A Density Functional Study of Ti-MgCl2-Supported Ziegler–Natta Catalyst Borealis

7/25/2019 A Density Functional Study of Ti-MgCl2-Supported Ziegler–Natta Catalyst Borealis

http://slidepdf.com/reader/full/a-density-functional-study-of-ti-mgcl2-supported-zieglernatta-catalyst-borealis 1/16

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



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.



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-




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.




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




(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.




(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




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




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




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




(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




(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




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.




(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.




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.

References

[1] J. Boor Jr., Ziegler–Natta Catalysts and Polymerisation (Academic

Press, New York, 1979).

[2] S. Weber, J.C.W. Chien and Y. Hu, in: Transition Metals

and Organometallics as Catalysts for Olefin Polymerisation, eds.

W. Kaminsky and H. Sinn (Springer, Berlin, 1988) p. 45.

[3] P. Cossee, J. Catal. 3 (1964) 80.

[4] J.S. Lin and C.R.A. Catlow, J. Mater. Chem. 3 (1993) 1217.

[5] J.S. Lin and C.R.A. Catlow, J. Catal. 157 (1995) 145.

[6] E.A. Colbourn, P.A. Cox, B. Carruthers and P.J.V. Jones, J. Mater.

Chem. 4 (1994) 805.

[7] E. Puhakka, T.T. Pakkanen and T.A. Pakkanen, J. Phys. Chem. A

101 (1997) 6063.

[8] O. Novaro, E. Blaisten-Barojas, E. Clementi, G. Giunchi and M.E.

Ruiz-Vizcaya, J. Chem. Phys. 68 (1978) 2337.

[9] J. Sauer, P. Ugliengo, E. Garrone and V.R. Saunders, Chem. Rev. 94

(1994) 2095.

[10] U. Eichler, C.M. Kolmel and J. Sauer, J. Comput. Chem. 18 (1996)

463.

[11] S.P. Greatbanks, P. Sherwood and I.H. Hillier, J. Phys. Chem. 98

(1994) 8134.

[12] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias and J.D.

Joannopoulos, Rev. Mod. Phys. 64 (1992) 1045.

[13] J.P. Perdew, in: Electronic Structure of Solids ’91, eds. P. Zeische

and H. Eschrig (Akademie, Berlin, 1991).

[14] L.J. Clarke, I. Stich and M.C. Payne, Comp. Phys. Comm. 72 (1992)

14.

[15] M. Kimura, K. Kimura, M. Aoki and S. Shibata, Bull. Chem. Soc.

Japan 29 (1956) 95.

[16] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson,

M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A.

Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski,

J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A.

Nanayakkara, M. Challcombe, C.Y. Peng, P.Y. Ayala, W. Chen,

M.W. Wong, J.L Andres, E.S. Replogle, R. Gomperts, R.L. Martin,

D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart,

M. Head-Gordon, C. Gonzalez and J.A. Pople, Gaussian94, Revi-

sion D.3 (Gaussian Inc., Pittsburgh, PA, 1995).




[17] A. Schafer, C. Huber and R. Ahlrichs, J. Chem. Phys. 100 (1994)

5829.

[18] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.

[19] C. Lee, W. Yang and R.G. Parr, Phys. Rev. B 37 (1988) 785.

[20] I.W. Bassi, F. Polato, M. Calcaterra and J.C.J. Bart, Zeitschrift f urKrist. 159 (1982) 297.

[21] F. Gygi, Phys. Rev. B 51 (1995) 11190.

[22] P.W. Fowler, Mol. Simul. 4 (1990) 313.

[23] H. Kawamura-Kuribayashi, N. Koga and K. Morokuma, J. Am.

Chem. Soc. 114 (1992) 2359.

[24] F.U. Axe and J.M. Coffin, J. Phys. Chem. 98 (1994) 2567.

[25] G. Natta and I. Pasquon, Adv. Catal. 11 (1959) 1.[26] J.C.W. Chien, J. Am. Chem. Soc. 81 (1959) 86.

A Density Functional Study of Ti-MgCl2-Supported Ziegler–Natta Catalyst Borealis

Documents

Transcript of A Density Functional Study of Ti-MgCl2-Supported Ziegler–Natta Catalyst Borealis