12670
J. Phys. Chem. 1994,98, 12670- 12678
Local-Mode Analysis of Complex Zeolite Vibrations: Sodalite Karthik A. Iyert and Sherwin J. Singer* Department of Chemistry, The Ohio State University, Columbus, Ohio 43210 Received: November 5, 1993; In Final Form: August I , 1994@
We have developed a systematic procedure to analyze vibrational motions in complex molecules and solids with large unit cells. This procedure, based on group theoretical arguments, has been used to analyze the normal modes of sodalite. We find that certain linear combination of normal modes are strongly spatially localized on the secondary building units (SBUs) of this zeolite. Further, some of these local motions are combinations of weakly coupled normal modes. This analysis leads us to believe that many of the normal modes can indeed be uniquely associated with the SBUs of sodalite.
1. Introduction Zeolites are microporous aluminosilicates containing cavities and channels. These are technologically important materials because of the ability of these cavities to play host to a variety of chemical transformations. The primary commercial applications of zeolites are as ion exchangers,’ molecular sieves,2and catalyst^.^ In each of these cases the framework topology plays a crucial role. The natural experimental probe of the potential surface governing zeolite framework motions is vibrational spectroscopy. Infrared and Raman spectroscopists commonly assign vibrational bands to local topological features of a zeolite framework: rings, polyhedra, et^.^-' However, the observed transitions involve excitations of phonon normal modes (Figure 1) which are highly delocalized in character. The extent to which the association of local topological features with particular normal modes is justified and can be made systematic is the subject of this paper. As has been noted by others: the major obstacle in comparing experimental and theoretical vibrational spectra of complex zeolitic solids is the small number of observed vibrational features. This is caused by either low intensity or failure to resolve bands. Our local-mode analysis cannot remedy this situation, but it can give additional clues by which calculated phonon modes can be physically characterized and assigned to observed spectral features. Often several calculated vibrational modes of the proper optical activity lie within reasonable theoretical “error bars” of each IR or Raman peak observed in complex zeolites. To date, the only tools available to select the calculated phonon mode for comparison with experiment are estimates of the spectral activity based on crude models whose reliability is not well calibrated. As a result, the search for a definitive analysis of zeolite framework vibrations continues, as gauged by the number of recent attempts,6-17 even though many analyses have provided simulated spectra in similar agreement with experiment. For example, at least five different models for the vibrational spectra of sodalite,4J2-16 the subject of the present work, have been proposed, each producing IR and Raman spectra in at least qualitative agreement with experiment. Clearly, several issues remain unresolved even aftcr a simulated vibrational spectrum in qualitative agreement with experiment is obtained. These issues involve assignment of vibrational features to local structural units, and a related issue, the validity of correlating features from the spectra of different t Present address: Department of Chemistry, University of Cincinnati, Cincinnati, OH 45221-0172. Abstract published in Advance ACS Abstracts, October 15, 1994. @
0022-3654/94/2098- 12670$04.50/0
Figure 1. Example of a complex and spatially delocalized normal mode of sodalite at 247 cm-’, calculated from the shell model potential of van Santen et a1.12 The motion of individual atoms in the sodalite cage is depicted by “arrows” that point in the direction of motion. The amount each atom has been displaced is indicated by the length of the arrows which has been exaggerated for clarity. However, the relative displacement of atoms with respect to each other has been preserved.
zeolites which contain a common secondary building unit. These are issues which can be explored in a systematic fashion using the tools described in this and a companion study of zeolite-A.18 The aluminum content of many zeolites is variable. In some cases the aluminum fraction can be brought down to zero19 to produce the “all-silicon” form of the material, a silicate. These “all-silicon” zeolites are the simplest examples to discuss. Therefore we treat silica sodalite (Figure 2) as an example in this paper and an all-silicon model of zeolite-A in an accompanying work.18 For a substantial fraction of the normal modes of sodalite and zeolite-A we find a strong correlation with particular local features of the framework. Zeolite frameworks can be broken into local units in various ways.2o Chains and layers typify the largest units commonly discussed. The smallest such unit is the TO4 (T = Si, Al) tetrahedron, the so-called primary building unit (PBU). At the next level above the primary tetrahedra are the secondary building units21*22 (SBUs) which include rings, double-rings and small polyhedra. This decomposition is not unique. For example, sodalite (Figure 2) can be viewed as built from 4-rings 0 1994 American Chemical Society
Complex Zeolite Vibrations: Sodalite
Figure 2. Model of sodalite. The truncated octahedral sodalite units can be decomposed into either 4-Ror 6-RSBUs. A complete sodalite cage, formed by two unit cells, is depicted.
(4-R’s) or 6-rings (6-R’s). We will focus on the association of normal modes to the larger of the basic units, the SBUs. The primary and secondary building units are the usual point of departure for assignment of vibrational spectral features. Lygin et al.23-25were among the first to study zeolite vibrations as a function of the SUA1 ratio, cation type, and state of hydration in a series of X and Y zeolites. In the mid-infrared region (400-800 cm-l), they assigned spectral features to intrutetrahedral and more complex intertetrahedral vibrations. After studying a large number of zeolites, Flanigen et a1.6 classified the vibrations in the mid-infrared region into two categories. The first category, which they noted were insensitive to variations in framework structure, were assigned to motions of PBUs. Modes that were sensitive to framework structure were attributed to SBUs. Ariai and Smith26used the modes of the TO4 molecule as a basis to assign peaks in the Raman spectra of sodalite. With the aid of the calculations of Blackwel17 and No et a1.8 and their own Raman studies of the zeolite-A framework with different SUA1 ratio, Dutta and Barco’O were able to make specific assignments. These related to stretches and bends of not only the PBUs but also motion predominantly associated with the SBUs. In later studies Dutta et al.lO*llfound that bands in the Raman spectra in the 300-600 cm-l region were sensitive to framework topology and were a good indicator of ring size. A more detailed analysis of their study is presented in the accompanying work. l8 The search to associate vibrational modes with local structural features of zeolites has continued in two very recent works. Creighton et al.4 devised a force field which reproduces most of the main features of sodalite vibrational spectra. They analyzed the normal modes obtained from their force-field model by projecting those normal modes onto bending and stretching coordinates which are symmetry-adapted to locul structural units. Our procedure is related to the analysis of Creighton et al. but relies on fewer assumptions on the nature of the local motions and yields more information. Our results are compared to those of Crieghton et al. below. Bartsch et obtained vibrational spectra and from that data obtained a force field for the octahydridosilasesquioxanefragment H8Si8012, a model for the double 4-ring (D4-R) unit found in zeolite-A. Despite frequent attempts to associate crystal normal modes with local structure features, no consensus on these assignments has emerged and the general validity of these assignments has been q~esti0ned.l~Models using the normal modes of small fragments as a basis to assign more complex zeolitic modes can qualitatively differentiate normal modes with regard to .
J. Phys. Chem., Vol. 98, No. 48, 1994 12671 stretching or bending character. However, fragment models are too crude to give precise associations of normal modes with specific topological features of the framework. Using the To4 tetrahedra as the basic unit, Sen and developed a simple coupled oscillator model to interpret the lattice dynamics of amorphous silica between 300 and 1200 cm-l. They demonstrated that as the T-0-T angle changes from 90” to 180°, the molecular normal modes corresponding to those of To4 become less useful. A T-0-T angle of 90” corresponds to no coupling between adjacent tetrahedra and 180” corresponds to maximum coupling. The T-0-T angle in zeolites usually varies between 140” and 160”. van Santen and Voge128used T-0-T as the basic unit, and this model was later extended to T(OT)4 units. They used a strongly coupled Bethe lattice model to generate vibrational density of states for threedimensional systems composed of these basic units. As with earlier studies, they only had partial success in assigning bands found in nuclear, Raman, and IR spectra of zeolites. de Man and van Santen15 have questioned whether associations can be made between normal modes and local topological features. They searched for correlations of normal modes with SBUs by (i) comparing spectra of subclusters with that of the crystal, (ii) comparing atomic displacement of subclusters in zeolite crystals with isolated fragments, and (iii) constructing difference spectra of species with and without particular SBUs. Finding no such evidence, they concluded that “No general theoretical basis for the correlation between the presence of large elements and spectral features, sometimes reported, is found to exist”.15 Our goal is to provide a systematic procedure for assigning normal modes to local structural units. Before analyzing complex zeolite structures, we reflect back to what constitutes a vibrational “assignment” for small molecules in section 2. Since assignment is a step in human understanding of data, it is perhaps not surprising that we do not find a unique answer to this question. Nevertheless, useful but not unique criteria for localization do exist. In fact, there are strong parallels with localized orbital theory in quantum chemistry and measures of localization developed for electronic wave functions in disordered systems. The discussion of these connections in section 2 may be skipped by readers not interested in these issues. In section 3 we describe a group theoretical procedure for associating normal modes with local structure. Finally, in section 4 we present results and discussion for a relatively simple example, sodalite. Zeolite-A, a more challenging case, is treated in an accompanying paper.lg
2. Criteria for Localization A normal mode can be viewed as a linear combination of relatively simple motions. Cartesian atomic displacements are the most primitive coordinates used to form normal modes. Normal modes composed of internal coordinates, such as stretching, bending, torsion, etc., are of greater physical significance. Normal modes in molecules, small and large, are typically assigned to these internal coordinates. For small molecules, such as water and ammonia, this task is trivial, and the partitioning of their normal modes into stretches and bends is hardly controversial. For complex molecules or crystals with large unit cells there is evident difficulty in making assignments. Therefore we pause to consider what is meant by a vibrational “assignment” in small molecules for guidance in larger, complex systems. We observe that there are at least two ways in which a normal mode is said to be assigned to a particular structural feature. In the first sense the normal modes can be written, to a good approximation, as a linear combination of a very restricted set
12672 J. Phys. Chem., Vol. 98, No. 48, 1994 of intemal coordinates, with little contribution from other intemal coordinates. For example, certain normal modes of benzene are assigned as symmetric or antisymmetric “C-H stretches” because these normal modes are almost exclusively linear combinations of the C-H bond distance intemal coordinates. There is a second meaning that a vibrational assignment sometimes conveys, that of weak coupling between local motions. The local motions assigned to the normal modes are good zero-order normal modes in the sense that the frequencies are not significantly shifted from the frequencies of the uncoupled local modes. The second meaning is exemplified by many of the vibrational modes of the stilbene molecule:29
Most stilbene modes are grouped in narrowly split doublets which represent weakly coupled motions localized on each of the phenyl rings of the molecule. Each doublet consists of one symmetric and one antisymmetric linear combination of two symmetry-related local modes concentrated on each of the rings. Just as many normal modes of stilbene are decomposable into linear combinations of weakly coupled ring motions, we also find that many of the normal modes of sodalite and zeolite-A are decomposable into linear combinations of weakly coupled motions on secondary building units. Naturally, the notion of “vibrational assignment” does not have a technical definition in the same sense as, say, “normal mode”. We have given an admittedly subjective account or two meanings carried by the notion of vibrational assignment. Hopefully, there is significant overlap between these definitions, which are our starting point for quantitative analysis below, and what others may constitute as a vibrational assignment. The second meaning carried by a vibrational assignment is more restricted than the first. Not only are the normal modes decomposable into particular local motions, but these local motions are weakly coupled as well. As mentioned above, many of the local modes of sodalite and zeolite-A satisfy the second, more restrictive notion of weakly coupling, in addition to the primary criterion of decomposability into local motions. The hope underlying vibrational analyses of fragments from the crystal lattice is that the full normal modes are linear combinations of weakly coupled fragment motions. However, results indicate that the fragment potentials do not provide an adequate description of the full crystal.30 Our local-mode analysis may be regarded as a generalization of the fragment approach in which couplings between the fragments in the full crystal are retained. Large molecules or crystals with large unit cells are too complicated for assignments to be made by inspection. We seek a procedtre that yields a small (
