3010
J . Phys. Chem. 1994,98, 3010-3014
Quantum Chemical Study of the Influence of Isomorphous Substitution on the Catalytic Activity of Zeolites: An Evaluation of Reactivity Indexes W. Langenaeker, N. Coussement, F. De Proft,? and P. Geerlings’ Eenheid Algemene Chemie (ALGC),Faculteit Wetenschappen, Vrije Universiteit Brume1 ( W B ) ,Pleinlaan 2, 1050 Brussels, Belgium Received: October 1 1 , 1993; In Final Form: January 7, 1994’
The influence of the isomorphous substitution of A1 (by B and Ga) and S i (by Ge) on the catalytic activity of zeolite systems is investigated using a range of reactivity indexes, some of them being density functional theory based. From the values of the local softness and the charge on the hydrogen atom of the bridging hydroxyl, used as a first approximation to the local hardness, it is concluded that the acidities of the zeolite-type model systems, used in the calculations, are dependent on several characteristics which are of importance within the framework of the hard and soft acids and bases (HSAB) principle. These include the hardness (softness) and electronegativity of the substituting atoms, properties which are closely related to the corresponding group values. The OH-bond length and the ionicity of the OH bond were found to be suitable descriptors of the acidity, whereas the dipole moment derivative with respect to the OH-bond length appears to fail as a reactivity index in this case.
Introduction are hydrated aluminosilicate minerals showing a “framework” structure based upon an extended three-dimensional network of Si04 and A104 tetrahedral units joint by their corner oxygens. Because of their capacity for reversible water loss, and their ability to exchange ions and to adsorb molecules selectively, they play a major industrial role as catalysts. Their acid properties are determined by the Brernsted acid sites located in the channels and cages that form in thezeolite. The Brernstedacidityof zeolites is largely associated with the bridging hydroxyls in the larger pores as their lower vibrational frequencies reflect their weaker OH bond and thus greater acidity, as compared to the terminal hydroxyls. The acidity of the former group is sensitive to changes in the zeolite composition. This is for example demonstrated by the decrease in acidity with a decrease of the Si:Al ratio (Le., a lower average framework ele~tronegativity)~ and a variation in acidity upon isomorphous substitution of A1 and SL43 The influence of changes in the average framework electronegativity, caused by these variations in the composition of the zeolites, on the acidity of the bridging OH group has been the subject of previous theoretical studie~.l,6?~ In the present work, our attention is focused on the influence of the isomorphous substitution of A1 by B and Ga and of Si by Ge. The acidity of a complete series of zeolites is investigated using quantities which emerge in a most natural way from density functional theory.8 The quantities considered are used to get an insight in the mechanism which leads to changing reactivity upon substitution in terms of Pearson’s hard and soft acids and bases (HSAB) prin~iple.~ They are the local softness1° and the charge on the hydrogen atom of the acid hydroxyl group, being local hardness related.llJ2 These quantities are obtained using ab initio calculations on the same type of model systems, successfully used in previous st~dies,~J3-l5 among others in the study of the influence of varying framework electronegativity on OH acidity. Besides these calculations, several more traditional quantities which proved to correlate with acidity, the OH equilibrium bond distance and the dipole moment derivative, are calculated. The result will be Aspirant NFWO. Author to whom correspondence should be sent. 0 Abstract published in Aduance ACS Abstracts, February 15, 1994. f
compared with other theoretical work on more limited ~eriesl”’~ or at a lower level of calculation20and with experimental data?’-27 Theory and Computational Details
In density functional theory, it is natural to define global softness, S,as the inverse of global hardness, 010:
s = 1/20
(1)
with the global hardness being defined as
where is the electronic chemical potential and E denotes the energy, N the number of electrons of the system, and v(r) the external (i.e., due to the nuclei) potential. Based on eqs 1 and 2 the local softness s(r) can be introduced as8-IO
S = Js(r) d r
(3)
with
(4)
permitting to identify s(r) with
The first term is the Fukui function, Ar), an intramolecular reactivity index for an N-electron system defined by Parr and Yang.28 Therefore, eq 5 is equal to
Due to the discontinuity of the first derivative in eq 5 at the N value considered, different intermolecular reactivity indexes29 can be defined based on eq 5 . In a finitedifference approximation, these indexes can be written as
0022-3654/94/2098-3010$04.50/0 0 1994 American Chemical Society
Catalytic Activity of Zeolites
The Journal of Physical Chemistry, Vol. 98, No. 11, 1994 3011
in the case of an electrophilic attack, and
s+(r) = S(PN+l(r> - P N W )
(8)
in the case of a nucleophilic attack. pM(r) is the electron-density function of the atomic or molecular anion (M= N 1) or cation (M = N - l), calculated at the geometry of the neutral system ( M = N). In a “condensed” version these indexes30J are
+
.14. .13.
T
.12 1
s i = S(q,(N) - 4k(N - 1))
(10)
+
where q k ( N ) , qk(N l), and qk(N - 1) are the Mulliken gross atomic charges32at the atom k for the N-, ( N + 1)-, and ( N 1)-electron systems. Using the finite-difference approach, the global softness can be approximated as33
S=Z- 1
I-A
where Zand A denote the ionization potential and electron affinity, respectively. The geometries of the model systems considered in the present study were completely optimized using the 3-21G basis set34 using the program This basis set was used to obtain results directly comparablewith those of our previous study where this basis was found7 to show an optimal quality/cost ratio and to be suitable for the calculation of metastable anions which are also expected to occur in the present study. The gross atomic charges, Z and A were obtained by SCF calculations using the 3-21G basis performed with the GAMESS program on the CRAY Y-MP/ll6 computer of the universities of Brussels. We used single determinental wave functionsof the RHF-type (for closedshell systems) and of the UHF-type (for open-shell systems), with orbitals being the solutions of the Roothaan36 and PopleNesbet” equations, respectively.
The model systems H3BOHSiH3, H3AlOHSiH3, H3GaOHSiH3, H3BOHGeH3, H3A10HGeH3, and H3GaOHGeH3, hereafter denoted as (B, Si), (Al, Si), (Ga, Si), (B, Ge),(Al, Ge), and (Ga, Ge), respectively, are considered in this study. First of all, their geometries were completely optimized starting from the 3-21G optimized geometry of (Al, Si), which was taken from a previous study: in the case of (B, Si) and (Ga, Si) and from the optimized geometry of (Al, Ge) in the case of (B, Ge) and (Ga, Ge). These geometries are available upon request from the authors. The final energies for the neutral systems, the anions, and cations, all at theequilibriumgeometryof theneutral systems, are given in Table 1 together with the (S2)values which are all reasonably close to the spin uncontaminated value of 0.750. Experimental dataz1-27indicated that the acidity of these systems decreases as follows: (Al, T’) 1 (Ga, T’)
>> (B, T’)
(T, Si) > (T, Ge)
with T’ = Si, Ge
with T = B, Al, Ga
The condensed local softnessfor a nucleophilicattack is studied at the hydrogen atom, &, as the OH-group interacts with electron-donor molecule^.^ The values of this intermolecular reactivity index are given in Table 2. As an increase in the value of s i indicates an increase in the acidity, the generated sequences are (Figure 1)
Ga
Figure 1. Integrated local softness, s i (in au):
X,
(T, Si); 0,(T, Ge).
TABLE 1: Calculated Values of the Energies for (T, T’) (T = B, Al, Ga; T’ = Si, Ce) (Neutral Systems and the Ions at the Equilibrium Geometry of the Neutral Systems)
(B, Si) (Al, Si) (Ga, Si) (B, Ge) (AI, Ge) (Ga, Ge)
neutral system energy (au)
anion energy (au)
-309.456 675 -606.523 684 -2279.781 335 -2168.409 717 -2384.476 866 -4057.734 252
-309.354 967 -606.440 269 -2279.696 278 -2168.179 293 -2384.396 589 -4057.652 637
cation
(P)energy (au)
(9)
0.760 0.759 0.758 0.760 0.760 0.759
0.776 0.833 0.831 0.776 0.832 0.831
-309.090 597 -606.188 567 -2279.449 353 -2167.942 382 -2384.144 393 -4057.404 963
TABLE 2 Calculated Values of the Quantities Related to the Acidity of the Bridging Hydroxyl Group for the Model Systems (T, T‘) (T = B, Al, Ga; T‘ = Si, Ge)
(B, Si) (Al, Si) (Ga, Si) (B, Ge) (Al, Ge) (Ga, Ge)
0.1970 0.1976 0.1707 0.1296 0.1786 0.1617
(Al, T’) (Al, T’)
Results and Discussion
A1
B
0.4689 0.4755 0.4735 0.4635 0.4682 0.4666
0.962(6) 0.967(3) 0.965(3) 0.962(0) 0.965(8) 0.964(8)
> (B, T’) > (Ga, T’) > (Ga, T’) >> (B, T’)
(T, Si) > (T, Ge)
0.4045 0.4449 0.4391 0.3967 0.4347 0.4294
1.947 1.829 1.810 1.898 1.730 1.696
with T’ = Si with T’ = Ge
with T = B, Al, Ga
An explanation for this less accurate description of the acidity (for the series with T’ = Si) by the local softness can be found in terms of the HSAB principle:384 Hard acids prefer to bond to hard bases and soft acids prefer to bond to soft bases. This indicates that a reaction between partners with a comparable hardness will be favorable. Therefore, it is necessary to consider the type of reaction partners used for determining the experimental acidity sequences. In the case of the acidity of the zeolites considered these often are small alcohols or amines, which are systems of intermediate h a r d n e ~ s . ~Hence . ~ ~ it is not unlikely that the local hardness, the counterpart (but not inverse)42 of the local softness, may give a more adequate description of the reactivity. As this property is not as easily accessible as the local softness,4245we will make use of the charge on the H atom of the acidic hydroxyl group, qH,which can intuitively be expected to give a first indication of the local hardness.ll~~~ The values of qH, obtained by subtracting the population of the free atom from the Mulliken population, are also given in Table 2. As higher values for q H also indicated a higher reactivity, the generated sequences with increasing reactivity are (Figure 2)
> (Ga, T’) > (B, T’) with T’ = Ge, Si with T = B, Al, Ga (T, Si) > (T, Ge)
(Al, T’)
3012 The Journal of Physical Chemistry, Vol. 98, No. I I, I994
:1
Langenaeker et al.
fi
qH
/
.472 .470.
.966 .965 .964 .963
.464.
.962,
T
.462 1
.
B
A1
.961 *
Ga
Figure 2. Charge on the hydrogen atom, q H (in au):
X,
(T,Si); 0, (T,
Ge).
Figure 3. OH-bond length, roH (in
which are in perfect agreement with the experimental sequences. Still, we would like to make a remark about these sequences. The sequence of the charges on the hydrogen atom is not that expected on the basis of the group electronegativities for TH3 and T’H3. If we consider the electronegativity values for the central atoms T and T’, XT and XTI, as an indication of the group electronegativities,which is a reasonable assumption based on the results of a previous study, where group electronegativities, hardnesses, and softnesses were obtained at the CISD level with the 6-3 l++G** basis set,47 the following acidity sequences are generated: (a) Using the Pauling-Allred scale48.49(XB = 2.04, XAI = 1.61, X G ~=
1.81, xsi
(B, T’)
1.90,
= 2.01):
X G ~
> (Ga, T’) > (Al, T’)
(T, Ge) > (T, Si)
with T’ = Ge, Si
with T = B, Al, Ga
These sequences are exactly the inverse of those generated by the charge on the hydrogen atom and the experimental acidity sequences. (b) Using the Sanderson scale5G5z(XB = 2.275, XAI = 1.714, 2.138, X G = ~ 2.618): X G = ~ 2.419, xsi (Ga, T’)
> (B, T’) > (Al, T’)
(T, Ge) > (T, Si)
with T’ = Ge, Si
with T = B, Al, Ga
Again the reactivity sequences are in disagreement with experiment and the charge on the hydrogen atom, even though the position of (B,T’) with respect to (Ga, T’) is now corrected. Mortier and co-workers53 proposed an adjustment to the Sanderson scale, based on experimental data, keeping in mind that electronegativityvalues are expected to increase when going from a third row element to a second-rowelement. They suggested a new electronegativityvalue for Ga, 1.59, yielding to the following acidity sequence:
(B, T’)
> (Al, T’) > (Ga, T’)
A1
A):
X,
Ga (T, Si); 0 , (T, Ge).
.40
T
.39,.
B A1 Ga Figure 4. Ionicity, )qwHI,of the OH bond (in au): X, (T, Si);0 ,(T, Ge). V,U = 2.77, t ) =~2.9, ~ $si = 3.38, and VG = 3.4 (all values in eV), the following reactivity sequence is obtained:
(Ai, T’)
> (Ga, T’) >> (B, T’)
(T, Si) 2 (T, Ge)
with T’ = Ge, Si
with T = B, Al, Ga
These sequences are in perfect agreement with experimental results. Still it is seen that the hardness values according to Pearson, which were used above, are not in agreement with the idea of an increase in softness when descending in Mendelyev’s table.56 As mentioned in the Introduction, the current study using density functional based quantities was extended by means of other quantities in the past frequently used to describe the same characteristicsfor similar systems. The values of these quantities, being the OH-bond length, the ionicity of the OH bond and the dipole moment derivative? are also given in Table 2. As an increasing value of the OH-bond length, rOH, is an indication for a weaker bond, and therefore for a higher acidity of the hydroxyl group, the following sequence is generated by this property (Figure 3):
with T’ = Ge, Si
This is only partially in agreement with experimental data as the acidity of (B, T’) is highly overestimated. At this moment it should be realized that Mortier and co-workers only considered electronegativitydifferencesas a possible sourceof the discrepancy without considering other quantities, such as the softness. We therefore looked at the influence of the group hardnesses, i.e. in a first approximation the hardness values for the central atom,4’ of the different AH3 (A = T, T’) groups on the reactivity (acidity) of the hydrogen atom in the bridging hydroxyl. The quantity might be important as an increasing group softness (charge capacity) is an indication for a better stabilization of a partial negative charge in the AH3 groupsS4leading to a higher positive charge on the hydrogen and thereforealso a higher acidity. Based on the hardness values55 of the central atoms, VB = 4.03,
T B
(Al, T’)
> (Ga, T’) > (B, T’)
(T, Si) > (T, Ge)
with T’ = Ge, Si
with T = B, Al, Ga
again we have a sequence which is in perfect agreement with experimental data. This was also the conclusion of previous studies, but for a more limited series of systems. The same conclusions are reached when considering )q@HI, which is a measurement for the ionicityll of the OH bond (Figure 4).
The dipole derivative with respect to the OH-bond length, (arc/ droH)o,calculated as [C-xy,(arc~/aroH)o2]’/’ is expected to be proportional to the square of the integrated IR intensity of the OH stretching mode in the double harmonic approximations7 and with the assumption of a perfectly localized oscillator.6J8
Catalytic Activity of Zeolites
The Journal of Physical Chemistry, Vol. 98, No. 11, 1994 3013 Scientific Research (NFWO) for a predoctoral position as “aspirant”. P.G. is indebted to the D.P.W.B. (National Service for Programmation of Scientific Policy, Impulse Program on Information Technology, Contract IT/SC/36) for a generous computer grant in support of this work. Prof. W. J. Mortier and Dr. B. Baekelandt (K.U. Leuven) are gratefully acknowledged for stimulating discussions.
References and Notes
1.70
1
1.65 1
1T
B AI Ga Figure 5. Dipole moment derivative with respect to the OH-bond length, (ap/aro~)o(set text) (in D A-’): X, (T, Si); 0 , (T, Ge).
The acidity sequence generated on this basis for our series of systems is (Figure 5 )
(B,T’)
>> (AI, T’) > (Ga, T’)
(T, Si) > (T, Ge)
with T’ = Ge, Si
with T = B, Al, Ga
The second sequence is in agreement with the experiments, but not the first. This might be a consequence of the fact that approximating the dipole derivative with respect to the normal coordinate by means of the derivative with respect to the OHbond length is less justified for (B, T’) due to a less clearcut localizationof the OH 0scillator,6~~~ in view of the smaller atomic mass of boron.
conclusioas Based on the values of the local softness and the charge on the hydrogen atom of the bridging hydroxyl, we are inclined to conclude that the acidity of the zeolite-type model systems is dependent on several characteristics which are of importance when working within the framework of the HSAB principle. The local softness gives a reasonably well description of the reactivity sequence, as was expected based on a previous study. On the other hand, this was not so obvious as the reaction partner used to determine the acidity in the experimental studies are of intermediate hardness. Therefore, the local hardness could not be ruled out as a descriptor for the reactivity of the zeolites. This was confirmed by the use of the charge on the hydrogen atom as a first approximation to the local hardness. These results generated a squence in perfect agreement with the experiment. qH was found to be dominated by the hardness of the substituting atoms, which were use as a measurement for the exact group values. This is in contrast with the case of the electronegativity, where no correlation was found with the charge on the hydrogen atom. The OH-bond length and 1q@&( were found to be good descriptors of the acidity, whereas the dipole moment derivative with respect to the OH-bond length appears to fail as a reactivity index. In future, a more elaborate study of the local hardness parameter, as recently defined, will be undertaken. Together with an effectivecalculation of the different HSAB related group quantities, this study is believed to give a better insight in the relation between the electron density and reactivity. Furthermore, it can elucidate the importance of considering the nature (e.g., hardness) of the reaction partner in the selection of a optimal reactivity index.
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Acknowledgment. W.L.is indebted to the Research Council of the Vrije Universiteit Brussel for a position as Research Assistant, and F.D.P. to the Belgian National Foundation for
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d;
