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Modelling the Chemistry of Zeolites by Computer Graphics.

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Modelling the Chemistry of Zeolites by Computer Graphics**
By Subramaniam Ramdas, John M. Thomas*, Paul W. Betteridge,
Anthony K. Cheetham, and E. Keith Davies
The unique structural, adsorptive, and catalytic properties of zeolites are particularly amenable to illustration by computer (especially color) graphics. The siting of cations, the accommodation of guest reactant or product species, as well as the occurrence of various kinds of
intergrowths (e.g. twin planes and coincidence boundaries) within these microporous solids
can all be effectively portrayed by graphical means in such a manner as to emphasize the
shape-selective character of the host zeolite. The dynamics of translational and angular motion of guest species (for example benzene) in a channel of molecular dimensions within a
typical zeolitic solid (for example silicalite) can also be probed interactively using appropriate potential functions.
[*] Prof. Dr. J. M. Thomas, Dr. S. Ramdas
Department of Physical Chemistry, University of C a d ridge
Lensfield Road, Cambridge CB2 IEP (UK)
Dr. A. K. Cheetham, P. W. Betteridge, Dr. E. K. Davi s
Chemical Crystallography Laboratory, University of 0. ford
9 Parks Road, Oxford 0x1 3PD (UK)
[**I The defect structure simulations outlined in Section 3 w :re displayed on
a Sigma 5684 raster graphics terminal linked to an IBM 3081 computer,
using locally written routines. The calculations described in Section 4
were carried out using the CHEMGRAF suite of programs on a VAX
11/750 computer (E. K. Davies: CHEMGRAF User Manual, Chemical
Crystallography Laboratory, University of Oxford, Oxford, U K 1984). A
Sigma 5688 raster graphics terminal was used to display the results,
which were photographed directly from the terminal.
Angew. Chem. Int. Ed. Engl. 23 (1984) 671-679
1. Introduction
Zeolites were discovered more than two hundred years
ago. They have been used for decades as water softeners
and cation exchangers, as well as vehicles for the separation of molecules according to shape and size. In addition
to their use as molecular sieves, they have, since the midsixties, been extensively employed as industrial catalysts”],
and, of late, highly siliceous variants of zeolites have led to
important new developments in shape-selective heterogeneous catalysis‘’’.
0 Verlag Chemie GmbH, 0-6940 Weinheim, 1984
0570-0833/84/09(19-0671 $02.50/0
67 1
Zeolites can be described by the general formula
m H 2 0 , where the cations M of valence n neutralize the charges on the aluminosilicate framework, which in turn is composed of corner-sharing Si04
and A104 tetrahedra. The linkages between these units
generate cages or pores of molecular dimensions (3 to 8
in diameter). Their surface area, which lies largely within
the bulk, is typically 500 m2 g-I. The neutralizing cations
are located in more or.less well defined sites in the various
cavities that exist within the structure, and the water molecules fill up the voids; the water can be expelled upon
heating and evacuation. In view of their exceptional porosity, the process of cation exchange in zeolites takes place
very readily. Likewise, they permit facile movement of
small neutral molecules into or out of the bulk structure.
By adjusting the valency and the size of the exchangeable
cation, the sieving and separation processes can, as it were,
be fine tunedC3].Moreover, by increasing the silicon to aluminum ratio of the macro-anionic framework by dealumination14j, the microporosity can be further enhanced. Introduction of hydrocarbons is easier when the Si/AI ratio of
the dehydrated framework is higher, not only because
there are fewer exchangeable cations but also because the
framework itself becomes progressively more hydrophobic
(i.e. more oleophilic) as aluminum is eliminated. A further
advantage possessed by these structures is that Br~nsted
acid sites, one type of which may be rather crudely represented as
are distributed quite uniformly throughout the structure.
These are active sites for many catalytic reactions involving hydrocarbons; and since they are situated at internal
surfaces accessible to reactant species, many subtle, shapeselective chemical conversions can be carried out using
zeolitic catalysts.
In order to understand all the various nuances of structural chemistry exhibited by zeolites, it is often essential to
construct appropriate models which, inter alia, emphasize
the framework topology and the shapes and sizes of the
cavities and tunnels. A beautiful illustration of such models of some of the zeolites has been shown by Sten Andersson in his review on the description of complex inorganic
crystal structures[51.Although such models are invaluable
for visual comprehension, their construction is usually
time consuming and they often have real limitations. For
example, a satisfactory representation of the extra-framework cations is difficult using conventional modelling
techniques, but the chemistry of zeolites is intimately
linked with the locations of these ions. This is one respect
in which computer graphics can play a useful role. But we
can go much further than merely providing effective illustrations for the understanding of structures. A computer
model can readily be manipulated to permit examination
of various structural features; for instance, the locations of
the cations can be rearranged, suspected order-disorder
phenomena in the cation sublattice can be monitored, and
defects of various kinds can be introduced. Furthermore,
calculations of the interaction energies can be performed,
provided suitable theoretical models exist, to monitor the
energetics of various operations that simulate the physicochemical aspects of adsorption, diffusion, etc. For example, interaction energies between the zeolite framework
and a guest molecule can be investigated using such procedures. We shall describe computer simulations that combine a facility for carrying out “experiments” (some of
which are, as yet, impossible with real substances) with a
powerful method for displaying and evaluating the results.
The possibilities of computer modelling and graphics have
been nicely appreciated in other areas of chemistry. For
example, in the last few years, pharmacologists have been
quick to capitalize on the scope and utility of these techniques in the design of drugs[6a1and other biologically important
In this paper, we provide an introduction to the application of computer graphics to the study of some problems
in zeolite chemistry, and in so doing we outline some of
the more significant results obtained to date. Three aspects
of computer graphics are emphasized:
1. The provision of clear illustrations depicting many
features of zeolitic structures determined by X-ray
2. More sophisticated applications, such as the modelling of possible intergrowths, twinning, and other
planar faults of the kind commonly encountered
among zeolites.
3. Dynamic simulation of interactions between organic
molecules and the framework.
Such studies provide novel and convenient methods for
probing the behavior of zeolitic catalysts under conditions
quite close to those used in catalytic reactions. Although
we will give typical examples of reactant and product
shape-selectivity, we expect that suitable extension of these
techniques will allow one to investigate even the “transiin real
tion state” selectivity of reaction intermediate~[~],
2. Color Illustrations of Zeolite Frameworks
2.1. Zeolites X and Y
Zeolites X and Y are structurally analogous to the mineral faujasite. The building units are truncated octahedra,
also known as sodalite cages, B-cages, or tetrakaidecahedra
(the three terms are synonymous), which are linked to adjacent cages via hexagonal biprisms, thereby yielding
larger “supercages”, also known as a-cages (Fig. 1). The
principal sites for the extra-framework cations are known
as the S(I), S(I’), S(II), and S(I1’) sites. The Si-0-A1
framework and the locations of the principal cation sites
are shown in Figure I, from which we can readily grasp the
significance of the occupancy factors reported for the various sites. The features to be noted are: (i) adjacent S(1)
and S(1‘) sites are not simultaneously occupied by cations,
whereas almost all the S(I1) sites in the wall of the supercage are occupied; (ii) cations preferring higher coordination numbers usually occupy the S(1) sites. The tetrahedral
Angew. Chem. Inr. Ed. Engl. 23 (1984) 671-679
clustering of S(I1’) sites within the b-cage precludes any
significant occupancy.
Fig. 1. Faujasite framework (oxygens not shown) with principal cation sites.
Whereas, sites S(1’) and S(I1’) are within the p a g e s , S(1) and S(I1) are in the
hexagonal biprisms and the supercages, respectively. In addition, there are
cation sites which are also known to be in the supercages.
New methods of achieving the isomorphous replacement of aluminum by silicon[41have made it possible to
render a zeolite cavity or channel relatively free from cations. As mentioned earlier, this changes the zeolite’s affinity towards neutral organic molecules by increasing the
free space available and also by enlarging the channel size;
there is also a reduction in the polarity of the zeolite. As a
typical example, in Figure 2 (top) we show an ethane molecule within the supercage in zeolite Y. The 12-membered
ring entrance to the a-cage is wide enough to accommodate a large organic molecule, for example azoisobutyronitrile (AIBN). The introduction of molecules like AIBN is
interesting because of the possible photogeneration of radicalsL8’that recombine to yield the tetramethyl dinitrile
with loss of N2. Preferential formation of this product over
other unsymmetrical ones[91is a possibility because of the
restricted rotation and translation of the trapped radicals
within the supercage. This is reflected in Figure 2 (bottom),
where the least squares best plane projection of AIBN
gives a maximum “van der Waals length” of 8.9 which
Also, the
is within the diameter of the supercage (9.2
“maximum overlap projection” of the molecule has a
diameter of 6.2
well within the 7 aperture (shown in
Figure 2b).
2.2. Zeolites A and ZK-4
The structure of zeolite A is also made up of connected
sodalite cages, but in this case the tetrakaidecahedra are
linked via cubes rather than hexagonal prisms. The locations of the extra-framework cations in the K’-form[’ol of
zeolite A are shown in Figure 3. This clearly shows that the
‘blue’ cations occupy most of the centers of the six-membered rings (0 atoms (red) not counted), slightly altering
Angew. Chem. Int. Ed. Engl. 23 (1984) 671-679
Fig. 2. The molecules. (top) ethane and (bottom) azoisobutyronitrile within
the supercage of the faujasitic framework. For clarity, the twelve-membered
ring opening to the supercage is alone shown in the bottom picture, with Si
and 0 colored in magenta and red (in their van der Waals radii), respectively.
the kinetic diameter of the channels and reducing the free
volume of the supercage. In addition, the large “blue” cations block the eight-membered ring channels. One way of
altering the zeolite to allow hydrocarbon molecules to diffuse through is to replace the monovalent cation by a divalent ion such as strontium. Not only is the number of
ions required to neutralize the framework charge halved,
but also the remaining ions tend to occupy the sites in the
six-membered ring windows leaving the channels free. Alternatively, and preferably, one may increase the silicon to
aluminum ratio, as in the zeolite ZK-4, which has a framework structure the same as that of zeolite A but with a
Si/AI ratio of at least 2.5. Zeolite ZK-4, therefore, requires
fewer cations than zeolite A to balance framework charge,
leading to freer channels. A straight chain hydrocarbon
can diffuse relatively freely through such channels.
This shape-selectivity of zeolites for some reactant and
product molecules, which is responsible for their novel catalytic role, rivaling that of certain enzymes, can be proved
effectively with computer graphics. In Figure 4 we show
the other hand, branched hydrocarbons are trapped inside
the channel intersections and undergo further isomerization to yield the above-mentioned products selectively.
Similarly, the fraction of p-xylene in xylene mixtures can
be increased. Figure 5 also shows how acid sites on the
surface with large pores and cavities can be effectively
blocked by 4-methylquinoline, leaving only the bulk acid
sites available to smaller bases that diffuse through the
3. Modelling of Defects and Intergrowth Phenomena
3.1. The Zeolites ZSM-5 and ZSM-11
Fig. 3. The framework and the cations in the K“-form of zeolite A. Red: 0,
yellow/light blue: WAI, dark blue (small and large): cation sites. The network covering the van der Waals surface is shown, with a molecule of ethane
in the channel. To permit adsorption and diffusion of this molecule, the K“
ions blocking the eight-membered rings must be removed. This is effected
either by increasing the W A I ratio (thereby decreasing the number of exchangeable cations per unit-cell, as in ZK-4) or, for a fixed Si/AI ratio, by replacement of monovalent by divalent ions.
the ease with which a methanol molecule can diffuse
through the straight channels of the zeolite ZSM-5, yielding products including n-alkanes in the gasoline range. O n
In addition to the illustrative capability that we have described so far, computer simulations can be used to test
various structural hypotheses and to check suggested models against the observed results, particularly in the electron
microscope. Electron microscopy is probably the most direct technique for identifying intergrowth phenomena in
crystalline solids. One recent success has been the identification of the precise nature of the intergrowths involving
the closely related zeoIites ZSM-5 and ZSM-lIf”l. In both
ZSM-5 and ZSM-11, chains of five-membered ring building units run parallel to the c-axis. The adjacent chains
along a, however, are related by inversion centers (denoted
by i) in ZSM-5 and by mirror planes (denoted by 0)in
ZSM-11. Figure 5 illustrates schematically the presence of
strips of ZSM-11 in a ZSM-5 matrix. In the computer experiment, various models of ZSM-S/ZSM-l 1 intergrowths
can be constructed by invoking mirror or inversion operations. By placing a “dot” at the locations of the silicon or
aluminum atoms, we can create a mask’*] for optical diffraction. The optical diffraction pattern can then be compared with the observed electron diffraction pattern. A
typical example characterizing the nature of a particular
intergrowth of ZSM-5 and ZSM-11 is shown in Figure 6.
3.2. Twinning in Zeolite Y
Similar studies have been carried out on the twinning
across the (1 11) planes in zeolite Y. If every layer of the
(111) planes is twinned with respect to the adjacent layer,
the framework, mask, and corresponding optical diffraction pattern in the [l 111 projection, will be as shown in Figures 7a, b, and c, respectively. The hexagonal symmetry of
the pattern is exactly what one would expect‘”] for the extended defect structure, which incidentally is identical to
that of the zeolite ZSM-3, originally reported by Kokotailo
and Ciri~I’~~.
This can be compared with the results for a n
untwinned zeolite Y shown in Figure 8. In the [ l l l ]projection, even if the twinned layers are juxtaposed between
(111) planes, the diffraction pattern and the mask will be
[*] The ‘mask‘ we refer to is the positive film of the structure of an object
big, 4. Illustration of shape selectivity of ZSM-5. The cross section 0 1 the
straight channel can be compared with the size and shape of the molecules
shown (approximately viewed along their molecular axis). Left, from top to
bottom: methanol, 2,2-dimethylpentane,p-xylene.Right, from top to bottom:
n-pentane, 4-methylquinoline, m-xylene. Yellow: CH,, white: C, pink: N,
red: 0, blue: H.
(Fig. 6a). In an experiment using an optical bench consisting of a laser
source, a series of convergent and diffraction lenses, and a recording medium, optical transformation of this mask produces the diffraction pattern shown in Figure 6b. The advantage of such graphical techniques lies
in the ability to create large supercells of non-periodic defects of the kind
identified here.
Angew. Chem. Int. Ed. Engl. 23 (1984) 671-679
. -. .
. .. .
. . .. ..
.... ,.
Fig. 5. Schematic view, along the b-axis, representing intergrowths between
ZSM-5 and ZSM-I 1 structures. Both these structures are built of five-membered rings forming a chain along the c-axis. Adjacent chains, in ZSM-5 (yellow) are related by centers of inversion, whereas those in ZSM-11 (blue) are
related by mirror planes, perpendicular to the a-axis. The framework remains
continuous despite the presence of these defects.
. . . . . . ,.
.. .. .. .. ..... . . .. .. .. .. .....
. . . .. .* .. .. .. .. . . .
.. .. .. .. .. .. ** ..
. . . .
Fig. 7. a) Framework of the recurrently twinned faujasite. Here twinning occurs at every adjacent (111) plane in the faujasite structure. The resulting
structure is hexagonal and the plane of projection now becomes (OO1)h,,. h)
The mask representing the framework is the same projection but depicting
the location of Si (or Al) atoms, without the bonds. c) The optical transform
of b), the zone axis being [001],.,.
color (Fig. 9) to distinguish the twinned layers. If the twinning had been random, the optical diffraction pattern of
the corresponding model would show streaking along
Fig. 6. a) A non-regular model of ZSM-5/ZSM-II intergrowth of average periodicity a =70 (see text). Adjacent strips along a are related by inversion
centers i or minor planes IS. The typical minor planes IS in ZSM-I 1 are separated from each other by various distances (50, 70, 90 A), which, however,
give a, on average.- b) Optical Fourier transform of a) with the reciprocal
vectors a* and c*, as well as the diffraction orders h and [belonging to the
principal reflections of the determined structure (ao= 18.4 A).- c) The electron diffraction pattern showing the 66 pseudo-periodicity superimposed
on the streaks along [loo].
the same as those in Figure 8, except for differences in the
relative inten~ities“~].
However, viewing along [110] one
can identify the defect regions of the crystal. For a hypothetical case in which every third layer is a twin of the second layer of the (111) planes, the optical mask is shown in
Angew. Chem. Int. Ed. Engl. 23 (1984) 671-679
.... .”. .
Fig. 8. a) Framework of the faujasite structure in the [I 111 projection; b) a
“mask” depicting the locations of the Si (or Al) atoms; c) the corresponding
optical transform of b).
Fig. 9. A hypothetical model of faujasite, viewed along [IlO]. in which twinning occurs at every third layer of ( I 1 I)planes(blue-red-green) running parallel to the vertical axis in the figure.
3.3. Variations in Stacking Sequences
There is a whole family of related zeolitic structures of
similar chemical composition with six-membered rings of
SiO, tetrahedra that are stacked in three different ways (A,
B, and C, see Fig. 10) along the hexagonal c-axis, giving
rise to an almost infinite number of framework structures[’sl. Although, by convention, these structures can be
classified as polytypes, their steric arrangements actually
differ. If only two types of sequences are present in a structure in any order, they will have large open channels in the
c direction, as in offretite (see Fig. 10 (top)). On the other
hand, if all three stacking arrangements are present, there
will be long and short cages, (with 12-membered ring apertures effectively blocked, as shown in Figure 10 (middle))
depending on the precise sequence present; e.g. liottite
and afghanite. I n Table 1 we list some of the known zeolites possessing stacking variations of this kind. Stacking
faults in the parent structures have often been noticed, particularly in high resolution lattice images’’61in the electron
microscope. Depending on the stacking sequence present,
the relative positions of the 8-membered ring apertures in
the [I 101 zone differ and are easily seen in the image, provided the material is electron-beam stable and the zone
axis is accessible.
Table 1. Chabazite family of zeolites with their stacking properties.
Lattice parameters
Fig. 10. Schematic representation of the “chabazite” family of zeolites: top:
“AB” and midd1e:“ABC” stacking sequences viewed along the hexagonal
axis; bottom: The possibility of intergrowths and stacking faults among these
zeolites is shown schematically, viewed on the bc plane.
We have devised a novel method[17] of simulating any
desired stacking sequence, from which we make a direct
comparison with the lattice image. In this way, one may
identify even a n isolated stacking fault in such materials.
Figure 10 (bottom) describes schematically the principle
Angew. Chern. Int. Ed. Engl. 23 (lY84) 671-679
behind such computer experiments. It clearly demonstrates how various zeolites, differing in their ordered sequences, can intergrow with each other. We would particularly like to draw attention to the relative arrangements of
the eight-membered ring apertures resulting from such intergrowths, which, with continuing improvements in technique, will become identifiable in the high resolution
Figure 11. One may note that even though there is a coincidence of lattice there is no coincidence of atomic positions. Figure 11 clearly shows that following the introduction of one such boundary there is a reduction in the number of open channels per unit area (only 8 percent in zeolite L) with a concomitant reduction in the diffusivity of
molecules along [OOl] channels.
3.4. Simulation of Non-Coherent Interfaces between
4. Interaction Energies of Organic Molecules and
There is increasing experimental evidence to suggest
growths of two different, yet related frameworks of zeolitic
structures upon one another. One such piece of evidence
was uncovered by Kerr et al.['*I in the case of zeolite L and
offretite (or erionite) growing across a common interface.
Similar occurrences in the cases of synthetic mazzite and
offretite, and mazzite and zeolite Y have also been observed["]. Simulation of such interfaces requires large periodicities in the growth plane, sometimes in excess of
100 Manipulation of such large unit cells in a graphics
system is probably a convenient way of visualizing the
structural consequences of such phenomena. We give below one specific example, namely the presence of the
d n i n R 3 2 . 2 " coincident lattice in the growth of zeolite L
(see Fig. 11). Similar descriptions apply to the systems
mentioned above["].
The sorption and diffusion of an organic molecule
within the zeolite is primarily governed by the shape and
size of the cages and channels in the framework, and we
have seen the capability of computer graphics in illustrating these aspects. In this section, we describe how an organic molecule can be "guided" through the cavities and
how one can estimate, quantitatively, the energetics involved in such a process. This work is ideally carried out
interactively using a graphics terminal; the movement of
the molecule within the framework and the interaction energies associated with the locations and orientation of the
molecule can be monitored in real time.
In order to calculate the interaction energies, we require
a model that is both reasonably accurate and, for interactive computations, uses relatively fast algorithms. For simplicity we ignore the interactions between the organic molecules themselves, i.e. we consider an infinitely dilute system. Similarly we assume that the framework remains
unaltered by the introduction of the guest molecules.
(There are good physico-chemical reasons for supposing
that some organic molecules will perturb the zeolitic
framework structure. The nature of this perturbation could
itself be monitored by computer graphical methods of the
kind described in this article.)
The model used in this work is a simple empirical treatment of van der Waals energy, with the addition of a n electrostatic term. The expression used for non-bonded atom
pairs is
Fig. 11. Plan view (down [OOl]) of the coincidence boundary
R32.2") generated by rotating one half of the crystal of zeolite "L" about
[OOI]by 32.2" with respect to the other (each vertex denotes a Si or Al site
joined together via oxygens, not shown here). The repeat distances in the
coincident lattice exceeds the original hexagonal mesh (ao= 18.4 by fl,
In the high resolution lattice image of zeolite L in
the [OOl] zone, small domains of lattice periodicity a0m
(ao= 18.4
were frequently observed. Optical diffractograms of the image indicated a near 30" rotation of one
half of the crystal over another. Exact coincidence of the
lattice at the interface, however, occurs at 32.2". A schematic diagram of such a coincidence boundary and its consequence, the overlap of fewer open tunnels, is shown in
Angew. Chem. Int. Ed. Engl. 23 (1984) 671-679
Aexp( - B r ) r"
where A, B, C and D are constants, q , and q2 are the
atomic charges, K is a unit conversion constant, and r is
the distance between the atom pair.
The parameterization of the van der Waals part of this
equation is that due to Del Re et a1.[211,using the coefficients of Kiselev et al![221.Most of the organic molecules of
interest are electrically neutral, but the net charges on the
atoms can be calculated using molecular orbital metho d ~ [ ' ~ Similarly,
theoretical estimates[241of the charges o n
the framework atoms are necessary in order to describe the
electrostatic interactions, which are relatively long range.
The value of the permittivity can be included in the constant K, and in this work a value of unity was used.
The total interaction energy is derived from the sum of
the atom-atom terms, an assumption widely and successfully used in predicting the conformations of proteins and
the packing of molecules in the solid state. A further ap611
proximation has been made to speed up the calculation for
widely separated atoms: the short-range repulsive terms
are ignored, and the attractive and electrostatic terms are
estimated for groups of atoms, rather than for individual
We illustrate the application of the above procedure by
describing results on the adsorption of benzene in silicalite, an aluminum-free zeolite that is isostructural with
ZSM-5. We have chosen this system not only because of its
industrial importance, but also for simplicity, since the calculations are not hampered by uncertainties in the locations of aluminum atoms and extra-framework cations.
The benzene molecule is placed at a suitable starting position within the straight channel of a fragment of zeolite
containing about 3500 atoms (Fig. 12). The interaction energy between the benzene molecule and the silicate framework is then calculated at intervals of 0.4A along the
channel for a range of angular orientations of the molecule
about the two-fold axis of the channel.
Fig. 13. A plot of interaction energy E against distance of travel (from an arfor a benzene molebitrary origin through the entire unit cell length of 20
cule moving along the straight channel direction, h, in silicalite, the pure silica variety of ZSM-5 (cf. Fig. 12), at a fixed orientation, i.e. 6'130".
Fig. 12. A molecule of benzene in the Straight channel of ZSM-5. For the energy calculations, the orientation of the molecule is varied such that the long
molecular axis remains always parallel to the channel axis b. It is the angle 6'
between the short molecular axis and the maximum diameter (in projection)
of the channel that is changed at regular intervals; in this case 8=0".
In a typical calculation, over 1600 values of the interaction energy are stored with the corresponding position and
orientation of the molecule. Figure 13 shows the energy at
a fixed angular orientation as a function of the distance
along the straight channel. A more effective method of displaying these results is in the form of a contour map using
colored regions to represent different energy levels in areas
of the conformational space over which the calculation
was performed. The maps reproduce geometrical features
such as the symmetry of the system, and they also reveal
the restrictions on the movement of the molecule within
the channel. For example, from Figure 14 one readily sees
that facile molecular diffusion along the channel occurs
only for a limited range of angular orientations. The colored contours also show the energy barriers and the
greater conformational freedom encountered at the intersections where the straight and sinusoidal channels meet.
Fig. 14. Adsorption energy contours based on the results of plots like Figure
13 for all possible orientations of 6' graded from positive to negative values in
terms of color codes (black - 10, dark blue -2, marine blue 0, light-green 2,
dark green 4, yellow-green 8, yellow 12, light Flue 16 kcal/mol) are plotted as
a function of 6' (ordinate) and the distance (A) along the h channel. The abscissa values (from left to right) are 60,65, 70, 75, and 80 A; the ordinate values (from bottom to top), -90, -45, 0, 45, and 90".
One of the great merits of using interactive graphics procedures is the ability to freeze these optimum configurations
to allow for more detailed studies, including the influence
of refined potentials and larger segments of the framework. We expect that this approach will play an important
role in future studies on adsorption and diffusion processes in zeolites.
We express our appreciation to many of our colleagues at
Oxford and Cambridge and to the following organizations
who in various ways and at various stages supported parts of
this work: 7'he University of Cambridge, 7'he University of
Angew. Chem. Int. Ed. Engl. 23 (1984) 671-679
Oxford, Exxon, and BP. We are most grateful to our photographic experts, Messrs. E. L. Smith, I . A . Cannell, and N .
F. Cray for their cooperation and skiii.
Received: April 19, 1984 [A 504 IE]
German version: Angew. Chem. 96 (1984) 629
[I] See also: J. A. Rabo: Zeolite Chemistry and Catalysis, ACS Monogr. No.
171, Washington 1976, and references cited therein.
[2] P. B. Weisz, Pure Appl. Chem. 52 (1980) 2091.
[3] D. W. Breck: Zeolite Molecular Sieves, Wiley, New York 1974.
141 a) R. M. Barrer: Hydrothermal Chemistry of Zeolites, Academic Press,
London 1982; b) J. M. Thomas, G. R. Millward, S. Ramdas, M. Audier
in G. D. Stucky, F. G. Dwyer: Intrazeolite Chemistry, ACS Symp. Ser.
No. 218, Washington 1983, p. 181.
I51 S. Anderson, Angew. Chern. 95 (1983) 67; Angew. Chem. Int. Ed. Engl.
22 (1983) 69.
[6] a) J. M. Blaney, E. C. Jorgensen, M. L. Connolly, T. E. Ferrin, R. Langridge, S. J. Oatley, J. M. Burridge, C. C. F. Blake, J. Med. Chem. 25
(1982) 785; b) R. Langridge, T.E. Ferrin, I. D. Kuntz, M. L. Connolly,
Science 211 (1981) 661.
[7] E. G. Derouane in M. S. Whittingham, A. J. Jacobson: Intercalation
Chemistry, Academic, New York 1982, p. 101.
[S] A. B. Jaffe, D. S. Malarrent, E. P. Slisz, J. M. McBride, J. Am. Chem.
SOC.94 (1972) 8515.
[9] L. J. Johnston, P. de Mayo, S. K. Wong, J. Chem. SOC.Chem. Commun.
1982, 1106.
[lo] J. J. Pluth, J. V. Smith, J. Phys. Chem. 83 (1979) 741.
[ I l l G. R. Millward, S. Ramdas, J. M. Thomas, M. T. Barlow, J. Chem. SOC.
Faraday Trans. 2 79 (1983) 1075.
[12] M. Audier, J. M. Thomas, J. Klinowski, D. A. Jefferson, L. A. Bursill, J.
Phys. Chem. 86 (1982) 581.
I131 G. T. Kokotailo, J. Ciric, Adu. Chem. Ser. 101 (1971) 109.
[I41 G. R. Millward, J. M. Thomas, S. Ramdas, M. T. Barlow, Proc. 6. I n t .
Zeolite ConJ, Reno, NV, U S A 1983, in press.
[IS] R. Rinaldi, H. R. Wenk, Acta Crystallogr. Sect. A35 (1979) 825.
[I61 G. R. Millward, J. M. Thomas, J. Chem. SOC. Chem. Commun. 1984,
(171 G. R. Millward, S. Ramdas, J. M. Thomas, unpublished.
I181 1. S. Kerr, J. A. Gard, R. M. Barrer, I. M. Galabova, Am. Mineral. 55
(1970) 441.
[I91 0. Terasaki, G. R. Millward, L.-X. Sheng, J. M. Thomas, unpublished
[20] 0. Terasaki, J. M. Thomas, S. Ramdas, J. Chem. SOC.Chem. Commun.
1984, 2 16.
[21] G. Del Re, E. Gavuzzo, E. Giglio, F. Leij, F. Mozza, V. Zappia, Acta
Crystallogr. Sect. 833 (1977) 3289.
[22] A. V. Kiselev, P. Q. Du, J. Chem. SOC.Faraday Trans. 2 77(1981) 17.
1231 GAUSSIAN 80 (QCPE 4061446): J. S. Binkley, R. A. Whiteside, R.
Krishnan, D. J. DeFrees, H. B. Schlegel, S. Topiol, L. R. Kahn, J. A. Pople, Department of Chemistry, Carnegie-Mellon University, Pittsburgh,
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On Stars, Their Evolution and Their Stability
(Nobel Lecture)**
By Subrahmanyan Chandrasekhar"
1. Introduction
When we think of atoms, we have a clear picture in our
minds: a central nucleus and a swarm of electrons surrounding it. We conceive them as small objects of sizes
measured in Angstroms (- lo-* cm); and we know that
some hundred different species of them exist. This picture
is, of course, quantified and made precise in modern quantum theory. And the success of the entire theory may be
traced to two basic facts: first, the Bohr radius of the
ground state of the hydrogen atom, namely
- 0.5 x lo-* cm
where h is Planck's constant, m is the mass of the electron,
and e is its charge, provides a correct measure of atomic
dimensions; and second, the reciprocal of Sommerfeld's
fine-structure constant,
[*I Prof. Dr. S. Chandrasekhar
The University of Chicago
Chicago, 1L 60637 (USA)
I**] Copyright 0 the Nobel Foundation 1984.-We thank the Nobel Foundation, Stockholm, for permission to publish this article.
Angew. Chem. Inf. Ed. Engl. 23 (1984) 679-689
gives the maximum positive charge of the central nucleus
that will allow a stable electron-orbit around it. This maximum charge for the central nucleus arises from the effects
of special relativity on the motions of the orbiting electrons.
We now ask: can we understand the basic facts concerning stars as simply as we understand atoms in terms of the
two combinations of natural constants (1) and (2)? In this
lecture, I shall attempt to show that in a limited sense we
The most important fact concerning a star is its mass. It
is measured in units of the mass of the sun, 0 , which is
g; stars with masses very much less than, or very
much more than, the mass of the sun are relatively infrequent. The current theories of stellar structure and stellar
evolution derive their successes largely from the fact that
the following combination of the dimensions of a mass
provides a correct measure of stellar masses:
H2 -
where G is the constant of gravitation and H is the mass of
the hydrogen atom. In the first half of the lecture, I shall
essentially be concerned with the question: how does this
come about?
0 Verlag Chemie GmbH. 0-6940 Weinheim, 1984
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chemistry, zeolites, modellina, computer, graphics
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