J . Phys. Chem. 1985,89, 3488-3493
3488
sitivity, the asymmetric stretching data (Figure 3) were preferred to the external linkage vibration (Figure 4) in the following discussion. It is seen that all calculated stretching frequencies, both for A10 and Si0 bonds, increase with increasing framework electronegativity. This is in agreement with the experimental observation on real zeolites that all TO stretching frequencies, for which however no distinction can be made between A10 and S i 0 vibrations, increase with increasing framework electronegativity, keeping in mind the limitations on these correlations as discussed earlier in this section. The calculated S i 0 and A10 frequency difference, varying between 235 and 379 cm-’, depending upon the number of fluorine atoms, is of the order of the TO stretching frequency difference between quartz ( u = 1089 cm-’ (this work), 1100 cm-’ (Flanigen20)) and an A104 tetrahedron frequency (730 cm-* 20) in a zeolitic framework. The calculated TO stretching frequencies vary almost linearly as a function of S , the slope for Si being appreciably larger than for Al, again indicating a larger sensitivity of the S i 0 bond. Considering for this once all experimental points in Figure 7 in globo, the slope of the “best” straight line (v vs. S ) is of the order of that for the theoretically calculated A10 case. The experimental data in Figure 3 revealed that a better linear correlation can be obtained if the complete series of experimental data is subdivided in three categories: zeolites with monovalent cations (I), with divalent cations (11), and H forms (I11 and IV). Our model calculations are most directly comparable with the series I11 and IV samples, concerning H forms (Le., all having the same “cation” content but showing a varying Si to A1 ratio). It is interesting to note that the slope of the best straight line for these high-silica zeolites (cf. Introduction) is much larger and becomes comparable
to that of the calculated S i 0 case. The influence of the cation, e.g., when passing from H to Na (points 9 and 5), cannot be directly discussed with the present model calculations as the cation is always the same (H). However, on the basis of these calculations the following statements can be made: when H is replaced by Na, the decrease in electronegativity will lead to a smaller electron transfer from T to 0 in the “first neighbor” TO bonds, and to bond strengthening. In the “second neighbor” T-0 bonds, which are more numerous, the opposite effect occurs, leading to bond weakening. These contradictions indicate that opposing effects are at work and more elaborate quantum chemical calculations in which the change of cation is explicitly considered should be performed in the future to settle this problem. Note moreover that the frequency values depicted in the figures are those corresponding with the absorption maximum of a band consisting of a large series of components. Finally, it should be mentioned that the calculations, indicating that all TO bond strengths increase with increasing framework electronegativity, are not only in agreement with IR data (TO stretching frequencies) but also with many experimental data of totally different nature. For example, it is well-known that thermal stability increases with increasing Si content (temperature of the exothermal peak as a function of the %/A1 ratio), in agreement with the calculations.
Acknowledgment. J.D. thanks the Flemish government (cultural exchange) for a grant allowing a stay at the V.U.B. and the K.U. Leuven, W.J.M. and P.A.J. thank the Belgisch Nationaal Fonds voor Wetenschappelijk Onderzoek for permanent research positions as “Onderzoeksleider” (Senior Research Associate).
Influence of the Overall Composition on Zeolite Propertles. 2. Framework Hydroxyls: A Quantum Chemical Study Jerzy Datka, Jagellonian University, Cracow, Poland
Paul Ceerlings,* Eenheid Algemene Chemie, Fakulteit Wetenschappen, Vrije Universiteit Brussel, B- 1050 Brussel, Belgium
Wilfried Mortier, and Peter Jacobs Laboratorium voor Oppervlaktechemie, K.U. Leuven, B-3030 Leuven (Heverlee), Belgium (Received: October 30, 1984)
The influence of the composition of zeolites on the interaction of the surface hydroxyls with adsorbed molecules was investigated by ab initio quantum chemical calculations on a model compound (H3A1-OH-SiH,) representing the bridging hydroxyl interacting with a water molecule. The average electronegativityof the framework was modelled by substitution of hydrogen atoms by fluorine. It is concluded that several properties of the unperturbed OH vary linearly with the geometric average electronegativity (in increasing order of sensitivity: the OH equilibrium distance, the OH stretching frequency, the ionicity of the OH bond, and the integrated intensity of the OH stretching band in IR). For hydrogen-bonded OH groups, the interaction strength increases with the average electronegativity of the framework, and the OH bond properties are much more sensitive for changes in the composition. These results are compared with the appropriate experimental observations from the literature.
Introduction Hydrogen forms of zeolites are active catalysts in acid-catalyzed reactions. A large number of studies were undertaken in order to correlate the acid properties of zeolites (especially the acid strength of the hydroxyl groups) with their composition. Generally the acid strength of OH groups in H forms of zeolites depends on the Si/Al ratio, the degree of cation exchange, and
the degree of dehydroxylation. The partial dehydroxylation of zeolites results in a decrease of the acid strength of the remaining O H groups.’ A decrease of the Na content for N a / H forms results in an k “ e d acid strength ofthe OH groUPS as evidenced by titration results’ and IR spectroscopic ~tudies.~“This effect (1) Datka, J.; J. Chem. Soc., Faraday Trans. 1, 1981, 77, 2877. (2) Barthomeuf, D.; Beaumont, R.J. Coral. 1973, 30, 288.
0022-3654/85/2089-3488$01.50/0 0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 16, 1985 3489
Properties of Zeolites can be interpreted as the result of substituting the less electronegative sodium by the more electronegative hydrogen, thus increasing the average electronegativity' of the zeolite! An increase of the Si/Al ratio in zeolites also increases the acid strength of the OH groups. Several concepts were developed in order to rationalize this dependen~y.~-'~ Re~ently,8*~.'~*'~ several parameters influencing the acid strength of OH groups were correlated with the average electronegativity of the zeolite. It has, e.g., been found that the OH stretching frequency, the extinction coefficient, the frequency shift after benzene adsorption, and the turnover number in reactions catalyzed by acid sites changed linearly with the average electronegativity. In order to get more insight into the relationship between these correlations and the electronic structure of these systems, we present in this paper a series of quantum chemical calculations in which various parameters characterizing the acid strength of the OH groups are evaluated by using ab initio methods.
oscillator approach, which in view of the mechanically localizg nature of this vibrator23and the comparative aim of our study, can be considered to be adequate for our purposes. The starting equation for the evaluation of the integrated intensity, A O H corresponding to the OH stretching vibration was the double-harmonic approximation expression24
Theoretical Framework As in our previous studiesl6I8 the zeolite framework was modelled by the H3Si-OH-AlH3 (I) molecule which turned out to be a successful model system for studying differences in intraand intermolecular properties of terminal and bridging hydroxy l ~ ~and ~ *for' ~discussing the influence of the variation of the average electronegativity on the framework T O (T = Si, Al) bonds.lS The change of the average electronegativity of the zeolite was modelled by substituting hydrogen atoms on A1 or/and Si by fluorine atoms. This way of electronegativity variation lends itself better to a comparision with those experimental data in which, for a given cation, the Si/Al ratio is varied in the zeolite than to those in which, for a given Si/Al ratio, the nature of the cation is varied.Is The quantum chemical calculations were performed on the ab ~ , ~used ~ initio level with the recently developed 3-21G b a ~ i s , 'also in the previous studies.'6*18The molecular charge distribution was analyzed by means of a Mulliken population analysis.21 The OH stretching force constants and equilibrium distances were obtained by numerical differentiation. As in some cases small effects needed to be considered, extreme care was taken in this procedure. Two subsequent parabolic fittings were performed: the OH distance corresponding to the minimum of the first "roughly" fitted parabola was used, together with two displacements of 0.001 nm from it, in order to construct the final parabola yielding a more accurate equilibrium distance and force constant. nuclear massesz2 This force constant, together with the 'H and l60 yielded the OH stretching vibration frequency within a diatomic
= ~OH'"~OH (2) where moH denotes the reduced mass of the OH diatomic oscillator. Combining eq 1 and 2 the (dp/drOH),derivative is related to the integrated intensity A o H through the working equation
(3) Bielanski, A.; Datka, J. J . Catal. 1975, 37, 383. (4) Datka, J. J . Chem. SOC.,Faraday Trans. 1 1980, 76, 2437. (5) Datka, J. J . Chem. Soe., Faraday Trans. I 1980, 76, 705. (6) Datka, J. J . Chem. SOC.,Faraday Trans. 1 1981, 77, 511. Aca(7) Sanderson, R. T. 'Chemical Bonds and Bond Energy", 2nd 4.; demic Press: New York, 1976. (8) Mortier, W. J. J . Catal. 1978, 55, 138. (9) Jacobs, P. A.; Mortier, W. J.; Uytterhoeven, J. B. J. Inorg. Nucl. Chem., 1978, 40, 1919. (10) Barthomeuf, D. J . Phys. Chem. 1974, 83, 249. (1 1) Barthomeuf, D. "Studies in Surface Science and Catalysis 5"; Elsewer: Amsterdam, 1980; p 55. (12) Abbas. S. H.: Al-Wood. T. K.: Dwver. J.: Fitch. F. R.: GeornDulos. A.; Machado, F ; Sm'ith, S. M. ref. 1 1 , 127. (13) Jacobs, P. A.; and Mortier, W. J. Zeolites 1982, 2, 226. (14) Dwyer, J.; Fitch, F. R.; Nkang, E. R. J. Phys. Chem. 1983,87, 5402. (15) Jacobs. P. A. Catal. Rev. Sci. Ena. 1982. 24, 415. (16j Mortier, W. J.; Sauer, J.; LercherYJ. A.; Noller, H. J . Phys. Chem. 1984, 88, 905. (17) Geerlings, P.; Tariel, N.; Botrel, A.; Lissilour, R.; Mortier, W. J. J . Phys. Chem. 1984,88, 5752. (18) Datka, J.; Geerlings, P.; Mortier, W. J.; Jambs, P. A., preceding paper in this issue. (19) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. SOC.1980, 102,939. (20) Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. J . Am. Chem. SOC.1982. 104, 2797. (21) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833. (22) 'The Handbook of Chemistry and Physics"; The Chemical Rubber Co.; Cleveland, OH.
The (0,O)compound was recalculated by using the more accurate OH optimization technique. The results on the OH force constant differ slightly from those presented in ref 17, without changing, however, any conclusion from that study: The vibration frequency and dipole moment derivative values were, as was the case for the isolated molecule, calculated in the diatomic oscillator approximation (for v) by using the expression 4 (for the dipole moment derivative). This approach may be justified in the comparative study since the OH normal vibration is expected to remain essentially "localized" in the OH bond (for a detailed analysis of this problem in case of a (weaker) hydrogen bonding between nitriles and chloroform, see ref 26). All quantum chemical calculations were performed with the MONSTERGAUSS program27on the CDC-CYBER 750-150 computer of the Free Universities of Brussels (VUB and ULB). The
\--I
-.
AOH= (NG/3C2)(dp/%?o~)02 (1) where p denotes the molecular dipole moment; Q O H stands for the normal coordinate of vibration, N for Avogadro's constant, and c for the velocity of light. The partial derivative is taken at the molecular equilibrium geometry. In view of the mechanically localized nature of the OH vibrator (cf. ref 23) the Q O H normal coordinate was considered to represent the pure OH stretching vibration; i.e., it was taken proportional to rOH (the corresponding internal displacement coordinate) pytting the contributions of all other internal displacement coordinates equal to zero. Q O H and rOH are related according to the expression*' QOH
A (cm pmol-I) = 4.457((dp/drOH),(D A-'))2
(3)
The partial derivative in (3) is approximated as
where rq stands for the equilibrium OH interatomic distance (in A) and p(rq) denotes the corresponding dipole moment value. Note that in the diatomic oscillator approach used here, (dp/drOH),is a vectorial quantity which in view of eq 2 is parallel to (dp/dQoH)o. The direction of (dp/drOH)O will however in general not coincide with that of the OH bond axis (actually, in all cases considered the deviation angle was calculated to be of the order of So). The strategy for the calculations on the H-bond complexes between I (and its fluorinated derivatives) and H20 (see text) was the same as followed in our previous study.I7 The intermolecular (i.e., nonbonded H.-0) distance R and the intramolecular distance rOH were optimized successively. For the fluorinated compounds the same 0 value was taken as for the (0,O) compound (27O). 0-H.. .O-------
\*.
\
(23) See, for example: Hadzi, D. In "Infrared Spectroscopy and Molecular. Structure"; Davies, M., Ed.; Elsevier: Amsterdam, 1963; p 228. (24) See, for example: Overend, J. In "Infrared Spectroscopy and Molecular Structure"; Davies, M., Ed.; Elsevier: Amsterdam, 1963; p 345. (25) See, for example: Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. "Molecular Vibrations"; McGraw-Hill: New York, 1955 Chapter 2. (26) Figeys, H. P.; Geerlings, P.; Berckmans, D.; Van Alsenoy, C. J . Chem. SOC.,Faraday Trans. 1981, 77, 721. (27) Peterson, M. R.; Poirier, R. A. Program MONSTERGAUSS, University of Toronto, Toronto, Canada, 1980.
3490 The Journal of Physical Chemistry, Vol. 89, No. 16, 1985
Datka et al.
TABLE I: Free OH Group Properties in Model Compound I and Its Fluorinated Derivatives (8,b)’ “pd (090)
(091) (1 $0)
(1,1) (24
S
rOH
fOH
Yon
qH
40
qHq0
3.44 3.61 3.61
0.9673 0.9678 0.9680 0.9686 0.9699
858.0 857.2 853.2 854.2 850.0
3920 3918 3909 391 1 3901
0.4755 0.4813 0.4858 0.4918 0.5074
0.9357 0.9507 0.95 17 0.9673 0.9949
0.4449 0.4576 0.4623 0.4757 0.5048
3.79 4.17
I(ap/arOH)Ol
AOH
1.829 1.879 1.925 1.978 2.163
14.9 15.7
16.5 17.4
20.8
“ a and b denote the number of fluorine atoms on si and AI, respectively. stands for the OH equilibrium distance (in A), foH for the stretching force constant (in N m-I), and wOH for the corresponding frequency (in cm-I). q H and qo denote the net atomic charges on H and 0 in (e). The absolute value of the dipole moment derivative l(&/&oH),,l is given in D A-1, the integrated intensity AoH in cm pmol-’. The average electronegativity values S were taken from ref 18.
average or intermediate electronegativity, S, of the compounds was calculated as in the preceding paper.’s
Results and Discussion Quantum chemical calculations were performed of a variety of properties which were described in the pastI5 to be a measure of the acidity of the hydroxyl group and thus of the catalytic activity of the zeolite. The properties were calculated as a function of the number of fluorine atoms introduced on Si and/or A1 in the model molecule, H3Si-OH-AIH3,’* in order to obtain quantitative information on the influence of zeolite framework electronegativity on the hydroxyl acidity. For the calculated properties a distinction can be made between (1) those related to “free”, i.e., nonbonded OH groups, and (2) those related to OH groups involved in an intermolecular interaction, Le., to “bonded” OH groups. Both categories will be discussed successively. 1 . Free OH Group Properties. Starting from the optimized framework geometries of the mono-, di-, and tetrafluorinated derivatives of the model compound I as reported in ref 18, we carefully optimized the OH distance as described above. The equilibrium distances and force constants obtained from the energy vs. distance curves are given in Table I where it is seen that the force constant for the non-fluorinated compound slightly differs from the value given in ref 17 (858 vs. 863 N m-l). The force constant values were then used to calculate the diatomic oscillator frequency. The features of the charge distribution in which we are primarily interested in this study are the charges on the oxygen and hydrogen atoms. The values calculated at the equilibrium geometry are also given in Table I, together with the product of their absolute value, which can be considered as a measure of the ionicity of the bond. Figure l a shows that, in the series of the symmetrically substituted compounds ((1,l) and (2,2) vs. (O,O)), the positive charge on hydrogen and the negative charge on oxygen almost linearly increase with the number of fluorine atoms and thus (cf. Table I) with the average electronegativity. This charge increase leads to an increase in bond ionicity which apparently weakens the OH bond as shown by the decrease in OH stretching force constant which also varies almost linearly with the number of fluorine atoms (Figure lb). The weakening of the OH bond upon increasing framework electronegativity is also seen in the small but continuous increase of the OH equilibrium distance. This correlation between bond strength and ionicity was also considered in our previous study on the differences between bridging and terminal hydroxyl groups.” Note that the results for the asymmetric substitution cases (0,l) and (1,O) follow the general trend of the symmetrically substituted compounds, the effect of increasing framework electronegativity being larger than in the symmetric cases when fluorine is introduced on Si (cf. Figure lb). Upon fluorine substitution on A1 the effect is smaller than in symmetrically substituted cases. Note that the asymmetry effect (which we will call the difference between the calculated properties of the (1,O) and (0,l) compounds) is much smaller for the OH bond than for the framework TO (T = Si,Al) bonds discussed in ref 18. The inductive acceptor effect of the fluorine atoms will indeed be felt more strongly in the neighboring TO bond than in the more remote OH bond. The diatomic oscillator frequencies calculated with the force constant values of Table I are depicted in Figure 2 and compared with experimental data. The theoretical values again show an
1
0.92
I nF-O
4.0 I
3.8 I
3.6 I
S
I
I .
4
2
1
.
S I
n -0 F
I
I
I
1
2
4
Figure 1. (a) Calculated charge (in electrons) on oxygen (qo, absolute value) and hydrogen (qH) atoms of the hydroxyl group in model compound I and its fluorinated derivatives as a function of the average electronegativity S. The number of fluorine atoms (nF)is also indicated on the abscissa. The ionicity of the bond, as measured by the absolute value of the product qH&-, is also plotted. Points denoted as 0 refer to symmetrically substituted derivatives. The points denoted as ( 0 )and (*) correspond to the (1,O) and (0,l) compounds (cf. Table I). (b) Similar plot for the OH stretching force constant foH (in N m-I).
almost linear decrease as a function of the number of fluorine atoms in the case of symmetrical substitution. The range of the F substitution (19 cm-I; calculated frequency shifts for H difference between frequencies of (0,O)and (2,2) compounds) can be considered to be very reasonable when comparing with the experimental frequency shift of the unassociated OH stretching frequency in a situation where the H F substitution is also made on an atom bonded to an OH group: the vOH frequency difference between methanol (3643 cm-’) and trifluoromethanol (3617 cm-1),2826 cm-’, is indeed quite close to the 19 cm-I mentioned
-
(28) Bellamy, L. J. “The Infrared Spectra of Complex Molecules”, Chapman and Hall: London, 1980; Vol. 11, p 95.
Properties of Zeolites
1.5
1
- 3640
1 -
3620
- 3600 1
nF.O
-
/ 3.6
3.8
3.6
' .4
I
I
I
1
2
4
.
Figure 2. Calculated OH diatomic oscillator frequency Y (in cm-I) for model compound I and its fluorinated derivatives as a function of the average electronegativity. Symbols used are the same as in Figure 1. The curves 1 and 2 were drawn on the basis of the experimental data in ref 15 (1) and 3 (2) (individual data for curve 1 were not drawn; data points for curve 2 are denoted by +).
above. When turning now to a comparison with zeolite structures the corresponding experimental data show the same trend, indicating a decrease in frequency upon increasing framework electronegativity. However, depending on the way in which the variation in average. electronegativity is introduced in the framework, and as expected on the basis of the correlations between the skeletal vibration frequencies and the average electronegativity S discussed in ref 18, linear relationships v vs. S are obtained with different slopes. If an electronegativity variation is brought in through a variation of the Si to A1 ratio15 (line 1 in the diagram), a much higher sensitivity of the hydroxyl group is observed than in case the electronegativity variation is caused by increasing the degree of exchange in Na-HY zeolites3 (line 2 in the diagram). In view of the model system used the former way of framework electronegativity variation should be more directly comparable with the results of our calculations.18 On this basis it can be said that our model system yields trends which are the same as the experimental but that, probably due to its size limitation, shows a sensitivity which is smaller than experimentally observed for real zeolites. The same feature emerges from a comparison between calculated and experimental dipole moment derivatives. Figure 3 shows again a linear increase of the theoretically calculated dipole moment derivative with increasing average electronegativity. When comparing the calculated derivatives and the experimental datasJ5~29 we first note that the overall agreement can be considered to be very satisfactory in view of the accuracy which can be expected both from quantum chemical dipole moment derivative calculations, even a t an a b initio leve130v31and from the experimentally measured integrated intensities. The experimental Bielanski, A.; Datka, J. Bull. Acad. Pol. Sci. 1974, 22, 341. (30) Figeys, H. P.Geerlings, P.;Van Alsenoy, C. J. Chem. SOC.,Faraday Trans. 2, 1979, 75, 528. (31) Figeys, H . P.;Berckmans, D.; Geerlings, P.J . Chem. Soc., Faraday Trans. 1981, 77, 2091. (29)
nF.O
1
3.8 2
4.0 4
Figure 3. Calculated dipole moment derivatives (dp/drOH),,(absolute value given in D A-l) for model compound I and its fluorinated derivatives as a function of the average electronegativity. Symbols used are the same as in Figure 1. The curves 1 and 2 were drawn on the basis of the experimental data in ref 15 (1) and 5 (2). Data points for curve 1 are not shown, data points for curve 2 being denoted as +. Data points taken from ref 29 are also indicated 0 (series 3).
trends are again reproduced by our model calculation. In analogy with the frequency, we note that the sensitivity of the dipole moment derivative, and consequently of the integrated intensity, to framework electronegativity variations is larger when this variation is brought in by changing the Si to A1 ratio15 (line 1 in Figure 3) than by changing the cation exchange degree (Na-HY zeolites; ref 5 and 29; line 2 and series 3 of data points in Figure 3). Concluding this part we may say that ab initio quantum chemical calculations on the "isolated molecule" properties of the model system I give a theoretical support for the series of correlations set up p r e v i o ~ s l y . ~ ~ ~ J ~ It may also be concluded that for probing the acidity by a change of the intrinsic properties, several parameters may be used, although there exists a difference in sensitivity. In ascending order we have (percentage increase) when passing from (0,O)to (2,2) as parameters: the equilibrium distance (0.27%)< the frequency (0.48%) < the charges on hydrogen and oxygen (6.7 and 6.3%) < and the integrated intensity (39.6%). 2. Bonded OH Group Properties. In order to investigate the influence of framework electronegativity variation on the properties of zeolite hydroxyls when involved in an intermolecular interaction, we performed a quantum chemical study of the H-bond type complexes between model system I (and it fluorinated derivatives) and a single H 2 0 molecule, the latter system being a typical example of an electron donating species. In Table I1 the equilibrium distances and OH force constants of the complexes of the symmetrically substituted compounds are given together with the stabilization energy (AE), the diatomic oscillator frequency vOH, and the frequency shift AvoH calculated as the difference between vOH before and after H-bond formation. It is seen that the strength of interaction, as measured by AE, increases with increasing framework electronegativity. It correlates with the amount of negative charge transfer from the electron donor (H,O) to the electron acceptor (OH) as it was also calculated for the difference between H-bond complexes of terminal
3492
Datka et al.
The Journal of Physical Chemistry, Vol. 89, NO. 16, 1985
TABLE 11: Bonded OH Group Properties in Model Compound I and Its Fluorinated Derivatives upon Interaction with H2W compd S AE R Aq rOH fOH Yon (0,O) (1,1) (22)
compd (0.0) (1,1)
(2J)
3.44 3.79 4.17
91.2 105.5 119.0
I(W~~OH)OI AOH 5.85 6.32 6.57
152.3 178.1 192.8
0.0969 0.1063 0.1137
1.744 1.557 1.528 U O H
Abondcd/Afrcc
137.4 160.7 172.0
575 514 419
1.0039 1.0140 1.0246
10.2 10.2 9.3
3208 3034 2739
AYOH
712 877 1162
qH
40
kHq01
qOH
0.5240 0.5419 0.5531
1.0035 1.0426 1.0725
0.5258 0.5650 0.5932
0.2049 0.1963 0.1892
“Stabilization energy A E (in klmol-I), intermolecular distance R (in A), and charge transfer Wq (in 5) are given as global properties of the complexes. OH bond properties given are equilibrium distance (roH in A), force constant (foHin N m-]), diatomic oscillator frequency (yoHin cm-I), (absolute value in D A-’),and integrated intensity (AOHin (cm pmol-I). Difference values (A) between dipole moment derivative l(&/&OH)O] between intensity values after and before bonded and free OH groups for frequency (cm-I) and intensity (cm pmol-l) and the ratio (Aha/&) complexation are also given. Charge distribution in the hydroxyl group is characterized by the charges (in electrons) on oxygen (qo; absolute value), and hydrogen (qH), the OH overlap population qoH, and the bond ionicity as measured by IqflHI. and bridging hydroxyl groups.” Furthermore it is accompanied by a decrease in intermolecular distance R (nonbonded H-0 distance) and an increase in the OH distance rOH. The OH bond weakening expected on the basis of these data is evident when force constants are compared before and after interaction with HzO (Tables I and 11). It is also recognized in the corresponding increase in the ionicity of the OH bond and in the decrease of the OH overlap population. The H-bond type interaction also leads to a strong increase in the dipole moment derivative resulting in an integrated intensity which is an order of magnitude larger than for free OH groups. In Figure 4 it is seen that the calculated stabilization energy, force constant, and dipole moment derivative show an approximately linear variation with the framework electronegativity. Note that after interaction with H20 the force constant sensitivity to the framework electronegativity variation is much higher than before (difference between foH values for (0,O)and (2,2) compounds: 156 N m-l after interaction, 8 N m-’ before interaction). The same phenomenon is encountered for the equilibrium distance (with difference values of 0.0026 and 0.0207 A) and the integrated intensity (difference values: 5.9 and 34.6cm pmol-I). In general it can be said that upon interaction of the hydroxyl group with an electron donor, the O H bond strength decreases and the corresponding dipole moment derivative increases. The influence of framework electronegativity is much larger for the complex. It is also in agreement with our previous statement” that the sensitivity to perturbation is larger for the weaker bond. We finally note that the evolution of the charge distribution upon H-bond formation follows the general trends put forward previou~ly.~~ We now look for experimental data with which our calculations may be directly or indirectly compared. Due to the,simultaneous hydrogen bonding of the water hydroxyl groups with the zeolite lattice oxygens, the OH stretching frequency shift of the zeolite hydroxyl group upon interaction with water may not be derived from the IR spectrum so that no direct comparison with our calculations can be made. However, Jacobs15and Datka6 studied the frequency shift of a series of zeolites with varying average electronegativity upon interaction with benzene. As evidenced by its donor number33(and its correlation with the H-bond forming capacity),” benzene is known to form much weaker hydrogen bonds than H 2 0 . However, we can expect that the influence of framework electronegativity on the H-bond strength may be similar. In Figure 5 we compare the calculated frequency shifts upon interaction with HzO with the experimental values upon adsorption of benzene as a function of the average electronegativity. Two series of experimental data are presented: those in which the average electronegativity is changed by varying the Si to AI ratioIs (line 1 in figure) and those where this variation occurs by changing the cation exchange degree (in the case of Na-HY zeolites; ref 6, line 2 in Figure 5 ) . In the former case (32) See, for example: Kollman, P. A,; Allen, L. C. Chem. Reu. 1972, 72, 283. (33) Gutmann, V . ‘The Donor-Acceptor Approach to Molecular Interactions”; Plenum Press: New York, 1978; p 20.
AE
Figure 4. Stabilization energy (AEin kJ mol-I), OH stretching force constant CfoH in N m-I) and dipole moment derivative (@I/&,,& absolute value in D A-l) of the complexes between model compound I (and its symmetrically substituted fluorinated derivatives) and H20, as a function of the average electronegativityS.
which lends itself more directly to a comparison with the quantum chemical results (cf. Theoretical Framework section) an approximate linear relationship between Av and S was obtained (the best straight line is drawn on the figure together with the line connecting the experimental points of ref 6). It is seen that our calculated data correspond to much higher Av values, as expected on the basis of the much higher H-bond forming capacity of HzO, and also lead to a linear Av vs. S relationship. The order of magnitude of the calculated frequency shift seems to be very reasonable when our calculations are compared with the experimental data, gathered by PaukshtisP4 on the OH frequency shift of Na-HY zeolites in interaction with acetone and diethyl ether. On the basis of their donor numbers34 (17.0 for acetone and 19.2 for diethyl ether), these electron donors are expected to show a (34) Paukshtis, E. A.; Yurchenko, E. N. React. Kinet. Catal. Lett. 1981, 16, 131.
The Journal of Physical Chemistry, Vol. 89, No. 16, 1985 3493
Properties of Zeolites
11
A
200
Figure 6. Correlation between calculated intensity changes (AA in cm amol-’) and frequency shifts (Au in cm-I) for the OH stretching vibration of model compound I (and its symmetrically substituted fluorinated
5J
350
3.6
I
/ /
derivatives) upon interaction with H20. Best straight line passing through the origin is drawn (---).
4.0
I
4.4
.
, s
Figure 5. Calculated frequency shift (Au) (in mi1)of the OH stretching vibration of the model compound I (and its symmetrically substituted fluorinated derivatives) upon interaction with H20against the average electronegativity (S) (upper curve). The curves 1 and 2 were drawn on the basis of the experimental data concerning OH frequency shifts upon interaction with benzene, of zeolites with varying Si to AI ratio (ref 15, line 1-or with varying cation exchange degree (ref 6, line 2).
As far as intensity changes are concerned, no experimental data are available for direct comparison. Note however that Figure 6 predicts that the intensity change AA correlates with the frequency shift AY the relationship deviating from linearity for stronger H bonds, as was previously described in e ~ p e r i m e n t a l ~ ~ , ~ ’ and theoretical26studies on organic compounds. This indicates that intensity shifts may also be used for quantifying interactions between zeolites and electron donors.
Conclusions
behavior similar to H 2 0 (donor number 18.0). The experimental frequency shifts of Na-HY zeolite OH groups upon interaction with acetone and diethyl ether are of the order of 900 and 1000 cm-’, respecti~ely.~~ Using the theoretical curve of Figure 5 and an average electronegativity of 4 which is the order of magnitude of that of Na-HY zeolites, we can predict a frequency shift of about 1000 cm-’, which is the order of magnitude expected on the basis of the donor number. There are no experimental data available for comparison with the theoretically calculated Av vs. S curve for H 2 0 but we may intuitively expect, on the basis of the much larger H-bond forming capacity of H 2 0 as compared to benzene, a much higher sensitivity to the composition. The trend of a linear Av vs.S relationship, as experimentally observed for benzene ad~orption,’~ is also encountered in our theoretical calculations. As the calculated AI3 values show an approximately linear correlation with Av (the correlation with (v: being even better, as was also found in our previous study”) we may conclude that, within a homologous series, an electronegativity increase leads to stronger intermolecular interactions which can be probed by IR frequency variations.
The results of the calculations on the model systems I and its fluorinated derivatives both as isolated systems and as species interacting with an H 2 0 molecule are comparable with experimental data available for real zeolites. The interaction strength of the hydroxyl group with an electron donor molecule becomes stronger when the average electronegativity of the framework increases, and correlates with various properties of both free and bonded OH groups, some of which can be observed in IR. Various “experimental” relationships between O H group properties and the average electronegativity were confirmed in the model calculations. The fact that a variety of catalytic properties also linearly correlate with S15indicates that some of the calculated OH group properties should directly correlate with the catalytic activity and can be used for quantificational purposes. As far as the relative sensitivity of OH group properties toward framework electronegativity variations is concerned, the sensitivity is shown to increase strongly upon interaction with an electron donor system, striking examples being the OH stretching frequency and intensity. For noninteracting, free OH groups the integrated intensity was calculated to be the most sensitive property, in accordance with experimental findings.
(35) Rao, C. N. R.; Dwivedi, D. C.; Ratajczak, H.; Orville-Thomas, W. J. J . Chem. Soc., Faraday Trans. 2, 1975, 71, 955.
(36) Huggins, C. M.; Pimentel, G. C. J . Phys. Chem. 1956, 60, 1615. (37) Becker, E. D. Specrrochim. Acta 1961, 17, 436.
