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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 

 

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Page 3 of 1

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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 E 8C3 6C2 6C4 3C2

(=C42)

i 6S4 8S6 3σh 6σd

A1g 1 1 1 1 1 1 1 1 1 1 x2+y2+z2

A2g 1 1 -1 -1 1 1 -1 1 1 -1 Eg 2 -1 0 0 2 2 0 -1 2 0 (2z2-x2-

y2, x2-y2)T1g 0 -1 1 -1 3 1 0 -1 -1 (Rx,Ry,

Rz)

T2g 3 0 1 -1 -1 3 -1 0 -1 1 (xz,yz,xy)A1u 1 1 1 1 1 -1 -1 -1 -1 -1 A2u 1 1 -1 -1 1 -1 1 -1 -1 1 Eu 2 -1 0 0 2 -2 0 1 -2 0 T1u 0 -1 1 -1 -3 -1 0 1 1 (x,y,z) T2u 3 0 1 -1 -1 -3 1 0 1 -1

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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Page 5 of 1

l field

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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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dz

Example: [CoCl4]2-

Cobalt is in the +2 state and provides 7 electrons (d7 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 t26a1

2e4t2*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 symmetry

s a1g

px and py eu pz a2u 2 a1g

dxy b2g 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) dπ-

σ*

(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 π-

bonding. But the t1u orbitals point towards the ligands and hence form σ-

bonds. 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]3- LGOs 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*)

t2g

(t2g)

-complex -complex ligand-orbitals

eg eg*( *)

o

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