be the only model used below. IV.2. Interaction energy calculation Using the CRY model, we then calculated the energy profiles along different directions passing through the center of a soda-

lite cage (Fig. 1, R ? 0 corresponding to the center of the cage). The deepest Na+-CO IE minimum was found near œ the NaII ion in NaY (Fig. 1 and 2(a)) at R ? 21 a0 (11.1 A) or near the RbII ion at R ? 17 a0 (Fig. 2(b)) in NaRbY. Both these sites were thus considered as the favoured positions for CO. One should mention that the dispersive IE component is very important for both cases (Fig. 2(a) and(b)). The situation inside NaRbY differs because of a higher contribution from the dispersive component. The position of CO with respect to the frameworks is shown in Fig. 3. The slope of the IE terms with the probe internuclear r distance (Fig. 4) does not correspond to the absolute IE values usually estimated at equilibrium re (as in Fig. 2(a) and (b)). It is clear that for both Me ? Na or Rb the `` dipole '' BS contribution largely dominates (Table 4) over the others in accordance with all previous estimations1,4 (Fig. 4(a) and (b)). This explains why the simple electrostatic model proposed in ref. 7 was able to reproduce the experimental BS of CO adsorbed within the ZSM-5 and MOR frameworks. An important point of our study is the charge dependences of the other atomic properties such as the polarizability and radius of the framework atoms (Table 1). In order to illustrate œ the influence of the variations of the Rb radius (2.48 A)23 on œ the BS calculations, we replaced the value 2.48 A of Rb by œ 2.28 and 2.68 A using the NaRbY model with q(Rb) ? 0.65 e and q0 ? 9.5 e and the SK intercombination rule. These replacements shift the BS from 12.9 cmÀ1 to 13.6 and 11.7 cmÀ1, respectively, to be compared to the experimental data of 14 cmÀ1. A small decrease in the BS by 0.2 cmÀ1 was also œ obtained on replacing the radius of Rb+, 1.52 A,24 by 1.48 œ A31 for the same zeolite model. This variation changes the final BS and IE values only very slightly. As we did not find polarizability data a(Rb+) substantially different from those œ adopted here (in ref. 22, a(Rb+) ? 1.8 A3), the influence of the a(Rb+) variation was not considered. IV.3. Approximation of the repulsive coefficients

The electrostatic repulsion is the main reason for the unstable O-CO linear orientation already discussed in the literature.19,32 As a result, repulsive O-CO coefficients cannot be calculated from the equilibrium position condition of the probe molecule relative to the negative framework O ion. Still, the BS calculation requires an approximation of the repulsive coefficients within the interval where the vibrational probability distribution with respect to the internuclear CO distance r cannot be neglected. Such an approximation can be based on the dependence of the CO dipole moment upon its internuclear distance r variation. The sign of the moment changes at larger r values and this corresponds to the inversion of the C and O charges leading to stable Ozeol-CO configurations for the higher vibrational states of CO. On this basis, we propose to

Table 2 Influence of the molecular CO model (cf. Table 7 in ref. 19) on the total interaction energy Utot (1 Â 10À3 Eh ? 2.627 kJ molÀ1) and band shift Dn values while adsorbed within the NaRbY zeolite, with q(Al)/q(Si) ? 0.8447,21 using parameters q(Rb) (e) and q0 (e), corresponding to the CRY and UDM models of oxygen charge distribution CRY CO model A q(Rb) 1.0 1.0 0.9 1.0 1.0 0.9 1.0 1.0 0.9 q0 9.5 8.5 9.5 9.5 8.5 9.5 9.5 8.5 9.5 Dn /cm 25.7 25.1 19.5 20.3 26.3 20.9 26.4 26.4 20.8
À1

UDM Utot/10
À3

Eh

Dn /cmÀ 18.8 20.0 13.9 20.3 20.5 13.9 20.6 20.7 13.9

1

Utot/10À3 E À9.170 À11.153 À9.193 À10.278 À10.420 À9.709 À10.463 À10.639 À9.951

h

C

D

À14.415 À14.712 À13.270 À14.187 À14.433 À13.618 À14.155 À14.390 À13.663

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Table 3 Total interaction energy Utot (1 Â 10À3 Eh ? 2.627 kJ molÀ1) and band shift Dn values of CO adsorbed within different NaY (Me ? Na) and NaRbY (Me ? Rb) zeolites, with q(Al)/q(Si) ? 0.8447,21 using parameters q(Me) (e) and q0 (e), corresponding to the UDM and CRY oxygen charge distribution models. The CO molecular spatial parameters correspond to the A model (cf. Table 7 in ref. 19) NaY Model UDM q(Me) 1.0 1.0 0.9 0.8 0.7 1.0 1.0 0.9 0.8 0.7
a

NaRbY
À1

q

0

Dn /cm 24.7 23.5 20.0 15.3 12.3 34.0 33.3 30.1 28.3 22.7 29.0

Utot/10

À3

Eh

Dn /cm 18.8 20.0 13.9 9.8 6.9 25.7 25.1 19.5 15.1 11.2 14.0

À1

Utot/10À3 Eh À9.170 À11.153 À9.193 À9.756 À8.811 À14.415 À14.712 À13.270 À12.752 À11.502

CRY

9.5 8.5 9.5 9.5 9.5 9.5 8.5 9.5 9.5 9.5

À13.410 À12.598 À11.186 À10.623 À8.471 À17.447 À17.417 À16.233 À15.038 À12.626

Experiment
a

Experimental Dn value from ref. 16.

extend the coefficient evaluated at larger r values to shorter r ones. Within the r re interval, two different effective estimations of the repulsive coefficients dependence on r were used: the first (a) obtained by neglecting completely the repulsion term between CO and the framework oxygens (hereafter named `` zero '' approximation) and the second (b) by using a `` dispersive '' approximation, where the r dependence on the repulsive coefficient corresponds to the variation with r of the dispersive IE contribution.19 Neglect of the O-CO repulsion component could generate an error in the respective IE and BS values within the r interval where this repulsive interaction is valid. We indeed observed a fault of the `` zero '' approximation when omitting all repulsion terms between the framework oxygens and CO at the shorter r distances. For example, the most stable position for spatial model D (cf. Table 7 in ref. 19) within NaRbY corresponds œ to 6.49, 7.80, and 8.01 a0 (3.43, 4.13, and 4.24 A, respectively) œ from the O atoms and to 6.50 and 8.87 a0 (3.47 and 4.69 A, respectively) from the Si atoms resulting in IE values of À13.1  10À3 Eh (1  10À3 Eh ? 2.627 kJ molÀ1), i.e., of the same IE order as for the NaY case, and in a very large BS of 65 cmÀ1. Applying now the dispersive approximation along the same direction, we obtain that the minimum is near NaII (separated by 6.73 a0) and near the O atoms of the 6-mem-

Fig. 1 Radial dependence (R ? 0 corresponding to the center of the sodalite cage, a0 ? ? 0.5292 Â 10À10 m) of the interaction energy Utot (1 Â 10À3 Eh ? 2.627 kJ molÀ1) between CO and zeolite NaY (q0 ? 9.5 e, q(Na) ? 0.8 e, CRY oxygen charge distribution) along the C3 axis passing through the hexagonal prism: dotted-dashed line for Na+- CO, dotted for Na+-OC; along the direction to the deepest minimum near Na+: long-dashed line for Na+-CO, short-dashed for Na+-OC.

Fig. 2 Radial dependence (R ? 0 corresponding to the center of the sodalite cage, a0 ? 0.5292 Â 10À10 m) of the components of the interaction energy Utot (1 Â 10À3 Eh ? 2.627 kJ molÀ1) between: (a) CO and zeolite NaY (Na-CO geometry, q0 ? 9.5 e, q(Na) ? 0.8 e, CRY oxygen charge distribution); (b) CO and zeolite NaRbY (Rb-CO geometry, q0 ? 9.5 e, q(Rb) ? 0.65 e, CRY oxygen charge distribution); (c) N2 and zeolite NaRbY (q0 ? 9.5 e, q(Rb) ? 0.65 e, CRY oxygen charge distribution). Full line Ui , long-dashed line Udisp , short-dashed line ULel (L is the order of the respective molecular multipole moment, given near each line), dotted Uind , dotted-dashed Urep .

Phys. Chem. Chem. Phys., 2002, 4, 2424-2433

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Fig. 3 Favoured positions of the CO (a), (b) and N2 (c), (d) molecules with respect to the closest framework atoms of the NaY (a), (c) and NaRbY (b), (d) zeolite forms. The nearest Rb cations are shown in (b) only.

bered ring (distances between 10.28 and 11.22 a0) while the IE has a reasonable value of À8.236 Â 10À3 Eh and the BS is 7 cmÀ1. The dispersive approach considering the repulsive interactions with the closest O atoms thus helps to minimise the error in the determination of the favoured location of the probe molecule. IV.4. Probe molecule location

Fig. 4 Internuclear distance r dependence (a0 ? 0.5292 Â 10À10 m) of the components of the interaction energy Ui between: (a) CO and zeolite NaY (Na-OC geometry, q0 ? 9.5 e, q(Na) ? 0.8 e, CRY oxygen charge distribution); (b) CO and zeolite NaRbY (Rb-CO geometry, q0 ? 9.5 e, q(Rb) ? 0.65 e, CRY oxygen charge distribution). Line notations as in Fig. 2.

Comparison between the X-CO distances (X ? Na and closest oxygens Oi) in NaY (Table 5) shows a situation which could be well represented by the isolated Na-CO pair model (Fig. 3(a)). The situation is different for NaRbY where the Rb-CO and Oi-CO distances (Oi ? closest oxygens, i ? 1, 2, 7, 8) differ by 0.6 a0 only, while for NaY this difference is about 2.3 a0 . In order to verify the reason for the differences between NaRbY and NaY, we varied the contribution of the dispersive part to the total IE. The results are as follows: when replacing the KM intercombimation rule (eqn. (2)) by the SK rule, the dispersive IE decreases and the favoured geometry changes. CO moves towards the axis passing through the center of the 6-membered ring and the RbII cation. This is clearly seen by comparing the X-CO distances (Table 5). With the SK model, the minimal difference between Rb-CO and O2-CO is a0 . Hence, replacement of the intercombination rule confirms the closer location of CO to the O atoms in NaRbY as compared to NaY. To complete the picture, we should also mention the strong dependence of the IE upon the intercombination rule (eqn. (2)). The IE for CO in NaY zeolite is À15.99 Â 10À3 Eh with KM and À12.68 Â 10À3 Eh with SK. These values are higher and lower than the binding energy of the Na+-CO pair, À14.65 Â 10À3 Eh obtained at the ab initio QSID(T) level.4 Furthermore, all theoretical results are higher than the reported experimental data, all contained in the À8.75 Â 10À3

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Table 4 Comparison of the band shift Dn components (cf. eqn. (15) in ref. 19) with V ? V0 + Ui for CO (model A) adsorbed within zeolites NaY (q(Na) ? 0.8 e, q0 ? 9.5 e, KM rule) and NaRbY (q(Rb) ? 0.65 e, q0 ? 9.5 e, SK rule) using the CRY oxygen charge distribution Dn /cmÀ1 Component of IE Dipole Quadrupole Octupole Hexadecapole Inductive Dispersive Repulsive Total Experimentc À7.9 cm 16.
a À1

NaY 50.3 10.9 À4.4 À2.3 À12.8 À11.4 À2.9 30.0 29.0
b

NaRbY 17.9 7.3 À0.7 À1.0 À2.4 À7.8 À0.6 12.9 14.0 with the SK rule.
c

a b

with the SK rule.

À4.2 cm

À1

Ref.

to À9.52 Â 10À3 Eh interval.33-35 For a correct comparison with experiment, our IE estimations could most probably be lowered after averaging over all available surface sites within the zeolite but this would require an additional statistical model not derived herein. However, it seems that the experimental data33-35 are rather underestimated because they are lower than the heat of adsorption of N2 in the NaZSM-5 and NaMOR forms (see Section V). Usually, this value for N2 is smaller than for CO in a similar type of adsorbent. In the IR spectra of CO in NaY and NaRbY reported in Fig. 2 of ref. 16, besides the dominant high frequency band, i.e., BS values of 29 and 14 cmÀ1, respectively, already extensively discussed and attributed to Me+-CO (carbon down) adducts, two minor features are also present: a shoulder at 2138 cmÀ1 (BS ? À5 cmÀ1) and a lower frequency (LF) band appearing at 2122 cmÀ1 (BS ? À21 cmÀ1) for NaY and at 2126 cmÀ1 (BS ? À17 cmÀ1) for NaRbY. As far as the 2138 cmÀ1 band is concerned, its attribution is trivial. In fact the independence of the peak position versus the CO coverage, together with the observation of the same band for pure siliceous (cation free) silicalite,36 confirms the assignment of this band to the `` liquid-like '' CO.16,36-39 To our understanding, the latter should simply correspond to probe molecules adsorbed in the framework with the cationic sites already occupied by other preadsorbed CO molecules. The experimental evidence for the LF band is much more interesting and has stimulated the study of a possible Me+-OC (oxygen-down) adduct. It is in fact worth noticing that the appearance of a minor LF band in the 2130-2110 cmÀ1 range (BS from À13 to À33 cmÀ1) in the spectra of adsorbed CO is not peculiar

to the faujasite forms (both X and Y);3,16,40 it has also been observed for several other zeolites.3,37-43 The fact that a very similar spectroscopic feature is observed in all zeolite forms means that such IR bands must have a common origin, probably an O-down adduct. Computationally, it has been reported that the O-down orientation of CO is stable within NaCaA.19 In the present work, we obtained a stable orientation Me+-OC for both cationic Y forms, characterized by BS values of À40.5 and À14.6 cmÀ1, for NaY and NaRbY models corresponding to the cationic charges of 0.8 and 0.65 e (with SK rule in Table 5), respectively, and with IE values of À7.501 and À7.158 Â 10À3 Eh smaller than those for the Me+-CO configuration, i.e., À14.410 and À8.283 Â 10À3 Eh , respectively. We can therefore assert that we have both experimental and computational evidence for the stable oxygen-down Me+- OC adducts in NaY and NaRbY since computed BS values are in qualitative agreement with the experimental ones (BS ? À21 and À17 cmÀ1, respectively). Furthermore, it is worth noting that the energetic barrier here computed for Na+-CO $ Na+-OC in NaY is in qualitative agreement only with the experimental result of 1.45 Â 10À3 Eh in NaZSM-5.43 Finally, in order to further assign the BS in the IR spectra of adsorbed N2 , we needed a zeolite Y model which led to a good agreement with the experimental BS values of CO. Namely, sufficiently precise cation charges needed to be determined (Table 5). The variation of the Rb charge from 0.75 to 0.7 e was considered to take into account a more pronounced BS variation for the NaRbY form, i.e., from 13.6 to 17.3 cmÀ1, when varying the intercombination rule from KM to SK and conserving the Rb charge of 0.75 e (Table 6). This decrease in Rb charge allows us to hold the BS within Æ1.3 cmÀ1 for the models obtained using the SK rule. Thus the models are of the same quality as those obtained with the KM rule, within Æ1.0 cmÀ1. Evidently, the real precision of our calculation is cruder than Æ1.0 cmÀ1, so that this step is a rather formal one and we did not try to reach a higher precision in the determination of the zeolite parameters (ionicity, charges). The chosen Na and Rb charges are denoted by an asterisk in Table 5.

V. N2 adsorption
Nitrogen is also often used as a probe molecule44-47 for zeolite studies. Its convenience comes from well known molecular parameters whose theoretical values (cf. Tables 1 and 2 in ref. 19) are in agreement with experimental ones. Different spatial N2 models could be analyzed with respect to the anisotropy k D? and vdW radius rm , e.g., which could be obtained from the third-order equation: r
? 3

þ are D? r

k

?

2

Àðrm =2Þ3 ? 0
k D?

ð3Þ ? (rk À r?)/re

where r? and rk are the molecular semi-axes,

Table 5 Influence of the intercombination rule (eqn. (2)) on the band shift Dn , total interaction energy Utot (1 Â 10À3 Eh ? 2.627 kJ molÀ1), electrostatic field T (Eh/ea0 ? 1 au ? 5.1423 Â 1011 V mÀ1), and distances RX (a0 ? 0.5292 Â 10À10 m) between CO and the framework atoms X ? Oi or MeII for the MeY zeolite model (Me ? Na or Rb) with ionicity q0 ? 9.5 e with/without nearest atom MeII (the latter value given after the slash). The four final models chosen to calculate the Dn and Utot values for adsorbed N2 are marked by an asterisk. The CO molecular spatial parameters correspond to the A model (cf. Table 7 in ref. 19) Case KM SK Me Na Rb Na q(Me) 0.80* 0.75* 0.70 0.75 0.80* 0.65 0.70* 0.75 Dn /cmÀ1 28.0 13.6 26.8 27.4 30.1 12.9 15.3 17.3 Utot/10À3 Eh À15.992/À5.723 À12.038/À5.223 À12.679/À4.766 À12.284 À14.410/À4.756 À8.283 À8.681/À4.859 À9.302 T/10À2 Eh/ea0 2.423/0.628 1.903/1.263 2.105/0.540 - - - 1.771/1.181 - RMe/a0 5.88 7.30 5.98 - 5.88 - 7.09 - Distance to nearest O atoms ROi/a0 8.19(O4 7.87(O2 8.22(O4 - 8.19(O4 - 8.06(O2 - ), 8.37(O7), 8.43(O4), 8.45(O7), 8.49(O4), 8.74(O7) ), 8.04(O8), 8.74(O1), 8.80(O7) ), 8.30(O7), 8.46(O4), 8.60(O7), 8.69(O4), 8.89(O7) ), 8.37(O7), 8.43(O4), 8.45(O7), 8.49(O4), 8.74(O7) ), 8.20(O8), 8.32(O1), 8.64(O8)

Rb

Phys. Chem. Chem. Phys., 2002, 4, 2424-2433

2429


Table 6 Influence of the ionicity q0 (e) and intercombination rule (eqn. (2)) on the total interaction energy Utot (1 Â 10À3 Eh ? 2.627 kJ molÀ1) and band shift Dn values of CO adsorbed within NaY (q(Na) ? 0.8 e) and NaRbY (q(Rb) ? 0.75 e) using the models shown in Table 5. The CO molecular spatial parameters correspond to the A model (cf. Table 7 in ref. 19) NaY q0 6.584 Case Dn /cmÀ 24.9 27.2 26.4 29.0 28.0 30.1 29.0
1

NaRbY Utot/10À3 E À15.185 À13.426 À15.734 À14.083 À15.992 À14.410
h

Dn /cmÀ1 12.0 14.8 12.6 14.5 13.6 17.3 14.0

Utot/10À3 E À13.207 À9.256 À12.450 À8.902 À12.038 À9.302

h

KM SK 8.5 KM SK 9.5 KM SK Experimenta Ref. 16.

a

is a dimensionless parameter, re being the equilibrium N2 internuclear distance, and a ? 1 or 3/2 for the ellipsoid or spherocylinder type volume, respectively. This equation is the consequence of the condition we imposed in order that the ellipsoid or spherocylinder model would correspond to a sphere of vdW radius rm of the same volume. We did not repeat here the optimizations of the molecular sizes of N2 , as developed for CO, principally owing to the unreliable small BS of adsorbed N2 as compared, for example, to the value of the three-body interaction dispersive terms disregarded in this paper (5 cmÀ1 for the N2/NaA zeolite system).48 We chose to study eight different spatial models for N2 , using the same zeolite models which provided a reasonable agreement between the theoretical and experimental BS for CO k (Table 7). Having no precise data about the anisotropy D? , we k considered a series of N2 models whose D? values range œ between 0 and 0.45 and rm ? 4.26 A.49 As presented in Table 8, all models lead to lower BS for NaRbY than for NaY. The differences Dn (NaY) À Dn (NaRbY) are usually lower than the experimental value,16 i.e., 8 cmÀ1. The configuration of the Me+-N2 pair is almost linear within both Y forms studied here, i.e., the angle varies around 178 for Na+-N2 (Fig. 3(c)) and 174 for Rb+-N2 (Fig. 3(d)). k As a result, the behaviour of the IE and BS with D? and rm is determined by an increase in the parallel semi-axis and in the Me+-N2 intermolecular distance at the favoured location. Higher Me+-N2 distances lead to a decrease in all IE components (in absolute value). The dispersive interaction (together with the inductive one) is the source of the negative contribution to the BS via an increase in molecular polarizability with

Table 7 Typea

N2 molecular spatial models D
k ?

œ rk/A 2.158 2.216 2.276 2.339 2.404 2.471 2.320 2.419

œ r?/A 2.103 2.051 2.001 1.954 1.909 1.867 1.825 1.924

œ rma /A 4.26 4.26 4.26 4.26 4.26 4.26 4.09 4.29 4.26b , 4.13c , 4.09d

A B C D E F G H Experiment

0.05 0.15 0.25 0.35 0.45 0.55 0.45 0.45

the vibrational excitation, while the positive BS component comes either from a decrease in the electrostatic IE or from an increase in the repulsive IE (Table 9). The resulting total k BS increase with D? noted in Table 9 comes from a relative increase in the repulsive BS contribution and from a decrease (in absolute value) of the inductive one. Finally, a qualitative coincidence between the calculated and experimental BS is k observed with the anisotropy D? ? 0.35, i.e., 1.3 and À4.3 À1 cm with the KM rule, or 2.5 and À1.9 cmÀ1 with the SK rule for NaY and NaRbY, respectively, as compared to the experimental data of 4 and À4 cmÀ1 for both Y forms, respectively. A nice correlation with the experimental BS is observed with k D? ? 0.45 (Table 9). Comparing this interval with the 0.25 found theoretically for molecular hydrogen,52 one may think that the interval 0.35-0.45 is not too exaggerated. In order to analyse the behaviour of the IE as a function of the vdW radius rm , we varied rm between the lower known œ œ experimental value 4.09 A and the upper limit 4.29 A obtained from the BS fitting procedure for CO (cf. Table 7 in ref. 19), whose molecular sizes are very close to those of N2 . The anik sotropy D? ? 0.45 for N2 shows a relatively good coincidence between the theoretical and experimental BS for both Y forms (Table 9 with ionicity q0 ? 9.5 e). An increase in rm and, consequently, in the parallel semi-axis results in a decrease in the IE and an increase in the BS (Table 9), while at smaller rm we observe a minimum IE with a dominant dispersive component and underestimated BS values. Analysis of the interaction between N2 and both Y forms allows us to propose several major distinctions between the NaY and NaRbY systems. They are summarised in Table 10. The favoured position for N2 is close to NaII for both vdW coefficient estimations, SK and KM, while with RbII , N2 is closer to two O framework atoms using the KM rule, and to one O with SK. This last difference regarding the number of closest oxygens can be easily explained due to the higher dispersive interactions estimated with the KM rule. Detailed results obtained for a lower ionicity, i.e., q0 ? 6.584 e21 (not discussed here), do not provide a better agreement with the experimental BS (Table 7), but the principal features in the geometry and BS relation for both Y forms are similar. Unfortunately, we do not have any data on the heat of adsorption of N2 within both Y forms so we can only compare the order of values. The overestimated dispersive IE usually addressed to the KM intercombination rule may be compared with available data for the isosteric heat of adsorption for N2 in the Na (À10.62  10À3 Eh , 1  10À3 Eh ? 2.627 kJ molÀ1) and Rb (À8.22  10À3 Eh) forms of ZSM-5.45 The first value is not far from the À11.42  10À3 Eh obtained for Na mordenite.46 For both NaY and NaRbY, the KM rule leads to IE values of À10.47 and À7.38  10À3 Eh , respectively, which correlate well with the upper given values. Evidently, any data available for the heat of adsorption within both forms could strongly limit the set of appropriate N2 models. Summarising this section, we conclude that the simultaneous comparison of the BS of both different CO and N2 probe molecules allows us to define a narrower range for the ionicity q0 value, because a qualitative coincidence with the experimental BS for N2 can be reached, for comparison, with q0 ? 8.5-9.5 e.

VI.

Electrostatic field calculation

a Perpendicular r? and parallel rk radius were calculated using the condition between an equivalent volume of sphere of vdW radius rm and a spherocylinder with r? and rk semi-axes, e.g., via eqn. (3). b Ref. 49. c Ref. 50. d Ref. 51.

The zeolite fragment consisting of 19 or more cells as explained above (see section III) allows us to estimate the electrostatic field created by the whole framework. We computed the field values at the CO (Table 5) and N2 (Table 10) favoured locations within both forms. Our estimations range between 2.4 and 2.1 Â 10À2 Eh/ea0 (1 Â 10À2 Eh/ea0 ? 5.1423 V nmÀ1) for NaY and between 1.9 Â 10À2 and 1.6 Â 10À2 Eh/ea0 for NaRbY. These field values for these Y forms are higher than

2430

Phys. Chem. Chem. Phys., 2002, 4, 2424-2433


Table 8 Total interaction energy Utot (1 Â 10À3 Eh ? 2.627 kJ molÀ1) and band shift Dn values of N2 molecule adsorbed within different NaY (Me ? Na) and NaRbY (Me ? Rb) zeolites with q(Al)/q(Si) ? 0.844721 using alkali-metal charge q(Me) (e), ionicity q0 (e), and CRY oxygen charge distribution. The N2 molecular spatial parameters are presented in Table 7 KM q0 Zeolite NaYa 9.5 q(Me)
k D?

SK
À1

Dn /cm

Utot/10

À3

Eh

Dn /cmÀ1

Utot/10À3 Eh

0.8

8.5

0.8

6.584 Zeolite NaRbY 9.5
d

0.8

0.05 0.15 0.25 0.35 0.45 0.45b 0.45c 0.55 0.05 0.15 0.45 0.05 0.35 0.35 0.45 0.55 0.05 0.15 0.35 0.45 0.15 0.45

À2.1 À0.5 0.4 1.3 2.6 À0.9 2.8 3.4 1.6 2.6 6.8 À7.5 À6.0 À4.3 À3.3 À2.6 À3.8 À2.6 À2.2 À1.4 À8.4 À8.6

À11.365 À10.965 À10.470 À9.933 À9.397 À12.466 À9.253 À8.886 À11.403 À10.931 À9.676 À11.393 À10.084 À8.120 À8.026 À7.892 À8.820 À8.630 À8.213 À8.106 À8.906 À8.579

À0.7 0.7 1.7 2.5 4.0 0.4 4.1 4.8 2.9 3.6 8.4 À5.4 À3.9 À1.9 À1.1 À0.1 À0.5 0.0 0.1 0.6 À4.8 À5.3

À9.926 À9.583 À9.170 À8.710 À8.247 À10.883 À8.119 À7.798 À9.886 À9.501 À8.413 À9.807 À8.141 À5.140 À5.075 À5.573 À6.138 À6.090 À5.888 À5.869 À5.056 À5.832

0.75e

8.5

0.75e

6.584

0.75e

a œ œ Experimental Dn value16 is 4 cmÀ1. b rm ? 4.09 instead of 4.26 A in other cases. c rm ? 4.29 instead of 4.26 A in other cases. d Experimental Dn values16 are 4 and À4 cmÀ1, the first value being related to the NaII ions remaining after ion exchange in accordance with the conclusions of ref. 16. 0.7 e for SK case.

the known experimental data, i.e., 0.99 Â 10À2 and 0.47 Â 10À2 Eh/ea0 for NaY and NaRbY,16 respectively, 1.18 Â 10À2 and 0.53 Â 10À2 Eh/ea0 for NaMOR and RbMOR,46 1.22 Â 10À2, 0.64 Â 10À2 Eh/ea0 for NaZSM-5 and RbZSM-5.45 This difference between the real and modelled field values can be mainly associated with the neglect of the high order multipole moments (higher than the charges) of the zeolite atoms as was observed while simulating the electrostatic field over TiO253 or within different sieves.30,54 Electrostatic potential can be overestimated up to 80-100% for both the H-form aluminosilicates30 and aluminophosphates (Al/P ? 1).54,55 In order to compare, for both Y forms, the importance of the closest cation to the adsorbed molecule, we calculated the field experienced by CO and N2 with and without the closest ion at position II. For NaY, the field values are

2.348 Â 10À2 and 0.730 Â 10À2 Eh/ea0 with and without Na (Table 10), respectively, at the N2 favoured location. The latter ratio clearly emphasizes the role of the Na cation in comparison to the analogous field variations in the absence of RbII in NaRbY, namely 1.692 Â 10À2 and 0.983 Â 10À2 Eh/ea0 . The rotation of the total electrostatic field vector obtained at the CO favoured position with/without alkali-metal cation can illustrate the situation: the vector turns by 113 for Na and by 52 for Rb, considering the SK rule. These field variations support the idea, already mentioned in section III, that the adsorption within NaY is governed by the Na ion, due mainly to its high contribution to the field as compared to an essentially lower field created by the Rb ion at the CO or N2 favoured positions.

Table 9 Comparison of the band shift Dn components (cf. eqn. (15) in k ref. 19) with V ? V0 + Ui for different N2 models (D? ? 0.05 and 0.45, œ rm ? 4.26 A) adsorbed in zeolite NaY using q(Na) ? 0.8 e, q0 ? 9.5 e, SK rule (eqn. (2)) Dn /cm IE component Quadrupole Hexadecapole Inductive Dispersive Repulsive Total
k
À1

VII. Conclusions
In this work, we have considered CO and N2 probe molecules adsorbed within NaY and NaRbY zeolites. The CO spatial parameters were taken from a preliminary fitting procedure relative to the adsorption over another zeolite, i.e.,Na4Ca4A,19 while N2 parameters were varied to keep the van der Waals radius close to the experimental value. Central multipole moments and polarizabilities of the probe molecules together with their internuclear distance dependences were validated considering their IE and BS calculations within the framework models. Good quantitative agreement between the calculated and experimental BS, within Æ1 cmÀ1,was achieved for CO. For N2 the agreement is only qualitative. Both results were Phys. Chem. Chem. Phys., 2002, 4, 2424-2433 2431

D? ? 0.05 6.0 1.1 À9.2 À6.2 7.7 À0.7

D? ? 0.45 4.9 0.5 À6.6 À5.6 10.3 4.0

k


Table 10 Influence of the intercombination rule (eqn. (2)) on the band shift Dn , total interaction energy Utot (1 Â 10À3 Eh ? 2.627 kJ molÀ1), electrostatic field T (Eh/ea0 ? 1 au ? 5.1423 Â 1011 V mÀ1), and distances RX (a0 ? 0.5292 Â 10À10 m) between N2 (model C, Table 7) and the framework atoms X ? Oi , Si or MeII for the MeY zeolite model with ionicity q0 ? 9.5 e with/without nearest atom MeII (the latter value given after the slash) Case KM SK Me Na Rb Na Rbb q(Me) 0.80 0.75 0.80 0.70 Dn a /cm 0.4 À4.4 1.7 À1.9
À1

Utot/10À3 Eh À10.470/À4.681 À7.396/À3.769 À9.170/À3.829 À5.140/À3.024

T/10À2 Eh/ea 2.348/0.730 1.692/0.983 2.337/0.728 1.600/0.940

0

R

Me/a0

RX/a0 7.74(O7 7.70(O7 7.76(O7 7.77(O7 ), ), ), ), 8.13(O4 7.90(O2 8.13(O4 8.06(O2 ), ), ), ), 8.31(O4), 8.36(O1), 8.34(O4), 8.33(O1), 8.70(Si), 8.68(O8), 8.71(Si), 8.86(O8), 8.77(O1), 8.90(Si), 8.78(O1), 9.02(Si), 8.90(Si) 9.22(Si) 8.92(Si) 9.24(Si)

6.17 7.91 6.19 7.92

a Experimental Dn values are 4 cmÀ1 for NaY and 4, À4 cmÀ1 for NaRbY, the first value for NaRbY being related to the NaII ions remaining after ion exchange in accordance with the conclusions of ref. 16. b the D model of the N2 molecule is used here instead of C in other cases, see Table 7.

obtained using an O charge distribution deduced from results of ab initio periodic Hartree-Fock computations. The best coincidence of the BS values was reached with very similar cationic charges for both zeolite forms. In such a way, we confirmed the applicability of the CO model in different zeolites of A and Y type presenting comparable atomic (ionic) characteristics. The importance of the dispersive interaction term was clearly shown for both CO and N2 favoured locations in the NaRbY form. The interaction of CO with a RbII cation of higher radius and lower electrostatic field than NaII , could be accompanied by a partial CO coordination with the O atoms in one of the three nearest 4-membered rings. Then, the representation of the adsorbed probe using the isolated `` cation-probe '' pair only is clearly not valid in this case. The decrease in the dispersive interaction calculated via the intercombination Slater-Kirkwood rule confirms that the CO favoured location remains close to the O atoms within NaRbY. In the case of N2 , the dispersive interaction is clearly more important. N2 is closer to the NaRbY framework oxygens than to Rb; such a configuration was obtained with any inter-combination rule applied herein. One of the main results is that the present parametrisation of the CO model based on the BS values and one IE value is not sufficient to yield energy differences quantitatively for both the CO and OC orientations toward the zeolite. But this parametrisation of the CO model fitted for the NaCaA type zeolite19 can satisfactorily produce correct BS values for both the CO and OC orientations in the Y framework. If the parametrisation were wrong then the errors should be different for the different A and Y frameworks with the different locations of the nearest oxygen atoms to the probe. We thus demonstrated, on the one hand, that the spatial CO model fitted over the NaCaA zeolite form can be applied to other zeolites, i.e., NaY and NaRbY and, on the other hand, that by replacing Na by a heavier cation such as Rb, the resulting location relative to the zeolite framework is essentially different owing to the increased dispersive interaction. Such a difference was noted earlier in the literature when spatial restrictions on the molecular motions were imposed by the respective size of the MOR zeolite,45 which is not the case for large Y cavities.

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Acknowledgement
The authors wish to thank the FUNDP for the use of the Namur Scientific Computing Facility (SCF) Center, a common project between the FNRS, IBM-Belgium, and FUNDP as well as Accelrys for the use of their data in the framework of the `` Catalysis 2000 '' consortium. They are grateful for the partial support of the Interuniversity Research Program on Quantum Size Effects in Nanostructured Materials (PAI/ IUAP 5/01) initiated by the Belgian Government. 2432 Phys. Chem. Chem. Phys., 2002, 4, 2424-2433


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