Table Of ContentContents
Metal-Ligand Bonding in 3d Sandwich Complexes
D. W. Clack, K. D. Warren . . . . . . . . . . . . . . . . . . . .
The Ligand Polarization Model for the Spectra of Metal
Complexes: The Dynamic Coupling Transition Probabilities
.S F. Mason . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Sulfur Interaction with Metallic Surfaces and
Interfaces Studied by Auger Electron Spectrometry
L. R. Balsenc . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Author-Index Volumes 1-39 . . . . . . . . . . . . . . . . . . . . 511
MetaI-Ligand gnidnoB
ni 3d Sandwich sexelpmoC
Denis W. Clack and Keith D. Warren
Department of Chemistry, UniversRy ,egelloC ,ffidraC ,selaW United Kingdom.
Table of Contents
1 Introduction ............................................ 2
2 The Study of Metal-Ligand Interactions in Sandwich Systems ................ 5
3 Molecular Orbital Treatments ................................... 12
4 Symmetrical Sandwich Systems ................................. 17
5 Mixed Sandwich Systems ..................................... 26
6 The Effects of Heteroatoms .................................... 36
7 Summary .............................................. 39
8 References ............................................. 40
Abbreviations used:
Cp = CsH s
Bz = C6H 6
Ch = C7H7
Cb = C4H 4
Cpr = C3H 3
Cot = C8H 8
py = CsHsN
BBz = CsHsBR
This review examines the bonding between the metal and the ligand rings for various series of
first row transition metal sandwich complexes containing three- to eight-membered carbocyclic
rings. The principal bonding contributions for all the complexes occur between the ring ~r-orbitals
and the central metal 3 d (e 1 and e2) levels, although there is also a significant involvement of the
ring a-system, particularly with the higher lying metal 4 s and 4 p orbitals. The extent of the split-
ting, and in some cases the ordering, of the metal 3 d orbitals is determined almost entirely by the
interactions with the ligand-~r e 1 and e 2 combinations. It is shown that the particular ground state
adopted for certain electronic configurations (espeically d 4 and d s) depends critically upon these
interactions~ The effect on the bonding, and the 3 d orbital splittings, of the introduction of the
hetero-atoms boron and nitrogen into six-membered ring systems is also discussed.
D.W. Clack and K.D. Warren
1 Introduction
Although transition metal sandwich complexes have now been known for more than
25 years1), it is probably true to say that our understanding of the essential nature of
the metal-ligand interactions therein has only begun to develop at an appreciable pace
within the last decade. To this extent therefore our knowledge of metal sandwich
species has lagged behind that of the more familiar octahedral and tetrahedral com-
plexes of the transition series, for which the early ligand field approaches, due to
Orgel2), amongst others, gained rapid acceptance, and for which both qualitative and
quantitative molecular orbital calculations were fairly quickly fruitful.
However, scientific progress frequently depends as much upon serendipity as
upon sheer effort or merit, and ruO insight into the bonding mechanisms obtaining
for sandwich species has been suffered to advance much less readily. Thus, most of
the early theoretical work on these systems was carried out by two Russian workers,
Shustorovich and Dyatkina, who performed molecular orbital calculations for bis-
benzene chromium3), and for most of the then known metallocenes, especially fer-
rocene 4), and the orbital energy diagrams resulting therefrom have since been widely
quoted in the literature (see for exampleS-7)). For ferrocene it was found that the
two highest occupied molecular orbitals were of g~a and e~ symmetry (of dominantly
~zd and ,~y-~xd dxy character respecitvely), but the virtual, anti-bonding, elg level
(mostly dxz, d~) lay some 51 eV. above the g2e level with numerous other virtual
levels, both mainly metal and mainly ligand, intervening between them. Now this sit-
uation arises chiefly from the fact that the metal 3 d levels and the ligand latibro-r7
combinations (which make the major contribution to the bonding, vide infra) are of
quite comparable energy, whereas for the more familiar ,iO 6XM complexes, e.g.
MF~- systems, the ligand levels lie well below those of the metal, so that the two
components (t~ and eg) of the d-orbitals in Oi, symmetry will generally be juxtaposed.
Moreover, it must always be borne in mind that the actual energies of the virtual SCF
levels have no real physical significance, and will in any case be appreciably lowered
upon occupation, whilst to complicate matters still further it is now realised that all
transition metal sandwich systems are prone to show wide deviations from the pre-
dictions of Koopmans' theorem.
Consequently, the establishment of a coherent picture of the metal-ligand bond-
ing in transition metal sandwich species was at an early stage beset with difficulties
and misunderstandings, in contrast to the relatively clear ideas that emerged for, say,
octahedral systems. Thus, in these latter it became apparent that in general a model
could be assumed in which the dominantly d-orbital levels of t2g and eg symmetry
lay quite close together, without other levels intervening, and that normally such sys-
tems corresponded formally to various d x configurations, with d-d transitions consti-
tuting the lowest energy excitations and charge-transfer bands (most often ligand ~ met-
al) lying at higher energies. On the other hand, for sandwich systems exceeding the
familiar 18-electron (or d 6) configuration, it was by no means clear where the ad-
ditional electrons might be located, and for systems such as cobaltocene and nickel-
2
dnagiL-lateM gnidnoB in d3 hciwdnaS sexelpmoC
ocene (now known to correspond to formally d 7 and d s arrangements) there was
speculation as to whether or not the metal 4s and 4p levels or the ligand e2u orbitals
might be occupied.
As a result it was only gradually, towards the end of the 1960s, that the accumu-
lating bulk of experimental evidence could be seen to be supporting the applicability
of a ligand field model: for example, such a model would treat niekelocene, NiCp2,
as formally Ni ÷2 2 Cp-, and thus as a d s system. In this the early efforts of Scott
and Becker 8- lo) and the later work of Scott and Matsen )11 were preeminent, and
this was followed by treatments of d2(dS), and d3(d 7) systems by Cerny and his col-
laborators, with analyses of d-d spectra and magnetic data 12-14), and the measure-
ments and calculations of Sohn, Hendrickson, and Gray Is )61, on d s and d 6 systems.
In addition a full ligand field treatment of all the d x configurations, and the d-d
spectra to be anticipated therein, assuming effectively pseudoaxial symmetry, was
given by Warren 17-19), who also gave a complete account of their magnetic proper-
ties2O,21), and a detailed survey of the results of the ligand field approach for transi-
tion metal sandwich systems )22 (quod vide for further details).
From such treatments it became clear that the metallocenes, bis-arene compounds,
and other sandwich species, gave quite large values of the one-electron &orbital split-
ting parameters, and values of the nephelauxetic ratio well below unity (usually ca.
0.5), thereby indicating a very extensive metal-ligand interaction. Thus, these systems
having been treated phenomenologicaUy, it remained to attempt to interpret any
systematic trends in the values of the parameters thereby obtained. Now it was of
course evident, as soon as the sandwich structures of ferrocene and bis-benzene chro-
mium had been experimentally established, that the dominant bonding interactions
in such molecules should involve the metal orbitals and the delocalised 7r-systems of
the ligand rings, and this was assumed in the early Russian work. Furthermore, the
nature of these interactions, especially those involving the metal 3 d levels, was
studied in some detail by Fischer )32 in 1963, who pointed out that the extent of the
involvement of the elg (dxz, dyz) and e2g (dx2_y2 , dxy ) orbitals in bonding with
the dnagil-r¢ combinations of the corresponding symmetry should depend quite
strongly upon the size of the ligand ring concerned. Thus, taking the metaUocenes as
an example, a situation such as that depicted in Figure 1 usually obtains: here the
ligand 7r-orbital combinations follow the energy sequence ~la r ~a2u < elg ~ elu < ,
e~ ~ e~, with E(I., elg) < ElM, sa)< ~0-, e~).
It is however well known that for conjugated cyclic ligands the energies of the
els and e2s ligand orbitals (Ir) become progressively more negative with increasing
ring size, and thus, assuming that E(M, 3 d) remains less than E(L, e2s), the extent of
the 3d e2s interaction should increase (the mainly 3d level becoming more bonding)
and that of the 3d elg interaction should decrease (the mainly 3d level becoming less
anti-bonding), as the ring size is increased. In the naive approximation E(L, als) re-
mains the same, and in any case, due to unfavourable overlap, the 3d alg level is not
expected to mix significantly with the ligands.
3
D.W. Clack and K.D. Warren
~2g
~2u " .- u2~
/
~lg /
3d / gllC ,/
~lu \ ~lu
\
~lg / /
u2Q 02u
Fig. 1. Metal 3 d-ligand-~r interaction in MCP2
g~O Olg
systems
It is of course true that the ligand a-framework may play some role in the metal-
ligand bonding, but normally this contribution is found to be a good deal less signifi-
cant than the 7r-interaction, although in interpreting certain phenomena, for example
tour contact shifts, the a-involvement proves to be important. Nevertheless, the expec-
tation remains that the major metal-ligand interactions should be markedly dependent
on ligand ring size, and it is therefore clearly desirable to examine the one-electron
splitting parameters obtained by the ligand field treatment, and any other experimen-
tally accessible quantities, so as to ascertain whether these results can support this
hypothesis, and further to scrutinise the results of any available molecular orbital cal-
culations with the same objective.
There has naturally been no shortage of molecular orbital calculations for the
transition metal sandwich complexes, although unfortunately most of these have
tended to be concerned only with ferrocene. Thus, after the early attempts of Shu-
storovich and Dyatkina, few workers appear to have treated any of the other metal-
locenes, or the bis-benzene species, and little attempt was made at a systematic cover-
age of both these series of compounds. Part of the problem arose however from the
size of the systems to be considered. Thus, including the usual nine orbitals of
the metal (3d, 4 ,s and 4p), there remain both the o-framework and the Ir-orbitals of
the ligand rings, together with the ring hydrogen atoms, so that if both carbons 2 s
and 2p orbitals are taken there results for ferrocene a basis set of no less than fifty
nine orbitals, increasing to sixty nine for bis-benzene chromium. Consequently, some
of the earlier MO treatments tended (unjustifiably) to neglect the o-frameworks of
the rings, whilst other later calculations, although including both a- and 7r-contribu-
tions and dealing with whole series of compounds, merely adopted the simple Ex-
tended Hiickel technique. Ideally, one would like to have available the results of
ab initio calculations for the whole range of sandwich systems, such as those car-
4
dnagiL-lateM gnidnoB in 1~3 hciwdnaS sexelpmoC
ried out by Veillard and his collaborators )42 for ferrocene, but the need to economise
in both time and cost suggests that some compromise between the rigour of the ab
inito and the crudity of the Extended Htickel methods should be sought.
One such approach is represented by the INDO SCF MO technique of Clack2S),
which has been thoroughly tested, both on octahedxal transition metal complexes,
where it was strikingly successful in reproducing Tanabe-Sugano type diagrams26-2a),
and on sandwich systems such as manganocene 29), chromocene a°), and bis-benzene
chromium31). Consequently this method has been used by the authors in a wide rang-
ing series of calculations on transition metal sandwich speciesa2-42), in which an at-
tempt has been made both satisfactorily to reproduce experimentally determined
quantities, and also to interpret these in terms of a self coherent understanding of
the principal contributions to the metal-ligand bonding process. It is not of course
pretended that the chosen INDO scheme constitutes the only satisfactory method for
tackling this problem, but whilst it employs a partial differential overlap approxima-
tion it retains the very important one-centre exchange terms, without which any hopes
of a correlation with the results of the ligaud field approach would be futile, and re-
presents a reasonable compromise in the hierarchy of available MO techniques.
The aim of this article is therefore to present a unified account of the picture of
the metal-ligand bonding in sandwich systems to which our results have led us. For
this purpose we first discuss the experimental methods whereby information about
this may be forthcoming. This is followed by a fuller description both of the molecu-
xal orbital scheme appropriate for sandwich species, and of the particular technique
used, and of the results thus obtained for metallocenes, bis-benzene compounds,
mixed sandwich systems, and systems containing ring heteroatoms. Throughout the
survey special emphasis is placed on determining the extent to which the dependence
of the metal-ligand interactions, predicted by the naive model, is or is not valid. More-
over, attention is also directed particularly towards examining the extent to which the
molecular orbital and ligand field approaches are compatible and may together con-
solidate our knowledge of such metal sandwich systems.
2 The Study of Metal-Ligand Interactions in Sandwich Systems
Although this survey is primarily concerned with the interpretation of the results of
molecular orbital calculations, it is apparent that a necessary prerequisite for such a
scrutiny is the availability of a sufficiently extensive body of experimental data, with
which comparisons may be made and the reliability of other theoretical predictions
established. Consequently, it is pertinent here to examine the practical methods by
which basic information about the bonding processes in sandwich species may be ob-
tained, and how the ligand field parameters thus derived may shed light on the nature
of the metal-ligand interactions.
.W.D Clack and K.D. nerraW
(i) Electronic Spectra. - The study of the d-d spectra of metal sandwich species
is naturally one of the most direct methods of deriving information about the bond-
ing in such systems. Thus, in principle, for any given d x configuration (x = 2 - 8),
the assignment and fitting of the d-d bands should enable both the effective Raeah
inter-electronic repulsion parameter, B, to be found (assuming an appropriate value
of the ratio C/B), and the two one-electron d-orbital splitting parameters, Ds and Dt,
which arise for systems of pseudo-axial symmetry, to be determined. Moreover, it
was shown by Scott and Matsen )11 that all d x sandwich systems with C5 or higher
rotation axes of symmetry could be treated on the assumption of v**C symmetry, the
one-electron energies of the dz~ (o or a lg), dxz, dyz r~( or elg), and dx2_y~ , dxy
(8 or e~) orbitals (using either the C®v labels on the one hand or those of the Dsa
or D6h point groups on the other) being given by the relationships: -
E(g) = e o = 2Ds-6Dt
E(Ir) = el = Ds + 4 Dt
and
E(8 ) = 2G = - 2 Ds - Dt .
The experimental data for metallocenes and for bis-benzene complexes clearly
indicate the sequence e2 < e0 < el, and the former series proves to be quite well fit-
ted with the parameterisation Dt ~ 0.55 Ds. Alternatively, it is often convenient to
define the parameters A E1 and A E2, which correspond to the actual one-electron
splittings with AE 1 = (el - )oG and AE 2 = oC( - e2), so that the above choice ot
the Dt/Ds ratio for the metallocenes would represent A E 1/A E 2 = 18/7. Furthermore,
the parameters A E 1 and A E 2 are in fact a rather direct measure of the extent of the
interactions of the metal dxz, dyx levels with the ~-ligand elg orbitals (A E 1), and of
that of the metal dx2_y~, dxy levels with the ~-ligand e~ orbitals (AE2): thus the
~zd metal level is usually essentially non-bonding and since the mainly dxz , dy z level
si inherently anti-bonding in character, and the dominantly dx~_y2, dxy level always
somewhat bonding in character, then the larger the values of either A El or A E2, the
greater should be the extents of the corresponding metal-ligand (e~g) and metal-ligand
(e2g) interactions (see Fig. 2).
16 I
AE
o 1 I
AE Fig. 2. Splitting of 3 d slevel in laixa-oduesp
6 2 symmetry
6
dnagiL-lateM gnidnoB in d3 hciwdnaS sexelpmoC
Unfortunately, the available electronic spectral data are neither as extensive nor
as readily interpreted as might have been wished, and apart from the metallocene
series the experimental information is rather sparse. Of the MCp2 series the d 3 and
d s systems of VCp2 and NiCp2 constitute especially favourable cases for deriving
definitive values of A El, A E2, and B (see22)), but although parameters have been
deduced for various other species (CrCp2 (d4), FeCp2 + (dS), FeCp2 (d6), and
CoCp2 (dT)), they are generally less precisely established. Nevertheless, for the MCp2
series it is clear that A E 1 is substantially larger than A E2, the former ranging from
about 14,000 to 22,000 cm -1 , and the latter from around 4,000 to 7,000 cm -~ .
For the bis-benzene complexes and the mixed sandwich systems however the spec-
troscopic information is not really adequate to establish reliable values of these
quantities although it is consistent again with the one-electron sequence g2e < al t <
elg.
In addition an analysis of the values of/3, the nephelauxetic ratio, derived from
the metallocene data, permits a more quantitative estimate of the extent of metal-
ligand interaction to be made. Thus, if one takes the limiting assumption of purely
symmetry restricted covalency, then .~ should show a fourth power dependence on
the metal mixing coefficient so that/3~ should be a tolerable estimate for the frac-
tion of metal 3 d character in the dominantly d-orbitals. Thus, since the observed/3
values are generally of the order of 0.5 + 0.1, the average d-orbital contribution to
these levels should lie in the range 0.7 + 0.07. However, the B (and/3) values derived
from the spin-allowed d-d bands generally relate to transitions which involve the exci-
tation of electrons from either the g2e or the alg levels to the much higher lying
elg level, so that the observed/3 values really represent only an average metal involve-
ment. Moreover, as the relatively small A E2 values observed suggest, the g2e metal
orbitals exa not very strongly engaged in the bonding, and our OM calculations (vide
infra) suggest that for both alg and g2e levels the 3 d contribution is of the order of
90% or so, although for the elg level it is only some 60%. It is therefore gratifying
that the experimental data clearly support this finding. Thus for VCp2 and CrCp2 +
the assignment of the transitions involving only the alg and g2e levels yields )22 If
values (~ oC 4 ~ c~) of ca. 0.70 to 0.75, so that o2C or ~c should be approximately
0.85, in reasonably good agreement with the OM result. Moreover, for NiCp2 the -sa
signment of the intra sub-shell (e~ ag e~g) transitions (involving changes only in the
elg occupations) yields a ~ value (~c~) of 0.40, so that ~c should be about 0.63,
again in good accord with the MO result. Also the average of the two/3' values
("~c~ ~c "c c~), 0.63 x 0.85 (= 0.54), is, as would be anticipated, very close to the
average/3 value of 0.5.
In the MCp2 series the charge-transfer spectra have also been measured, both for
the parent systems and for the 1 ,l'-dimethyl analogues M( = V, Cr, Mn, Fe, Co, Ni)43).
For the d 3-6 species the bands were all found to be of the L *- M (elu >-- g2e or alg),
but for the d 7 and d 8 systems it was concluded that M ~- L (elg ~ e2u) transitions
probably took place as well as those from ligand to metal (elu ~- ezg ). The available
evidence from this source therefore supports the previous conclusion of a substantial,
anti-bonding, elg interaction, with a smaller, bonding, eeg , involvement. (See also
D.W. Clack and K.D. Warren
qualitative OM scheme, Fig. 1). Thus, in terms of orbital populations, the picture in-
dicates a strong elg (Cp ~- M) donation, with a weaker g2e M( ~- Cp) electron acces-
sion.
(ii) Magnetic Moments and ESR Spectra. - Although the study of electronic
spectra is a direct and obvious method of investigation, it suffers as Ammeter )44 has
pointed out, from the drawback that the observables depend in a complex way on
the total electronic wave functions of more than one state at a time. By contrast, ESR
spectroscopy, although only applicable to paramagnetic systems, may yield parame-
ters which, to a first approximation, depend only upon the wave functions of singly
occupied valence levels, and is thereby capable of giving much more precise infor-
mation about such orbitals. However, early studies of paramagnetic sandwich systems
were more concerned with the measurement of the magnetic susceptibilities and mo-
ments of these species, and although this can afford valuable information, especially
in determining the nature of the ground state, it is generally a much less sensitive
technique than the related ESR experiment. In this section therefore we first deal
briefly with the results of susceptibility measurements, and then in more detail with
the ESR data.
For orbitally non-degenerate ground states the measurement of the magnetic
moment will of course provide no useful information since the spin-only value should
always result. On the other hand systems with orbitally degenerate ground states will
in principle be subject to distortions from pseudo-axial symmetry due to Jahn-Teller
activity (ff to no other cause), and the determination of the temperature dependence
of the magnetic susceptibilities of these species can lead to estimates of two useful
experimental parameters, namely (a) the splitting, A, of the degenerate elg or ~2e
level due to orthorhombic distortions, and (b) the orbital reduction parameter, k',
by which the L terms of the Zeeman operator, L + 2~, are reduced, due to electron
delocalisation from the metal onto the ligands. (Strictly speaking it is only the ratio,
A/G, which is derived, so that an effective value of ,~ the spin-orbit coupling constant,
must be assumed).
Theoretical treatments of the temperature dependence of the magnetic moments
have been made by Warren2°), and for some cases by Cerny14), in which details were
given of the derivation of the quantities A and k', although the distortions from pseu-
do-axial symmetry represented by A were therein assumed to be static. However,
Ammeter and his collaborators have shown 4s ,46), that if the distortions arc of dy-
namic Jahn-TeUer origin, as seems to be the case for the metallocenes, then the ap-
parent orbital reduction parameter, ,'c really represents a composite quantity which
is actually the product of the true orbital reduction factor,/ell, and a quantity, ,FI
which is the vibrational overlap integral between the two orbital components of the
ground state.
In fact the available susceptibility data relate mainly to the metallocenes, but
are not sufficiently accurate to determine either A or k' very precisely. Howcver, it
does appear that the A values deduced are greater for the elg than for the g2e dege-
neracies, and in accordance with this the k' values are smaller for el# than for g2e
levels. Since/¢' is associated with a one-electron operator the true orbital reduction
8
Metal-Ligand Bonding in 3d Sandwich Complexes
parameter should show a quadratic dependence on the metal mixing coefficient for
the orbital concerned, and thus be roughly equivalent to the fraction of metal char-
acter therein. Consequently, the magnetic moment data also support the view that
the elg 3d levels are more mixed with the ligands than are the e2s, and in addition
the Jahn-Teller distortions would be expected, as observed, to be greater for the level
more involved in the bonding process for the metallocenes (elg) than for that less
significantly mixed .)g2e(
However, almost all the reported magnetic susceptibility data refer only to the
isotropic (average) values of × and/z (only one measurement of the anisotropic ll×
and ±X being recorded47)), and in most cases the results yield markedly less useful
information than the corresponding ESR experiment. We therefore now consider
what insights the latter technique may afford for (a) non-orbitally degenerate, and
(b) orbitally degenerate ground states. (See also reference )44 for a detailed and lucid
review).
Systems belonging to the former category will possess ground state configura-
tions in which the orbitally degenerate levels are evenly occupied, with a single elec-
tron in the gla (mainly 2zd ) level, e.g. VCp2 and CrCp2 + (e~ als), ,g2A4 and
VBz2 and CrBz2 + (e~r alg), 2Alg. The accessible information thus relates essential-
ly to the properties of the alg orbital, and since spin-orbit coupling to excited states
is relatively weak the llg and g± values are both quite close to 2. The results show
that the odd electron is located in an essentially pure metal ~zd level in all the cases
mentioned (see 22 ,44) and references therein cited), and since for V and Cr the metal
hyperfine splitting constants could also be determined, it proved possible also to
deduce that a smaller admixture (ca. 2-5%) of 4 s character into the open-shell orbi-
tal took place too.
For the manganoeene systems ESR data also proved to be of great value in study-
gah the spin cross-over behaviour (e.f. also22)). Thus, by a suitable variation of the
host lattice it was found that either a high-spin, 6Alg (e~ alg es), or a low-spin,
2E2g (e~r a~g), ground level could be observed, thus providing additional evidence for
the propinquity of these two levels, in accordance with both PES data 4s) and the
results of INDO SCF MO calculations29).
Furthermore, low-spin, 2E2g, manganocene also represents one of the four acces-
sible orbitally degenerate metallocene ground states which have been studied exten-
sively by the ESR technique, the other systems being FeCp2 +, 2Ezg (e~ a2g), to-
gether with CoCp2 and NiCp2 +, 2Elg (e~ 4 ale 2 elg ). These species are all in princi-
ple susceptible to Jahn-Teller distortions, although the accumulated evidence indi-
cates that at all times EjT- (the Jahn-Teller stabilisation energy) will be less than the
energy of the appropriate active vibrational mode, and that the Jahn-Teller distor-
tions in the rings will therefore remain entirely dynamic. However, detailed ESR
studies of the orbitally degenerate metalloeenes necessitate low temperature measure-
ments on solid samples diluted in various host lattices, and as Ammeter )44 has pointed
out this inevitably results in the imposition of an additional asymmetric potential
due to the lattice environment. Nevertheless, it has been shown 44,46) that the ESR
data for this complicated situation (static distortion + dynamic Jahn-Teller effect)
9
