The Electronic Structure of Ferrocene

The Electronic Stru

• The two cyclopentadienyl (Cp) rings of
extremes of either an eclipsed (D5h) or st

• The energy of rotation about the Fe‐Cp
state structures of ferrocene may show e

• There is also very little difference in e
symmetries however the D5d point group
in the description of the electronic str
symmetry matching of ligand molecular o

• The primary orbital interactions that f
occur between the Fe d orbitals and the

• If D5d symmetry is assumed, so that ther
molecule through the Fe atom there
symmetric (u) combinations.

ucture of Ferrocene

f ferrocene may be orientated in the two
taggered (D5d) conformation.

axis is very small (~ 4 kJmol‐1) and ground
either of these conformations.

electronic states between the D5h and D5d
p irreducible representations are used here
ructure of ferrocene as they simplify the
orbitals (SALCs) and metal atomic orbitals.

form the metal‐ligand bonds in ferrocene
‐orbitals of the Cp ligand.

re is a centre of symmetry in the ferrocene
e will be centro‐symmetric (g) and anti‐

 MOs of Cyclop

• C5H5 , has three pairs of electrons delo
pentagonal ring.

• The five 2p orbitals perpendicular to the
form three bonding (1, 2, 3) and three

• The symmetries and forms of these MOs
the point group D5h to a set of five vec
carbon, to generate a reducible represent

pentadienyl, C5H5‐

ocalized in a  system extending around the

e ring on the five carbon atoms combine to
antibonding (4*, 5*, 6*) MOs.
can be deduced by applying the operations of
ctors perpendicular to the ring, one at each
tation  .

 MOs of Cyclop

D5h E 2C5 2C52 5C2

5 0 0 -1

A1' 5 0 0 -5

A2' 5 0 0 5

E1' 10 0 0 0

E2' 10 0 0 0

A1'' 5 0 0 -5

A2'' 5 0 0 5

E1'' 10 0 0 0

E2'' 10 0 0 0

pentadienyl, C5H5‐

h 2S5 2S35 5 v /h h = 20
-5 0 0 1

-5 0 0 5 0 0
-5 0 0 -5 0 0
-10 0 0 0 0 0
-10 0 0 0 0 0
5 0 0 -5 0 0
5 0 0 5 20 1
10 0 0 0 20 1
10 0 0 0 20 1

d

• The five p‐orbitals on the planar Cp r
produce five molecular orbitals according

• One combination has the full symmetry o
• There are two doubly degenerate comb

planar nodes at right angles to the plane
• The relative energies of these orbitals inc
• The a2’’ and e1’’ orbitals are both fully o

the Cp‐ anion whereas the e2’’ orbitals ar

ring (D5h symmetry) can be combined to
g to the reducible representation:

of the ring (a2’’)
binations (e1’’ and e2’’) having one and two
e of the ring.
crease as the number of nodes increases.
occupied in the electronic configuration of
re net anti‐bonding and are unfilled.

The ‐molecular orbitals of th

E2''
(4 nodes)

anti-bonding

E1''
(2 nodes)

weakly bonding

A2''
(0 nodes)

bonding

• The five p‐orbitals on the planar Cp
produce five molecular orbitals.

he cyclopentadienyl ring (D5h)
ring (D5h symmetry) can be combined to

• For a bis‐cyclopentadienyl metal comp
orbitals of the two Cp ligands are co
adapted linear combination of molecula
the irreducible representations of the D

A1g E

plex (5‐Cp)2M , such as ferrocene, the ‐
ombined pairwise to form the symmetry‐
ar orbitals (SALC’s) which are described by
D5d point group.

1g E2g A2u E1u E2u

• The  SALCs of the (Cp)2 framework a
of SALCs from the two contributing Cp
the irreducible components of  (Cp)2 ,

(1+1), (1‐1); (2
where, for example, '1+1' gives rise to

• This gives rise to three sets of ligan
ungerade (u) symmetry with respect to t
 a low lying filled bonding pair of A1g
 a filled weakly bonding pair of E1g an
 an unfilled anti‐bonding pair of E2g a

are also defined by the sum and difference
ligands whose results must correspond to
, i.e.

2+2), (2‐2) ...etc.
o a molecular orbital of A1g symmetry.

nd molecular orbitals of gerade (g) and
the centre of inversion;
g and A2u symmetry
nd E1u symmetry
and E2u symmetry.

SALCs for a (5‐

e2g

e1g

Z

Y
X

a1g

A1g E1g

‐Cp)2M complex

e2u

e1u
a2u

E2g A2u E1u E2u

• Using the reducible representation of
found

A1g E1g E2g

• Thus, in D5d the bonding metal orbitals tra

A1g :  (s , dz2)

E1g :  (dyz , dxz)

E2g :  (dx2 ‐ dy2, dxy)

A2u :   (pz)

E1u :  (px, py)

• By considering the AO and SALC symmet
MO bonding picture of ferrocene can be c

• Each combination of AOs and SALCs
[(ligand molecular orbital)+(metal atomic orbital)] an
orbital [(ligand molecular orbital)‐(metal atomic o
two component sets are sufficiently close

SALCs the corresponding metal AOs are

A2u E1u E2u

ansform as

tries and how overlap can be affected the
constructed.

leads to a bonding molecular orbital
nd a corresponding anti‐bonding molecular
orbital)] providing that the energies of the
e for overlap.

Symmetry matching of the SALC

dxy dx2-dy2
e2g

d yz d xz

e1g

Z

Y
X

s d z2
a1g

C’s with the metal atomic orbitals

no metal no metal
orbital of orbital of
appropriate appropriate
symmetry symmetry
available available

e2u

py px
e1u

pz
a1u

A qualitative molecular orbital

FeII

Fe

pz py px a2u , e1u
a1u e1u

a1g
a1g , e1g , e2g

dyz dxz
e1g

l diagram for ferrocene (D5d)
SALC's

e2g , e2u
e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u
a1u e1u

a1g a1g
a1g , e1g , e2g a1g

dyz dxz
e1g

l diagram for ferrocene (D5d)
SALC's

e2g , e2u
e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u
a1u e1u

a1g a1g*
a1g , e1g , e2g a1g

dyz dxz a1g
e1g

l diagram for ferrocene (D5d)
SALC's

e2g , e2u
e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u
a1u e1u

a1g a1g*
a1g , e1g , e2g a1g

dyz dxz a1g
e1g

l diagram for ferrocene (D5d)
SALC's

e2g , e2u
e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u a2u*
a1u e1u a1g*

a1g a1g
a1g , e1g , e2g

dyz dxz
e1g

a2u
a1g

l diagram for ferrocene (D5d)
SALC's

e2g , e2u
e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u a2u*
a1u e1u a1g*

a1g e1g*
a1g , e1g , e2g a1g

dyz dxz e1g
e1g
a2u
a1g

l diagram for ferrocene (D5d)
SALC's

e2g , e2u
e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u e1u*
a1u e1u a2u*

a1g*

a1g e1g*
a1g , e1g , e2g a1g

dyz dxz e1u
e1g e1g

a2u
a1g

l diagram for ferrocene (D5d)
SALC's

e2g , e2u
e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u e1u*
a1u e1u a2u*

a1g*
e2g

a1g e1g*
a1g , e1g , e2g a1g
e2g
dyz dxz
e1g e1u
e1g

a2u
a1g

l diagram for ferrocene (D5d)
SALC's

*
g

e2g , e2u

e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u e1u*
a1u e1u a2u*

a1g*
e2g

e2u

a1g e1g*
a1g , e1g , e2g a1g
e2g

dyz dxz e1u
e1g e1g

a2u
a1g

l diagram for ferrocene (D5d)
SALC's

*
g

e2g , e2u

e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u e1u*
a1u e1u a2u*

a1g*
e2g

e2u

a1g e1g*
a1g , e1g , e2g a1g
e2g

dyz dxz e1u
e1g e1g

a2u
a1g

l diagram for ferrocene (D5d)
SALC's

*
g

e2g , e2u

e1g , e1u
a1g , a2u

A qualitative molecular orbital
FeII
Fe

pz py px a2u , e1u e1u*
a1u e1u a2u*

a1g*
e2g

e2u

a1g e1g*
a1g , e1g , e2g a1g
e2g

dyz dxz e1u
e1g e1g

a2u
a1g

l diagram for ferrocene (D5d)
SALC's

*
g

e2g , e2u

LUMO
HOMO

e1g , e1u

a1g , a2u

• Due to a difference in energies the low
ligand based with a slight admixture of t

• Similarly the a2u level has little if any m
orbital with which it is formally able to c

• The e1g molecular orbital arises from th
orbitals with the Fe 3dxz and 3dyz orbit
of orbitals in the two Cp rings that ha
orbitals to act as an efficient donor and
responsible for the stability of the comp

• The corresponding anti‐bonding orbital
ferrocene but they are involved in excite

• The e1u bonding molecular orbitals are a
contribution from the higher energy Fe

• The a1g HOMO mostly consists of the Fe
dz2 orbital result in little or no overlap.

• The e2g (dx2‐y2, dxy) metal orbitals are
overlap with the e2g SALC orbitals.

west energy a1g molecular orbital is mainly
the Fe 4s and 3dz2 orbitals.

metal character due to higher lying Fe 4pz
combine.

the bonding combination of the ligand e1g
tals. This is the only symmetry combination
as appreciable overlap with the metal 3d
d it is thus this interaction which is mainly
plex.

ls, e1g*, are unfilled in the ground state of
ed state transitions.

again mainly ligand based but with a small
3 px , py orbitals.

e 3dz2 orbital as the a1g SALC and the metal

e considered weakly‐bonding due to poor

• Since the occupied orbitals are of either
barrier to internal rotation is predicted a
symmetric about the axis of rotation.

• The very low values observed for this ro
van der Waals forces between the two C

• The attachment of additional groups or 
ferrocene thus significantly altering the 

1. S. Barlow, H. E. Bunting, C. Ringham, J. C. Green, G. U. Bublitz, S. 
121, 3715‐3723.
2. J. C. Calabrese, L. T. Cheng, J. C. Green, S. R. Marder, W. Tam,  J. A
3. D. R. Kanis, M. A. Ratner, T. J. Marks, Chem. Rev. 1994, 94, 195‐24

r a1g , e1g or e2g type symmetry no intrinsic 
as each of these molecular orbitals are 

otation (~ 4 kJmol‐1) may be attributed to 
Cp rings.
 ligands destroys the D5d/D5h symmetry of 
 MO diagram.

 G. Boxer, J. W. Perry, S. R. Marder, J. Amer. Chem. Soc. 1999,   
Amer. Chem. Soc. 1991, 113, 7227‐7232.
42.

The Electronic Structure
Cr(6‐

• Similar to ferrocene, primary orbital inte
in occur between the Cr d orbitals and th

• The two benzene rings of Cr(6‐C6H6)2
conformation.

e of bisbenzenechromium
‐C6H6)2

eractions that form the metal‐ligand bonds
he ‐orbitals of the benzene ligand.

are ideally orientated in an eclipsed (D6h)

 MOs of Be

B2g
(6 nodes)

anti-bonding

E2u
(4 nodes)

anti-bonding

E1g
(2 nodes)

bonding

A2u
(0 nodes)

bonding

enzene, C6H6

B2g E1g A2u + E2u