JAIST Repository
https://dspace.jaist.ac.jp/

Title

Origin of Broad Molecular Weight Distribution ofPolyethylene Produced by Phillips‑type Silica‑
Supported Chromium Catalyst

Author(s)Tonosaki, Kiwamu; Taniike, Toshiaki; Terano,
MinoruCitation

Journal of Molecular Catalysis A: Chemical,
340(1‑2): 33‑38

Issue Date

2011‑03‑15

Type

Journal Article

Text version

author

URL

http://hdl.handle.net/10119/10716

RightsNOTICE: This is the author's version of a work
accepted for publication by Elsevier. Kiwamu
Tonosaki, Toshiaki Taniike, Minoru Terano,
Journal of Molecular Catalysis A: Chemical,
340(1‑2), 2011, 33‑38,
http://dx.doi.org/10.1016/j.molcata.2011.03.005

Description

Japan Advanced Institute of Science and Technology

Full Paper for
Journal of Molecular Catalysis A: Chemical

Origin of Broad Molecular Weight Distribution of Polyethylene Produced by Phillips-type
Silica-Supported Chromium Catalyst

Kiwamu Tonosaki, Toshiaki Taniike*, Minoru Terano

School of Materials Science, Japan Advanced Institute of Science and Technology, 1-1
Asahidai, Nomi, Ishikawa 923-1292, Japan*Corresponding author.
Tel: +81-761-51-1622, Fax: +81-761-51-1625, E-mail address: taniike@jaist.ac.jp1Abstract
The origin of the broad molecular weight distribution of polyethylene produced byPhillips-type silica-supported chromium (Cr/SiO2) catalysts was studied by density
functional calculations using active site models with various coordination environments.
Difference of the coordination environment of chromium showed remarkable variations forboth of the insertion and the chain transfer energies, resulting in a broad range of molecularweight from 102 to 1010 g/mol at 350 K. The results clarified that the special catalytic
property of Cr/SiO2 for broad molecular weight distribution is attributed to theheterogeneity of the coordination environment of the chromium species.

Keywords
Phillips catalyst; density functional theory; molecular weight distribution; polyethylene(PE)2

1. Introduction
Phillips catalysts [1] composed of CrOx supported on SiO2 (Cr/SiO2) have long maintained
their industrial importance after the discovery in 1950’s in the polyolefin manufacture to
produce nearly 7 million tons of a special grade of high density polyethylene (HDPE) per
year over the world. The specialty of the Cr/SiO2 catalysts is an ability to produce HDPE
with fine mechanical properties such as elasticity and impact resistance, and with superiormoldability due to its high melt viscosity.

They come from both broad molecular weight

distribution (MWD) and adequate amounts of short and long chain branches, which areautomatically produced in ethylene homopolymerization [2]. As finer controls of polymer
structures with the Cr/SiO2 catalysts have been continuous demands for further
multi-purpose materials, significant efforts still deposit obscurities in the mechanistic originof the unique catalytic features.
The broad MWD has been believed to be mainly of a chemical origin, while somephysical influences such as monomer concentration gradients within catalyst particles werealso reported [3].

The chemical origin has been regarded as the heterogeneity of

supported Cr species.

Specifically, the conventional catalyst synthesized by animpregnation method makes a mixture of several types of potentially active Cr(VI) species
and inactive Cr2O3 clusters [4-9]. In past years, many researchers have tried to investigate
structures of Cr(VI) species.

Applying UV-vis diffuse reflectance, Raman and X-ray

adsorption spectroscopies (XAS), Weckhuysen et al. [10] found mono- and dichromate
with tetrahedral symmetry mainly present on the surface.

Dichromate species are

dominant among Cr(VI) at high Cr loadings and/or high calcination temperatures.

3However, since surface structures can be sensitive to the surface chemistry of oxide
supports, the nuclearity of Cr(VI) is still under debate [11].

Furthermore, reduced Cr

species, which are transient states between Cr(VI) and lower valence active species, exhibit
a variation in the bonding and the interaction with surface oxygen. Such heterogeneity of
coordination environment around Cr leads to a variety of symmetry and oxidation states of
reduced Cr species. For example, UV-vis spectroscopy and XAS showed the presence ofpseudo tetrahedral Cr(II), pseudo octahedral Cr(II) and pseudo octahedral Cr(III) on a
reduced catalyst [12,13].

A recent report by Gianolio et al. [14] showed a direct evidenceof the coordination of surface siloxane ligands to reduced Cr species by the EXAFS, which
is believed to be crucial for giving a variety of coordination environments around reduced
Cr species. In an IR study by Zecchina et al. [15-17], three types of reduced species wereidentified (named as species A, B and C) through the adsorption of CO. Thus, Cr specieson SiO2 can be roughly classified in terms of two kinds of heterogeneities: (1) nuclearity
and (2) coordination environment.
Several Philips-type model catalysts with uniform Cr structures have been designed
in order to reduce the above-mentioned heterogeneity. For example, Amor Nait Ajjou andScott [18-20] supported dialkylated Cr(IV) mononuclear species on SiO2 by chemical vapor
deposition (CVD) of CrNp4 (Np = Neopentyl). Ikeda et al. reported a model catalyst withmonoalkylated Cr(III) mononuclear species supported on SiO2, using a molecular precursorof Cr(CH(SiMe3)2)3 [21]. Both of the model catalysts showed quite high activity for
ethylene polymerization, and the MWDs of produced HDPEs were surprisingly very broad
comparable with that obtained from impregnated catalysts, in spite of the almost uniform4Cr nuclearity and oxidation state.

It is believed that the heterogeneity of Cr species exists

for these model catalysts due to the difference of the coordination environment around Cr
species. On the other hand, Nenu et al. reported that an impregnated Cr/SiO2 catalyst
behaved like a single-site catalyst, giving very narrow MWD close to 2, when
1,3,5-tribenzylhexahydro-1,3,5-triazine was added as a coordinative ligand to Cr species[13,22,23].

Obviously, all these results suggest much larger contribution of thecoordination environment of Cr to broaden MWD than that of the nuclearity.
In this contribution, we present the first molecular-level investigation for influencesof coordination environments of Cr on the MW of PE. The apparent free energies ofactivation for the ethylene insertion to growing chain and chain transfer (CT) to
coordinated ethylene were calculated by density functional theoretical (DFT) calculationfor various active site models.

The results obtained here have disclosed active site

structures of Cr for broadening MWD of PE, and have provided valuable insights in the
catalytic properties of Cr/SiO2 catalysts as well as in molecular chemistry of theseelemental reactions. To the best of our knowledge, DFT investigation on the origin of
unique structures of produced PE by Phillips catalysts has never been undertaken so far.

2. Numerical Details
All the DFT results were obtained using DMol3 as implemented in the Materials Studio(Version 4.2) [24]. The exchange-correlation functional of Perdew-Burke-Ernzerhof [25](PBE), which is one of the most frequently used functional on the study of catalytic
reactions on heterogeneous metal oxide catalysts, was employed.

5

The basis set was thedouble numeric with d-polarization functions except for hydrogen (DND) combined witheffective core potentials (ECP) [26,27]. The real space cutoff radius was 4.400 Å. The
convergence criterion for SCF calculations was 1.0 × 10－5 Hartree, and those for geometry
optimization were 2.0 × 10 － 5 Hartree for energy and 4.0 × 10 －3 Hartree/Å for the
maximum force. A high-spin state was always favored for Cr(IV), Cr(III) and Cr(II).
Transition states (TS) of both ethylene insertion and CT reaction were obtained by TS
optimization based on the Newton-Raphson algorithm.

The CT reaction in ethylene

polymerization with Cr/SiO2 catalysts is known to mainly occur through -hydrogentransfer to ethylene [28].
The size of the employed basis set was rather small in obtaining converged energies.
Especially, the lack of diffuse functions on Cr leads to underestimation of the energies of
-complexes and TSs compared with the energy of gas-phase ethylene and a monomer-free
active site, resulting in overestimation of -complexation energies and underestimation ofactivation energies.

However, as described later, the present task is to estimate theenergetic difference between two activation energies (see Eq. (3)) rather than quantitativeevaluation of the above values. Considering the cancellation of errors for differential
values, the employed basis set could fulfill our target to compare MWs among various
coordination environments.

Actually the magnitude of MW estimated for the most basic

active site (Fig. 1, model a) was the same when a larger basis set (DNP) and higher
convergence criteria (fine) were employed.
To elucidate effects of coordination environments on the MW of PE, five clustermodels a-e were employed in Fig. 1.

Cr was basically supported on the minimum

6

−O−Si(H2)−O−Si(H2)−O− framework, although the effects of the chromasiloxane ring size
and those of the hydrogen termination were also investigated.

Such 6-membered

chromasiloxane ring was regarded as one of the most plausible species by Espelid et al.
[29], and Demmelmaier et al. reported that the 6-membered chromasiloxane was mosteasily activated by ethylene [30].

The model a possesses a tetrahedral symmetry, whichhave been employed in most of the previous calculations [29,31].

However, the presenceof Cr(II) and Cr(III) situated in a distorted octahedral symmetry was also experimentallyevidenced. Such octahedral species were modeled by adding a third ligand to the basic
framework having two Cr−ester bonds.

The third ligand is likely coordinative siloxane orsilanol for Cr(II) and an additional Cr−ester bond for Cr(III) in real Cr/SiO2 catalysts. We
used coordinative H2O and Cr−OH as these third ligands for Cr(II) and Cr(III), respectively.
Electronic effects of H2O and OH on Cr species were confirmed by us to be similar to thoseof (SiH3)2O and OSiH3, respectively. Furthermore the H2O and OH ligands enabled us toenforce a desired octahedral symmetry with the minimal steric effects, thus being suitablefor our objective. Supposing that the chromasiloxane ring composes an equatorial planewith Cr at the origin, a series of octahedral Cr species was prepared by placing H2O (b, c)
or OH (d, e) at an axial or equatorial position.
The models a-e were firstly optimized without ethylene monomer as neutral Cr(II) or
Cr(III) species, where the chromasiloxane ring was restricted in the YZ plane with the Cratom fixed at the origin. The restriction of the chromasiloxane ring to the planar structure
was essential to keep octahedral symmetry for b-e, and it hardly affected the results for a.
In order to maintain the desired symmetries, the coordinating O atom of the H2O ligand and7all the atoms of the OH ligand allowed to relax along the axial direction on the X axis forthe models b and d, or within the equatorial face on the YZ plane for the models c and e.
Thus obtained Cr(II) and Cr(III) atoms with different coordination environments were
employed in subsequent calculations for ethylene polymerization, where the position of the
H2O and OH ligands was fixed in order to keep the desired symmetry. The fixation of thethird ligands might more or less overestimate their influences on the polymerization
properties, but we believed that the obtained results qualitatively are held for the realsurface, where the position of third ligands must be constrained.
The most probable MW (MW) of PE under the dominance of the CT to ethylene isgiven bykp
MW
 Pn 
28.06
k tr

(1),

where P n , kp and ktr are the most probable polymerization degree, and the rate constantsfor the propagation (insertion) and of the CT, respectively.
  G ‡ p/tr RTk p/tr 
exp 
N AhRTMaking use of(2),

Eq. (1) becomes (G ‡ p  G ‡ tr )
MW
 exp
28.06
RT

(3),

where R, NA, G‡p and G‡tr are the gas constant, the Avogadro constant and the apparent
Gibbs energies of activation for the propagation and the CT, respectively.

8

3. Results and Discussion

Effects of the coordination environments on MW were mainly investigated formonoalkyl-Cr(III) and -Cr(IV) (alkyl: methyl or n-propyl) active species. Although somerecent experimental results suggested the possibility of dialkyl-Cr(IV) active species for the
propagation [18-20,32], we found that a -complex was not formed at both
dimethyl-Cr(IV) and chromacyclopentane(IV) species, and the activation energies for theethylene insertion into the dimethyl-Cr(IV) and chromacyclopentane(IV) were 13.0 and24.8 kcal/mol, respectively, higher than that into monomethyl-Cr(III). The difficulty of
ethylene insertion to the dialkyl-Cr(IV) and chromacycloalkane(IV) has been also reportedby Espelid et al. [29].
An ethylene insertion pathways on monomethyl-Cr(III) of a is described in Scheme 1.
Even if the model a was situated in tetrahedral symmetry, the ethylene insertion proceeded
at octahedral sites. The methyl group was oriented to an axial position and the ethylene
coordinated at an equatorial position. The structure of the -complex with the methylgroup at an equatorial position and coordinated ethylene at an axial position was 20.0
kcal/mol less stable than the most stable one. Thus, the alkyl and the hydride disfavoredthe trans position of O ligands, especially for covalently bonding O. On the contrary, coordination preferred the trans position of O ligands. Those trans influences caused
significant differences in ethylene polymerization properties of monoalkyl-Cr species withadditional H2O and OH ligands, which is described below.
Table 2 shows the energies of the ethylene coordination, insertion and -hydrogentransfer to ethylene for Cr−n-propyl situated in various coordination environments together

9with the most probable MWs of PE produced at each active site. Exceptionally, d could
not accept -complexation since n-propyl was strongly forced to a tetrahedral position toescape from the trans position of the three covalent O.

The existence of the third ligands

reduced the adsorption energies of the ethylene (Ead) regardless those electronic properties
and positions, suggesting that the third ligands sterically narrowed the coordination spacefor ethylene.

The apparent activation energies (Eap) of the ethylene insertion into

Cr−n-propyl were basically increased by the presence of the third ligand compared with thevalue for a, and the degree of the increase was dependent on the position and kind of theligands. For the -hydrogen transfer to coordinated ethylene, the ligands at an equatorial
position hardly affected Eap for c and e compared with that for a. On the contrary, Eap
became much higher for b and d, with the ligands at an axial position, than that for a.
Especially, even a TS was not obtained for d.
G‡ was calculated for both the insertion and CT in order to incorporate theinfluences of the temperature into account. The temperature was set to 350 K, typical forindustrial ethylene polymerization with Cr/SiO2 catalysts. Table 1 shows G‡p – G‡tr,
whose exponential gives the most probable MW based on Eq. (3). The values of G‡p –G‡tr are only 1.0 - 4.6 kcal/mol higher than those of E‡p – E‡tr, which means that theentropic contribution slightly enhances CT compared with the insertion. On the other
hand, the variation of the G‡p – G‡tr values among the different active site models issimilar to that of the E‡p – E‡tr values, indicating that the variation of MWs is mostly
decided by the electronic contribution.

10

For monoalkyl-Cr(III) in different coordination environments a-c, the variation of theenergetic difference between the insertion and CT enabled a wide range of MWs from 8.6 ×
102 to 7.0×1010. The coordination of H2O at the axial position led to a higher MW as aresult of the inhibited CT, and that at the equatorial position to a lower MW. As formonoalkyl-Cr(IV), the enchainment did not proceed for e at 350 K in consequence of therelative enhancement of the CT.

The -complex was not formed for d.

Thus,monoalkyl-Cr(IV) species were not likely relevant in the ethylene polymerization with
Cr/SiO2 catalysts.
Though the results presented here assumed rather ideal tetrahedral or octahedral
symmetry, probably leading to quantitative over- or under-estimation, it could be safely
concluded that one of the dominant factors of the broad MWD of PE produced by Cr/SiO2
catalysts is the coordination environment of Cr.

Also, the O−Cr−O angle of achromasiloxane ring has been considered as one of the decisive factors for thepolymerization activity [30]. However in our calculations (Table 2), it was much lessassociated with MWD of produced PE, while the activity was surely influenced by it.
To confirm the effects of the hydrogen termination, a larger cluster model named asa’ was employed with a 6-membered chromasiloxane structure (Fig. 2). a’ was cut off

from a (100) surface of -crystobalite. Surfaces of amorphous SiO2 has been explained asa mixture of the (100) and (111) surfaces of -crystobalite [33], and the dehydroxylated(100) surface was reported to stabilize a 6-memberd metallasiloxane [34,35]. The edge
parts of the cluster were again capped with hydrogen in order to keep electronic neutrality.
All atoms in the SiO2 support except those in the chromasiloxane framework were fixed11during calculations.

As shown in Table 3, the larger cluster a’ increased the

-complexation energy compared with that of the minimal cluster a, resulting in similar
reductions of the Eap values for insertion and CT.

Consequently, the resulting MW of

produced PE was almost similar with that of a. Thus, the effects of the cluster size for the
support on MW could be regarded to be much less important than those of the coordination
environment.
To address the origin of the effects of the coordination environment on the insertion
and CT, the elemental activation barriers, Eel, was decomposed according toE ap  E ad  E el
 E ad  E detach  E M C  E def  E M TS  E attach(4).

The energetic decomposition was conducted based on Scheme 2, where ethylene and alkyl
anion were stepwisely separated from a chromasiloxane cation for both a -complex andTS, and the energies of the separated fragments were calculated without geometry
optimization. A similar decomposition was previously reported by Margl et al. [36,37].
Edetach andEattach indicate the binding force of ethylene. EM-C and EM-TS indicate theCr-alkyl bond strength for a -complex and TS, respectively. Edef is the deformationenergy of the fragments in the transformation from a -complex to TS.

All the values

shown in Table 4 are differential values from those for a. As explained in the discussions
for Table 2, the existence of the third ligand sterically prevented the ethylene coordination
to increase Ead. Correspondingly, Edetach decreased in the presence of the third ligand.
However, the sum of Ead and Edetach are not necessarily zero, since the sum contains
the degree of the deformation in forming a -complex. As for b, the sum of Ead and12Edetach is almost zero, indicating that the third ligand at the axial position induced asimilar degree of structural distortion of the -complex to that for a. The distortion islarger for c with the positive value, and smaller for e with the minus value for the sum ofEad and Edetach for the insertion.

The third ligand at the equatorial position altered

the degree of the distortion in forming the -complexes, and the direction of the alternation
was opposite for electron donating H2O and accepting OH. In the case of CT, the ethylene
coordination took place at the axial position of Cr for c and e, since the equatorial position
was occupied with -hydrogen of alkyl. Much weaker coordination of ethylene to theaxial position significantly reduces the distortion in forming the -complexes, where theabsolute values of Ead and Edetach are almost equal.

As shown in EM-C for bothinsertion and CT, the Cr−n-propyl bond tended to be destabilized (decrease of EM-C) by
H2O and ethylene, both electron donors, especially when they coordinated to the equatorial
position. This was due to effective electron donation from the ligands at the equatorial
position to the Cr−ester bond. On the contrary, OH, an electron acceptor, at the equatorial
position slightly stabilized the Cr−n-propyl bond (increase of EM-C).
insertion is higher for b, having a more deformed TS, than for a.

Edef for the

For b, an axial position,

which would have stabilized the newly forming alkyl, was already filled by H2O.
Meanwhile, when the third ligands came to the equatorial position for c and e, thesymmetry of the active site was forced to be bipyramidal, and then the distortion in TS for
the insertion became slightly smaller than that for a. In CT, a significant increase of Edef
is observed for b, since both the newly forming ethyl and hydride were enforced to the13unfavorable equatorial position by H2O at TS. The influences of ligands on EM-TS andEattach for both the insertion and CT are similar to those on Edetach and EM-C, eventhough the location of each TS affects Edetach and EM-C.
Table 5 summarizes the energetic effects of the additional ligand for the key steps in
the ethylene insertion and CT.

E-R in Table 5 is the difference of the binding forces of

ethylene and alkyl to Cr between a -complex and TS, defined as,

E π  R  (E detach  E M C )  (E M TS  E attach )(5).

In the cases of the ethylene insertion, E-R shows insignificant differences among the threemonoalkyl-Cr(III), a, b, and c.

As a result, the most important contribution of theadditional ligand, H2O, was on the increase of Ead, which led to elevate Eap comparedwith that of a. Then, the final values of Eap were modulated by Edef according to theposition of H2O. Espelid et al. reported that Cr(IV) was less active for the ethylene
insertion due to the weak coordination of ethylene [29]. This is also seen in Ead for e.
In addition, a higher E-R indicating the destabilized Cr-fragment bondings at TS also
increased Eap. The oxidation state of monoalkyl-Cr is not important for CT as seen inEap of c and e, where Edef is nearly zero, and E-R and Ead are well canceled tohave a similar Eap to that of a. The highest Eap for b obviously arises from high Edef
indicating the decisive contribution of the structural distortion of TS for CT.

4. Conclusions

14

The heterogeneity of the interaction of Cr with SiO2 supports generates a variety of Cr
species situated in different coordination environments in industrial Cr/SiO2 ethylene
polymerization catalysts. In this density functional study, we have investigated the effectsof the coordination environment around Cr active species on the molecular weight ofproduced polyethylene.

On the basis of chromasiloxane having two Cr−O−Si bonds,

various kinds of alkyl-Cr species were modeled by adding suitable third ligands such as
H2O and OH to an equatorial or axial position of the basic chromasiloxane structure. H2O
and OH mimicked a coordinative O of siloxane or silanol and an additional O covalently
bound to Cr, respectively. The results obtained are summarized briefly as follows. The
molecular weight of produced polyethylene at monoalkyl-Cr(III) species was significantly
sensitive to the additional ligand. The coordinative O at the equatorial position increased
the activation energy of ethylene insertion through the reduction of the -complexationenergy, leading to a lower molecular weight (~ 102). On the contrary, the O at the axial
position led to a higher molecular weight (~ 1010), since the chain transfer was significantly
inhibited in a steric reason.

The basic bipodal monoalkyl-Cr(III) species gave

intermediate molecular weights (~ 103-5), depending on the size of the chromasiloxane ring.
Monoalkyl-Cr(IV) species were not active for the ethylene polymerization. Thus, thecharacteristic broad molecular weight distribution of polyethylene produced by Phillips
catalysts is concluded to be originated from the heterogeneity of coordination environments
for monoalkyl-Cr(III) species on SiO2.

This study suggests a possibility for finer control

of a molecular weight and its distribution in polyethylene production with Cr-based
supported oxide catalysts.

Modification of the distribution of surface hydroxyl groups or15

surface chemical treatment which introduces different Lewis basic sites is a plausible way
to control the coordination environment of active species.

16References[1] J.P. Hogan, R.L. Banks, U.S. Patent 2,825,721, 1958.
[2] M.P. McDaniel, Adv. Catal. 33 (1985) 47.
[3] M.P. McDaniel, J. Catal. 261 (2009) 34.
[4] B. Liu, M. Terano, J. Mol. Catal. A: Chem. 172 (2001) 227.
[5] B. Liu, Y. Fang, M. Terano, J. Mol. Catal. A: Chem. 219 (2004) 165.
[6] Y. Fang, B. Liu, M. Terano, J. Mol. Catal. A: Chem. 131 (2005) 279.
[7] M.P. McDaniel, J. Catal. 67 (1981) 71.
[8] M.P. McDaniel, J. Catal. 76 (1982) 17.
[9] M.P. McDaniel, J. Catal. 76 (1982) 29.
[10] B.M. Weckhuysen, L.M. De Ridder, R.A. Schoonheydt, J. Phys. Chem. 97 (1993)4756.
[11] J.M. Jehng, I.E. Wachs, B.M. Weckhuysen, R.A. Schoonheydt, J. Chem. Soc., Faraday
Trans. 97 (1993) 4756.
[12] B.M. Weckhuysen, I.E. Wachs, R.A. Schoonheydt, Chem. Rev. 96 (1996) 3327.
[13] C.N. Nenu, J.N.J. van Lingen, F.M.F. de Groot, D.C. Koningsberger, B.M.
Weckhuysen, Chem. Eur. J. 12 (2006) 4756.
[14] D. Gianolio, E. Groppo, J.G. Vitillo, A, Damin, S. Bordiga, A. Zecchina, C. Lamberti,
Chem. Commun. 46 (2010) 976.
[15] G. Ghiotti, E. Garrone, A. Zecchina, J. Mol. Catal. A: Chem. 46 (1988) 61.
[16] G. Ghiotti, E. Garrone, A. Zecchina, J. Mol. Catal. A: Chem. 65 (1991) 73.
[17] A. Zecchina, G. Spoto, G. Ghiotti, E. Garrone, J. Mol. Catal. A: Chem. 86 (1994) 423.

17

[18] J. Amor Nait Ajjou, S.L. Scott, V. Paquet, J. Am. Chem. Soc. 120 (1998) 415.
[19] J. Amor Nait Ajjou, S.L. Scott, J. Am. Chem. Soc. 122 (2000) 8968.
[20] S.L. Scott, J. Amor Nait Ajjou, Chem. Eng. Sci. 56 (2001) 4155.
[21] H. Ikeda, T. Monoi, J. Polym. Sci. A: Polym. Chem. 41 (2002) 413.
[22] C.N. Nenu, B.M. Weckhuysen, Chem. Commun. (2005) 1865.
[23] C.N. Nenu, B. Philippe, B.M. Weckhuysen, J. Mol. Catal. A: Chem. 269 (2007) 5.
[24] B. Delley, J. Phys. Chem. 92 (1990) 508.
[25] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.
[26] M. Dolg, U. Wedig, H. Stoll, H. Preuss. J. Chem. Phys. 86 (1987) 866.
[27] A. Bergner, M. Dolg, W. Kuechle, H. Stoll, H. Preuss, Mol. Phys. 80 (1993) 1431.
[28] R. Blom, A. Follestad, O. Noel, J. Mol. Catal. 91 (1994) 237.
[29] Ø. Espelid, K. J. Børve, J. Catal. 195 (2000) 125.
[30] C.A. Demmelmaier, R.E. White, J.A. van Bokhoven, S.L. Scott, J. Catal. 262 (2008)44.
[31] Ø. Espelid, K.J. Børve, J. Catal. 205 (2002) 366.
[32] E. Groppo, C. Lamberti, S. Bordiga, G. Spoto, A. Zecchina, J. Catal. 240 (2006) 172.
[33] I. S. Chuang, G. E. Maciel, J. Phys. Chem. B, 101 (1997) 3052.
[34] J. J. Mortensen, M. Parrinello, J. Phys. Chem. B, 104 (2000) 2901.
[35] J. Handzlik, J. Phys. Chem. C, 111 (2007) 9337.
[36] P. Margl, L. Deng, T. Ziegler, J. Am. Chem. Soc. 120 (1998) 5517.
[37] P. Margl, L. Deng, T. Ziegler, J. Am. Chem. Soc. 121 (1999) 154.

18

Tables

Effects of coordination environment for activation energies and MW of

Table 1.

produced PE a)

model

a)

Eadb)

Eapc)
insertionCTG‡p－G‡ trd)

MW

a

－12.0

－1.1

7.0

－4.8

2.8×104

b

－8.2

4.3

24.2

－15.0

7.0×1010

c

－8.2

0.4

6.2

－2.4

8.6×102

d

-

21.3

-

-

-

e

－7.7

4.9

6.7

0.7

~0

Energies are in kcal/mol.

b)

Ead is the adsorption energy of ethylene.

c)Eap is theapparent activation energy, the height of the TS from the reactant before  complexation.
d)G‡p and G‡tr are the Gibbs energies of activation for the insertion and CT at 350 K.

19

Table 2.

Effects of chromasiloxane ring size for activation energies and MW of produced

PEa)

ring

a)

Eapc)

Eadb)

G‡p－G‡ trd) MW

insertionCT

4-membered

－15.4

－4.4

1.6

－3.2

2.7×1036-membered

－12.0

－1.1

7.0

－4.8

2.8×104

8-membered

－8.2

0.8

8.8

－6.6

3.9×105

Energies are in kcal/mol.

b)

Ead is the adsorption energy of ethylene.

c)Eap is theapparent activation energy, the height of the TS from the reactant before  complexation.
d)G‡p and G‡tr are the Gibbs energies of activation for the propagation and CT at 350 K.

20Effects of the cluster size on the activation energies and MW of produced PEa)

Table 3.

Model

a)

Eapc)

Eadb)

G‡p－G‡ trd) MW

insertion

CT

a

－12.0

－1.1

7.0

－4.8

2.8×104

a’

－12.5

－1.7

5.8

－4.7

2.4×104

Energies are in kcal/mol.

b)

Ead is the adsorption energy of ethylene.

c)Eap is theapparent activation energy, the height of the TS from the reactant before  complexation.
d)G‡p and G‡tr are the Gibbs energies of activation for the propagation and CT at 350 K.

21

Table 4.

Decomposition of the activation barriers for the ethylene insertion and CTa)reactionmodel EadEattach Eap

0.0

0.0

0.0

(－12.0) (16.0)(254.5)(14.1)(－240.8) (－32.9) (－1.1)

0.0aEdetach EM-C Edef EM-TS
0.0

0.0

0.0

insertion b

3.8

－4.1

－8.2

0.2

12.2

1.5

5.4

c

3.8

－1.2

－20.0

－0.8

21.9

－2.2

1.5

e

4.3

－7.3

1.6

－3.4

4.0

6.8

6.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

(－12.0) (16.0)(254.5)(24.5)(－259.4) (－16.5) (7.0)

a

CT

a)

b

3.8

－4.1

－8.2

17.0

15.6

－6.8

17.2

c

6.8

－10.4

－11.2

－0.7

19.4

－4.8

－0.6

e

7.1

－10.9

5.7

－2.2

1.8

－1.8

－0.3

Energies are in kcal/mol. All E components whose definition is illustrated in

Scheme 2 are differential values from E for a written in the parentheses.

22

Table 5.

Simplified decomposition of the activation barriers for the ethylene insertion andCTa)reactionEadE-Rb)

Edef

Eap

0.0

0.0

0.0

0.0

(－12.0)(－2.3)(14.1)(－1.1)

b

3.8

1.4

0.2

5.4

c

3.8

－1.5

－0.8

1.5

e

4.3

5.1

－3.4

6.0

0.0

0.0

0.0

0.0

(－12.0)(－5.4)(24.5)

(7.0)

b

3.8

－3.5

17.0

17.2

c

6.8

－7.0

－0.7

－0.6

e

7.1

－5.2

－2.2

－0.3

model

a

insertion

a

CT

a)

Energies are in kcal/mol.

b)

E-R shows the difference of the binding strength ofethylene and alkyl fragments to Cr between at TS and at  complex, which is defined as Eq.
(5).

23

Figure/Scheme caption
Fig. 1. Active site models with various coordination environments. Black: Cr, darkgray: Si, gray: O, white: H.
Fig. 2. Cluster models with a 6-membered chromasiloxane structure. Black: Cr, darkgray: Si, gray: O, white: H.
Scheme 1. Insertion pathway for (a). Black: Cr, dark gray: Si, gray: O, light gray: C,

white: H.
Scheme 2. Schematic representation of decomposition of the activation barriers

24

y

x

x
1.84 Å

z
114°

z

y

y
2.49 Å

x2.22 Å

z

81°

109°

112°

a (Cr(II), Td )b (Cr(II), Oh)c (Cr(II), Oh)
1.80 Å

1.82 Å

y
x
z

101°
109°

y

d (Cr(III), Oh)

103°

z
x

e (Cr(III), Oh)
Fig. 1. Tonosaki et al.

25

a

a’
Fig. 2.

26

Tonosaki et al.

y

x
z

ax

eq

eq
10.9 kcal/mol

ax

reactant (0.0 kcal/mol) complex (－12.1 kcal/mol)

TS (－1.1 kcal/mol)

Scheme 1. Tonosaki et al.

27

Scheme 2. Tonosaki et al.

28