5752
J. Phys. Chem. 1984, 88, 5752-5759
wherefsiA = CkIk-aAis the fraction of the total Si in site A. For the general case in which the partitioning of A1 and Si between sites A and B is different we can write
hiA
=
f” + 1/ R V - f i A )
(‘4.4)
wheref” is the fraction of crystallographic sites of type A, fala is the fraction of total aluminum in site A, and R is the Si/A1 ratio. Assuming that Lowenstein’s rule is obeyed we have the relation3
=4/R
which combined with (A.3) and (A.4) gives the silicon to aluminum ratio. R =
+ a@
-fAIA)
CkIk - af”
(‘4.6)
k
Note that the sum over is known from the 29SiN M R data,f” from the crystal structure, andfAIAmay, in principle, be determined from high-field 27AlNMR. Registry No. 29Si,14304-87-1.
(‘4.5)
Interaction of Surface Hydroxyls with Adsorbed Molecules. A Quantum-Chemical Study Paul Geerlings, Vrije Universiteit Brussel, Eenheid Algemene Chemie. Pleinlaan 2, B- 1050 Brussel, Belgium
Nicolas Tariel, Alain Botrel, Roland Lissillour, Laboratoire de Chimie Theorique-L.A. CNRS 254, Universite de Rennes, Campus de Beaulieu, F-35042 Rennes- Cedex. France
and Wilfried J. Mortier* K.U. Leuven, Laboratorium voor Oppervlaktescheikunde, Kard. Mercierlaan 92, B-3030 Leuven (Heverlee), Belgium (Received: April 3, 1984: In Final Form: June 1 , 1984)
An attempt has been made to rationalize the interaction mechanisms of (bridging and terminal) surface hydroxyl groups with molecules, using ab initio, EHT, and CNDO/2-FA quantum-chemical calculations. Bond strength variations and charge shifts were found to be in complete agreement with Gutmann’s rules, and provide a basis for the understanding of the Brransted acid properties of zeolites and amorphous silica-alumina. A quantitative measure of the interaction strength is possible by referring to the experimentally determined donor number (Gutmann) following may molecules, but care should be taken for those molecules for which the donor strength was determined by indirect methods. Only a few exceptions to Gutmann’s rules should exist, e.g., in those cases where the atom interacting with the proton is not the most electronegative of the donor molecule (such as for CO). Individual bonds in a given complex are more susceptible to perturbations (changes in composition and interactions with adsorbing molecules) if the coordination number increases. These rules are in agreement with the observations and apply to all reactions (inter- or intramolecular) involving a change in coordination.
Introduction Insight into the properties of the surface hydroxyls of amorphous silica-alumina and of zeolites forms the basis of the scientific understanding of surface reactions and of catalytic processes. Apart from the intrinsic properties of these hydroxyls, which are more or less easily estimated, a prediction of their reactivity is far more complex. The intrinsic properties are being probed by a variety of physicochemical techniques and among the most important the following may be cited: IR spectroscopy (most recent publications on zeolites, silica gel, and aluminosilicates: Kustov et al.; on amorphous silica-alumina: Borovkov et aL2 (1) 149.
Kustov, L. M.; Borovkov, V. Yu.;Kazansky, V. B. J . Catal. 1981, 72,
and Bremer et al.3) and N M R (most recent work on amorphous aluminosilicates: Freude et al.; and for silica gel, aluminum oxides, and zeolites: Freude et aL5). A consistent picture of the fundamental difference between hydroxyls of high and low acidity has emerged from both experiments and theoretical calculations, Le., the structural distinction between “bridging” and “terminal” hydroxyls? Incompletely pdymerized silicic acid (%(OH),), for (2) Borovkov, V. Yu.; Alexeev, A. A.; Kazansky, V. B. J . Catal. 1983,80, 462. (3) Bremer, H.; Jank, M.; Fahlke, B.; Starke, P.; Wendlandt, K.P. Z. Anorg. Allg. Chem. 1983, 500, 5 1. (4) Freude, D.; Pfeiffer, H.; Bremer, H.; Jank, M.; Wendlandt, K. P. Chem. Phys. Lett., in press. ( 5 ) Freude, D.; Hunger, M.; Pfeiffer, H. Chem. Phys. Lett. 1982, 91, 307.
0022-365418412088-5752$01.50/0 0 1984 American Chemical Society
Interaction of Surface OH with Adsorbed Molecules example, contains a considerable number of free hydroxyls terminating the polymer network. These are the terminal hydroxyls. The isomorphous substitution of Si4+ by A13+ in the three-dimensionally four-connected tetrahedral aluminosilicate network of zeolites necessitates the presence of extraframework cations, which may be replaced by appropriate pretreatments by protons attached to the framework oxygens. These form the hydroxyls of the bridged type. Far more complicated is the probing of the reactivity since not only the intrinsic properties of the surface hydroxyls are to be considered, but also other parameters of these and of the reactant molecules. A direct link between the properties of the isolated “active” sites and the rationalization of adsorption phenomena and catalytic processes is by no means easy to make. This is partly due to the lack of a theoretical framework by which surfacemolecule interactions may be rationalized, and partly due to the fact that the parameters influencing the reactivity are not well understood. The deprotonation energies are obviously different for terminal and bridging hydroxyls, but this includes not only the removal of the proton, but also a stabilization of the surface after the reaction has taken place. The latter is difficult to estimate from the intrinsic properties of the surface hydroxyls alone. One particular set of experiments has been successfully applied for the probing of the reactivity of surface hydroxyls and has shed some light on the different parameters involved. The weakening of the OH bond by interaction with adsorbed molecules may be quantified by following the bathochromic shift of the OH stretching frequency. For terminal hydroxyls (in silica gel), the bathochromic shift was linearly correlated with the donor number of the adsorbing m o l e c ~ l e . ~The donor number is an empirical parameter defined as -AH of a complexation reaction of the molecule with SbCls in an inert solvent.’ In a similar approach, Paukshtis and Yurchenko9 used an independently determined proton affinity of the adsorbed molecules to correlate with the bathochromic shift of the surface hydroxyls in aerosil and decationated Y-type zeolites. The difference in sensitivity of bridging and terminal hydroxyls may be illustrated by the difference in frequency shift for the adsorption of acetone: aerosil, 300 cm-’; HY, 900 cm-I. The reactivity of the surface hydroxyls however depends also on parameters other than the configuration. It was already shown by Jacobs and Mortier’O that the OH stretching frequency of the bridging OH groups in zeolites could be correlated with the average electronegativity calculated from the unit-cell composition, irrespective of the Si/Al ratio, the cation content, and the framework type. Similar influences are found by Lercher and Noller’l for the variation of the O H stretching frequency shift, for mixed oxides, upon adsorption of acetone. An increased acid strength was reported (larger shift) with increasing intermediate electronegativity of the mixed oxides SiO,/MgO, SiOz/AlZO3, and Al,03/Mg0. The same is true for bridged hydroxyls in H zeolites for the variation of the frequency shift after benzene adsorption. l 2 Exploring some rules rationalizing the surface reactivity is the subject of this paper. It may be expected from these that they accurately predict the outcome of the intermolecular interactions between the molecules and the surface hydroxyls. These include eventual charge transfer and weakening of the bonds involved in the interaction and predict further transformations and charge density rearrangements around the “active” sites. These rules should further constitute a firm basis for the explanation of the surface reactions.
(8) Gutmann, V. “The Donor-Acceptor Approach to Molecular Interactions”; Plenum Press: New York, 1978. (9) Paukshtis, E. A.; Yurchenko, E. N. React. Kinet. Catal. Lett. 1981, 16, 131. (10) Jacobs, P. A.; Mortier, W. J. Zeolites 1982, 2, 226. (1 1) Lercher, J. A.; Noller, H.J. Carol. 1982, 77, 152. (12) Jacobs, P. A. Catal. Reu.-Sci. Eng. 1982, 24, 415.
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5753
(11’)
(1‘)
(111’)
Figure 1. Model systems for terminal and bridging OH groups.
The obvious choice of the methods for the investigation of these interactions is that of the theoretical chemist. It is clear also that the sophistication of the methods chosen will depend on the complexity of the systems which are considered. Attention will be paid to the following topics: (i) the difference in reactivity of the bridging and terminal hydroxyls, (ii) the type of adsorbed molecule, and (iii) the difference in sensitivity of the properties of the bridging and terminal hydroxyls for compositional changes. Because of the analogy of these interactions with the rationalization of the intermolecular interactions by Gutmann’ using a donor-acceptor approach, it is appropriate to consider these in a separate paragraph.
Gutmann’s Rules The chemical changes occurring as a result of intermolecular interactions involve a charge density rearrangement (chargetransfer and polarization effects), which is also reflected in a change in the molecular structure. A particularly useful framework applicable to this type of interaction is considering these as interactions of the EPA (electron-pair acceptor, Lewis acid)-EPD (electron-pair donor, Lewis base) type. On the basis of experimental evidence, Gutmann’ formulated a few simple rules: the so-called bond length variation rules, describing the structural changes in interacting molecules. Changes in bond length are intimately related with changes in charge densities: the internuclear distance becomes longer as the heteropolarity in the bond increases. A first rule predicts a lengthening of the bonds directly adjacent to the site of interaction: the smaller the intermolecular donor-acceptor atom distance, the greater the induced lengthening of the adjacent bonds. The charge transfer, being extended over the entire molecule, induces a bond lengthening for a shift from a less to a more electronegative atom (or the inverse): second rule. The third rule relates an increased coordination number with increased bond lengths of the bonds originating from the coordination center. The charge density rearrangement (which can be demonstrated by quantum-chemical calculations) is furthermore accompanied by a polarization of the donor-acceptor bond: the positive charge is enhanced at the acceptor site and at the donor site the negative charge is accentuated, because of a ”spillover” and a “pileup” of electrons, respectively. I t will be shown that these simple empirical rules (see ref 8 for a variety of applications in chemistry) will also considerably contribute to the understanding of molecular interactions at zeolite and silica-alumina surfaces. Theoretical Approach Ab Initio Calculations. In order to limit the size of the problem, in a b initio studies, the surfaces with terminal and bridging hydroxyl groups were modeled by molecules I and 11. (See Figure
5754 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
Figure 2. Geometry of the complexes studied.
1.) These systems should be sufficiently large for describing the intrinsic properties of the hydroxyl groups and for displaying the main features of their interaction with electron-donating systems. The calculations were performed with the STO-3-21G splitvalence basis which was recently developed for all elements up to Ar.13,14 When computational results are compared with experiments, STO-3-21G turns out to be superior to the STO-3G minimal basis15 and of comparable quality to the larger and thus more expensive STO-4-3 1G b a ~ i s ’ ~which , ’ ~ was moreover not defined for Al. (In particular, STO-3-21G leads to equilibrium distances which on the average deviate from the experiment by 1.5 pm and to vibrational stretching frequencies deviating about 5%, which is less than for STO-3G.) The completely gradientoptimized STO-3-21G equilibrium geometries for I and I1 were taken from ref 6. For the molecules interacting with the zeolite surface, CO, HzO, and NH3 were chosen as typical donors, capable of forming hydrogen bonds with the hydroxyl groups of the model systems I and 11. On the basis of the donor number (DN),8 and previous quantum-mechanical c a l ~ u l a t i o n s , H ’ ~2~0~and ~ NH,, both possessing a large permanent dipole moment, are expected to yield interaction energies which are substantially larger than for CO, which, despite its overall almost apolar character,a is nevertheless expected to show important interaction with a O H group through the lone pair on C or 0. Starting from the STO-3-21G equilibrium geometry for I and I1 on one hand, and for CO, NH,, and H 2 0 on the other (from ref 13), we performed a partial geometry optimization of the 1:l complexes of I and I1 with CO, NH,, and H20. Only “linear” complexes, Le., with collinear O-H...B (B = C, N, 0)bonds, were considered, since hydrogen bonds are most often linear or show only small deviations from linearity.z1 The H...B distance was the first parameter to be optimized. For N H 3 and CO, the approach of the electron-donor molecule was considered to occur via the lone pair, respectively, on N and C, yielding (as seen in Figure 2) complexes in which the C3axis of NH3 and the CO axis are collinear with the OH bond. (CO complexes with the 0 lone pair were not explicitly considered in our studies as previous quantum-chemical studies on comparable systems indicated the complexes beC atom as the preferential interaction site: 187z3*z4
(13) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. SOC.1980, 102, 939. (14) Gordon, M. S.; Binkley, J. S.;Pople, J. A.; Pietro, W. J.; Hehre, W. J. J . Am. Chem. SOC.1982. 104. 2797. (15) Hehre, W. J.; Ditchfield; R.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1970,52,2169. (16) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 124 . - .. (17) Hehre, W. J.; Lathan, W. A. J . Chem. Phys. 1972, 56, 5255. (18) Umeyama, H.; Morokuma, K. J . Am. Chem. SOC.1976, 98, 7208. (19) Kollman, P.;McKelvey, J.; Johansson, A.; Rothenberg, S. J . Am. Chem. SOC.1975, 97,955. (20) Muenter, J. S. J. Mol. Spectrosc. 1975, 55, 490. (21) See, for example: Kollman, P. A. In “Applications of Electronic Structure Theory”; Shaeffer, H. F., 111, Ed.; Plenum Press: New York, 1977; p 134. (22) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833.
Geerlings et al. tween C O and hydrogen and with BH3.18) By analogy with the water dimer>5we chose a linear geometry for the water complexes in which the angle 0 (Figure 2) was also optimized. All intramolecular parameters were kept at their isolated-molecule equilibrium value when optimizing R and 0. Afterward, the O H distance r was optimized and the corresponding force constant was obtained by numerical differentiation. All calculations were performed with the MONSTERGAUSS programz6 on the CDC-CYBER 750-150 computer of the ULB-VUB. EHT. For a study of the bond length variation further in the molecule (Gutmann’s second rule), larger model systems are required, prohibiting ab initio studies. For a known relationship between bond length and overlap population, it is possible to determine the equilibrium distance. It has been possible to establish a generally quadratic relation between experimental bond length (RrJ and the calculated bond order (Prs) (Rrs = a bP,, cPm2),the parameters of which are calibrated by using accurately determined molecular geometrie~.~’An extrapolation to other systems within the validity range of the relation is realized by modifying an initial geometry to the calculated bond orders in an iterative scheme until internal consistency is obtained. This kind of approach necessitates numerous calculations, which can only be practical at the level of approximate MO theories such as CNDO or EHT. Parametrization problems due to the presence of aluminum made us choose the E H approximation.28 The bond length-bond order relationships have been calibrated by using 8 experimental bond lengths for Si-0,29 6 for Al-0,30 8 for O-H,,l and 10 for N-H.32 A least-squares fit (correlation coefficient consistently better than 0.98) of these experimental bond lengths (angstroms) and the corresonding calculated bond orders leads to the following equations:
+
+
Rsio = 2.160
- 1.329Ps10 + 0.638Psio2
+
RAlO = 3.087 - 5.113P~10 4 . 4 4 2 P ~ l o ~ ROH = 1.761 - 1 . 3 2 o P o ~ R”
= 1.605 - 0.884P”
The calculations were performed on the model systems I’ ((HO)3-Si-O-), 11’ ((HO),-Si-O--Al-(OH),), and 111’ ((OH),Si-0-Si-(OH),) as shown in Figure 1. The names of the protonated model systems carry an index P, and those of the complexes of the protonated systems with ammonia an index a. In these calculations, the bond angles were fixed at the following (23) Hincliffe, A. Ado. Mol. Relaxation Interact. Processes 1981, 21, 151. (24) Politzer, P.; Kammeyer, C. W.; Bauer, J.; Hedges, W. L. J . Phys. Chem. 1981,85, 4057. (25) See, for example: ref 21, p 114. (26) Peterson, M. R.; Poirier, R. A.; program MONSTERGAUSS, University of Toronto, Toronto, Canada, 1980. (27) GuCrillot, C. R.; Lisssillour, R.; Le Beuze, A. Theor. Chim. Acta 1979, 52, 1. (28) Hoffmann, R. J . Chem. Phys. 1963, 39, 1397. Hoffmann, R.; Lipscomb, W. N. J. Chem. Phys. 1962, 36, 2179; 37, 2872. (29) S i 0 bond-Si(OCH,),, (CH,),SiOSi(CH,),, Cl,SiOSiCI,: Yamasaki, K.; Kotera, A.; Yokoi, M.; Ueda, Y. J . Chem. Phys. 1950, 18, 1414. [(CH3)2Si0]1: Aggarwal (Weller), E.; Bauer, S. H. J. Chem. Phys. 1950, 18, 42. Si(OH)4: O’Keefe, M.; Navrotsky, A. “Structure and Bonding in Crystals”; Academic Press: New York, 1981; Vol. I. H,SiOSiH,: Meier, R.; Kyutla, T. Phys. Chem. Miner. 1980, 6, 37. SiO: “Tables of Interatomic
Distances and Configuration in Molecules and Ions”; The Chemical Society: London, 1958. F3SiOSiF3: Airey, W.; Glidewell, C.; Rankin, D. W. M.; Robiette, A. G.; Sheldrick, G. M.; Cruickshank, D. W. J. Trans. Faraday SOC. 1970, 66, 551. com(30) A10 bond-Al(OH),-, AI(OH),”-: Same reference as pound. A120: “Landolt-Bornstein Numerical Data and Functional Relationships in Science Technology Group 11”; Springer-Verlag: West Berlin, 1976; Vol. 7. Al(OH),: Naray-Szabo, I. “Inorganic Crystal Chemistry”; Akademia Kiado: Budapest, 1969. AlO: Same reference as S i 0 bond. (31) OH bond-HNO,, HINO, H 2 0 , ClOH, CH30H, HzOz: “LandoltBornstein Numerical Data and Functional Relationships in Science and Technology, Group 11”; Springer-Verlag: West Berlin, 1976; Vol. 7. (32) N H bond-”,, CHNO, CH2N2,F2H2NP,NH,, CH,N, H,NO, NzH4, HNSO: Same reference as OH bond.
Interaction of Surface OH with Adsorbed Molecules
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5755 TABLE I: Overall Characteristics of Complexes“ ED AE R Aq q(B...H) EA = I
(1)
co
15.5 55.7 56.2
2.208 1.744 1.853
co
27.1 91.2 101.2
2.049 1.744 1.691
H2O6 NH3
0.i708
t?
0.4123
HzOc NHI -0 1789
H
(I I>
H
H
.S 1 0.35+8’
-OPIq7
/
‘\
0.3470
\
0.3507
1 1946 ,,’
,0.0993
5 8 9 9
H -0.21 03
\
0.3522
‘H
‘0-’0:9157
I
H 0.4755
H
\ 91/ H
0.7956
0.3597
H
0.0184 0.0603 0.0527
1 2 3
0.0290 0.0736 0.0736
4 5
EA = I1 0.0334 0.0968 0.1145
6
“Ab initio 3-21G results. Stabilization energy (AE in kJ/mol), intermolecular distance (Rin angstroms), electron transfer (Aq in electrons) between electron donor and electron acceptor, overlap population between OH hydrogen atom and nearest donor atom q(B.-.H). boptimized angle 8, 43O. coptimized angle 8, 27’.
-0.3350
0.2591
AlH,
0.0197 0.0728 0.0734
complex
-0.2652
Figure 3. Net atomic charges and overlap populations for the model systems I and I1 and AIH3.
values: 109.45’ for 0-T-0 and T-0-H, and 141’ for T-0-T (T = Si or Al), and bond lengths of the terminating OH groups to 0.097 nm. CNDOIZ-FA. A modified CND0/2,, approach was made by Chen et al.34for the study of the acidities of silica-alumina. It was observed by these authors that suitable clusters were difficult to obtain in the traditional formalism, because the hydrogen charge, for example, depends on the extent of the model. To account for the effects of the framework termination, the framework moieties were terminated by hypothetical hydrogen-like atoms, L, with a different electronegativity. In this way, systems were obtained in which the positive charge on Si equals the negative charge of oxygen, hereby simulating framework fragments with a large number of tetrahedra. By variation of the electronegativity of these hypothetical atoms, the differences in sensitivity of the bridging and terminal hydroxyls for the framework composition were investigated. Results and Discussion Ab Initio Studies. Intramolecular Interactions. Before turning to the interaction of the model systems I and I1 with CO, NH3, and HzO, we rationalize the differences in electron density distribution between the two model molecules by considering I1 as resulting from an electron donor-acceptor interaction between I and AlH,. The net atomic charges and overlap populations, obtained by Mulliken population analysis,22for I, 11, and AlH3 (also calculated at is equilibrium geometry, taken from ref 14) are shown in Figure 3. When analyzing this charge distribution we see that the formation of I1 out of I and AlH,, yielding a calculated energy lowering of 155 kJ/mol, is accompanied by an electron transfer of 0.1662 e from I to the AlH3 Lewis acid. Upon interaction the oxygen atom becomes more negative whereas the hydrogen atom loses electrons, leading to a more polar bridging OH bond in I1 as compared with the terminal OH in I. This increased ionicity is accompanied by a decrease in OH overlap population. The OH bond thus weakens when the oxygen passes from two-coordination in I to three-coordination in 11. These results are in agreement with Gutmann’s rules and confirm the predictions made in ref 6 . (The larger positive charge on the bridging O H supports the (33) Pople, J. A.; Segal, G . A. J . Chem. Phys. 1966,43,S136. (34) Chen, Z.; Wang, Z.; Hong, R.; Zhaug, Y. Catal. 1983, 79,271.
statement made in ref 6 that proton occurring with a large downfield NMR chemical shift5correspond to bridging hydroxyls.) The Si-0 bond which is adjacent to theEPA-EPD interaction shows a marked decrease in overlap population, which is again interpreted in line with Gutmann’s rules as due to an electron flow from a more electropositive to a more electronegative atom, resulting in an increased ionicity and decreased bond strength. The electron flow into the AlH3 unit yields a spillover effect on the hydrogen atoms, again decreasing the corresponding AlH bond strength as the electron flow is in the direction of the more electronegative element. These results illustrate that Gutmann’s rules8 can also be used at an intramolecular level, Le., when comparing two molecules I and I1 in which a different coordination a t a given atom occurs, provided that some acceptable “fragmentation” of the system with the higher coordination can be made to simulate an electron acceptor-electron donor (EA-ED) interaction. Intermolecular Interactions. Overall Characteristics. We now turn to the results of the intermolecular interaction calculations. In Table I, we report, for the six complexes studied, some general characteristics such as computed stabilization energy (AE),the calculated equilibrium geometry, the intermolecular distance parameter R, the overlap population between the hydroxyl H atom and the nearest atom B of the electron donor, and the total electron transfer Aq from electron donor to electron acceptor. The optimized angle 0 for both complexes with HzO is also reported. The tabulated values are of the order of magnitude of the comparable 4-31G value for the water dimer, Le., 37°.25 However, for I1 a nearly identical energy minimum was found with 0 = 0. The latter geometry will not be considered in what follows, the overall features of the charge distribution being the same for both geometries. The overall characteristics for complexes of a given electron acceptor show the sequence expected on the basis of the donor number8 or the proton affinity9 of the electron-donor molecule, Le., an increased strength of the interaction as reflected by the increasing stabilization energy, from CO over H20 to NH3. The lower proton affinity of CO (approximately 610 kJ/mol) as compared to NH3 (approximately 840 kJ/mol) correlates with the much smaller value of AE for C O in interaction with I and 11, the longer intermolecular distance R, the smaller charge transfer q, and B e -H overlap population. However, the relative magnitude of Gutmann’s donor number for HzO and NH, is not reflected in the AE values, the value for NH3 (i.e., 59) being more than 3 times larger than for HzO (Le., 18). In view of other comparative quantum-chemical studies on the H-bond-forming capacity of N H 3 and Hz0,19in which N H 3 always appears to be a better H-bond-forming molecule (AE being 5-20% larger than for HzO), the difference between HzO and NH, in I is smaller than expected. However, the D N difference between NH, and HzO seems to use unrealistically large. This view is supported by recent data on the differential heats of adsorption of various bases on zeolite H-Y.35 The sequence of values, extrapolated
-
(35) Mitani, Y.;Tsutsumi, K.; Takahashi, H. J . Chem. SOC.Jpn. 1983, 56, 1917.
5756 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
Geerlings et al.
TABLE II: Variation of OH Bond Characteristics upon Intermolecular Interactiono ED r Ar qOH &OH q0qH fOH
AfOH
uOH
A'OH
EA = I
b
co H20 NH3
0.959 0.960 0.975 0.983
+1 +16 +24
0.2708 0.2602 0.2399 0.2399
+5 +37 +62
0.2591 0.2310 0.2049 0.1967
0.362 0.395 0.434 0.420
-0.0106 -0.0309 -0.0309
892 885 741 706
-7 -151 -186
3995 3980 3642 3555
(3811) (3797) (3475) (3392)
863 785 558 432
-78 -305 -43 1
3931 (3750) 3748 (3576) 3160 (3015) 2781 (2653)
15 (14) 353 (336) 440 (419)
EA = I1
b
co H2O "3
0.967 0.972 1.004 1.029
-0.028 1 -0.0542 -0.0624
0.445 0.492 0.535 0.526
183 (174) 771 (735) 1150 (1097)
@abinitio 3-21G results. OH equilibrium (r) in angstroms; Ar in angstroms/1000; qoH is the OH overlap population; q0qH is the product of net atomic charges on 0 and H; force constantfoH in N m-I; stretching frequency voHin cm-I; values after scaling are given in parentheses; increments (A...) between values after and before interaction are also given. Isolated-moleculevalues; r and f taken from ref 6. to zero coverage, is piperidine (168 kJ/mol), pyridine (160 kJ/ mol), and ammonia (125 kJ/mol), whereas the D N of NH, (59) is higher than for pyridine (51) and much higher than for piperidine (33). Our criticism on the too large ratio between the donor numbers for NH, and H 2 0 is also supported by Erlich's and Popov's results. When 23NaN M R shifts for sodium tetraphenylborate and sodium perchlorate solutions were correlated with the (directly measured) donor number of the solvent, a linear relationship was obtained, the only discrepancy being H 2 0 , which, according to the N M R data, should have a donor number almost twice as large as proposed by G ~ t m a n n . ~These ~ . ~ experimental ~ data indicate that care should be taken when using Gutmann's donor number values for comparing interaction strengths of electron donors with a hydroxyl group, especially when not all values are determined in the same way (calorimetric measurement of the molar enthalpy change for the reaction of the donor with SbCls in a 0.001 M dichloroethane solution) but are obtained by indirect methods, as is the case for N H 3 and piperidine.8 A second overall feature in Table I is that, for a given electron donor, the stabilization energy is always larger for I1 than for I, the ratios varying between 1.65 and 1.80. This confirms the higher acidity of the bridging hydroxyl group as compared to the terminal hydroxyl, as reflected in a more favorable interaction energy with electron-donor molecules. This behavior, foreseen on the basis of the weaker bond strength of the bridging hydroxyl (cf. the discussion of the overlap population) parallels the deprotonation energies calculated in ref 6. Table I further shows that the charge transfer q between ED and EA and the intermolecular overlap in the B e . .H bond are always much smaller in the CO case than for the two other donors, the intermolecular distance R being much larger. The differences between the H20and the NH3 complexes are relatvely small at this level and do not always show regularity. The comparative discussion of the behavior of these two electron donors will be postponed to the level of the OH bond where the most striking differences are revealed. OH Bond Characterstics. In Table I1 various characteristics related to the OH bond are reported such as the calculated equilibrium distance r, the force constant f, and the vibrational stretching frequencies (obtained within a diatomic oscillator approximation) and their difference values with the isolated molecules. W e also report the product of the net atomic charges on H and 0 as a measure of the bond polarity and the OH overlap population. These data reveal that, upon interaction with an electron donor, the OH distance always increases and the O H overlap population decreases. Moreover, the oxygen atom always becomes more negatively charged, the hydrogen atom acquiring more positive charge, so that the absolute value of the product q ( 0 ) q(H) always increases, indicating an increased ionicity upon interaction. This result corresponds to the weakening of the OH bond calculated by Beran by considering the Wiberg bond order for the OH bond in CNDO/2 studies on the *-complexes between a cluster,
modeling zeolite H-Y, and ethene and propene.38 These findings can all be interpreted in terms of Gutmann's rules: upon interaction of the OH bond with an electron donor, electron flow through the OH bond to the rest of the electron-acceptor molecule occurs, resulting in a higher positive charge on H and a higher negative charge on 0. This increasing ionicity of the bond is accompanied by a decrease in overlap population and an increase in the O H interatomic distance. Table I1 again shows that, for a given ED, all these effects are much stronger for I1 than for I, indicating again a higher sensitivity of the bridging vs. the terminal group toward interaction. Again also, the effects are much more pronounced for NH3 and H20than for CO as electron donors, in line with the AE and R values in Table 11. As stated in ref 6, the difference in O H force constant between the isolated systems I and I1 is relatively small (29 N m-') leading to an OH stretching frequency difference of 64 cm-' between terminal and bridging OH'S, in fair agreement, if the numerical accuracy of this procedure is taken into account, with the observed values of 80 cm-' (3745 vs. 3665 cm-' for terminal and bridging OH, respectively; see references cited in ref 6). The frequency values, obtained by scaling the force constant by the factor 0.9102 (the average factor for H20 and NH,) as described in ref 6, 38 11 and 3750 cm-' lead to a slightly smaller difference of 61 cm-'. When comparing the shift in force constant and frequency upon interaction of the hydroxyl group with an electron donor, we see that the shifts for the bridging hydroxyl are at least double those for the terminal OH. The differences in shift between bridging and terminal OH groups for a given electron donor (calculated values based upon scaled frequencies of Table 11: 160, 399, and 678 cm-') are much larger than the above-mentioned difference of 61 cm-' for the "isolated" molecules. This indicates that the difference in sensitivity of bridging and terminal OH groups toward external perturbations is larger than the difference in isolated-molecule properties. In other words, when terminal- and bridging-hydroxyl potential curves are compared, much larger differences are observed when the hydroxyls are in interaction with an electron donor. These results are an ab initio confirmation of the more qualitative statements of higher sensitivity of the bridging hydroxyls formulated in ref 6. The calculated shifts for NH, are appreciably larger than for H 2 0 , both values being much larger than for CO. These selected results show an interesting correlation with the data of Paukshtis and Yurchenko: these authors plotted the frequency shift of the O H groups in aerosil and HNa-Y against the proton affinity of the base forming a hydroxyl bond with the O H group. They obtained similar, but separated, curves, with consistently higher shifts for the bridging hydroxyls in the H zeolite. For CO, the shift difference is on the order of 150 cm-', the larger shift being on the order of 220 cm-', in fair agreement with our calculations (shift differences 160 cm-I, largest shift 174 cm-'; values after scaling). The curves depict a shift difference for NH3 on the order of 550 cm-' (1000 vs. 450 cm-'), which seems in reasonable agreement with our calculated shifts (1097 and 419 cm-') and
(36) Erlich, R. H.; Roach, E.; Popov, A. I. J . Am. Chem. SOC.1970,92, 4989.
(37) Erlich, R. H.; Popov, A. I. J. Am. Chem. SOC.1971, 93, 5620.
(38) Beran, S.; Jim, P.; Kubelkova, L. J . Mol. Card. 1981, 22, 341.
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5757
Interaction of Surface O H with Adsorbed Molecules
/
/': /
I
/
X=H
X=OH (EHT:
* 4
H 0 B
288
sen -
848
1120 L
1
4
isan
~ IBSU ~
(
,b'-
2240
'2)
2528
2800
(b)
1/2
Figure 4. Energy vs. frequency relationship.
their difference (678 cm-'). (The values reported here were estimated from Figure 1 of ref 9.) The data by Jacobs et al.,,' in a comparative study of the acidity in H-ZSM-5, H-ZSM-11, and dealuminated H-Y zeolites showing a frequency shift upon benzene adsorption of the 3700- and 3600-cm-' bands, also support our theoretical results as they indicate a much higher shift for the bridging than for the terminal OH (300-350 vs. 40-80 cm-I). It is interesting to combine the data given in Tables I and I1 for describing the linear relationship found by Horill and Noller' between the O H frequency shift for aerosil (terminal OH) and the donor number for a series of electron donors. Recalling that the donor number is a molecular enthalpy of formation (all values used by Horill and Noller can effectively be seen as such, since electron donors for which only an indirectly measured value (e.g., NH3!) is available are not considered in their study), this relationship is of the type of the well-known Badger-Bauer AH-Av linear relation for H-bonded systems.'' After extensive tests there is now nearly unanimous agreement that no general linear correlation exists between these two proper tie^.^^ Recently, it has been shown42on the basis of Mulliken's charge-transfer theory that a better correlation can be obtained if the enthalpy is not plotted against Av, but against (v; - v ~ ) ' /v,~, ,being the frequency of the unperturbed oscillator. This is confirmed by our calculations, where a satisfactory linear relationship through the origin is obtained between AE and (v; - vz)ll2,indicating that the latter frequency-shift parameter is more suited to study the strength of EA-ED interactions at surface hydroxyls (see Figure 4). Electron Distribution in Non-Hydroxyl Parts of the Complexes. W e finally report a brief analysis of the equilibrium charge distribution of the remaining parts of the various complexes and we will try to analyze these results in terms of Gutmann's rules. As shown in Figure 5a for a typical case, the Mulliken population analysis (numerical data available from the authors on request) reveals that electron transfer from the electron donor to the electron-acceptor molecule upon H-bond formation is accompanied by an electron flow across the electron acceptor leading to a spillover effect on the SiH3 (and AlHJ groups. In a first approximation the increase in electronic population of the SiH, group can be related to the upfield 29Sishift for silanols and silylamines which was shown to correlate with the (directly measured) donor number of the solvent.43 An electron flow from a more electronegative atom to a more electropositive atom (0to Si or Al) is always accompanied by an increase in overlap population, indicating bond strengthening (indicated by broken arrows in Figure 5a), whereas the reverse is true for shifts from H to 0, (39) Jacobs, P. A.; Martens, J. A.; Weitkamp, J.; Beyer, H. K. Faraday Discuss. Chem. SOC.1981, 72, 353. (40) Badger, R. M.; Bauer, S.H. J. Chem. Phys. 1937, 5, 839. (41) Rataiczak, H.: Orville-Thomas, W. J.; Rao, C. N. R. Chem. Phys. i9?6,17, i 9 i . (42) Rao. C. N. R.:Dwivedi, D. C.: Rataiczak. H.: Orville-Thomas, W. J. J. Chem. SOC.,Faraday Trans. 2, 1975, 71, 955.
(43) Williams, E. A.; Cargidi, J. D.; Larochelle, R. W. J. Organomet. Chem. 1976, 108, 153.
\
-
B
-H-
A
/
Figure 5. Schematic representation of electron flow upon H-bond formation.
Si to H, and A1 to H (indicated by a solid arrow). These effects further parallel the strength of interaction as given by AE, e.g., the H20 and NH3 differences for I as always being less clear-cut. In line with these strengthening and weakening effects, it would be interesting to investigate experimentally eventual shifts in the framework vibrations upon interaction with donor molecules. Again, for a given electron donor, all bond strengthening and weakening effects are more pronounced in I1 than in I. Turning now to the effects in the donor molecules, NH, and H 2 0are expected to show a similar behavior as the electron flow occurs from the hydrogen atoms to the more electronegative N and 0,leading to a decrease in overlap population (this is however also already predicted by Gutmann's first rule, Le., bond lengthening of all bonds adjacent to the site of interaction). This turns out to to be true except for the complex between I1 and HzO, where the O H overlap population is almost constant. On the other hand, in CO, the electron flow occurs in the direction of the more electropositive atom and an increase of the bond strength is calculated (increase from 0.4375 to 0.4454 in I and 0.4616 in 11, respectively). This indicates that Gutmann's first rule no longer applies, since the CO bond is also adjacent to the site of interaction. The calculated and observed bond strength evolution is however still in agreement with the second rule. For the large majority of H-bond complexes, the electron flow in bonds adjacent to the H bond will occur in the direction of the more electronegative atom, leading to bond lengthening. In the notation of Figure 5b, A will usually be more electronegative than H (typical cases C, N, 0, and F), and the atoms bound to B (typical cases 0 and N ) are usually more electropositive than B. The CO donor, attacking through its C lone pair, is indeed an exceptional situation. Bond strengthening is expected for these cases in which the back-donation from the electron acceptor is not too strong. This is confirmed by various theoretical and experimental results where the back-donation effects are minimal. Angell and Shaffer4 found CO vibration frequencies of 2213 cm-' for CO adsorbed on Mg-Y and 2205 m-' when adsorbed on Mg-X, both values being appreciably larger than the isolated gas-phase frequency of 2169 cm-'. This trend was confirmed in our previous theoretical studies at the more approximate C N D 0 / 2 For the CO overlap population in the complex between a faujasite-type six-ring at site 11, with a Mg2+ in the center and CO adsorbed, we found an increase of the CO overlap population from 0.98 to 1.04 (data not included in ref 46). More elaborate force constant calculations at C N D 0 / 2 and STO-3G (44) Angell, C.L.;Shaffer, P. C. J . Phys. Chem. 1966, 70, 1413. (45) Mortier, W. J.; Geerlings, P.; Van Alsenoy, C.; Figeys, H. P. J . Phys. Chem. 1979.83, 855. (46) Mortier, W. J.; Geerlings, P. J. Phys. Chem. 1980, 84, 1982. (47) Geerlings, P., unpublished results.
5758
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
TABLE 111: Calculated EHT Equilibrium Distances (Angstroms) for the Model Svstems
Si-0
0-H Si-0 AI-0
I‘P
I’,
1.615 0.970
1.589 1.780
I I’
11‘.
II‘,
1.608 1.816
1.621 1.903 1.229
1.610 1.845 1.790
111‘
111‘”
111‘.
1.623
1.638 1.260
1.625 1.795
0-H Si-0 OH
i 1;
Geerlings et al. TABLE IV: CNDO/2-FA Results for Charges on Oxygen and Hydrogen, Overlap Population (90H),and Ionicity of the OH Bond as a Function of the Electronegativity of the Hypothetical Atom L for the Bridging and Terminal Hydroxyls
L electroneg
40
qH
100014n9wl
Terminal OH 0.05 0.096 0.15
-0.5203 -0.5172 -0.5 13 1
0.05 0.096 0.15
-0.5130 -0.5 150 -0.5 17 3
0.0762 0.08 18 0.0855
39.6 42.3 43.9
Bridging OH 0.1380 0.1440 0.1513
70.8 74.2 78.3
Gutmann’s second rule, although the actual effects are rapidly attenuated. These results are summarized schematically in Figure 6. The approach of only one type of donor molecule, NH,, where the effects are expected to be most pronounced, was studied for both types of hydroxyls. In all three cases, the initial intermolecular distance R (Figure 2) was taken as 0.15 nm,which changed to a final nitrogen-oxygen equilibrium distance ( R r ) on the order of 0.28 nm. (The 0-N equilibrium distance derived from the ab initio study for the same geometry turned out to be 0.2836 nm for I and 0.2720 nm for 11, respectively.) For terminal hydroxyls (I’, to 1’, transition), the Si-0 bond adjacent to the site of interaction decreases significantly (approximately 0.003 nm). The overall evolution of the bond lengths is again in agreement with Gutmann’s predictions. However, the comparison of these results does not allow the investigation of the third rule, i.e., for a different coordination of the oxygens in the hydroxyls of the bridged and terminal type. In the three cases, the calculations suggest a deprotonation of the model molecules and the formation of NH4+. It must be emphasized that the final iterations are performed outside of the validity range of the PO*-ROH relation. The first iteration however, which proceeds within the validity range, strongly indicates a more rapid change of roH for the bridging O H (Ar = 0.014 nm) than for the terminal O H (Ar = 0.007 nm). CNDOIZ-FA. The equilibrium OH distance for two molecules corresponding to terminal ((OL),-Si-O-H; Si--H angle 1loo) and bridging ((OL)3-Si-OH-A1-(OL)3; Si-0-A1 angle 140O; T-0-H angle 1loo) hydroxyls, respectively, was calculated from the variation of the total energy vs. the 0-H distance. Equilibrium distances of 104.0 and 105.1 pm were found respectively. For these configurations, the electronegativity of L was varied from 0.05 to 0.15, respectively (for comparison: 0.096 is the recommended value for aluminosilicates, and 0.2637 the original value for H). The charges are given in Table IV. Table IV indicates a general agreement with the foregoing calculations. As shown in the ab initio part, the ionicity of the bond is a good indication of the differences in acidity of these model molecules which correlates with the bond strength, and may be quantified by the product of the charges on oxygen and hydrogen (also included in the same table). The variation of this product allows an analysis of the influence of the framework composition (as modeled by the electronegativity of the hypothetical atoms) on the intrinsic properties of these hydroxyls. A first observation which is in line with the general picture is that the ionicity of the O H bond is consistently larger for the bridging hydroxyls than for the terminal hydroxyls. If it is plotted against the electronegativity parameter, it is furthermore observed that the sensitivity toward the composition is also much larger for bridging hydroxyls than for terminal O H (change in ionicity of 4.3 vs. 7.5 units for the same change in electronegativity of L). The ionicity consistently increases with increasing electronegativity in both cases. How do the observations comply with these model calculations? The higher ionicity of the bridging O H bond is in agreement with the lower stretching frequency of the bridging hydroxyls (around 3650 cm-I) vs. the terminal OH (3745 cm-I). The O H stretching frequency for the bridging OH however strongly depends on the
+
H+
111;
Figure 6. Electron flow and bond length variation upon protonation of the model systems 11’ and 111’ (EHT).
.
in the Mg2+. .CO system confirmed the bond strength increase; an increase in the CO force constant was calculated by both methods, the STO-3G values before and after interaction being 2458 and 2657 N m-’. We finally remark that when CO approaches the Mg2+cation through the oxygen lone pair, a ”natural” electron flow to the more electronegative 0 is expected, leading to a decrease in bond strength (STO-3G force constant decreases to 1949 N m-*). Our results on the C O complexes are also an ab initio confirmation of the recently published more approximate CND0/2 calculation by Beran: 48 the interaction of the C O group with a hydroxyl group of a faujasite type cluster was shown to occur preferentially via the carbon lone pair, leading to an increased Wiberg bond order, indicating bond strengthening upon interaction. EHT. Two series of calculations have been performed: the protonation of the model systems 11’ and 111’ forming 11’, and III’,, and subsequently the approach of NH3 on all three protonated systems. A study of the protonation was indeed required for determining the equilibrium 0-H, AI-0, and Si-0 bond lengths before the study of the adsorption complex. The results are given in Table 111. The main interest of the results given in Table I11 is their relative values. In this way, the comparison of the first two columns in Table I11 illustrates the effect of the protonation on 11’ and 111’. A significant lengthening of the bonds adjacent to the site of interaction is found. This effect is more pronounced for A1-0 than for Si-, which is indicative for a higher sensitivity of the weaker A1-0 bond. The variation of the bond lengths further in the molecule (distances not reported) are all in agreement with (48) Beran, S. J . Phys. Chem. 1983, 87, 5 5 . (49) Sanderson, R.T. “Chemical Bonds and Bond Energy”, 2nd ed.; Academic Press: New York, 1976.
