79
Hypothetical molecular sieve frameworks
Jacek Klinowski
There are various ways to describe the frameworks of
molecular sieves and their enumeration. As the number of
possible three-dimensional 4-connected nets is infinite, all
enumerations reported so far have been derived by empirical
methods, although many interesting and potentially viable
structures, particularly with low framework density (rich in 3-
and 4-membered rings), have been found as a result. It is likely
that recent progress in mathematical tiling theory will lead to
new advances in systematic enumeration not only of molecular
sieves, but also of a variety of chemical structures.
Addresses
Department of Chemistry, University of Cambridge, Lensfield Road,
Cambridge CB2 1EW, UK; e-mail: jkl &@cam.ac.uk
Current Opinion in Solid State & Materials Science 1998,
3:79-85
Electronic identifier: 1359-0286-003-00079
0 Current Chemistry Ltd ISSN 1359-0286
Abbreviations
FD framework density
SBU secondary building unit
T-atoms Si. Al and P atoms
Introduction
The contrast between the small number of physical laws
and the enormous number of structures to which these
laws give rise is an intriguing aspect of the natural world.
The handful of rules of chemical bonding results in many
thousands of crystalline inorganic compounds with a bewil-
dering number of different structures, even when only a
few chemical elements are involved. For example, about a
half of all known minerals are silicates with distinct struc-
tures, although their frameworks are built only of Si and 0
(plus Al in the case of aluminosilicates). Enumeration of
networks of atoms in inorganic structures is a matter of
considerable interest, but a formidable task for a scientist,
as the number of three-dimensional nets is infinite.
Derivation of chemically viable hypothetical networks is
particularly desirable for microporous molecular sieves, of
which there are now 105 recognized structure types, with
several new ones being added to the list every year [l].
Molecular sieves, particularly zeolites, are widely applied
as catalysts, sorbents and ion-exchangers. The annual
industrial consumption of zeolites is = 550,000 tonnes, of
which 135,000 tonnes are used in catalysis, 375,000 as ion-
exchangers in detergent powders and 40,000 as sorbents.
New wide-pore (> 2 nm) molecular sieves are much in
demand, and a systematic and reliable enumeration proce-
dure would not only reveal possible further structures, but
could also assist in the design of new synthetic routes by
using suitable `structure-directing' molecules. It is noted
that in this context that the use of nonaqueous media for
the synthesis of molecular sieves has barely been explored.
The structure of crystalline molecular sieves
This review is concerned with crystalline molecular sieves,
a class of porous crystalline open-framework solids which
includes aluminosilicates (zeolites), aluminophosphates
and related materials [Z-4]. Zeolites are built from corner-
sharing Si04 and AlO, tetrahedra linked by the apical oxy-
gen atoms to form frameworks of high internal surface area
with regular one-, two- or three-dimensional channel sys-
tems and cavities of molecular size (Figure 1). Other ele-
ments, such as Ga, Ge, B and Fe can substitute for Si and
Al in the framework. The net negative charge of the frame-
work, equal to the number of the constituent Al atoms, is
balanced by exchangeable cations located in the channels
which normally also contain water. The name `zeolite'
(from the Greek @II = to boil and hdoo= stone) was
coined to describe the behaviour of the mineral stilbite
which loses water on heating and thus seems to boil. There
are = 40 identified zeolite minerals and another 40 recog-
nized synthetic species with a wide range of compositions.
All known zeolites, both natural and synthetic, contain
channels circumscribed by 12 or fewer tetrahedrally coor-
dinated Si or Al atoms. Microporous silicates with windows
of insufficient size to sorb water molecules reversibly are
known as clathrasils [S].
The AlPO, molecular sieves, the porous crystalline equiv-
alents of aluminium phosphate, are built from alternating
AlO, and PO4 tetrahedra [6]. Incorporation of an Si source
into AlPO, gives silicoaluminophosphates, SAPO, and the
incorporation of a metal (Me) into AlPO, and SAP0 gives
the MeAPO and MeAPSO sieves, respectively. Other zeo-
lite-related structures with novel compositions such as zin-
cosilicates, gallophosphates, aluminoarsenates, galloarsen-
ates and beryllophosphates have also been reported [11.Of
the 43 recognized AlPO, and related structures, 16 have
the framework topologies of known zeolites, and the rest
are novel structures (Table 1 and Figure 2). Unfortunately,
although some microporous aluminophosphates contain
wider channels than any known zeolite (> 1 nm), their
practical value is limited by their poor thermal stability.
The structures of all known zeolitic, AlPO, and related
structures are listed in the `Atlas of Zeolite Structure
Types' by Meier, Olson and Baerlocher [l], while their
topology and geometry have been extensively reviewed by
Smith [7].
Topological considerations
In the vast majority of molecular sieves Si, Al and P atoms
(known as T-atoms) occupy 4-connected vertices of a
three-dimensional net, and the 0 atoms occupy Z-con-
nected positions between the 4-connected vertices. Thus
each T-atom is surrounded by four oxygens and each oxy-
gen by two T-atoms, which is written symbolically as (4;Z).
However, in some frameworks oxygen atoms are linked to
80 Solid catalysts and porous solids
Figure 1
r-
SOD
FAU
KFI
Current Op~nmn in Solid State & Materfals Scmc~
LTA
CAN
RHO
Framework structures of uninodal zeolites of structure types SOD
(sodalite), LTA (zeolite A), FAU (faujasite), CAN (cancrinite), KFI (zeolite
ZK-5) and RHO (zeolite Rho). The positions of tetrahedral atoms are at
the crossings of the straight lines which symbolize T-T linkages.
Oxygen atoms (not shown) lie approximately half-way between the
T-atoms. The types of cages involved in each structure are represented
by polyhedra which have been shrunk towards their centres. Sodalite
(structure type SOD) is formed by direct face-sharing of four-
membered rings in the neighbouring truncated octahedra, more
correctly described as tetrakaidodecahedra (also known as `sodalite
cages' or `P-cages'). Zeolite A (structure type LTA) is formed by linking
the sodalite cages through double four-membered rings. Faujasite
(structure type FAU) is formed by linking the sodalite cages through
double six-membered rings. Cancrinite is formed by direct linking of
1 1-hedra (`e-cages' or `cancrinite cages'). Other polyhedra are also
present: the `cL-cage' (26.hedron of type I); double E-membered ring;
double B-membered ring (hexagonal prism) and the 16-hedron
(`y-cage'). Exchangeable nonframework cations are not shown for
clarity.
one or three T-atoms; in others, T-atoms may be connect-
ed to 5 or 6 oxygens [8]. Given that each oxygen always
lies between two T-atoms, the topology of the framework
may be considered simply in terms of the connectivity of
the T-atoms. Thus each T-atom is treated as a vertex of a
three-dimensional net, and each vertex lies at the inter-
section of four T-T edges. Such a net is said to be 4-con-
netted. If all vertices in a net are topologically identical,
the net is described as uninodal; binodal, trinodal and so
on, nets are those with two, three and more topologically
distinct types of vertices.
How are the different periodic nets described and classi-
fied? The diversity of known structures and the current
state of mathematical knowledge are such that a topologi-
cal classification of structures is necessarily based on com-
mon subunits of linked tetrahedra, known as secondary
building units (SBUs) (Figure 3) [9]. The SBlJs are the
smallest number of simple units from which all known
structures can be built. Some SBlJs are thought to be prc-
cursor molecular fragments present in the synthesis gel
from which the molecular sieve was crystallized. As new
structures are discovered, new SBLJs are added to the list.
Polyhedral cages, the larger building blocks, are each com-
posed of a handful of SBUs and can in turn be combined to
form an infinite framework. For example, the truncated
octahedron (or p-cage), may be linked directly to other
P-cages to form the SOD (sodalite) structure type, via dou-
ble 4-membered rings to form zeolite A (LTA structure
type), or via double 6-membered rings to form the zeolitic
mineral faujasite (FAU) (Figure 3). Polyhedra are described
by their face symbol: thus the sodalite cage is described as
4666, which specifies a polyhedron built from six 4-mem-
bered rings and six 6-membered rings. Alternatively,
frameworks may be described in terms of chains of linked
tetrahedra. LJsing a limited number of chains as building
blocks, it is possible to generate molecular sieve structures
in a similar way to that used to generate SBIJs.
A periodic network of tetrahedral atoms can be described
in terms of the `circuit symbol' of each T vertex. Each T
vertex participates in six Ti-T-Tj angles, and for each
angle there is a shortest circuit of edges T-Ti...`I'j-T. The
set of six numbers forms the circuit symbol of the vertex
[lo], which reflects the degree of compactness of a net. A
simplified form of the circuit symbol is `loop coordination':
a graph showing only the number of 3- or 4-membered
rings in which a given T-atom participates (see Figure 4).
A very powerful description of a net involves the concept
of a `coordination sequence' (CS), originally introduced by
Brunner and Laves [ll] and first applied to molecular
sieves by Meier and Moeck [12]. Thus in a 4-connected
network each T-atom is connected to N, = 4 neighbouring
T-atoms through oxygen bridges. These are then linked to
N, `T-atoms in the next shell, in turn connected to N.3
`T-atoms and so on, including each T-atom only once. For
example, the coordination sequence for faujasite is: 4, 9,
16, 2.5, 37, 53, 73, 96, 120, 14.5. The coordination sequence
satisfies the condition chat N,, = 1, N, = 4, N, 2 12, N.3 =
36, Nk $4.3k-1 and is a periodic function [131. Although
the coordination sequence for each kind of T-atom is not
Figure 2 Table 1
I AlPo4-5 AlPo4-11 VP15
I
Current Ooinion in Solid State 8 Materials Science 1
Framework projections of AIP04-5 along 1001 I, AIPO,-1 1 along 11001
and VPI-5 along [OOl]. Neither of the three structures has a naturally-
occurring analogue.
Figure 3
0 004 5 6 6
moo4-4 6-6 6-6
dQ@4-1 4=1 4-4=1
5-2 Spiro - 5
0
06-2
CT5-1
6~1
Secondary building units (SBUs) found in molecular sieve structures.
The numbers indicate in how many known structure types a given SBU
is found. Reproduced with permission from [l I.
completely unique to a given structure, and occasionally
distinct structures (such as LTA and RHO or ABW and
ATN; see Table 1) have the same coordination sequence,
it is a very useful guide because structures with different
coordination sequences are guaranteed to be different.
Framework density (FD) is defined as the number of
Hypothetical molecular sieve frameworks Klinowski 81
Microporous zeolitlc and related molecular sieves.
Silicates Silicates and Phosphates
phosphates
AFG FER MFI RSN ABW
`BEA GME MFS RTE AFI
BIK GO0 MON RTH ANA
BOG HEU MOR RUT AST
BRE IFR MTN SGT BPH
CAS JBW Ml-T STI CAN
CHI KFI MTW TER CHA
CON LIO MWW THO ERI
DAC LOV NAT TON FAU
DDR LTL NES VET GIS
DOH LTN NON VNI LAU
EAB MAZ OFF vsv LEV
EDI MEI -PAR WEI LOS
EMT MEL PAU -WEN LTA
EPI MEP PHI RHO
EUO MER -RON SOD
AEI
AEL
AET
AFO
AFR
AFS
AFT
AFX
AFY
AHT
APC
APD
ATN
AT0
ATS
ATT
ATV
AWW
CGF
CL0
CZP
DFO
OSI
SAO
VFI
WEI
ZON
T-atoms per 1000 Ax, whereas topological density, ~10, is
defined such that lOOOpl0 is the number of T-atoms in the
first ten coordination shells of a given T-atom [14,16] and
also reflects the degree of compactness of a net.
The most recently introduced structural descriptions of
molecular sieves use the concept of nodal surfaces [17]
defined by wave vectors in a reciprocal space; equipotential
surfaces, defined by point charges in real space, and triply
periodic minimal surfaces (TPMS), that is surfaces with
zero mean curvature at all points [1%201. If a minimal sur-
face has space group symmetry, it is periodic in three inde-
pendent directions. Minimal surfaces have been shown to
appear in a variety of real structures including cristobalite,
diamond, quartz, ice and many molecular sieves. These
concepts are fundamentally different from the `conven-
tional' approaches described above in that they do not con-
sider chemical bonds and bond angles but treat structures
as an assembly of atoms `decorating' an infinite surface.
Structural enumeration
In two dimensions, there are 11 different topological types
of uninodal nets, a result already shown by Kepler [Zl].
Similarly, there are 508 and 16,774 types of binodal and
trinodal nets, respectively. However, in three dimensions
even the number of types of uninodal nets is infinite
(although the number of `realizable' ones may well be
finite, see below). Finding interesting new nets therefore
amounts to selecting a subset of an infinite set using cer-
tain criteria. The basic topological discussion of three-
dimensional nets was given by Wells [10,22,23], who
attached special importance to uniform nets in which the
shortest rings at every angle are equal in length.
Enumerations reported so far have been derived by empir-
ical methods, and new structures were predicted by link-
ing together structural subunits (SBUs, chains or cages) in
new ways, either by building models or by computer sim-
82
J
I 1
Loop configurations and the number of structures in which they occur.
Solid lines represent T-O-T linkages, dotted lines nonconnected T-O
bonds found in interrupted frameworks. Reproduced with permission
from [l].
ulation. As the T-O distances in all known zeolites are in
0
the range 1.58-1.78 A (such that all T-T edges are close to
3.1 A) and the T-O-T angles in the range 130-160", mod-
els of these can be built using identical sections of plastic
tubing attached at each end to tetrahedral nodes.
However, of the many structures which are generated,
only some will be `chemically reasonable' [24]. Topology
takes no account of chemistry and the basic requirement
for chemically realistic structures is that bond lengths and
angles are within a certain acceptable range. For example,
one must reject hypothetical structures in which the dis-
tance between the vertices is smaller than the sum of
atomic radii of the T-atoms involved. O'Keeffe [14]
describes `realizable' nets which can be realized geometri-
cally with each vertex having only four equidistant nearest
neighbours and with the T-T linkages corresponding to
the edges of the net, and he believes that the number of
such uninodal nets is not only finite, but amounts to `some
hundreds'. Given a realizable hypothetical structure, a
least-squares fit leading to optimal T and 0 positions can
then be performed by computer.
A very powerful criterion of realizability is the framework
density. For the known zeolites and zeolite-type materials,
FD values range from 12.5 to = 20.5. Brunner and Meier
[ZS] have shown that the range of the observed FD values
in tetrahedral networks depends on the type and relative
number of the smallest rings (Figure 5). The frameworks
of lowest density have a maximum number of 4-membered
rings, and the minimum framework density increases with
the size of the smallest rings. They have demonstrated [ZS]
that there is a clear gap in the FD values between zeolitic
and dense frameworks and a lower limit to framework den-
sity, with the position of both dependent on the size of the
smallest rings present in a given structure. These results
have considerable predictive value for assessing the viabil-
ity of hypothetical structures and can serve as a guide for
the synthesis of low-density framework structures.
Brunner [26] addressed the question of the likelihood of
preparing highly siliceous frameworks of a given topology,
much in demand by industry, in terms of the loop config-
uration. In an article significantly entitled `Quantitative
zeolite topology can help to recognize erroneous structures
and to plan syntheses' [27] he characterized open and
dense tetrahedral structures with respect to the smallest
rmgs, bond angles, symmetry, loop configuration and
framework density. The conclusion was that the lowest
density is obtained for structures of high symmetry. The
largest cavities are usually found in the positions of high-
est symmetry of the space group, and two 4-rings with a
common edge prefer the ci.s conformation, with nearly pla-
nar rings and a maximum of T-O-T angles near 109" over
the tram conformation.
Aware of the practical importance of nets with very open
frameworks (FD < 12) and wide channel openings (con-
taining a maximum of 3- and 4-rings), Barrer and Villiger
[`28] were the first to find a chemically realistic net with uni-
dimensional l&ring channels, and Meier [29] and Hansen
[30,31] derived a series of low-density nets. In a long
sequence of papers, Smith and his coworkers have
described a large number of hypothetical stereochemically
realizable structures [32-46]. One of their most interesting
results was the prediction [47] of the (4;2) net with l&rings
(described as net 81(l) in the original paper) which was sub-
sequently identified in the aluminophosphate VPI-5 (VFI
structure type) [48]. IJsing four different kinds of geometri-
cal transformations, Andries and Bosmans [49] were able to
enumerate, systematically, (4;2)-connected 3D nets related
to the (nonzeolitic) tridymite group.
O'Keeffe et aL. [14-16,50-551 have derived many new
structures using empirical computer search algorithms. A
point was moved in small increments throughout the
asymmetric unit of the unit cell of all the cubic, hexagonal,
tetragonal and orthorhombic space groups in turn. All the
equivalent points in the cell, generated by the group-sym-
metry operations, were then identified. The topology of
the net defined by the four nearest neighbours of the ini-
tial point was then characterized by its coordination
sequence. In this way, O'Keeffe was able to describe and
characterize topologically, 11 uninodal nets in which the
shortest rings containing each pair of edges are N-rings
(N > 4) and 13 nets without 3- or 4-rings [14], 19 uninodal
nets containing 3-rings [15] and 21 nets in which at least
Hypotheticalmolecularskve frameworksKlinowski 83
Figure 5
FD
i
q-
26
elogaaite
III AN
.
.*
.
l*
.
:
3+ 4 4+ S 5+ 6
size of smallestRing
Distribution of framework densities versus the smallest ring in the network. The hatched region represents the gap between dense and
microporous framework types (251, and the dotted line marks the lower limit for the framework density. The `+' sign next to a ring size indicates that
some T-sites are associated with larger rings than the one in question. Please refer to Table 1 for teolite and microporous sieve type. Reproduced
with permission from Ii].
84 Solid catalysts and porous solids
three of the shortest rings containing each pair of edges are
4-rings [54]. Most of these nets are new. He has also shown
[16] that the coordination sequence for many simple
4-connected nets can be expressed by sets of quadratic
equations, which can in some cases be reduced to a single
equation. The coefficient of the quadratic term is related
to the geometric density. O'Keeffe described low-density
nets with a high proportion of three rings and showed that
in terms of density correlations they form a group separate
from typical zeolite nets.
Very recently, Treaty [56] described a computer method
for generating periodic 4-connected frameworks. Given
the number of unique tetrahedral atoms and the type of
crystallographic space group, the algorithm systematically
explores all combinations of connected atoms and crystal-
lographic sites, seeking the 4-connected graphs. The
resulting symmetry-encoded graphs are realaxed by simu-
lated annealing and to identify the the regual tetrahedral
frameworks. Results were given for one unique tetrahedral
atom in each of the 230 crystallographic spave group types.
Over 64,000 unique 3-dimensional and 4-connected unin-
odal graphs were found when the search was restricted to
those topologies which connect to nearest-neighbour
asymmetric units. In any given space group, the number of
graphs can depend on the choice of asymmetric unit.
About 3% of the 4-connected graphs refined to reasonable
tetrahedral conformations, and many were described. The
combinatorial explosion of graphs as the number of unique
vertices is increased at present restricts this method to
consideration of small numbers of unique atoms.
Hyde el al. [57,58] have shown that many low-density
frameworks are related to periodic minimal surfaces of
known surface area, thus providing a connection between
FD and the average size of rings decorating the surface.
Having considered the relation between density and bond
lengths and angles, they gave upper and lower bounds of
density as a function of the average ring size. The fact that
the area per vertex on the surfaces is the same as that for
related sheet silicates implies that framework density can
be inferred from the average ring size alone. The lower
bound for the density is consistent with the preferred
bonding geometry of SiO, networks. The results were
considered in light of framework densities of highly
siliceous zeolites, clathrasils and dense silicates in order to
separate the roles of geometry and chemistry in determin-
ing framework topology. LJsing an analogy with three-con-
nected networks of hyperbolically-curved single sheets,
Fogden and Jacob [59] described a method for construc-
tion of frameworks corresponding to their interconnected,
double-sheet relatives, and gave models of hypothetical
frameworks fitting the triply-periodic minimal surfaces P,
D and G. The channels and cavities in these structures are
significantly larger than those in known zeolites.
Finally, it is important to mention that recent advances in
mathematical tiling theory [60] are likely to lead to new
ways of systematic enumeration of a variety of chemical
structures, including molecular sieves [61].
Conclusions
Enumeration of networks of atoms in inorganic structures
in general and in the commercially important microporous
molecular sieves in particular is a highly desirable objec-
tive. (Jnfortunately, there is still no systematic procedure
for such enumeration. As a result, all hypothetical struc-
tures reported so far were derived by empirical methods,
and new structures were predicted by linking together
structural subunits in new ways, either by building models
or by computer simulation. A systematic and reliable enu-
meration procedure would not only reveal possible further
structures, but could assist in the design of new synthetic
routes by using suitable `structure-directing' molecules.
However, recent advances in tiling theory may lead to new
ways of systematic enumeration of a variety of chemical
structures.
Acknowledgements
`l`his paper is dcdicatcd to Sir John hlcurig Thomas (FKS) on the OCCASION
of his 65th birthday. 1 am gratefill to 0 Dclgudo l;riedrichs, Ilnixcrsity of
RielefL-Id, for Figure 1.
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