On the nature and incidence of β-agostic interactions in ethyl derivatives of early transition metals: Ethyltitanium trichloride and related compounds

Article abstract of DOI:10.1021/ja9737578

In light of the structures and spectroscopic properties of the ethyltitanium compounds EtTiCl₃ (1), and EtTiCl₃(dmpe) (dmpe = Me₂PCH₂CH₂PMe₂) (2), extensive DFT calculations have been carried out to explore the structures, energetics, potential energy surfaces, and spectroscopic properties not only of these but also of related ethyl derivatives of early transition metals, M. The analysis has sought to assess the true nature of so-called β-agostic interactions in these systems and how such interactions depend on the atomic number, coordination number, valence electron (VE) count, and net charge of M. The calculations reproduce well the experimentally determined properties of 1 and 2. Analysis of wave functions indicates that, where significant β-interactions occur, the M-C bonding electrons are delocalized over the entire ethyl group, the marked reduction of the MCC valence angle allowing the metal atom to establish covalent bonding interactions with the β-C atom and, perhaps to a lesser extent, with its appended proximal H atom. A β-agostic alkyl group may be considered a two-electron ligand, and the main contribution to the stabilization arises from Ti···C(β) bonding. Barriers to conformational change of the M-Et unit depend inter alia on the space available in the coordination sphere of the central M atom, with rearrangement of the ethyl group to accommodate significant β-interaction being opposed by interligand repulsion. Such interaction is found not in 1, but in its dmpe adduct 2 because the increase in coordination number is offset by elongation of the Ti-C and Ti-Cl bonds and by the extra pliability of the EtTiCl₃ moiety resulting from complexation by the dmpe ligand.

Full text of DOI:10.1021/ja9737578

3762
J. Am. Chem. Soc. 1998, 120, 3762-3772
On the Nature and Incidence of â-Agostic Interactions in Ethyl
Derivatives of Early Transition Metals: Ethyltitanium Trichloride and
Related Compounds
Arne Haaland,† Wolfgang Scherer,*,‡ Kenneth Ruud,† G. Sean McGrady,*,
Anthony J. Downs, and Ole Swang§
Contribution from the Department of Chemistry, UniVersity of Oslo, Box 1033 Blindern,
N-0315 Oslo, Norway, Anorganisch-chemisches Institut, Technische UniVersita¨t Mu¨nchen,
Lichtenbergstrasse 4, D-85747 Garching, Germany, Inorganic Chemistry Laboratory, UniVersity of
Oxford, South Parks Road, Oxford OX1 3QR, UK, and SINTEF, Applied Chemistry, Department of
Hydrocarbon Process Chemistry, Box 124 Blindern, N-0314 Oslo, Norway
ReceiVed October 30, 1997
Abstract: In light of the structures and spectroscopic properties of the ethyltitanium compounds EtTiCl3 (1),
and EtTiCl3(dmpe) (dmpe ) Me2PCH2CH2PMe2) (2), extensive DFT calculations have been carried out to
explore the structures, energetics, potential energy surfaces, and spectroscopic properties not only of these but
also of related ethyl derivatives of early transition metals, M. The analysis has sought to assess the true
nature of so-called â-agostic interactions in these systems and how such interactions depend on the atomic
number, coordination number, valence electron (VE) count, and net charge of M. The calculations reproduce
well the experimentally determined properties of 1 and 2. Analysis of wave functions indicates that, where
significant â-interactions occur, the M-CR bonding electrons are delocalized over the entire ethyl group, the
marked reduction of the MCC valence angle allowing the metal atom to establish covalent bonding interactions
with the â-C atom and, perhaps to a lesser extent, with its appended proximal H atom. A â-agostic alkyl
group may be considered a two-electron ligand, and the main contribution to the stabilization arises from
Ti‚‚‚Câ bonding. Barriers to conformational change of the M-Et unit depend inter alia on the space available
in the coordination sphere of the central M atom, with rearrangement of the ethyl group to accommodate
significant â-interaction being opposed by interligand repulsion. Such interaction is found not in 1, but in its
dmpe adduct 2 because the increase in coordination number is offset by elongation of the Ti-C and Ti-Cl
bonds and by the extra pliability of the EtTiCl3 moiety resulting from complexation by the dmpe ligand.
1. Introduction
evidence for agostic interactions accumulated up to 1988 has
been the subject of two seminal reviews.1
The apparent attraction between a transition metal center and
a CH fragment in an organic ligand is commonly referred to as
an “agostic” interaction. More specifically, the attraction
between a transition metal M and the â-CH fragment of an
appended alkyl ligand is termed â-agostic.1 â-Interactions
appear to be the most prevalent type reported,1 presumably on
account of the favorable geometry enjoyed by such an arrange-
ment. The primary structural evidence of a â-agostic interaction
is a reduction of the MCRCâ valence angle, in several cases to
values below 90°. Agostic interactions may also be signaled
by a significant reduction in the C-H stretching frequency,
although only in a few cases has the identity of the mode been
Increased knowledge about these interactions is vital to a
proper understanding of several important chemical reactions
involving transition-metal compounds and organic molecules,
where products, intermediates, and transition states may be
stabilized in this manner. Thus, olefin insertion into M-H
bonds and the reverse reactionsolefin elimination from transi-
tion-metal alkylssare both believed to proceed through â-ago-
stic transition states.2b Similarly, the industrial production of
aldehydes from olefins, CO, and H2 with HCo(CO)4 as a catalyst
is believed to proceed through the formation of two â-agostic
intermediates.3 Such interactions may also be present in the
resting state of the cationic species derived from Group 4
metallocenes which are catalytically active in the promotion of
olefin polymerization.4
1
authenticated.1,2a In addition, a low-frequency shift of the H
resonance and a reduced C,H coupling constant in the NMR
spectrum are taken to be diagnostic of agostic behavior.1,2a The
Agostic interactions have in the past been envisaged as
involving the donation of a C-H bonding electron pair to the
metal atom M.1 On this basis, the alkyl ligand is to be regarded
as a four-electron ligand. It is an essential prerequisite,
† University of Oslo.
‡ Technische Universita¨t Mu¨nchen.
University of Oxford.
§ SINTEF.
(1) (a) Brookhart, M.; Green, M. L. H. J. Organomet. Chem. 1983, 250,
395-408. (b) Brookhart, M.; Green, M. L. H.; Wong, L.-L. Prog. Inorg.
Chem. 1988, 36, 1-124.
(3) Ziegler, T. Can. J. Chem. 1995, 73, 743-761.
(2) (a) Elschenbroich, Ch.; Salzer, A. Organometallics, 2nd ed.; VCH:
Weinheim, Germany, 1992; pp 267-268. (b) Elschenbroich, Ch.; Salzer,
A. Organometallics, 2nd ed.; VCH: Weinheim, Germany, pp 186-191.
(c) Elschenbroich, Ch.; Salzer, A. Organometallics, 2nd ed.; VCH:
Weinheim, Germany, pp 198-200.
(4) (a) Brintzinger, H. H.; Fischer, D.; Mu¨lhaupt, R.; Rieger, B.;
Waymouth, R. M. Angew. Chem., Int. Ed. Engl. 1995, 34, 1143-1170. (b)
Woo, T. K.; Fan, L.; Ziegler, T. Organometallics 1994, 13, 2252-2261.
(c) Woo, T. K.; Margl, P. M.; Lohrenz, J. C. W.; Blo¨chl, P. E.; Ziegler, T.
J. Am. Chem. Soc. 1996, 118, 13021-13030.
S0002-7863(97)03757-8 CCC: $15.00 © 1998 American Chemical Society
Published on Web 04/04/1998

â-Agostic Interactions in Early Transition Metals
J. Am. Chem. Soc., Vol. 120, No. 15, 1998 3763
moreover, that M carry a vacant valence orbital having an energy
and disposition that are compatible with those of the C-H
bonding orbital; M‚‚‚H-C attractions should therefore be
favored if the formal valence electron (VE) count for M is 16
or less. The dative character of the interaction also suggests
that agostic behavior will be favored if M carries a net positive
charge.
With regard to coordination number, the metal atoms in [EtPt-
{But2P(CH2)3PBut2}]+ and [EtNi{But2P(CH2)3PBut2}]+ are three-
coordinate, and, if we regard the Cp* ligand as occupying one
coordination site, so too is the metal atom in [EtCo(η-Cp*)-
{P(p-tolyl)3}]+. These are, in fact, the only three-coordinate
metal complexes in our sample; all are cationic and all are
evidently agostic. Although the crystal structures have not been
determined, two neutral pseudo-tri-coordinated complexes are
reported to show â-agostic behavior: IR spectroscopy9a and
kinetic studies9b on the 14 VE metallocene Cp*2ScEt and IR,
EPR, and electronic spectroscopy10a,b on the 15 VE metallocene
Cp*2TiEt point to the presence of weak agostic interactions in
both compounds. The cationic zirconium complex [EtZr(η-
C5H4Me)2(PMe3)]+ is one of only two cationic complexes and
the only one out of a total of 19 four-coordinate complexes in
our sample to manifest agostic behavior. None of the five five-
coordinate complexes (all neutral) appears to be agostic. That
leaves three six-coordinate complexes (all neutral) of which only
one, viz. the 12 VE EtTiCl3(dmpe) (2) is agostic.5,6,14 These
findings suggest that, while â-agostic interactions may be
common in three-coordinate complexes, they are rare in four-
coordinate and perhaps also in five- or six-coordinate com-
pounds. Furthermore, these same interactions may be better
favored in cationic than in neutral species.
When we turn our attention to the 29 ethyl-transition metal
complexes with VE > 16, we find that none is three-coordinate;
four are either four- or five-coordinate, all of them neutral; the
remaining 25 are six-coordinate, six of them being cationic.
However, not one of the 29 complexes shows signs of agostic
properties. It is evident therefore that the complex EtTiCl3-
(dmpe) is unique in being a six-coordinate complex featuring a
â-agostic structure and insofar as it is possible to generalize on
the basis of a sample containing only one such structure, the
data available suggest that â-agostic interactions are better
favored in complexes with VE e 16. We note, however, that
only 12 of these complexes are early transition-metal systems,
two of which are agostic and that the exceptionally low VE
count for EtTiCl3(dmpe) may be significant.
Two compounds provide experimental benchmarks for con-
sideration of â-agostic interactions. These are ethyltitanium
trichloride, EtTiCl3 (1), with a VE count of 8, and its complex
EtTiCl3(dmpe) (dmpe ) Me2PCH2CH2PMe2) (2) with a VE
count of 12. Electron diffraction measurements on gaseous 1
indicate an anagostic structure with TiCC ) 116.6(11)° and
a staggered ethyl group geometry (here and henceforth the ethyl
group conformation is defined with respect to the Ti-CR bond).5
Neither these dimensions nor the vibrational6 and NMR proper-
ties give the slightest hint of agostic behavior. Yet the crystal
structure of the diphosphine complex 2, as redetermined at low
temperature (105 K),5 clearly manifests such behavior; in
addition, the vibrational6 and NMR properties exhibit unusual
features that can be interpreted only on the assumption that
complexation induces a significant change not just in the TiCRCâ
valence angle but in the bonding of the whole ethyl ligand.
Central to our analysis of the results reported to date have been
Density Functional Theory (DFT) calculations; these have
sought to enquire into the equilibrium structures, MCC bending
potentials, ethyl group conformations, and M-C2H5 bonding
modes in 1, 2, and several related species. Here we report in
detail on the results of the analysis, with particular reference to
the light they shed on the true nature of â-agostic bonding and
on the factors giving rise to such bonding.
2. Results and Discussion
2.1. Structures of Ethyl-transition Metal Compounds: A
Survey. A survey based on the Cambridge Crystal Structure
File (Release 5.10)7a,b but augmented by a literature search7c,d
has yielded the structures of 58 complexes of transition metals
M drawn from Groups 3-11 and bearing terminal ethyl groups.
Out of these 29 involve M atoms with a formal count of 16 or
fewer VE, 24 being neutral compounds and five cationic species.
From all the 24 neutral complexes only one, Viz. the 12 VE
compound EtTiCl3(dmpe) (2), displays clear signs of a â-agostic
interaction. According to the latest study,5 the TiCRCâ angle
at 84.57(9)° is conspicuously acute; the orientation of the ethyl
group is such that one Câ-H bond eclipses the Ti-CR bond
giving a Ti‚‚‚H distance of only 206(2) pm.5 Out of the five
cationic ethyl complexes no less than four exhibit acute MCRCâ
angles suggestive of â-agostic interactions, viz. [EtPt{But2P(CH2)3-
PBut2}]+,7c VE ) 14, PtCRCâ ) 75(1)°; [EtNi{But2P(CH2)2-
PBut2}]+,8a VE ) 14, NiCRCâ ) 74.5(3)°; [EtCo(η-Cp*){P(p-
tolyl)3}]+ (Cp* ) pentamethylcyclopentadienyl),8b VE ) 16,
CoCRCâ ) 74.5(2)°; and [EtZr(η-C5H4Me)2(PMe3)]+,8c VE
) 16, two independent molecules in the asymmetric unit cell
with ZrCRCâ ) 84.7(5) and 83.0(6)°, respectively.
2.2. The Properties of EtTiCl3 (1). Ethyltitanium trichlo-
ride, EtTiCl3 (1), is formally an 8 VE compound. In view of
the behavior of the more electron-rich complex EtTiCl3(dmpe)
(2) the base-free molecule might be expected to display, if
anything, an even more robust â-interaction.1 The reality, as
(8) (a) Conroy-Lewis, F. M.; Mole, L.; Redhouse, A. D.; Litster, S. A.;
Spencer, J. L. J. Chem. Soc., Chem. Commun. 1991, 1601-1603. While
the NMR spectra of [EtNi{But2P(CH2)3PBut2}]+ indicate that it retains the
â-agostic alkyl group in solution, those of the Pt analogue, whose crystal
structure is unknown, suggest a rapidly equilibrating mixture of â-agostic
alkyl and an ethylene hydride complex, [C2H4(H)Pt{But2P(CH2)3PBut2}]+.
(b) Cracknell, R. B.; Orpen, A. G.; Spencer, J. L. J. Chem. Soc., Chem.
Commun. 1984, 326-328. (c) Jordan, R. F.; Bradley, P. K.; Baenziger, N.
C.; LaPointe, R. E. J. Am. Chem. Soc. 1990, 112, 1289-1291.
(9) (a) Thompson, M. E.; Baxter, S. M.; Bulls, A. R.; Burger, B. J.;
Nolan, M. C.; Santarsiero, B. D.; Schaefer, W. P.; Bercaw, J. E. J. Am.
Chem. Soc. 1987, 109, 203-219. (b) Burger, B. J.; Thompson, M. E.; Cotter,
W. D.; Bercaw, J. E. J. Am. Chem. Soc. 1990, 112, 1566-1577.
(10) (a) Luinstra, G. A.; ten Cate, L. C.; Heeres, H. J.; Pattiasina, J. W.;
Meetsma, A.; Teuben, J. H. Organometallics 1991, 10, 3227-3237. (b)
Lukens. W. W., Jr.; Smith, M. R., III.; Andersen, R. A. J. Am. Chem. Soc.
1996, 118, 1719-1728.
(5) Scherer, W.; Priermeier, T.; Haaland, A.; Volden, H.-V.; McGrady,
G. S.; Downs, A. J.; Boese, R.; Bla¨ser, D. Organometallics Submitted for
publication.
(6) McGrady, G. S.; Downs, A. J.; Haaland, A.; Scherer, W.; McKean,
D. C. J. Chem. Soc., Chem. Commun. 1997, 1547-1548.
(11) Scherer, W.; Haaland, A.; Herrmann, W. A.; Geisberger, M.
Unpublished results.
(7) (a) Allen, F. H.; Kennard, O.; Taylor, R. Acc. Chem. Res. 1983, 16,
146-153. (b) A study of M‚‚‚H-C interaction geometries in some 50
transition metal compounds from the Cambridge Structural Database has
recently been published: Braga, D.; Grepioni, F.; Biradha, K.; Desiraju,
G. R. J. Chem. Soc., Dalton Trans. 1996, 3925-3930. (c) Mole, L.; Spencer,
J. L.; Carr, N.; Orpen, A. G. Organometallics 1991, 10, 49-54. (d) Davies,
C. E.; Gardiner, I. M.; Green, J. C.; Green, M. L. H.; Hazel, N J. J. Chem.
Soc., Dalton Trans. 1985, 669-683.
(12) (a) McKean, D. C.; McQuillan, G. P.; Robertson; A. H. J.; Murphy,
W. F.; Mastryukov, V. S.; Boggs, J. E. J. Phys. Chem. 1995, 99, 8994-
9002. (b) Suzuki, S.; Bribes, J. L.; Gaufre`s, R. J. Mol. Spectrosc. 1973, 47,
118-125.
(13) Bondi, A. J. Phys. Chem. 1964, 68, 441-451.
(14) Dawoodi, Z.; Green, M. L. H.; Mtetwa, V. S. B.; Prout, K.; Schultz,
A. J.; Williams, J. M.; Koetzle, T. F. J. Chem. Soc., Dalton Trans. 1986,
1629-1637.

3764 J. Am. Chem. Soc., Vol. 120, No. 15, 1998
Haaland et al.
Table 2. Comparison of Principal Force Constants in Selected
Table 1. Relevant Structural Parameters of EtTiCl3(dmpe) (2) and
EtTiCl3(dhpe) (2a)
Ethyl Compounds
2
2
2
2
2a
force constanta (N m-1
)
X-ray BP86/III BP86/III BP86/III BPW91/I
molecule
E-Cb
C-C stretching
ECC bendingb
parametera
105 K
eclipsed staggered staggered eclipsed
EtClc
EtBrd
EtReO3
323.9
244.9
235.2
180.9
445.3
456.1
401.9
404.1
95.7
98.9
49.8
28.2
b
∆Erel
0
85.5
217.0
254.9
151.7
113.0
110.0
0.177
93.10
216.0
271.5
153.4
110.7
110.2
232.6
233.9
260.6
258.8
110.6
123.3
76.4
1.84c
112.0
TiCC
84.57(9)
214.7(1)
250.1(2)
150.1(2)
103(2)
85.4
216.1
253.9
151.9
113.0
109.8
236.4
233.6
256.7
259.6
114.6
130.5
74.5
e
Ti-C
215.1
307.4
153.4
110.5
110.1
228.4
233.8
263.8
263.8
110.3
115.3
78.7
f
EtTiCl3
Ti‚‚‚Câ
a Force constants were obtained from the scaled Cartesian force field.
See Experimental Section for further information. b E ) Cl, Br, Re, or
Ti. c Reference 12a. d Reference 12b. e Reference 11. f This work.
CR-Câ
C-Hâ′
C-Hâ′′d
Ti-Cl(1)
Ti-Cl(2)
Ti-P(1)
Ti-P(2)
CCHâ′
98(2)
241.54(4) 238.9
231.54(4) 233.0
255.56(4) 258.5
257.27(4) 258.6
112.3(10) 114.2
129.61(4) 129.3
adiabatic TiCC bending potential in EtTiCl3 was further explored
by fixing the TiCC angle at values ranging from 120 to 87°
and carrying out DFT optimization of all the other structure
parameters under retention of Cs symmetry. The resulting
potential energy curve is shown in Figure 1. Hence it appears
that an energy input of no more than 2.8 kcal mol-1 (i.e., an
amount equal to the rotational barrier in ethane) is needed to
reduce the TiCC angle by 20°. The potential energy curve for
the eclipsed conformer is even softer: reduction of the TiCC
angle by 20° now requires an energy input of less than 1.5 kcal
mol-1. As a result, the eclipsed conformer is favored over the
staggered one for TiCC angles less than 97° (see Figure 1).
The nonbonded Câ‚‚‚Cl′′ distance in the calculated equilib-
rium structure is 383 pm, slightly larger than the sum of the
van der Waals’ radii of a methyl group and a Cl atom, namely
375 pm.13 Optimization of a model with an eclipsed ethyl group
conformation and the TiCC valence angle fixed at 87° leads to
a calculated distance of 343 pm. At the same time, the
coordination geometry of the Ti atom distorts in a manner
indicative of CâH3‚‚‚Cl′′ repulsion; the two CRTiCl′′ valence
angles increase while the CRTiCl′ valence angle decreases. We
suggest therefore that the extreme pliability of the Ti-C-C
skeleton in 1 is due to the near-cancellation of two opposing
forces, i.e., â-agostic attraction, which favors a small angle, and
CâH3‚‚‚Cl′′ repulsion, which favors a large one.
CTiCl(1)
CTiP(1)
CTiP(2)
CTiCl(2)
74.84(4)
149.53(4) 151.6
89.92(5) 89.7
75.9
151.8
90.5
153.2
90.4
148.9
90.6
Cl(2)TiCl(3) 172.31(2) 167.4
165.4
75.6
84.8
-4.5
179.8
162.7
74.9
91.3
-20.2
175.8
164.7
74.5
80.6
-5.1
-1.5
P(1)TiP(2)
P(2)TiCl(1)
74.98(1)
80.77(1)
75.9
79.1
-7.8
0.1
τCâCRTiCl(1) -3.88(9)
τHâ′CâCRTi 1.4(12)
a Atom in the symmetry plane is denoted by (′); atom out of the
symmetry plane is denoted by (′′). b E in kcal mol-1 c Constrained
.
value. d Averaged value.
revealed by electron diffraction5 and vibrational6 and NMR
spectroscopies, confounds this expectation. For the gaseous
molecule 1 has a normal structure with Cs symmetry overall;
the ethyl group assumes a staggered conformation about the
C-C bond, with the bond distances (ra in pm) Ti-C )
209.0(15), C-C ) 152.6(11), and Ti-Cl ) 219.5(3) and the
valence angles (in deg) TiCC ) 116.6(11) and ClTiC )
104.6(4). The structural parameters thus signify the absence
of a significant â-agostic interaction. Indeed, the magnitude
of the TiCC angle suggests that the CâH3 group is not so much
attracted to the metal center as repelled by the Cl atoms in
We now turn to a discussion of the bonding and begin by
describing the frontier molecular orbitals derived from calcula-
tions on the [C2H5]- anion and [TiCl3]+ cation (see Figure 2).
A constant density contour map of the LUMO of the [TiCl3]+
1
gauche positions. Neither the IR6 nor the H and 13C NMR
spectra suggest anything other than a normal or anagostic
structure.
2
DFT structure optimizations carried out without imposition
of molecular symmetry also converged to a model with Cs
symmetry and with the TiC2H5 group in a staggered conforma-
tion about the C-C bond. The energy obtained by optimization
of a Cs model in which the TiC2H5 group was locked in an
ion is shown on the left; it corresponds to a nearly pure dz
metal atom orbital. A similar diagram of the HOMO of the
[C2H5]- anion is shown on the right; as a first rough approxima-
tion, it may be regarded as an sp3 lone pair orbital on CR but
considerably delocalized. This orbital may be considered to
be derived from one of the degenerate HOMO’s of ethane by
removal of H+ from the R-C atom or to be derived from ethylene
by addition of H- to the â-C atom. Accordingly, it is very
similar to one of the HOMO’s of C2H6 and to the corresponding
LUMO of C2H4. The orbital is C-C antibonding but C-H
bonding, and in the following account we shall refer to it as
the πz* orbital of the ethyl ligand. Contour maps of the HOMO
and LUMO of EtTiCl3 are shown in the center of Figure 2.
Both these orbitals have A′ symmetry. The HOMO is a Ti-C
eclipsed conformation was 1.7 kcal mol-1, so that the calcula-
11
tions on this and other ethyl-metal compounds (e.g., EtReO3
)
favor equilibrium structures that are staggered. The parameters
calculated for 1, listed in Table 5, are in close agreement with
those determined experimentally.5 In fact, the optimized
eclipsed model corresponds not to a minimum on the potential
energy surface but to a saddle-point. The rotation of the methyl
group into an eclipsed conformation brings one methyl group
hydrogen atom closer to the metal atom. At the same time, the
optimal TiCC angle is reduced by 5° to 112.2°.
2
σ-bond orbital formed by combination of the Ti dz orbital and
Perhaps the most striking result to emerge from the experi-
mental and computational studies of EtTiCl3 is the extreme
pliability of the TiC2H5 moiety. In Table 2 we compare the
E-C and C-C stretching force constants and ECC bending
force constants for the compounds EtCl,12a EtBr,12b EtReO3,11
and EtTiCl3, where E ) Cl, Br, Re, or Ti. Both the E-C
stretching and ECC bending force constants are seen to decrease
markedly in the sequence E ) Cl > Br > Re > Ti correspond-
ing to increasing polarization of the E-C2H5 fragment. The
the πz* orbital of the ethyl group: the main bonding interaction
is clearly between Ti and CR, with a slight antibonding
interaction between the metal atom and the Câ and Hâ atoms.
This antibonding character is, of course, in keeping with the
wide TiCC valence angle.
2.3. The Properties of EtTiCl3(dmpe) (2) and the Model
Compound EtTiCl3(dhpe) (2a). The molecular structure
determined for a single crystal of a carefully prepared sample
of the adduct EtTiCl3(dmpe) (2) at 105 K5 indicates the

â-Agostic Interactions in Early Transition Metals
J. Am. Chem. Soc., Vol. 120, No. 15, 1998 3765
Figure 1. Variation of the total energy with the TiCC angle in EtTiCl3 (1) for eclipsed and staggered conformers. Superscript footnote a: correction
for zero point vibrational energy yields ∆Eν ) 1.5 kcal mol-1. The primes indicate the location of an atom either in (′) or out of (′′) the Cs symmetry
plane of the molecule.
Figure 2. Frontier orbital interaction diagram and constant probability density contours for EtTiCl3 (1).
coordination geometry of the metal to be distorted octahedral
with the entire ethyl group occupying one coordination site;
Table 1 lists the structural parameters. Most remarkable is the
TiCC valence angle of 84.57(9)°, a value close to the 86.3(6)°
determined originally for a crystal at room temperature.14 At
150.1(2) pm, the C-C bond distance within the ethyl group
appears more or less normal;15 the earlier study14 had reported
a rather shorter distance [146.7(15) pm] suggestive of partial
(15) Statistical analysis of the C-C bond distances in transition metal
ethyl compounds based on 107 X-ray structures in the Cambridge Structural
Database 5.10 (ref 7a) yields an average of 147.5 pm. These bond distances
may, however, suffer from systematic shortening due to polarisation effects.

3766 J. Am. Chem. Soc., Vol. 120, No. 15, 1998
Haaland et al.
Table 3. Experimental and Calculated (DFT-GIAO) 13C Chemical
Shifts δ (in ppm Relative to TMS) for Me2TiCl2, MeTiCl3, EtTiCl3
(1), and EtTiCl3(dmpe) (2)
olefinic character. Electron density maps are in agreement with
the eclipsed conformation of the ethyl group and identify a
curiously short Ti‚‚‚Hâ distance of about 206(2) pm. No less
remarkable, though, is the Ti‚‚‚Câ distance, 250.1(2) pm, which
is only 17% longer than the bonded Ti-CR distance.
molecule
nucleus
δ (exp)a
δ (calc)b
b
Me2TiCl2
CR
CR
CR
Câ
99.6
118.2
139.65
21.35
82.6
93.2
117.7
26.5
b
MeTiCl3
The IR spectra of 2 in its normal and specifically deuterated
forms reveal an unusually low stretching frequency for the
unique in-plane Câ-H′ bond.6 Thus, the isotopomer CHD2CD2-
TiCl3(dmpe) (2-h1) gives an “isolated” mode, νis(CH),16 with a
frequency of 2585 cm-1. This is some 200 cm-1 lower than
that of any νis(CH) mode reported hitherto (cf. 2799 cm-1 in
NMe3 where the C-H bonds are weakened through interaction
with the antiperiplanar lone pair16). At the same time, the ν-
(CH) modes associated with the methylene portion of the ethyl
ligand in 1 suffer a significant increase in frequency on
coordination by dmpe [from 2878, 2933 cm-1 in 1 to 2933,
3028 cm-1 in 2].6 Hence it appears that complexation results
in an appreciable weakening of the in-plane Câ-H′ bond and a
strengthening of the CR-H bonds as well as a widening of the
HCRH angle. To facilitate the interpretation of the vibrational
spectra of 2 in its different isotopic guises, we optimized also
the molecular structure of the model compound EtTiCl3(dhpe)
(2a; dhpe ) H2PCH2CH2PH2), with the ethyl group in an
eclipsed conformation, and calculated the molecular force field
and vibrational frequencies. The optimized structure was very
similar to the calculated and experimentally determined struc-
tures found for 2 (see Table 1), so that the methyl groups on
the P atoms appear to have very little effect on the overall
structure of the complex. Hence the calculated harmonic
frequencies of the eclipsed conformer of 2a may be used with
some confidence to aid the assignment of the IR spectrum of
26 and indeed reproduce the principal ν(CH) features of the
measured spectrum remarkably well (see Supporting Informa-
tion).
b
EtTiCl3
EtTiCl3(dmpe)c
T ) 213 K/T ) 273 K
ecl/stag
CR
Câ
81.04/85.16
3.81/5.76
69.2/83.4
5.6/11.1
PCH2
PCH2
PCH3
PCH3
27.77/28.11
23.08/23.58
14.05/13.91
13.80/13.91
34.3/34.1
30.1/30.1
19.2/19.6
18.0/17.2
d
d
a All experimental shifts in CD2Cl2 solution. b This work: experi-
mental values measured at 243 K. c Reference 14. d Averaged values.
∆ ) [δ(CH3) - δ(CH2D)] of about 0.019 which varies slightly
with temperature. By contrast, 2 has an isotope shift varying
between -0.05 and -0.01 in the temperature range 193-313
K; the magnitude and temperature-dependence of the IPR are
both small, but, to our knowledge, this is the first example of
a molecule with a negatiVe IPR.19
Structure optimization of 2 was carried out by DFT calcula-
tions without the imposition of symmetry constraints. The
global energy minimum was found for a TiCRCâ angle of 85.5°
and an eclipsed ethyl group conformation. Comparison with
the structure parameters determined by X-ray crystallography
reveals good agreement between threory and experiment (see
Table 1). The strength of the agostic interaction may be
estimated from the calculations by subtracting the energy of
the agostic equilibrium structure from the energy of an optimized
model with a staggered conformation and the TiCRCâ valence
angle fixed at 112°: this gives a stabilization energy, to be
Empirical equations described elsewhere16 point (i) to an in-
plane Câ-H′ bond in 2 3.6 pm longer and with a dissociation
enthalpy 31 kcal mol-1 smaller than its out-of-plane (Câ-H′′)
counterparts and (ii) to CR-H bonds roughly 1.3 pm shorter
and 5 kcal mol-1 stronger than those in 1.6 Inspection of the
calculated force field reveals the normal mode characterizing
the Câ-H stretching vibration to consist exclusively of a
rectilinear motion almost perpendicular to the Ti-H directrix
and thus vitiates against description of the â-agostic interaction
in terms of a Câ-H-M bridging bond.
denoted D112, of 1.84 kcal mol-1 20b,c
.
A more extensive search of the potential energy surface led
to the identification of another local energy minimum corre-
sponding to a second conformer which is also agostic, being
characterized by a TiCRCâ angle of 93.1° and a staggered ethyl
group conformation. This conformer is calculated to lie only
0.18 kcal mol-1 above the equilibrium structure and 1.66 kcal
mol-1 below the optimized anagostic model with TiCRCâ )
112°. The energy difference between the two agostic conform-
ers is so small that their relative stabilities cannot be regarded
as established on the basis of the DFT calculations alone, and
the structure adopted in the crystal may well be determined in
the final analysis by intermolecular forces. The crucial conclu-
sion to emerge from the calculations is that agostic interactions
do not necessarily require an ethyl group in which a Câ-H
bond points toward the metal atom. We shall return to this
point subsequently.
The 13C NMR spectra of 1 and 214 in CD2Cl2 solution show
that, as expected, coordination by dmpe shifts both the CR and
Câ resonances to lower frequency, whereas JCH for the CâH3
unit decreases somewhat (from an averaged value of 130.0 to
125.7 Hz), and JCH for the CRH2 unit increases significantly
(from 134.3 to 147.3 Hz). The last value is in accord with the
corresponding parameter reported for other â-agostic ethyl
complexes8a,b,9a and also, notably, for cyclopropane (161 Hz);9a
In Table 3 we compare the 13C chemical shifts of Me2TiCl2,
MeTiCl3, EtTiCl3, and EtTiCl3(dmpe) calculated at the DFT-
1
it is consistent too with the IR properties described above. H
NMR studies have also been carried out on CDH2CH2TiCl3
(1-d1) and its dmpe adduct 2-d1, appealing to the isotopic
perturbation of resonance (IPR) method of Shapley et al.17,18
for evidence of Ti‚‚‚H interactions. 1 displays an isotope shift
(19) Green, M. L. H.; Hughes, A. K.; Popham, N. A.; Stephens, A. H.
H.; Wong, L.-L. J. Chem. Soc., Dalton Trans. 1992, 3077-3082. For an
alternative explanation of the observed IPR see: Maus, D. C.; Copie´, V.;
Sun. B.; Griffiths, J. M.; Griffin, R. G.; Luo, S.; Schrock, R. R.; Liu, A.
H.; Seidel, S. W.; Davis, W. M.; Grohmann, A. J. Am. Chem. Soc. 1996,
118, 5665-5671.
(20) Higher stabilization energies were found for the model systems
EtTiCl2H(PH3)2 and EtTiCl3(PH3)2 on the basis of SCF and LDF-DFT
calculations. For further information, see: (a) Endo, J.; Koga, N.; Moro-
kuma, K. Organometallics 1993, 12, 2777-2787. (b) Munakata, H.;
Ebisawa, Y.; Takashima, Y.; Wrinn, M. C.; Scheiner, A. C.; Newsam, J.
M. Catal. Today 1995, 23, 402-408. (c) Koga, N.; Obara, S.; Morokuma,
K. J. Am. Chem. Soc. 1984, 106, 4625-4626.
(16) See, for example: McKean, D. C. Chem. Soc. ReV. 1978, 7, 399-
422; Croat. Chem. Acta 1988, 61, 447-461; Int. J. Chem. Kinet. 1989, 21,
445-464.
(17) (a) Saunders: M.; Telkowski, L.; Kates, M. R. J. Am. Chem. Soc.
1977, 99, 8070-8071. (b) Calvert, R. B.; Shapley, J. R. J. Am. Chem. Soc.
1978, 100, 7726-7727.
(18) Hansen, P. E. Annu. Rep. NMR Spectrosc. 1983, 15, 105-234;
Harris, R. K. Nuclear Magnetic Resonance Spectroscopy; Longman:
London, 1986; p 194.

â-Agostic Interactions in Early Transition Metals
J. Am. Chem. Soc., Vol. 120, No. 15, 1998 3767
Figure 3. Constant probability density contours of the HOMO’s of the eclipsed and staggered conformers of EtTiCl3(dhpe) (2a).
GIAO level with the experimental results. Despite the lack of
quantitative agreement between theory and experiment21 (in the
case of MeTiCl3 the values differ by 25 ppm), the calculations
successfully reproduce the monotonic increase of CR shifts
observed for the series
dence of the IPR) may be expected also to be reduced by the
presence of the staggered conformer with calculated CâH3 shifts
of 1.80, 1.92, and 2.21 ppm (see the table in the Supporting
Information for further information about the calculated 1H shifts
in 1 and 2). We conclude then that the results of the Shapley
experiment as applied to 2 may not prove, but are wholly
accordant with, the deshielding of the agostic H atom in 2
foretold by the DFT-GIAO calculations.
Me2TiCl2 < MeTiCl3 < EtTiCl3(CR)
They also reproduce the large difference in chemical shift
between CR and Câ in EtTiCl3 as well as the increased shielding
of both carbon atoms on coordination with dmpe. We have
some confidence therefore in the ability of the calculations to
estimate the difference between the chemical shifts of the CR
and Câ nuclei in the eclipsed and staggered conformers of 2.
On the evidence of the calculations, both CR and Câ resonate at
lower frequency in the eclipsed conformer of 2, a result of some
significance since the experimental CR and Câ resonances both
move to lower frequency as the temperature decreases. Green
et al.14 noted this temperature dependence and suggested an
equilibrium between the structure deduced by X-ray crystal-
lography and another conformer in which the ethyl group has
been rotated through 90° into a plane normal to that defined by
the TiP2 geometry. We have attempted to optimize the structure
of such a conformer and find that it converges to the observed
geometry. Hence we propose that the temperature variation in
the chemical shifts arises from an equilibrium between staggered
and eclipsed conformers, with the latter being the more stable.
The measured NMR spectra are in keeping therefore with the
greater stability of the eclipsed conformer and with the thermal
accessibility of the staggered conformer predicted by the DFT
calculations.
A possible explanation for the negative IPR revealed by the
1H NMR spectra of 2 and 2-d1 is that the agostic H atom of the
CH3 group (Câ-H′) is not more but less shielded than the
anagostic ones (Câ-H′′). This proposal is in contrast with the
original assumption that agostic hydrogen atoms always display
a low-frequency shift.22 It accords, however, with the results
of calculations at the DFT-GIAO level, which yield 1H chemical
shifts of 3.63 ppm for the agostic and 1.51/1.45 ppm for the
anagostic H atoms on the â-carbon atom, and also with the
vibrational properties deduced for the Câ-H′ bond. The
magnitude of the Shapley effect (i.e., the temperature depen-
Constant electron density contours of the HOMO of eclipsed
and staggered conformers of 2a are depicted in Figure 3.
Comparison with the HOMO of the anagostic compound 1
(Figure 2) is instructive: both HOMO’s may be described as
Ti-CR bonding orbitals, but the ethyl group in the dhpe adduct
has been canted in such a way that there is now positive overlap
2
between the torus of the Ti dz atomic orbital and the CâH′
fragment. In addition, though, there is an antibonding interac-
tion between Ti and the in-plane Cl(1) atom which may facilitate
the distortion of the coordination geometry of the metal
accompanying the reduction of the TiCRCâ angle.
We turn next to the results of further DFT calculations carried
out on a variety of model ethyl-transition metal compounds with
the aim of probing the effects of varying the net charge, the
nature, or the coordination number of the metal atom.
2.4. DFT Calculations on [EtTiCl2]+ (3): Strong Agostic
Interactions. Structure optimization of a model of the cation
[EtTiCl2]+ (3) with Cs symmetry and an eclipsed ethyl group
conformation yielded an acute MCC angle of 85.0° and a short
Ti‚‚‚Hâ distance of 206 pm. Calculation of the molecular force
field yielded no imaginary frequencies, showing that the eclipsed
conformer corresponds to a minimum on the global potential
energy surface. The â-agostic stabilization energy, estimated
by comparison with an optimized model in which the TiCC
angle has been fixed at 112°, is 8.36 kcal mol-1
following discussion we shall classify an agostic interaction as
strong if the interaction energy is larger than 5 kcal mol-1
. In the
.
Optimization of a Cs model with a staggered ethyl group
conformation yielded an even more acute TiCC valence angle
of 80.0°. The energy of this model is 0.68 kcal mol-1 above
that of the eclipsed conformer and 7.68 kcal mol-1 below that
of the optimized, nonagostic model with TiCC ) 112°.23 As
in the case of EtTiCl3(dmpe), we find that the agostic stabiliza-
tion energy of a model with a staggered ethyl group is only
(21) The large methyl 13C shift of 83.1 ppm observed for W(CH3)6 was
also underestimated by DFT calculations (62 ppm). For further information
see Kaupp, M. J. Am. Chem. Soc. 1996, 118, 3018-3024.
(22) Emsley, J. W.; Feeney, J.; Sutcliffe, L. H. High-Resolution NMR
Spectroscopy; Pergamon: Oxford, 1966. Vol. 2, pp 825-826.
(23) (a) Woo et al. have published the results of high-quality DFT
calculations on [(n-propyl)ZrCp2]+ that indicate the existence of a γ-agostic
conformer where two Hγ atoms are about equally far from the metal atom
(ref 4b). (b) Fan et al. have computed the equilibrium structure of [EtTiCl2]+

3768 J. Am. Chem. Soc., Vol. 120, No. 15, 1998
Haaland et al.
Table 4. Salient Structural Parameters of the Model System
[EtTiCl2]+ (3)a
parameter [EtTiCl2]+ eclb [EtTiCl2]+ stagb [EtTiCl2]+ stagb/112°
∆Erel
Nimag
0
0
0.68
1
8.36
MCC
85.0
80.0
112.0
M-C
201.4
152.1
115.4
109.7
215.0
199.9
154.4
110.3
111.4
215.0
200.5
153.5
110.4
110.1
214.8
C-C
Câ-H′ c
Câ-H′′ c
M-Cl
MCH
113.0
114.5
113.6
116.1
109.0
116.2
109.8
114.6
114.8
108.8
105.9
107.6
113.5
111.3
108.1
CCHâ′ c
CCHâ′′ c
ClMCl
CMCl
d
M‚‚‚Hâ
M‚‚‚Câ
206.0
241.7
243.8
230.3
319.2
294.6
a Bond distances in pm, angles in deg, and energies in kcal mol-1
.
Nimag ) number of imaginary frequencies. b The labels “ecl” and “stag”
specify the ethyl group conformation. The value of 112° relates to the
TiCC angle. c Atom in the symmetry plane is denoted by (′); atom out
of the symmetry plane is denoted by (′′). d Shortest Ti‚‚‚Hâ distance.
about 10% lower than for an eclipsed model. We assume that,
in general, the conformation adopted by an ethyl group bonded
to a transition metal atom will be determined by the balance of
two opposing forces: (i) the inherent barrier to rotation about
the C-C bond which favors a staggered conformation and (ii)
the strength of the â-agostic interaction which favors an eclipsed
conformation.
For EtTiCl3(dmpe) the staggered model corresponds to a local
minimum on the potential energy surface. In the case of
[EtTiCl2]+, calculation of the molecular force field shows that
the staggered model corresponds to a transition state for internal
rotation of the methyl group. In summary, the calculations yield
a barrier to internal rotation of the methyl group of 0.68 kcal
mol-1 and indicate that rotation occurs with only a small change
of TiCC angle. Such “in-place” rotation of a methyl group
involved in a â-agostic interaction has been inferred from NMR
measurements in at least one case.24
Optimized structure parameters for both the eclipsed equi-
librium structure and for the staggered transition state of 3 are
listed in Table 4.
2.5. The Nature of â-Agostic Interactions in Ethyl
Derivatives of Early Transition Metals. We now turn our
attention to the bonding between the transition metal atom and
the â-agostic ethyl group. In Figure 4 we display constant-
probability-density contours in the TiCC plane as well as a three-
dimensional constant probability surface of the HOMO for the
eclipsed equilibrium structure of [EtTiCl2]+. The nature of the
HOMO is clearly similar to that of EtTiCl3(dhpe) (see Figure
3), but the smaller number of ligands and the higher symmetry
(Cs versus C1) cause the HOMO now to be localized on the
EtTi fragment. For this reason, and since the agostic interaction
is strong, we prefer to base our discussion of the nature of
â-agostic interactions on the case of [EtTiCl2]+.
Figure 4. Top: constant probability density contours in the TiCC plane
of the HOMO and LUMO of [EtTiCl2]+ (3). Bottom: three-dimensional
constant probability density surfaces of the HOMO, HOMO-8, and
HOMO-9 orbitals.
Comparison of [EtTiCl2]+ with the anagostic compound
EtTiCl3 (Figure 2) shows that the HOMO’s of both may be
described as Ti-CR σ-bonding orbitals formed by combination
2
of the metal-based dz atomic orbital (with a small admixture
of s and p functions) with the C-H bonding but C-C
antibonding πz* orbital of the ethyl fragment. As in 2a,
however, the ethyl group in [EtTiCl2]+ has been canted in such
a way that there is now a positive overlap between the torus of
and report parameters in good agreement with ours: Fan, L.; Harrison, D.;
Deng, L.; Woo, T. K.; Swerhone, D.; Ziegler, T. Can. J. Chem. 1995, 73,
989-998. These studies explored neither the potential surface around the
equilibrium geometry nor the nature of the bonding therein.
(24) Derome, A. E.; Green, M. L. H.; Wong, L.-L. New J. Chem. 1989,
13, 747-753.
2
the Ti dz orbital and the CâH′ fragment. At the same time,
comparison of orbital energies shows that the HOMO in 3 is

â-Agostic Interactions in Early Transition Metals
J. Am. Chem. Soc., Vol. 120, No. 15, 1998 3769
stabilized by 6.5 kcal mol-1 when the TiCC angle is reduced
from 112 to 85°. We suggest therefore that the â-agostic
interaction should be regarded as a covalent interaction which
can be understood only in terms of a Ti-CR bonding orbital
that is delocalized oVer the entire ethyl group: the reduction
of the MCC valence angle allows the metal atom to establish
bonding interactions with the â-C and its appended H atom.
The geometry of the M-Et interaction is such that bonding to
both CR and Câ is effected by the same orbital on M. Such a
situation is well established for other transition-metal-C2 ligand
interactions, the classic example being the Dewar-Chatt-
Duncanson description of M-olefin bonding.25
Comparison of orbital energies shows that reduction of the
TiCC angle also leads to significant stabilization of two deeper
lying MO’s, viz. the HOMO-8 and HOMO-9 orbitals. Three-
dimensional constant-probability-density surfaces (Figure 4)
show that the former is a C-C σ-bonding orbital, while the
latter is a delocalized C-H bonding orbital. Both orbitals
appear to be slightly delocalized onto the metal atom. The
delocalization is, however, so small that a â-agostic alkyl group
may still be considered a two-electron ligand.26
Mulliken population parameters of the orbitals obtained by
calculations on an anagostic structure (i.e., with TiCC greater
than 112°) suggest that the ethyl group carries a net negative
charge. When the MCC angle is closed, there appears to be a
slight depolarization of Et-Ti bonding, with a small amount
of negative charge being returned to the metal atom. The bond
distances and valence angles listed in Table 4 indicate that
establishment of agostic interactions leads to a small reduction
of the C-C bond distance, a slight increase of the in-plane C-H′
bond distance, and an opening of the CCH′ angle in the eclipsed
conformer. These structural changes are consistent with
depopulation of the πz* ligand orbital.
the C-C bond distance is too short to allow optimal interaction
of Ti with both carbon atoms of the ethyl group.
2.6. DFT Calculations on EtScCl2 (4) and EtTiCl2 (5):
Weak Agostic Interactions. Structure optimizations of 4 and
5 indicate that the equilibrium structures have eclipsed ethyl
group conformations, acute MCC angles of 86.5 and 85.6°, and
short M‚‚‚Câ distances of 255 and 247 pm, respectively (see
Supporting Information). The strength of the â-agostic interac-
tions, estimated by comparison with optimized models with
MCC fixed at 112°, is 2.85 kcal mol-1 for 4 and 0.99 kcal
mol-1 for 5. Accordingly we classify both interactions as weak.
Optimization of a staggered model of 4 yields an ScCC angle
of 83.5° and an imaginary methyl torsion frequency indicating
a transition state; as in the case of [EtTiCl2]+, internal rotation
of the methyl group occurs without rupture of the agostic
interaction. The calculated barrier to methyl group rotation is
0.95 kcal mol-1. Optimization of a staggered model of 5 yields
a TiCC angle of 107.5° indicating that the agostic interaction
has been broken. Inspection of the methyl group rotation mode
shows that the staggered model corresponds to a local minimum
on the potential energy surface, i.e., to a higher energy
conformer. Since the energy difference, 0.98 kcal mol-1, is
comparable with the thermal energy available at room temper-
ature (RT ) 0.6 kcal mol-1), both conformers may coexist in
the gas phase or in solution in a weakly interacting solvent.27
EtScCl2 is related to the complex EtScCp*2 and EtTiCl2 to
EtTiCp*2 through the isolobality of the Cp* group and the Cl
atom.28 As mentioned in section 2.1, there is strong spectro-
scopic and kinetic evidence for â-agostic interactions in both
Cp* compounds.9,10 Lukens et al. have assigned separate
electronic absorptions of EtTiCp*2 in hydrocarbon solution to
agostic and anagostic conformers. The temperature variation
of the intensities yielded an estimated energy difference of 1.9
kcal mol-1 10b
The properties calculated for the model com-
.
Figure 4 also shows constant-probability-density contour plots
for the HOMO of the transition state to methyl group rotation.
These suggest that rotation of the methyl group into a staggered
position eliminates the bonding interactions between the metal
atom and â-hydrogen atoms; the H atoms that are now closest
to Ti are situated near a nodal surface. We suggest, therefore,
that the stabilization of the small TiCC angle is best described
as an agostic Ti‚‚‚Câ, rather than a Ti‚‚‚H2Câ interaction. The
fact that the strength of the agostic interaction increases by less
than 10% on rotation of the methyl group from a staggered to
an eclipsed conformation implies that in the eclipsed conforma-
tion too the main contribution to the â-agostic stabilization
energy derives from Ti‚‚‚Câ bonding. In this context, it may
be remarked, Mulliken population analyses on Et-M com-
pounds consistently indicate that, as expected, the metal atom
and all H atoms carry net positive charges, while the C atoms
carry net negative charges. The agostic interaction could
therefore be enhanced by Coulomb attraction between the M
and Câ atoms and opposed by Coulomb repulsion between M
and Hâ atoms. Coulomb attraction between M and Câ provides
a possible rationalization of the apparent strengthening of the
agostic effect in complexes such as 3 carrying a net positive
charge.
pound EtTiCl2 are thus in good agreement with those estimated
experimentally for EtTiCp*2.
Geometric rearrangement of an ethyl ligand to allow estab-
lishment of â-agostic interaction requires additional space in
the coordination sphere of the metal atom. The rearrangement
may therefore be opposed by interligand repulsion. This is
hardly a problem in three-coordinate species such as 3, 4, or 5,
since the orientation of the ethyl group is such that the MCRCâ
and MCl2 planes are perpendicular. As a result, the shortest
Cl‚‚‚Câ distance in [EtTiCl2]+ is 399 pm, as compared to 383
pm (by DFT calculations) in the nonagostic molecule EtTiCl3.
In the same vein, one would not expect serious strain in the
pentamethylcyclopentadienyl analogue [EtTiCp*2]+ since the
agostic ethyl group could occupy the cleft between the
nonparallel Cp* rings.
2.7. DFT Calculations on the Four-Coordinate Model
Compounds EtZrCl3 (6), EtVCl3 (7), EtNbCl3 (8), and
[EtVCl3]+ (9): Repulsion between Ligands and a Rigid
Coordination Geometry May Obstruct â-Agostic Interac-
tions Even with a Net Positive Charge on the Metal. We
have seen (section 2.2) that it requires no more than 2.8 kcal
mol-1 to reduce the TiCC angle in EtTiCl3 from 115 to 95°.
We have also seen (sections 2.4 and 2.6) that the agostic
interaction in the cationic complex [EtTiCl2]+ is some 5.5 kcal
Within the agostic molecule the maximum electron density
in the TiCR bonding region is no longer found on the Ti-CR
directrix; instead the bond appears to be “bent”. We suggest
that this bending is a consequence of canting of the ethyl group;
(27) The potential energy curve calculated for staggered EtTiCl2 is
extremely flat, and so we should add two cautionary notes. First, even small
changes in the computational approach could have a large effect on the
optimal value of the TiCC angle. Second, the shape of the barrier to methyl
group rotation might be significantly changed, particularlarly in the range
from τ ) 40 to 60°.
(25) Reference 2, pp 259-260.
(26) Eisenstein and co-workers have also suggested a two-electron
description of â-agostic interactions on the basis of extended Hu¨ckel
calculations on the species [EtTiH5]2-: Demolliens, A.; Jean, Y.; Eisenstein,
O. Organometallics 1986, 5, 1457-1464.
(28) (a) Reference 2, pp 396-401. (b) Hoffmann, R. Angew. Chem.,
Int. Ed. Engl. 1982, 21, 711-724.

3770 J. Am. Chem. Soc., Vol. 120, No. 15, 1998
Haaland et al.
Table 5. Salient Structural Parameters of the Model Systems EtTiCl3 (1), EtZrCl3 (6), EtVCl3 (7), EtNbCl3 (8), and [EtVCl3]+ (9)a
EtTiCl3
stagb
EtTiCl3
eclb
EtZrCl3
stagb
EtZrCl3
eclb
EtVCl3
stagb
EtVCl3
eclb
EtNbCl3
eclb
EtNbCl3
stagb
[EtVCl3]+
stagb
[EtVCl3]+
eclb
e
e
parameter
∆Erel
Nimag
MCC
0
0
1.71
1
112.3
0
0
0.98
1
99.7
0
0
0.76
0
91.1
0
0
91.9
0.55
1
106.1
0
0
1.57
1
110.4
117.2
112.2
111.2
117.4
M-C
205.2
153.0
110.3
109.9
220.7
220.6
204.7
153.9
110.3
110.4
220.5
220.9
217.5
155.6
110.6
110.4
238.9
239.2
216.6
156.1
111.9
110.1
238.7
239.9
201.5
153.1
110.4
109.8e
216.1
217.2e
199.7
152.6
112.1
109.8e
216.5
218.8e
210.4
155.5
112.8
110.0
234.8
237.5
211.5
155.9
110.6
110.3
234.6
236.4
197.2
152.1
110.4
109.8
209.8
209.5
196.8
153.1
110.4
109.8
209.5
209.9
C-C
C-Hâ′ c
C-Hâ′′ c
M-Cl′ c
M-Cl′′ c
MCH
103.3
110.6
111.9
113.4
113.0
105.3
105.6
104.8
113.9
111.1
114.4
112.2
105.3
105.9
107.3
110.5
111.8
115.1
112.9
104.7
105.0
111.4
114.5
111.2
117.7
110.5
105.1
106.0
105.9
109.6
112.3e
110.1
114.1e
102.3
107.9e
111.4
114.1
112.1e
113.7
109.1e
98.6
113.5
114.8
111.4
111.5
112.1
97.9
110.0
109.3
112.2
108.6
115.8
99.7
100.4
107.6
112.6
112.0
112.0
107.0
106.7
102.8
115.0
109.9
113.6
110.7
106.4
107.5
CCâH′ c
CCâH′′ c
Cl′′MCl′′ c
Cl′MCl′′ c
CMCl′ c
CMCl′′ c
112.6e
111.2
108.1
d
M‚‚‚Hâ
M‚‚‚Câ
329.1
306.9
289.9
299.2
329.7
311.7
263.7
287.5
314.3e
293.9
224.2
253.6
236.0
265.8
312.2
295.5
324.9
299.4
281.4
288.5
a Bond distances in pm, angles in deg, and energies in kcal mol-1. Nimag ) number of imaginary frequencies. b The labels “ecl” and “stag”
specify the ethyl group conformation. c Atom in the symmetry plane is denoted by (′); atom out of the symmetry plane is denoted by (′′). d Shortest
M‚‚‚Hâ distance. e Average values; geometry was optimized without symmetry constraints.
EtTiCl3 < [EtVCl3]+ < EtZrCl3 < EtVCl3 < EtNbCl3
mol-1 stronger than in the isoelectronic neutral complex EtScCl2.
Expecting that an increase in the formal charge on the metal
would have a similar effect in four-coordinated species,
therefore, we carried out calculations on [EtVCl3]+ (9). To our
surprise, however, we found that the equilibrium structure is
anagostic with VCC ) 117.4° and a staggered ethyl group
conformation. Optimization of a model in which the ethyl group
is fixed in an eclipsed conformation yields VCC ) 110.4°
and an energy 1.57 kcal mol-1 above that of the anagostic
equilibrium structure. We conclude that agostic interaction is
not inVariably faVored by a net positiVe charge on M.
Structure optimization of 6 and 7 yields equilibrium structures
similar to that obtained for the Ti analogue 1; the valence angles
ZrCC and VCC are slightly larger than tetrahedral and the ethyl
group conformations staggered (see Table 5). Optimization of
models in which ethyl groups are fixed in eclipsed conforma-
tions yield MCC angles of 99.7° (6) and 91.1° (7), as compared
with 112.3° for the Ti analogue (1).29 The energy of the
optimized eclipsed conformer relative to that of the anagostic
equilibrium structure decreases from 1.71 in 1 through 0.98 in
6 to 0.76 kcal mol-1 in 7. The optimized eclipsed models of 1
and 6 correspond to transition states for internal rotation of the
methyl groups. The corresponding model for 7, however,
corresponds to a local minimum on the potential energy surface,
indicating that gaseous EtVCl3 may consist of a mixture of an
anagostic, staggered and a less stable agostic, eclipsed con-
former.30 â-Agostic interactions in 6 and 7 may be described
as incipient, since structures with MCC valence angles less than
100° and with eclipsed ethyl group conformations are thermally
accessible at room temperature.
We have suggested (see section 2.2) that the pliability of the
TiCC valence angle in 1 is due to near-cancellation of agostic
M‚‚‚CâH attraction and steric CâH3‚‚‚Cl′′ repulsion. This
repulsion should be reduced if a Fourth Period atom such as Ti
or V is replaced by the larger Fifth Period congener Zr or Nb,
and the agostic structure should become more stable. A referee
suggested that we optimize the model system [EtZrCl2]+ for
comparison with [EtTiCl2]+ in order to explore the effect of
electronic differences between Fourth and Fifth Period elements.
The interaction energy obtained for [EtZrCl2]+, D112 ) 6.0 kcal
mol-1, is 1.0 kcal mol-1 smaller than that calculated for the Ti
analogue 3 (BPW91/II level), indicating that in these sterically
unhindered systems the agostic interaction is, if anything, weaker
in the Zr than in the Ti species. But why should agostic
interactions be more favored in the Group 5 than in the Group
4 derivatives in these four-coordinated model systems? We
believe that the answer may be sought partly in the nature of
the HOMO which contains the additional electron and partly
in the direction of the distortion which relieves CâH3‚‚‚Cl′′
repulsion (see Figure 5).
Examination of the anagostic equilibrium structure of EtVCl3
shows that, while the three ClVCl valence angles are ap-
proximately equal, the VCl3 fragment has been tilted relative
to the V-CR bond axis in such a way that the nonbonded
CâH3‚‚‚Cl′′ distance has increased (see Table 5 and Supporting
Information). A similar distortion is found in the Ti analogue
when the TiCC angle is reduced to 87°. The HOMO’s of 7
and 8 both correspond to a nearly pure dxy orbital on the metal
atom with a small admixture of antibonding interaction with
Cl p orbitals. Introduction of the additional electron is thus
expected to weaken the M-Cl bonds. Inspection of Figure 5
also suggests that Coulomb repulsion between the dxy electron
density and the M-Cl′′ σ-bonding electrons would tend to
increase the CRMCl′′ angle. Indeed, the CRMCl′′ angle of the
anagostic equilibrium structure of EtVCl3 is 107.9°, as compared
with 105.6° in the Ti analogue. Accordingly we suggest that
the presence of the additional electron lowers the energy required
for distortion of the metal atom coordination geometry ac-
companying a reduction of the MCC angle.
Finally, calculations on 8 yield a â-agostic equilibrium
structure with NbCC ) 91.9° and an eclipsed ethyl group.
These results indicate that the stability of a â-agostic model
relative to that of its anagostic counterpart increases in the order
(29) Endo et al. have optimized at the MP2 level a Cs model of 7 with
the ethyl group locked in the eclipsed conformation and obtained geometric
parameters in reasonable agreement with ours; see ref 20a.
(30) The torsional mode in EtVCl3 has a very low frequency, however,
and it is impossible to exclude the possibility that calculations at a higher
level would convert the staggered model to a transition state for methyl
group rotation.

â-Agostic Interactions in Early Transition Metals
J. Am. Chem. Soc., Vol. 120, No. 15, 1998 3771
EtTiCl2 < EtScCl2 , [EtTiCl2]+
The constant-probability-density contours imply that the
HOMO in each of the d0 species [EtTiCl2]+ and EtScCl2 is an
M-CR bonding orbital which is delocalized over the entire ethyl
group; it may be described as a combination of a nearly pure
2
dz orbital on M with a C-C antibonding but C-H bonding
orbital (π*) on the ethyl ligand. Canting of the ethyl group to
establish an agostic structure leads to a covalent interaction
2
between the CâH3 fragment and the torus of the dz orbital on
M. Even though the favored conformation of the ethyl group
is such that one Câ-H bond is pointing toward the metal atom,
rotation of the CâH3 group by 60° to generate the staggered
conformer is not opposed by a significant barrier and does not
necessarily result in a widening of the MCC valence angle.
Assumption of a positive charge by the complex evidently
strengthens the agostic interaction, Coulomb attraction between
M and Câ possibly augmenting the covalent attraction.
DFT calculations on four-coordinated complexes of the type
[EtMCl3]n+ (n ) 0, M ) Ti, V, Zr or Nb; n ) 1, M ) V) show
that anagostic equilibrium structures are the rule. However,
EtNbCl3 is predicted to have a weakly agostic structure with
NbCC ) 91.9° and an eclipsed ethyl group conformation, and
EtVCl3 to show incipient agostic behavior since a conformer
with VCC ) 91.1° and an eclipsed ethyl group is calculated
to lie only 0.76 kcal mol-1 above the global minimum. The
properties of these four-coordinated complexes may be rational-
ized if it is assumed that the reduction of the MCC angle is
opposed by repulsion between the CâH3 group and the two out-
of-plane Cl atoms. Such repulsion may be alleviated either (i)
by replacing a Fourth Period element like Ti or V by its Fifth
Period congener Zr or Nb to create more space around the metal
center or (ii) by replacing a d0 by a d1 metal center (e.g., Ti or
Zr by V or Nb) to create a less rigid coordination geometry.
Space and skeletal flexibility appear to be more important
considerations here than does the assumption of a positive charge
on M.
These same influences appear also to be decisive in trans-
forming the anagostic behavior of four-coordinated EtTiCl3, with
VE ) 8, into the â-agostic behavior clearly and uniquely
authenticated for the six-coordinated complex EtTiCl3(dmpe),
VE ) 12. For DFT calculations suggest that coordination of
the diphosphine opens out the coordination geometry of the
metal atom and also renders it more pliable, thereby leading to
a reduction of the forces opposing â-agostic interaction.31 The
structure [ TiCC ) 84.57(9)°; eclipsed ethyl group]5 and
spectroscopic properties of the dmpe complex are well repro-
duced by the calculations which reveal, in addition, the existence
of a second conformer with TiCC ) 93.1° and a staggered
ethyl group only slightly less stable than the first, and which
may be expected to participate in the solution chemisty of the
complex.
Figure 5. Top: coordination geometry of the eclipsed (agostic)
conformer of EtVCl3 (7). Bottom: contour maps of frontier MO’s; the
HOMO of EtVCl3 contributes to a weakening of the V-Cl bonds and
a widening of the CRVCl′′ valence angles.
This hypothesis may also provide an explanation for the
anagostic nature of [EtVCl3]+. For four-coordinate complexes,
therefore, it would seem that a flexible coordination geometry
is more important for the adoption of an agostic structure than
is a net positive charge on the metal atom.
3. Conclusions
We have drawn on DFT calculations, together with the
structures and spectroscopic properties determined by experi-
ment, to probe the nature and incidence of â-agostic interactions
affecting ethyl groups coordinated to an early transition metal
M. Our analysis has sought specifically to examine how such
interactions vary with the atomic number, coordination number,
valence electron (VE) count, and net charge on M.
â-Agostic behavior appears in practice to require that the
valence shell of M be unsaturated with VE e 16. It is most
prone to occur when M is three-coordinated, being seldom
encountered in four- and six-coordinated systems (with only
one example of each having been registered), and unknown in
five-coordinated systems. Our DFT calculations on the three
model three-coordinated complexes [EtTiCl2]+, EtScCl2, and
EtTiCl2 yield agostic structures with MCC angles of about 85°
and eclipsed ethyl group conformations; the strength of the
interaction varies in the order
In summary, therefore, the calculations reveal that agostic
stabilization derives not from C-H f M electron donation but
from delocalization of the M-C bonding orbital, usually the
HOMO in d0 complexes. The bonding between the metal atom
and the ethyl group is effectively provided by one electron pair
(31) On the basis of extended Hu¨ckel calculations, Eisenstein and co-
workers have suggested that canting of the alkyl group is favored by the
presence of a ligand in the trans position: Eisenstein, O.; Jean, Y. J. Am.
Chem. Soc. 1985, 107, 1177-1186. The presence of a P atom trans to the
ethyl group in 2 may well reduce the factors opposing the â-agostic
interaction, but this is unlikely to be the dominant factor since DFT
calculations at the BPW91 level indicate that the equilibrium geometry of
a model of EtTiCl3(PH3) with a phosphine ligand trans to the ethyl group
is anagostic.

3772 J. Am. Chem. Soc., Vol. 120, No. 15, 1998
Haaland et al.
DFT calculations on 2 made use of the program system ADF.43 The
Vosko-Wilk-Nusair parametrization,44 with the gradient corrections
of Becke36 for exchange and of Perdew37a,b for correlation, was used
for the exchange-correlation energies (denoted as BP86 in the follow-
ing). The gradient corrections were included self-consistently. The
accuracy of the numerical integration was set to 10-4.0 for each integral.
This is assumed to give a numerical noise level of less than 0.5 kcal
mol-1 in the final energies.43e We employed a triple-ú valence basis
on Ti and double-ú valence plus polarization on the other atoms. The
atomic orbitals up to 2p were frozen on Ti, V, and Cl, while 1s was
kept frozen on C. This basis set combination is designated “III”.
The initial optimizations on all compounds were achieved without
symmetry restriction and started from geometries without any symmetry.
Invariably, however, the optimization of 1, 3-6, 8, and 9 converged
to Cs symmetry. The final molecular geometry of each of these
compounds was therefore optimized within the constraints of the Cs
point group. The DFT Cartesian force constants and Cartesian dipole
moments for 1, 2a, and 3-9 were determined at the theoretical
equilibrium geometries.
and one orbital on the metal. Factors such as the Lewis acidity
or VE count of the metal center are not decisive; instead, the
form and rigidity of the metal-ligand framework appear to be
crucial factors in permitting or inhibiting the development of
the interaction. It remains to be seen how far the conclusions
we have reached regarding the nature of â-agostic bonding are
applicable to R-, γ-, and other types of agostic interaction1 and
also to late transition-metal systems.
4. Experimental Section
Synthesis of EtTiCl3 and EtTiCl3(dmpe). Standard Schlenk and
rigorous high-vacuum techniques were used throughout. EtTiCl3 was
prepared by the literature method exploiting the reaction between
tetraethyllead and titanium tetrachloride.32 In this method a molar
excess of TiCl4 is required to remove the alkylating agent and prevent
the formation of di- or triethyltitanium derivatives. In practice, samples
of EtTiCl3 prepared via this route were invariably contaminated with
substantial amounts (5-10%) of TiCl4 impurity. This was removed
by repeated fractional condensation in vacuo, the EtTiCl3 being retained
by a trap held at 228 K. The purity of the sample was checked carefully
13C and 1H chemical shifts were calculated at the BPW91/I level of
theory for the BPW91/I- or BP86/III-optimized structures using the
Gauge-Independent Atomic Orbital (GIAO) method in Gaussian 94.
Chemical shifts are given with respect to TMS at the same computa-
tional level. Absolute shieldings of carbon and hydrogen in TMS at
the BPW91/I level are 183.3 (C) and 31.96 (H).
1
by reference to the H NMR spectrum of a CD2Cl2 solution32 and to
the IR spectrum of the vapor.6,33 Deuterated samples of EtTiCl3 were
prepared in an analogous manner, the corresponding isotopomer of Et4-
Pb being synthesized by the reaction of Pb(OAc)4 with a THF solution
of the appropriate version of EtMgCl (itself prepared from CHD2CD2-
Cl or CH2DCH2Cl).34 The adducts CH3CH2TiCl3(dmpe), CHD2CD2-
TiCl3(dmpe), and CH2DCH2TiCl3(dmpe) were prepared from the
corresponding pure ethyltitanium trichloride by methods described
previously.14
Acknowledgment. We are grateful to the Deutsche Fors-
chungsgemeinschaft for a postdoctoral fellowship (to W S.), to
Jesus College, Oxford for a research fellowship (to G.S.M.), to
the EPSRC for assistance with the purchase of equipment, to
the VISTA program of STATOIL and the Norwegian Academy
of Science and Letters for financial support, and to the Research
Council of Norway for a generous grant of computing time.
We thank Prof. Malcolm Green, Prof. Donald McKean, and
Dr. John Turner for helpful discussions and the referees for
constructive comments and suggestions.
Structure Determination and Spectroscopic Measurements. Es-
sential details of the structure determinations carried out on gaseous
EtTiCl3 (by electron diffraction at Oslo) and on a single crystal of
EtTiCl3(dmpe) at 105 K (by X-ray diffraction at Munich) are to be
found elsewhere.5 NMR spectra of CD2Cl2 solutions of EtTiCl3 and
EtTiCl3(dmpe) and their specifically deuterated isotopomers were
recorded at Oxford with the aid of a Bruker AM-300 (300 MHz) or a
Varian 500 (500 MHz) FT-NMR spectrometer. Infrared spectra were
measured with a Mattson “Galaxy” FT-IR spectrometer, typically at a
Supporting Information Available: Observed and calcu-
lated C-H(D) stretching frequencies for the ethyl groups of
EtTiCl3 (1), CHD2CD2TiCl3 (1-h1), EtTiCl3(dmpe) (2), and
CHD2CD2TiCl3(dmpe) (2-h1) and calculated scaled harmonic
frequencies for 1, 1-h1, EtTiCl3(dhpe) (2a), and CHD2CD2TiCl3-
(dhpe) (2a-h1); GIAO chemical shifts at the DFT level for Me2-
TiCl2, MeTiCl3, EtTiCl3 (1), and EtTiCl3(dmpe) (2); optimized
geometries of EtTiCl3 (1) and EtVCl3 (7) at different compu-
tational levels; salient structural parameters for EtScCl2 (4) and
EtTiCl2 (5); and Gaussian basis sets employed for calculations
(6 pages). See any current masthead page for ordering and Web
access instructions.
resolution of 2 cm-1
.
Quantum-Chemical Calculations. Gaussian 9435 DFT calculations
were carried out using the BPW91 density functional with the gradient
correction of Becke36 for exchange and of Perdew-Wang37c for
correlation. Basis set information is listed in the Supporting Informa-
tion. Unless specified otherwise in the text we employed the basis set
combination denoted “I”38-40 for calculations on compounds EtTiH3,
1, 2a, 3-5, 7, and 9 and basis set combination “II”41,42 for compounds
6 and 8.
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