2116
J. Phys. Chem. B 1997, 101, 2116-2119
Quantum-Chemical Justification of the Zeolite Acid Strength Measurement by Infrared Spectroscopy Maxim V. Frash, Marina A. Makarova, and Anthony M. Rigby* Shell Research and Technology Centre, P.O. Box 38000, 1030 BN Amsterdam, The Netherlands ReceiVed: June 4, 1996; In Final Form: NoVember 11, 1996X
The quantitative measurement of the strength of Brønsted acid sites in zeolites would be very useful in catalyst development. One possible method is the measurement of the shift in the stretching frequency of Brønsted hydroxyls on adsorption of a weak base. An empirical correlation for deprotonation energy versus infrared shift has been suggested in the literature, but it cannot be directly experimentally tested. We have performed quantum-chemical calculations of the variation of the infrared shift with Brønsted acid strength. The three probe bases considered are as follows: ethene, carbon monoxide, and nitrogen. The calculations were carried out at the MP2 level with a basis set close to 6-31G** and with explicit consideration of anharmonicity of the OH stretching potential. The results show that the experimental correlation for carbon monoxide gives both absolute acid site deprotonation energies and differences between them to within 10%, supporting the quantitative use of this correlation.
Introduction Zeolites are widely used in chemical industry as solid acid catalysts.1 The strength of their active Brønsted acid sites is an important parameter determining their performance. However, direct measurement of the acid strength of these sites is difficult. In liquid acids, it is known that there is a quantitative correlation between the acid strength and the shift in the infrared frequency of the acidic O-H bond on the adsorption of a weak base.2 The acidic proton is not transferred, but the OH bond is perturbed by the base with the formation of a hydrogen bond: ZOH + B f ZOH‚‚‚B, and the resulting shift in infrared frequency of the OH bond can be relatively easily and accurately measured. This method has been extrapolated for use in zeolites and other solid acids by Paukshtis and Yurchenko.3 They proposed that the logarithm of the shift of the frequency log(∆νOH) depends linearly on the deprotonation energy of the acid ∆Hacid depr:
log(∆νOH) ) A + B*∆Hacid depr
(1)
where A depends on the base involved, while the B value is independent on base and was extrapolated from the liquid case.4 For shifts greater than 400 cm-1, it was suggested that the correlation will no longer hold. Carbon monoxide is the most popular weak base for acid strength testing in zeolites.5 Based on the formula 1, a specific correlation for the shifts with this probe molecule was suggested6 as follows:
log(∆νOH) ) 5.0956 - 0.00226*∆Hacid depr
(2)
where ∆νOH is in cm-1 and ∆Hdepr is in kJ/mol. Given there are uncertainties about the reliability of the method due to a lack of direct measurements of the zeolite acid strength, the method is generally used in the literature to rank acid site strengths rather than for quantitative measurements. The validity of using the technique for quantitative measurements has therefore been investigated with quantum-chemical X
Abstract published in AdVance ACS Abstracts, January 1, 1997.
S1089-5647(96)01622-7 CCC: $14.00
calculations of the variation in the infrared shifts with acid strength for four popular probe bases: ethene, carbon monoxide, nitrogen, and hydrogen. The Paukshtis-Yurchenko correlation can also be used to predict the dependence of the infrared shift with the acid strength of silanol groups, but this is not addressed since these are not usually important for the catalytic reactions in the zeolite. No previous quantum-chemical calculations have addressed the variations of the infrared shifts with acid strength of the Brønsted site. However several calculations considered the absolute infrared frequencies and shifts upon carbon monoxide, nitrogen, and ethene adsorption.7-12 These calculations show that quite a sophisticated technique is required to obtain good agreement with experiment (see review of Sauer et al.13). In particular, electron correlation effects and anharmonicity of the OH stretching potential should be taken into account. Computational Details Models and Basis Set. The calculations were all carried out using the GAMESS-UK program.14 The zeolite Brønsted acid site was modeled by a H3Si(OH)AlH3 cluster as shown in Figure 1a and as used in previous works.7-12 This is the smallest cluster to have the correct chemical environment for the acidic bridging hydroxyl group. The Pople 6-31G basis set ((H);15 (C, N, O);16 (Si);17 (Al)18) was used in computations. It should be noted that there are two slightly different versions of the 6-31G basis set for silicon. Here the GAMESS-UK default17 was applied, but in other codes such as Gaussian another version18 is used. This has negligible influence on the quantities of interest such as interaction energies. The standard polarization functions were added for all atoms apart from the cluster’s terminal hydrogens (on the silicon and aluminum atoms) and those in ethene. The overall basis is almost equivalent to the standard 6-31G** basis set. The geometries of the free cluster and of the adsorption complexes with carbon monoxide, ethene, nitrogen, and hydrogen were optimized at the MP2(FULL) level. The adsorption complexes with ethene, carbon monoxide, and nitrogen all have Cs symmetry. In the free acid site the oxygen is calculated to be slightly nonplanar in the true minimum, but the difference in energy with the Cs configuration is very small © 1997 American Chemical Society
Quantum-Chemical Calculation of Zeolite Acid Strength
J. Phys. Chem. B, Vol. 101, No. 12, 1997 2117 complexes with all four investigated bases. This suggests the effects of the mixing are negligible. BSSE Influence on Calculated Shifts. The effect of basis set superposition error (BSSE) is found to be important for the physisorption energies (35-40% of the calculated values for ethene, carbon monoxide, and nitrogen). It is therefore conceivable that the BSSE will also have an effect on the calculated frequency shifts. However in the work23 devoted to water, methanol, and silanol dimers, the effect of BSSE on frequencies and frequency shifts has been found to be negligible. For our system and the basis set applied, we checked the effect by calculating the frequency shift caused by placing the ghost orbitals of carbon monoxide at the position of the molecule in the frequency calculations. In agreement with the abovementioned work,23 the effect is very small (2 cm-1) and was not considered further. Results and Discussion
Figure 1. (a) Model Brønsted acid site cluster. (b-d) Adsorption complexes of ethene, carbon monoxide, and nitrogen.
(less than 0.01 kcal/mol). Therefore, for computational convenience, Cs configurations were considered for the free site and hydrogen adsorption complex. Lowest energy conformations of adsorption complexes (Figures 1b-1d) were chosen. For ethene adsorption, conformations with the molecule perpendicular to and in the plane of the cluster were tested, and the former was found to be lower in energy. For carbon monoxide and nitrogen, the lowest energy conformations found by Neyman et al.7 were considered. The calculated cluster deprotonation energies were corrected for the zero-point energy (taken from harmonic frequency calculations; unscaled frequencies were used) and for the basis set superposition error (BSSE), calculated via the formula previously used by Bates and Dwyer.9) Variation of Cluster Acid Strength. It has been shown19-22 that the acid strength of model clusters can be varied by constraining the lengths of the terminal Si-H bonds. This method was applied to the cluster of Figure 1a varying the lengths of the Si-H and Al-H bonds between 1.300-1.700 and 1.420-1.820 Å, respectively. This gave five clusters of different acid strength which was measured by calculating their deprotonation energy. Anharmonic Frequency Calculations. In order to calculate the anharmonic frequencies a procedure similar to that used by Neyman et al.7 was applied. The potential for the stretching of the O-H mode was calculated by taking the optimized structure and moving the acidic proton along the OH bond, in steps of 0.05 Å up to 0.3 Å, away from and 0.2 Å toward the oxygen. The other atoms were kept fixed in their equilibrium positions. The potential energy surface obtained was fitted by a sixthorder polynomial, and its overlap matrix with a basis set of the 20 lowest energy eigenfunctions of the harmonic oscillator was calculated. Diagonalizing this matrix gave the vibrational energy levels of the potential, and the infrared frequency corresponds to the gap between the two lowest levels. The addition of more eigenfunctions has a negligible effect on the results. The above procedure essentially neglects the mixing of the O-H stretch mode with other internal modes, and the effect of this was checked in the harmonic potential approximation. For this, harmonic internal modes of the system were compared with the normal modes. The differences between the two results are not larger than 5 cm-1 for free OH sites and for adsorption
We first discuss the magnitudes of the calculated OH stretching shifts upon adsorption and compare them with the experimental data. Then we address the main point of this worksthe variation of the frequency shifts with zeolite acid strength. Magnitudes of Calculated Shifts and Their Comparison with Experiment. The reported experimental shifts for the selected set of probe molecules cover a wide range: N2, 100122 cm-1;7,24-26 CO, 250-350 cm-1;6,7,24,27-35 C2H4, 270-440 cm-1.24,36-38 The difference in the reported shifts for the same base is due to the difference in the acid strengths of the zeolites used. Previous calculations of the stretching frequency shifts of the Brønsted OH groups upon adsorption of weak bases show that explicit treatment of electron correlation effects and the anharmonicity of the OH stretching potential is required. Early calculations at the SCF level with the harmonic approximation8,9 for carbon monoxide gave 74 cm-1 9 against 250-350 cm-1 in experiment; Bates and Dwyer suggested ways to resolve such disagreement.9 Recent calculations including electronic correlation corrections via either the MP2 expansions10 or DFT theory7,11 and with explicit consideration of anharmonicity produced a good agreement with experiment for this shift: 224 cm-1,10 293 cm-1,7 269 cm-1.11 A reasonable shift value for nitrogen adsorption, 109 cm-1, was also calculated.7 As mentioned in the Computational Details section, these calculations also include the effects of the electronic correlations (via MP2 theory) and anharmonicity. The anharmonicity has a large influence on the calculated OH stretch frequencies, reducing them by up to 250 cm-1, as shown in Table 1. The effect is larger for the adsorption complexes39 and therefore increases the calculated OH shifts. The effect of anharmonicity on the shift on adsorption of carbon monoxide (20-22%) is close to that found in the previous MP210 and DFT7,11 calculations (16-22%). However for nitrogen adsorption we find a much stronger effect than was reported in the DFT calculation7 (14-20% rather than 2%). The reason for this difference is unknown. In addition to the fully optimized cluster (deprotonation energy 1293 kJ/mol), we consider a cluster of increased acid strength (cluster 5 in the following section, deprotonation energy 1234 kJ/mol). The latter value is closer to the “average” zeolite deprotonation energy of 1236 kJ/mol as deduced from the calculations40 including the effects of cluster size, larger basis sets, and the effect of the O:Si ratio. The results for both the fully optimized cluster and cluster 5 are shown in Table 1. It can be seen that the infrared shifts for ethene, carbon monoxide,
2118 J. Phys. Chem. B, Vol. 101, No. 12, 1997
Frash et al.
TABLE 1: Constrained Bond Lengths (Å) for the Five Clusters Used, Calculated Deprotonation Energies of the Clusters (kJ/mol, Corrected for BSSE and ZPE), and Calculated and Experimental Frequencies (cm-1) of the Acidic OH Group and Frequency Shifts (cm-1) on Adsorption of the Bases IR shifts upon adsorption adsorbate
free cluster data cluster fully optimized cluster 1 cluster 2 cluster 3 cluster 4 cluster 5
Si-H
Al-H
∆Hdepr
OH frequency
C2H4
CO
N2
1.30 1.40 1.50 1.60 1.70
1.42 1.52 1.62 1.72 1.82
1294 1351 1322 1293 1263 1235
3768 3789 3778 3766 3753 3739
-351 -283 -318 -358 -403 -451
-226 -177 -202 -231 -264 -299
-70 -48 -59 -72 -88 -105
3601
-439
-308
-122
20% 21%
21% 22%
14% 20%
experimental shifts with a single sample [24]
Anharmonicity Contribution in OH IR Shift with cluster 1 with cluster 5
mol for deprotonation energies or 1.5 cm-1 for frequency shifts. For comparison the deviations from a linear correlation are 1 order of magnitude greater than for the logarithmic form. Thus, the functional form of eq 1 is supported by the calculational results. (ii) The best fit correlation lines are given below together with the experimental equation3,6 for carbon monoxide:
C2H4 CO Figure 2. Variation of logarithm of calculated frequency shift on adsorption with calculated cluster deprotonation energy together with suggested correlation from eq 2: (O) ethene (calculated), (]) carbon monoxide (calculated, (‚ ‚ ‚) carbon monoxide (eq 2), and (4) nitrogen (calculated).
and nitrogen adsorption calculated with cluster 5 are all within the experimental range, whereas the shifts for a fully optimized cluster are around 20-30 cm-1 too low to fit the ranges. Moreover the results can be compared to the shifts measured on a single experimental sample24 (H-ZSM-5, Si/Al ) 16, 77 K, fractional coverage of the hydroxyls with the bases close to 1; also given in Table 1) rather than the ranges. For one cluster (cluster 5) the calculated shifts due to ethene, carbon monoxide, and nitrogen adsorption are simultaneously within 14% of the experimental values, indicating a good modeling of the system. Variation of Frequency Shifts with Acid Strength. The main point of our investigation is the variation of the frequency shifts with zeolite acid strength and the testing of the PaukshtisYurchenko correlation described in the Introduction. The three issues to be considered are as follows: (i) the functional form of the general eq 1, (ii) the numerical values of the constants involved, and (iii) the precision of the deprotonation energies predicted from the experimental eq 2 for carbon monoxide adsorption. The frequency shift calculations for ethene, nitrogen, and carbon monoxide were repeated with five clusters of different acid strength (i.e., with five clusters for which the terminal Si-H bonds have been constrained to different values). The variation of the logarithm of the calculated infrared shifts on adsorption of the bases with the calculated deprotonation energy of the five clusters is shown in Figure 2, and the data are given in Table 1. (i) The results obtained indicate that for all three probe molecules considered the fit to the logarithmic correlation is excellent. The deviations from the line do not exceed 2 kJ/
N2
calculations
experimental3,6
log(∆νOH) ) 4.8085-0.001744∆Hdepr log(∆νOH) ) 4.8870-0.001952∆Hdepr log(∆νOH) ) 5.6409-0.002928∆Hdepr
log(∆νOH) ) 5.0956-0.00226∆Hdepr
where ∆νOH is in cm-1 and ∆Hdepr is in kJ/mol. It can be seen that there is a good agreement between the values of the constants in the calculated and experimental equations for carbon monoxide adsorption. Indeed, the difference in offsets between the calculated and experimental equations is about 4%, and the difference in gradients is about 14%. There are no experimental values for the offsets of equations for ethene and nitrogen adsorption available for comparison. However the gradients of the correlation can be compared since it is suggested3 that these gradients should be equal for all bases. Hence there is some disagreement between the calculations and the suggestion:3 the calculated gradients for ethene and nitrogen adsorption differ from the calculated carbon monoxide gradient by about 11% and 50%, respectively. (iii) Finally, one can estimate the error made in using the suggested carbon monoxide correlation.3,6 In the range of shifts investigated (180-300 cm-1) absolute deprotonation energies predicted for a given shift using the correlation differs from the calculated value by less than 90 kJ/mol (or 10%). Predicted differences in deprotonation energies deduced from a difference in shift between two sites are also within 10%. Thus there is an agreement to within 10% between the results from two quite different methodssthe fitting to the experimental data and the quantum-chemical calculations. This supports the quantitative use of eq 2 for the acid strengths determination from the infrared data. Conclusion Quantum-chemical modeling has been performed for the variation of the shift in the stretching frequency of Brønsted hydroxyls on adsorption of a weak base. The variation of the shift with acid strength is found to be accurately logarithmic, in agreement with the Paukshtis-Yurchenko correlation.3 In
Quantum-Chemical Calculation of Zeolite Acid Strength addition, the experimental6 and calculated equations for the shifts upon carbon monoxide adsorption agree within 10% in the deprotonation energies for a given shift. Given this confidence in the modeling, the results suggest that the infrared data can be used for the quantitative measurement of the deprotonation energies of acid sites in zeolites. References and Notes (1) Maxwell, I. E.; Stork, W. H. J. In Introduction to Zeolite Science and Practice; van Bekkum, H., et al., Eds.; Elsevier: Amsterdam, 1991; p. 571. (2) Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; Freeman & Co.: San Francisco, CA, 1960. (3) Paukshtis, E. A.; Yurchenko, E. N. Russ. Chem. ReV. 1983, 52, 242. (4) Iogansen, A. V. Teor. Eksp. Khim. 1971, 7, 302. (5) Kno¨zinger, H. In Elementary Reaction Steps in Heterogeneous Catalysis; Joyner, R. W., van Santen, R. A., Eds.; Plenum Press: New York, 1993; p 267. (6) Makarova, M. A.; Al-Ghefaili, K. M.; Dwyer, J. J. Chem. Soc., Faraday Trans. 1994, 90, 383. (7) Neyman, K. M.; Strodel, P.; Ruzankin, S. Ph.; Schlensog, N.; Kno¨zinger, H.; Ro¨sch, N. Catal. Lett. 1995, 31, 273. (8) O’Malley, P. J.; Dwyer, J. Chem. Phys. Lett. 1988, 143, 97. (9) Bates, S.; Dwyer, J. J. Phys. Chem. 1993, 97, 5897. (10) Senchenya, I. N.; Ugliengo, P.; Garrone, E. J. Mol. Struct. (THEOCHEM), in press. (11) Farnworth, K. J.; O’Malley, P. J. J. Phys. Chem. 1996, 100, 1814. (12) Ugliengo, P.; Ferrary, A. M.; Zecchina, A.; Garrone, E. J. Phys. Chem. 1996, 100, 3632. (13) Sauer, J.; Ugliengo, P.; Garrone, E.; Saunders, V. R. Chem. ReV. 1994, 94, 2095. (14) Guest, M. F.; Fantucci, P.; Harrison, R. J.; Kendrick, J.; van Lenthe, J. H.; Schoeffel, K.; Sherwood, P. GAMESS-UK User’s Guide and Reference Manual: ReVision C.0, Computing for Science (CFS); Daresbury Laboratory: Daresbury, 1993. (15) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. (16) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (17) Gordon, M. S. Chem. Phys. Lett. 1980, 76, 163.
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