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Basicity of the framework oxygen atom of alkali and alkaline earth-exchanged zeolites: a hard–soft acid–base approach
29 December 2000
Chemical Physics Letters 332 (2000) 576±582
www.elsevier.nl/locate/cplett
Basicity of the framework oxygen atom of alkali and alkaline earth-exchanged zeolites: a hard±soft acid±base approach Ramesh Ch. Deka *, Ram Kinkar Roy, Kimihiko Hirao Department of Applied Chemistry, Graduate School of Engineering, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Received 27 July 2000; in ®nal form 27 October 2000
Abstract The basicity of framework oxygen atoms of alkali and alkaline earth-exchanged zeolites has been studied using reactivity descriptors based on a local hard±soft acid±base (HSAB) concept. We have calculated the `local softness' and the `relative nucleophilicity' values of the framework oxygen atoms of zeolite clusters as the measure of basicity. The local softness and relative nucleophilicity appear to be more reliable descriptors to predict the experimental basicity trend, compared to the negative charge on the oxygen atom. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction In recent years, density functional descriptors such as global hardness g and global softness (S) have appeared as powerful tools to understand reactivity of various chemical systems [1,2,3]. A major breakthrough in this ®eld is the introduction of the Fukui function [4] and local softness [5] to understand the local reactivity of a chemical species. The local hard±soft acid±base (HSAB) principle proposed by Gazquez and Mendez [6] predicts the reactive centers of two chemical systems on the basis of equal softness. Krishnamurty et al. [7] showed the validity of the local HSAB principle in the case of interaction of small gaseous molecules with zeolite clusters. Although the local softness is successfully used in determining the reactive centers of molecules, a recent study by Roy et al. [8] proposed a new scheme based on the
*
Corresponding author. Fax: +81-3-5841-7241. E-mail address: [email protected] (R.C. Deka).
ratio of electrophilic and nucleophilic local softness values and its inverse. These newly de®ned descriptors are called `relative electrophilicity', and `relative nucleophilicity' that are found to be more reliable in predicting the reactive sites of the aliphatic and aromatic compounds. Although theory and experimental studies have contributed signi®cantly to understand acidity of zeolites [9,10], very few theoretical calculations have been performed to study the basicity of zeolites [11,12]. In cation-exchanged zeolites, the cations act as Lewis acid sites and the framework oxygen atoms bearing partial negative charge behave as basic sites. These basic sites are called structural basic sites or framework basic sites. The basicity may also originate from other sites like basic hydroxyls, encaged oxide clusters, supported metals etc. Experimentally, the basicity of zeolites has been characterized by using either direct methods or indirect ones with the help of probe molecules [13,14,15,16]. In this Letter, we are interested in studying the framework basicity of cation-exchanged zeolites. The O1s binding energy
0009-2614/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 0 ) 0 1 2 9 6 - 3
R.C. Deka et al. / Chemical Physics Letters 332 (2000) 576±582
evaluated by X-ray photoelectron spectroscopic (XPS) studies re¯ect the electron density of the framework oxygen atoms [13,16]. A decrease in O1s binding energy can be interpreted as an increase in basicity (electron density) of oxygen. Thus, using O1s binding energy it was shown that the framework basicity of faujasite-type zeolites increases in the order Li < Na < K < Rb < Cs [13]. Theoretical calculations of the framework oxygen charges based on Sanderson electronegativity equalization methods support this trend [11]. However, a recent density functional study by R osch and co-workers [12] showed that oxygen charges obtained from either a Mulliken population analysis (MPA) or a natural bond orbitals (NBO) remains essentially unchanged in the alkaliexchanged zeolites. Basicity of alkaline earthexchanged zeolites also increases with the increase in ionic radii from Mg to Ba [17]. However, alkaline earth cations show less basicity than the alkali-exchanged zeolites. Recently, we have studied the in¯uence of isomorphous substitution on the acidity of zeolite clusters using `local softness' and relative electrophilicity values [18]. In this Letter, we will use local softness and relative nucleophilicity values to study the basicity of alkali and alkaline earthexchanged zeolites.
2. Theoretical aspects Density functional theory has provided the framework for a coherent quantitative description of hardness and softness functionals [1]. However, the active sites in a chemical system (basic sites in the present study) cannot be described using the global descriptors, and some local reactivity descriptors are required to serve the purpose. Indeed, several local reactivity descriptors, based on the HSAB concept, have been proposed. One such descriptor is local softness which is de®ned as [5] ! oq r oN f rS; 1 s r oN ol v r v r
where f r is the Fukui function originally proposed by Parr and Yang [4] and S is the global
577
softness [1]. From the de®nition of local softness, one can infer that the local softness can be used as a reactivity measure. A large local softness value indicates greater reactivity of the site. A simple procedure to obtain information about s r is to condense its value around each atomic site into a single value that characterizes the atom in the molecule. Thus, in a ®nite dierence approximation, for an atom k in a molecule, we have three dierent types of local softness values: s k qk N0 1 ÿ qk N0 S
2a
(for nucleophilic attack on the system) sÿ k qk N0 ÿ qk N0 ÿ 1S
2b
(for electrophilic attack on the system) s0k 12qk N0 1 ÿ qk N0 ÿ 1S
2c
(for radical attack on the system) where qk N0 , qk N0 1 and qk N0 ÿ 1 are electronic populations on atom k for N0 , N0 1 and N0 ÿ 1 electron systems, respectively. Although the condensed local softness values have been used successfully to explain a variety of experimentally observed phenomena, a recent ÿ study by Roy et al. [8] found that s k and sk fail to reproduce the experimentally observed intramolecular reactivity trends in aliphatic and aromatic carbonyl compounds. After analyzing the factors that cause the irregular reactivity trends, they proposed two new local reactivity descriptors as ÿ relative electrophilicity s k =sk and relative nucleÿ ophilicity (sk =sk [8] and these descriptors oered a much better description of the site selectivity of aliphatic and aromatic carbonyl compounds [8]. A greater value of sÿ k =sk is expected to give greater basicity of the framework oxygen. 3. Computational details While performing quantum chemical calculations to study the properties of zeolites, it is necessary to take a large cluster. Embedding techniques [19] or periodic Hartree±Fock methods [20], which correspond to a step further in accuracy, become useful when long-range eects play a non-negligible role or when the structure of dif-
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R.C. Deka et al. / Chemical Physics Letters 332 (2000) 576±582
ferent solids needs to be compared. However, wellchosen clusters may indeed be good models for studying framework properties and their interaction with small molecules [21]. In the present study, we have chosen a trimer cluster of the form H3 TOXT(OH)2 OTH3 , where T Si or Al, X Li , Na , K , Rb , Cs , Be , Mg , Ca , Sr or Ba . All the calculations were performed with the DMol program [22] using DND and DNP basis sets and the FINE integration grid referred in the program. 4. Results and discussion 4.1. Optimized geometry 4.1.1. Alkali-exchanged clusters The cluster used to model the basicity of alkaliexchanged zeolites is shown in Fig. 1a and geometric parameters of the optimized clusters are summarized in Table 1. The environment of an oxygen atom in zeolite is similar to that of O8 or O9 atoms. It is seen from Table 1 that small cations, namely Li and Na , have two-fold coordinations as these two cations are bonded to O8 and O9 atoms and lie at long distances from O11 and O12 atoms. On the other hand, large cations, K , Rb and Cs , have three-fold coordinations as these cations are bonded to O8 , O9 and O12 atoms and lie at a far distance from O11 oxygen atom. Cation±oxygen bond distance increases with the increase of cation radii. The interaction of the cations with the zeolite framework leads to a substantial deformation of the zeolite structure around the cation (Table 1). Elongation of Si±O and Al±O bond lengths, decrease of O8 ±Al±O9 bond angle and the trends of X ±O bond lengths indicate that the cation±oxygen bond is strongest in the case of Li and weakest in the case of the Cs -exchanged zeolite cluster. 4.1.2. Alkaline earth-exchanged clusters The optimized geometry of alkaline-earth exchanged zeolite clusters is shown in Fig. 1b and their geometric parameters are given in Table 2. Unlike alkali cations, all alkaline earth cations have two-fold coordinations with the zeolite
Fig. 1. Optimized geometry of the trimer cluster model, H3 TOXT(OH)2 OTH3 where T Si or Al and X alkali cations (Li , Na , K , Rb , Cs ) (a) or alkaline earth metal cations (Be , Mg , Ca , Sr , Ba ) (b). Cations such as K , Rb and Cs have three-fold coordinations as seen from Table 1, whereas other cations have two-fold coordinations (see Tables 1 and 2).
framework. The cation±oxygen distance increases with the increase in ionic radii in the series Be < Mg < Ca < Sr < Ba . Similar to alkali-exchanged zeolites, the O8 ±Si±O9 bond angle in alkaline earth-exchanged zeolites deviates from the tetrahedral angle. 4.2. Basicity of the framework oxygen We have used negative charge, local softness and relative nucleophilicity of the framework
R.C. Deka et al. / Chemical Physics Letters 332 (2000) 576±582
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Table 1 Variation of selected internal coordinates of the optimized trimer cluster of alkali cation-exchanged zeolites Internal coordinates
a
X ±O8 X ±O9 a X ±O11 a X ±O12 a Si3 ±O8 a Si5 ±O9 a Al4 ±O8 a Al4 ±O9 a O8 ±Al±O9 b Si3 ±O8 ±Al4 b Si5 ±O9 ±Al4 b O8 ±X ±O9 b a b
Exchanged cations Li
Na
K
Rb
Cs
1.849 1.849 3.968 3.759 1.666 1.669 1.852 1.849 89.9 133.3 130.8 90.0
2.232 2.236 4.409 4.066 1.657 1.660 1.835 1.832 95.0 133.0 130.3 74.4
2.769 2.824 4.801 2.668 1.644 1.641 1.805 1.808 99.6 139.6 142.4 59.1
2.959 2.943 4.958 2.797 1.643 1.641 1.803 1.807 100.1 139.0 141.1 55.9
3.153 3.132 5.159 2.973 1.641 1.640 1.803 1.804 100.5 139.7 140.6 52.4
Values are in A. Values are in degrees.
Table 2 Variation of selected internal coordinates of the optimized trimer cluster of alkaline earth-exchanged zeolites Internal coordinates
a
X ±O8 X ±O9 a X ±O11 a X ±O12 a Al3 ±O8 a Al5 ±O9 a Si4 ±O8 a Si4 ±O9 a O8 ±Si±O9 b Al3 ±O8 ±Si4 b Al5 ±O9 ±Si4 b O8 ±X ±O9 b a Values are in A. b
Exchanged cations Br
Mg
Ca
Sr
Ba
1.701 1.704 3.593 3.563 1.887 1.880 1.676 1.689 92.1 135.6 128.0 90.7
2.082 2.074 4.034 3.883 1.858 1.855 1.668 1.661 97.4 148.4 147.0 74.0
2.295 2.392 4.287 4.162 1.855 1.829 1.670 1.648 99.8 135.8 148.2 65.5
2.465 2.556 4.453 4.325 1.854 1.828 1.668 1.645 101.2 135.1 149.8 61.3
2.651 2.737 4.657 4.488 1.853 1.825 1.666 1.643 102.2 133.9 150.6 57.1
Values are in degrees.
oxygen atom (O8 ) as a measure of the basicity of alkali and alkaline earth-exchanged zeolites. 4.2.1. Basicity of alkali-exchanged zeolites The Mulliken and Hirshfeld charge values of the oxygen atom (O8 ) of alkali-exchanged zeolites calculated using DNP and DND basis sets are presented in Table 3. It is seen that the Mulliken charge (negative values) on the oxygen atom increases from Li to Na indicating more basicity for Na -exchanged zeolites. However, there is a
decrease in O8 negative charge from K to Cs exchanged zeolites. Thus the higher basicity observed in the Cs -exchanged zeolites cannot be explained using Mulliken charges. The Hirshfeld charge also does not change much on going from Li to Cs . They are almost constant irrespective of the exchanged cation, indicating the same basicity of the framework oxygen atoms. Since the negative charges on the framework oxygen atom of zeolites fail to predict the correct basicity order, we studied the basicity of zeolite
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Table 3 The MPA and HPA derived charge, local softness and relative nucleophilicity of the bridging O8 atom of the zeolite cluster, H3 SiOX Al(OH)2 OSiH3 Exchanged cations
Basic set
Li Na K Rb Cs Li Na K Rb Cs
MPA derived parameters
HPA derived parameters
qO a
b s k
c sÿ k
d sÿ k =sk
qO a
b s k
c sÿ k
d sÿ k =sk
DNP
)0.919 )0.944 )0.896 )0.887 )0.882
)0.1423 )0.1497 )0.1303 )0.1186 )0.1221
0.1198 0.1497 0.2250 0.2293 0.2363
)0.8421 )1.000 )1.727 )1.933 )1.935
)0.3618 )0.3646 )0.3647 )0.3647 )0.3651
0.0277 0.0182 0.0193 0.0162 0.0157
0.1610 0.1781 0.2329 0.2360 0.2371
5.8108 9.7777 12.0408 14.5610 15.0500
DND
)0.909 )0.957 )0.892 )0.884 )0.874
)0.1533 )0.1582 )0.1332 )0.1225 )0.1207
0.1384 0.1703 0.2260 0.2287 0.2336
)0.9024 )1.0769 )1.6970 )1.8667 )1.9355
)0.3621 )0.3670 )0.3678 )0.3700 )0.3656
0.0265 0.0166 0.0186 0.0163 0.0152
0.1656 0.1870 0.2377 0.2344 0.2328
6.2394 11.2439 12.8044 14.3501 15.3332
a
Charge. Local softness for nucleophilic attack. c Local softness for electrophilic attack. d Relative nucleophilicity. b
clusters using local softness for electrophilic attack ÿ ÿ sÿ k and relative nucleophilicity sk =sk . The sk , sk ÿ and sk =sk values of framework oxygen atom derived from MPA and Hirshfeld population analysis (HPA) are given in Table 3. In general it is perceived that for a particular atom in a molecule, the simultaneous increase in sÿ k values and decrease in ÿ s k values is an indication of its high basicity. The sk values, calculated by using both the population analysis schemes, increase from Li to Cs -exchanged clusters. Therefore, from local softness sÿ k values we can conclude that the basicity of alkali-exchanged zeolites increases in the order Li < Na < K < Rb < Cs . This trend in basicity is observed using both DNP and DND basis sets. However, the s k values calculated using MPA pose some problems as it provides negative values. It is not clear whether one should consider the absolute value as the measure of activity in such cases. The factors responsible for providing negative softness values were described by Roy et al. [23] in a recent paper. In the present study, we have considered the absolute values of s k obtained from MPA to compare the basicity of the framework oxygen atoms. The absolute values of sÿ k =sk in crease in the order Li < Na < K < Rb < Cs . This trend in basicity is similar to that of sÿ k =sk values derived from HPA which produces nonnegative local softness values.
4.2.2. Basicity of alkaline earth-exchanged zeolites The negative charges on framework oxygen atom, its local softness and relative nucleophilicity values calculated using MPA and HPA for alkaline earth-exchanged zeolites are given in Table 4. Like in alkali-exchanged zeolites, the negative charge of oxygen is less signi®cant to predict the basicity correctly. The absolute values of relative nucleophilicity calculated using MPA increase in the order Mg < Ca < Sr < Ba . The sÿ k =sk value of oxygen atom of the Be -exchanged cluster is found to be a little higher than those of the Mg and Ca -exchanged clusters. This may be due to dierent bonding natures of the cations to the zeolite framework. The relative nucleophilicity values calculated by using HPA show a much improved basicity trend except for a small disorder in case of Ba . HPA derived sÿ k =sk values of O8 increase slightly from Ca to Sr . However, ÿ sk =sk value for the Ba -exchanged cluster is observed to be lower than those of the Ca and Sr -exchanged clusters. 5. Conclusions In this article, for the ®rst time we have used DFT-based local reactivity descriptors to study the basicity of zeolites. Our study reveals that
R.C. Deka et al. / Chemical Physics Letters 332 (2000) 576±582
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Table 4 The MPA and HPA derived charge, local softness and relative nucleophilicity of the bridging O8 atom of the zeolite cluster, H3 AlOX Si(OH)2 OAlH3 Exchanged cations
Basic set
Be Mg Ca Sr Ba Be Mg Ca Sr Ba
MPA derived parameters
HPA derived parameters
qO a
b s k
c sÿ k
d sÿ k =sk
qO a
b s k
c sÿ k
d sÿ k =sk
DNP
)0.803 )0.932 )0.958 )0.921 )0.918
)0.0474 )0.0562 )0.0518 )0.0300 )0.0215
0.1286 0.0975 0.1355 0.0985 0.0947
)2.7143 )1.5294 )2.6154 )3.2857 )4.4000
)0.2808 )0.3427 )0.3514 )0.3486 )0.3480
0.0670 0.0487 0.0351 0.0403 0.0430
0.1100 0.1166 0.1040 0.1195 0.1140
1.6414 2.3923 2.9660 2.9681 2.6500
DND
)0.801 )0.992 )1.010 )1.007 )0.945
)0.0478 )0.0785 )0.0516 )0.0446 )0.0282
0.1286 0.1157 0.1314 0.1289 0.1080
)2.6923 )1.4737 )2.5455 )2.8889 )3.8333
)0.2860 )0.3504 )0.3618 )0.3776 )0.3488
0.0750 0.0537 0.0525 0.0347 0.0521
0.1272 0.1376 0.1811 0.1527 0.1292
1.6961 2.5615 3.4464 4.4000 2.4775
a
Charge. Local softness for nucleophilic attack. c Local softness for electrophilic attack. d Relative nucleophilicity. b
although negative charges on oxygen atoms are supposed to provide the trend of basicity, these values remain nearly constant irrespective of the exchanged cations. The local softness values sÿ k =s values and also the relative nucleophilicity sÿ k k are found to be more reliable parameters to predict the basicity of cation-exchanged zeolites. The MPA derived sÿ k =sk values provide correct basicity trends only when the absolute values are considered, although we should mention here that the consideration of absolute value of sÿ k =sk does not have much theoretical support. In alkaline earth-exchanged zeolite clusters, the most reliable basicity trend is obtained when HPA -exderived sÿ k =sk values are used. Only the Ba changed cluster lies outside the trend. In this case also the absolute values of MPA derived sÿ k =sk parameters provide the correct basicity trends except for the Be -exchanged zeolite cluster. ÿ ÿ The s k , sk and sk =sk values have not been extensively used to compare the intermolecular re activity. However, we notice that sÿ k =sk values of alkali-exchanged zeolites (Table 3) are higher compared to those of alkaline-earth exchanged zeolites (Table 4). From these results, we can conclude that framework basicity of alkali-exchanged zeolites are more than those of alkaline earth-exchanged zeolites.
Acknowledgements The present research is supported in part by the Grant-in-Aid for Scienti®c Research on Priority Areas `Molecular Physical Chemistry' from the Ministry of Education, Science and Culture of Japan and by the grant from the Genesis Research Institute. R.C.D. thanks the Intelligent Modeling Laboratory (IML), The University of Tokyo, for providing a post-doctoral research fellowship. R.K.R. is thankful to the Japan Society for the Promotion of Science (JSPS).
References [1] R.G. Parr, R.G. Pearson, J. Am. Chem. Soc. 105 (1983) 7512. [2] J.L. Gazquez, A. Martinez, F. Mendez, J. Phys. Chem. 97 (1993) 4059. [3] S. Pal, N. Vaval, R.K. Roy, J. Phys. Chem. 97 (1993) 4404. [4] R.G. Parr, W. Yang, J. Am. Chem. Soc. 106 (1984) 4049. [5] W. Yang, R.G. Parr, Prod. Natl. Acad. Sci. USA 82 (1985) 6723. [6] J.L. Gazquez, F. Mendez, J. Phys. Chem. 98 (1994) 4591. [7] S. Krishnamurty, R.K. Roy, R. Vetrivel, S. Iwata, S. Pal, J. Phys. Chem. A 101 (1997) 7253. [8] R.K. Roy, S. Krishnamurty, P. Geerlings, S. Pal, J. Phys. Chem. A 102 (1998) 3746. [9] J. Sauer, Chem. Rev. 89 (1989) 199.
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[10] R.A. van Santen, G.J. Kramer, Chem. Rev. 95 (1995) 637. [11] L. Uytterhoeven, D. Dompas, M.J. Mortier, J. Chem. Soc. Faraday Trans. 88 (1992) 2753. [12] A.M. Ferrari, K.M. Neyman, N. R osch, J. Phys. Chem. B 101 (1997) 9292. [13] D. Barthomeuf, Catal. Rev. 38 (1996) 521. [14] D. Barthomeuf, Stud. Surf. Sci. Catal. 65 (1991) 157. [15] Y. Okamoto, M. Ogawa, A. Maezawa, T. Imanaka, J. Catal. 112 (1988) 427. [16] T.L. Barr, M.A. Lishka, J. Am. Chem. Soc. 108 (1986) 3178. [17] W.J. Mortier, J. Catal. 55 (1978) 138.
[18] R.C. Deka, R. Vetrivel, S. Pal, J. Phys. Chem. A 103 (1999) 5978. [19] U. Eichler, C.M. K olmel, J. Sauer, J. Comput. Chem. 18 (1997) 463. [20] J.B. Nicholas, A.C. Hess, J. Am. Chem. Soc. 116 (1994) 5428. [21] G. Valerio, J. Plevert, A. Goursot, F. di Renzo, Phys. Chem. 2 (2000) 1091. [22] B. Delley, J. Chem. Phys. 92 (1990) 508. [23] R.K. Roy, S. Pal, K. Hirao, J. Chem. Phys. 110 (1999) 8236.
Chemical Physics Letters 332 (2000) 576±582
www.elsevier.nl/locate/cplett
Basicity of the framework oxygen atom of alkali and alkaline earth-exchanged zeolites: a hard±soft acid±base approach Ramesh Ch. Deka *, Ram Kinkar Roy, Kimihiko Hirao Department of Applied Chemistry, Graduate School of Engineering, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Received 27 July 2000; in ®nal form 27 October 2000
Abstract The basicity of framework oxygen atoms of alkali and alkaline earth-exchanged zeolites has been studied using reactivity descriptors based on a local hard±soft acid±base (HSAB) concept. We have calculated the `local softness' and the `relative nucleophilicity' values of the framework oxygen atoms of zeolite clusters as the measure of basicity. The local softness and relative nucleophilicity appear to be more reliable descriptors to predict the experimental basicity trend, compared to the negative charge on the oxygen atom. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction In recent years, density functional descriptors such as global hardness g and global softness (S) have appeared as powerful tools to understand reactivity of various chemical systems [1,2,3]. A major breakthrough in this ®eld is the introduction of the Fukui function [4] and local softness [5] to understand the local reactivity of a chemical species. The local hard±soft acid±base (HSAB) principle proposed by Gazquez and Mendez [6] predicts the reactive centers of two chemical systems on the basis of equal softness. Krishnamurty et al. [7] showed the validity of the local HSAB principle in the case of interaction of small gaseous molecules with zeolite clusters. Although the local softness is successfully used in determining the reactive centers of molecules, a recent study by Roy et al. [8] proposed a new scheme based on the
*
Corresponding author. Fax: +81-3-5841-7241. E-mail address: [email protected] (R.C. Deka).
ratio of electrophilic and nucleophilic local softness values and its inverse. These newly de®ned descriptors are called `relative electrophilicity', and `relative nucleophilicity' that are found to be more reliable in predicting the reactive sites of the aliphatic and aromatic compounds. Although theory and experimental studies have contributed signi®cantly to understand acidity of zeolites [9,10], very few theoretical calculations have been performed to study the basicity of zeolites [11,12]. In cation-exchanged zeolites, the cations act as Lewis acid sites and the framework oxygen atoms bearing partial negative charge behave as basic sites. These basic sites are called structural basic sites or framework basic sites. The basicity may also originate from other sites like basic hydroxyls, encaged oxide clusters, supported metals etc. Experimentally, the basicity of zeolites has been characterized by using either direct methods or indirect ones with the help of probe molecules [13,14,15,16]. In this Letter, we are interested in studying the framework basicity of cation-exchanged zeolites. The O1s binding energy
0009-2614/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 0 ) 0 1 2 9 6 - 3
R.C. Deka et al. / Chemical Physics Letters 332 (2000) 576±582
evaluated by X-ray photoelectron spectroscopic (XPS) studies re¯ect the electron density of the framework oxygen atoms [13,16]. A decrease in O1s binding energy can be interpreted as an increase in basicity (electron density) of oxygen. Thus, using O1s binding energy it was shown that the framework basicity of faujasite-type zeolites increases in the order Li < Na < K < Rb < Cs [13]. Theoretical calculations of the framework oxygen charges based on Sanderson electronegativity equalization methods support this trend [11]. However, a recent density functional study by R osch and co-workers [12] showed that oxygen charges obtained from either a Mulliken population analysis (MPA) or a natural bond orbitals (NBO) remains essentially unchanged in the alkaliexchanged zeolites. Basicity of alkaline earthexchanged zeolites also increases with the increase in ionic radii from Mg to Ba [17]. However, alkaline earth cations show less basicity than the alkali-exchanged zeolites. Recently, we have studied the in¯uence of isomorphous substitution on the acidity of zeolite clusters using `local softness' and relative electrophilicity values [18]. In this Letter, we will use local softness and relative nucleophilicity values to study the basicity of alkali and alkaline earthexchanged zeolites.
2. Theoretical aspects Density functional theory has provided the framework for a coherent quantitative description of hardness and softness functionals [1]. However, the active sites in a chemical system (basic sites in the present study) cannot be described using the global descriptors, and some local reactivity descriptors are required to serve the purpose. Indeed, several local reactivity descriptors, based on the HSAB concept, have been proposed. One such descriptor is local softness which is de®ned as [5] ! oq r oN f rS; 1 s r oN ol v r v r
where f r is the Fukui function originally proposed by Parr and Yang [4] and S is the global
577
softness [1]. From the de®nition of local softness, one can infer that the local softness can be used as a reactivity measure. A large local softness value indicates greater reactivity of the site. A simple procedure to obtain information about s r is to condense its value around each atomic site into a single value that characterizes the atom in the molecule. Thus, in a ®nite dierence approximation, for an atom k in a molecule, we have three dierent types of local softness values: s k qk N0 1 ÿ qk N0 S
2a
(for nucleophilic attack on the system) sÿ k qk N0 ÿ qk N0 ÿ 1S
2b
(for electrophilic attack on the system) s0k 12qk N0 1 ÿ qk N0 ÿ 1S
2c
(for radical attack on the system) where qk N0 , qk N0 1 and qk N0 ÿ 1 are electronic populations on atom k for N0 , N0 1 and N0 ÿ 1 electron systems, respectively. Although the condensed local softness values have been used successfully to explain a variety of experimentally observed phenomena, a recent ÿ study by Roy et al. [8] found that s k and sk fail to reproduce the experimentally observed intramolecular reactivity trends in aliphatic and aromatic carbonyl compounds. After analyzing the factors that cause the irregular reactivity trends, they proposed two new local reactivity descriptors as ÿ relative electrophilicity s k =sk and relative nucleÿ ophilicity (sk =sk [8] and these descriptors oered a much better description of the site selectivity of aliphatic and aromatic carbonyl compounds [8]. A greater value of sÿ k =sk is expected to give greater basicity of the framework oxygen. 3. Computational details While performing quantum chemical calculations to study the properties of zeolites, it is necessary to take a large cluster. Embedding techniques [19] or periodic Hartree±Fock methods [20], which correspond to a step further in accuracy, become useful when long-range eects play a non-negligible role or when the structure of dif-
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ferent solids needs to be compared. However, wellchosen clusters may indeed be good models for studying framework properties and their interaction with small molecules [21]. In the present study, we have chosen a trimer cluster of the form H3 TOXT(OH)2 OTH3 , where T Si or Al, X Li , Na , K , Rb , Cs , Be , Mg , Ca , Sr or Ba . All the calculations were performed with the DMol program [22] using DND and DNP basis sets and the FINE integration grid referred in the program. 4. Results and discussion 4.1. Optimized geometry 4.1.1. Alkali-exchanged clusters The cluster used to model the basicity of alkaliexchanged zeolites is shown in Fig. 1a and geometric parameters of the optimized clusters are summarized in Table 1. The environment of an oxygen atom in zeolite is similar to that of O8 or O9 atoms. It is seen from Table 1 that small cations, namely Li and Na , have two-fold coordinations as these two cations are bonded to O8 and O9 atoms and lie at long distances from O11 and O12 atoms. On the other hand, large cations, K , Rb and Cs , have three-fold coordinations as these cations are bonded to O8 , O9 and O12 atoms and lie at a far distance from O11 oxygen atom. Cation±oxygen bond distance increases with the increase of cation radii. The interaction of the cations with the zeolite framework leads to a substantial deformation of the zeolite structure around the cation (Table 1). Elongation of Si±O and Al±O bond lengths, decrease of O8 ±Al±O9 bond angle and the trends of X ±O bond lengths indicate that the cation±oxygen bond is strongest in the case of Li and weakest in the case of the Cs -exchanged zeolite cluster. 4.1.2. Alkaline earth-exchanged clusters The optimized geometry of alkaline-earth exchanged zeolite clusters is shown in Fig. 1b and their geometric parameters are given in Table 2. Unlike alkali cations, all alkaline earth cations have two-fold coordinations with the zeolite
Fig. 1. Optimized geometry of the trimer cluster model, H3 TOXT(OH)2 OTH3 where T Si or Al and X alkali cations (Li , Na , K , Rb , Cs ) (a) or alkaline earth metal cations (Be , Mg , Ca , Sr , Ba ) (b). Cations such as K , Rb and Cs have three-fold coordinations as seen from Table 1, whereas other cations have two-fold coordinations (see Tables 1 and 2).
framework. The cation±oxygen distance increases with the increase in ionic radii in the series Be < Mg < Ca < Sr < Ba . Similar to alkali-exchanged zeolites, the O8 ±Si±O9 bond angle in alkaline earth-exchanged zeolites deviates from the tetrahedral angle. 4.2. Basicity of the framework oxygen We have used negative charge, local softness and relative nucleophilicity of the framework
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Table 1 Variation of selected internal coordinates of the optimized trimer cluster of alkali cation-exchanged zeolites Internal coordinates
a
X ±O8 X ±O9 a X ±O11 a X ±O12 a Si3 ±O8 a Si5 ±O9 a Al4 ±O8 a Al4 ±O9 a O8 ±Al±O9 b Si3 ±O8 ±Al4 b Si5 ±O9 ±Al4 b O8 ±X ±O9 b a b
Exchanged cations Li
Na
K
Rb
Cs
1.849 1.849 3.968 3.759 1.666 1.669 1.852 1.849 89.9 133.3 130.8 90.0
2.232 2.236 4.409 4.066 1.657 1.660 1.835 1.832 95.0 133.0 130.3 74.4
2.769 2.824 4.801 2.668 1.644 1.641 1.805 1.808 99.6 139.6 142.4 59.1
2.959 2.943 4.958 2.797 1.643 1.641 1.803 1.807 100.1 139.0 141.1 55.9
3.153 3.132 5.159 2.973 1.641 1.640 1.803 1.804 100.5 139.7 140.6 52.4
Values are in A. Values are in degrees.
Table 2 Variation of selected internal coordinates of the optimized trimer cluster of alkaline earth-exchanged zeolites Internal coordinates
a
X ±O8 X ±O9 a X ±O11 a X ±O12 a Al3 ±O8 a Al5 ±O9 a Si4 ±O8 a Si4 ±O9 a O8 ±Si±O9 b Al3 ±O8 ±Si4 b Al5 ±O9 ±Si4 b O8 ±X ±O9 b a Values are in A. b
Exchanged cations Br
Mg
Ca
Sr
Ba
1.701 1.704 3.593 3.563 1.887 1.880 1.676 1.689 92.1 135.6 128.0 90.7
2.082 2.074 4.034 3.883 1.858 1.855 1.668 1.661 97.4 148.4 147.0 74.0
2.295 2.392 4.287 4.162 1.855 1.829 1.670 1.648 99.8 135.8 148.2 65.5
2.465 2.556 4.453 4.325 1.854 1.828 1.668 1.645 101.2 135.1 149.8 61.3
2.651 2.737 4.657 4.488 1.853 1.825 1.666 1.643 102.2 133.9 150.6 57.1
Values are in degrees.
oxygen atom (O8 ) as a measure of the basicity of alkali and alkaline earth-exchanged zeolites. 4.2.1. Basicity of alkali-exchanged zeolites The Mulliken and Hirshfeld charge values of the oxygen atom (O8 ) of alkali-exchanged zeolites calculated using DNP and DND basis sets are presented in Table 3. It is seen that the Mulliken charge (negative values) on the oxygen atom increases from Li to Na indicating more basicity for Na -exchanged zeolites. However, there is a
decrease in O8 negative charge from K to Cs exchanged zeolites. Thus the higher basicity observed in the Cs -exchanged zeolites cannot be explained using Mulliken charges. The Hirshfeld charge also does not change much on going from Li to Cs . They are almost constant irrespective of the exchanged cation, indicating the same basicity of the framework oxygen atoms. Since the negative charges on the framework oxygen atom of zeolites fail to predict the correct basicity order, we studied the basicity of zeolite
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Table 3 The MPA and HPA derived charge, local softness and relative nucleophilicity of the bridging O8 atom of the zeolite cluster, H3 SiOX Al(OH)2 OSiH3 Exchanged cations
Basic set
Li Na K Rb Cs Li Na K Rb Cs
MPA derived parameters
HPA derived parameters
qO a
b s k
c sÿ k
d sÿ k =sk
qO a
b s k
c sÿ k
d sÿ k =sk
DNP
)0.919 )0.944 )0.896 )0.887 )0.882
)0.1423 )0.1497 )0.1303 )0.1186 )0.1221
0.1198 0.1497 0.2250 0.2293 0.2363
)0.8421 )1.000 )1.727 )1.933 )1.935
)0.3618 )0.3646 )0.3647 )0.3647 )0.3651
0.0277 0.0182 0.0193 0.0162 0.0157
0.1610 0.1781 0.2329 0.2360 0.2371
5.8108 9.7777 12.0408 14.5610 15.0500
DND
)0.909 )0.957 )0.892 )0.884 )0.874
)0.1533 )0.1582 )0.1332 )0.1225 )0.1207
0.1384 0.1703 0.2260 0.2287 0.2336
)0.9024 )1.0769 )1.6970 )1.8667 )1.9355
)0.3621 )0.3670 )0.3678 )0.3700 )0.3656
0.0265 0.0166 0.0186 0.0163 0.0152
0.1656 0.1870 0.2377 0.2344 0.2328
6.2394 11.2439 12.8044 14.3501 15.3332
a
Charge. Local softness for nucleophilic attack. c Local softness for electrophilic attack. d Relative nucleophilicity. b
clusters using local softness for electrophilic attack ÿ ÿ sÿ k and relative nucleophilicity sk =sk . The sk , sk ÿ and sk =sk values of framework oxygen atom derived from MPA and Hirshfeld population analysis (HPA) are given in Table 3. In general it is perceived that for a particular atom in a molecule, the simultaneous increase in sÿ k values and decrease in ÿ s k values is an indication of its high basicity. The sk values, calculated by using both the population analysis schemes, increase from Li to Cs -exchanged clusters. Therefore, from local softness sÿ k values we can conclude that the basicity of alkali-exchanged zeolites increases in the order Li < Na < K < Rb < Cs . This trend in basicity is observed using both DNP and DND basis sets. However, the s k values calculated using MPA pose some problems as it provides negative values. It is not clear whether one should consider the absolute value as the measure of activity in such cases. The factors responsible for providing negative softness values were described by Roy et al. [23] in a recent paper. In the present study, we have considered the absolute values of s k obtained from MPA to compare the basicity of the framework oxygen atoms. The absolute values of sÿ k =sk in crease in the order Li < Na < K < Rb < Cs . This trend in basicity is similar to that of sÿ k =sk values derived from HPA which produces nonnegative local softness values.
4.2.2. Basicity of alkaline earth-exchanged zeolites The negative charges on framework oxygen atom, its local softness and relative nucleophilicity values calculated using MPA and HPA for alkaline earth-exchanged zeolites are given in Table 4. Like in alkali-exchanged zeolites, the negative charge of oxygen is less signi®cant to predict the basicity correctly. The absolute values of relative nucleophilicity calculated using MPA increase in the order Mg < Ca < Sr < Ba . The sÿ k =sk value of oxygen atom of the Be -exchanged cluster is found to be a little higher than those of the Mg and Ca -exchanged clusters. This may be due to dierent bonding natures of the cations to the zeolite framework. The relative nucleophilicity values calculated by using HPA show a much improved basicity trend except for a small disorder in case of Ba . HPA derived sÿ k =sk values of O8 increase slightly from Ca to Sr . However, ÿ sk =sk value for the Ba -exchanged cluster is observed to be lower than those of the Ca and Sr -exchanged clusters. 5. Conclusions In this article, for the ®rst time we have used DFT-based local reactivity descriptors to study the basicity of zeolites. Our study reveals that
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Table 4 The MPA and HPA derived charge, local softness and relative nucleophilicity of the bridging O8 atom of the zeolite cluster, H3 AlOX Si(OH)2 OAlH3 Exchanged cations
Basic set
Be Mg Ca Sr Ba Be Mg Ca Sr Ba
MPA derived parameters
HPA derived parameters
qO a
b s k
c sÿ k
d sÿ k =sk
qO a
b s k
c sÿ k
d sÿ k =sk
DNP
)0.803 )0.932 )0.958 )0.921 )0.918
)0.0474 )0.0562 )0.0518 )0.0300 )0.0215
0.1286 0.0975 0.1355 0.0985 0.0947
)2.7143 )1.5294 )2.6154 )3.2857 )4.4000
)0.2808 )0.3427 )0.3514 )0.3486 )0.3480
0.0670 0.0487 0.0351 0.0403 0.0430
0.1100 0.1166 0.1040 0.1195 0.1140
1.6414 2.3923 2.9660 2.9681 2.6500
DND
)0.801 )0.992 )1.010 )1.007 )0.945
)0.0478 )0.0785 )0.0516 )0.0446 )0.0282
0.1286 0.1157 0.1314 0.1289 0.1080
)2.6923 )1.4737 )2.5455 )2.8889 )3.8333
)0.2860 )0.3504 )0.3618 )0.3776 )0.3488
0.0750 0.0537 0.0525 0.0347 0.0521
0.1272 0.1376 0.1811 0.1527 0.1292
1.6961 2.5615 3.4464 4.4000 2.4775
a
Charge. Local softness for nucleophilic attack. c Local softness for electrophilic attack. d Relative nucleophilicity. b
although negative charges on oxygen atoms are supposed to provide the trend of basicity, these values remain nearly constant irrespective of the exchanged cations. The local softness values sÿ k =s values and also the relative nucleophilicity sÿ k k are found to be more reliable parameters to predict the basicity of cation-exchanged zeolites. The MPA derived sÿ k =sk values provide correct basicity trends only when the absolute values are considered, although we should mention here that the consideration of absolute value of sÿ k =sk does not have much theoretical support. In alkaline earth-exchanged zeolite clusters, the most reliable basicity trend is obtained when HPA -exderived sÿ k =sk values are used. Only the Ba changed cluster lies outside the trend. In this case also the absolute values of MPA derived sÿ k =sk parameters provide the correct basicity trends except for the Be -exchanged zeolite cluster. ÿ ÿ The s k , sk and sk =sk values have not been extensively used to compare the intermolecular re activity. However, we notice that sÿ k =sk values of alkali-exchanged zeolites (Table 3) are higher compared to those of alkaline-earth exchanged zeolites (Table 4). From these results, we can conclude that framework basicity of alkali-exchanged zeolites are more than those of alkaline earth-exchanged zeolites.
Acknowledgements The present research is supported in part by the Grant-in-Aid for Scienti®c Research on Priority Areas `Molecular Physical Chemistry' from the Ministry of Education, Science and Culture of Japan and by the grant from the Genesis Research Institute. R.C.D. thanks the Intelligent Modeling Laboratory (IML), The University of Tokyo, for providing a post-doctoral research fellowship. R.K.R. is thankful to the Japan Society for the Promotion of Science (JSPS).
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