Theoretical modeling of “constrained geometry catalysts” beyond the naked cation approach

Topics in Catalysis 7 (1999) 45–60 45

Theoretical modeling of “constrained geometry catalysts” beyondthe naked cation approach

Giuseppe Lanza a and Ignazio L. Fragala b,∗

a Dipartimento di Chimica, Universita della Basilicata, 85100 Potenza, Italyb Dipartimento di Scienze Chimiche, Universita di Catania, 95125 Catania, Italy

Mechanistic aspects of constrained geometry catalyst generation, catalyst-cocatalyst structural energetics, and olefin activa-tion/insertion have been studied at the MP2/HF level of theory including solvation effects for the prototypical catalytic species (C5H4

SiH2NR)Ti(CH3)2 (R = CH3 and tBu) and strong Lewis acid [BF3, BCl3 and B(C6F5)3] cocatalysts. It is seen that counteranion andsolvation effects are substantial and strongly affect the olefins polymerization processes.

Keywords: constrained geometry catalysts, naked cation, cocatalyst, contact ion-pairs, solvent effect, olefin activation/insertion

1. Introduction

Since the discovery of single site, structurally character-ized metallocene catalysts for olefin polymerization, a largeamount of research activities have been addressed to theirupgrading in the perspective of finding a better fit to therequired properties of products [1–7]. Nowadays, desiredtacticity, molecular weight, and comonomer distribution canbe obtained through a suitable modulation of the molecularstructure and composition of catalysts [1–7].

In this context, the novel single-site “constrained geome-try catalysts” (CGC) have proven capable of great advancesin polymer design with unprecedented control over macro-molecular architecture, superior processing/mechanicalproperties due to the narrow molecular weight distributioncombined with long chain branching, and high degrees ofcomonomer incorporation [8–13]. Moreover, the replace-ment of a cyclopentadienyl ligand with a simpler amidogroup favors polymerization of long chain α-olefins andcopolymerization of a large series of monomers due to theenhanced acidity and reduced crowding at the metal center[8–13].

The mechanism of catalyst activation seems now to bewell understood. It involves the formation of highly reac-tive species whose properties must include: (i) mostly a d0

metal electron configuration,1 (ii) the presence of an elec-tronically and sterically unsaturated metal center, and (iii)one or more vacant coordination sites cis to the transitionmetal-bound alkyl ligand. These specific prerequisites playa crucial role in the activation of the characteristic polymer-ization propagation mechanism in which specific α-agosticinteractions are believed to facilitate the olefin insertion step[15–18].

Many theoretical studies have been focused on themechanistic aspects associated with the catalytic processes

∗ To whom correspondence should be addressed.1 There are also various catalysts which have partial filled d shells based

on Ni, Pd, Co, Fe and Cr. See [14].

[19–41]. Research, however, has been limited to the “nakedcation” approach.2 Solvent and counterion species havenever been considered in spite of growing experimentalevidence indicating that cocatalyst/counterion and solventplay a significant role in the energetics of ion pairing, hencein the catalytic activity [1–7,44–52]. It is well known, infact, that the polymerization activity, stereospecificity, andmolecular weight of the resulting polymers significantly de-pend upon several operational parameters including the cat-alyst concentration, the amount and nature of the adoptedcocatalyst, and the reaction solvent.

For example, the ethylene polymerization activity of theperfluorinated Cp′2ThCH+

3 B(C6F5)−4 is about 3500 timeshigher than that of the Cp′2ThCH+

3 B(C6H5)−4 analogue [50].Combined studies on a series of metallocene catalyst ionpairs [C5H3(CH3)2]2MCH+

3 CH3B(C6F5)Ar−2 (M=Zr andHf, Ar=C6F5, C6H3F2, C6H5, C6H3(CH3)2) have showna clear correlation between the ethylene polymerization ac-tivities and the enthalpies of methide abstraction, hence ofthe cocatalyst nature [51,52]. Moreover, gas-phase studies[53,54] on the reactivity of various Zr-metallocene nakedcations have shown that their reactivities with several or-ganic substrates decrease in the order Me2SiCp2ZrCH+

3 ≈CGCZrCH+

3 > Cp2ZrCH+3 > (indenyl)CpZrCH+

3 >(indenyl)2ZrCH+

3 > (fluorenyl)2ZrCH+3 .

These data are in apparent contrast with the experimentaltrend observed for the ethylene polymerization processes insolution since the stronger donor permethylated cyclopen-tadienyl and indenyl ligands have enhanced catalytic activ-ities whereas electron-withdrawing substituents have oppo-site effects [53,54].

It therefore transpires that any realistic theoretical mod-elling study of metallocene CGC catalysts requires the ex-plicit inclusion of cocatalyst and solvent effects, thus goingbeyond the “naked cation” approach [55,56].

2 To our knowledge a unique study which includes the counter-anion ef-fects has been reported for the (C5H5)2TiCH3Al(CH3)2Cl2 [42,43].

J.C. Baltzer AG, Science Publishers

46 G. Lanza, I.L. Fragala / Modeling of constrained geometry catalysts

This consideration prompted accurate ab initio SCFand MP2 theoretical investigations on olefin polymeriza-tion processes mediated by the CGC-Ti precatalyst [η5 : η1-C5(CH3)4Si(CH3)2N-tBu]Ti(CH3)2 (hereafter L2M(CH3)2)1 including counteranion and solvation effects on cata-lyst generation, catalyst-cocatalyst structural energetics andolefin activation insertion reaction.

In section 2, a brief outline of theoretical methods andmodels adopted is presented. Section 3 is focused on struc-tural aspects of the CGC precatalyst 1 and of heterolyticallyactivated naked cation (equation (1)) as well as on the sub-sequent ethylene insertion process (equation (2)).

L2M(CH3)2 + Lewis Acid→ L2MCH+3

+ (Lewis Acid)–CH−3 (1)

(2)

These processes have never been analyzed using traditionalab initio theory. A DFT study has been proposed by Ziegleret al. [24–32] adopting, however, a simpler model than thepresent one.

In section 4 these data are put in the perspective of con-tact ion pairing processes involving the precatalyst and var-ious borane cocatalysts (equation (3)) as well as of the pos-

sible occurrence of ion pair total charge separation (equa-tion (4)).

L2Ti(CH3)2 + BX3 → L2TiCH3•CH3BX3 (3)

L2TiCH3•CH3BX3 → L2TiCH+3 + CH3BX−3 (4)

The energetics of these processes are also analyzed in-cluding specific and non-specific solvent contributions. Itwill be seen that, on energy thermodynamic grounds, re-action (4) is far from being compatible with any catalyticprocess.

Finally, section 5 presents energetics of ethylene acti-vation/insertion in CGC contact ion pairs and the energybarriers are analyzed depending upon the cocatalyst nature.Concluding remarks are made in section 6.

2. Computational details

The effective core potentials (ECP) of Hay and Wadt[57], which explicitly treat 3s and 3p electrons and a basisset contracted as [3s, 3p, 2d], were used for the titaniumatom. The standard all-electron 6-31G basis was used forthe remaining atoms [58,59]. Geometry optimization usedanalytical gradient techniques within the restricted Hartree–Fock (HF) formalism. Correlation effects were evaluatedadopting MP2 wavefunctions where all valence electrons,including the titanium 3s and 3p, were correlated.

The “distinguished reaction coordinate procedure” wasused in the determination of the transition state geometry inthe ethylene insertion process and the reaction coordinatewas associated with the vector along the new C–C σ bond(TiCH3–CH2=CH2). The energy profiles were constructed

Figure 1. Optimized structure of the model CGC precatalysts (C5H4SiH2NCH3)Ti(CH3)2 (2a) and (C5H4SiH2NtBu)Ti(CH3)2 (2b).

G. Lanza, I.L. Fragala / Modeling of constrained geometry catalysts 47

Table 1

Label Model molecule Relevant stage Theoretical level

1 [C5(CH3)4Si(CH3)2NtBu]Ti(CH3)2 CGC precatalyst

2a (C5H4SiH2NCH3)Ti(CH3)2 Model precatalyst HF, MP22b (C5H4SiH2NtBu)Ti(CH3)2 HF

3a (C5H4SiH2NCH3)TiCH+3 Naked cation HF, MP2

3b (C5H4SiH2NtBu)TiCH+3 HF

4a (C5H4SiH2NCH3)Ti(CH3)•(C2H4)+ π-complex HF, MP24b (C5H4SiH2NtBu)Ti(CH3)•(C2H4)+ HF

5a (C5H4SiH2NCH3)Ti(C2H4)(CH3)+ Transition state HF, MP25b (C5H4SiH2NtBu)Ti(C2H4)(CH3)+ HF

6a (C5H4SiH2NCH3)TiCH2CH2CH+3 γ-agostic product HF, MP2

6b (C5H4SiH2NtBu)TiCH2CH2CH+3 HF

7a (C5H4SiH2NCH3)TiCH3•CH3BF3 Contact ion-pair HF, MP27b (C5H4SiH2NCH3)TiCH3•CH3BCl3 formation/separation HF7c (C5H4SiH2NCH3)TiCH3•CH3B(C6F5)3 and ethylene HF7d (C5H4SiH2NtBu)TiCH3•CH3B(C6F5)3 insertion HF

along this vector optimizing all the other geometrical para-meters without any constraints. In some cases, the natureof the stationary points was determined by numerical eval-uations of the complete matrix of force constants and of theassociated harmonic vibrational frequencies. The basis setsuperposition error was estimated in some selected casesby the counterpoise method [60].

Solvent effects (C6H6; ε = 2.274) were modeled usingthe self-consistent isodensity polarized continuum formal-ism (SCI-PCM). The SCI-PCM method models the solventas a continuum of uniform dielectric constant and the soluteis placed into a cavity within the solvent. The cavity isdefined as an isodensity surface and is coupled with theelectron density of solute. In this method the effects of sol-vation are folded into the iterative SCF procedure [61–63].

All calculations necessarily adopted simpler moleculeshaving H atoms rather than methyl groups on the cyclopen-tadienyl ring (Cp) and silyl group.

The CGC precatalyst [C5(CH3)4Si(CH3)2N-tBu]Ti(CH3)2

was modeled both by (C5H4SiH2NCH3)Ti(CH3)2 and(C5H4SiH2NtBu)Ti(CH3)2 to evaluate effects of the bulkieramido ligand (figure 1). The interactions with boranecocatalysts have been modeled using the BF3, BCl3 andB(C6F5)3 Lewis acids. Table 1 summarizes the model mol-ecules adopted along with the relevant stages of the catalyticprocess.

All the calculations were performed using the HONDO95.3 and G94 codes [63,64] on IBM-SP and Cray C90systems.

3. The naked cation approach

3.1. The naked cation

The geometry of cation models (C5H4SiH2NCH3)TiCH+3

(3a) and (C5H4SiH2NtBu)TiCH+3 (3b) (figure 2) adopts a

Side view

Top view

Figure 2. Optimized structure of the naked cation (C5H4SiH2NtBu)TiCH+

3 (3b).

pseudo-trigonal arrangement around the titanium atom. Themolecules both possess Cs symmetries, with the symmetryplane through the Ti, C(1), N, and Si atoms bisecting the


Table 2HF bond lengths (A) and bond angles (deg) of precatalysts and related naked cations. MP2 values are given in parentheses.

(C5H4SiH2NCH3)Ti(CH3)2 (C5H4SiH2NtBu)Ti(CH3)2 (C5H4SiH2NCH3)TiCH+3 (C5H4SiH2NtBu)TiCH+

32a 2b 3a 3b

Bond lengthsa

Ti–C(1) Ti–C(2) 2.08 (2.10) 2.08 2.03 (2.06) 2.03Ti–Cpcentr. 2.16 (2.13) 2.18 2.07 (2.09) 2.07Ti–C(3) 2.37 (2.39) 2.35 2.31 (2.39) 2.29Ti–C(4) Ti–C(7) 2.45 (2.43) 2.45 2.35 (2.38) 2.34Ti–C(5) Ti–C(6) 2.57 (2.52) 2.60 2.49 (2.50) 2.50Ti–N 1.90 (1.90) 1.92 1.83 (1.87) 1.84N–Si 1.79 (1.84) 1.81 1.85 (1.91) 1.86N–C(8) 1.46 (1.49) 1.49 1.48 (1.50) 1.50Si–C(3) 1.89 (1.91) 1.88 1.90 (1.91) 1.90C(1)–H(1) 1.08 (1.10) 1.08 1.09 (1.11) 1.09C(1)–H(2) 1.08 (1.10) 1.08 1.09 (1.11) 1.09C(1)–H(3) 1.08 (1.10) 1.08 1.08 (1.10) 1.08

Bond anglesa

C(1)–Ti–C(2) 102.7 (100.2) 98.4N–Ti–Cpcentr. 106.0 (108.5) 108.3 110.2 (109.7) 111.4Ti–N–Si 105.4 (104.4) 102.9 105.3 (104.3) 103.6Ti–N–C(8) 131.2 (129.4) 134.3 133.4 (131.8) 133.7Ti–C(1)–H(1) 110.3 (105.2) 110.4 108.8 (105.1) 108.9Ti–C(1)–H(2) 110.5 (109.1) 110.6 108.8 (105.1) 108.9Ti–C(1)–H(3) 110.7 (113.5) 110.8 116.0 (120.4) 115.9

a Atom labeling refers to figures 1 and 2.

Cp ring. The vibrational analysis indicates that these struc-tures are minima on the potential energy surfaces. Relativeto the parent precatalyst models 2a and 2b (figure 1)3, theN–Si, N–C(8) and Si–C(3) bond distances (table 2) areslightly contracted (∼0.05, ∼0.02 and ∼0.01 A, respec-tively) while all bond lengths involving the titanium atom,namely the Ti–Cpcentr., Ti–N and Ti–C(1), significantly de-crease (∼0.09, ∼0.07 and ∼0.05 A, respectively). This isa direct consequence of the electron-deficient character ofthe metal center.

The computed geometrical parameters lie very close atboth the HF and MP2 levels even though correlated wave-function shortens the Ti–C(Cp) bonds and increases theother bond lengths in 2a. These are well known effects,since π(Cp–M) interactions are generally underestimated atHF level while σ bonds are overestimated [65,66]. Uponmoving to the tBu substituted molecule (2b and 3b), a gen-eral lengthening (relative to 2a and 3a) of all bonds involv-ing the N center is observed, similar to that found in X-raystructures [67,68].

The energetics of bending the Ti–CH3 group out ofthe symmetry plane has been analyzed via HF and MP2single point energy calculations (figure 3). There is evi-dence of a single minimum associated with the symmetri-cal structure even though the relatively flat potential energysurface (4.3 kcal/mol, required for a 50◦ bending of theCH3 group) clearly indicates that the Ti–CH3 vector canbe easily deformed upon olefin approach to the metal cen-ter. These data are in agreement with recent calculations

3 Geometries of the models 2a and 2b have been optimized within theCs symmetry. Any asymmetric structure always results in forces whichrestore the molecular plane.

Figure 3. Potential energy dependence upon out-of-plane (Cs) bending (θ)of the vector Ti–CH3.

(ab initio, SCF and GVB-CI) [19–23] on (C5H5)2TiCH+3

and SiH2(C5H4)2TiCH+3 cations which similarly suggest

that the methyl group lies in the Cp(centroid)2Ti planeand that the potential energy surface for the out-of-planeCH3 motion is very flat (∼4 kcal/mol for 50◦ bending)[19–23]. The present metrical parameters are similar tothe DFT results of Ziegler et al. [24–32] on related (C5H4

SiH2NH)TiCH+3 , even though the latter data indicate a

pyramidal structure about the titanium center with the Ti–CH3 vector pointing 61.2◦ out of the Cpcentr.–N–Ti plane.


This difference prompted further MP2 investigations us-ing a larger basis set (6-31G∗∗). Even the improvedlevel of theory, does not change the results and complex3a remains with a Cs planar structure about the titaniumatom.

The present HF-derived bond angle and bond length val-ues associated with the Ti-bonded methyl group (Ti–C(1)–H(1), Ti–C(1)–H(2), Ti–C(1)–H(3) and C(1)–H(1), C(1)–H(2), C(1)–H(3) in figure 2) point to a remarkable devi-ation from local C3v symmetry, thus suggesting α-agosticinteractions involving two σ(C–H) bonds (C(1)–H(1) andC(1)–H(2) in figure 2). Somewhat more pronounced dis-tortions are found at the MP2 level. This is indication thatinclusion of correlation effects enforce α-agostic interac-tions [19–23,33–41].

In this context, it becomes of interest to contrast thesedata with those of (C5H5)2TiCH+

3 and SiH2(C5H4)2TiCH+3

where a single α-agostic C–H bond is found. Presentresults, however, are like those of Cl2TiCH+

3 where twoα-agostic interactions have been similarly found [33–41].These observations are of relevance as far as the reac-tion pathway for the olefin insertion is concerned. In both3 and Cl2TiCH+

3 (two α-agostic C–H bonds) the spatialarrangement of methyl hydrogen atoms precludes any fa-vorable pathway for ethylene insertion. Therefore, theymust rearrange to spatially and energetically more suit-able conformations to promote the olefin insertion tran-sition state (vide infra). An obvious consequence is thatsuch a geometrical reorganization requires sizable ener-getic barriers whereas in the parent (C5H5)2TiCH+

3 andSiH2(C5H4)2TiCH+

3 the corresponding insertion processis less energetically demanding since only minor struc-tural reorganizations are required upon olefin approach[20,21].

3.2. The activated olefin complex

The geometry of the intermediate π-complex 4b alongthe olefin insertion reaction coordinate is pictured in fig-

ure 4. Relevant data are compiled in table 3. Changesupon switching from the >N–CH3 to the >N–tBu ligand aswell as those due to inclusion of correlation effects (MP2)parallel (table 3) the findings described previously for cat-ions 3.

Compared to 3, the Ti–CH3 vector undergoes ≈ 40◦ dis-placement from the Ti–N–Cpcentr. plane, thus favoring theethylene coordination. In addition, the Cp ring twists ≈ 4◦

about the C(3)–Cpcentr. vector away from the symmetricconformation found in 3. The differing Ti–C(12) and Ti–C(13) metal-ethylene contacts are indicative of an asym-metric bonding because of repulsive interactions with theCp ring. The same lengths shorten (∼0.1 A) at the MP2level. This is an indication that correlated wavefunctionsenhance the ethylene π donation.

Similar rearrangements, and hence comparable geomet-rical data, have been described for (C5H5)2TiCH+

3 and SiH2

(C5H4)2TiCH+3 π-complexes [20,21] upon ethylene coordi-

nation. Interestingly enough, the DFT-derived geometry ofthe CGC(C5H4SiH2NH)TiCH+

3 model π-complex reportedby Ziegler is similar to that presently found for 4, eventhough the Ti–C (ethylene) contacts are considerably dif-ferent (2.44 and 2.39 A vs. 2.78 and 2.50 A) [29] probablydue to the different theoretical approach.

3.3. The insertion transition state

The geometry of the ethylene insertion transition state 5b(figure 4) shows a highly distorted conformation (relativeto 3 and 4) of Ti–CH3 hydrogen atoms, which are pseudo-eclipsed with respect to the ethylene fragment. There isevidence of strong α-agostic interactions with the Ti–C(1)–H(1) bond angle (table 3) considerably smaller (75◦) thanthe others (125◦). This arrangement closely resemblesthat found for (C5H5)2TiCH+

3 [21] SiH2(C5H4)2TiCH+3 [20]

and Cl2TiCH+3 [21,40]. The present four-membered Ti–

C(1)–C(13)–C(12) transition state geometry exhibits eithera 19.7◦ (MP2), or a 12.3◦ (HF) folding angle along theC(1)–C(13) internuclear vector, and the puckering can be

Figure 4. Optimized structures of species involved in the ethylene activation/insertion into (C5H4SiH2NtBu)TiCH+3 (3b): π-complex (4b), transition

state (5b), and final inserted product (6b).


Table 3HF bond lengths (A) and bond angles (deg) of structures involved in the ethylene activation and insertion into (C5H4SiH2

NCH3)TiCH+3 and (C5H4SiH2NtBu)TiCH+

3 (in square brackets) catalysts. MP2 data are compiled in parentheses.

π-complex (4) Transition state (5) Final structure (6)

Bond lengthsa

Ti–C(1) 2.04 (2.09) [2.05] 2.12 (2.10) [2.14] 2.51 (2.33) [2.56]Ti–Cpcentr. 2.11 (2.11) [2.12] 2.12 (2.10) [2.12] 2.09 (2.09) [2.10]Ti–C(3) 2.32 (2.35) [2.30] 2.32 (2.31) [2.28] 2.30 (2.31) [2.29]Ti–C(4) 2.45 (2.46) [2.45] 2.57 (2.41) [2.57] 2.33 (2.34) [2.32]Ti–C(7) 2.32 (2.33) [2.31] 2.42 (2.36) [2.38] 2.40 (2.41) [2.42]Ti–C(5) 2.55 (2.57) [2.58] 2.53 (2.55) [2.57] 2.49 (2.51) [2.52]Ti–C(6) 2.50 (2.50) [2.52] 2.36 (2.52) [2.39] 2.51 (2.55) [2.56]Ti–N 1.84 (1.86) [1.86] 1.86 (1.86) [1.86] 1.84 (1.86) [1.85]N–Si 1.83 (1.89) [1.85] 1.83 (1.88) [1.84] 1.84 (1.88) [1.85]N–C(8) 1.47 (1.50) [1.50] 1.47 (1.49) [1.50] 1.47 (1.50) [1.50]Si–C(3) 1.90 (1.91) [1.89] 1.89 (1.90) [1.89] 1.90 (1.91) [1.89]C(1)–H(1) 1.09 (1.11) [1.09] 1.11 (1.14) [1.11] 1.09 (1.11) [1.10]C(1)–H(2) 1.09 (1.11) [1.09] 1.08 (1.09) [1.08] 1.09 (1.11) [1.09]C(1)–H(3) 1.09 (1.10) [1.09] 1.08 (1.09) [1.08] 1.08 (1.10) [1.08]Ti–C(13) 2.60 (2.50) [2.66]Ti–C(12) 2.90 (2.78) [2.91] 2.19 (2.25) [2.16] 2.02 (2.07) [2.03]C(1)–C(13) 3.25 (3.18) [3.21] 2.16 (2.16) [2.12] 1.56 (1.60) [1.56]C(12)–C(13)b 1.34 (1.36) [1.34] 1.41 (1.41) [1.42] 1.56 (1.58) [1.56]

Bond anglesa

N–Ti–Cpcentr. 108.6 (110.1) [110.3] 108.8 (111.4) [111.3] 109.6 (111.1) [111.1]Ti–N–Si 105.8 (104.2) [103.5] 105.3 (103.2) [102.5] 105.2 (103.6) [103.0]Ti–N–C(8) 130.7 (129.2) [134.8] 134.4 (132.3) [136.2] 132.8 (129.3) [135.6]Ti–C(1)–H(1) 110.0 (106.8) [109.7] 75.4 (68.0) [73.1] 114.7 (114.7) [115.1]Ti–C(1)–H(2) 108.4 (106.7) [109.5] 128.9 (137.1) [133.9] 113.9 (115.1) [115.6]Ti–C(1)–H(3) 114.2 (116.3) [112.9] 119.5 (111.3) [115.7] 109.0 (108.2) [109.0]

Torsion anglesa

Ti–N–Si–C(3) 5.1 (5.1) [3.90] 1.1 (2.0) [1.9] 0.7 (4.7) [2.5]Si–C(3)–Cpcentr.–C(4) 93.5 (92.7) [93.8] 89.6 (89.3) [88.8] 87.7 (86.3) [87.4]Si–C(3)–Cpcentr.–C(7) 85.8 (86.3) [85.2] 89.7 (90.0) [89.1] 91.8 (93.0) [91.8]Si–C(3)–Cpcentr.–C(5) 93.3 (93.9) [94.3] 90.6 (90.2) [90.9] 89.0 (87.2) [89.0]Si–C(3)–Cpcentr.–C(6) 87.7 (88.0) [87.4] 90.4 (90.8) [91.6] 91.7 (94.0) [92.4]

a Atom labeling refers to figure 4.b Vaues of the free ethylene are: HF = 1.32 A; MP2 = 1.35 A.

associated with repulsive interactions involving the methyland ethylene hydrogen atoms. These data can be com-pared with a similar ring folding in the transition states ofCl2TiCH+

3 (10.7◦) and (C5H5)2TiCH+3 (12.8◦) [21]. Con-

siderably smaller puckering, with an almost planar confor-mation, has been reported in the case of the bridged-bis-cyclopentadienyl SiH2(C5H4)2MCH+

3 (M = Ti, Zr and Hf)[20,23], where the near planarity may be due either to con-straints imposed by the silylene bridging or to artifacts ofthe geometry optimization procedures.

In this context, it becomes of interest to place the tran-sition state geometry (table 3) in the perspective of thoseof the related cation 3 and of inserted final product 6 (videinfra). There is evidence of an asynchronous mechanismalong the insertion pathway since the formation of the newTi–Cethylene σ bond has no counterpart in a synchronizedalkyl chain lengthening. Thus, the relevant Ti–C(12) andTi–C(1) lengths are only slightly longer than in 6 and 3.Moreover, the C–C ethylene bond is 0.05 A longer than inthe free olefin and, even more important, the C(1)–C(13)distance, 0.5 A longer than in the 6, is indicative of almostunbound atoms.

Finally, it is worthy of note that the geometry presentlydescribed shows significant differences compared to DFTdata reported for a similar CGC model [29]. Those data,in fact, point to a longer (than present) C(1)–C(13) (3.00 Avs. 2.16 A) contact which, in reality, remains closer to thevalue found in the related π-activated complex (3.35 A).The Ti–ethylene (Ti–C(12)) bonds, by contrast, are simi-lar (2.3 A vs. 2.25 A) at both ab initio and DFT levels.The discrepancy might be probably due to the local den-sity approximation in the energy evaluation for geometryoptimization. Note, in addition, that the longer Ti–olefindistance in the insertion transition state may explain thesmaller (than with ab initio) energy barrier found at theDFT level.

3.4. The final γ-agostic propylmetal insertion product

Previous studies of the ethylene insertion process in-volving several bis-cyclopentadienyl alkyl metal complexeshave shown that the final propylmetal inserted productcan assume several conformations which depend upon pre-dominance of either α, or β, or γ agostic interactions


between the alkyl-chain and the metal center [19–32].The following discussion refers, however, to the γ-agosticpropyl structure since it represents the initial direct inser-tion product. The optimized structure of 6b is picturedin figure 4, and the most significant geometrical parame-ters are compiled in table 3. As expected, there is ev-idence of strong γ-agostic interactions since the Ti–C(1)distance (HF = 2.51 A; MP2 = 2.33 A) is slightly longerthan the direct propylmetal Ti–C(12) σ bond. In additionthe C(1) deviates from a local C3v symmetry, with C(1)–H(1) and C(1)–H(2) bond lengths 0.02 A longer than theC(1)–H(3) remaining bond. In accordance, also the Ti–C(12)–C(13) bond angle (HF = 96.1◦; MP2 = 87.4◦)differs markedly from that expected for sp3 hybridiza-tion of the C(12) atom. All these geometrical data are,of course, consistent with γ-agostic interactions involv-ing the C(1)–H(2) and C(1)–H(3) σ bonds. These dataagree well with results for both (C5H5)2TiC3H+

7 and SiH2

(C5H4)2TiC3H+7 obtained at ab initio level [20,21] as well

as for the (C5H4SiH2NH)TiC3H+7 DFT-derived structure

[24–32].

3.5. Energetics of the ethylene insertion process intonaked cations

The calculated potential energy profile along the ethyl-ene activation/insertion pathway into the model naked cat-ion 3a is shown in figure 5. Relevant HF and MP2 data ofboth 3a and 3b are compiled in table 4 and compared withsome related literature data. The energy values are stronglyaffected by correlation energies, the effect being of majorrelevance for the insertion processes.

The energies associated with the formation of the ethyl-ene π-complex are similar (∆E ≈ 2 kcal/mol) for both 3aand 3b and point to a smaller stabilization compared to theearly adopted model Cl2TiCH3•(C2H4)+ (table 4). This is,of course, a consequence of the greater steric congestion aswell as of the smaller electron-deficient character of the Ticenter in CGC molecules.

Present insertion energy barriers, in addition, lie closerto data reported for Cl2TiCH+

3 . By contrast, either smallervalues or no barrier (hence a direct insertion) have beenfound for SiH2(C5H4)2TiCH+

3 and (C5H5)2TiCH+3 , respec-

Figure 5. Energetic (RHF/RHF, MP2/RHF and MP2/MP2) of the ethylene insertion pathway involving (3a). The energies of the isolated reagents arealways assumed as reference for the energy scale.


Table 4π-complexation, insertion and formation energies (kcal/mol) for ethylene insertion into the CGC [C5H4SiH2NR]

TiCH+3 , and metallocene SiH2(C5H4)2TiCH+

3 , and (C5H5)2TiCH+3 and Cl2TiCH+

3 model catalysts.

π-complex Insertion energy Final product Reference

[C5H4SiH2N(CH3)]TiCH+3

RHF/RHF −19.1 +20.7 −21.1MP2/RHF −29.7 +11.8 −33.3 [56]MP2/MP2 −30.3 +8.1 −35.4

[C5H4SiH2NtBu]TiCH+3

RHF/RHF −17.2 +18.5 −19.0MP2/RHF −27.8 +9.0 −31.0 [56]

SiH2(C5H4)2TiCH+3

RHF/RHF −13.0 +14.3 −22.8MP2/RHF −28.6 +1.3 −34.7 [20]RQCISD/RHF −21.9 +7.1 −29.3

(C5H5)2TiCH+3

RHF/RHF −5.3 +17.8 −21.7MP2/RHF −23.7 no barrier −32.3 [21]MP2/MP2 no barrier −45.1

Cl2TiCH+3

RHF/RHF −41.5 +13.8 −45.0 [40]DPUMP2/RHF −45.3 +4.3 −56.4RHF/RHF −35.0 −39.9 [36]MP2/RHF −34.7 −48.9MP2/MP2 −42.0 +2.6 −57.9 [21]CCSD(T)/MP2 −38.7 +5.2 −51.2

tively (table 4). The higher values (than in metallocenes)presently found depend upon smaller α-agostic “assistance”in CGC catalysts. The different spatial conformation of themethyl group (vide supra) requires a remarkable, energydemanding rearrangement to promote ethylene insertion inCGC systems. The associated energy results, of course,in higher energy barriers. Moreover, the energy trendon traversing the series (C5H5)2TiCH+

3 < SiH2(C5H4)2

TiCH+3 < (C5H4SiH2NCH3)TiCH+

3 , finds analogous coun-terpart in DFT data reported for the homologous zirco-nium (C5H5)2ZrCH+

3 (0.7 kcal/mol), SiH2(C5H4)2ZrCH+3

(l.0 kcal/mol), and (C5H4SiH2NH)ZrCH+3 (6.0 kcal/mol)

[24–32].Finally, the total energies associated with the formation

of the propylmetal inserted products (table 4), relative tostarting reagents (3 + ethylene), are very similar to thoseof both (C5H5)2TiC3H+

7 and SiH2(C5H4)2TiC3H+7 [20,21].

This observation points to comparable electronic and stericeffects in the final inserted products.

4. Geometries and energetics of contact ion pairformation and separation

All the studies reported to date have been focused almostexclusively on free naked group 4 cations [19–41], eventhough there is no conclusive evidence that they can existin solution [1–7]. By contrast, the active species generatedabstractively, or oxidatively consist of ion-paired species

and there is growing experimental evidence that effects dueto cocatalyst/counteranion and to solvents play a major rolefor catalytic activities of metallocene as well as of CGCcatalysts [1–13].

In the catalyst/cocatalyst energetics associated with theactivation of the prototypical CGC species 1, the acidityof the Lewis acid acceptor plays a major role. In addi-tion, any heterolytic ion pair dissociation is far from beingenergetically feasible unless favored by intervening olefinactivation or solvent stabilization.

Several acidic species have been adopted for CGC cat-alyst generation. They include methylalumoxane (MAO)[1–7,69–72], perfluoroarylboranes (B(C6F5)3) [8–13,73–77], and tetrakis(pentafluorophenylborate) derivatives ((C6

H5)3C+B(C6F5)−4 ) [8–13,73–77].In our studies we have focused on boron derivatives in-

cluding simpler models BF3 and BCl3 as well as on the per-fluorotriphenylborane B(C6F5)3 which is commonly used incatalytic processes of 1. It is well known, however, that thesimpler trihaloboranes cannot be used for catalyst activationsince they irreversibly transfer F− or Cl− to the metal cen-ter thus affording inactive metallocene halides [1–7]. Nev-ertheless, trihaloboranes can be useful model cocatalystssince there is unequivocal evidence that the adducts (C5H4

SiH2NCH3)TiCH3•CH3BF3 and (C5H4SiH2NCH3)TiCH3•CH3BCl3 represent stable local minima on the overall en-ergy surfaces [56]. It therefore transpires that the related“frozen” geometries can be adopted to model the catalyticprocesses and in particular to understand how the cocata-


Figure 6. Optimized structure of contact ion pairs (C5H4SiH2NCH3)TiCH3•CH3BF3 (7a) and (C5H4SiH2NtBu)TiCH3•CH3B(C6F5)3 (7d).

lyst acidity influences the precatalyst activation and, hence,ion-pairing energies.

In this context, we have analyzed the energetics of boththe methide abstraction processes to form contact ion pairswith representative Lewis acid boranes [BF3, BCl3 andB(C6F5)3]:

(C5H4SiH2NR)Ti(CH3)2 + BX3 →(C5H4SiH2NR)TiCH3•CH3BX3 + ∆Hdr (5)

R = CH3; X = F, Cl, C6F5 (7a, 7b, 7c)R = tBu; X = C6F5 (7d)

and of the related heterolytic ion-pair separation:

(C5H4SiH2NR)TiCH3•CH3BX3 →[C5H4SiH2NR]TiCH+

3 + CH3BX−3 + ∆Hips (6)

4.1. Geometrical structure of contact ion pairs

The titanium centers in adduct complexes 7 all havepseudotetrahedral arrangements with asymmetrically bond-ed alkyl ligands (figure 6 and table 5). The CH3–Ti–CH3

angle, however, remains almost constant upon BX3 co-ordination whilst the contacted Ti–CH3 bond length suf-fers a considerable elongation (0.13–0.39 A), relative tothe remaining unaffected methyl group. Consideration ofboth bond lengths and bond orders suggest that the con-tacted CH3 group still remains bonded to the metal center.The methyl hydrogen atoms, however, suffer an evidentconformation inversion (figure 6) thus bridging the metalcenter. This is indicative of a µ3–Ti· · ·H3C–B coordina-tion with an almost linear Ti–CH3–B bond angle (171◦–

175◦). Data in table 5 show clear evidence that the relatedTi–C(2)H3 bond distance strongly depends upon the bo-rane nature and, in particular, that it increases in the orderB(C6F5)3 > BCl3 > BF3. The nature of the substituents onthe Ti-coordinated amido group somewhat affects the Ti–C(2)H3 bond since a 0.03 A elongation is observed uponswitching from the methyl (7c) to tBu (7d) derivatives.

The (C5H4SiH2NCH3)TiCH3•CH3BF3 adduct has alsobeen analyzed at MP2 level. The MP2 geometrical parame-ters are similar to those obtained at uncorrelated level (HF)and show only minor differences (table 5). The B–CH3

bond length is almost equal for 7a, 7c and 7d while a shorterdistance is observed in the case of the BCl3 derivative (7b).The boron atom always assumes a pseudotetrahedral coor-dination, at variance to the trigonal planar geometry foundin the unadducted BX3 molecules4. The X–B–X bond an-gles, lie, however, between the values found in the “free”BX3 and in the CH3BX−3 anions. The B–X bond lengths incontact ion pairs, are similarly intermediate between thoseof BX3 and CH3BX−3 . These observations suggest some-what reduced B–X π-bonds due to partial sp2 → sp3 rehy-bridization.

Comparison of the metrical data of adducts 7 with thosefound in precatalysts 2 (tables 2 and 5) shows a general

4 BF3 and BCl3 have planar trigonal (D3h) structures at HF level.B(C6F5)3 possesses a D3 symmetry with the boron and the (C6F5) cen-troids all lying in the same plane. Each C6F5 unit is 45◦ twisted aroundthe B–(C6F5)centr. vector. The CH3BX−3 anions have a C3 symme-try with a pseudotetrahedral arrangement around the boron atom. Theboron atom moves from a sp2 to a sp3 hybridization with a consequentreduction of X–B–X bond angle and a consistent increase of the B–Xbond length.


Table 5HF bond lengths (A) and bond angles (deg) of contact ion pairs (7) (C5H4SiH2NR)Ti(CH3)•(CH3)BX3, (R=CH3 and tBu; X=F, Cl, and C6F5).

(C5H4SiH2NCH3)Ti(CH3) (C5H4SiH2NtBu)Ti(CH3) (C5H4SiH2NCH3)Ti(CH3) (C5H4SiH2NtBu)Ti(CH3)•(CH3)BF3 •(CH3)BCl3 •(CH3)B(C6F5)3 •(CH3)BX3

7aa 7b 7c 7d

Bond lengthb

Ti–C(1) 2.05 (2.10) 2.05 2.05 2.05Ti–C(2) 2.29 (2.23) 2.36 2.41 2.44Ti–C(3) 2.33 (2.35) 2.32 2.32 2.31Ti–C(4) 2.42 (2.39) 2.42 2.40 2.42Ti–C(5) 2.54 (2.50) 2.54 2.53 2.56Ti–C(6) 2.52 (2.50) 2.51 2.52 2.54Ti–C(7) 2.38 (2.40) 2.36 2.38 2.37Ti–Cpcentr. 2.12 (2.10) 2.11 2.11 2.12Ti–N 1.86 (1.88) 1.85 1.86 1.87N–C(8) 1.47 (1.50) 1.47 1.47 1.50N–Si 1.81 (1.85) 1.81 1.81 1.83Si–C(3) 1.89 (1.91) 1.89 1.89 1.88C(2)–B 1.70 (1.70) 1.63 1.71 1.71B–Xaver. 1.42 (1.44) 1.91 1.66 1.66C(1)–H(1) 1.08 (1.10) 1.08 1.08 1.08C(1)–H(2) 1.09 (1.11) 1.09 1.09 1.08C(1)–H(3) 1.09 (1.11) 1.09 1.09 1.09C(2)–H(4) 1.08 (1.10) 1.09 1.08 1.09C(2)–H(5) 1.09 (1.11) 1.09 1.09 1.09C(2)–H(6) 1.09 (1.11) 1.09 1.09 1.09

Bond angleb

Cpcentr.–Ti–N 107.8 (108.8) 108.2 107.9 109.3Ti–N–Si 106.3 (105.4) 106.2 106.0 103.9N–Si–C(3) 89.9 (90.0) 89.6 89.8 90.9Ti–N–C(8) 128.6 (127.4) 128.6 131.8 134.6C(1)–Ti–C(2) 99.8 (101.5) 99.6 101.7 99.4Ti–C(2)–B 172.9 (170.8) 171.8 175.6 175.2Ti–C(1)–H(1) 113.3 (116.1) 113.2 112.6 112.0Ti–C(1)–H(2) 107.4 (104.3) 106.9 108.0 108.4Ti–C(1)–H(3) 110.3 (108.2) 110.9 110.1 110.9C(2)–B–X(aver.) 107.4 (107.1) 108.1 107.9 107.6

a MP2 data in parentheses.b Atom labeling refers to figure 6.

contraction of all bond lengths involving the titanium atompossibly because of the reduced titanium electron densityupon BX3 coordination.

In this context, it becomes of interest to contrast thegeometrical parameters of the adduct complexes 7 (table 5)with those of the free cations 3 (table 2). In the nakedcations the titanium center has a pseudotrigonal arrange-ment, with the metal methyl group lying in the Cpcentr.–Ti–N plane. In the contact adducts, the same Ti–CH3

vector moves ∼40◦ out of this plane together with otherimportant structural modifications. In particular, the Ti–Cpcentr., Ti–C(1)H3 and Ti–N bond lengths become longerrelative to the naked cations, and, even more importantly,the internal hydrogen conformation undergoes a remark-able rearrangement thus suggesting reduced α-agostic in-teraction than in the free cation. Thus, the CH3 grouprotates ∼30◦ around the Ti–C vector while all the inter-nal Ti–C–H angles and C–H distances are close to thoseexpected for the classical C3v symmetry. It is noted, how-ever, that geometrical parameters for one hydrogen atom(among the three) is somewhat reminiscent (table 5) of

some α-agostic interaction with a smaller Ti–C–H angle(∼107◦).

4.2. Energetics

At the HF level the formation of contact ion pairs withthe BX3 Lewis acids (equation (5)) appears unfavorableon thermodynamic grounds (table 6). At the MP2 level,however, all the species are bonded due to the expectedstabilizing contribution of correlation energies.

The methyl abstraction capabilities (equation (5)) paral-lel the acidities of cocatalysts (BF3 < BCl3 < B(C6F5)3).The formation energies depend slightly on the nature ofthe amido group and almost comparable values (−32 and−31 kcal/mol) are observed on moving from >N–CH3 (7c)to the >N–tBu group (7d). Effects due to the basis setsuperposition error have been also evaluated for (C5H4

SiH2NtBu)Ti(CH3)•(CH3)B(C6F5)3 CGC model and thevalue thus inferred (−10 kcal/mol) lies closely to calorimet-ric titrimetry data of the [C5(CH3)4Si(CH3)2NtBu]Ti(CH3)•(CH3)B(C6F5)3 (−18 kcal/mol) [51]. The inclusion of non-


Table 6Calculated ion-pair contact (∆Hdr) and separation (∆Hips) energies (kcal/mol) for (C5H4SiH2NR)Ti(CH3)•(CH3)

BX3 species.

∆Hdr ∆Hips

HF MP2a HF MP2a

(C5H4SiH2NCH3)Ti(CH3)•(CH3)BF3 +2 −9 (−9) +96 +110 (+111)(C5H4SiH2NCH3)Ti(CH3)•(CH3)BCl3 −5 −19 +79 +96(C5H4SiH2NCH3)Ti(CH3)•(CH3)B(C6F5)3 +2 −32 +81 +100(C5H4SiH2NtBu)Ti(CH3)•(CH3)B(C6F5)3 +3 −31 +76 +96

a Values parentheses refer to MP2/MP2 data.

Table 7Non-specific solvation (benzene) energies (kcal/mol).

(C5H4SiH2NtBu)Ti(CH3)2•B(C6F5)3 10(C5H4SiH2NtBu)TiCH+

3 28CH3B(C6F5)−3 17(C5H4SiH2NtBu)Ti(CH3)2 1B(C6F5)3 6

specific solvent effects (table 7) slightly affects the result(−13 kcal/mol), with a better agreement with experiment.

The gas-phase ion-pair separation reactions (equa-tion (6)) are always strongly endothermic at both HF andMP2 levels (table 6). The energy values depend on the BX3

nature and, in particular, decrease in the order B(C6F5)3 <BCl3 < BF3. It is noted again that there is a sizeable depen-dence on the nature of the coordinated amido group sincesmaller values are associated with >N–tBu (96 kcal/mol)than with >N–CH3 (100 kcal/mol). The calculated ∆Hips

values are correlated with both the Ti–CH3BX3 bond lengthand with methide abstraction (equation (5)) energies. Infact, shorter distances result in greater heterolytic ion-pairdissociation energies while lower ∆Hdr values afford morefeasible ion pair dissociation.

Finally, it is worthy of note in the perspective of therelated catalytic activities, that the stronger acidic cocata-lyst B(C6F5)3 forms a related contact ion-pair adduct withsmaller ∆Hips and longer Ti–CH3B(C6F5)3 bonds as well asthe fact that even more favorable conditions (for catalyticprocesses) occur on moving from >N–CH3 to >N–tBu.

The presently calculated ∆Hips values are similar to re-cent DFT data reported for (C5H5)2MCH3•(CH3)2AlCl2(+100 kcal/mol) [42,43]. These values, however, re-main substantially in excess compared to enthalpies as-sociated with ion-pair-separating symmetrization processesmeasured by dynamic NMR in aromatic solvents(∼ +15 kcal/mol for [C5(CH3)4Si(CH3)2NtBu]TiCH3•CH3

B(C6F5)3; +15–20 kcal/mol for typical metallocenes)[51,52].

To conclude this survey analysis, it transpires that anyion-pair total charge separation, and hence the formationof naked cationic catalysts, is far from being practicableon energetic grounds unless ancillary Lewis bases stabilizeactive species. Therefore, donating solvents might play acrucial role.

Table 7 reports non-specific solvation energies associatedto all the species intervening in equation (6). It becomes ev-

ident that major stabilizing effects are, not surprisingly, as-sociated to charged species with an overall solvation effectwhich bring about a ∆Hips value (+43 kcal/mol) closer, butstill substantially in excess of experimental measurements.

It is well known, however, that the homologous[C5(CH3)4Si(CH3)2NtBu]ZrCH+

3 B(C6F5)−4 forms an isola-ble π-toluene complexes [45]. Calculations, therefore,were next carried out including Ti–ηn–C6H6 complexation(n = 3 was found to be the lowest energy, equation (7)).

(C5H4SiH2NtBu)TiCH+3 •CH3B(C6F5)3 + C6H6 →

(C5H4SiH2NtBu)TiCH+3 •C6H6 + CH3B(C6F5)−3 (7)

In this case, the computed ion-pair dissociation enthalpy isreduced to +58 kcal/mol for the gas-phase process and to+23 kcal/mol including non-specific solvent effects. Theseresults argue that, especially in satured hydrocarbon sol-vents, chain propagation is unlikely to involve a completelyseparated ion pair and that solvation effects are not insignif-icant.

5. Ethylene insertion in contact ion pairs

Three possible pathways have been considered for theethylene activation/insertion processes of the simpler (C5H4

SiH2NCH3)TiCH3•CH3BF3 model (figure 7). Along thepathway A, the ethylene approach does not result in theactivation/insertion. Rather, the process evolves to hydro-gen α-elimination with formation of titanium-hydride andcyclopropane (figure 8). The involved energy barrier ishigher than 40 kcal/mol. The ethylene approach, in fact,causes a remarkable distortion of the Ti–CH3 methyl group.An H atom becomes involved in a strong α-agostic inter-action (figure 8) while the remaining two H atoms adoptan eclipsed conformation relative to ethylene hydrogens.In the transition state, the Ti–H length (1.90 A), slightlylonger than typical metal-hydrido σ bond, finds counterpartin a strongly elongated C–H (1.22 A) σ bond and in a close(2.00 A) C–C contact. Slight perturbations are observed inthe µ3-bridged Ti–CH3BF3 moiety in terms of lengthening(0.04 A) of the metal–methyl bonds. The final state (fig-ure 8) consists of a Ti–hydride–fluoride complex and of aneliminated cyclopropane molecule.

The concerted pathway C (figure 9) involves olefin ac-tivation distal to the CH3BF3 group. In early stages of the


Figure 7. Schematic view of possible pathways for ethylene insertion into (C5H4SiH2NCH3)TiCH3•CH3BX3 contact ion adducts.

Figure 8. Schematic reaction route of (C5H4SiH2NCH3)TiCH3•CH3BF3 + C2H4 along the pathway A. (a) the “Early stage”; (b) the transition state;(c) the final product.

Figure 9. Schematic reaction route of (C5H4SiH2NCH3)TiCH3•CH3BF3 + C2H4 along the pathway C. (a) the “Early stage”; (b) the transition state;(c) the final product.

reaction the ethylene approach causes bending of the Ti–CH3 vector toward the Ti–N–Si plane simultaneous witha considerable Ti–CH3BF3 lengthening. Close approachesresult in an unexpected rearrangement of the Ti–CH3BF3

moiety. In particular, the CH3BF3 group moves apart from

the titanium center and rearranges to a twisted conformationwith the BF3 pointing toward the metal. The final optimizedgeometry (figure 9), considerably more stable than initialreagents, is clearly indicative of a direct Ti–F bonding in-teraction which ultimately affords a metal center inactive


Figure 10. Schematic reaction route of (C5H4SiH2NCH3)TiCH3•CH3BF3 + C2H4 along the pathway B. (a) the “Early stage”; (b) the transition state;(c) the final product.

toward catalytic insertion. Calculations performed to testthe ethylene insertion process (imposing a 2.2 A distance)show a very high energy since the fluorine atom is not ab-stracted by the BF2CH3 acid and remains strongly bondedto titanium.

In pathway B the ethylene activation/insertion directlyaffects the space volume of the Ti–CH3BF3 framework,hence a more congested region. Even in the early stage(longer C–C contacts) the ethylene approach forces awaythe CH3BF3 group with a sizeable elongation of the relatedTi–CH3BF3 bond (figure 10). Closer contacts (< 3.2 A)result in a geometrical rearrangement, closely reminiscentof the naked cation π-complex, with metrically compara-ble relevant data. Thus, the Ti–C2H4 average distance is2.9 A (vs. 2.8 A). Even more interesting, the CH3BF3 groupmoves apart from the Ti center while twisting (90◦) arounda rotation axis normal to the H3C–BF3 bond (figure 10).This conformation provides a remarkable energy stabiliza-tion to the system. The following insertion transition statesimilarly resembles the naked cation, hence an almost totalion-pair separation, with a very large Ti–F3BCH3 distance(4.5 A). In the final inserted propyl-metal product, a vacantcoordination site is left at the metal center, and the CH3BF−3group remains unbonded, far away from the metal. It there-fore transpires that, although pathway B apparently allowsthe ethylene activation/insertion with feasible energy barri-ers, the contact ion pair (C5H4SiH2NCH3)TiCH3•CH3BF3,7a cannot, in any case, represent a working model for CGCcatalytic processes.

The contact ion pair C5H4SiH2NtBuTiCH3•CH3B(C6

F5)3, 7d was analyzed next since the pentafluorotriaryl-borate cocatalyst is widely used in metallocene catalysis.Similar to previous models, pathways A, B and C (figure 7)can represent possible routes for ethylene insertion. Prelim-inary HF calculations straightforwardly rule out A and B asenergetically unreasonable. Concerted pathway C involv-ing olefin activation and insertion distal to the CH3B(C6F5)3

group has been studied.The energy profile related to reaction pathway C involv-

ing ethylene insertion into 7d, is reported in figure 11 atthe HF, MP2 and MP2 (corrected for solvent effects) levels.The potential energy surface is very flat in early stages ofthe reaction. The transition state is found for a 2.20 A value

Figure 11. HF/HF, MP2/HF, MP2/HF non-specific solvation energiesof C2H4 activation/insertion into (C5H4SiH2NtBu)TiCH3•CH3B(C6F5)3.The reference point for the energy scale relates to the isolated reagents.

of the reaction coordinate. There is evidence that the en-ergy barrier values strongly depend on the theoretical leveladopted. Thus, a remarkable barrier (35 kcal/mol) is foundat HF level. Not unexpectedly, the inclusion of correla-tion effects considerably reduces this value (18 kcal/mol)and introduction of non-specific solvent effects further low-ers the energy barrier to a final value (14 kcal/mol), inreasonable agreement with the limited available data re-ported for metallocene derivatives (Ea ≈ 14 kcal/molfor [C5(CH3)4Si(CH3)2NtBu]TiCl2/MAO, Ea ≈ 7 kcal/molfor (neomenthylC5H4)2ZrCl2/MAO, Ea ≈ 2–10 kcal/molfor L2Zr(CH3)2/B(C6F5)3, L=various cyclopentadienyl lig-ands) [78–80]. It is worthy to note that there is no evidenceof any intermediate π-complex formation since interactionsinvolving the ethylene and the electrophilic metal centerclearly appear repulsive. This is the consequence of astrong contact ion pair CpSiH2NtBuTiCH3•CH3B(C6F5)3

with no coordination sites available at the metal cen-ter.

Upon moving toward the transition state (figure 12), theTi–C(1)H3 vector bends toward the Ti–N–Si plane simul-


Figure 12. Optimized structures of transition state and final product for ethylene insertion into (C5H4SiH2NtBu)TiCH3•CH3B(C6F5)3 (7d).

taneously with sizeable elongation of the Ti–CH3B(C6F5)3

contact. These structural modifications leave room and cre-ate some partial charge separation (hence increasing themetal electrophilicity), thus “preparing” the titanium atomfor the following activation/insertion. In the transition statethe Ti–CH3B(C6F5)3 distance is 3.48 A while the Ti–CH3

vector almost lies in the Ti–N–Si plane.The four-membered metallacyclobutane ring (Ti–C(1)–

C(13)–C(12) resembles that found in the related naked cat-ion (figure 12) and shows a highly distorted (relative to C3v)conformation of the Ti–CH3 hydrogen atoms. Two of themare pseudo-eclipsed with respect to the ethylene fragmentwhile the reminder has some α-agostic interaction with thetitanium center (Ti–H = 2.4 A). Some puckering of thering (10◦) is also observed.

Similar to the naked cation, the transition state involvesformation of the new metal–ethylene σ bond (Ti–C(12))and partial breaking of both ethylene-π (C(12)–C(13)) andTi–methyl (Ti–C(1)=2.30 A) bonds, asynchronously withthe alkyl chain lengthening since the distance C(1)–C(13)(2.20 A) remains indicative of a bond which is still veryweak.

Other interesting structural changes are observed in theCH3B(C6F5)3 fragment. Thus the CH3–B(C6F5)3 bond ap-pears shorter than initially (1.66 vs. 1.71 A) and the methylH–C(2)–B average bond angle lies close to the tetrahe-dral value (110.3◦ average). These geometrical parametersfound in the transition state are close to the related val-ues in the free CH3B(C6F5)−3 anion. It therefore transpiresthat the coordinative expansion of the titanium atom (hencethe greater electrophilicity) required in the transition stateis favored because of some metal charge depletion asso-ciated with a sizeably enhanced anionic character of theCH3B(C6F5)3 group.

In the final propyl-metal inserted product the CH3B(C6F5)3 group moves back toward the metal center, even

though the Ti–CH3B(C6F5)3 distance (3.12 A) remainslonger than in the initial state (figure 6 and table 5). Thepropyl chain assumes a conformation similar to that foundin the γ-agostic propyl naked cation 6, with almost coplanarTi–C(1)–C(13)–C(12) atoms. The directly inserted product,however, does not show relevant γ-agostic interactions sim-ilar to those in 6. The Ti–C(1) contact (2.93 A), is consid-erably longer than the Ti–C(12) (2.09 A) σ bond (2.51 and2.09 A in 6, respectively). In addition, the Ti–C(12)–C(13)bond angle (109.7◦) is close to tetrahedral value and differsmarkedly from that found in 6 (96.1◦). These observationsare all consistent with weaker γ-agostic interactions, pos-sibly a consequence of reduced electronic insaturation onthe metal center due to the closer approach of the CH3

B(C6F5)−3 group.It is worth commenting on the total stabilization energy

along the insertion process. Compared to the naked cat-ion (−31 kcal/mol), the value associated to contact ionpair 7d is considerably smaller (−10 kcal/mol). Never-theless these data refer to the initial (the natural evolu-tion of the transition state) conformation of the insertedproduct. Preliminary conformational analysis upon rotationaround the C(12)–C(13) bond shows that a deeper mini-mum (−20 kcal/mol) is associated with the 120◦ twistedconformer.

6. Concluding remarks

The catalyst generation and olefin insertion at the ho-mogeneous CGC-Ti site have been studied using ab initioMP2/HF and analytical gradient methods to understand re-action pathways and related energies. There is evidencethat the energetics associated with the formation of contaction pairs as well as structural reorganizations are sensitivefunctions of borane acidities. Nevertheless, total charge


separation (hence the formation of the naked cationic cat-alysts) cannot be generally favored unless some ancillaryLewis base plays a stabilizing role. In fact, the remark-ably high associated energies are hardly compatible withany catalytic process. The free “naked cation model”cannot be, therefore, representative of the real catalyticprocess.

On energetic grounds, the direct insertion into the intactcontact ion-pair adduct appears entirely compatible withsuch a process and involves push-pull effects between theentering ethylene and the adducted methylborane. Thus,the less energy demanding path for the ethylene inser-tion into (C5H4SiH2NtBu)Ti(CH3)+CH3B(C6F5)−3 systeminvolves the olefin approach distal to the Ti–H3CB(C6F5)3

linkage causing a remarkable elongation of the same con-tact. The activation enthalpy for the insertion process de-pends crucially on solvent effects and in the benzene solu-tion is +14 kcal/mol.

Less computationally demanding models, including(C5H4SiH2NCH3)Ti(CH3)+CH3BX−3 [X=F, Cl, B(C6F5)3],have been tested to study further aspects of the CGC cat-alytic processes. Preliminary results with the simpler [C5H4

SiH2N(CH3)]Ti(CH3)+CH3BF−3 pair proved elusive since,upon olefin approach, alternative reaction channels to in-active titanium fluorides appear more favored than activa-tion/insertion steps.

Studies are currently in progress (i) to estimate the ionpair separation energy for longer chain alkyl-metal systemswhich better model the real polymerization propagationprocesses; (ii) of the resting state, to define the configu-rations of both the alkyl chain bonded to the metal and ofthe counteranion prior to the insertion of a further olefinunits; (iii) to understand mechanistic aspects of chain elon-gation also in view of stereospecifical properties of polymerproducts and, finally, (iv) to rationalize the higher efficiencyof CGC catalysts.

Acknowledgement

The authors gratefully thank Professor T.J. Marks(Northwestern University, Evanston, IL) for stimulat-ing suggestions and helpful discussions. The Ministerodell’Universita e della Ricerca Scientifica e Tecnologica(MURST, Rome) and the Consiglio Nazionale delle Ricer-che (CNR, Rome) are also gratefully acknowledged for fi-nancial support.

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Documents

Theoretical modeling of “constrained geometry catalysts” beyond the naked cation approach