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CyclopentadienylЧActinide Complexes Bonding and Electronic Structure.

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Cyclopentadienyl-Actinide Complexes: Bonding and Electronic
Structure
By Bruce E. Bursten" and Richard J. Strittmatter
Shortly after the discovery of ferrocene, Reynolds and Wilkinson demonstrated that actinide
elements are capable of forming organometallic compounds containing the cyclopentadienyl
(Cp) ligand. The compound they reported, [Cp,UCI], was the first of a host of organoactinide
complexes that contain Cp and substituted Cp ligands. In 1968, Streitwieser and Miiller- Westerhoffsynthesized uranocene, [(C,H,),U], a molecule whose existence had been predicted five
years earlier by R. D . Fischer. Because uranocene has no analogue in transition-metal chemistry, its synthesis stimulated new interest in organoactinide chemistry and in comparisons with
organotransition-metal chemistry. Since that time, Cp and substituted Cp ligands, such as
pentamethylcyclopentadienyl (Cp *), have become the most important and flexible ligands in
actinide organometallic chemistry. In the past 15 years especially, the bonding of Cp ligands
to actinide elements has been extensively probed by both experiment and theory. There are
both significant similarities and equally significant differences in the bonding of the Cp ligand
to the f-element metals compared to the d-element metals.
1. Introduction
Since the discovery of the remarkable structure of ferrocene, [($-C,H,),Fe] (I), in 1952,"' the cyclopentadienyl
(Cp) ligand has played a central role in organometallic chemistry. In the flurry of activity that followed the synthesis of
I, alkali cyclopentadienides were allowed to react with a
wide variety of metal halides in an effort to synthesize new
organometallics with n-bonded Cp ligands. The birth of the
organometallic chemistry of the actinide elements came in
1956, with the report by Reynolds and Wilkinson of
[Cp,UCI] (2), which contains three Cp ligands n-bonded to
uranium.[21In the early 1960s, E. 0. Fischer and co-workers
reported the preparation of [Cp,An] complexes (3; An =
Th, U);13]the presence of four n-bonded Cp ligands is without precedent among the transition elements.
1
2
3
4
The distinct nature of organoactinide chemistry compared
to organotransition-metal chemistry was boldly underscored
in 1968 with the synthesis of uranocene [(~'-C,H,),U] (4) by
Streitwieser and Miiller- Westerhoff?'] This beautiful molecule, whose existence had been considered theoretically five
years earlier by R. D. Fischer,[sl consists of two planar C,
rings sandwiching a uranium atomt6]and has no analogue
among the transition elements. Actinocenes of many of the
other actinide elements were subsequently synthesized"] and
studied both spectroscopically['] and the~retically.['~The
electronic structure of uranocene is still a matter of intense
experimental and theoretical interest; in 1989, for example,
state-of-the-art photoelectron spectroscopic[' O1 and ab initio
[*] Prof. B. E. Bursten, Dr. R. J. Strittmatter
Department of Chemistry
The Ohio State University
Columbus. OH 43210 (USA)
Angeu. Chem. Int. Ed. Engl. 30 (1991) 1069-1085
theoretical" '1 studies of the molecule were reported. The
synthesis of uranocene is often considered the beginning of
modern organoactinide chemistry, and many excellent review articles and monographs on this field have appeared in
recent years.["]
In the past two decades organoactinide chemistry has
fluorished with the synthesis of the first isolable compounds
containing uraniumxarbon o bonds in 1973,['31the discovery of facile activation of CO by thorium and uranium alkyls
in 1978,["] the synthesis of the first uraniumxarbon multiple bond in 1981,[15]the synthesis of the first compounds
containing supported['61 and uns~pported[''~metal-metal
bonds involving an actinide element in 1985, the synthesis of
the first molecular actinide carbonyl complex that is stable at
room temperature in 1986,"'] and the synthesis of both the
first mixed C,H,-Cp complex of an actinide metal['91 and
the first neutral homoleptic uranium alkyl complex in
1989.[201All but the last of these significant developments
have involved organoactinide complexes with Cp or substituted Cp ligands.
In this review, we will present the development of bonding
models for Cp-actinide complexes, a topic that has been
studied in detail only in the last decade. We will focus particularly on the use of molecular orbital (MO) theory as an
electronic structural probe of these systems. When possible,
we will discuss the relationship of the MO results to experimental studies, particularly those involving photoelectron
spectroscopy (PES), which has been the most widely used
experimental probe of bonding in organoactinide chemistry.["] We begin with a brief historical discussion of the
challenges posed by the presence of valence f orbitals. The
remainder of the discussion is separated, somewhat arbitrarily, into a focus on Cp-to-actinide bonding and the bonding
of Cp-actinide complexes to other ligands.
2. The Electronic Structural Challenge
of the 5f Elements
Although the development of organoactinide chemistry
came shortly after the birth of modern organotransition-
0 VCH
Verlugsgesellschufi mbH, W-6940 Weinheim,1991
0570-0833191jO909-1069$3.50+ .25/0
1069
metal chemistry, the level of understanding of the former has
lagged well behind that of the latter. For example, in transition-metal organometallics, the effective-atomic-number (or
eighteen-electron) rule allows one to predict, a priori, the
existence and inherent stability of many compounds. No
such rule exists in organoactinide chemistry : compounds
have been reported with formal electron counts as low as
nine, [U{CH(SiMe,),},],[201 and as high as twenty-eight,
The reasons for the comparatively low
[Cp,Np . 3 thfl
level of understanding of the bonding in organoactinide
complexes are manifold: (1) There is a paucity of experimental results in organoactinide chemistry relative to organotransition-metal chemistry. The high radioactivity and transient existence of most actinide elements preclude systematic
studies of organoactinide complexes in which the metal atom
is varied. Thorium and uranium are the only actinide elements that are relatively easy to study in the laboratory. (2)
The large sizes of actinide atoms lead to highly variable and
unpredictable coordination numbers. ( 3 ) The number of
electrons in organoactinide complexes is large enough to
make rigorous quantum-chemical calculations exceptionally
demanding computationally. (4) Relativistic effects are profound for the actinide elements. Although there have been
numerous studies demonstrating the importance of relativistic effects in the heavy
these phenomena remain
poorly understood by many chemists, hindering the understanding of electronic-structure results on the actinide elements. ( 5 ) Actinide metals contain valence f orbitals, with
which many chemists are uneasy.[241Furthermore, the computer codes for many quantum-chemical methods are not
able to accommodate valence f orbitals.
Even before the emergence of organoactinide chemistry,
the relative importance of the valence 5f orbitals in describing the bonding and electronic structure in actinide compounds had been, and continues to be, a question of considerable debate among theoretical and experimental chemists.
In one of the earliest references to f orbitals, Van Vleck point-
ed out that they are essential for describing the bonding in
complexes with high coordination numbers (as are commonly found in organoactinide complexe~).[~
'] Eisenstein used a
group-theoretical approach to argue for the involvement of
5f orbitals in covalent bonding in [UO,]'+, [VCI,], and
[UCl,] .Iz6]
Kettle and co-workers presented stereochemical
arguments for f-orbital involvement in bonding,r2'] but later
concluded that f-orbital bonding is usually weak because of
the small size and energetic inaccessibility of the f orbitals.[281
The first chemical evidence that 5f orbitals are involved in
bonding was presented by Glueckauf and McKay in 1950 in
connection with their work on uranyl nitrate.[291These conclusions were challenged less than five months later by Katzin,[301
starting the persistent controversy over the bonding in
the uranyl ion.[311Further work in the 1950s on uranyl and
uranyl-like ions also focused on the question of f-orbital
participation in bonding.[321Coulson and Lester surveyed
this early work and concluded that f-orbital covalency is
significant, although they suggested that the important orDifferences in
bitals are the 6f rather than the 5f
the complexing behaviors of the lanthanide and actinide
halides led Seaborg and co-workers to invoke hybridization
of the 5f, 6d, and 7s orbitals in order to account for the
greater tendency of the actinides to form covalent complex
The question of f-orbital participation has also been at the
fore of organoactinide chemistry. Moffitt reported a qualitative discussion of the orbital interactions in [Cp,U]+ in the
report of the synthesis of Z.[351An early review on bonding
in f-element organometallics concluded that the properties
of these materials, both chemical and physical, are intermediate between the covalent organotransition-metal complexes and the ionic carbocyclic salts of the alkali
It
further noted that evidence exists for some appreciable f-orbital contribution to the bonding in the early An'" complexes. Later empirical studies of the bonding have concentrated
on trends in molecular geometry and steric factors. One such
Bruce E. Bursten was born in Chicago, Illinois, in 1954. He received his S. B. degree with honors
in chemistry from the University of Chicago (1974) and his Ph.D. degree (with R. E Fenske)
form the University of Wisconsin (1978). Following two years as an NSF Postdoctora! Fellow
at Texas A & M University (with E A . Cotton), he joined the faculty of The Ohio State
University, where he is currently Professor of Chemistry. He has been a Fellow of the
Alfred P. Sloan Foundation and a Camille and Henry Dreyfus Foundation Teacher-Scholar and
he has received both the Distinguished Teaching Award and the Distinguished Scholar Award at
his university. His research interests include the electronic structure of transition-metal and
actinide complexes, organometallic photochemistry, metal-metal bonding, and applied quantum
chemistry.
Richard J. Strittmatter was born in Washington, DC, in 1963. He received his B. S . degree in
chemistryfrom Wake Forest University (1985) and his Ph.D. degree in inorganic chemistry (with
B. E. Bursten) from The Ohio State University (1990). He spent six months of his graduate
studies at Los Alamos National Laboratory under the supervision of Dr. A. P. Sattelberger. His
dissertation research involved computational and experimental investigations of the bonding and
electronic structure of organoactinide and related transition-metal compounds. He is currently a
Senior Chemist at Nalco Chemical Company in Naperville, Illinois, where he is a member ofthe
Advanced Recycling Technologies Department in the Water and Waste Treatment Division.
1070
Angew. Chem. I n [ . Ed. Engl. 30 (1991) 1069-1085
study, based on the limited number of structures available at
the time, concluded that the bonding in organoactinides is
predominantly ionic.[37]A cone-packing model based on
steric effects has been developed and used to explain molecular geometry, reaction pathways, ligand rearrangement,
and di~proportionation.[~~]
One very recent study defines a
“steric coordination number” that can be used for molecular
structure comparison and bond-length prediction,[391while
another uses statistical analysis of structural data to seek
evidence for covalency in Cp complexes of the alkaline earths
and f elements.[401The debate over metal-ligand covalency
in organoactinide complexes is clearly an unresolved issue.1411
3. Cyclopentadienyl-Actinide Bonding
Because the Cp ligand has such a dominant role in organotransition-metal chemistry, actinide cyclopentadienyls lend
themselves more readily to comparison with transition-metal
systems than do the actinocenes. A major theme of this section will be the similarities and differences in the bonding of
Cp ligands to actinides and transition metals. In one of the
first direct theoretical comparisons of the bonding of a Cp
ligand to an actinide and a transition metal, Tatsumi and
Hoffmann used quasi-relativistic extended Hiickel (EH)
molecular orbital theory[421to compare the interaction of a
Cp- ligand with a U 6 + (5f‘) and an Fe2+ (3d6)
They
found a vanishingly small U-Cp overlap population for
[CpU]’ in contrast to a sizable one for [CpFe] . This report
suggests that the interaction between Cp and U“‘ is largely
ionic, consistent with the fact that only a very small number
of organoactinide complexes contain neutral n-donor ligands. It is apparent, however, that covalency could become
more important for lower oxidation states of uranium; most
known actinide cyclopentadienyls involve metals in a formal
+ 3 or 4 oxidation state, and we will focus on these systems
in the ensuing discussion.
+
L
d
+
+
3.1. Tetrakis(cyclopentadieny1) Complexes
[Cp,An] compounds (3) have been synthesized for An =
Th,[3b1Pa,1441U,[3a1and NP.[~’’ The crystal structure of
[Cp4U] shows that it is pseudotetrahedral with all four Cp
ligands bound in an q5 fashion.[461From the isotropic ‘H
NMR shift in [Cp,U], a total spin delocalization of 24 % was
estimated over the four Cp ligand~,[~’Ia result that seemed
incompatible with the rather long U-C distance and the
generally contracted radial distribution of 5f orbitals. Although aspects of this work were questioned,[481the temperature dependence of the paramagnetic shift between 165 and
428 K confirms the original indication of a remarkably large
indirect electron-spin transfer.[491
The 237NpMossbauer spectrum of [Cp4Np] shows an
isomer shift of + 0.72 cm s - ~ , [ ” ]appreciably different from
those of ionic Np” compounds. This observation suggests a
significant electron contribution from the Cp ligands to the
metal orbitals in [Cp4Np], although not as great as that
found for [(q8-C,H,),Np]. This spectroscopic evidence for
covalent contributions to the bonding in [Cp,Np] agrees
with chemical evidence for covalent contributions to the
Angen,. Chrm. Int. Ed. Engl. 30 ( 1 9 9 / ) 1069-1085
bonding in [Cp3UC1], which does not react with FeCI, to
form ferrocene.[’]
Many theoretical studies of the electronic structure of
[Cp,An] systems have been undertaken. In an effort to interpret the temperature dependence of the magnetic susceptibility of [Cp4U], calculations were performed on the model
tetrahedral system [(q6-C,H6),An] .I5’]
Three different
semiempirical approaches were used, all of which led to essentially the same results and successfully simulate the temperature dependence of the magnetic susceptibility. In a
related study, the bands of the room-temperature absorption
spectrum of [Cp,U] have been identified, with good agreement between observed and calculated values.[’ ’]
Quasi-relativistic EH and Xa-SW molecular orbital calculations on [Cp,Th] and [Cp,U] have been reported.[521In
both the EH and Xu-SW results, the calculated molecular
orbitals are energetically grouped in a fashion well described
by tetrahedral symmetry (Fig. 1). Apart from a small An 7 s
t2
uL’
e
3
------al
ICp,UI
XI
a,
(V5-Cp)t-
cp-
Fig. 1, Qualitative MO diagram of [CpIU] under pseudotetrahedral symmetry.
contribution, the Xa-SW results show no important metal
contributions to the Cp n1 orbitals. The Cp n, orbitals donate significantly into both the An 5f and 6 d orbitals; the
ligand donation into the metal 6d orbitals is comparable to
or even greater than the donation into the metal 5f orbitals.
It was shown further that donation into the 6d orbitals is a
more stabilizing interaction than donation into the 5 f orb i t a l ~ . Under
~ ~ ~ ] tetrahedral symmetry, the energetic ordering of these Cp n,-based orbitals was calculated to be
t , > t , > e. The HOMO of the uranium complex is essentially a pure 5f atomic orbital, in which the two unpaired metalbased electrons reside. In general, the EH calculations show
much less metal 5f and 6 d involvement in the metal-ligand
bonding orbitals than do the Xcr-SW calculations.
Prior to these calculations, the valence PE spectra of
[Cp,Th] and [Cp,U] were reported.[541 Four ionization
bands are evident in the 6-10-eV ionization energy (IE)
region of [Cp4U](Fig. 2). As is the case for uranocene,[’O1the
first ionization band is readily assigned to ionization of the
U-based 5 f electrons. The other three bands are due to the
ligand-based n, MOs. On the basis of relative band intensities under both He(1) and He(I1) ionization sources, the authors assigned the Cp x2 ionization energies in the order
1071
t , < e < t , . In conjunction with the above EH and Xu-SW
calculations, the He(1) and He(I1) PE spectra of the methylsubstituted cyclopentadienyl complexes, [CpkTh] and [CpkU]
(Cp’ = $-C,H,CH,), were also reported.[521A satisfactory
agreement was found between the calculated Xu-SW transition-state IEs and the experimental ones, although the calculated values are uniformly too low by about 0.3 eV. The
calculations support an assignment for the Cp K, ionizations
of t , < t , < e, in disagreement with the earlier assignment
The authors therefore questioned the
made by Green et
assumption that the increase in the He(1I) PE cross section is
greater for the 5f orbitals than for the 6d
8
He-I
8
3
IE[eVI
-
9
8
He-II
-
8
9
IE[eVl
7
10
10 12
6
1L
10 14 18
. -
16 1.8
3.2. Tris(cyclopentadieny1) Complexes
The binding of three q5-Cp ligands is arguably the most
common coordination sphere found in organoactinide complexes. For actinides in the + 3 oxidation state, both the
“base-free” [Cp,An] complexes (5) and those with an additional bound Lewis base, [Cp,AnL] (6), are commonly
known. The tetravalent actinides often form neutral complexes of the type [Cp,AnX] (7), where X is a formally anionic ligand such as halide or alkyl. In this section we will focus
on the bonding of the three Cp ligands to the actinide center;
the discussion of the An-L and An-X (5 bonds is deferred to
Section 4.
Compounds 5 are known for the actinide elements from
Th to Cf, and the Cm and Cf adducts represent the only
well-characterized organometallic compounds of those elements. Two such compounds have been structurally characterized: both [ C ~ ; ’ T h l [ (Cp”
~ ~ l = q5-1,3-(Me3Si),C,H3) and
[Cp;’’U][571(Cp”’ = q5-Me,SiC,H4) exhibit planar, pseudoD,, structures with respect to the metal-Cp(centroid) vectors. Compounds of type 6 or 7 are pseudotetrahedral molecules in which the centroids of the Cp rings occupy three
v e r t i ~ e s . [ ~ *These
- ~ ~ ] molecules have actual or near C,,
point symmetry.
22
5
He-l
fi
6
7
Placing Cp ligands in threefold symmetry about a metal
center imposes interesting symmetry restrictions on the metal-ligand interactions. This fact was first recognized by M O J
f i t t , who presented a qualitative treatment of the orbital
interactions in [Cp,U]+ as part of the paper on the synthesis
of [Cp3UCI].[351 Under C,, symmetry, the K, orbitals of the
Cp ligands are bases for the a , az 2e representations.
The symmetry-allowed metal-ligand orbital interactions are
given in Table 1 . It is particularly notable that the ligand-
+ +
6
8
10
IEleVI-
-
6 8 10 12 I(. I6 18 20
IE[eVI
Fig. 2. He(1) and He(I1) photoelectron spectra of [Cp,Th] and [Cp,U] [54].
Table 1. Metal orbital interactions with Cp:- under C,, symmetry.
~
Cp:
Because the coordination of four $-Cp ligands is unique
to the 5f elements, the preference of actinides for q5- over
q’-Cp bonding has been studied. Tatsumi and Nakamura
have used EH calculations to compare [($-Cp),U] and [($Cp),(q’-Cp)U], the latter being similar to the well-known
[Cp3UR](R = alkyl) complexes. They find [($-CP)~U]to be
more stable than [(q5-Cp),(q1-Cp)U], in agreement with ex~ e r i m e n t . [ Similar
~~]
calculations on the ally1 derivatives
[Cp,U(q3-allyl)] and [Cp,U(q’-allyl)] predict the latter to be
more stable than the former, again in agreement with experiment. The authors propose that the preference for monohapto over polyhapto coordination is a consequence of several delicately balanced factors, including the fact that q’-allyl is a stronger (5 donor than ql-Cp.
1072
~
orbital
Metal
s, p, d orbitals
f orbitals
e
a2
based a, orbital cannot interact with s, p, or d orbitals on the
central metal, but is allowed to interact with one of the f
orbitals. This observation has been used to explain how
the seemingly 20-electron transition-metal complex [(q5Angew. Chem. I n l . Ed. Engl. 30 (1991) 1069-1085
Cp),(q'-Cp)Zr] is, in actuality, an 18-electron complex that
satisfies the effective-atomic-number rule.1611The allowed
interaction of the u2 ligand-based orbital with an f orbital
has been proposed as a reason for the abundance of [Cp,An]
complexes vis-a-vis the scarcity of [Cp,M] complexes among
the transition metals.[621
Quantitative MO calculations on [Cp,An] systems corroborate Moffitt's symmetry analysis. EH calculations on
[Cp,U]' indicate 8 Yo U 5f contribution to the ligand-based
a2 orbital.[55] Quasi-relativistic Xa-SW calculations on
[Cp,U] put the U 5f contribution at 2 9 % 0 . [ ~
These
~ ] latter
calculations were also used to analyze the other donations
from the n2 orbitals of the Cp;- ligand fragment to the U3+
center. The ligand e orbitals, which can donate to the U 5 f,
6d, or 7 p orbitals, preferentially interact with the 6 d orbitals, as was found for the [Cp,An] complexes. Thus, only
the 5f orbital of a, symmetry is significantly affected by the
ligand field. The ligand a , orbital, which is spatially less
favorable for interaction with the 6 d,, orbital, interacts more
weakly with the U atom than the other ligand orbitals. The
overall result of these interactions is depicted in Figure 3.
ground electron configuration. The Xa-SW calculations
showed an exceedingly small energy difference between the
5f26d' and the 5 f36d0 ground electron configurations for
[Cp,U] , although more rigorous calculations that include
spin-orbit coupling favor the 5 f36do configuration.[65]
The nature of the An"'-Cp bonding has been investigated
spectroscopically and chemically. An early study involved
estimation of the nephelauxetic parameters of [Cp,Am] and
[Cp,Cm] by a comparison of their visible absorption and
emission spectra with those of the aqueous ions.[661Although the parameters are greater than those of [Cp,M]
compounds of the lanthanide series, the covalency relative
to the aqueous + 3 ions of 2.8 YOand 2.5 % for [Cp,Am] and
[Cp,Cm], respectively, is indicative of highly ionic
organometallic bonding. The Mossbauer isomer shift of
[Cp,Np. thfl ( + 3.64 cms-') is very close to that of
[NpCI,] (+ 3.54 cm s- I ) , suggesting very little difference in
the bonding of the Cp and CI ligands.[221Protolysis of the
metal-Cp bonds in [Cp,U] [Eq. (a)] has been taken as
chemical evidence for significant ionic character in the
metal-ligand bonding.[671
[Cp,U]
-2
4
\
\
\
\
t
-3E lev1
-4
-
-5 -X
Fig. 3. MO diagram showing the interaction of Cp:- with U 3 +to form [Cp,U]
~91.
A molecular orbital comparison of the bonding in [Cp,U]
and [UCI,] indicates significantly greater ligand-to-metal donation in the former than in the latter.[621Similar conclusions were drawn in a comparison of [Cp,U] and [UC14].[531
The greater donation by Cp was taken as evidence of greater
covalency in U-Cp bonding than in U-Cl bonding.
EPR spectra of powdered samples and solutions of
[Cp;'Th] were obtained in the temperature range 10300 K.[631Using a simplified crystal field model, the authors
found that the data are only consistent with a 5 f06d' ground
electron configuration for the Th"' compound. This conclusion was corroborated by quasi-relativistic Xa-SW calculations on [Cp,Th],[641which showed a single 6d orbital lower
in energy than the Th 5 f block of orbitals. These authors also
investigated [Cp,An] compounds where An = Pa to Pu, and
found that the 5f block of orbitals was lowered in energy
across the series, while the energy of the 6d-based a, orbital
increased slightly. These results led to the predictions that
[Cp,Pa] should have a 5f16d1ground electron configuration
and that the transuranium compounds should have a 5 f"6 do
Angen.. Chem. I n t . Ed. Engl. 30 (1991) 1069-1085,
+ HCN
--t
[Cp,(CN)U]
+ C,H,
(a)
A preliminary account of the bonding in the transuranium
[Cp,An] compounds compares the [Cp,An] series to the corresponding [AnCI,] compounds.[68]Proceeding from Th to
Cf, the 5f orbitals drop dramatically in energy for [AnCI,]
compounds. Although the same qualitative trends are followed in the [Cp,An] series, the Cp ligand is a much better
donor to the actinide metal than the C1 ligand and consequently buffers the charge on the metal, resulting in a much
less dramatic 5f orbital energy drop.[691
[Cp,ThX] and [Cp3UX] compounds (7), including Th"
and U" compounds with the modified Cp ligands Cp' and
indenyl, have been extensively investigated by PES.154.7 0 - 7 2 1
The lowest ionization band in the U'" complexes, at 6.5 to
7.0 eV, is not present in the Th" compounds and is therefore
assigned to the 5f2 electrons of U". This assignment has
been corroborated by He(I1) spectroscopic studies. As expected with a change in oxidation state of the metal, the first
ionization band in the U"' complex [Cp,U . thfl occurs at
lower IE than in the U" complexes.[541
The ionizations due to the Cp n, orbitals in both [Cp,ThX]
and [Cp3UX] complexes appear as three bands in their PE
spectra. The ionization energies vary with the nature of the
Cp ligand in the order indenyl < Cp' < Cp. Comparison of
the He(1) spectra with the He(I1) spectra indicates much
greater 5 f-orbital participation in the metal-ring bonding in
the uranium compounds than in the thorium compounds
(Fig. 4). Moreover, the spectra indicate that the 5 f covalency
in the indenyl compounds is much greater than in the unsubstituted Cp corn pound^.^^^^
All [Cp,AnX] compounds with X = CI exhibit one ionization band slightly above the Cp K, bands, which is assigned
to ionization from a lone pair of the chloride ligand (band d,
Fig. 4).t711This assignment is supported by a shift of this
band to lower energy when X = Br or OCH,, and by its
complete absence when X = BH, or CH, .
Nonrelativistic DV-Xa calculations on [Cp3UX] (X = F,
C1, Br) have been performed in conjunction with a PES in1073
a
iy
h
p dd)H.w
J
b)
neii
m b
titi
6
8
6
10
IE[eVl
.
8
10
6
8
x
)
IE[eVI
v e s t i g a t i ~ n . The
~ ~ ~above
]
general assignments agree quite
well with the calculations. Transition-state ionization energies were calculated for [Cp3UCI]and are in good agreement
with experiment, including the correlation between the relative intensities of the He(1) spectra and orbital population
analysis. The uranium 6 d contribution to the metal-ligand
bonding orbitals appears to be underestimated in the calculations owing to the nonrelativistic approach.
3.3. Bis(cylcopentadieny1)actinide Complexes
A multitude of early-transition-metal [Cp,MX,] compounds are known, and their chemistry has been studied
extensively. The corresponding An" complexes with unsubstituted cyclopentadienyl ligands, [Cp,AnX,], are a relatively uncommon class of compounds, largely because of the
high affinity of the actinide centers for Cp ligands. Thus, the
reactions of [AnCI,] with cyclopentadienide salts generally
yield either [Cp,AnCl] or [ C P ~ A ~ ] it; [is~ not
* ~ possible
~
to
"stop" the reaction at [Cp,AnCI,] .[731 Some [Cp,AnX,]
complexes have been isolated when X is a strong n-donor or
chelating bidentate ligand.[741
Sterically hindered cyclopentadienyl ligands, especially
pentamethylcyclopentadienyl(Cp *), have been used to generate bis(cyc1opentadienyl)actinide complexes. For example, the reaction between [AnCI,] and [Cp *MgCI] leads to
the replacement of two CI ligands by Cp * ligands, yielding
[Cp;AnCl,] (8; An = Th, U).t751Complexes 8 are structurally analogous to transition-metal [Cp,MX,] and [CpTMX,]
systems, with a pseudotetrahedral geometry about the ac-
8
1074
6
8
1
)
Fig. 4. Low-energy region of He(1) and He(I1)
spectra of a) ILT(indenyl),CI], b) [Th(indenyl),CI],
c ) [U(indenyl),CH,], and d) [Th(indenyl),CH,] [70].
tinide
Because the ligand array in 8 is identical
to that of well-characterized transition-metal systems, the
direct comparison of homologous actinide and transitionmetal complexes is facilitated.
The valence PE spectra of [CpfThCI,] and [CpTUCI,] are
quite similar to those of analogous Zr and Hf comp o u n d ~ . [781
~ ~The
. first ionization band of the uranium complex is due to the 5f electrons of this fz complex. The ionization bands due to the Cp n, orbitals are lower in energy than
the bands due to the chloride lone pairs in [Cp:MCl,]
(M = Zr, Th, U); this ordering is reversed in [Cp,WCI,].
Furthermore, the bands assigned to the Cp n2 orbitals are
essentially isoenergetic for the [Cp:MCl,] complexes, suggesting that either the metal-ring bonding is similar for the
three compounds or that metal-ring interactions are of little
importance in determining the relative energies of these ring
molecular orbitals. Comparison of these compounds with
several Cp-containing organometallic compounds indicates
that the metal-ring bonding in these organoactinides tends
to be much more ionic than the bonding in [Cp:MoCI,] and
[Cp,VCI], although it is less ionic than in lanthanide compounds such as [(Cp,GdCI),] and [(Cp,YCI),] .lS4]
Comparison of the PE spectra of [CpTAnMe,] compounds with those of the dichlorides reveals the greater electron-releasing ability of the two methyl ligand~.[~']
The 5f
ionization in [CpTUMe,] is at lower IE than that in
[Cp:UCI,] although the energy difference is much smaller
than would have been expected in a similar d Z system. The
Cp n, bands, which are also at lower IE than in the chloride
complexes, show greater energetic dispersion in the actinide
spectra than in the spectrum of [CpzZrMe,], probably due
to enhanced metal-ring interaction involving the 5 f orbitals.
PES investigations of [Cp,UX,] compounds with unsubstituted Cp ligands and chelating or n-donating X ligands
have been
The lowest-energy ionization band in
each of these compounds is due to the 5fz electrons of the U'"
metal center, with the energetic ordering inversely related to
the electron-donating ability of the ligand X: S,CNEt,
(6.19 eV) < NEt, (6.24 eV) < O,CC(CH,), (6.73 eV) <
Angew. Chem. Znf. Ed. Engl. 30 (1991) 1069-1085
BH, (7.97 eV). For [Cp,U(BH,),], which has no low-energy
bands due to ionization from the BH, ligands, the next three
lowest bands have a 1 :2:1 ratio and are due to ionizations
from the Cp x2 orbitals. The splitting between the extremes
of these bands is comparable to that of other [CpTUX,]
complexes; as expected, the splitting is smaller than that of
the Cp K, bands in [Cp,UX] compounds or Cp,U. The large
energy dispersion of the x, ionization bands and their variable He(I)/He(II) intensity ratios indicate that the splitting is
not solely due to interligand repulsion, and it was concluded
that there is a sizable interaction between Cp x 2 molecular
orbitals and uranium 5f and 6d orbitals. The pivalate complex [Cp2U{0,CC(CH3)3},], which is dimeric in soluti~n,['~
possesses
~l
a pseudooctahedral geometry and is more
sterically crowded than other [Cp,UX,] systems. The greater
repulsion within the Cp, framework results in a broad featureless band for the Cp x2 ionizations of this complex. The
spectra of the NEt, and S2CNEt, complexes are complicated
by the overlap of bands due to ionizations from nitrogen 2 p
lone pairs and from sulfur 3 p lone pairs, respectively, with
the Cp x 2 bands. Nevertheless, in the case of the amido
complex, the authors assigned the lowest of these bands to be
nitrogen lone-pair orbitals, whereas for the dithiocarbamate
complex the lowest-energy band is assigned to the Cp n2
orbitals.
The PES results have been used to rationalize the reactivity of these complexes.[791The IEs of the Cp x 2 orbitals in
[Cp,U(BH,),] are the highest yet observed for [Cp,UX,] and
[Cp:UX,] complexes, consistent with the high stability and,
hence, the low reactivity of the complex. With the exception
of the 5f2 electrons, the highest occupied orbital of
[Cp,U(NEt,),] is an almost pure nitrogen 2 p lone pair, consistent with the higher reactivity of the complex toward molecules containing dipolar double bonds and acidic hydrogens. In [Cp,U(O,CCMe,),] and [Cp,U(S,CNEt,),], the orbital immediately below the 5f2 electrons is localized on the
Cp ligands, but is energetically close to molecular orbitals
centered on the X ligands. These relative orbital energetics
could be responsible for the greater lability of the U-Cp
bonds in these complexes relative to [Cp,U(NEt,),], in
which the U-N bond is more labile.
The bonding in [Cp:UX,] (X = C1, Me) has been studied
via quasi-relativistic Xa-SW calculations on the corresponding Cp complexes.[801Although the calculated IEs are uniformly too low, the calculated band splittings are in excellent
accord with the experimental PES data, indicating that the
extent of the uranium-ligand interaction is properly estimated by the quasi-relativistic calculations. The bonding of the
Cp rings is similar in the two compounds, with sizable contributions from the metal 6d and 5f orbitals. The CH; ligand
is a stronger o donor than the CI- ligand, as evidenced by
the higher energy of the 5f orbitals in [Cp,UMe,] than in
[Cp,UCI,]. The calculations show no evidence that CI- acts
as a x donor to uranium. Support for this conclusion comes
from a comparison of [Cp,UCl,] with [Cp,U] and [UC1,].[531
The 5f block of orbitals in [Cp2UC12]is much closer in energy to the corresponding block in [Cp4U] than in [UCI,]; the
energy of the 5 f orbitals is principally governed by interaction with the Cp ligands. The remaining two U'" electrons
are in essentially pure uranium 5f atomic orbitals that are
clustered in a narrow band, consistent with the paramagAngew. Chem. Int. Ed. Engl. 30 (1991) 1049-1085
netism of the molecules. By contrast, analogous calculations
on [Cp,MoCI,] predict it to be diamagnetic, again consistent
with experiment.
4. Cyclopentadienyl-Actinide Complexes
with a-Bonded Ligands
In addition to An-Cp bonds, the [Cp,AnL], [Cp,AnX] ,
and [Cp,AnX,] complexes discussed in the preceding section
also contain (3 bonds between one or more ligands and the
actinide atom. The nature of these actinide-ligand o bonds
and their similarities to and differences from actinide-ligand
R bonds are the focus of this section.
The differences between o and x bonds involving the actinide atoms was first addressed theoretically by Tatsumi and
H0ffmann.[~~1
Using extended Huckel theory, they found a
far more substantial interaction between a CH; ligand and
a U6+ ion than between a Cp- ligand and the same ion. The
U-C overlap population in U-CH;+ is large and comparable to that found for Fe-CH; . The U 5 f,, ,6d,, , 7 s, and 7 p,
orbitals all contribute to the U-C o bond.
4.1. Tris(cyclopentadieny1)actinide Complexes
4.1.1. The Nature of An-X n Bonding
As mentioned in Section 3.2, when a fourth ligand binds to
a [Cp,An] fragment, the Cp ligands pyramidalize to open a
coordination site for the ligand to approach. Quasi-relativistic EH calculations on [Cp,U]' show that, upon pyramidalization, orbitals possessing primarily uranium 6 d character
are stabilized owing to increased 6d-7p mixing.[551This effect is most pronounced for the 6d,, orbital and the 7p,
orbital, resulting in an energetically low-lying, hybridized
a-bonding orbital situated to accept electron charge from an
incoming fourth ligand. This orbital, which is primarily uranium 6d,,, is approximately 4 eV above the 5f block of orbitals in the EH calculations.
Xa-SW results also indicate a low-energy o-bonding orbita1;[641however, this orbital is approximately isoenergetic
with the 5f block of orbitals in [Cp,U] and is actually lower
in energy than the 5f block of orbitals in [Cp,Th] (cf. Section 3.2). The different oxidation states of uranium in
[Cp3U]+and [Cp,U] could account for some of the energetic
discrepancy between the EH and Xa-SW results, and the two
methods differ in the energetic placement of the 5 f orbitals
relative to the 6 d orbitals. As was the case in the EH calculations, the Xa-SW results also show hybridization of this
orbital upon pyramidalization of the Cp ligands.
Ziegler et al. have used local density functional (LDF)
theory to study the An-R o-bond energies in [CI,AnR]
(An = Th, U ; R = H, CH,) complexes.[811Their methodology employed Becke's density functionalt821and the HartreeFock-Slater LCAO program of Baerends et al.1831In addition to nonrelativistic calculations on the molecules, two
levels of relativistic correction were studied: a first-order
relativistic method based on perturbation theory, and a
quasi-relativistic method based on optimization of the valence density with respect to the first-order relativistic
1075
Hamiltonian. The authors found that the bond energies calculated by the latter method were in excellent accord with the
experimental An-R bond energies for [Cp:An(R)(CI)] comp l e x e ~ .Interestingly,
~~~~
the nonrelativistic calculations,
which give very poor calculated bond energies, indicate that
the An 5 fz3orbital is the most important one in the formation of the An-R bond. When the quasi-relativistic method
is used, the energy of the 5f orbitals increases; as a result,
the 6d,, orbital becomes the dominant An orbital in the
bond.
It is clear from all of the above studies that a hybridized
o-bonding orbital possessing primarily 6d,, character is responsible for the high Lewis acidity of [Cp,U]. An Xu-SW
investigation of the interaction of [Cp,U] with a hydride
ligand, to form the hypothetical “o-only” compound
[Cp,UH], indicates that the metal participation in the U-H
bond is indeed dominated by the 6d,, orbital with minor
contributions from the 5 fz37p,, and 7s orbitals.[621Also, the
5f block of orbitals in [Cp,U] shows no increased splitting
upon interaction with the hydrogen atom, further supporting the minor role of the 5f orbitals in (3 bonding. The
authors note that this o-bonding interaction is typical for all
Cp,U-X or Cp3U-L o bonds. It is interesting to note here
a suggestion, based on thermochemical data, as to why
[Cp3UH]has never been isolated despite numerous synthetic
attempts.1851If the bond disruption energy D(U-H) is assumed to be 10 kcalmol-’ greater than D(U-CH,), then
bimolecular H, elimination from [Cp3UH] may be sufficiently close to thermoneutrality to be entropically driven.
Support for this notion comes from the results of LDF calculations on [CI,AnR]
which indicate that
actinides, like the early transition metals,rS6]form bonds of
nearly equal strength to hydrogen and alkyls.
140-1
130j
[ kcal mol-’]
90
- 60
20
40
30
50
60
80 90
-
70
D(U-R 11 kcal m d ’ l
Fig. 5. A plot of U-R bond energies in [CpTUR] versus R-H bond energies
wl.
Among the alkyl groups studied thermochemically, the
U-CGCPh bond is the strongest, consistent with the relative
shortness of the U-C bond in [Cp,UCrCPh].[871EH studies
of [Cp,UR] complexes indicate a significant increase in the
U-C overlap population of the model complex
[Cp,UC-CHI relative to [Cp,UCH,].[551 Interestingly, o
interactions in [Cp,UC-CHI account for half of the increase
in the overlap population, indicating that rr interactions are
less important than might be inferred from the short U-C
bond. Thus, the calculated results are in good accord with
the conclusions of the thermochemical studies.
4.1.3. An-X Multiple Bonds and n Bonding
Cramer, Gilje et al. have explored multiple U-C bonding
in [Cp3UR] systems where R is a ph~sphoylide.~’~]
The U-C
bond in [Cp,UCH{P(CH,),(C,H,)}] (9) is the shortest yet
4.1.2. An-X Bond Energies
Marks and co-workers have reported extensive thermochemical studies of the nature of actinide-ligand o bonding.
A thermochemical study of alkyl adducts of [Cp,U] reveals
that the U-R bond energies, D(Cp,U-R), span a wide
range of about 58 kcal mol- .IB5]
These values are roughly
20 kcal mol - lower than the analogous D(Cp,UR-R)
values; this difference is attributed to the greater steric congestion in the [Cp3UR]systems. The experimental bond energies indicate that severe nonbonded interligand repulsions
destabilize the U-R bond in [Cp,UR]. The bond enthalpies
for [Cp,UR,] and [Cp3UR] follow qualitatively similar
trends with U-Me 2 U-CH,CH,CH,Me > U-CH,Ph.
Consistent with the calculations of Ziegler et al.,r81Jthe actinide-alkyl bond enthalpies parallel those of the group 4
transition-metal complexes. A plot of D(Cp3U-R) versus
D(R-H) shows a roughly linear correlation (Fig. 5). The
greatest deviations are observed for R = nBu and R =
CH,Ph, for which the D(U-R) values are lower and higher
than anticipated, respectively. The deviation in the former
may reflect the steric demands of the nBu ligand, while the
deviation in the benzyl complex may be indicative of inductive effects in the benzyl ligand. Both R = vinyl and R =
CZCPh fall on the linear plot, evidence that U-R K bonding
is not a major effect.
’
1076
’
cp,u -c
/H
\PMe,Ph
-
cp,u=c
\
PMe,Ph
s+
9
observed (2.29 A); even after correcting for the difference in
hybridization of the carbon atom, the U-CH(PR,) bond is
still 0.11 A shorter than the uraniumxarbon bond in
[Cp,U(nB~)l.[~
~ lwas the case for [Cp,UC=CH], EH
As
calculations on the model complex [Cp,UCHPH,] show a
significant increase in the U-C overlap populations relative
to [Cp,UCH,] .[551 In contrast to the acetylide complex, however, this increase is almost entirely due to a n interaction
between the C pn orbital of CHPH, and the uranium Sf,,,,
(7%), 6d,, (2%), and 7p, (1 YO)
orbitals.
The n-bonding effects have been found to be important in
[Cp3UL]compounds where the fourth ligand is not an alkyl.
For example, phosphite (P(OR),) and isocyanide (CNR)
ligands, which are generally classified as rr-acceptor ligands,
bind more strongly to [Cp,U] than do pyridine, THF, or
nitriles, which are o-only ligand~.[*~]
Andersen and Brennan
demonstrated that exposure of carbon monoxide to a hydrocarbon solution of [Cp;”U] leads to quantitative evidence for
Angew. Chem. h i . Ed. Engl. 30 (1991) 1069-1085
U-L IT bonding.“ ‘1 The carbonyl adduct, [Cp;’UCO] (lo),
exhibits a carbonyl stretch in the IR spectrum at vco =
1976 cm- about 170 cm- lower than ,v for free carbon
monoxide. This lowering of the C-0 stretching frequency is
indicative of metal-to-carbonyl n back-bonding.
’
’,
Me,Si
10
The electronic structure of 10 has been investigated via
quasi-relativistic Xa-SW calculations on the model complex
[Cp,UCO].[90] The U-CO o bond is similar to the U-H o
bond discussed above, with the CO carbon “lone-pair’’ orbital donating into the predominantly U 6 d,, o-acceptor
orbital. A significant x interaction occurs between the CO x *
orbitals and the U 5 fx orbitals. The resultant doubly-degenerate U-CO x-bonding molecular orbital is stabilized below
the remaining 5 f block of orbitals. As such, it is the HOMO
of the complex, and, consistent with the experimental findings, it represents significant metal-to-carbonyl x backbonding (Fig. 6). The interaction of [Cp,U] with the even
stronger x acid NO to give the hypothetical [Cp,UNO] complex results in greater x back-bonding, which would stabilize
the HOMO more than in [Cp,UCO].[62J Because NO has
one more electron than CO, it is predicted that this still
unknown molecule could be the first diamagnetic U’” compound.
Fig. 6. Contour plot of the HOMO of [Cp,UCO] in a plane containing the U,
C, and 0 atoms [90].
The U-CO bond disruption enthalpy for 10 is about
10 kcalmol- 1.[8s] Compared to the typical disruption enthalpies of about 40 kcalmol- for early transition-metal
carbonyls, the U-CO value is quite low, comparable to
D(Cp,U-thf). Because the C-0 stretching frequency of 10
suggests bonding similar to that in typical transition-metal
complexes, the low bond enthalpy is attributed to severe
interligand nonbonded repulsions.
Because the molecular structure of 10 has not been determined conclusively and uranium is known to be highly oxophilic, the possibility of an oxygen-bound isocarbonyl adduct, [Cp,UOC], was considered.[901The n * orbitals of CO
are localized on the carbon atom, which is not adjacent to the
uranium atom in the isocarbonyl complex, precluding any
’
Angew. Chem. Inr. Ed. Engl. 30 (1991) 1069-1085
significant x back-bonding. The probable reason that the
isocarbonyl complex is unstable relative to the carbonyl
complex is that the U-OC o bond involves the oxygen “lonepair” orbital of carbon monoxide, which is at too low an
energy to interact with the empty o-acceptor orbital of
uranium. Instead, the isocarbonyl interacts with the filled
“semi-core” 6p orbitals of uranium, resulting in a “filledfilled” interaction and no net bonding.
Crystallographic studies also provide support for uranium-to-fourth-ligand A back-bonding.[’lI A comparison of
isostructural uranium and cerium compounds reveals that
the M-N distances are comparable in [Cp;U(quin)] (quin =
[N(CH,CH,),CH]) and [CpiCe(quin)], whereas the M-P
distances in [Cp;UPMe,] and [Cp;U(P(OCH,),CEt)] are
significantly shorter than those in the corresponding cerium
complexes. The authors conclude that there is A back-bonding from [Cp;U] to the phosphine and phosphite ligands,
whereas the lanthanide compound, [CpiCe], can only interact with the Lewis bases in a o-only or purely electrostatic
manner. Similarly, the M-0 distances in [Cp,Pr(thf)] and
[Cp,U(thf)] are comparable, while the M-C distance in
[Cp;”UCNEt] is considerably shorter than that in
[Cp,PrCNEt], giving evidence for uranium-to-isocyanide x
back-bonding.
Further evidence for the different bonding interactions of
lanthanides and early actinides with isocyanide ligands comes
from an IR spectroscopic investigation of [Cp,MCNEt]
c o r n p o u n d ~ . [The
~ ~ JC-N stretching frequencies for the lanthanide compounds are all at about 2200cm-’, approximately 50 cm- higher than v, in free CNEt. The increase
in vcN is common for CNR ligands bound to higher-valent
transition-metal atoms and is indicative of little or no n
ba~k-bonding.[~,]
By contrast, the C-N stretching frequencies of the early actinide (Th to Am) compounds span a
range of 60 cm-I, with [Cp,ThCNEt] exhibiting the
lowest ,v
(2140 cm-’) and [Cp,AmCNEt] the highest
(2202 cm- ’). The greater sensitivity of vCN to the metal atom
in the actinide series relative to the lanthanide series, while
not conclusive evidence of significant x back-bonding, does
portend different bonding in the organoactinide complexes
from that in the organolanthanide complexes.
Multiple bonding between the [Cp,U] fragment and nitrogen- and oxygen-containingdonor ligands has been extensively investigated both e~perirnentally~’~.
9s1 and theoreticalA variety of different N-donor complexes, spanning a
broad range of U-N bond lengths, have been made and structurally characterized : [Cp,UNPh,], 2.29 A; [Cp,UNPPh,] ,
2.07 A; [Cp,UNC(Me)CHPMePh,], 2.06 8,; [Cp,UNPh],
2.02 A. All of these U-N bonds are significantly shorter than
those generally observed in complexes that contain neutral
N-donor ligands bound to uranium, which are typically 2.42.8 A,[91,951
’
The great variations observed in U-N bond length and the
difficulties in describing the above structures with single resonance forms have prompted EH calculations on the model
complexes [Cp,UNH,]+ and [Cp,UL] (L = NH,, NPH,,
NHCHCHPH, , NPh).[961The calculations indicate significant N 2px-to-U x donation, primarily into the 6 d orbitals,
~
for the latter three complexes. The authors propose that the
strongest U-N n bonding should be observed in a uranium
nitride complex such as [Cp,UN]q-. No such organoactinide
1077
nitride complexes are yet known. The o donation from nitrogen to uranium is much greater for the formally anionic
nitrogen ligands than for the neutral NH, ligand. The authors demonstrate an excellent correlation between the total
U-N overlap population (calculated at a constant U-N
bond length of 2.06 8, for all compounds) and the crystallographically observed U-N bond length for this series of five
compounds (Fig. 7). The positive charge on U is largest for
[Cp,UNPh], consistent with its formulation as a 5f' Uv complex.
1 02
9
V
P-
*
Fig. 7. Plot of observed U-N distances r, versus, U-N overlap populations
P calculated at U - N = 2.06 A for a series of [Cp,UX] systems: M =
[Cp3UNH3]; N = [Cp,UNH,]; 0 = [Cp,UNPH,]; P = [Cp,UNCHCHPH,];
R
=
[Cp,UNPh] [96].
The same authors also performed calculations on the series of model complexes [Cp,UOH,), [Cp,UOPH,],
[Cp,UOCHCHPH,] +,and [Cp,UOCH,] in order to investigate variations in U-0 bonding.[961Again, an excellent
correlation between calculated U-0 overlap population and
observed U-0 bond length (over a range of > 0.4 A) was
obtained. On comparing homologous compounds containing U-N and U-0 bonds, the authors conclude that the
nitrogen donors are better able to form multiple bonds to
uranium.
Xa-SW calculations on [Cp,UOH] corroborate the conclusions of the EH studies.[62]Significant donation from the
0 2pn orbitals into the U 6d and, to a lesser extent, the 5f
orbitals was observed. The n donation from alkoxide ligands
to actinide atoms has been used to rationalize the unusually
large U-0-R bond angles observed in actinide alkoxide
compIe~es.[~'~
"1
4.2. Bis(cyclopentadieny1)actinide Complexes
4.2.1. The An-X
CT
Bond
Among the most extensively studied actinide-ligand o
bonds are those in the host of [CpzAnX,] (An = Th, U]
systems. The An-X bonds in these complexes exhibit a remarkably diverse chemistry, which often parallels that observed in [Cp2MX2]complexes of the transition metals. The
unoccupied frontier orbitals of a [Cp2UI2+fragment as obtained from EH calculations are shown in Figure 8.["l These
orbitals, which are primarily 6d in character, closely resemble those of [Cp2Ti]2+,[6'1although the [Cp2UI2+orbitals
are somewhat higher in energy and more diffuse. In both the
actinide and transition-metal systems, the frontier orbitals
are able to accept charge from formally anionic o-donor
1078
Fig. 8. Contour plots of the important valence orbitals in a [Cp,U]*+ fragment
[991.
ligands, leading to metal-ligand bonds of a,, b,, and, for the
actinide systems only, b , symmetry.
The donor ability of the X ligands in [Cp:AnX,] systems
directly affects the valence orbital energies of the complexes.
A comparison of the PE spectra of [CpTAnMe,] and
[CpTAnCl,] reveals that the Cp n, ionization bands are at
lower IE in the former than in the latter.['*] Similarly, the 5f2
ionization in [CpTUMe,] occurs at lower IE than that in
[CpfUCl,], although the difference between the two
(0.21 eV) is significantly less than that observed in d2 transition-metal systems (e.g., a difference of 0.7 eV between the
first IEs of [ C ~ ; M O C ~ , ]and
[ ' ~ [~C~ ~ , M O M ~ , ] ~ 'It~ seems
'~).
surprising that, in spite of strong An-Me o-bond formation,
the decrease in 5f2 IE for [CpfUMe,] relative to [CpTUCI,]
is so much less than that for [CpTUCl,] relative to [UCI,].
Xu-SW calculations on [Cp,AnX,] (X = C1, Me) also indicate that CH; is a stronger o donor than C1-, and that C1is not a significant T donor to uranium.[*']
Marks et al. have done detailed studies on the structures,
reactivities, and bond energies of [CpgAnR,] (R = hydride
or alkyl) systems." O2] The bis(neopenty1) complex
[CpTTh(CH,CMe,),] (11) exhibits an unusual geometry in
which the two neopentyl groups are significantly inequivalent: one has a much shorter Th-C bond and shows a very
obtuse Th-C-C angle['03] (Fig. 9). This behavior is attributed to an agostic interaction['041 between the a C-H bonds
and the Th center. An EH analysis of the model complex
[Cp2Th(C,H,),] indeed indicates a significant agostic interaction at large Th-C-C angles.'99. lo'] The calculated potential energy curve as a function of one Th-C-C angle is at a
minimum near the experimentally observed angle of 158".
The potential curve is quite shallow, consistent with the observed stereochemical nonrigidity of the alkyl groups in 11.
The apparent affinity of Th" for additional electron density, as evidenced in the agostic behavior described above,
Angew. Chem. Inr. Ed. Engl. 30 (1991) 1069-1085
are listed in Table 2. The Th-R bonds are generally about
5-10 kcalmol-' stronger than the analogous U-R bonds.
The An-R bonds are generally stronger than the corresponding M-R bonds, where M is a middle or late transition
metal,"' 31 and slightly stronger than, or comparable to,
M-R bonds of the early transition metals.[' 141 As mentioned
earlier, the trends in bond disruption enthalpies have been
successfully modeled theoretically, and the greater strength
of the M-R bonds of the early transition metals is attributed
to the repulsive interactions between the filled d orbitals of
the late transition metals and the occupied ligand orbitals.[1151
Fig. 9. The 50 K neutron diffraction structure of 11. Significant bond angles
and distances: Th-CIA-C2A = 132.1"; Th-CIA = 2.543 A, Th-CIB-C2B =
158.2";Th-C1B = 2.456 8, [103].
Table 2. Bond disruption enthalpies D(M-R) [kcalmol-'1 for selected M-R
bonds.
has been used to explain the remarkable ability of such compounds to activate C-H and H-H bonds.['061 For example,
11 can be entropically driven to strained thoracyclobutane
12, which undergoes facile ring-opening C-H activation reactions [Eq. (b)].['07*'] Oxidative addition of R-H to 12
11
12
13
can be ruled out as a possible step in the transformation of
12 to 13; such a step would require the formal oxidation of
dofOTh'". The kinetic data on reactions such as 12 + 13 are
consistent with a concerted, four-center heterolytic C(H)-H
activation pathway, involving precoordinaton of the activated bond (Scheme l).[loSlThis mechanism parallels those that
Interestingly, the Th-R bond disruption enthalpies in
[Cp,ThR] complexes are significantly larger (by about
5 kcal mol- ') than those in the corresponding [Cp:ThR,]
complexes." * 61 These results were somewhat surprising in
that the presence of three Cp ligands should increase the
steric congestion about the Th center. The authors propose
that the bond-strength difference in the two systems might be
due to differences in the Th-R orbital overlap, although
significant differences in the bonding are not evident in the
PE spectra.[781
4.2.3. CO Insertion Products and Other Adducts
Scheme 1. Four-center C(H)-H activation mechanism.
have been proposed[' 097 ' l o ] and studied theoreticallyr"
for C-H bond activation by do transition-metal and
lanthanide organometallics. In both of these latter types of
systems, the metal d orbitals are the most important ones
with respect to precoordination, suggesting a similar role of
the 6d orbitals in the actinide systems.
4.2.2. An-X Bond Energies
Thermochemical studies of [Cp:AnR,] and [CpzMRz]
have yielded experimental values for the An-R and M-R
bond disruption enthalpies." * -114] Representative values
of the bond disruption enthalpies for Equations (c) and (d)
Angew. Chem. Int. Ed. Engl. 30 (1991) 1069-1085
Marks et al. have demonstrated that, like the early transition-metal metallocene alkyls, [CpfAn(R)(X)] and
[CpfAnR,] systems readily insert CO and other small
molecules into their An-R bonds [Eq. (e)] .['17]
c1
+CO
c H cn
C1
Cp:Th:cj(
//
0
14
The crystal structure of 14 (Fig. 10) reveals an unusually
short Th-0 distance, 0.07 8, shorter than the Th-C(acyl)
bond. In contrast, the M-0 distances observed in most transition-metal acyls are invariably longer than the M-C distances. These observations led the authors to favor formulation of the actinide-acyl moiety as a carbene-like dihapto
acyl (15) rather than as a "normal" metal acyl group (16).
Similar observations have been made for the insertion of CO
into An-NR, bonds, yielding $-carbamoyl complexes[' *I
and for the insertion of isocyanides into An-R bonds.[l 19]
The carbene-like description (15) of the bonding in actinide1079
essentially isoenergetic, in accord with the experimental observations.
The electronic structure of the 1,3-diene compounds of
[Cp:Th] and [CpTU] has also been investigated. The 1,3-diene complexes of zirconium, [Cp2Zr(l,3-diene)], can exhibit
either s-cis (19)or s-trans (20) structures.[1241On the other
19
20
Fig. 10. ORTEPdrawingofthe nonhydrogen atomsforthe[Thj(CH3),C,j,jr12COCH,C(CH,),}]CI molecule [117].
acyl and related complexes is in accord with the remarkable
C-C coupling reactions that they exhibit.['4as"71
/O
M -:C
\
/."\\
M-C-R
-R
15
16
A notable difference in the structures of actinide acyls
and those of transition metals is the orientation of the
q2-acyl C-0 bond relative to the other o-bonded ligand.
Actinide acyls exhibit both the "0-outside'' (17) and "0inside" (18) structures; in the carbamoyl complexes
[Cp:An(CONMe,)CI], for example, both isomers exist in
equilibrium in solution.[1201By contrast, all structurally
characterized acyl complexes of the group4 metals show
only the 0-inside structure 18.[121122] Tatsumi, Hofmann,
17
18
Hoffmann et al. have used EH calculations to investigate the
preference for '1'- versus q2-acyls and, for the latter, the
preference for 0-outside versus 0-inside
The question of q' versus 4' coordination was addressed by
comparison of the interactions of a COCH,- ligand with the
[Mn(CO),]+, [Cp,ZrMe]+, and [Cp,UC1]3+ metal fragments. Each fragment has a frontier orbital appropriate for
the formation of a M-C o bond with the acyl ligand. The
latter two fragments also contain an unoccupied orbital that
is capable of accepting density from the acyl oxygen lone
pair, thus favoring the q2-acyl geometry. In the more electron-rich [Mn(CO),]+ fragment, the 3d orbital that would be
appropriate to accept charge from the acyl oxygen is occupied, precluding a Mn-O(acyl) interaction and leading to an
q'-acyl structure. The shape of the U-based hybrid orbital in
[Cp,UC1]3+ that fosters the q2-acyl bonding stabilizes the
0-outside structure 17 in the actinide-acyl relative to that in
the transition-metal complex: for [Cp,Zr(COMe)Me], structure 17 is calculated to be about 5 kcalmol- ' less stable than
structure 18; for [Cp,U(COMe)C1]2+, the two structures are
1080
hand, [Cp:Th(C,H6)] shows only the s-cis structure.['25]EH
calculations show a sizable energy gap between the minima
of the s-cis and the s-trans isomers for both [Cp,Th(C,H6)]
(0.74 eV) and [Cp,U(C,H6)] (0.42 eV), favoring the s-cis
geometry in each case.[991 Similar calculations on
[Cp,Zr(C,H,)] show that the s-cis and the s-trans geometries
are well balanced (0.07 eV in favor of s-cis). The difference
between the actinide and the zirconium results stems from
the 3a, frontier orbital of the [Cp2M]fragment (Fig. 8). For
zirconium this a , orbital interacts with the 7~: orbital of
butadiene equally well in either the s-cis or the s-trans geometry, but for the actinide compounds the 3a1-7c; interaction
is much greater in the s-cis geometry. The butadiene terminal
carbon atoms in the actinide compounds have a large negative charge. The high polarity in the Th-C(termina1) bonds
is consistent with the violent reactivity of the complex with
organic carbonyls and with the facile insertion of pyridine
into the Th-C bond.
Tatsumi and Nakamura have also compared two isomers
of [Cp,U(C,H,)], namely, the actinacyclopentadiene comI
,
plex, [Cp,UCH=CHCH=CH], and the cyclobutadiene
complex, [Cp,U(q4-C,H,)] .19" While no examples of actinide cyclobutadiene compounds exist, there is a known
actinacyclopentadiene complex, [Cp:U(C,Ph,)] .['261 The
metallacyclopentadiene complex is calculated to be 2.5 eV
more stable than the hypothetical cyclobutadiene complex.
However, the authors note that [Cp,U(q4-C4H,)] would be
kinetically stable because (1) the U-to-q4-C,H, bonding is
reasonably strong (actually stronger than U-to-Cp bonding)
and (2) a C-C bond cleavage of [Cp,U(q4-C,H4)] with
simultaneous formation of two U-C o bonds is symmetry
forbidden.
The bonding in the bis-pyrazolate complexes
[CP,MO(PZ)J [CP,MO(PZ),I~+,and [CP~U(PZ)~J
(PZ =
C,H,N;) has been investigated via EH calculations.[' 271
The pz ligand can adopt either an q1 (two-electron donor) or
an q2 (four-electron donor) coordination geometry, as it
does in the case of [Cp,U( pz)] .[I2*] The electronically favored structures for the molybdenum complexes are those
predicted by the effective-atomic-number rule, that is ql,q l
for the neutral complex and q2,q2 for the dicationic complex.
In contrast, [Cp,U(pz),] exhibits an q2,q2minimum with the
calculated U-N-N angles in close agreement with the crystal
structure of [ C ~ ~ U ( ~ Z ) , ]The
. [ ' choice
~ ~ ~ of q1 versus q2
coordination is similar to that of the acyl complexes and can
be explained in terms of the same frontier orbitals.
There have been several studies of the mechanism of CO
insertion into the actinide-alkyl bonds of [CprAnR,] sysAngew. Chem. h t . Ed. Engl. 30 (1991) 1069-1085
tems. EH calculations have been used to investigate the pathway by which a CO molecule approaches [Cp2U(CH3),I2+
prior to insertion into the M-R bond.['231Approach of the
CO ligand along a path perpendicular to the plane containing the two Cp centroids and the metal atom is found to have
no appreciable barrier, consistent with the experimental result that CO insertion is extremely facile.
[CpTAnR,] and [CprAnRX] have been shown to undergo
facile carbonylation with subsequent C = C bond formation
to yield monomeric or dimeric products such as 21 and
22.['30]A possible mechanism for the formation of 21 via
Fig. 11. Crystal structure of [CpSThS,] [134].
22
21
stepwise CO insertion to yield the bis(q2-acyl) complex, with
subsequent coupling of the two acyl ligands, has been considered." 'I The bis-acyl complex [Cp,U(COR),]2C is predicted to have a bis-q2 structure, in contrast to early-transition-metal complexes in which the q',qz structure is found to
be the most stable. The HOMO of [Cp,Ti(COR),] is destabilized on proceeding from the q',q2 structure to the q2,q2
structure by an unfavorable out-of-phase interaction of the
acyl lone pairs. For [Cp,U(COR),], the HOMO also has
out-of-phase acyl lone-pair orbitals in the q2,q2 structure;
now, however, these can interact favorably with a U 5f orbital. The HOMO is therefore stabilized on going from q',q2
to qZ$. These results are consistent with the observed q2,$
structure of [CpfU(CONMe,),] .[1321
The least-motion pathway for acyl coupling (C=C bond
formation) in [Cp,U(COR),]2 is a symmetry-forbidden
process with a calculated barrier as high as 1.6 eV. The optimum reaction path is one in which the two acyl groups rotate
up to 30" out of planarity on the approach to the transition
state, which then collapses to the planar enediolate product
21. The barrier for this pathway is 0.7 eV. The resulting enediolate compound is 2.9 eV more stable than the (q2-COR),
structure, indicating that the coupling is highly exothermic.
The twisting of the q2-COR groups out of the equatorial
plane costs surprisingly little energy (0.1 eV), and support
for this motion comes from the structure of the complex [Cp~U(CONMe,),], which has twisted cabamoyl
The absence of carbamoyl coupling is due to the
electronic influence of the NR, groups, which results in a
"more-forbidden" least-motion pathway with a barrier of
2.9 eV and a non-least-motion pathway having a barrier of
1.1 eV. A completely different pathway has been proposed
for acyl coupling to enediolates at a [Cp,Zr] ~ e n t e r . 1 ~ ~ ~ 1
Polysulfide ligands such as S i - form metallacycles with
both actinide and transition-metal atoms. In contrast to
transition-metal MS,-containing complexes, which all exhibit chair conformations of the MS, ring, [Cp:ThS,] shows
an unprecedented twist-boat conformation (Fig. 1I).[' 341
This compound has unusually short Th-P-S distances, indicative of some interaction between the metal and the terminal S-S bonds (S,-S, and S,-S,) of the S:- ligand. EH calcu-
lations on [Cp,ThS,] indicate donation from the two highest
occupied MOs of Si- into empty orbitals (predominantly
6d) on the [Cp,Th]'+ fragment. While the Th-cr-S bonding
dominates, significant Th-P-S bonding is also indicated.
4.3. Mono(cyclopentadieny1)actinide Complexes
[CpU((CH,)(CH,)P(C,H,),),] (23) has the longest U-C
cr bonds yet reported (2.66 A). EH calculations on this compound give an average U-C cr-bond overlap population of
0.26 compared with an overlap population of - 0.03 for
U-C(Cp), indicating covalency in the U-C CY bonds.['351
However, the overlap populations for the U-C cr bonds in
this compound are much smaller than that found for the
U-C cr bond in [Cp3UCH,]. That the difference is not a
result of the long U-C bonds in 23 was supported by calcu-
+
Angen. Chem. Inr. Ed. Engl. 30 ( 1 9 9 1 ) 1069-1085
P
PhZ
23
lations on the compound with U-C distances of 2.4 8, (the
same as in [Cp,UCH,]. At this distance the overlap population increases only slightly to 0.27. The small overlap populations (and, hence, the long U-C distance) are due to the
outward deformation of the ylide-carbon lone pairs along a
direct line to the uranium atom. In addition, the coplanarity
of the five carbon atoms and slight repulsive interactions
between the lone pairs on adjacent ylides will further reduce
the size of the inward-pointing orbital lobes.
5. ActinideCyclopentadienyl Complexes
Containing Metal-Metal Bonds
To date, no bonds between two actinide centers have been
observed in organoactinide chemistry. The possibility of 5fbased metal-metal bonds in the naked uranium and neptunium dimers have been investigated via nonrelativistic Xu-SW
molecular orbital calculations.[' 361 These results suggest a
1081
027c46442
configuration for U,, leading to a sextuple bond,
~4~
for Np,, yielding a septuple
and a 0 ~ 7 1 ~ 6configuration
bond. The separation between the +” and the +g orbitals is
only 0.3 eV in Np,, which might lead to a high-spin configuration and a pentuple bond. A recent ab initio calculation
of the electronic structure of U,, including relativistic effective core potentials and electron correlation, casts doubt on
the simple f-orbital overlap model for U-U bonding.“ 371
Two systems that contain phosphido-bridged bonds between Th and a transition metal have recently been reported.
Reaction of [CpTTh(PPh,),] with [Pt(cod),] in the presence
of PMe, yields complex 24a, which has a Th-Pt distance of
2.98 A, 0.2 A shorter than the sum of the covalent radii of
the metal
On the basis of this structural information, along with 31PNMR data and comparisons with other
heterobimetallics, the authors conclude that 24 a contains a
direct Th-Pt bond. Their Hartree-Fock and generalized valence bond (GVB) ab initio calculations on the model compound [Cl,Th(p-PH,),Pt(PH,)] lead to qualitatively similar
descriptions of the metal-metal bonding. The bond is formed
between the 5dX2-,>orbital on Pt and the 6d,2-y2orbital on
Th, with a larger fraction of electron density on the Pt center.
A Mulliken population analysis reveals a charge of + 1.48
on the Th atom and a charge of 0.00 on the Pt atom. The
authors conclude that the Th-Pt bond can be regarded as a
formal donor-acceptor, or dative, bond from the “fiiled”
5d” shell of Pt into the “empty” 6d shell of Th.
the Th 5f orbitals. Similar conclusions were reached on thebasis of an Xu-SW calculation on compound 24b.[1403
Marks et al. have prepared the first two complexes that
contain a direct, unsupported bond between an actinide
atom and a transition metal. The reaction of [CpTThX,] with
[CpRu(CO),Na] yields compounds 25a (X = CI, I).1171The
iodo derivative has a Th-Ru bond length of 3.028 A, comparable to the Zr-Ru bond length of 2.910 A in compound
25b (X = OCMe3).[’411The nature of the metal-metal
bonding in compounds 25 has been investigated using quasirelativistic Xu-SW calculations on the model systems
The M-Ru bond[Cp,(I)M-RuCp(CO),] (M = Zr, Th).r1421
ing is virtually the same in these two systems and consists of
donation from the filled 4d,, orbital of Ru into the empty d,,
orbital of Th or Zr. The result is a slightly “bent” M-Ru o
bond (Fig. 12) that is highly polarized (ca. 70 %) toward the
Ru atom. Thus, the bond is best described as a dative donor-
Ph2
24 a: ML, =IPtPMe31
b: ML, =INi(C0)21
Complex 24b has a Th-Ni distance of 3.206 A, shorter
than that expected from ionic model assumptions. EH calculations indicate that the Th-Ni overlap population, although
negative at all distances investigated, is most favorable at the
experimental distance of 3.2 8, and becomes increasingly
more negative as the Th-Ni distance is lengthened to
3.7
Furthermore, of the major interactions among the
metals and the bridging phosphido ligands, the Th-Ni interaction is the most sensitive to this geometrical change, indicating that the M-P bonds have some geometrical flexibility.
When the molecule is divided into two fragments, two principal sources of Th-Ni interaction are discernible. The first
is the filled-filled repulsion between the d levels of the Ni
atom and the Th-PH, bonding orbitals resulting in a net
antibonding interaction between Th and Ni. The second is
the interaction between the filled d levels of mi(CO),] and
the frontier orbitals of [Cp,Th(PH,),]. The largest of these
is a K interaction between the HOMO of [Ni(CO),], which is
a hybrid of d,, and p, that points toward the Th atom, and
the 3b, frontier orbital of Th. A o interaction takes place
between the SHOMO of [Ni(CO),], a mixture of Ni d,,,,,
d,,, pz, and s orbitals, and the 3a, frontier orbital of Th, a
mixture of d,,, pz, and s orbitals. Owing to the superior
radial extension of the Th 6d orbitals, both the o and the 7c
interactions are dominated by the Th 6d orbitals rather than
1082
Fig. 12. Contour diagrams of the metal-metal bonding orbitals in the heterobimetallic complexes [Cp,(I)M-RuCp(CO),] (M = Zr, Th) (1421.
acceptor bond formed by donation from [CpRu(CO),]- to a
do or dofOMIv center. The authors note that [CpRu(CO),]can be regarded as an “organometallic pseudohalide”. This
notion has been extended in the synthesis of several [Cp3AnMCp(CO),] (An = Th, U; M = Fe, Ru) derivatives.[’431
6. Conclusion and Outlook
In this review, we have tried to emphasize the interplay
between experimental and theoretical electronic structure investigations in the comparatively new and very exciting field
of organoactinide chemistry. As is evident from the compounds discussed in this review, the lion’s share of electronic
structural study of organoactinide chemistry has involved
complexes of the two most experimentally accessible actinide
elements, namely, thorium and uranium. These studies point
to some general conclusions concerning the qualitative description of the bonding in these systems:
1. The strong donor ability of formally anionic ligands leads
to a generally high degree of covalency in organoactinide
complexes, particularly compared to the actinide halides.
Angew. Cheni. Ini. Ed. EngL 30 ( I 9 9 f j 1069-1085
2. The actinide 6d orbitals are generally greater participants
in the metal-ligand bonding than are the 5f orbitals, a
notion first proposed by Clark and Green in their interpretation of the PE spectrum of u r a n o ~ e n e . ~ As
’ ~ ~a ]result, the 6d orbitals are more affected by the organic
“ligand field” than are the 5 f orbitals.
3 . The actinide 5f orbitals participate in metal-ligand bonding when symmetry dictates that no other actinide orbitals are available.
4. The metal-localized electrons in “non-fo” complexes
(such as those of U”) reside in nearly pure actinide 5f
orbitals. Exceptions to this generalization can occur in
coordinatively unsaturated early actinide complexes,
such as [Cp,Th].
The picture that emerges is one in which there is a dichotomy in the roles of the actinide 5 f and 6 d orbitals, wherein the
latter are used to bind the ligands and the former are used to
house metal-based electrons. By contrast, in organotransition-metal complexes the valence nd orbitals serve as both
the principal source of metal-ligand bonding and as the
repository of metal-based electrons. This situation is shown
schematically in Figure 13, wherein it can be seen how this
simple description accounts for the paramagnetism of U‘”
complexes vis-a-vis the diamagnetism usually observed in d2
transition-metal organometallics, such as [Cp,MoCI,] .r801
9
7
nd
Fig. 13. Qualitative MO diagram comparing the roles of the metal-based orbitals in transition-metal complexes (left) and actinide complexes (right).
What is the future of organoactinide electronic structure
investigations? The studies to date have focused primarily on
the relative roles of the actinide orbitals in bonding and on
the relationship of this bonding to that in transition-metal
systems. From a quantum-chemical point of view, the electronic structure calculations on organoactinides have been
comparatively crude; very little has been done with respect
to electron correlation in these systems, and, although quasirelativistic corrections have been employed, there has been
scant consideration of the effects of spin-orbit coupling.
This situation is changing rapidly as the speed and accessibility of supercomputers increases. The recent spin-orbit configuration interaction calculation on uranocene by Chang
and Pitzed’ is a portent of what may be expected in this
field in the future.
Glossary: A Brief Outline of Electronic Structure Methods
for Actinide Systems
As is apparent from the preceding discussion, a wide variety of electronic structure methods have been applied to large actinide-containing
molecules. Each method employs certain approximations in the construcAngen. Chem. Int. Ed. Engl. 30 (f991) 1069-1085
tion or solution of the electronic-structure problem, and each has inherent advantages and disadvantages. The following is a very brief summary
(without references) of the methods cited in this review; for an in-depth
discussion of the electronic structure methodologies, we refer the reader
to our recent detailed review of these methods as well as their applications
in organometallic and nonorganometallic actinide chemistry [145].
Nonrelativistic versus Quasi-relativistic versus Relativistic Methods:
“Conventional” molecular electronic structure calculations, based on the
Schrodinger wave equation, include no consequences of subjecting the
system to the tenets of special relativity. These nopirelazivistic methods
assume that the mass of every electron in the system is equal to the rest
mass of the electron and that the electron-spin coordinate can be treated
completely independently of the spatial coordinates. For the heavier
elements, such as the third-row transition metals and the actinide elements, these assumptions are invalid. The classical angular speeds of the
core electrons in these elements are nonnegligible fractions of the speed
of light and thus a relativistic mass correction is necessary. Quasi-relativistic methods are those that include such mass corrections (as well as
more arcane effects, such as the Darwin correction) but still maintain
separate spin and spatial coordinates. The results of quasi-relativistic
molecular orbital methods resemble those of nonrelativistic methods in
that spatial molecular orbitals, to which spin functions can be attached,
are derived. The quasi-relativistic extended Hiickel and quasi-relativistic
Xu-SW methods are examples of quasi-relativistic molecular orbital
methods.
In addition to the effects noted above, relativistic methods include the
interaction of the spatial and spin properties of the electrons, that is,
spin-orbit coupling. The Dirac equation, which merges quantum mechanics and special relativity, is the usual starting point for relativistic
electronic structure methods. The application of the Dirac equation to
molecules is far more complex than that of the nonrelativistic Schrodinger equation, and several calculational approaches to solving the
equation have been used. The relativistically parametrized extended
Hiickel (REX) method of Lohr and Pyykkli is probably the simplest
approach to a fully relativistic calculation. Because relativistic approaches explicitly include spin-orbit coupling, the states and orbitals that result
are bases for the double group of the molecule rather than the more
familiar single group. Owing to the computational complexity of fully
relativistic methods, relatively few such calculations have been performed
to date on organoactinide systems.
Molecular Orbital Methods: Most of the electronic structure calculations reported here employ the molecular orbital approximation, in which
it is assumed that each electron experiences the average field of all the
other electrons in the molecule. The molecular orbitals arc usually expanded as a linear combination of atomic orbitals (LCAO), which can be
either analytical or numerical functions. In the Hartree-Fock method,
which has been used sparingly for heavy element systems, all of the
relevant integrals are solved exactly. In order to make such calculations
computationally feasible, relativistic ej!!ective core potentials (ECPs or
RCPs) are generally used. ECPs, which are based on relativistic atomic
calculations, replace the core atomic orbitals and thus greatly reduce the
number of molecular integrals while preserving the relativistic effects on
the core electrons. Approximate LCAO-MO methods, such as the extended Hiickel method, use either empirical or semiempirical approximations
to some of the molecular integrals.
A family of molecular orbital methods that has moved to the fore in
recent years is that based on local density functional (LDF) methods.
These methods replace the nonclassical, nonlocal exchange interaction
inherent to the Hartree-Fock method with a local exchange operator,
which is dependent on the electron density raised to a fractional power.
Because the equations involving the local exchange operator cannot be
solved readily using analytical methods, the application of LDF methods
depends on several numerical methodologies. The earliest LDF method,
the Xu scattered-wave (Xu-SWj or multiple-scattering Xu (MS-Xuj
method, uses a model Hamiltonian based on surrounding each atom of
the molecule with a sphere. Scattering theory techniques are used to
satisfy the boundary equations at the sphere surfaces. The orbitals ob-
1083
tained are hybrid numerical/analytical functions that are based in part on
(101 J. G. Brennan, J. C. Green, C. M. Redfern, 1 Am. Chem. SOC.f11(1989)
a multicenter scattering wave function. Quasi-relativistic corrections can
be easily added to Xa-SW calculations, and a fully relativistic version of
2373.
1111 A. H. H. Chang, R. M. Pitzer, J. Am. Chem. Soc. l f l (1989) 2500.
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the method has also been implemented.
The newer L D F methods use an atomic orbital basis in which to
expand the molecular orbitals. The necessary molecular integrals are
calculated by using numerical integration techniques. The discrete-variational XG((DV-Xu) method uses numerical atomic orbitals that are obtained from atomic calculations. A fully relativistic implementation of
this method, called the Dirac-Slater discrete variational ( D S - D V ) method, provides a relatively inexpensive means of performing relativistic
calculations on large molecules. The Hartree-Fock-Slarer ( H F S ) method is very similar to the DV-Xa method, except that analytical functions
are used to represent the atomic orbitals. Quasi-relativistic and relativistic
effects have also been incorporated into the HFS method.
Electron Correlation Methods: The importance of including electron
correlation in electronic structure calculations has been well established
for light-atom systems. Using a molecular orbital solution as a starting
point, correlation is generally included via additional configuration interacrion ( C I ) or niulticonfigurotion selfconsistent-field ( M C S C F ) calculations. Because these techniques are extremely computationally demanding, only recently have they seen application to organoactinide complexes. ECPs are used to replace core electrons in such calculations, and
spin-orbit effects can be included explicitly. The generalized valence bond
(GVB) method, which includes electron correlation relative to a molecular orbital description, has also seen limited application to organoactinide
systems. The GVB method uses a different form of the wave function
than d o molecular-orbital-based methods.
It is a great pleasure to acknowledge our co-workers at The
Ohio State University, especially Anne Fang, Kevin NovoGradac, Melanie Pepper, Larry Rhodes, and Bill Schneider,
who have made signficant contributions to our understanding
of organoactinide chemistry. We are also grateful to many
colleagues elsewhere for stimulating discussions and to the
Isotope and Nuclear Chemistry Division of Los Alamos National Laboratory for generously hosting both of us. We wish
to thank the U S . Department of Energy, (he Petroleum Research Fund (administered by the American Chemical Socie t y ) , the Ohio Supercomputer Center, the Associated Western
Universities, and the Ohio State University Graduate School
for their generous support of our research in actinide chemistry.
Received: September 12,1990 [A 830 IE]
German version: Angen. Chem. 103 (1991) 1085
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1085
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