Download Coordination Chemistry: Bonding

NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
Coordination Chemistry: Bonding
Molecular orbital theory
K.Sridharan
Dean
School of Chemical & Biotechnology
SASTRA University
Thanjavur – 613 401
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Table of Contents
1 Molecular Orbital Theory ............................................................................................................. 3 1.1 Molecular orbital ............................................................................................................. 3 1.2 How to find the symmetries of the metal 3d, 4s and 4p orbitals? ........................................ 4 1.3 Why t2g orbitals do not overlap? ........................................................................................... 5 1.4 M.O. Diagram for an octahedral complex ............................................................................. 7 1.4.1 Magnetic and spectral properties of complexes based on this MO diagram ................ 7 1.5 M.O. diagram of a tetrahedral complex ................................................................................ 8 1.6 Square planar complex .......................................................................................................... 9 1.6.1 M.O. Diagram for a square planar complex ................................................................. 10 2. Pi bonding & M.O.Theory .......................................................................................................... 10 2.1 Types of π interactions ........................................................................................................ 11 2.2 Metal orbitals used for π‐complex in an octahedral complex ............................................ 11 2.2.1 PR3 ligand is stronger than NH3 .................................................................................. 13 2.2.2 Stabilization .................................................................................................................. 14 3 References .................................................................................................................................. 14 Page 2 of 14
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1 Molecula
M
r Orbita
al Theory
y
1.1 Molecula
M
ar orbital
Mole
ecular orbiitals are formed by
y the ove
erlap of a
atomic orb
bitals. The
e
numb
ber of mo
olecular orb
bitals forme
ed will be equal to tthe number of atomicc
orbita
als overlapping. One of
o the mole
ecular orbita
als formed w
will be lowe
er in energyy
comp
pared to the
e atomic orrbitals and the
t other w
will be highe
er in energyy. The lower
mole
ecular orbita
al is known as bonding orbital be
ecause the electrons p
present in it
favorr bond form
mation and the
t other higher orbita
al is known as antibon
nding orbita
al
beca
ause the ele
ectrons pre
esent in the
ese orbitals will opposse bond formation. For
an example,
e
let us consid
der the form
mation of h
hydrogen m
molecule (fo
ormed) and
d
heliu
um molecule
e (not forme
ed):
σ* *
HA
σ HB
H2
He
e
N
No He2
He
Bond
d order = ½[number of electron
ns in the b
bonding orrbitals – nu
umber of
electrons in the antib
bonding
orbitals]
Bond
d order in hydrogen = ½[2-0] = 1;
Bond
d order in helium
= ½[2-2]
½
=0
In th
he case of complexes
s, the meta
al d-orbitalls and the ligand gro
oup orbitalss
(LGO
Os) will ove
erlap to form
m the molec
cular orbitalls.
Exam
mple:
3+
[Co(N
NH3)6]
.
The metal atomic
a
orbitals involve d in formin
ng the MOss are 3d, 4ss
and 4p. The lig
gand orbitals are the sp3 hybridized orbitalls on NH3. They form
m
ma bonds with
w the mettal orbitals.
sigm
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It is important to note that the metal orbitals and the LGOs should have the
same symmetry in order to overlap.
1.2 How to find the symmetries of the metal 3d, 4s and 4p
orbitals?
The symmetries of the metal atom orbitals can be found out from the Oh
character Table 1.2.1.
Oh
A1g
A2g
Eg
E 8C3 6C2 6C4 3C2
(=C42)
1 1
1
1
1
1 1
-1
-1
1
2 -1
0
0
2
T1g
T2g
A1u
A2u
Eu
T1u
T2u
3
1
1
2
3
6S4 8S6 3σh 6σd
i
1
1
2
1
-1
0
1
1
-1
1
1
2
1
-1
0
0
-1
1
-1
3
1
0
-1
-1
0
1
1
-1
0
0
1
1
-1
0
-1
1
-1
1
-1
0
1
-1
-1
1
1
2
-1
-1
3
-1
-1
-2
-3
-3
-1
-1
1
0
-1
1
0
-1
-1
1
0
0
-1
-1
-1
-2
1
1
1
-1
1
0
1
-1
x2+y2+z2
(Rx,Ry,
Rz)
(2z2-x2y2, x2-y2)
(xz,yz,xy)
(x,y,z)
The ‘s’ orbital is represented by x2+y2+z2 in the last column of the
character table and its symmetry is A1g as shown by the first column of the
character table. Hence, we say that the ‘s’ orbital transforms as a1g
in an
octahedral field. Similarly, the ‘p’ orbitals are represented by (x,y,z) in the last
but one column of the Oh character table and their symmetry is T1u. Thus, we
say that the ‘p’ orbitals transform as t1u in the octahedral field. Similarly, it can be
seen that the dx2-y2 and dz2 orbitals transform as eg orbitals and dxy,
dyz, and dzx orbitals transform as t2g orbitals. These can be summarized as
follows:
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eleme
ents)
Meta
al atom orbiitals
symm
metry in an octahedrall field
s
a1g
p
t1u
dxy, dyz, dzx
t2g
dx2-y
y2, dz2
eg
1.3 Why t2g orbitals
o
do
d not ove
erlap?
The LGOs will point alo
ong the ax
xes. Since the a1g
orbital is sphericallyy
symm
metrical, it can overlap with LGO
Os on all th
he axes. Th
he t1u and eg orbitalss
have
e their lobes
s pointed on
o the axes
s and hence
e can overlap with LG
GOs leading
g
to bo
ond formation. However, the t2g orbitals willl have their lobes in b
between the
e
axes
s and hence
e cannot ov
verlap with the
t LGOs a
as shown in
n Figure 1.3
3.1:
dx2-y2
dxy
Fig
F 1.3.1 eg and t2g
2 orbitals overla p with LGOs
The LGOs and the symme
etry matched metal ato
om orbitals are shown in Figure
1.3.2
2.:
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Fig 1.3.2 Metal atom orbitals and matching LGOs
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1.4 M.O. Diagram for an octahedral complex
The M.O. diagram for an octahedral complex is shown in Figure 1.4.1.
Fig 1.4.1 M.O. Diagram of σ-only octahedral complex
M
ML6
6LGOs
1.4.1 Magnetic and spectral properties of complexes based on
this MO diagram
[Co(NH3)6]3+ is diamagnetic and is explained as follows:
Total number of electrons = 18; 6 electrons from Co3+ (3d6) and 12 electrons
from the six NH3. These electrons are distributed to the MOs in the increasing
order of energy of the orbitals. The arrangement is: (a1g)2
(t1u)6
(eg)4
(t2g)6. Here all the electrons are paired and hence the complex will be
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diamagnetic. In this case, ∆o > pairing energy. Hence, pairing takes place
readily and a diamagnetic complex results.
[CoF6]3- is paramagnetic and is explained as follows:
Totally 18 electrons; six from Co3+ (d6) and 12 electrons from six F-. The
electrons are arranged as follows: (a1g)2 (t1u)6 (eg)4 (t2g)4 (eg*)2 (one
electron in each of the two eg* orbitals). Here, ∆o < pairing energy. Hence, the
electrons remain unpaired.
Thus, MOT is able to explain the magnetic and spectral property of complexes.
1.5 M.O. diagram of a tetrahedral complex
The symmetries of the metal atom orbitals are obtained from the Td character
table. The ‘s’ orbital (x2+y2+z2) transforms as a1; dx2-y2 and dz2 transform as
e; p orbitals (x,y,z) transform as t2 and dxy, dyz and dzx also transform as t2.
The LGOs constructed from four ligands will consist of a t2 set and one orbital
of a1 symmetry. The MO diagram is shown in Figure 1.5.1.
Fig 1.5.1 M.O. diagram of a tetrahedral complex
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2-
Example: [CoCl4]
7
Cobalt is in the +2 state and provides 7 electrons (d
system) and four Cl-
will provide 8 electrons. In total, there will be 15 electrons. They will be
accommodated two electrons per orbital starting from the lowest orbital. The
arrangement of electrons will be t26a12e4t2*3.
1.6 Square planar complex
This has got D4h symmetry and the symmetry of the metal atom orbitals are
derived from the D4h character table. Thus, the ‘s’ orbital (x2+y2) will transform as
a1g; px and py orbital will transform as eu, pz orbital will transform as a2u, dz as
b2g, dxz and dyz will transform as eg.
Orbital
s
px and py
pz
symmetry
a1g
eu
dz
a2u
a1g
dxy
b2g
2
dxz and dyz
eg
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1.6.1 M.O. Diagram for a square planar complex
M.O. diagram for a square planar complex is given in Figure 1.6.1.1
Fig 1.6.1.1 M.O.Diagram of square planar complex
2. Pi bonding & M.O.Theory
Metal atom and ligand orbitals should have the proper symmetry for π
bond formation in addition to energy. π bond has a nodal surface and this
includes the bond axis. The π bonding orbital will have lobes of opposite sign
on each side of this nodal surface. The important difference between a
sigma and π bonding complex is that the metal as well as ligand orbitals will
be perpendicular to the internuclear axis.
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2.1 Types of π interactions
There are essentially four types, viz., (1) pπ-dπ (2) dπ-dπ (3) dπ- π* and (4) dπσ*
(1) pπ-dπ complex
Here, electrons are donated from the filled p-orbitals of the ligand to the
empty d-orbitals of the metal. Examples for such ligands are: RO-, RS-,
O2-, F-, Cl-, Br-, I-, R2N(2) dπ-dπ complex
Here, electrons are donated from filled d-orbitals of the metal to the
empty d-orbitals of the ligand. Examples: R3P, R3As, R2S
(3) dπ- π* complex
Here, electrons are donated from filled d-orbitals of the metal to the
empty π - antibonding orbitals (π*) of the ligand. Examples: CO, RNC,
pyridine, CN-, N2, NO2-, ethylene
(4) dπ-σ* complex
Here, electrons are donated from filled d-orbitals of the metal to the
empty σ - antibonding orbitals (σ*) of the ligand. Examples: H2, R3P,
alkanes
2.2 Metal orbitals used for π-complex in an octahedral complex
As far as the LGOs are concerned, there will be four groups belonging to four
symmetries, viz., t2g, t1u, t2u, and t1g. However, the transition metal will have a1g,
t1u, t2g, and eg. Comparing these two, it is clear that the metal atom orbitals
with t2g (dxy, dyz and dzx) and t1u (px, py, and pz) symmetries are suitable for πbonding. But the t1u orbitals point towards the ligands and hence form σbonds. Hence, only t2g orbitals are involved in π-bonds. The LGOs having the
t2u, and t1g symmetries will remain non-bonding because there is no matching
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symmetry in the metal atom orbitals.
Example: [CoF6]3LGOs constructed from the fluorine 2p orbitals with t2g symmetry interact with
t2g metal orbitals to form π bonding and antibonding MOs. The corresponding
M.O.diagram is shown in Figure 2.2.1.
Fig 2.2.1 M.O.diagram for a π-complex
Fluorine is more electronegative than cobalt and has filled orbitals. Hence the
orbitals are lower in energy than the metal d orbitals. Hence, the π-bonding
MOs will resemble more closely the ligand orbitals than the metal orbitals. The
antibonding π* orbitals resemble the metal orbitals more closely than the ligand
orbitals. The electrons from the F- ligands (2p orbitals) will fill the t2g π-orbitals.
The electrons from the metal d orbitals (t2g) will be present in the π* orbitals.
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These new π* orbitals will be at a higher energy than the original t2g orbitals
due to π-bonding. The eg* orbitals are not affected. Because of this new π*
orbitals, Δo decreases. That is, the splitting will be less. This is the reason for
the halides being the weak ligands in spectrochemical series in spite of their
negative charges.
2.2.1 PR3 ligand is stronger than NH3
NH3
ligand can only donate electrons to the metal and cannot accept
electrons from the metal because it has no d orbitals, while P in PR3 can
accept electrons from metal because it has got empty d orbitals. The LGOs
from this ligand will be having higher energy because the orbitals are empty
and P is less electronegative than metal. This type of ligand is known is known
as acceptor ligand. The MO diagram for this type of ligand is shown in Figure
2.2.1.1:
*(t2g*)
t2g
eg
eg*( *)
t2g
o
(t2g)
-complex
-complex
ligand
-orbitals
Fig 2.2.1.1 π-complex M.O.diagram for PR3 type ligands
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The net effect is the increase in the splitting (Δo) and thus PR3 is
stronger than NH3.
2.2.2 Stabilization
The flow of electrons from metal to ligand stabilizes the complex when the metal
is in the low oxidation state because the excess electron density built up
around the metal due to σ-donation by ligands is removed. However, this back
donation of electrons from metal to ligands does not stabilize the complex when
the metal is in a higher oxidation state.
3 References
1. “Inorganic Chemistry: Principles of Structure and Reactivity”, James
E.Huheey, Ellen A.Keiter, Richard L.Keiter, Okhil K.Medhi,
Pearson
Education, Delhi, 2006
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