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Topics in Catalysis 9 (1999) 235–250 235
A density functional study of Ti/MgCl2-supported Ziegler–Nattacatalysts
Julian D. Gale a,∗ C. Richard A. Catlow b and Michael J. Gillan c
a Department of Chemistry, Imperial College of Science, Technology and Medicine, South Kensington SW7 2AY, UK b Davy-Faraday Laboratory, The Royal Institution of Great Britain, 21 Albemarle Street, London W1X 4BS, UK
c Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
Total energy pseudopotential calculations have been used to examine the adsorption of TiCl4 at both the 110 and 100 surfaces of
magnesium chloride. Titanium(IV) chloride is found to bind most strongly on the 100 surface resulting in the formation of a complex
with approximately trigonal bipyramidal coordination of titanium, which will dissociate to form TiCl+3 and Cl− with an energy of
127.7 kJ mol−
1. Cluster calculations indicate that this site only weakly binds ethene, but does catalyse the formation of C–C bonds withan activation energy consistent with experimental estimates.
Keywords: Ziegler–Natta, density functional theory, adsorption, polymerisation
1. Introduction
Ziegler–Natta catalysis, first discovered in 1953, repre-
sents one of the most important commercial processes for
the production of polymers [1]. It was found that certain
transition metal species were able to catalyse the polymeri-
sation of alkenes at relatively low temperatures and without
the use of high pressures as had been previously necessary.
Although the use of metallocenes and other homogeneouscatalysts is becoming increasingly important, heterogeneous
systems have been traditionally used as they were the first
to be discovered which showed stereospecific properties.
The most widely used heterogeneous catalyst to date is
titanium supported on the surface of magnesium chloride
which adopts two different polymorphs, α and β , both of
which are layered structures differing only in the stacking
pattern. This system is prepared by first ball milling MgCl2
in the presence of an ester to increase its surface area, and
in particular of surfaces other than the basal plane. On to
these particles TiCl4 is adsorbed along with an alkyl alu-
minium co-catalyst. Experimental evidence suggests thatwhile titanium chloride is initially adsorbed as 90% Ti 4+,
after the introduction of AlEt3 titanium is reduced to 71%
Ti3+ and 29% Ti2+ [2].
Having generated a number of active titanium sites the
alkene is believed to co-ordinate to the transition metal.
Cossee [3] has proposed that the polymerisation then occurs
by the insertion of the alkene into a Ti–C bond at the same
centre, where C is the terminal atom of the alkyl chain.
What is less certain is exactly how the catalyst favours
formation of the isotactic product and what the role of the
base is in this process.
Given the uncertainty about the precise details of the
mechanism for polymerisation there have been numeroustheoretical studies addressing the problem. Lin and Cat-
∗ To whom correspondence should be addressed.
low [4] have used shell model interatomic potentials to
perform a detailed study of the surface energies for var-
ious cuts of MgCl2 and the relative energies of a wide vari-
ety of surface defects, including both the binding of TiClx(x = 2–4) as an adsorbate and the incorporation of titanium
as an impurity at the surface. Subsequently they went on to
study the nature of selected adsorbed titanium complexes
using point charge embedded quantum mechanical calcula-tions at the Hartree–Fock level [5]. In a parallel study, Col-
bourn et al. [6] have also studied the surface structure using
interatomic potentials and then followed this by perform-
ing density functional calculations on clusters representing
different parts of the surface. Puhakka et al. [7] have also
studied how electron donor molecules interact with various
surface sites based on ab initio cluster calculations.
There have also been several studies probing the reaction
mechanism for C–C bond formation. In some of the earlier
studies it was necessary to assume geometries for the inter-
mediates [8]. More recently many of the calculations have
assumed that the active species can be represented by thecationic species RTiCl+2 and binding energies for alkenes,
followed by activation energies, have been determined on
this basis. Generally speaking, most studies have concen-
trated on the simplest possible case of R = CH3 and with
ethene as the alkene.
In this study we present results obtained using a com-
bination of quantum mechanical techniques to characterise
the properties of titanium(IV) at the surface of MgCl2. In
the first part, density functional calculations using periodic
boundary conditions, as opposed to cluster methods, are
used to study the surfaces of magnesium chloride and the
adsorption of TiCl4. Having located the most stable bind-ing site, we then proceed to use cluster based methods to
estimate the likely activity of such sites towards polymeri-
sation.
© J.C. Baltzer AG, Science Publishers
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236 J.D. Gale et al. / DFT study of Ziegler–Natta catalysts
2. Methods
Quantum mechanical approaches to adsorption and re-
activity at surfaces can largely be divided into two cate-
gories. Most early calculations in this field were forced
to use cluster methods in which small fragments of the
system were extracted to generate a representative model
for the active site which is feasible for study. In many
cases this approach works well, particularly where the na-
ture of the active site is already known, as is the case, for
example, in zeolite chemistry [9]. More recently the re-
alism of such approaches has been increased by the use
of embedding techniques to model either the spatial con-
straints of the surrounding material [10] or the longer range
interactions, in particular the electrostatic ones [11], or
both. A major strength of the cluster approaches is that
they can normally take advantage of the greater rangeof quantum mechanical approximations presently avail-
able for finite systems, as well as exploiting the more
mature implementations of transition state searching algo-
rithms.
Despite these advantages the use of cluster methods is
more problematical where there is little prior knowledge
of the active site since the choice of fragment is likely to
be biased towards a particular possibility. As the size of
cluster that can be studied becomes larger this will obvi-
ously become less of a difficulty, but we have yet to reach
this point on a routine basis. Hence, the second approach
based on the use of the supercell method, coupled with pe-riodic quantum mechanical techniques, has been growing
in popularity as such calculations become computationally
competitive. Here the problem of artificial boundaries are
traded against fictitious image interactions, though the latter
can be checked in principal by the use of increasing sizes
of supercells.
Energy minimisation and even molecular dynamics are
readily available within supercell methods. However, the
location of transition states is more rarely performed. For-
tunately, though, the major component of an activation
energy generally arises from relatively local changes in
chemical bonding and therefore cluster methods will nor-
mally be acceptable here. In order to take advantage of thestrengths of both methodologies we examined the nature of
the Ti/MgCl2 catalyst in two stages. In the first, the struc-
ture of the surface of MgCl2 and the initial adsorption of
molecular TiCl4 is examined using supercell methods. Sub-
sequently we use cluster methods to examine the possible
interaction of an alkyl group and an alkene with titanium
leading to the formation of an extended alkyl chain, based
upon the information obtained for the location of Ti(IV)
obtained from the first part of the study.
For the periodic boundary condition study of the sur-
faces of MgCl2 and the adsorption of TiCl4 we have used
the total energy pseudopotential method with a planewavebasis set [12]. These calculations were all performed within
the formalism of non-local density functional theory us-
ing the GGA gradient corrected functional of Perdew and
Wang [13]. All atomic cores are represented by non-
local pseudopotentials, using a real space representation
of the non-local projectors, with the exception of magne-
sium which is treated as being purely local. All planewavecalculations have been performed using both the program
CETEP [14] running in parallel on the T3D/T3E computers
at the Edinburgh Parallel Computing Centre and using the
version of CASTEP distributed by Molecular Simulations
Inc running on a Power Challenge.
The reliability of the pseudopotentials and the conver-
gence with respect to the planewave cut-off energy was
checked by performing test calculations on TiCl4 and for
bulk MgCl2. A cut-off of 450 eV was found to be suffi-
cient for all atom types to obtain converged geometries to
the accuracy required. For example, the converged opti-
mised Ti–Cl bond length in TiCl4 was found to be 2.187 A
as compared to an experimental value of 2.185 A [15]. In
the calculations in which an organic adsorbate is present
the cut-off is increased to 550 eV, due to the nature of
the pseudopotentials introduced, for some calculations. As
only Ti(IV) is formally considered in these calculations the
spin-restricted formalism was used. Test calculations using
the non-local spin density approximation showed that this
had no discernible effect on the results.
All calculations were performed with Brillouin zone
sampling only at the gamma point. As the supercell sizes
needed to allow surface adsorption to occur at a reason-able coverage are quite large anyway this is a reasonable
approximation, whereas if we were concerned only with
bulk material it would be more efficient to integrate over
multiple k points instead.
As the calculations in the present study are for the sur-
faces of MgCl2, but we are constrained to maintain three-
dimensional periodicity, it is necessary to create a finite
gap in one direction. The convergence of the results with
respect to the size of this gap has been examined and illus-
trative values will be given in the results section.
For the cluster calculations all runs were performed
using the program Gaussian94 [16] and the all elec-tron TZVE basis sets of Ahlrichs and co-workers [17]
with a single polarisation function for all atoms except
for titanium, leading to contractions of (842111/631/411)
for Ti, (732111/6111/1) for Cl, (62111/411/1) for C and
(311/1) for H. The majority of the cluster calculations have
been performed using Becke’s three parameter hybrid non-
local exchange functional [18] combined with the Lee–
Yang–Parr [19] gradient-corrected correlation functional
(B3LYP). However, selected calculations were also run at
the MP2 level for comparison. Finally, most of the cluster
calculations were run using the Z-matrix optimisation algo-rithm as selected geometrical parameters were constrained
to mimic the surface configuration, as described in the next
section.
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J.D. Gale et al. / DFT study of Ziegler–Natta catalysts 237
3. Results and discussion
3.1. Bulk MgCl2
As a prerequisite for the subsequent calculations it is
necessary to briefly examine how well the total energy
pseudopotential method performs for magnesium chloride
and what computational parameters are needed. For a fixed
unit cell at the experimental dimensions, as we use in this
study for reason discussed below, there is only one symme-
try non-equivalent free parameter for the structure which is
the chlorine z co-ordinate. Hence we will use the optimised
value of this parameter as the measure of convergence.
Firstly, we can consider the effect of increasing the
planewave cut-off. In going from 450 to 500 eV the change
in the fractional co-ordinate is in the fifth decimal place and
corresponds to a percentage change of less than 0.01%.Hence the forces are well converged with the cut-off cho-
sen of 450 eV. Secondly, as we are only working with
the gamma point wavefunctions, it is necessary to examine
the convergence of the properties with increasing supercell
size. With a 2× 2× 1 hexagonal supercell the z parameter
optimises to 0.22693 which is significantly below the ex-
perimental value of 0.23 [20]. Increasing to a 3 × 3 × 1
supercell leads to a definite improvement with a value of
0.2297 now in good agreement with experiment. Because
of the layered nature of the structure there is very little dis-
persion perpendicular to the layers and creating supercells
in this direction has only a small effect on the forces.
3.2. Surfaces of MgCl2
Before we can begin to consider adsorption and reactiv-
ity at the surfaces of β -MgCl2 we must decide which sur-
faces, of the many possibilities, should be considered. The
natural surface of this material is the 001 face as this results
in a low energy cleavage between the layers. However,
given that this surface offers a complete layer of chloride
ions with no vacancies, the interaction of TiCl4 is likely to
be very weak and will only be a physisorbed complex. As
the predominate interaction would be dispersion forces, and
we are employing mainly density functional theory in thisstudy, where such terms are not likely to be accounted for
accurately, we shall exclude this surface from our study as
have previous workers in this field. It is highly unlikely that
the majority of the chemistry occurs at such co-ordinatively
saturated surfaces.
Having excluded the 001 face there are still a variety
of different surfaces to choose between. However, we can
broadly characterise them by the co-ordination number ex-
hibited by magnesium, which primarily tends to be either
four or five. To make this study practical, we have cho-
sen to study two different surfaces, one which has exclu-
sively four-fold co-ordinate magnesium (110) and one of which has exclusively five-fold coordination (100). As a
first approximation we can speculate that surfaces which
contain a mixture of these two types of sites will exhibit
Table 1
Fractional coordinates for the alternative orthorhombic unit cell of β -
MgCl2 used through out this work. The value of the z parameter is 0.23
in the experimental crystal structure.
Atom x y z
Mg1 0 0 0
Mg2 1/2 1/2 0
Cl1 1/2 1/6 +z
Cl2 0 1/3 −z
Cl3 0 2/3 +z
Cl4 1/2 5/6 −z
characteristics of both extremes. Surfaces with even lower
coordination numbers are possible in principle, though the
surface energy is likely to be sufficiently higher such that
they do not contribute to the particle morphology.
To make the generation of the above two surfaces morestraightforward an orthorhombic supercell of the primitive
hexagonal unit cell has been constructed whose cell parame-
ters in terms of the hexagonal values are a = a, b =√
3a,
c = c and whose fractional coordinates are given in table 1.
In this modified frame of reference the 110 surface becomes
the 100 plane and the 100 surface maps to the 010 plane.
Subsequently all references to the number of unit cells used
will be in terms of this orthorhombic cell. While it is possi-
ble to perform planewave calculations with a variable unit
cell, by working with high accuracy cut-offs and inclusion
of a correction for the finite basis set size, we have chosen
to work with a fixed unit cell based on the experimental cell
parameters, a = 3.641 A and c = 5.927 A. Apart from the
fact that this is necessary to make the calculations feasible
in this case, we would not necessarily expect good results
for the c parameter as this again is largely determined by
dispersion forces.
In studying the surface, we are forced by the use
of a planewave basis set to approximate the real two-
dimensional system by a three-dimensional model. This
implies that we need to introduce a gap between the layers
which is sufficiently large so that there is no significant in-
teraction between them. Since neither the 110 or the 101
surface is dipolar this can be achieved quite readily. Based
on test calculations for the clean surface we find that a gapof 8 A is sufficient to converge the energy per formula unit
to better than 1× 10−4 eV. However, to be consistent with
later stages, where we wish to consider adsorption on the
surfaces, a gap of 10 A has been used through out.
In addition to the problem of the gap, we also need to
ensure that enough atomic layers separate the two sides of
the slab. For the 110 surface three orthorhombic unit cells
are used to create the slab depth, while for the 100 surface
two cells are sufficient because of the cell parameter being√ 3 greater in this direction. Both of these correspond to a
depth of six charge neutral atomic layers. With this depth an
acceptable level of convergence is achieved in the surfaceenergy and the relaxed geometry. When allowing for the
requirement for supercells in the surface plane to achieve
cell vectors of equivalent dimensions to the 3 × 3 × 1 he-
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238 J.D. Gale et al. / DFT study of Ziegler–Natta catalysts
xagonal cells needed to obtained a good representation of
the electronic structure, this results in an overall 3 × 2× 2
supercell of the orthorhombic form for both surfaces with
a gap inserted along the appropriate axis. The resultingunit cell parameters are for the 110 surface, a = 20.923 A,
b = 12.6128 A, c = 11.854 A, and for the 100 surface,
a = 10.923 A, b = 22.6128 A, c = 11.854 A, with a
composition Mg24Cl48.
(a)
(b)
Figure 1. Relaxed structure of the (a) 110 and (b) 100 surfaces of MgCl2showing the four and five coordination of magnesium, respectively, where
the smaller spheres represent Mg.
The relaxed surface structures are illustrated in figure 1.
For the 110 surface the main change is that a rumpling
effect occurs to what was a flat surface as cleaved. This
results in magnesium adopting a geometry which is inter-mediate between tetrahedral and square planar. The Mg–Cl
bond lengths at the surface are 2×2.3054 and 2×2.3949 A,
where the shorter distances are to the outer most chlorines.
Both of these distances represent a considerable shortening
of the Mg–Cl bond relative to the bulk value of 2.5045 A
for octahedral coordination. In the case of the 100 surface,
magnesium remains in a distorted five co-ordinate site, with
a mirror plane of symmetry passing through it normal to the
surface plane, with bond lengths of 2× 2.3929, 2× 2.5680
and 1 × 2.4581 A. Again the shortest distances are to the
outer most chlorines whose coordination number has been
reduced to two. The Mg–Cl bonds to these surface chlo-
rines are displaced away from the surface plane, thus en-
hancing the rumpling.
The surface energies for the 110 and 100 cuts are 0.263
and 0.199 J m−2, respectively. These values are much lower
than those obtained by Lin and Catlow [4] from interatomic
potential methods of 0.517 and 0.346 J m−2. The fact that
lower values are obtained here can again be partly ascribed
to the absence of the very large dispersion term present
in the potential calculations and also partly to the partial
charge density redistribution that is possible in the quantum
mechanical case.
3.3. Adsorption of TiCl4 at the surface of MgCl2
Having determined the relaxed surface structure for the
two prototypical surfaces of MgCl2 we now turn to consider
the binding of TiCl4 at these. This represents the first stage
in the catalyst preparation, prior to any subsequent redox
processes. Using the same supercells as in section 3.2 we
have placed the TiCl4 molecule above a number of differ-
ent surface positions, taking care to avoid high symmetry
starting configurations and with either the corner or a face
of the tetrahedral adsorbate directed towards the surface.
Each configuration was then minimised to the nearest local
minimum. Ideally a small dynamical run would be useful totry to ensure that no minimum has been missed. However,
this was not feasible with the size of system considered
and norm-conserving pseudopotentials. In practice, given
the relatively high degree of symmetry present at each sur-
face it is unlikely that very many distinct minima exist.
While it is normally desirable to apply an adsorbate mol-
ecule to each face of the slab to avoid an overall dipole
moment, in this case only one surface was covered. To ad-
sorb on both sides would require a large increase in gap size
which would in turn greatly increase the cost of the calcula-
tion when working with a uniform Fourier grid. This situa-
tion could be improved in future work by the use of a curvi-linear co-ordinate transformation [21]. Given that neither
the surface or the adsorbate have a dipole moment at infinite
separation, any net dipole moment will be relatively small.
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J.D. Gale et al. / DFT study of Ziegler–Natta catalysts 239
For titanium(IV) chloride adsorbed on the 110 face all
runs resulted in one of two weakly bound physisorbed com-
plex as shown in figures 2(a) and (b) with binding ener-
gies of 3.6 and 8.5 kJ mol
−1
, respectively. Both of thesebinding energies are considerably less than the value of
150.3 kJ mol−1 obtained from interatomic potential calcu-
lations by Lin and Catlow [4]. The origin of the difference
can be traced to the very large C 6 term needed in the short
range component of the interatomic potentials to counter the
inter-layer repulsion that results from electrostatics in the
limit of the fully ionic model. However, the quantum me-
chanical calculations will also represent an underestimate
due to the partial absence of dispersion forces. In future
work this could be corrected for by the superposition of a
−C 6 / r6 term where the coefficient is determined from the
polarisability of the chloride ion in MgCl2.
As a first approximation, we have estimated what the dis-persion contribution would be based on the final geometries
obtained. Using the theoretically calculated Cl–Cl C 6 term
based on NaCl of 95.41 eV A6 [22], the additional contri-
bution to the above binding energies would be 36 kJ mol−1
in both cases.
In the first configuration, with the lowest binding en-
ergy, TiCl4 adsorbs on the end of a cleaved MgCl2 layer
and adopts a position which is consistent with trying to
continue the underlying structure in accord with the ratio-
nale for why magnesium is a particularly suitable support
for titanium chloride. Two chlorines are directed towards
the surface and could be described as bridging two magne-siums. However, the distances involved are nearly twice a
typical Mg–Cl bond length at 4.5332 and 4.5365 A. In fact
these chlorines have a shorter contact distance with the sur-
face chloride ions of 4.47 A. The geometry of TiCl4 remains
very close to tetrahedral with the variation in bond lengths
only spanning from 2.1886 to 2.1902 A. This binding site
resembles that found by Lin and Catlow using interatomic
potentials, at least qualitatively.
The second more stable configuration has a similar ori-
entation of the adsorbate, except that titanium(IV) chloride
is now bridging between two magnesiums in adjacent lay-
ers. The reason why this arrangement is more stable is
because two of the chlorines of TiCl4 are able to achievemuch closer contacts of 3.645 and 3.646 A with Mg ions of
the surface, though these are still considerably longer than
bonding contacts.
It might have been anticipated that TiCl4 would bind
strongly to the surface with four co-ordinate magnesium,
as the adsorbate chlorides could be used to increase the
Mg coordination number at the surface. However, as a
result of the large surface reconstruction that takes place
the magnesium ions effectively become shielded by an over
layer of chloride ions, thus allowing only van der Waals
forces and higher order multipole moments to interact with
the incoming TiCl4. In an attempt to overcome this and tosee if there was a more strongly adsorbed state with a small
activation energy for its formation, several minimisations
were started with the adsorbate close to bonding contact
to magnesium with the unrelaxed surface structure. Even
starting from this configuration again leads to the above
weakly bound minima.
Turning now to consider the adsorption of titanium(IV)chloride on the 100 surface where magnesium is in five-
fold co-ordination. Here we obtain a contrasting result to
that seen on the 110 surface – instead of having only long
contacts with the surface ions, the minimised structure, as
shown in figure 3, contains new bonds formed between the
adsorbate and the surface. Two of the chloride ions of
TiCl4 bridge between two adjacent magnesium ions, thus
returning them to octahedral co-ordination, while a surface
chloride ion bonded to the same magnesiums forms a bond
to titanium. The net result is that titanium increases its
co-ordination number to five with an approximately trigo-
nal bipyramidal geometry. This is exactly the same mini-
mum as obtained by Colbourn et al. [6] based on a densityfunctional cluster calculation, though no bond lengths were
given in this study so it is not possible to make a detailed
comparison. The geometry of the final structure is given in
figure 4. Lin and Catlow [5] have also studied this struc-
ture using point charge embedded cluster calculations at the
Hartree–Fock level. This earlier study yielded a distance
from the Mg of the surface to the chlorine of the adsorbate
of 3.055 A, when using a double-zeta basis set, as com-
pared to values of 2.635 and 2.639 A in this work. While
some of the difference can be ascribed to the neglect of
electron correlation in the earlier study, the main reason for
such a large disagreement is likely to be due to the accu-racy with which the surface is represented and the degree
of relaxation allowed.
Our calculations yield a binding energy for TiCl4 on
the 100 surface of 18.48 kJ mol−1 – more than double that
found for the 110 face. The quantum mechanical bind-
ing energies for TiCl4 obtained by Colbourn et al. [6] and
Lin and Catlow [5] in their studies of five co-ordinate sites
are 107.6 and 43.7 kJ mol−1, respectively, both very much
higher than we find. Part of the discrepancy will be related
to the quality of the calculation, in particular the basis set,
given that neither of the above results were corrected for ba-
sis set superposition error, which as we shall see later can be
rather large for such systems. Furthermore, the binding en-ergy will be very sensitive to how well the model represents
the true surface and the presence of any spurious multipole
moments. In both of the above respects the planewave su-
percell approach should represent the most reliable method,
subject to the accuracy of the pseudopotentials.
Again we consider that the density functional value for
the binding energy of TiCl4 represents an underestimate of
the true value due to the neglect of a large proportion of the
dispersion energy. Using the same procedure as performed
for the 110 surface, we estimate that the extra contribution
to the binding energy due to dispersion should be of the
order of 70 kJ mol−1
for this configuration.Based on the adsorption behaviour observed at surfaces
with both four- and five-co-ordinate magnesium, it appears
that the latter is more likely to be the main binding site
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240 J.D. Gale et al. / DFT study of Ziegler–Natta catalysts
(a)
(b)
Figure 2. Optimised geometries for the TiCl4 molecule adsorbed on the 110 surface of MgCl2: (a) above the cleaved layers, (b) bridging between the
layers of the bulk structure.
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J.D. Gale et al. / DFT study of Ziegler–Natta catalysts 241
(a)
(b)
Figure 3. Optimised geometry for TiCl4 adsorbed on the 100 surface of
MgCl2 viewed from both parallel to the underlying layers and perpendic-
ular to them.
as a result of the strong reconstruction that occurs at faceswith lower co-ordination numbers. Making allowance for
the dispersion contribution only serves to favour the five
co-ordinate sites further.
Figure 4. Bond lengths (in A) around the five-co-ordinate Ti binding site
on the 100 surface of MgCl2.
3.4. Adsorption of ethene on the Ti/MgCl2 catalyst
Having located the most likely binding site for TiCl4 on
the surface of MgCl2, we are now in a position to ponder
how this site might interact with other species. In principlewe need to know how both alkenes and alkyl aluminium
compounds will adsorb at the catalyst surface. For the
purposes of this study we will investigate only how the
major reactant binds, namely the alkene, and for simplicity
we will use ethene as a probe, rather than propene. It is also
known from experiment that the titanium becomes partially
reduced when activated. Hence, in order to have a complete
picture of what occurs during the catalytic cycle we need
to know how the oxidation state of titanium influences the
structure and energetics. For this work we have restricted
ourselves just to the initial oxidation state of Ti(IV), while
Ti(III) and Ti(II) will be the subject of future research.
While we might conceive that an extra ligand could bindto the titanium complex adsorbed on the 100 surface to give
an octahedral configuration, this is unlikely to occur as the
angle of 116.3 ◦ between two of the equatorial chlorines
in the trigonal bipyramidal arrangement is severely con-
strained by coordination to magnesium in the underlying
surface. The only other way effectively to activate the ti-
tanium towards an incoming ligand is by losing a chloride
ion from its coordination sphere. While this would be a
highly endothermic process in the gas phase, at a cleaved
surface such as the 100 where there are a large number of
magnesium ions with adjacent chlorine vacancies this could
be quite a feasible reaction.To this end we have examined the energetics of a con-
figuration in which one of the singly coordinated chloride
ions bound to titanium has been removed and placed in the
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242 J.D. Gale et al. / DFT study of Ziegler–Natta catalysts
Figure 5. Optimised geometry for TiCl
+
3 and Cl−
adsorbed at the 100 surface.
nearest vacant site within the same layer. The final op-
timised geometry is displayed in figure 5. The first key
feature is that the adsorbate does remain dissociated with
the abstracted chlorine completing the octahedral environ-
ment of a surface magnesium with a strong Mg–Cl cova-
lent bond of length 2.1737 A which is much shorter than
the equivalent bond length in bulk MgCl2. Titanium ap-
proaches tetrahedral coordination slightly, as would be ex-
pected, with three of the Ti–Cl bonds having similar dis-
tances to those in TiCl4, but the fourth to the singly co-
ordinated chlorine is much shorter at 1.9804 A and the
former equatorial angle between the chlorines bridging tomagnesium only decreases by one degree to 115.3 ◦. The
chlorine which was initially partially bonded to titanium,
which started as part of the surface, has now become fully
bonded at the expense of its interaction with the two nearest
magnesium ions. As a result of this there is significant re-
construction at the surface immediately below the titanium
site.
Overall the process of removing a chloride ion is found
to be endothermic to the extent of 127.7 kJ mol−1. While
this is appreciable it represents a significant reduction of
the energy cost that would be associated with moving a
chloride ion the same distance in the gas phase (from a sim-ple electrostatic argument we would expect a value close
to 400 kJ mol−1). If we consider the binding energy that
would be released by introducing a different ligand at ti-
tanium to return it trigonal bipyramidal coordination then
the total energy change for the process would be much less
endothermic.
Analysis of the density of states indicates that the
HOMO for the dissociated TiCl+3 /Cl− system resides pri-
marily on the abstracted chloride ion making it the main
target for Lewis acids. Therefore we can speculate that the
adsorption of the co-catalyst, AlEt3, acts to stabilise this
dissociated state as this will enhance the Lewis acid–base
interaction over the situation where aluminium coordinates
to a chlorine which is bonded to titanium.
Lin and Catlow [4] have studied the dissociation of TiCl4
into TiCl+3 and Cl− at three different surfaces of MgCl2
based on interatomic potentials. They predict that the en-
ergy for this process is lowest at the 100 surface as charac-
terised above quantum mechanically. However, their dis-
sociation energy is much higher at 350 kJ mol−1 which
indicates the importance of charge redistribution during the
reaction.
Further to the above calculation we have also studied the
effect of trying further to dissociate TiCl+3 to yield TiCl2+2
and a second surface bound chloride anion, the aim being
to see if it is possible to reduce the coordination number of
titanium to three (although we formally write the species asbeing TiCl2+
2 to indicate the loss of two chloride ions, there
are actually three chlorines coordinating to titanium, one of
which comes from the surface). This process turns out to
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J.D. Gale et al. / DFT study of Ziegler–Natta catalysts 243
Figure 6. Ethene coordinated to the proposed titanium active site on the 100 surface as optimised by planewave supercell calculation.
be less endothermic than the first abstraction with an energy
of +60 kJ mol−1. However, when the resulting geometry is
analysed it is found that titanium has removed a different
chlorine atom from the surface to preserve its four-fold
coordination at the expense of disrupting the magnesium
chloride surface. Our preliminary investigation indicates
that titanium species with less than four ligands are unlikelyto be stable on the 100 surface.
Based on the geometry for the dissociated TiCl+3 /Cl−
surface complex we have performed an optimisation of
ethene adsorbed in the now vacant equatorial titanium co-
ordination site. Initially these calculations were performed
using a cut-off of 450 eV, however, runs have also been per-
formed with higher values to examine its influence given
the introduction of the carbon pseudopotential and bare
Coulomb potential for hydrogen.
Energy minimisation did indeed lead to a stable bind-
ing configuration for ethene coordinated to titanium whose
geometry is shown in figure 6. Ethene remains quitesymmetrically bonded with Ti–C distances of 2.6315 and
2.6488 A, the asymmetry arising from the influence of the
displaced chloride ion bound to the surface. Again the
geometry about titanium is close to trigonal bipyramidal
with the equatorial Cl–Ti–Cl angle being only weakly per-
turbed at 115.66◦, while the axial chlorines are slightly
shifted towards the adsorbed ethene narrowing the axial
Cl–Ti–Cl angle to 161.26 ◦.
The binding energy for ethene is found to be quite low
compared with some previous estimates based on differentmodels. With the lowest planewave cut-off of 450 eV the
value is 10.89 kJ mol−1. It is important to note that because
the basis set is not atomic centred this result is free from any
basis set superposition errors. As a check on the conver-
gence of the binding energy with respect to planewave cut-
off a single point calculation was performed at the 450 eV
optimised geometries using a cut-off of 550 eV. This led to a
slight decrease of the binding energy to 10.54 kJ mol−1. In-
creasing the cut-off gave rise to negligible forces on nearly
all the atoms except for carbon, where the force indicates
that the C–C bond should elongate, and to a lesser extent
hydrogen. Although it is desirable to repeat this calcula-tion with an increased cut-off, the indications are that this
will not change the overall binding energy by too much.
Calculations for this complex were repeated for a range
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244 J.D. Gale et al. / DFT study of Ziegler–Natta catalysts
of planewave cut-offs for the system where the number of
MgCl2 layers in the slab was halved. The main change on
going from 450 eV to convergence was that the C–C bond
length increased by just over 0.002 A˚
while other distanceswere altered by significantly less.
No previous calculation, to the best of our knowledge,
has considered ethene adsorption at exactly the same type
of site as found in our model, thus making it difficult to
compare binding energies. The closest study is that of Col-
bourn et al. [6] where they examined the adsorption of
propene on to an active site configuration similar to the
one found in this study for the initial complex of TiCl4,
i.e., before chloride was abstracted. Their binding energy
was an order of magnitude larger at 163 kJ mol−1. Such
a large difference is quite surprising given that both cal-
culations have used density functional theory and that we
would not expect a dramatic change in the value in goingfrom ethene to propene. In fact we might expect that the
value in this work to be more exothermic as the titanium
coordination number has been reduced to activate the site
for an incoming alkene. Further discussion of the relative
binding energies is given below after the cluster results have
been presented.
3.5. Cluster model for ethene binding and C–C bond
formation
At this point, while it is possible to proceed further with
the planewave calculations, this represents a time consum-ing approach (a typical optimisation of the systems consid-
ered in this study requires of the order of a thousand T3E
processor hours). Hence, in the remainder of the study,
as we turn to consider alkene adsorption and reaction fur-
ther, it is preferable to use a cluster model which should
be a reasonable first approximation when we are concerned
with local bonding changes. Furthermore, it is known that
pure density functional approaches are in some cases less
accurate when calculating activation energies than they are
for the properties of local minima. Therefore in our clus-
ter calculations we use the B3LYP hybrid functional with
some calculations repeated at the MP2 level to examine the
accuracy.The key problem now is to choose a suitable cluster
model to represent the titanium active site. In previous stud-
ies the model usually chosen is CH3TiCl+2 where Ti4+ is in
a tetrahedral environment, the fourth spatial direction be-
ing occupied by the incoming alkene. Based on the results
above this appears not to be a very likely model as there
are plenty of terminal chloride ions available to increase the
titanium coordination number and to make the site locally
electroneutral. Therefore we have chosen to represent the
active site found previously by using the cluster CH3TiCl3
where the chlorine which is directed away from the surface
in the initial complex has been replaced by a methyl group.Ideally we would represent the underlying surface by use of
a combined QM/MM approach as the effect of its presence
is largely to place geometric constraints on the adsorption
complex. However, as a first approximation we can include
this effect by applying explicit geometric constraints to the
cluster such that two of the chloride ions are forced to re-
main equatorial and the third chloride is restricted to beingaxial by fixing the bond angles between them. The Ti–Cl
bond lengths are still allowed to optimise freely and the
reactants/products of the polymerisation are unconstrained.
For comparison with earlier results and to contrast against
the CH3TiCl3 cluster we have also repeated the calculations
for the cationic species, CH3TiCl+2 .
Three of the key optimised geometries for CH3TiCl+2are illustrated in figure 7 with corresponding geometrical
parameters given in table 2. These structures correspond
to the initial adsorption geometry of ethene (one of three
possible configurations all very close in energy as described
by Kawamura-Kuribayashi et al. [23]), the initially formed
propyl complex resulting from insertion of ethene into theTi–methyl bond and finally an alternative configuration for
(C3H7)TiCl+2 . All three structures agree with those found
both by Axe and Coffin [24] (for the first two only) and by
Kawamura-Kuribayashi et al. [23], with the exception that
Axe and Coffin have the methyl group in the ethene adsorp-
tion complex in an eclipsed conformation which we find to
be 3.2 kJmol−1 higher in energy than the staggered form.
Also as the intermediate propyl complex has an imaginary
mode of 32.6i cm−1 which breaks the Cs symmetry we have
optimised this structure in C1, though this only lowers the
energy by 0.32 kJ mol−1.
Comparing the bond lengths obtained for the three dif-ferent minima against those from previous work shows
some small differences. These can be attributed to differ-
ences in the non-local density functionals chosen and the
fact that Axe and Coffin employed a basis set of double-
zeta + polarisation function quality whereas we have used a
triple-zeta + polarisation function basis. While Kawamura-
Kuribayashi et al. used improved quality calculations for
their energetics, the geometries were optimised at the HF/3-
21G (except augmented MIDI4 for Ti) level. All the cal-
culations demonstrate that there is a strong agostic inter-
action between the methyl group and titanium in the low-
est energy propyl complex leading to a Ti
· · ·C distance of
2.216 A and Ti· · ·C–H angles of 82.09/89.93 ◦. Repeatingthese optimisations at the MP2 level yields very similar
results.
All the results obtained to date suggest that ethene is
strongly adsorbed on the complex CH3TiCl+2 and that the
reaction to form the propyl complex is exothermic. Further-
more Kawamura-Kuribayashi et al. have estimated that the
activation energy for this process is only about 18 kJ mol−1.
Indeed, we find that if the optimisation of the alkene com-
plex is started with ethene rotated by 180 ◦ about the short-
est Ti· · ·C interaction then the system drops straight into
the propyl minimum without an activation barrier. How-
ever, for the polymerisation process to continue the propylcomplex must rearrange to the less stable configuration (fig-
ure 7(c)) from the more stable form with the agostic bond
(figure 7(b)) so that a further alkene molecule can bind to
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J.D. Gale et al. / DFT study of Ziegler–Natta catalysts 245
(a)
(b)
(c)
Figure 7. Final geometries obtained by cluster optimisation of: (a)
CH3TiCl2(C2H4)+, (b) (C3H7)TiCl+2 with methyl agostic bond to tita-
nium and (c) (C3H7)TiCl+2 in a second configuration without the methyl
agostic interaction. Atom labels refer to geometric parameters given in
table 2.
Table 2
Energies and selected geometrical parameters for the three configurations
based on the CH3TiCl+2 cluster model at the B3LYP/TZVP level: (a)
with ethene adsorbed, (b) having reacted to form a propyl ligand with an
agostic interaction, (c) having reacted to form a propyl ligand but in a
second conformation in which there is no interaction between the methyl
group and Ti.
(a) (b) (c)
Relative energy +34.80 0.0 +67.48
(kJmol−1)
Ti–Cl1 (A) 2.1559 2.1604 2.1471
Ti–Cl2 (A) 2.1559 2.1571 2.1471
Ti–C1 (A) 2.7553 1.9785 1.9383
Ti–C2 (A) 2.3479 2.3838 −
Ti–C3 (A) 1.9877 2.2161 −
C1–C2 (A) 1.3473 1.5477 1.5012
C2–C3 (A) − 1.5845 1.5336
C1–H1 (A) 1.1273 1.1306 1.1645
C2–H2 (A) 1.1319 1.1294 1.1329C3–H3 (A) 1.1362 1.1304 1.1287
C3–H4 (A) 1.1336 1.1628 1.1297
Cl1–Ti–Cl2 (◦) 114.62 117.21 113.79
Cl1–Ti–C1 (◦) − 110.77 106.25
Cl1–Ti–C2 (◦) 111.61 130.08 −
Cl1–Ti–C3 (◦) 107.41 117.54 −
Ti–C1–C2 (◦) − 84.12 141.81
Ti–C3–H4 (◦) 111.90 82.09 87.20
C1–C2–C3 (◦) − 117.08 112.93
titanium. This process is endothermic by 67.5 kJ mol−1
with an activation barrier that must exceed this. Hence,
this second step would be likely to be the rate determining
one, though if the rearrangement is accompanied by alkene
adsorption this would lower the barrier. Finally, we should
comment that although the CH3TiCl+2 species is an active
polymerisation catalyst our earlier calculations indicate that
such three co-ordinate complexes are unlikely to exist, at
least not at the 100 surface.
Now, we turn to consider the binding of ethene to the
cluster CH3TiCl3 which represents the titanium binding site
as found from our earlier calculation. There are several
different configurations to consider in this case. Ethene may
bind either in the equatorial or axial position and may have
the C–C bond lying either within the mirror plane of thecomplex or perpendicular to it. Minimisations have been
performed for all of these possibilities within Cs symmetry,
with checks also being made for the preferred orientation of
the methyl group for each configuration. The lowest energy
configuration for each combination is shown in figure 8,
with the key geometrical parameters and energies being
given in table 3.
On analysis of the relative energies, it is apparent that
ethene will actually adsorb preferentially in the axial posi-
tion, rather than the equatorial position chosen in the earlier
supercell calculations. Indeed, the configuration in which
ethene is at right angles to the mirror plane when in theequatorial position although being a local minimum has an
endothermic binding energy. The most stable arrangement
with a binding energy of 18.75 kJ mol−1 has the ethene
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246 J.D. Gale et al. / DFT study of Ziegler–Natta catalysts
(a) (c)
(b) (d)
Figure 8. Four conformations for ethene adsorbed on CH3TiCl3: (a) equatorial with C2–C3 in the mirror plane, (b) equatorial with C2–C3 perpendicular
to mirror plane, (c) axial with C2–C3 in the mirror plane and (d) axial with C2–C3 perpendicular to mirror plane
molecule in the axial position with the carbon–carbon dou-
ble bond aligned with the Ti–C bond below, which is the
desired arrangement for the polymerisation mechanism of
Cossee [3].
The values of the binding energies obtained from the
cluster models confirm qualitatively the result of the su-
percell calculation, in that both indicate that ethene is onlyweakly adsorbed at the titanium site under consideration
in marked contrast to the case where titanium is three-co-
ordinate and the cluster carries an overall positive charge.
Given that for a heterogeneous catalyst the system will be
locally charge neutral, perhaps the binding energies ob-
tained here are more realistic.
Now let us specifically consider the energy of the second
equatorial configuration which is the one that most closely
resembles the geometry modelled in the planewave study.
In the periodic calculations ethene is definitely bound withan energy of 10.89 kJ mol−1, whereas in the cluster case it
is unbound by 17.60 kJ mol−1. This is also apparent from
the Ti–C distances which are of the order of 2.64 A in the
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J.D. Gale et al. / DFT study of Ziegler–Natta catalysts 247
Table 3
Binding energies (where a positive value indicates a bound state) and
selected geometrical parameters for the four configurations based on the
CH3TiCl3 cluster model for ethene adsorption at the B3LYP/TZVP level:
(a) equatorial with C2–C3 in the mirror plane, (b) equatorial with C2–C3
perpendicular to the mirror plane, (c) axial with C2–C3 in the mirror plane
and (d) axial with C2–C3 perpendicular to the mirror plane.
(a) (b) (c) (d)
BE (kJ mol−1) 6.77 (−17.60) 18.75 17.16
Ti–Cl1 (A) 2.2283 2.3341 2.2323 2.2329
Ti–Cl2 (A) 2.2176 2.2073 2.2373 2.2377
Ti–C1 (A) 2.0190 2.0568 2.0391 2.0431
Ti–C2 (A) 5.1034 2.9523 3.0660 3.0319
Ti–C3 (A) 4.7813 2.9523 3.1374 3.0319
C2–C3 (A) 1.3269 1.3369 1.3325 1.3328
C1–H1 (A) 1.1344 1.1379 1.1298 1.1283
C2–H2 (A) 1.1247 1.1236 1.1234 1.1241
C3–H3 (A) 1.1245 1.1233 1.1229 1.1223
Cl1–Ti–C1 (◦
) 116.81 152.11 105.19 101.47Ti–C1–H1 (◦) 109.76 99.35 107.71 114.29
former calculation and much longer at 2.952 A in the lat-
ter. Part of the reason for the difference, at least, is due
to the change of substituent from chloride to methyl, thus
leading to a change in the direction of the sigma inductive
effects and the loss of π-donation by chlorine. However,
a cluster calculation for ethene coordinated to the chlorine
substituted complex still gives an endothermic binding en-
ergy of 12.16 kJ mol−1 and an intermediate Ti–C distance
of 2.784 A.
One further reason for some of the difference in bind-
ing energies might be the change in the density functionals
used. If the cluster calculation is repeated using the Becke
non-local exchange functional and the PW91 correlation
functional then ethene is again unbound with an endother-
mic binding energy of 21.5 kJ mol−1 suggesting that most
density functionals will not give a favourable binding en-
ergy. In contrast, if we perform the same calculation at the
MP2 level then a stable complex is found with a binding
energy of 15.18 kJmol−1 and the Ti–C bond lengths of
2.700 A agree much more closely with those found in the
planewave calculations.
When such low binding energies are involved it is im-portant to make allowance for the basis set superposition
error (BSSE). For the complex where ethene is bound in
the equatorial position we have estimated the BSSE us-
ing the full counterpoise method as a first approximation.
The corrections to the energy obtained in this way at the
B3LYP and MP2 levels are 10.95 and 27.50 kJ mol−1, re-
spectively. Given that these errors are of the same order as
the total binding energy it is obvious that we should regard
the cluster results for both the binding energy and geome-
try of ethene as unreliable in this case. Clearly very large
basis sets beyond triple-zeta plus a single set of polarisa-
tion functions are going to be needed to treat this problemaccurately, unless the BSSE is eliminated by construction.
As the error is much larger at the MP2 level than for the
density functional one, this is the most likely cause of the
Table 4
Relative energies and selected geometrical parameters of four conforma-
tions of the (C3H7)TiCl3 cluster model at the B3LYP/TZVP level as il-
lustrated in figure 9. Conformations (a) and (b) are derived from ethene
being in an equatorial position, whereas (c) and (d) are based on ethene
having been axial initially.
(a) (b) (c) (d)
Relative energy +8.26 0.0 +8.20 +7.46
(kJmol−1)
Ti–Cl1 (A) 2.2302 2.2374 2.2304 2.2284
Ti–Cl2 (A) 2.2243 2.2319 2.2222 2.2235
Ti–Cl3 (A) 2.2236 2.2318 2.2238 2.2213
Ti–C1 (A) 2.0289 2.0208 2.0211 2.0210
C1–C2 (A) 1.5285 1.5205 1.5238 1.5242
C2–C3 (A) 1.5282 1.5235 1.5252 1.5292
C1–H1 (A) 1.1382 1.1290 1.1483 1.1464
C3–H2 (A) 1.1364 1.1294 1.1303 1.1303
Ti–C2 (A) 2.9610 2.5502 3.1069 3.0824
Ti–H2 (A) 2.8789 3.4411 3.3673 5.2895Cl1–Ti–C1 (◦) 115.57 115.69 118.64 116.85
Ti–C1–C2 (◦) 111.91 91.01 121.80 120.14
Ti–C1–H1 (◦) 104.45 113.56 95.25 99.56
C1–C2–C3 (◦) 112.96 115.38 113.27 112.97
C2–C3–H2 (◦) 113.09 111.84 112.25 111.62
Ti–C1–C2–C3 (◦) +59.07 +110.28 +75.18 +176.38
discrepancy between the results of the two methods. This
result also highlights the merits of the use of planewaves or
real space alternatives for such calculations as this problem
is eliminated.
In searching for the minimum energy conformation forthe propyl derivative of the cluster as the end point of the
first C–C bond formation reaction we have performed op-
timisations from two different starting configurations with
the Ti–C bond initially either axial or equatorial as well
leading to four different structures overall. The final bond
lengths and relative energies are given in table 4 and the
structures are illustrated in figure 9. Three of the struc-
tures have very similar energies to each other, however one
form is lower by 7.5 kJ mol−1. The reason for this can
be seen to be due to the short non-bonded Ti–C distance
of 2.550 A associated with an agostic interaction between
the methylene group and the transition metal centre. This
is also apparent from the fact that the C–H bond nearesttitanium has a length of 1.172 A as opposed to the other
C–H bond from the same carbon which has a more typical
value of 1.132 A. Compared with the most stable propyl
complex of the cationic titanium species, this species is
relatively open at titanium and so we would expect that
the rate determining factor would no longer be creating a
vacant binding site for an incoming alkene.
The key question in this study is whether the tita-
nium(IV) adsorption site characterised here is likely to be
an active site for polymerisation. The answer to this de-
pends on the activation energy for C–C bond formation as
much as the binding energy for ethene. In fact it is possiblethat any site which has too large a binding energy would
rapidly become blocked by strong adsorption of an electron
donor.
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248 J.D. Gale et al. / DFT study of Ziegler–Natta catalysts
(a) (b)
(c) (d)
Figure 9. Four conformations of the cluster (C3H7)TiCl3 where the chlorines are constrained to be in a trigonal bipyramidal geometry.
Although much more exploration is needed to locate all
the possible transition states which give rise to C–C bondformation, we have characterised the energy surface for the
formation of the first of the propyl complex configurations
(shown in figure 9(a)) using the CH2–CH3 bond length as
the reaction co-ordinate. Constrained optimisations were
performed for steps of the C2–C3 bond length of 0.1 A
which were reduced to 0.05 A in the region of the transition
state. This pathway leads to the reactant species in which
the methyl group is axial and the C–C bond of ethene lies
within the mirror plane of CH3TiCl3 – the first of the ethene
binding configurations, shown in figure 8(a).
The estimated activation energy for ethene insertion into
the Ti–C bond based on this preliminary calculation is53±1 kJmol−1, where the uncertainty comes from the res-
olution of the energy surface scan. This value is remarkably
close to the two experimental estimates for the activation
energy for polymerisation of Natta [25] and Chien [26] who
obtained values of roughly 50 kJ mol
−1
. It should be notedthat neither of these values correspond to exactly the same
catalyst system as being studied here. However, it is likely
that the key mechanistic step will be quite similar. Also we
need to be cautious given the tendency of density functional
methods to underestimate activation energies and therefore
future studies need to confirm this result with more accu-
rate correlation methods. Despite these qualifications, it
is encouraging that the present model for the active poly-
merisation site appears to give a sensible activation energy
which is broadly consistent with experimental information.
The approximate geometry of the transition state which has
a four centred cyclic arrangement, as depicted in figure 10,is also consistent with the model of Cossee [3] and with
the observations of previous studies [23] on the CH3TiCl+2cluster model.
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J.D. Gale et al. / DFT study of Ziegler–Natta catalysts 249
Figure 10. Approximate transition state geometry for the insertion of
ethene into the Ti–CH3 bond for the cluster model CH3TiCl3(C2H4).
4. Conclusions
A combination of planewave supercell calculations and
cluster techniques has been used to address the problem of
the nature of the Ti/MgCl2 catalyst system for Ziegler–Natta
polymerisation. Based on the first of these approaches we
have found that TiCl4 binds relatively weakly at the 110surface, taken as a model for faces where four co-ordinate
magnesium is present, and prefers to bridge between the
layers of the underlying structure rather than to try to con-
tinue the cleaved sheets. A greater binding energy is found
when the same molecule is adsorbed on the 100 surface
where magnesium is five co-ordinate, leading to the for-
mation of an approximately trigonal bipyramidal species of
titanium. This species may well lose a chloride ion, partic-
ularly in the presence of a Lewis acid co-catalyst, to form
what we propose may be the active site for polymerisation.
It is found that the non-local density functional used sig-
nificantly underestimates the binding energies of titanium
chloride at the surface through neglect of the dispersion
contribution. Hence, in future work it would be desirable
to correct for this through the inclusion of an interatomic
potential representation of the attractive dispersion terms
during the quantum mechanical optimisation.
Both cluster models, constructed to mimic the adsorbed
titanium species, and periodic supercell calculations indi-
cate that ethene is only relatively weakly coordinated to
titanium. However, the reaction to form a propyl group is
exothermic and the activation energy for the process quite
moderate, consistent with experimental estimates suggest-
ing that such sites will be catalytically active.
Finally, we can conclude that the model for the activesite found in this study is likely to be more realistic than
the CH3TiCl+2 cluster considered in previous calculations,
since we know that the system must be charge neutral over-
all and because the cationic species is likely to be a more
active catalyst than is observed experimentally based on the
low value for the activation energy. Furthermore the result-
ing minimum energy conformation of the propyl group forthe cationic species has a strong agostic interaction between
the terminal methyl group and titanium which effectively
blocks the active site to further adsorption of alkenes. The
corresponding situation is not found for the trigonal bipyra-
midal model. More work is needed though to examine the
effect of reduction of the titanium on all of the stages con-
sidered above, as well as investigating the influence of more
extensive basis sets in the cluster study to lower the basis
set superposition error.
Acknowledgement
JDG would like to thank the Royal Society for a Univer-
sity Research Fellowship and funding, Victor Milman and
Molecular Simulations Inc. for the use of CASTEP, and
EPSRC for computer time at EPCC as part of the Materials
Chemistry consortium. We are also grateful to EPSRC for
the provision of ROPA grant in support of this work.
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7/25/2019 A Density Functional Study of Ti-MgCl2-Supported Ziegler–Natta Catalyst Borealis
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250 J.D. Gale et al. / DFT study of Ziegler–Natta catalysts
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