DFT STUDY OF THE ADSORPTION OF TITANIUM...

1

DFT STUDY OF THE ADSORPTION OF

TITANIUM TETRACHLORIDE ON

MAGNESIUM DICHLORIDE SURFACES IN

THE HETEROGENEOUS ZIEGLER-NATTA

CATALYST SYSTEM

Peter Zorve

Master´s thesis

Department of Chemistry

Physical Chemistry

582/2018

2

DFT STUDY OF THE ADSORPTION OF TITANIUM TETRACHLORIDE ON MAGNESIUM

DICHLORIDE SURFACES IN THE HETEROGENEOUS ZIEGLER-NATTA CATALYST

SYSTEM

Peter Zorve

Supervisors: Prof. Mikko Linnolahti, Prof Tapani A. Pakkanen

University of Eastern Finland, Joensuu Campus, Chemistry Department, 2018

3

ABSTRACT

The discovery of the heterogeneous Ziegler-Natta (ZN) catalyst by Karl Ziegler and Giulio Natta

was a breakthrough in the production of synthetic polymers. For at least the past decades, more

than half of world-wide polyethylene (PE) are produced using the MgCl2 supported-titanium-based

ZN catalyst. These polymeric materials have become part of our everyday life. Intensive work and

research have been carried out on the ZN catalysis, but there are still areas not yet exploited. In

this research, the DFT method was used to study the chemisorption of titanium tetrachloride

(TiCl4) on magnesium dichloride (MgCl2) surfaces in the ZN catalysis system.

Adsorption of TiCl4 molecules onto nine (MgCl2)𝑛 clusters (𝑛 = 1 − 9) were thoroughly studied.

The under-coordinated surface Mg atoms, representing the (110) and (104) surfaces of crystalline

MgCl2, were the driving force for the chemisorption of the TiCl4 molecules. The (110)−MgCl2

surface has the surface magnesium atoms four−coordinated and the (104)−MgCl2 surface has the

surface magnesium atoms five-coordinated. The electronic energies and Gibbs energies of the nine

clusters were first examined as a function of increasing 𝑛. The stabilities of the clusters were found

to increase as the size of the cluster increases. Clusters with the same value of 𝑛, but different

shapes, were found to have different energies. To explore the adsorption of TiCl4 onto the clusters,

the reaction energies and Gibbs energies for the formation of (MgCl2)𝑛―(TiCl4)𝑚 complexes were

systematically screened to locate the global minima of the complexes as a function of 𝑛 and 𝑚.

Altogether 1721 complexes were studied to complete the task, eventually enabling to deduce the

preferred composition of the clusters and the binding modes of TiCl4. The study revealed three

preferential binding modes of TiCl4: mononuclear, binuclear and trinuclear binding. In small

clusters, 𝑛 = 1―3, monomeric binding was preferred, leading to five-coordination of the Ti atoms

Also five-coordinated Ti atoms were found adsorbed onto the (104) − MgCl2 surfaces. Six-

coordinated binuclear binding modes were found in most of the global minima. Notably, trinuclear

binding was noticed in this study at the sites that can be considered as defects, with substantially

improved stabilities. Overall, the result deepen the understanding of adsorption of TiCl4 on MgCl2

and strongly indicate that TiCl4 molecules can stabilize MgCl2 surface more strongly than has

been suggested by previous literature.

4

TABLE OF CONTENTS

ABBREVIATIONS ........................................................................................................................ 6

1. INTRODUCTION TO THE ZIEGLER-NATTA CATALYSIS ............................................ 7

2. TYPES AND STRUCTURES OF ZIEGLER – NATTA CATALYSIS ................................ 8

2.1. Homogeneous Catalysis ................................................................................................... 8

2.1.1. Group IV metallocenes ............................................................................................. 8

2.1.2. Co-catalyst ................................................................................................................ 9

2.2. Heterogeneous Catalysis ................................................................................................ 10

2.2.1. Aluminium Alkyl AlR3 ........................................................................................... 10

2.2.2. Magnesium Dichloride MgCl2 ................................................................................ 11

2.2.3. Titanium Chloride ................................................................................................... 12

2.2.4. Electron Donors ...................................................................................................... 14

3. MODELING OF MgCl2 CATALYST IN THE ZIEGLER-NATTA CATALYSIS ............. 15

3.1. Surfaces and Adsorption Characterization Theorem of MgCl2 ...................................... 15

3.2. Binding of Electron Donor to MgCl2 surfaces ............................................................... 18

3.3. Adsorption of Titanium Tetrachloride TiCl4 on Magnesium Dichloride MgCl2 Surface

18

3.4. Co-adsorption of Electron Donors and TiCl4 onto MgCl2 surfaces ............................... 19

4. RESULTS AND DISCUSSION ............................................................................................ 20

4.1. Aims of the Study ........................................................................................................... 20

4.2. Computational Details .................................................................................................... 21

4.3. Stability of the (MgCl2)𝑛 clusters .................................................................................. 21

4.4. Stability of the (MgCl2)𝑛―(TiCl4)𝑚 clusters ............................................................. 25

4.4.1. MgCl2―(TiCl4)𝑚 .................................................................................................... 25

4.4.2. (MgCl2)2―(TiCl4)𝑚 ............................................................................................... 28

4.4.3. (MgCl2)3―(TiCl4)𝑚 ............................................................................................... 31

5

4.4.4. (MgCl2)4―(TiCl4)𝑚 ............................................................................................... 33

4.4.5. (MgCl2)5―(TiCl4)𝑚 ............................................................................................... 36

4.4.6. (MgCl2)6―(TiCl4)𝑚 ............................................................................................... 38

4.4.7. (MgCl2)7―(TiCl4)𝑚 ............................................................................................... 41

4.4.8. (MgCl2)8―(TiCl4)𝑚 ............................................................................................... 44

4.4.9. (MgCl2)9―(TiCl4)𝑚 ............................................................................................... 47

4.5. Summary ........................................................................................................................ 50

5. CONCLUSION ..................................................................................................................... 53

6. ACKNOWLEDGEMENT ..................................................................................................... 55

7. REFERENCES ...................................................................................................................... 56

6

ABBREVIATIONS

ZN Ziegler-Natta

LLDPE Linear Low-Density Polyethylene

Cp Cyclopentadienyl

PE Polyethylene

PP Polypropylene

TMA Trimethylaluminum

TEA Triethylaluminum

MAO Methylaluminoxane

ID Internal Donor

BA Battlement Pattern

ST Staircase Pattern

MWD Molecular Weight Distribution

DBP Dibutyl Phthalate

DFT Density Functional Theory

TZVP Triple-Zeta (ζ) basis set augmented by a Polarization function

7

1. INTRODUCTION TO THE ZIEGLER-NATTA CATALYSIS

In 1947, a German organic chemist Karl Ziegler (1898–1973) and co-workers discovered the

formation of 1–butene from the reaction of ethyllithium and ethene as they were purifying

ethyllithium as shown in equation 1.1 and 1.2. [1]

C𝑛H2𝑛+1Li + C2H4 → C𝑛H2𝑛+1CH2CH2Li (1.1)

C𝑛H2𝑛+1CH2CH2Li → C𝑛H2𝑛 + LiH (1.2)

Six years later, Ziegler made another discovery: the combination of Al(CH2CH3)2Cl and

TiCl4catalyst gave high activities to the production of synthetic polymeric materials.

In 1952, an Italian chemist Giulio Natta (1903-1979) and co-workers worked on Ziegler’s

discovery until 1954, when they applied Ziegler’s earlier discovery to produce the first synthetic

polymeric material (isotactic polypropylene) from propylene. They achieved this by reacting

Al(CH2CH3)3 with crystalline α−TiCl3. In 1963, a Noble Prize was rewarded to both Ziegler and

Natta, and their breakthrough has since been known as the Ziegler–Natta (ZN) catalysis. [2]

In the 1970’s, magnesium dichloride (MgCl2) was discovered to greatly improve the activity of

the ZN catalyst (also known as the titanium–based catalyst). MgCl2 enhanced the activity of the

titanium based catalyst so much that, it wasn’t necessary to remove the residual titanium from the

product. [3] The MgCl2 catalyst made it possible to produce large amount of linear polymers

(polyethene) with short branches. These polymers have low densities and they were referred to as

Linear Low–Density Polyethylene (LLDPE). Before the discovery of the ZN catalysts, chromium

catalysts were used in the production of the ethylene polymers, which only work well at low

temperature polymerization of ethylene. The applications of the ZN catalysis in the production of

synthetic polymers have exponentially increased. Today, over 80 million tons of polymers are

produced using ZN supported catalysts [4] [5] In this fourth generation, ZN catalyst system

consists of MgCl2/TiCl4/internal donors, pre-catalyst, soluble aluminium trialkyl/external donors

and co-catalysts. Polymeric materials are now essential part of our everyday life. They are use for

instances in housing, transportation, clothing, recreations and food production.

The ZN catalysts are classified into homogeneous and heterogeneous catalysts. The focus of this

study is the heterogeneous ZN catalyst which consist of magnesium dichloride (MgCl2), titanium

8

tetrachloride (TiCl4), alumorganic co-catalyst, internal electron donor and external electron donor.

However this research is narrowed down to the interaction of TiCl4 with MgCl2. The discovery

that chemically and mechanically activated MgCl2 was an excellent support became the basis for

the exponential growth of the production of ZN-supported polymers. [6] The yearly production of

polyethylene and polypropylene from 2004 to 2015 is shown in the fig 1. The ZN catalysis system

is very complicated which is almost impossible to fully understand with only experimental studies.

There is therefore the need for computational studies to support the experimental studies. [7]

Fig. 1. Bar chart representation of the worlds demand for some polymers from 2004 to 2015. (a) represents polyethylene (PE) and

(b) represents polypropylene (PP) [5]

2. TYPES AND STRUCTURES OF ZIEGLER – NATTA CATALYSIS

2.1. Homogeneous Catalysis

2.1.1. Group IV metallocenes

The group IV metallocenes are the main component of the homogeneous catalysts. In the

metallocene compound, there is a central metal, M, atom (group IV metal) and two

cyclopentadienyl, abbreviated as Cp, (C5H5) rings. The metal is a sigma σ–ligand and the Cp rings

have the p–orbital in the 𝜋-complexation with a d0–orbital. The metallocene catalysts have

homogeneous active sites and form uniform microstructures. They are mainly used for the

production of narrow molecular weight polymers with uniformly distributed long-chain and short-

chain branches. The stereoregularity and the polymerization activity depend on the Cp ligand’s

9

geometry. [8] Metallocenes do not only have cyclopentadienyl rings attached to them but also

dihalide atoms. In a chemical reaction involving metallocenes, they are first alkylated and activated

using a co-catalyst to produce an active cationic site. The metallocene halides and alkylated

metallocenes are referred to as pre-catalysts. [9] After the alkylation and activation, there are

insertions of olefin monomers which grow into the polymer. The insertions of the monomers

involve a chain propagation mechanism which is repeated until the required polymer length is

obtained after which the reaction is terminated.

The structural modifications of the metallocene greatly affect the catalytic properties, the

molecular weight and the tacticity of the polymer. The type of metal in the group IV metallocene

also affects the polymerization activity of the polymer. Examples of the metallocenes are

zirconocenes, hafnocene and titanocenes. Zirconocene is the most active catalyst compared to its

counterpart hafnocene and titanocene catalysts. Titanocenes have the lowest activity since at

higher temperature, they are deactivated. Hafnocenes on the other hand have lower activity

because of the stronger bond between the Hf and C atoms. [10] Ancillary ligands, such as indenyl,

phenanthrene, fluorenyl, etc, which are electron rich are sometimes used in place of the Cp-based

catalysts. Ligands which are more electron-rich increase the polymerization activity, however,

sterrically hindering ligands can have a negative influence on the polymerization process. Indenyl

ligands have a positive influence on the polymerization process. Co-catalysts affect the property

of the metallocene catalysts, which in turn also influence the stereoregularity of the polymer.

2.1.2. Co-catalyst

The main role of the co-catalyst is to activate the pre-catalysts, which is needed to initiate the

polymerization of the olefin. Examples of co-catalysts are trialkylaluminium (trimethylaluminium

(TMA), triethylaluminium (TEA)), methylaluminoxane (MAO), etc. [9] Different co-catalysts are

used because of their unique characteristics. MAO is used as co-catalyst because it can provide

high activity. TMA is used because when mixed with water, it can also provide high activity. When

TMA’s are hydrolyzed, they form dominantly cage-like MAO structures. Two mechanisms have

been proposed to describe how the MAO activates the pre-catalyst. The first is the direct removal

of Me− or Cl− from the pre-catalyst and the second is a transfer of [AlMe]+ ionic end from the

10

MAO to the pre-catalyst as shown in fig. 2 below. Co-catalysts also have great influence on the

catalytic activities and the molecular weight of the polymer produced. [11]

Fig. 2. The equilibrium between MAO1 and MAO2 structures and TMA association/dissociation. Active site of MAO1 is colored

yellow and the active site of MAO2 is colored purple [10]

2.2. Heterogeneous Catalysis

2.2.1. Aluminium Alkyl (𝐀𝐥𝐑𝟑)

Organo-aluminium compounds became very useful when they were discovered to play essential

role in the production of polymers. A typical example of an organoaluminium compound is the

aluminium alkyl complex (AlR3). Aluminium alkyl complexes are used as co-catalysts in the ZN

production of polymers. The most used aluminium alkyl compound is TMA, however, TEA and

other similar compounds are equally important. Alkyl aluminium compounds form dimers, which

are known to be more stable compare to the monomeric form. [12] TMA form more strongly

dimerized complexes than TEA. This is due to the steric hindrance involved in dimerization of

TEA. When aluminium alkyl co-catalysts are adsorbed on the MgCl2 surface, they form bridged

complexes with either the alkyl group or with chlorine atom. The chlorine-bridged complexes are

more stable compared to the alkyl-bridged complexes. The dimerization of the aluminium alkyl

depends on the temperature, the solvent and the concentration. Dissociations of the dimeric

11

compounds take place at high temperatures. Methyl-bridged dimeric aluminium alkyls are unstable

at high temperatures, dissociating into monomers. [12]

2.2.2. Magnesium Dichloride (𝐌𝐠𝐂𝐥𝟐)

Magnesium dichloride (MgCl2) is an inorganic compound with a cluster formulae of (MgCl2)𝑛.

The stability of (MgCl2)𝑛 increases as a function of increasing 𝑛. The structure of the crystalline

MgCl2 can be grouped into three categories. 𝛼―MgCl2, 𝛽―MgCl2 and 𝛿―MgCl2. The 𝛼―MgCl2

crystal has a rhombohedral structure, the 𝛽―MgCl2 has a closed packed hexagonal structure and

the 𝛿―MgCl2 has a rotational distorted form of the 𝛽―MgCl2. The 𝛼―MgCl2 and 𝛽―MgCl2

structures differ from each other in how the layers are stacked together. Sheets obtained from

𝛽―MgCl2 are more stable compared to that of the 𝛼―MgCl2. [13] In the bulk of the MgCl2 clusters,

the magnesium atoms are six-coordinated whiles the chlorine atoms are three-coordinated. [14]

The bulk MgCl2 is described to have a closed-packed cubic geometry. The Magnesium atoms fill

almost half of the octahedral sites which are available whiles the chlorine atoms fill almost all the

octahedral sites. [15] When the MgCl2 layer is cut, two types of unsaturated surface magnesiums

are obtained which is the basis for the classification of the MgCl2 surfaces. The two ways used to

describe the MgCl2 surfaces are the (104) surface and the (110) surface. The (104) surface is

used to describe a surface in which the magnesium atoms have coordination number of five. The

(110) surface is used to describe the surface where magnesium atoms are four-coordinated, as

shown in fig. 3. [16]

Fig. 3. The cuts of crystallite MgCl2 surface showing the relevant catalytic surfaces. Light green represents magnesium

atoms and dark green chlorine atoms. [16]

12

The unsaturated surface magnesium atoms promote the active adsorption sites for electron donors,

TiCl4, and so on. These adsorbed compounds are turned into polymerization active sites by

activation involving a co-catalyst.

2.2.3. Titanium Chloride

Titanium chloride is an inorganic compound where the titanium atom can adopt different oxidation

states. The possible oxidation states of the titanium cation are; Ti(II), Ti(III) and Ti(IV). Titanium

chlorides are very important in the ZN catalysis. In the next sub-sections, the various type of

titanium chlorides are discussed.

2.2.3.1. Titanium Dichloride (𝐓𝐢𝐂𝐥𝟐)

Titanium dichloride has a high affinity for oxygen and therefore serves as a very strong reducing

agent. Ti(II) is known to be inactive in the production of propene. [17] Titanium dichloride does

not provide enough stability to the MgCl2 surfaces compare to titanium trichloride and titanium

tetrachloride hence are less used in the production of polymers.

2.2.3.2. Titanium Trichloride (𝐓𝐢𝐂𝐥𝟑)

Titanium trichloride became very useful in the mid-1950′s with inventions of Karl Ziegler. TiCl3

and alkylaluminium compound greatly transform the MgCl2 surface when they are co-adsorbed

[3] When an adsorbed Ti(IV) species is reduced, it forms a Ti(III) species; first Ti2Cl7 and then

Ti2Cl6. The Ti(III) species can form a dimer with formula Ti2Cl6. The dimeric form is more stable

than the monomeric form since it increases the coordination number of the Ti atoms. Further

reduction of Ti(III) results in the formation of Ti(II). [17] When TiCl3 molecules are adsorbed

onto MgCl2 surfaces, they can adopt any of the following structures; tetrahedral structure, shown

in fig 4a, distorted octahedral, fig 4b, or trigonal bipyramidal fig 4c, structure as represented below.

13

Fig. 4. Optimized structure of different types of TiCl3 structures when adsorbed onto a MgCl2 surface. (a) tetrahedral

structure, (b) distorted octahedral structure (c) trigonal bipyramidal structure [17]

2.2.3.3. Titanium Tetrachloride (𝐓𝐢𝐂𝐥𝟒)

Several works have been done to understand how TiCl4 is adsorbed onto MgCl2 surfaces. The

adsorption characteristics of the TiCl4 depends on the type of magnesium dichloride surface. TiCl4

can adopt different geometrical structures when adsorbed onto the MgCl2 surfaces. [17] There are

various types of binding on the MgCl2 surfaces: mononuclear binding, binuclear binding and

sometimes the trinuclear binding.

The mono nuclear binding is classified according to the coordination number adopted by the

titanium cation after binding to the MgCl2 surface, and the type of MgCl2 surface it is bonded to.

There are three ways to classify the mononuclear binding. The first is called the 5―104. In the

5―104 mode of binding, the titanium atoms adopt a coordination number of 5 on a (104) MgCl2

surface. The 5―104 binding mode is the only possible way a TiCl4 can bind to a (104) MgCl2

surface. On the (110) MgCl2 surface, the titanium atom can adopt a coordination of either 4 or 6;

leading to the second and third type of binding mode. The second is the 4―110 binding mode,

where the titanium obtains a coordination of four after binding to (110) MgCl2 surface. Lastly

there is the 6―110 binding mode, where the titanium atoms obtain a coordination of six on the

(110) MgCl2 surface. [18] The stability of the monomeric binding increases as a function of the

increasing coordination. In the binuclear binding, two chlorine atoms connect two octahedrally

coordinated titanium atoms in a bridge-like manner. The dimer, Ti2Cl8, is only possible on a [104]

MgCl2 surface leading to 6―104 binding mode. [17] [18] [19] These binding modes are illustrated

in fig. 5 below

14

a b c d

Fig. 5. Pictorial illustration showing the various types of TiCl4 binding on the MgCl2 surface. (a) mononuclear 5-104,

(b) mononuclear 4-110, (c) 6-110 and (d) binuclear 6-104 binding mode

2.2.4. Electron Donors

An electron donor is a chemical species that is capable of donating electrons (unpaired electrons)

to another species which is electron deficient. Electron donors help to enhance the polymer’s

isotacticity. [20] Other roles of electron donors include: stabilization of the MgCl2 crystallites

surface, help to promote good adsorption of titanium chloride (mostly TiCl4), help in creating more

active sites for the stabilization of the (MgCl2)𝑛―(TiCl4)𝑚 complexes and lastly help to promote

the formation of multiple active sites which enables polymers with wider molecular weight to be

produced. [21] Electron donors were formally used with titanium trichloride (TiCl3) but the

usefulness of the electrons donors became extremely important when they were discovered to have

very high activities with MgCl2 supported initiation system. There are two types of electron donors;

internal electron donors and external electron donors. The difference between the two is the time

they are added in the production of the polymer.

2.2.4.1. Internal Electron Donors

In the production process of polymers, the internal electron donor, mostly known as internal donors

(ID) are added during the preparation of a catalyst. The main role of the ID is to control the

distribution and the amount of the TiCl4 on the surface of the catalyst. Internal electron donors also

help in the formation of new active sites. [22] The influences of the ID on the polymeric

characterization of polyolefin are greater than that of external donors. Diesters and diethers are the

15

most common internal donors however there are other compounds such are 1, 3-diol dibenzoate

and P-substituted sulphonyl-containing compounds [5], which are equally effective when used as

internal donors. Some other advantages of the ID’s include: they are able to change a catalyst´s

stereoregularity, help to change polypropylene tacticities to isotactic polymers, help in enhancing

the catalyst´s activity, help in controlling the molecular weight distribution (MWD) and help

change the response of hydrogen in order to control the weight of the polymer produced. [23] [24]

2.2.4.2. External Electron Donors

External electron donors also known as external donors (ED) are added during the polymerization

process. There is no exact explanation to the behavior of the external donors. T. Keii [25] reported

that external electron donors poison selective atactic sites which result in an increase in the relative

isotactic index. According to him, the molecular weight of the polymer increases since there is a

decrease in the amount of the co-cotalyst. [20] [25]

Park and Soga et al [26] agreed that the aspecific sites are converted into isospecific sites.

However, they said this conversion does not affect the rate of polymerization. In effect, the external

electrons increase the relative isotactic index and the polymer production is reduced. When the

isotactic index is increased, polymer’s molecular weight increases because the total amount of co-

catalysts in the system is decreased as they form complexes with the electron donors. [21]

3. MODELING OF 𝐌𝐠𝐂𝐥𝟐 CATALYST IN THE ZIEGLER-NATTA CATALYSIS

3.1. Surfaces and Adsorption Characterization Theorem of 𝐌𝐠𝐂𝐥𝟐

The energy of the MgCl2 surface is very important since it contributes to the stability of the catalyst.

An ideal (110) surface is one which has all the surface magnesium atoms 4-coordinated whereas

in an ideal (104), all surface magnesium atoms are 5-coordinated. When a surface has both 4- and

5-coordinated surface magnesium atoms, it is referred to as a surface defect. A ratio, R, [27] shown

in equation 1, describes the ratio of the number of 4-coordinated atoms to the total number of

surface magnesium atom. R gives an indication of the extent of surface defect.

16

R = N4

N4 + N5 (1)

where N4 is the total number of 4-coordinated magnesium atoms in a unit cell and N5 is the total

number of 5-coordinated magnesium atoms. R can be a value from 0 to 1. R equals to zero

describes an ideal (104) surface. R equals to one describes an ideal (110) surface.

For two-dimensional cut of MgCl2 sheet, two types of repetitive patterns have been considered.

The first is when the surface takes the form of a staircase (ST) and in the second, the surface takes

a form of a battlement (BA). These are shown in fig. 6. below

Fig. 6. (a) Unit cell of the ideal (104) and (110) MgCl2 surfaces and (b) surface defect patterns [27]

The BA is referred to as a mono-atomic step since it describes only the upper part of the cut ribbon.

The ST takes into account both sides of the ribbon and is referred to as a diatomic step in

exploration of the MgCl2 surface. The relative stabilities, ∆E, of the two types of pattern are

calculated using different equations. A MgCl2 sheet reference is used when calculating the ∆E.

The relative stability energy, ∆EST, [27] of the staircase (ST) pattern is calculated as

∆EST = 0.5 × E − mEsheet

L (2)

17

Where E (kJmol−1) is the total energy of the defected surface, Esheet (kJmol−1) is the total energy

of the sheet estimated by MgCl2 unit, m is an integer which defines the total number of magnesium

dichloride (MgCl2) unit, and L (Å) is the length of the surface

The relative stability, ∆EBA, [27] of the battlement (BA) pattern is calculated using the equation;

∆EBA = E − mEsheet − 𝛼Efix

L (3)

αis the lattice-parameter of the unit cell, Efix (kJmol−1Å−1) is the total energy of the (104) surface

or the (110) surface where all the atoms are fixed at the bulk calculated position per unit length.

In the presence of an adsorbate, the relative stability energy, ∆EΣ, [7] of the surface/adsorbate

complex of the ST pattern is calculated using the expression

∆EΣ = 0.5 × EΣ − mEsheet − ∑ k𝑖E𝑖

L (4)

Where EΣ is the total electronic energy of the surface/adsorbate complex expressed in kJmol−1, E𝑖

is the total electronic energies of the isolated molecule of the 𝑖th adsorbate, expressed in kJmol−1

and k𝑖 is the number of molecules in the unit cell.

The adsorbate molecules possess what is referred to as the absolute adsorption energy ∆Eads [7]

and it is calculated as

∆Eads = EΣ − Es − 𝑘Em

k (5)

Em (kJmol−1) defines the total electronic energies of an isolated adsorbate in a cell

The relative stabilization effect, ∆Estab, is the difference between the relative stability energy of

the surface/adsorbate complex and the relative stability energy of the surface and its given as;

∆Estab = ∆EΣ − ∆ES (6)

18

3.2. Binding of Electron Donor to 𝐌𝐠𝐂𝐥𝟐 surfaces

Since the MgCl2 surfaces have magnesium atoms that are electron deficient, they accept electron

pair from the electron donors. The role of the electron donor is to stabilize the unsaturated surface

magnesium atoms. Different electron donors are adsorbed differently on the MgCl2 surface.

Considering the binding mode of electrons donors, they are grouped into monodentate and

bidentate. The monodentate electron donor has one binding site and it binds to the MgCl2 surface

with it. Examples of monodentate electron donors are tetrahydrofuran, methanol, ethylbenzoate,

etc. [28] Bidentate electron donors have two binding sites. In binding to the MgCl2 surface, it can

use either only one or both binding sites. When it uses one binding site, it behaves like a

monodentate donor. When it uses both binding sites, it either serves as a bridging or as a chelating

donor. [23]

3.3. Adsorption of Titanium Tetrachloride (𝐓𝐢𝐂𝐥𝟒) on Magnesium Dichloride (𝐌𝐠𝐂𝐥𝟐)

Surface

As said earlier in the previous section, the surfaces of the MgCl2 sheets are unstable since the

surface magnesium cations are under-coordinated. [29] Different molecules have been used to

increase the relative stability of the surface Mg atoms. Among such molecules are; titanium

dichloride, titanium trichloride, titanium tetrachloride, electron donors (internal and external

electron donors), alkylaluminium and so on. A common and the most used molecule is the titanium

tetrachloride which is the focus of this study. The active sites of MgCl2 surface; where titanium

tetrachloride and other compounds (electron donors, alkylaluminium, etc) bind to, can withstand

several pre-catalyst preparations. This stability is the starting point for a reasonable catalyst design

and the catalyst improvement [15] Computational studies take into consideration the behaviour,

characteristics and the stability of these active sites and how the stability of the sites can be

improved upon by the adsorption of another compound. [30]

The recent catalyst generation involves chemisorption of two or more different molecules to

MgCl2. For instance, there is the co-adsorption of electron donors and titanium tetrachloride on the

same MgCl2 surfaces. There are other instances of such sorts. The use of more than one different

compounds to stabilize the surface has been found to significantly enhance the stability of the

magnesium dichloride sheet. [31]

19

The stability of MgCl2 sheets is a function of the coordination numbers of the surface Mg atoms.

The higher the coordination number of the surface Mg atom(s), the more stable the surface is. The

5-coordinated surfaces are more stable than the 4-coordinated surfaces. In situations where there

are 3-coordinated surface Mg atoms, the 3-coordinated Mg atoms become the least stable

compared to the 4 and 5-coordinated surfaces. Earlier works on Ziegler-Natta catalysis gave rise

to some controversies concerning which type of titanium chloride will bind more strongly to MgCl2

surfaces. Ziegler and his co-workers predicted that TiCl2 and TiCl3 would bind more strongly to

the MgCl2 surfaces than TiCl4. [32] [33] However, Parrinello and co-workers, and Busico and co-

workers proved otherwise. According to Parrinello, et al, TiCl4 binds more strongly on MgCl2

[104] surfaces. Busico and his co-workers, also demonstrated that TiCl4 could bind more strongly

to the MgCl2 [110] surface than to the [104] surface. [33] The aim of this research was not to

examine which surface to which TiCl4 could bind more strongly. However the observations made

by Parrinello and Busico contradict what Ziegler and co-workers earlier predicted. In the Z-N

catalyst system, the MgCl2-supported titanium-based catalysts play the most significant role in the

industrial production of olefin polymers, [34] but because of the multisite catalysts nature of the

MgCl2-supported Ziegler-Natta catalysts, the modelling and design are extremely complicated and

are very difficult to understand. [35] Titanium tetrachloride(TiCl4), generates active sites on

MgCl2 surfaces. These sites have high degree of porosities which form the basis for high degree

of nanoporosity. The exact characteristics of these active sites and the foundation of the degree of

the nanoporosity is still not fully understood.

3.4. Co-adsorption of Electron Donors and 𝐓𝐢𝐂𝐥𝟒 onto 𝐌𝐠𝐂𝐥𝟐 surfaces

Titanium tetrachloride alone does not provide enough stability to magnesium dichloride. There is

therefore the need for another species that can add to the stability that titanium tetrachloride

provides. Electron donors and titanium tetrachloride are co-adsorbed to the magnesium dichloride

surfaces. [31] In a typical Ziegler-Natta catalyst system, where TiCl4 and electron donors (internal

donors) are co-adsorbed, the internal donors are first used to saturate the surface of the MgCl2,

after which the TiCl4 molecules fill the remaining sites which were inaccessible by the internal

donors due to their steric difficulties. [36] A typical illustration is shown in fig. 7. below. In this

research, only TiCl4 molecules were adsorbed onto the MgCl2 surface.

20

Fig 7. Co-adsorption of dibutyl phthalate DBP and TiCl4 molecules on MgCl2 [104] surface. [36]

Since the internal donors occupy most of the adsorption sites compared to TiCl4, it is difficult to

estimate the magnitude to which the TiCl4 stabilizes the MgCl2 surface. However, it can be said

with high level of confidence that internal donors bind more strongly to MgCl2 sheet than TiCl4,

when the two are co-adsorbed. TiCl4 and other compounds such as the internal donors are not

easily removed after they have been adsorbed onto the MgCl2 surfaces. They can only be removed

when extreme thermal measures or strongly coordinating solvents are used. Removal of these

compound might even result in destroying the identity of the starting reactants. This is due to the

fact that (MgCl2)𝑛―(TiCl4)𝑚 or (MgCl2)𝑛―𝑖ID complexes are very stable and become almost

impossible to reverse to the starting materials.

4. RESULTS AND DISCUSSION

4.1. Aims of the Study

The objective of this study was to examine the effect of the adsorption of TiCl4 molecules onto

MgCl2 surfaces. These include finding the most stable (MgCl2)𝑛―(TiCl4)𝑚 complex after TiCl4

molecules have been adsorbed onto the surface. To be able to achieve this, all possible

combinations of the adsorption of TiCl4 onto the MgCl2 surface were explored. The basis for the

21

chemisorption of TiCl4 is the assumption that TiCl4 can only be adsorbed to unsaturated MgCl2

surfaces. [37]

The stability of the (MgCl2)𝑛 clusters were first examined with respect to the increasing number

of MgCl2-units in the (MgCl2)𝑛 cluster without the adsorption of TiCl4 molecules. After that the

(MgCl2)𝑛 clusters were examined when TiCl4 molecules were adsorbed. Last, the change in the

Gibbs energy of reaction (∆𝑟G) and the electronic energy (∆𝑟E) for the formation of

(MgCl2)𝑛―(TiCl4)𝑚 complexes was calculated. 𝑛 is the number of MgCl2-units in the MgCl2

cluster and 𝑚 is the number of TiCl4 molecules the MgCl2 cluster adsorbed.

4.2. Computational Details

The adsorption of TiCl4 molecules onto different MgCl2 surfaces was studied using M06-2X

Density Functional Theory (DFT) method. [38] This method was combined with TZVP basis set.

[39] All the calculations were carried at a constant temperature of 298.15K and constant pressure

of 1atm. Calculations were carried using the Gaussian 09 package. [40] The structures were

optimized without any symmetry limitations. The energies reported were the changes in electronic

(∆𝑟E) and Gibbs free energies of reaction (∆𝑟G), which corresponds to the global minimum at the

said temperature and pressure.

4.3. Stability of the (𝐌𝐠𝐂𝐥𝟐)𝒏 clusters

The first task carried was to determine the relative stability of the magnesium dichloride (MgCl2)𝑛

clusters as a function of 𝑛 without the adsorption of the TiCl4 molecules. The optimized structures

of the (MgCl2)𝑛 clusters are shown in fig. 8. below. The monomer MgCl2 is a linear molecule

where the magnesium atom has a coordination of 2. The dimer (MgCl2)2 has a planar shape in

which two chlorine atoms bridge the magnesium atoms.

MgCl2 (MgCl2)2 (MgCl2)3

22

(MgCl2)4 (MgCl2)5 (MgCl2)6

(MgCl2)7 (MgCl2)8 (MgCl2)9

Diamond (MgCl2)14 Pipe (MgCl2)14

Fig 8. The optimized structures of (MgCl2)𝑛 cluster for 𝑛 = 1 − 9 and the structure of a diamond-shaped (MgCl2)14

and a pipe-shaped (MgCl2)14. Mg atoms are in yellow Cl atoms in green.

In the trimer, (MgCl2)3, two terminal Mg atoms were 3-coordinated with a 4-coordinated central

Mg atom. The shape of the (MgCl2)4 cluster was a quadrangle with 2×2 Mg atoms; two Mg atoms

in a row and two Mg atoms in a column. All the Mg atoms in the (MgCl2)4 cluster were 4-

coordinated. (MgCl2)5 had a pyramid shape with three Mg atoms at the base. Four out of the five

Mg atoms in the (MgCl2)5 cluster were 4-coordinated. The fifth Mg had a coordination of 5. The

(MgCl2)6 cluster also had a quadrangle shape with 3×2 Mg atoms; three Mg atoms in a row and

two Mg atoms in a column. Four of the Mg atoms in the (MgCl2)6 cluster were 4-coordinated and

the remaining two were 5-coordinated. (MgCl2)7 had a hexagonal shape with one bulk Mg atom

which was 6-coordinated. There are six surface Mg atoms, four are 4-coordinated and two are 5-

23

coordinated. (MgCl2)8 has a distorted geometry with some of the Mg atoms dislocated resulting

in an increase in certain Mg-Cl distances. Lastly (MgCl2)9 cluster, had a quadrangle shape with

3×3 Mg atoms. The stabilities of the clusters were calculated relative to that of the monomer

MgCl2. Table 1. shows the relative energies of the different (MgCl2)𝑛 clusters and fig. 9 shows the

graphical illustration of ΔE/𝑛 and ΔG/𝑛 as a function of 𝑛.

Table 1. The relative energies and Gibbs energies of calculated (MgCl2)𝑛 clusters as a function of 𝑛

𝑛 Cluster Energy (E) /a. u. Gibbs Energy (G) /a. u. ΔE/𝑛 (kJmol−1𝑛−1) ΔG/𝑛 (kJmol−1𝑛−1)

1 MgCl2 -1120.578549 -1120.601702 0.0 0.0

2 (MgCl2)2 -2241.224770 -2241.256971 -88.8 -70.3

3 (MgCl2)3 -3361.875268 -3361.912510 -122.2 -94.0

4 (MgCl2)4 -4482.532410 -4482.570046 -143.2 -107.2

5 (MgCl2)5 -5603.188899 -5603.230065 -155.5 -116.3

6 (MgCl2)6 -6723.851179 -6723.895014 -166.2 -124.6

7 (MgCl2)7 -7844.477121 -7844.523072 -160.3 -116.7

8 (MgCl2)8 -8965.143930 -8965.195176 -169.2 -125.2

9 (MgCl2)9 -10085.834399 -10085.885050 -183.0 -137.0

14 Diamond (MgCl2)14 -15689.12646330 -15689.187322 -192.6 -143.2

14 Pipe (MgCl2)14 -15689.13522660 -15689.194476 -194.2 -144.5

From fig. 9, shown below, the stability of the (MgCl2)𝑛 increases as a function of increasing 𝑛

value. The stability of a cluster depends on the coordination numbers of magnesium atoms. The

higher the coordination of Mg atoms in a (MgCl2)𝑛 cluster, the more stable the cluster is.

Increasing 𝑛 −value results in an increasing possibility of higher coordination numbers for

magnesium, leading to improved stability.

24

Fig 9. A graphical illustration showing the relative stabilities of various (MgCl2)𝑛 clusters as a function of the number

of MgCl2 (𝑛) in the cluster.

If two or more (MgCl2)𝑛 clusters have the same 𝑛 value, then the relative stability of cluster will

depend on other factors like the shape of the cluster, size, lateral cut of the faces and so on. To

demonstrate this, two (MgCl2)𝑛 clusters with the same formula, (MgCl2)14 were optimised. The

first (MgCl2)14 cluster had the shape of a pipe while the second (MgCl2)14 had a diamond shape.

Structures are shown in fig. 8 and their relative energies are shown in table 1.

The relative energy of the pipe-(MgCl2)14 was found to be −194.2kJmol−1𝑛−1 and that of the

diamond-(MgCl2)14 −192.6kJmol−1𝑛−1. Though the difference between the stability energies

was small (~1.6kJmol−1), it showed that different shapes have different energies even if their

molecular formula are the same. In a thorough work carried by Turunen, et al [41], they reported

(MgCl2)𝑛 with shape like, hexagon, diamond, quadrangles, etc, are more stable than shapes such

as pipe and slab.

The next task was to saturate the under-coordinated surface magnesium atoms with various number

of TiCl4 molecules. The change in Gibbs energy (∆𝑟G) for the formation of each

-200.0

-180.0

-160.0

-140.0

-120.0

-100.0

-80.0

-60.0

-40.0

-20.0

0.0

0 1 2 3 4 5 6 7 8 9 10

En

ergy

, 𝛥E

/n(k

J/m

ol⋅

n)

Number of MgCl2 units (n)

ΔE/n

ΔG/n

25

(MgCl2)𝑛―(TiCl4)𝑚 complex was determined for each cluster. In finding the change in the Gibbs

free energy of reaction (∆𝑟G), equation 7, shown below, was used.

∆𝑟G = ∑ ∆G𝑝𝑟𝑜𝑑 − ∑ ∆G𝑟𝑒𝑎𝑐𝑡 (7)

To calculate the electronic reaction energy of each complex formed, the equation 8, shown below,

was used.

∆𝑟E = ∑ ∆E𝑝𝑟𝑜𝑑 − ∑ ∆E𝑟𝑒𝑎𝑐𝑡 (8)

The high surface energies associated to the under-coordinated Mg atoms were the driving force

for the chemisorption of TiCl4 on the MgCl2 surface. [42] This work reports a detailed examination

of the interaction of TiCl4 molecules and with small MgCl2 clusters.

4.4. Stability of the (𝐌𝐠𝐂𝐥𝟐)𝒏―(𝐓𝐢𝐂𝐥𝟒)𝒎 clusters

4.4.1. 𝐌𝐠𝐂𝐥𝟐―(𝐓𝐢𝐂𝐥𝟒)𝒎

In the adsorption of TiCl4 molecules onto the monomer, MgCl2 was reacted with different number

of TiCl4 molecules. In each set of reaction, the global minimum, which corresponds to the complex

with the minimum Gibbs free energy of formation (∆𝑟G), was determined. In order to identify the

minimum ∆𝑟G, 31 different combinations of the MgCl2―(TiCl4)𝑚 were calculated but the

structures and energies of only the most stable complexes for each 𝑚 are reported. The optimized

structures obtained from the reaction between MgCl2 and the various number of TiCl4 molecules

are shown in fig. 10.

MgCl2―(TiCl4)1 MgCl2―(TiCl4)2 MgCl2―(TiCl4)3

26

MgCl2―(TiCl4)4 MgCl2―(TiCl4)5

Fig. 10. Optimized structures of the MgCl2―(TiCl4)𝑚 complexes. Magnesium atoms are in yellow, chlorine atoms are

in green and titanium atoms are in white.

After optimization, the ∆𝑟G and the ∆𝑟E were analyzed for each MgCl2―(TiCl4)𝑚 complex. When

MgCl2 adsorbed one molecule of TiCl4 forming a MgCl2―(TiCl4)1 complex, the ∆𝑟G was

−32.4kJmol−1. In the geometrical structure of the MgCl2―(TiCl4)1 complex, the magnesium atom

had a coordination number of 3 while the titanium atom had a coordination number of 5. The most

stable MgCl2―(TiCl4)𝑚 complex was obtained at 𝑚 = 2. The ∆𝑟G for the formation of

MgCl2―(TiCl4)2 was −64.8kJmol−1, almost twice that of MgCl2―(TiCl4)1. The ∆𝑟G for the

formation of MgCl2―(TiCl4)𝑚 is shown in table 2 below. In the geometry of MgCl2―(TiCl4)2

complex, shown in fig. 10, the two TiCl4 molecules bonded to the MgCl2 on opposite ends. This

enabled the electron density to be evenly distributed around the MgCl2.

Table 2. Reaction energies and Gibbs energies for the formation of MgCl2―(TiCl4)𝑚 complexes

Gibbs Energy of reaction Electronic Energy of reaction

𝑚 G [ MgCl2] /au G [TiCl4]/ au

G[ MgCl2―(TiCl4)𝑚]

/au

∆𝑟G/ kJ

/mol E [ MgCl2] /au E[TiCl4]/ au E[MgCl2―(TiCl4)𝑚]/au

∆𝑟E/ kJ

/mol

1 -1120,601702

-

2690,480871 -3811,09492400 -32,4 -1120,5785489 -2690,4539269 -3811,06050650 -73,6

2 -6501,58812300 -64,8 -6501,54499415 -153,8

3 -9192,06137400 -44,8 -9192,01135385 -186,5

4 -11882,53677800 -30,4 -11882,49311250 -259,5

5 -14573,01527200 -24,2 -14572,96842620 -315,7

27

Each titanium atom in the MgCl2―(TiCl4)2 complex had a coordination of 5, while the magnesium

atom had a coordination number of four. This stability can be associated with the increase in the

coordination of the magnesium atom and the symmetrical nature of the MgCl2―(TiCl4)2 complex.

When the number of TiCl4 molecules was increased to three forming a MgCl2―(TiCl4)3 complex,

the Gibbs free energy of reaction was found to be −44.8kJmol−1. An increment in the ∆𝑟G from

−64.7kJmol−1 for MgCl2―(TiCl4)2 to −44.8kJmol−1 for MgCl2―(TiCl4)3. Magnesium atom was

fully coordinated after the adsorption of five molecules of TiCl4 after which there was no room for

further adsorption. Comparison between the electronic and Gibbs energies show that the lowered

stability above 𝑚 = 2 is due to entropy lost upon complexation as the electronic energies continue

decreasing until 𝑚 = 5. In fig. 11 is a graphical illustration of the Gibbs energy (∆𝑟G) and the

electronic energy (∆𝑟E) of reaction of the MgCl2―(TiCl4)𝑚 complexes plotted as a function of 𝑚.

Fig. 11. A graph of the reaction energies (∆𝑟E) and Gibbs energies (∆𝑟G) for the formation of MgCl2―(TiCl4)𝑚

complexes plotted as a function of the number of TiCl4 molecules (𝑚). ∆𝑟G is in black and ∆𝑟E is in red.

-350

-300

-250

-200

-150

-100

-50

0

-70.0

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

0 1 2 3 4 5 6

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)

Number of TiCl4 molecules (m)

28

4.4.2. (𝐌𝐠𝐂𝐥𝟐)𝟐―(𝐓𝐢𝐂𝐥𝟒)𝒎

In identifying the global minimum of the adsorption of TiCl4 molecules by the dimeric (MgCl2)2

clusters, 63 possible adsorptions were calculated. The most stable complex for each number of

TiCl4 is reported. The dimer (MgCl2)2 was reacted with various number of TiCl4 molecules and

the most stable (MgCl2)2―(TiCl4)𝑚 complexes were identified. The optimized structures of the

(MgCl2)2―(TiCl4)𝑚 complexes are shown in fig. 12.

(MgCl2)2―(TiCl4)1 (MgCl2)2―(TiCl4)2 (MgCl2)2―(TiCl4)3


Fig. 12. Optimized structures of the (MgCl2)2―(TiCl4)𝑚 complexes. Magnesium atoms in yellow, chlorine atoms are

in green and titanium atoms are in white

The (MgCl2)2 cluster adsorbed one molecule of TiCl4 forming a (MgCl2)2―(TiCl4)1 with ∆𝑟G of

−32.3kJmol−1. In the geometry of the (MgCl2)2―(TiCl4)1 complex, the TiCl4 molecule bonded

to one of the Mg atoms causing that Mg atom to have a coordination number of four while the

other magnesium atom still having the coordination number of three. Addition of the second TiCl4

29

molecule to form a (MgCl2)2―(TiCl4)2 gave a ∆𝑟G of −66.3kJmol−1. The results of the ∆𝑟G of

the (MgCl2)2―(TiCl4)𝑚 complex and their corresponding electronic energies ∆𝑟E are shown in

table 3.

Table 3. Reaction energies and Gibbs energies for the formation of (MgCl2)2―(TiCl4)𝑚 complexes


𝑚

G [ (MgCl2)2]

/au G [TiCl4]/ au

G[ (MgCl2)2―(TiCl4)𝑚]

/au ∆𝑟G/ kJ/mol E [ (MgCl2)2] /au E[TiCl4]/ au

E[(MgCl2)2―(TiCl4)𝑚]

/au

∆𝑟E/ kJ

/mol

1 -2241,256971 -2690,480871 -4931,750129 -32,3 -2241.22476981 -2690,4539269 -4931.71000060 -82,2

2 -7622,243968 -66,3 -7622.19494395 -163,6

3 -10312,718674 -50,1 -10312.66152670 -196,8

4 -13003,195667 -39,9 -13003.14450610 -273,1

5 -15693,671826 -27,6 -15693.61742260 -323,0

6 -18384,145737 -9,3 -18384.08693720 -363,9

The ∆𝑟G of the formation of (MgCl2)2―(TiCl4)2 complex is slightly greater than twice that of

(MgCl2)2―(TiCl4)1, which implies the formation of (MgCl2)2―(TiCl4)2. In the geometry of the

(MgCl2)2―(TiCl4)2, the second TiCl4 molecule bonded to the opposite end relative to the first

TiCl4 molecule. Each of the magnesium atoms obtained a coordination of 4 while the titanium

atoms obtained coordination number of 5 each. (MgCl2)2―(TiCl4)2 complex was the most stable

(MgCl2)2―(TiCl4)𝑚 complex with the minimum ∆𝑟G, which can be again traced to lost entropy

upon further TiCl4 adsorption. In fig. 13, which presents ∆𝑟G and ∆𝑟E as a function of the number

of TiCl4 molecules (𝑚), it can clearly be seen that the global minimum was found when 𝑚 is equal

to 2.

30

Fig. 13. The change in the Gibbs free energy of reaction (∆𝑟G) and the electronic energy of reaction (∆𝑟E) plotted

as a function of the number of TiCl4 molecules (𝑚).

Addition of one more TiCl4 molecule ended up in an increase in the ∆𝑟G of the

(MgCl2)2―(TiCl4)𝑚 complex. The ∆𝑟G for the (MgCl2)2―(TiCl4)3 complex was found to be

−50.1kJmol−1. Further addition of TiCl4 resulted in an increment of Gibbs free energy of reaction.

The ∆𝑟G of reaction for the (MgCl2)2―(TiCl4)4 was found to be −39.9kJmol−1. In the structure

of (MgCl2)2―(TiCl4)4 complex, three of the molecules of TiCl4 formed a trimeric binding around

one of the Mg atom, each with coordination of 6, while the fourth TiCl4 molecule bonded to the

other Mg atom obtained a coordination of 5. Adsorption of the fifth TiCl4 molecule onto Mg2Cl4

surface gave a ∆𝑟G of −27.6kJmol−1 for the (MgCl2)2―(TiCl4)5 complex. (MgCl2)2―(TiCl4)6

complex was the least stable complex with ∆𝑟G of −9.3kJmol−1. In this complex, all the

magnesium atoms had a coordination of six, and all the titanium atoms, except one which have

coordination of five, had coordination of six as well.

-400.0

-350.0

-300.0

-250.0

-200.0

-150.0

-100.0

-50.0

0.0

-70.0

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

0 1 2 3 4 5 6 7

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)


31

4.4.3. (𝐌𝐠𝐂𝐥𝟐)𝟑―(𝐓𝐢𝐂𝐥𝟒)𝒎

The trimer (MgCl2)3 was reacted with a various number of TiCl4 molecules and in each case, the

most stable isomer was identified. In order to identify the global minimum, 144 possible

combinations of (MgCl2)3―(TiCl4)𝑚 interactions were studied with 𝑚 varying from 1 to 8. The

maximum number of TiCl4 molecules (MgCl2)3 could adsorb was eight. The ∆𝑟G when (MgCl2)3

adsorbed one TiCl4 was found to be −33.4kJmol−1 forming a (MgCl2)3―(TiCl4)1 complex. The

TiCl4 molecule bonded to one end of the (MgCl2)3 cluster resulting in five-coordinated titanium

atom. Addition of a second TiCl4 forming a (MgCl2)3―(TiCl4)2 complex gave ∆𝑟G of

−67.0kJmol−1, almost twice of that of (MgCl2)3―(TiCl4)1. The two TiCl4 molecules bonded to

the Mg3Cl6 cluster at opposite end making the complex symmetrical. Addition of more TiCl4

molecules decreases the stability (MgCl2)3―(TiCl4)𝑚 complexes. (MgCl2)3―(TiCl4)3 complex

had ∆𝑟G of −46.9kJmol−1. The optimised structures of (MgCl2)3―(TiCl4)𝑚 complexes are

shown in fig. 14 below. Table 4 presents ∆𝑟E and ∆𝑟G for the formation of the

(MgCl2)3―(TiCl4)𝑚 complexes.



32

(MgCl2)3―(TiCl4)7 (MgCl2)3―(TiCl4)8

Fig. 14. Optimized structures of the (MgCl2)3―(TiCl4)𝑚 complexes. Magnesium atoms are in yellow, chlorine atoms

are in green and titanium atoms are in white.



𝑚

G [ (MgCl2)3]

/au G [TiCl4]/ au


/au

∆𝑟G/ kJ

/mol E [ (MgCl2)3] /au E[TiCl4]/ au


/au

∆𝑟E/ kJ

/mol

1

-

3361,912510

-

2690,480871 -6052,406107 -33,4 -3361,875268 -2690,4539269 -6052,360163 -81,3

2 -8742,899767 -67,0 -8742,844982 -162,4

3 -11433,372974 -46,9 -11433,31159 -195,7

4 -14123,850601 -38,4 -14123,79305 -268,0

5 -16814,329134 -32,2 -16814,26549 -316,6

6 -19504,801358 -9,5 -19504,73654 -361,6

7 -22195,281157 -6,7 -22195,21913 -436,8

8 -24885,759592 -0,3 -24885,69414 -492,2

The ∆𝑟G for the formation of (MgCl2)3―(TiCl4)4 complex was −38.2kJmol−1. Addition of a fifth

TiCl4 molecule gave ∆𝑟G to be −32.2kJmol−1. The ∆𝑟G further increased to −9.5kJmol−1 when

the sixth TiCl4 molecule was adsorbed. The ∆𝑟G for the addition of the seventh and eighth TiCl4

molecules were −6.7kJmol−1 and −0.3kJmol−1 respectively. ∆𝑟G for the addition of the eighth

TiCl4 molecule was almost zero, which implies that the formation of the of (MgCl2)3―(TiCl4)8

complex is almost as equal as to that of the (MgCl2)3 cluster. In the case of the trimer (MgCl2)3,

the global minimum was −67.0kJmol−1 which belongs to the (MgCl2)3―(TiCl4)2 complex.

(MgCl2)3 is thus most likely to bind to two molecules of TiCl4. In fig 15, ∆𝑟E and ∆𝑟G are plotted

as a function of the number of TiCl4 molecules (𝑚). From fig. 15, it is clearly shown that the

global minimum was located when 𝑚 = 2

33

Fig. 15. A graph of the reaction energies (∆𝑟E) and Gibbs energies (∆𝑟G) for the formation of (MgCl2)3―(TiCl4)𝑚


4.4.4. (𝐌𝐠𝐂𝐥𝟐)𝟒―(𝐓𝐢𝐂𝐥𝟒)𝒎

In studying the interactions of the tetramer (MgCl2)4 and TiCl4 molecules, (MgCl2)4―(TiCl4)𝑚

273 interactions were calculated, with only the most stable complex for each number of TiCl4

molecules reported. When one molecule of TiCl4 was adsorbed onto (MgCl2)4 forming a

(MgCl2)4―(TiCl4)1 complex, the ∆𝑟G was −24.3kJmol−1. The TiCl4 molecule was adsorbed to

the end where there was a 1-coordinated chlorine atom resulting in a 5-coordinated titanium atom

from a 4-coordinated atom. The optimized structures of the (MgCl2)4―(TiCl4)𝑚 complexes are

shown in fig. 16 and their corresponding ∆𝑟G and ∆𝑟E energies shown in table 5. Fig 17 presents

a graphical illustration of the ∆𝑟G and ∆𝑟E as a function of the number of TiCl4 molecules.

-600.0

-500.0

-400.0

-300.0

-200.0

-100.0

0.0

-80.0

-70.0

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

0 1 2 3 4 5 6 7 8 9

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)


34






Upon the addition of the second TiCl4 molecule, ∆𝑟G reduced to −51.2kJmol−1. The second TiCl4

molecule was adsorbed at the opposite end relative to the first TiCl4 molecule. It also formed 5-

coordinated titanium atom just like that of the first one. When (MgCl2)4―(TiCl4)3 complex was

formed, the ∆𝑟G was found to be −58.9kJmol−1. The ∆𝑟G for the formation of

(MgCl2)4―(TiCl4)𝑚 complexes are shown in table 5 below.


Gibbs energy of reaction Electronic Energy of reaction

35

𝑚

G [ (MgCl2)4]

/au G [TiCl4]/ au


/au

∆𝑟G/ kJ



/au

∆𝑟E/ kJ

/mol

1 -4482,570046 -2690,480871 -7173,060183 -24,3 -4482.53241002 -2690,4539269 -7173.01494650 -75,1

2 -9863,551303 -51,2 -9863.49626204 -147,0

3 -12554,035086 -58,9 -12553.98216220 -231,0

4 -15244,520664 -71,2 -15244.46690150 -311,9

5 -17935,004217 -78,3 -17934.93231470 -342,0

6 -20625,483552 -74,2 -20625.41240130 -410,7

7 -23315,966288 -79,1 -23315.89928400 -497,2

8 -26006,441841 -65,2 -26006.37030350 -542,1

The ∆𝑟G for the formation of (MgCl2)4―(TiCl4)4 and (MgCl2)4―(TiCl4)5 complexes were

−71.2kJmol−1 and −78.3kJmol−1 respectively. When the sixth TiCl4 was adsorbed, the ∆𝑟G was

−74.2kJmol−1. The global minimum was found when the seventh TiCl4 molecules were adsorbed

onto the (MgCl2)4 surface.



-600.0

-500.0

-400.0

-300.0

-200.0

-100.0

0.0

-90.0

-80.0

-70.0

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

0 1 2 3 4 5 6 7 8 9

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)


36

The ∆𝑟G for the formation of the (MgCl2)4―(TiCl4)7 complex was −79.1kJmol−1. The geometry

of the (MgCl2)4―(TiCl4)7 was such that one TiCl4 molecule bonded onto the MgCl2 surface with

one of its chlorine atoms and maintaining its coordination of four, while a second Ti atom had a

coordination of five. There is one binuclear binding and lastly, the remaining three TiCl4 formed

a trinuclear binding. The addition of the eighth TiCl4 molecule resulted in an increase in the ∆𝑟G

as a result of lost entropy. The formation of the (MgCl2)4―(TiCl4)8 complex gave ∆𝑟G of

−65.2kJmol−1. Within the scope of the adsorption of TiCl4 molecules by the (MgCl2)4 cluster,

the electronic energy ∆𝑟E of the (MgCl2)4―(TiCl4)𝑚 increases as the number of TiCl4 molecules

were increased from 1 to 8 as shown in fig. 17 above.

4.4.5. (𝐌𝐠𝐂𝐥𝟐)𝟓―(𝐓𝐢𝐂𝐥𝟒)𝒎

In the study of the adsorption of TiCl4 molecules by (MgCl2)5 clusters, 360 different

(MgCl2)5―(TiCl4)𝑚 were calculated, with 𝑚 of value of 1 to 8. For each value of 𝑚, the most

stable (MgCl2)5―(TiCl4)𝑚 was reported. Adsorption of one molecule of TiCl4 onto (MgCl2)5

surface which formed (MgCl2)5―(TiCl4)1 complex gave a ∆𝑟G of −26.6kJmol−1. The Ti atom

obtained a coordination number of six. The ∆𝑟G when the second TiCl4 molecule was adsorbed

was found to be −50.2kJmol−1, approximately twice that of the adsorption of one molecule of

TiCl4. The ∆𝑟G for the formation of (MgCl2)5―(TiCl4)3 and (MgCl2)5―(TiCl4)4 were found to

be −66.2kJmol−1 and −74.9kJmol−1 respectively. It was −91.0kJmol−1 for the formation of

(MgCl2)5―(TiCl4)5 and −108.5kJmol−1 for (MgCl2)5―(TiCl4)6. Fig. 18 shows the optimized

structures of (MgCl2)5―(TiCl4)𝑚 complexes and their ∆𝑟G and ∆𝑟E shown in table 6.


37







𝑚

G [ (MgCl2)5]

/au G [TiCl4]/ au


/au

∆𝑟G/ kJ



/au

∆𝑟E/ kJ

/mol

1 -5603,230065 -2690,480871 -8293,721052 -26,6 -5603,188899 -2690,4539269 -8293,676845 -89,3

2 -10984,210909 -50,2 -10984,153110 -148,0

3 -13674,697471 -66,2 -13674,640598 -236,1

4 -16365,182063 -74,9 -16365,121058 -305,7

5 -19055,669074 -91,0 -19055,611965 -402,8

6 -21746,156626 -108,5 -21746,097590 -486,1

7 -24436,642308 -121,2 -24436,578675 -557,4

8 -27127,107509 -80,0 -27127,035680 -565,4

The global minimum was located when (MgCl2)5 adsorbed the seventh TiCl4 forming

(MgCl2)5―(TiCl4)7 complex. The ∆𝑟G of the (MgCl2)5―(TiCl4)7 complex was −121.2kJmol−1.

38

In the geometry of the (MgCl2)5―(TiCl4)7, there were three binuclear bindings, Ti2Cl8, with 6-

titanium atom each. The last TiCl4 molecule bonded as a monomer with 5-titanium atom. All the

magnesium atoms in the (MgCl2)5―(TiCl4)7 complex were 6-coordinated. Fig. 19 shows a graph

of the reaction energies (∆𝑟E) and Gibbs energies (∆𝑟G) of the formation of (MgCl2)5―(TiCl4)𝑚

plotted as a function of 𝑚.



The adsorption of the eighth TiCl4 molecule resulted in an increased ∆𝑟G. The ∆𝑟E however

decreased.

4.4.6. (𝐌𝐠𝐂𝐥𝟐)𝟔―(𝐓𝐢𝐂𝐥𝟒)𝒎

-600.0

-500.0

-400.0

-300.0

-200.0

-100.0

0.0

-140.0

-120.0

-100.0

-80.0

-60.0

-40.0

-20.0

0.0

0 1 2 3 4 5 6 7 8 9

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)


39

The next cluster studied was the hexamer (MgCl2 )6. 220 different (MgCl2)6―(TiCl4)𝑚

complexes were calculated and the most stable complex for each value of 𝑚 was reported.

Adsorption of one TiCl4 molecule onto (MgCl2 )6 surface, which leads to the formation of

(MgCl2)6―(TiCl4)1, resulted in ∆𝑟G of −25.3kJmol−1. The adsorption of two molecules of TiCl4

gave a ∆𝑟G of −51.8kJmol−1. The second TiCl4 molecule bonded to the opposite end relative to

the first TiCl4 molecule. Fig. 20 shows the optimized structures of (MgCl2)6―(TiCl4)𝑚

complexes.



(MgCl2)6―(TiCl4)7



40

In both the (MgCl2)6―(TiCl4)1 and the (MgCl2)6―(TiCl4)2 complexes, the Ti adopted

coordination of five. The adsorption of the third TiCl4 resulted in only a small change in ∆𝑟G

compared to that of the adsorption of the second TiCl4 molecule. The ∆𝑟G for the formation of

(MgCl2)6―(TiCl4)3 was −55.8kJmol−1. In the geometry of the (MgCl2)6―(TiCl4)3, the third

TiCl4 was adsorbed between the already adsorbed TiCl4 molecules. The formation of

(MgCl2)6―(TiCl4)4 resulted in ∆𝑟G of −63.3kJmol−1. Table 7 shows the ∆𝑟G and ∆𝑟E for the

formation of (MgCl2)6―(TiCl4)𝑚 complexes.



𝑚

G [ (MgCl2)6] /

au G [TiCl4]/ au

G[ (MgCl2)6―(TiCl4)𝑚]/

au

∆𝑟G/ kJ


E[(MgCl2)6―(TiCl4)𝑚]/

au

∆𝑟E/ kJ

/mol

1 -6723,895014 -2690,480871 -9414,385527 -25,3 -6723,851179 -2690,4539269 -9414,333260 -73,9

2 -12104,876470 -51,8 -12104,815234 -147,6

3 -14795,358868 -55,8 -14795,292310 -208,3

4 -17485,842604 -63,3 -17485,786065 -312,9

5 -20176,327084 -72,8 -20176,257316 -358,4

6 -22866,810283 -78,9 -22866,741227 -437,1

7 -25557,284848 -62,3 -25557,205526 -464,3

The adsorption of the fifth TiCl4 further decreased the ∆𝑟G value. The ∆𝑟G for the

(MgCl2)6―(TiCl4)5 complex was −72.8kJmol−1. The global minimum was located when

(MgCl2)6 adsorbed six molecules of TiCl4 which resulted in the (MgCl2)6―(TiCl4)6. The ∆𝑟G for

the formation of (MgCl2)6―(TiCl4)6 was −78.9kJmol−1, as shown in table 7. In the geometry of

the (MgCl2)6―(TiCl4)6 complex, there were two set of binuclear binding of TiCl4 at opposite

ends. In between the binuclear binding were two sets of monomeric binding in which the titanium

atoms obtained a coordination of five each.

The ∆𝑟G and ∆𝑟E for the formation of the (MgCl2)6―(TiCl4)𝑚 complexes are plotted as a function

of the number of TiCl4 molecules in fig. 21.

41



The adsorption of the seventh TiCl4 resulted in an increase in the Gibbs free energy of reaction.

The ∆𝑟G for the formation of the (MgCl2)6―(TiCl4)7 was −62.3kJmol−1. From fig 21, (MgCl2)6

would bind more strongly to six TiCl4 molecules forming more stable (MgCl2)6―(TiCl4)6

complex than any other number of TiCl4 molecules. The electronic energies of the

(MgCl2)6―(TiCl4)𝑚 complexes were found to be decreasing as the number of TiCl4 molecules

increase from 1 to 7 within the scope of the interactions.

4.4.7. (𝐌𝐠𝐂𝐥𝟐)𝟕―(𝐓𝐢𝐂𝐥𝟒)𝒎

141 possible (MgCl2)7―(TiCl4)𝑚 interactions were calculated in the attempt to locate the global

minimum. For each number of TiCl4 molecule, only the complex with the minimum ∆𝑟G was

reported. The heptamer (MgCl2)7 was reacted with different number of TiCl4 molecules, beginning

-500.0

-450.0

-400.0

-350.0

-300.0

-250.0

-200.0

-150.0

-100.0

-50.0

0.0

-90.0

-80.0

-70.0

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

0 1 2 3 4 5 6 7 8

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)


42

from one molecule of TiCl4 until the surface of the (MgCl2)7 was fully saturated with of TiCl4

molecules. The optimized structures of the (MgCl2)7―(TiCl4)𝑚 complexes are shown in fig. 22.






43

The ∆𝑟G observed when (MgCl2)7 adsorbed one TiCl4 molecule was −65.7kJmol−1. The Ti atom

had a coordination number of six. The ∆𝑟G for the formation of(MgCl2)7―(TiCl4)2 complex was

−139.8kJmol−1. The ∆𝑟G kept decreasing as the number of TiCl4 molecules were increased. It

was −161.2kJmol−1 for (MgCl2)7―(TiCl4)3 complex, −172.9kJmol−1 for (MgCl2)7―(TiCl4)4

complex and −185.2kJmol−1 for (MgCl2)7―(TiCl4)5. The ∆𝑟G for the formation of

(MgCl2)7―(TiCl4)6 and (MgCl2)7―(TiCl4)7 complexes were −196.7kJmol−1 and

−203.6kJmol−1 respectively. The ∆𝑟G and the ∆𝑟E for the formation of the (MgCl2)7―(TiCl4)𝑚

complexes are shown in table 8. The global minimum was found when (MgCl2)7―(TiCl4)8

complex was formed. The ∆𝑟G for the formation of (MgCl2)7―(TiCl4)8 was to be

−217.3kJmol−1. Fig. 23 shows the Gibbs energy (∆𝑟G) and the electronic energy (∆𝑟E) of

reaction of the (MgCl2)7―(TiCl4)𝑚 complexes plotted as a function of 𝑚.



𝑚

G [ (MgCl2)7]

/au G [TiCl4]/ au


/au

∆𝑟G/ kJ

/mol

E [ (MgCl2)7]

/au E[TiCl4]/ au


/au

∆𝑟E/ kJ

/mol

1 -7844,523072 -2690,480871 -10535,028965 -65,7 -7844,477121 -2690,4539269 -10534,981066 -131,3

2 -13225,538046 -139,8 -13225,485525 -264,0

3 -15916,027095 -161,2 -15915,967169 -336,8

4 -18606,512397 -172,9 -18606,448753 -409,4

5 -21296,997955 -185,2 -21296,929135 -478,8

6 -23987,483211 -196,7 -23987,416588 -566,9

7 -26677,966734 -203,6 -26677,896806 -635,9

8 -29368,452792 -217,3 -29368,384215 -723,8

9 -32058,920526 -182,8 -32058,840252 -729,3

In the geometry of the (MgCl2)7―(TiCl4)8 complex, two of the TiCl4 molecules formed a mono

nuclear binding at opposite ends of the (MgCl2)7 cluster. The other six TiCl4 molecules formed a

tri nuclear binding, situated in between the two monomeric TiCl4, also at opposite ends. The

coordination number of all the Mg atoms was six with 6-coordination as well for all the Ti atoms.

44


complexes plotted as a function of the number of TiCl4 molecules (𝑚). ∆𝑟G is in black and ∆𝑟E in red.

From the graph, the ∆𝑟E of the (MgCl2)7―(TiCl4)𝑚 complexes decreased upon the adsorption of

the eighth TiCl4 molecule though the ∆𝑟G increased. This is because of entropy lost when the

eighth TiCl4 molecule was adsorbed.

4.4.8. (𝐌𝐠𝐂𝐥𝟐)𝟖―(𝐓𝐢𝐂𝐥𝟒)𝒎

To locate the global minimum of the adsorption of TiCl4 molecules onto the surface of (MgCl2)8, 212

different (MgCl2)8―(TiCl4)𝑚 interactions were calculated. The reported structures and energies

correspond to the (MgCl2)8―(TiCl4)𝑚 complexes with the minimum ∆𝑟G of formation. (MgCl2)8

gave different ∆𝑟G when it adsorbed different number of TiCl4 molecules. In fig. 24, the optimized

structures of (MgCl2)8―(TiCl4)𝑚 complexes are shown.

-800.0

-700.0

-600.0

-500.0

-400.0

-300.0

-200.0

-100.0

0.0

-250.0

-200.0

-150.0

-100.0

-50.0

0.0

0 1 2 3 4 5 6 7 8 9 10

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)


45






The formation of (MgCl2)8―(TiCl4)1 complex resulted in a ∆𝑟G of −56.0kJmol−1. When two

TiCl4 molecules were adsorbed onto the (MgCl2)8 surface, the ∆𝑟G was −72.0kJmol−1. The

structures of both (MgCl2)8―(TiCl4)1 and (MgCl2)8―(TiCl4)2 were distorted after the adsorption

of the TiCl4 molecule(s). The ∆𝑟G for the formation of (MgCl2)8―(TiCl4)3 and

(MgCl2)8―(TiCl4)4 complexes were −102.3kJmol−1 and −133.5kJmol−1 respectively.

46

−142.9kJmol−1 for the formation of (MgCl2)8―(TiCl4)5 complex, −176.3kJmol−1 for

(MgCl2)8―(TiCl4)6 complex and −183.1kJmol−1 for (MgCl2)8―(TiCl4)7 complex. These ∆𝑟G

and ∆𝑟E for the formation of the (MgCl2)8―(TiCl4)𝑚 are shown in table 9.



𝑚

G [ (MgCl2)8]

/au G [TiCl4]/ au


/au

∆𝑟G/ kJ

/mol

E [ (MgCl2)8]

/au E[TiCl4]/ au


/au

∆𝑟E/ kJ

/mol

1 -8965,195176 -2690,480871 -11655,697373 -56,0

-

8965,14393008 -2690,4539269 -11655,6428765 -118,2

2 -14346,184342 -72,0 -14346,1252908 -193,0

3 -17036,676754 -102,3 -17036,6167289 -291,5

4 -19727,169525 -133,5 -19727,1096205 -393,8

5 -22417,653976 -142,9 -22417,5875195 -456,7

6 -25108,147540 -176,3 -25108,0817952 -562,7

7 -27798,631004 -183,1 -27798,5559893 -615,9

8 -30489,115031 -191,4 -30489,0369390 -686,8

9 -33179,586801 -167,5 -33179,5000900 -711,0

The ∆𝑟G which corresponds to the global minimum was found when (MgCl2)8 adsorbed eight

molecules of TiCl4 forming (MgCl2)8―(TiCl4)8 complex. In the (MgCl2)8―(TiCl4)8 complex, all

the magnesium atoms were 6-coordinated likewise the titanium atom, except two. The ∆𝑟G of the

(MgCl2)8―(TiCl4)8 was −191.4kJmol−1. The adsorption of the ninth TiCl4 resulted in ∆𝑟G of

−167.7kJmol−1. In fig 25 is a graph that shows ∆𝑟G and ∆𝑟E of the formation of

(MgCl2)8―(TiCl4)𝑚 plotted as a function of the number of TiCl4 molecules.

47



In this graph, the electronic energy of the complexes kept reducing as the number of TiCl4

molecules were increased.

4.4.9. (𝐌𝐠𝐂𝐥𝟐)𝟗―(𝐓𝐢𝐂𝐥𝟒)𝒎

The nonamer’s interactions with TiCl4 molecules were the last studied. In locating the global

minimum, 277 (MgCl2)9―(TiCl4)𝑚 interactions were calculated. The complexes with the

minimum ∆𝑟G were reported. When one molecule of TiCl4 was adsorbed by (MgCl2)9 which

formed a (MgCl2)9―(TiCl4)1 complex, the ∆𝑟G was −22.2kJmol−1. The adsorbed TiCl4 molecule

was positioned such that the titanium atom obtained a coordination number of five. The ∆𝑟G kept

decreasing upon the addition of more TiCl4 molecules until the global minimum was located at

-800.0

-700.0

-600.0

-500.0

-400.0

-300.0

-200.0

-100.0

0.0

-250.0

-200.0

-150.0

-100.0

-50.0

0.0

0 1 2 3 4 5 6 7 8 9 10

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)


48

𝑚 = 8. The optimized structures of the (MgCl2)9―(TiCl4)𝑚 complexes are shown in fig. 26 and

their corresponding ∆𝑟G and ∆𝑟E shown in table 10.






The ∆𝑟G for the formation of (MgCl2)9―(TiCl4)2 complex was −45.4kJmol−1. Those of

(MgCl2)9―(TiCl4)3 and (MgCl2)9―(TiCl4)4 complexes were −40.3kJmol−1 and −48.3kJmol−1

respectively. Adsorption of the fifth TiCl4 molecules gave a ∆𝑟G of −63.0kJmol−1. Upon the

49

adsorption of the sixth TiCl4, the ∆𝑟G was −76.8kJmol−1 and that of the seventh TiCl4 was

−84.7kJmol−1.



𝑚

G [ (MgCl2)9] /

au G [TiCl4]/ au

G[ (MgCl2)9―(TiCl4)𝑚]/

au

∆𝑟G/ kJ


E[(MgCl2)9―(TiCl4)𝑚]/

au

∆𝑟E/

kJ/mol

1 -10085,88505 -2690,480871 -12776,374367 -22,2 -10085,8344 -2690,4539269 -12776,3213237 -86,6

2 -15466,864074 -45,4 -15466,8074239 -171,1

3 -18157,343018 -40,3 -18157,2836191 -229,6

4 -20847,826935 -48,3 -20847,7657938 -303,7

5 -23538,313397 -63,0 -23538,2468840 -375,1

6 -26228,799538 -76,8 -26228,7272757 -444,5

7 -28919,283405 -84,7 -28919,2104412 -521,3

8 -31609,773882 -109,9 -31609,7017243 -619,4

9 -34300,223529 -27,9 -34300,1383766 -574,0

The global minimum was obtained when the eighth TiCl4 molecule was adsorbed. The ∆𝑟G for the

formation of (MgCl2)9―(TiCl4)8 complex was −109.9kJmol−1. This is clearly shown in fig. 27.

where the ∆𝑟G and ∆𝑟E are plotted as a function of 𝑚. In the geometry of the (MgCl2)9―(TiCl4)8,

the eight TiCl4 molecules formed binuclear binding on the four sides of the quadrangle (MgCl2)9

cluster. Each magnesium atom in the (MgCl2)9―(TiCl4)8 complex was 6-coordinated, likewise

each titanium atom. Addition of the ninth TiCl4 increased the instability, the ∆𝑟G of the

(MgCl2)9―(TiCl4)9 complex increased to −27.9kJmol−1. In the plot, the stability of the

complexes increases as 𝑚 increases from 1 to 8. The stability of the complex decreased upon the

adsorption of the ninth TiCl4 molecule.

50



4.5. Summary

In the interaction of the (MgCl2)𝑛 clusters with TiCl4 molecules, three clusters had their global

minimum when they adsorbed eight TiCl4 molecules: (MgCl2)7―(TiCl4)8, (MgCl2)8―(TiCl4)8

and (MgCl2)9―(TiCl4)8 complexes. Among these complexes, the most stable was the

(MgCl2)7―(TiCl4)8 complex which had two sets of trinuclear binding and two mononuclear

bindings. With such findings, it can be predicted that larger clusters can form trinuclear binding

with TiCl4 molecules with substantially improved stability. The next most stable complex was

(MgCl2)8―(TiCl4)8 which had two sets of binuclear binding. It explains the fact the binuclear

bindings are likely to form. In fig. 28, the Gibbs energies of reaction of all the complexes are

plotted as a function of the number of TiCl4 molecules.

-700.0

-600.0

-500.0

-400.0

-300.0

-200.0

-100.0

0.0

-120.0

-100.0

-80.0

-60.0

-40.0

-20.0

0.0

0 1 2 3 4 5 6 7 8 9 10

∆𝑟E

(k

J/m

ol)

∆𝑟G

(k

J/m

ol)


51

Fig. 28. A graph of the ∆𝑟G for the formation of the (MgCl2)𝑛―(TiCl4)𝑚 complexes as a function of the number of

TiCl4 molecules (𝑚).

Two (MgCl2)𝑛 clusters had their global minimum when they adsorbed seven TiCl4 molecules,

(MgCl2)4―(TiCl4)7 and (MgCl2)5―(TiCl4)7. (MgCl2)5―(TiCl4)7 which had a lower ∆𝑟G value

had one mononuclear and three sets of binuclear binding. The other complex had two

mononuclear, two binuclear and one trinuclear binding modes. (MgCl2)6―(TiCl4)6 was the only

complex which had its global minimum upon the adsorption of the sixth TiCl4. In the

(MgCl2)6―(TiCl4)6 complex, there were two mononuclear bindings and two sets of binuclear

binding modes. Three clusters, MgCl2, (MgCl2)2 and (MgCl2)3 had their global minimum when

they adsorbed two molecules of TiCl4. The binding mode of these three clusters were similar, the

two TiCl4 molecules bonded to the opposite ends of the (MgCl2)𝑛 and in each, the Ti atom had a

coordination of 5. They gave approximately the same ∆𝑟G values which were −64.7kJmol−1,

-250

-200

-150

-100

-50

0

0 1 2 3 4 5 6 7 8 9 10

ΔG

(k

J/m

ol)


MgCl2-(TiCl4)m (MgCl2)2-(TiCl4)m (MgCl2)3-(TiCl4)m

(MgCl2)4-(TiCl4)m (MgCl2)5-(TiCl4)m (MgCl2)6-(TiCl4)m


52

−66.3kJmol−1 and −67.0kJmol−1 for MgCl2―(TiCl4)2, (MgCl2)2―(TiCl4)2 and

(MgCl2)3―(TiCl4)2 respectively.

The ∆𝑟E of reaction of all the complexes were plotted as a function of the number of TiCl4

molecules. This graph is shown in fig. 29 below. A general trend of increasing stability of

(MgCl2)𝑛―(TiCl4)𝑚 was found in all the clusters.

Fig. 29. The electronic energy (∆𝑟E) of the (MgCl2)𝑛―(TiCl4)𝑚 complexes plotted as a function of the number of

TiCl4 molecules (𝑚)

From fig. 29, the heptamer (MgCl2)7, which had a hexagonal shape, formed the lowest energy

complex upon the adsorption of TiCl4 molecules, followed by octamer (MgCl2)8, nonamer

-800

-700

-600

-500

-400

-300

-200

-100

0

0 1 2 3 4 5 6 7 8 9 10

ΔE

(k

J/m

ol)


MgCl2-(TiCl4)m (MgCl2)2-(TiCl4)m (MgCl2)3-(TiCl4)m



53

(MgCl2)9, and pentamer (MgCl2)5. In fig. 30, the global minimum of all the complexes are plotted

as a function of the number of MgCl2-units in the (MgCl2)𝑛 clusters.

Fig. 30. A graphical illustration of the global minimum (∆𝑟G) of the various (MgCl2)𝑛―(TiCl4)𝑚 complexes as a

function of the number of MgCl2-units in the (MgCl2)𝑛―(TiCl4)𝑚 clusters.

5. CONCLUSION

The surfaces of different magnesium dichloride (MgCl2)𝑛 clusters were stabilized using different

amount of TiCl4 molecules. The stability of the (MgCl2)𝑛 clusters were first examined without the

adsorption of TiCl4 molecules which led to the conclusion that the stability of (MgCl2)𝑛 increases

-64.8 -66.3 -67.0

-79.1

-121.2

-78.9

-217.3

-191.4

-109.9

-250

-200

-150

-100

-50

0

0 1 2 3 4 5 6 7 8 9 10

(∆𝑟

G)

The number of MgCl2-units in the (MgCl2)n-(TiCl4)m molecules (n)

54

as a function of increasing 𝑛. In the adsorption of TiCl4 molecules onto (MgCl2)𝑛 surface, nine

clusters were studied, 𝑛 = 1 − 9, and in each cluster, all possible combination of the

chemisorption of TiCl4 were calculated in order to identify the global minimum. Three binding

modes were found in the global minima in this study; mononuclear binding, binuclear binding and

trinuclear binding

a. Mononuclear binding

For the smaller clusters with, 𝑛 = 1 ― 3, the TiCl4 bonded mainly at the opposite end of

the cluster in the global minima. This binding was such that there were two chlorine atoms

that bridged the TiCl4 molecules and the (MgCl2)𝑛 surface. The Ti atom obtained a

coordination of 5. The second mononuclear binding observed was 5-104 binding mode.

The Ti atoms obtained a coordination of 5 adsorbed onto the 104 surfaces. This binding

mode was observed in (MgCl2)𝑛 clusters with 𝑛 = 4 ― 5. The 4-110 binding mode was

never observed in any of the global minima. This confirmed that the 4-coordinated binding

mode of TiCl4 molecules is unstable and unlikely to be formed. The last mononuclear

binding found was the 6-coordinated Ti atoms.

b. Binuclear binding.

The 6-104 binuclear binding mode was found in most of the global minima and it

dominates over the other binding modes. Such findings confirm that the 6-104 binding

mode the most likely to be formed on 104 surfaces.

c. Trinuclear binding

Trinuclear binding mode was also found in this study. The global minimum of the complex

with the trinuclear binding was the most stable. With such findings in the heptamer, it can

be predicted with high level of confidence that larger (MgCl2)𝑛 clusters can bind to TiCl4

molecules in trinuclear modes with substantially improved stabilities.

55

6. ACKNOWLEDGEMENT

I would like to express my profound gratitude to my supervisors, Prof. Mikko Linnolahti and

Prof. Tapani A. Pakkanen for their support, time and attention during my studies.

To all my friends and love ones, I say thank you.

56

7. REFERENCES

[1] L. Cerruti, "Historical and Philosophical Remarks on Ziegler-Natta Catalysts," An

International Journal for the Philosophy of Chemistry, vol. 5, pp. 5-9, 1999.

[2] J. Huang and G. L. Remple, "Ziegler-Natta Catalysis for Olefin Polymerizaion: Mechanistic

Insights from Metallocene Systems," Great Britain, 1995, pp. 462-466.

[3] V. Busico, R. Cipullo, A. Mingione and L. Rongo, "Accelerating the Research Approach to

Ziegler−Natta Catalysts," Industrial and Engineering Chemistry Research, vol. 55, pp. 2686-

2695, 2016.

[4] M. D'Amore, K. S. Thushara, A. Piovano, M. Causà, S. Bordiga and E. Groppo, "Surface

Investigation And Morphological Analysis Of Structurally Disordered MgCl2 And

MgCl2/ TiCl4 Ziegler-Natta Catalysts," ACS Catalysis, vol. 6, pp. 5786-5796, 2016.

[5] M. C. Sacchi, I. Tritto, C. Shan and R. Mendichi, "Role of the Pair of Internal and External

Donors in MgC12-Supported Ziegler-Natta Catalysts," Macromolecules, vol. 24, pp. 6823-

6826, 1991.

[6] F. Malizia, A. Fait and G. Cruciani, "Crystal Structures of Ziegler–Natta Catalyst Supports,"

Chemistry A- European Journal, vol. 17, pp. 13892-13897, 2011.

[7] A. Bazhenov, "Computational Chemistry of Ziegler-Natta Catalysis," in Towards Deeper

atomic-level understanding of the structure of magnesium dichloride and its performance as

a support in the Ziegler-Natta catalytic system., Joensuu, 2014, pp. 9-16.

[8] S. Yao, T. Shoji, Y. Iwamoto and E. Kamei, "Consideration of an activity of the metallocene

catalyst by using molecular mechanics, molecular dynamics and QSAR," Computational and

Theoretical Polymer Science, vol. 9, pp. 41-46, 1999.

57

[9] M. S. Kuklin, "Introduction," in Towards Optimization of metallocene olefin Polymerization

catalyst via Structural modification: A Computational Approach, Joensuu Finland, 2015, pp.

11-15.

[10] M. S. Kuklin, J. T. Hirvi, M. Bochmann and M. Linnolahti, "Toward Controlling the

Metallocene/Methylaluminoxane-Catalyzed Olefin Polymerization Process by a

Computational Approach," Organometallic Chemistry, vol. 34, pp. 3586-3597, 2015.

[11] I. Tritto, M. C. Sacchi, P. Lacatelli and S. X. Li, "Low-temperature 1H and 13C NMR

investigation of trimethylaluminium contained in methylaluminoxane cocatalyst for

metallocene-based catalysts in olefin polymerization," Macromolecular Chemistry and

Physics, vol. 197, pp. 1537-1544, 1996.

[12] A. Tarazona and E. Koglin, "Structure and Stability of Aluminum Alkyl Cocatalysts in

Ziegler-Natta Catalysis," Journal of Physical Chemistry B, vol. 101, pp. 4370-4378, 1997.

[13] T. N. P. Luhtanen, M. Linnolahti and T. A. Pakkanen, "Molecular Structures of Magnesium

Dichloride Sheets and Nanoballs," Inorganic Chemistry, vol. 43, pp. 4482-4486, 2004.

[14] T. N. P. Luhtanen, M. Linnolahti, A. Laine and T. A. Pakkanen, "Structural Characteristics

of Small Magnesium Dichloride Clusters: A Systematic Theoretical Study," Journal of

Physical Chemistry B, vol. 108, pp. 3989-3995, 2004.

[15] K. Xie, A. Huang, B. Zhu, J. Xu and P. Liu, "Periodic DFT investigation of methanol

coverage on surfaces of MgCl2-supported Ziegler–Natta catalysts," Applied Surface Science,

vol. 356, pp. 967-971, 2015.

[16] A. Bazhenov, M. Linnolahti, A. J. Karttunen, T. A. Pakkanen, P. Denifl and T. Leinonen,

"Modeling of Substitutional Defects in Magnesium Dichloride Polymerization Catalyst

Support," Journal of Physical Chemistry C, vol. 116, pp. 7957-7961, 2012.

58

[17] G. Monaco, M. Toto, G. Guerra, P. Corradini and L. Cavallo, "Geometry and Stability of

Titanium Chloride Species Adsorbed on the (100) and (110) Cuts of the MgCl2 Support of

the Heterogeneous Ziegler-Natta Catalysts," Macromolecules, vol. 33, pp. 8953-8962, 2000.

[18] M. Linnolahti, T. A. Pakkanen, A. S. Bazhenov, P. Denifl, T. Leinonen and A. Pakkanen,

"Alkylation of titanium tetrachloride on magnesium dichloride in the presence of Lewis

bases," Journal of Catalysis, vol. 353, pp. 89-98, 2017.

[19] T. Garoff, V. Virkkunen, P. Jääskeläinen and T. Vestberg, "A qualitative model for

polymerisation of propylene with a MgCl2-supported TiCl4 Ziegler–Natta catalyst,"

European Polymer Journal, vol. 39, pp. 1679-1685, 2003.

[20] M. Ratanasak and V. Parasuk, "Understanding the roles of novel electron donors in Ziegler–

Natta catalyzed propylene polymerization," RSC Advances, vol. 6, pp. 112776-112783,

2016.

[21] L. Sang-Yun and S.-J. Choung, "Effects of External Electron Donor on Catalyst Active Sites

in Propylene Polymerization," Journal of Applied Polymer Science, vol. 67, pp. 1779-1787,

1998.

[22] M. C. Sacchi, F. Forlini, I. Tritto and P. Locatelli, "Stereochemistry of The Initiation Step in

Ziegler-Natta Catalysts Containing dialkyl Propane diethers: A Tool For Distinguishing The

Role Of Internal And External Donors," Macromolecular Sympposium, vol. 89, pp. 91-100,

1995.

[23] A. Correa, F. Piemontesi, G. Morini and L. Cavallo, "Key Elements in the Structure and

Function Relationship of the MgCl2/ TiCl4/Lewis Base Ziegler-Natta Catalytic System,"

Macromolecules, vol. 40, pp. 9181-9189, 2007.

[24] N. Cui, Y. Ke, H. Li, Z. Zhang, C. Guo, Z. Lv and Y. Hu, "Effect of Diether as Internal

Donor on MgCl2-Supported Ziegler–Natta Catalyst for Propylene Polymerization," Journal

of Applied Polymer Science, vol. 99, p. 1399–1404, 2006.

59

[25] T. Keii, "Transition metal catalysed polymerization alkenes and dienes," Switzerland, Part

A,Harwood Academic Publishers, 1983, pp. 97-114.

[26] K. Soga, J. R. Park, H. Uchino, T. Uozumi and T. Shiono, "Perfect Conversion of Aspecific

Sites into Isospecific Sites in Ziegler-Natta Catalysts," Macromolecules, vol. 26, pp. 3824-

3826, 1989.

[27] A. Bazhenov, M. Linnolahti, T. A. Pakkanen, P. Denifl and T. Leinonen, "Modeling the

Stabilization of Surface Defects by Donors in Ziegler−Natta Catalyst Support," Journal of

Physical Chemistry C, vol. 118, pp. 4791-4796, 2014.

[28] M. S. Kuklin, A. S. Bazhenov, P. Denifl, T. Leinonen, M. Linnolahti and T. A. Pakkanen,

"Stabilization of Magnesium Dichloride Surface Defects by Mono- and Bidentate Donors,"

Surface Science, vol. 635, pp. 5-10, 2015.

[29] K. Vanka, G. Singh, D. Iyer and V. K. Gupta, "DFT Study of Lewis Base Interactions with

the MgCl2 Surface in the Ziegler-Natta Catalytic System: Expanding the Role of the Donors,"

Journal of Physical Chemistry C, vol. 114, pp. 15771-15781, 2010.

[30] A. Andoni, J. C. Chadwick, H. J. Niemantsverdriet and P. C. Thüne, "The role of electron

donors on lateral surfaces of MgCl2-supported Ziegler–Natta catalysts: Observation by AFM

and SEM," Journal of Catalysis, vol. 257, pp. 81-86, 2008.

[31] A. S. Bazhenov, P. Denifl, T. Leinonen, M. Linnolahti and T. A. Pakkanen, "Modeling

Coadsorption of Titanium Tetrachloride and Bidentate Electron Donors on Magnesium

Dichloride Support Surfaces," Journal of Physical Chemistry C, vol. 118, pp. 27878-27883,

2014.

[32] M. Seth, P. M. Margl and T. Ziegler, "A Density Functional Embedded Cluster Study of

Proposed Active Sites in Heterogeneous Ziegler−Natta Catalysts," Macromolecules, vol. 35,

pp. 7815-7829, 2002.

[33] R.-H. Cheng, J. Luo, Z. Liu, J.-w. Sun, W.-h. Huang, M.-g. Zhang, J.-j. Yi and B.-p. Liu,

"Adsorption of TiCl4 and Electron Donor on Defective MgCl2 Surfaces and Propylene

60

Polymerization Over Ziegler-Natta Catalyst: A DFT Study," Chinese Journal of Polymer

Science, vol. 31, pp. 591-600, 2013.

[34] B. Liu, T. Nitta, H. Nakatani and M. Terano, "Stereospecific Nature of Active Sites on

TiCl4/MgCl2 Ziegler–Natta Catalyst in the Presence of an Internal Electron Donor,"

Macromolecular Chemistry and Physics, vol. 204, pp. 395-402, 2003.

[35] A. Correa, R. Credendino, J. T. M. Pater, G. Morini and L. Cavallo, "Theoretical

Investigation of Active Sites at the Corners of MgCl2 Crystallites in Supported Ziegler−Natta

Catalysts," Macromolecules, vol. 45, pp. 3695-3701, 2012.

[36] D. V. Stukalov, V. A. Zakharov, A. G. Potapov and G. D. Bukatov, "Supported Ziegler–

Natta catalysts for propylene polymerization. Study of surface species formed at interaction

of electron donors and TiCl4 with activated MgCl2," Journal of Catalysis, vol. 266, pp. 39-

49, 2009.

[37] M. D’Amore, R. Credendino, P. H. Budzelaar, M. Causá and V. Busico, "A periodic hybrid

DFT approach (including dispersion) to MgCl2-supported Ziegler–Natta catalysts – 1: TiCl4

adsorption on MgCl2 crystal surfaces," Journal of Catalysis, vol. 286, pp. 103-110, 2012.

[38] Y. Zhao, N. E. Schultz and D. G. Truhlar, "Design of Density Functionals by Combining the

Method of Constraint Satisfaction with Parametrization for Thermochemistry,

Thermochemical Kinetics, and Noncovalent Interactions," Theoretical Chemistry Accounts,

vol. 2, pp. 364-382, 2006.

[39] A. Schaefer, C. Huber and R. Ahlrichs, "Fully optimized contracted Gaussian basis sets of

triple zeta valence quality for atoms Li to Kr," Chemical Physics, vol. 100, pp. 5829-2835,

1994.

[40] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman,

G. Scalmani, V. Barone, .. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.

P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng and J. L. Sonnenberg, "Gaussian 09;

Revision A.02; Gaussian; Inc.; Wallingford CT," 2009.

61

[41] A. Turunen, M. Linnolahti, V. A. Karttunen, T. A. Pakkanen, P. Denifl and T. Leinonen,

"Microstructure control of magnesium dichloride crystallites by electron donors: The effect

of methanol," Journal of Molecular Catalysis, vol. 334, pp. 103-107, 2011.

[42] E. Magni and G. A. Somorjai, "Preparation and Surface Science Characterization of Model

Ziegler-Natta Catalysts. Role of Undercoordinated Surface Magnesium Atoms in the

Chemisorption of TiCl4 on MgCl2 Thin Films," Journal of Physical Chemistry B, vol. 102,

pp. 8788-8795, 1998.

DFT STUDY OF THE ADSORPTION OF TITANIUM...

Documents

Transcript of DFT STUDY OF THE ADSORPTION OF TITANIUM...