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To Boldly Pass the MetalЦMetal Quadruple Bond.

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Highlights
DOI: 10.1002/anie.200504322
Bond Theory
To Boldly Pass the Metal–Metal Quadruple Bond
Udo Radius* and Frank Breher*
Keywords:
arene ligands · bond theory · metal–metal interactions ·
multiple bonds
The
theory of chemical bonding is
intriguing and of fundamental importance. Bonding concepts were developed and rules were established over
the years to describe and subdivide
molecular compounds consisting of either single, double, or triple bonds. The
latter was believed to be the highest
accessible bond order for a long time.
Although compounds that contain
quadruple bonds between transition
metals were already prepared in the
19th century, for example [Cr2(mO2CMe)4(H2O)2]),[1] it was not until
1964, when Cotton et al. reported on
the crystal structure of K2[Re2Cl8]·2 H2O
featuring a surprisingly short Re Re
distance of 2.24 /,[2] that such a quadruple bond between two transition-metal atoms was confirmed unequivocally.
The [Re2Cl8]2 ion has become the
prototype for this type of complexes,
and a new era of inorganic chemistry
and a rich chemistry has evolved around
this class of transition-metal complexes.[3]
The well-known qualitative description of a s2p4d2 quadruple bond is
elegant and deceptively simple (and
familiar), but it is based on a oneelectron model and the inherent assumption that four bonding orbitals are
doubly occupied. Today we know that
this is not entirely true for weak intermetallic bonds. The small overlap between d orbitals results in a relatively
weak interaction, thus making a simple
[*] Priv.-Doz. Dr. U. Radius, Prof. Dr. F. Breher
Institut f.r Anorganische Chemie
Universit1t Karlsruhe (TH)
Engesserstrasse 15
76131 Karlsruhe (Germany)
Fax: (+ 49) 721-608-8440
E-mail: radius@aoc1.uni-karlsruhe.de
breher@aoc1.uni-karlsruhe.de
3006
Dedicated to Professor Hansgeorg
Schnckel on the occasion of his 65th
birthday
molecular orbital (MO) description of
the quadruple bond inappropriate.[4] A
more accurate, but less transparent
description of the quadruple bond requires an approach that goes beyond
single configuration methods inherent
to simple MO formalisms. To properly
describe systems already in the ground
state, treatments must include correlation effects. A bond order analysis of
[Re2Cl8]2 relying on CASSCF (complete active-space self-consistent field)
calculations,[5] for example, has shown,
that the Re Re bond has an effective
(calculated) bond order of 3.2 and the
net bond order contribution of the d
bond is about 0.5. The reason is mainly a
partial occupation of the antibonding d*
orbitals. Whether it should be called a
triple or a quadruple bond or whether
the d bond should be called a weak bond
or half a bond is more or less a matter of
definition of the term “bond” or “bond
order”. The alternatives here are to
describe the bonding as a “weak” quadruple bond (four orbitals with relevant
overlap) or as a bond involving four
electron pairs with an effective bond
order of about three.
Various orbitals contribute to a different extent to metal–metal bonding, as
demonstrated by intriguing compounds
such as the silicon analogue of an
alkyne, RSiSiR, reported by Sekiguchi
et al. or Wiberg et al.[6] and the corresponding germanium, tin, and lead compounds REER (E = Ge–Pb) comprising
bulky aryl ligands (Ar’ and Ar*)[7]
described not long before by Power
et al.[8] For the REER compounds, the
term alkyne analogue does not imply
that each of the three valences available
for the Group 14 element contribute
equally to chemical bonding to retain a
triple bond featuring an integer bond
order of three. As a result of the
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
gradually increasing, nonlinear, transbent geometries on descending the
group, a considerable weakening of
one component of the degenerate p
bonding was suspected. Although the
structural data, as well as quantumchemical calculations point towards
bond orders approaching three for Si,
approximately two for Ge and Sn, and
one for Pb, the correlation of bond
length and bond order is questionable
and should be treated with care, especially when counterions are involved.
This has led to controversial discussions
in the past, for example, whether [Ar*GaGaAr*]2 (formally isoelectronic to
neutral RGeGeR) is the first experimentally proven gallium–gallium triple
bond or not.[9] Although not capable of
distinguishing between covalent and
electrostatic contributions, the best experimental tool for a classification of
such bonds might be the force constant
of the metal–metal bond.[10]
A milestone for multiple-bond
chemistry involving transition metals
was recently reported by Power and
co-workers, who impressively succeeded
in isolating “a stable compound with
fivefold bonding between two chromium(i) centers”.[11] To achieve the highest
bond order possible in an isolable compound, the number of ligands has to be
minimized, since their binding reduces
the number of valence orbitals available
to form metal–metal bonds. Furthermore, the steric requirements for the
ligand system is of crucial importance
since large ligands prevent oligomerization and undesirable bridging motifs are
usually disfavored for steric reasons.
Relying on their background in main
group chemistry,[8] Power et al. have
synthesized and characterized a dinuclear metal–metal-bonded complex with
one ligand per metal atom in the ligand
Angew. Chem. Int. Ed. 2006, 45, 3006 – 3010
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Chemie
sphere. The reduction of [{Cr(mCl)Ar’}2][7] with a slight excess of potassium graphite afforded the thermally
robust complex [Ar’CrCrAr’] (1) in
41 % yield.
Following the simplified picture developed for [Re2Cl8]2 , the bonding in a
(hypothetical)
linear
complex
[RCrCrR] (R = monoanionic ligand)
can be described as a quintuple (tenelectron–two-center)
Cr Cr
bond
formed by a fivefold overlap between
metal d orbitals (Figure 1). Five electron
Figure 1. Schematic MO picture for linear [RCrCr-R].
pairs play a dominant role in holding the
metal atoms together, but it does not
necessarily imply that the bond order is
five or that the bonding is very strong.
As pointed out for [Re2Cl8]2 , the
ground state of the molecule possibly
involves mixing of other higher energy
configurations with less bonding character.
The molecular structure of [Ar’CrCrAr’] (1) (Figure 2) reveals a planar
Figure 2. Molecular structure and numbering
scheme of [Ar’CrCrAr’] (1).
Angew. Chem. Int. Ed. 2006, 45, 3006 – 3010
core geometry with a Cr Cr bond length
of 1.8351(4) /. The chromium–chromium distance is slightly longer than the
bond length reported for a quadruply
bonded, but ligand-bridged CrII dimer
[Cr2(m2-OMe-5-MeC6H3)4] (1.828(2) /),
which has the shortest metal–metal
bond distance observed so far.[12] The
atoms C1, Cr1, Cr1A, and C1A of the
central Cr2C2 unit in 1 are aligned in a
plane, but deviate significantly from
linearity
(angle
Cr1A-Cr1-C1
102.78(3)8), adopting a trans-bent structure. Each chromium atom is bonded to
the
ipso-carbon
atom
(Cr1 C1
2.131(1) /) of the Ar’ ligand and
through a somewhat weaker interaction
(Cr1 C7A 2.2943(9) /) to an ipso-carbon atom of a flanking dipp ring (dipp =
C6H3-2,6-iPr2) of the ligand. The interaction of the dipp moiety with the
chromium atom can also be considered
as that with a distorted h6-coordinated
arene ligand; the chromium–carbon distances range from 2.29 to 2.97 /.
The simple bonding model given
above, therefore, has to be adjusted to
the geometry observed. Additionally,
mixing of orbitals can occur due to the
lower symmetry of the complex. DFT
single-point calculations on the experimentally verified structure presented by
the authors support the view that there
are five orbital interactions (one s, two
p, and two d) between the CrI ions
(Figure 3). HOMO and HOMO 1,
which differ in energy by 0.41 eV, correspond to d bonds, and the LUMO,
which is 2.01 eV higher in energy than
the HOMO, corresponds to a d* orbital.
The chromium–chromium s-binding orbital (HOMO 2) that emerges from the
single-point DFT calculations on 1 is
comparatively high in energy, above the
two p-binding orbitals (HOMO 3 and
HOMO 4). This might be due to significant orbital mixing and/or due to
reduced overlap along the chromium–
chromium axis. Although the authors
provided first results on CASSCF calculations in the Supplementary Material
of the original article, the meaning of
this feature for metal–metal bonding
remains to be evaluated in a more
thorough theoretical treatment of 1 or
models of this compound.
Before entering into a further discussion of the bonding in complex 1, it is
most instructive to briefly outline the
Figure 3. Electron density surfaces and energies
for the Cr–Cr frontier orbitals in [Ar’CrCrAr’] (1)[11a]
(reprinted with permission from Science 2005,
310, 844. Copyright 2005 AAAS).
bonding situation in the dichromium
dimer, Cr2, which has attracted considerable interest in recent years.[13] By
continuing with the concept of minimizing the number of metal ligands to
maximize the number of free metal
valence orbitals available to form metal–metal bonds to an extreme, even
larger bond orders than five should be
feasible. The bare dimers of the open dshell transition metals provide an opportunity to examine multiple bonds
between metal atoms in the absence of
ligand effects. Among the dimers of the
first transition series, Cr2 potentially
provides one of the most intriguing
examples of multiple metal–metal bonding. Since the chromium atom has a
high-spin 7S ground state (a (3d)5(4s)1
valence electron configuration with one
electron in each of six valence orbitals),
closely spaced energy levels result. The
spin pairing of two ground-state atoms
results in a 1Sg+ Cr2 molecule with a
valence electron configuration (4ss)2(3ds)2(3dp)4(3dd)4 comprising two s,
two p, and two d bonds giving formal
chromium–chromium bond order of six.
The complexity of the bonding in Cr2,
however, was for a long time a challenge
for ab initio quantum chemistry because
of this “hextuple” bond and the unusual
shape of the Cr2 potential energy curve
(Figure 4).
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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3007
Highlights
Figure 4. Experimental and calculated potential energy curves for Cr2 using CASSCF and
CASPT2 according to Roos[13d] (reproduced
from reference [13d] with permission of the
Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech
Republic).
At a short internuclear Cr Cr distance (re = 1.6788 /), the molecule is
multiply bonded and exhibits a relatively deep potential. As the atoms separate,
the rapid loss of bonding between the
compact 3d orbitals is partially compensated by increased interatomic exchange
stabilization, as well as by 4s–4s bonding. As a result, the potential curve rises
more slowly with increased internuclear
separation than would be expected,
which renders the curve highly anharmonic with a shelf or a shallow minimum at intermediate chromium–chromium separations. The nature of the Cr
Cr interaction changes qualitatively
with increased internuclear separation,
from multiple 3d–3d bonding at short
distances to single 4s–4s bonding (with
the 3d electron cores of the two atoms
antiferromagnetically coupled to give a
singlet state) at long distances. The Cr2
potential provides a beautiful illustration of this phenomenon. Using highly
correlated CASSCF and CASPT2 calculations, Anderson and Roos et al.[13d–h]
gave a qualitatively correct description
of the Cr2 potential energy surface and
calculated a total chromium–chromium
bond order of 4.4 at equilibrium distance. Accordingly, the chromium–chromium bond consists of one s bond of
primarily 4s and 3d contributions, two p
bonds totally 3d in character, two d
bonds totally 3d in character, and one
antiferromagnetically coupled electron
pair. This assignment avoids the rather
counterintuitive description of two chromium–chromium s bonds. The distinc-
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tion between antiferromagnetic coupling and bonding, however, is in this
case not clearly defined.
As with Cr2, the chromium–chromium bond in the complex 1 presented by
Power et al. might alternatively be described as a quadruple bond with two
antiferromagnetically coupled electrons
residing in chromium-localized orbitals.
Magnetic measurements on [Ar’CrCrAr’] revealed a temperature-independent weak paramagnetism of
0.000112(5) emu per mol Cr, which is
consistent with strongly coupled paired
electrons (S = 0) and an first excited
state (S = 1) relatively high in energy,
without a significant population of S > 0
states at room temperature. The most
common metrics used to gauge the
quality of calculations of the electronic
structure of quadruple bonds are the
geometry-optimized metal–metal bond
length and the d–d* excitation energy.
The electronic absorption spectrum of
[Ar’CrCrAr’] displays a broad absorption at 488 nm, which lies in the range
observed for d–d* transitions of compounds with metal–metal quadruple
bonds.
Without doubt, the analysis of the
bonding situation in [Ar’CrCrAr’] as
well as those for the iron and cobalt
analogues, briefly mentioned by Power
and co-workers, will be an interesting
topic among theoreticians. It is very
interesting to note that the structurally
related [Ar’FeFeAr’] (+ 4 electrons) and
[Ar’CoCoAr’] (+ 6 electrons) dimers
have much longer metal–metal contacts
(2.53 / (Fe Fe) and 2.80 / (Co Co)).
Assuming the classical bonding picture,
this would imply an increase of the bond
length of approximately 0.7 / due to
occupation of two antibonding d* orbitals. A bonding distance as long as
2.53 / would result for a formal iron–
iron triple bond!
Going one step further to f block
elements, the uranium atom holds, similarly to a chromium atom, six electrons
in its valence shell. However, whereas
chromium has exactly six valence orbitals, there are 16 such orbitals close in
energy available for uranium; that is the
seven 5f, five 6d, one 7s, and three 7p
orbitals. Gagliardi and Roos recently
presented calculations on hypothetical
diuranium U2 using CASSCF calculations.[14a] As the authors stated, the
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
maximum flexibility for describing electronic structures and the capability of
handling arbitrary spin as offered by the
CASSCF method is important, because
“we cannot assume anything concerning
the final number of paired electrons in
U2”. Indeed, when considering heavy
actinide elements, metal–metal bonds
proved to be particularly complicated.
Although the ground-state electronic
configuration of an uranium atom is
(5f)3(6d)1(7s)2 (quintet ground state),
the energy cost of unpairing the 7s
electrons is low, revealing in principle
six electrons available for each U atom
to form chemical bonds. The bonding
situation for uranium, however, is considerably more complex than the situation found for Cr2—in fact unique, as
reported by Gagliardi and Roos.[14a]
Their calculations revealed that
three (two-electron–two-center) electron pair bonds are formed by hybrid
orbitals with predominantly 7s and 6d
character, that is one s-type and a
degenerate set of p-type orbitals (Figure 5, first row). Furthermore, two singly occupied orbitals of s-type (6dsg)
and of d-type (6ddg), which show mainly
d-orbital character, give rise to two oneelectron–two-center bonds between the
two uranium atoms. Two singly occupied
orbitals of d- and p-type (5fdg/5fpu and
5fdu/5fpg, respectively), with predominantly f character, form two additional
one-electron bonds. Finally, two electrons occupy a localized 5f orbital (5ffu
and 5ffg) equally distributed over both
uranium atoms with the electron spins
aligned parallel. To summarize, the
bonding in U2 arises from three twoelectron–two-center electron pair bonds
(s + 2 p), four one-electron–two-center
bonds (s + p + 2 d), and two localized
electrons. For U2, all single spins are
predicted to be parallel (“ferromagnetically” coupled) and the S = 3 septet state
is the ground state of the molecule.[15]
The calculated (CASPT2-SO, including
spin-orbit coupling, SO) equilibrium
bond length of (2.43 0.05) / and a
harmonic vibrational frequency of
265 cm 1 suggests comparability of the
strength of the U2 bond to that of other
multiple bonds between transition metals. Overall, the unprecedented ground
state of U2 is expressed as
s2p4s1d1d1p1 f1 f1 (with f1 = localized 5f
orbital, S = 3, L = 11, ground state
Angew. Chem. Int. Ed. 2006, 45, 3006 – 3010
Angewandte
Chemie
Figure 5. The molecular orbitals forming the chemical bond between two uranium atoms in U2.
Orbital labels are given below each orbital, together with the number of electrons occupying this
orbital or pair of orbitals in the case of degeneracy[14a] (reprinted by permission from Macmillan
Publishers Ltd: Nature 2005, 433, 848, copyright 2005).
7
1114), and is more complex than any
other known diatomic bond.
If two of the twelve electrons of U2
were removed, some simplifications of
the electronic structure are predicted.[14b] Quantum-chemical calculations,
based on multiconfigurational wave
functions and including relativistic effects, show that the U22+ system has a
large number of low-lying electronic
states with S = 0–2 and L ranging from
zero to ten. A bond length of approximately 2.30 / (cf. 2.43 / for neutral
U2) is common for these states. The
lowest electronic state corresponds to an
electron configuration (sg)2(pu)4 and
suggests a triple bond. The s orbital is
a hybrid comprising 7s, 6ds, and 5fs
atomic orbitals, and the pu orbitals are
mainly 6d in character. The next four
electrons, two localized on each of the
uranium atoms, occupy 5fd and 5ff
orbitals, which are essentially nonbonding.
Recently, a related theoretical paper
presented model calculations on linear
singlet [HThThH], which should be a
likely candidate for the so far unknown
multiple, in this particular case triple,
bond between f elements.[14c] The orbital
picture and the bonding analyses suggest substantial f character in the Th Th
Angew. Chem. Int. Ed. 2006, 45, 3006 – 3010
bond in linear 1Sg-[HThThH] bonding
orbitals. The molecular orbitals of this
compound correspond to s(Th H)
bonds,
one
s(Th Th)
bond
(HOMO 1), and a double p(Th Th)
bond (HOMO) featuring up to 22 % f
character in the bond. According to the
calculations the f-orbital participation
stabilizes the linear geometry of the
molecule.
The model of the two-electron–twocenter bond, as introduced by G. N.
Lewis in 1916, which features a single
bond to be formed by one pair of
electrons, is one of the most important
concepts in chemistry. This also covers
multiple bonds since they are regarded
as composed of two, three or four twoelectron components. The last few years
have witnessed an in depth discussion on
multiple bonding between main group
elements, which has revealed that simple concepts mainly emerging from the
peculiarities of carbon (or the second
period of elements) chemistry are not
valid for heavier elements. Apparently,
the models, which are consistent and
clear for the lighter main group elements, become considerably more complicated than anticipated when applied
to their heavier counterparts. The same
holds true for the term “bond order”,
which is in fact more or less a matter of
definition—not trivial if reasonable at
all. The decrease of orbital overlap and
increase of nonbonding lone-pair character for molecules of multiply bonded
main group elements, and hence the
deviation from planarity (for R2EER2)
or linearity (REER) has shown that the
concepts developed for elements of the
second period are certainly not appropriate to describe the nature of an
element–element “multiple” bond. The
involvement of d orbitals certainly complicates the situation due to moderate
overlap for d-type d orbitals. The work
of Power et al., in unraveling the quintuple bond in trans-bent [Ar’CrCrAr’]
(1), has added a further dimension to the
concept of multiple bonding in transition-metal chemistry. It is likely, however, that the bonding situation in
[Ar’CrCrAr’] is not fully understood
and that the trans-bending of this complex will add an additional level of
complexity to the analysis of bonding.
The current state of the bond description for 1 is that five pairs of overlapping
orbitals are more or less involved in
metal–metal bonding; a situation that
chemists usually would describe as a
quintuple bond.[16] A detailed theoretical analysis of the nature of the chemical bond in 1 will certainly be undertaken in the future and it is likely that
there will be a renewed debate about
metal–metal multiple bonding. To fully
understand the bonding in this complex
is of crucial significance and many
fundamental questions remain to be
answered. Whatever the conclusion
turns out to be regarding the bond
multiplicity in the newly synthesized
compound [Ar’CrCrAr’], this work undoubtedly inspires scientists from a
theoretical and experimental point of
view.
The greatest achievement here is the
preparative work, which has opened a
new area previously considered nonexistent. This work will certainly encourage others to investigate transitionmetal complexes bearing “ultralarge”
ligands in more detail. The combination
of both the isolation of further compounds of the type [RMMR] on the one
hand, and their precise characterization
on the other, may facilitate an accurate
experimental assessment of the bonding
situation and the bond strength in these
2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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3009
Highlights
types of complexes. The main objective
for experimental as well as theoretical
chemists is undoubtedly to work together to develop an understanding of this
unusual bonding situation between dblock metals—and similar compounds
comprising f-block metals are not out of
reach!
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3010
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433, 848; b) L. Gagliardi, P. PyykkP,
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2005, 7, 2415; c) M. Stratka, P. PyykkP, J.
Am. Chem. Soc. 2005, 127, 13090.
[15] Note the difference to Cr2 featuring
“antiferromagnetic” coupling, which
causes spin-pairing of the electrons and
usually provides some additional small
bonding contributions and some extra
stabilization. In the particular case of
U2, this ferromagnetic coupling can be
attributed to favorable exchange stabilization, that is interaction between nonbonding 5f electrons and one-electron
bonds.
[16] Bonding pictures might also be totally
unexpected, as experienced in the case
of U2 ; see also: M.-M. Rohmer, M.
BUnard, Chem. Soc. Rev. 2001, 30, 340
Angew. Chem. Int. Ed. 2006, 45, 3006 – 3010
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