How to Manage Global Discount in Odoo 18 POSCeline George
MANAS NAG PRESENTATION(LIGAND FIELD THEORY) (1).pptx
1. LIGAND FIELD THEORY
INTRODUCTION
Ligand Field Theory (LFT) is an extension of Crystal Field Theory (CFT) that incorporates molecular orbital theory to provide
a more comprehensive understanding of the bonding, electronic structure, and properties of transition metal complexes.
Developed by adapting concepts from quantum mechanics, LFT describes the interaction between the metal ion’s d-orbitals
and the surrounding ligands’ electron clouds, accounting for the covalent as well as ionic contributions to the bonding. This
theory was developed by J.H. Van Vleck.
The Ligand field theory goes beyond the crystal field theory, the chemical bond between the metal & the liagands and the
origins of orbital spilitting are ascribed not only to electrostatic forces but also to a small degree of overlap of metal and
ligand orbitals and a delocalization of metal and ligands electrons.
Transition metal ions are characterized by partially filled d-orbitals. When these ions are surrounded by ligands in a complex,
the degeneracy of their d-orbitals is broken due to electrostatic and covalent interactions between the ligands and the metal
centre. This splitting of d-orbitals leads to various spectroscopic, magnetic, and structural properties, which LFT seeks to
explain.
NEED OF LIGAND FIELD THEORY
The crystal field theory assumes that the source of metal – ligand bond is the pure electrostatic interaction between the
metal ion & the ligands. The theory predicts the splitting of d orbitals as due to electrostatic potential of the ligands to which
the d electrons of the metal ions get exposed. Apart from this, a pure electrostatic interactions between the metal ion and the
ligands fails to explain the relative position of ligands in the spectrochemical series. In addition , there are also some of the
following points which will clearly state the limitations of cystal field theory –
This theory takes only d-orbitals of a central atom into account. The s and p orbitals are not considered for the study.
The theory fails to explain the behaviour of certain metals which cause large splitting while others show small splitting.
For example, the theory has no explanation as to why H stronger ligand as compared to OH.
The theory rules out the possibility of having πbonding. This is a serious drawback because is found in many complexes.
The theory gives no significance to the orbits of the ligands. Therefore, it cannot explain any properties related to
ligand orbitals and their interaction with metal orbitals.
2. Hence in order to explain all the points a new theory was developed which is now known as Ligand field theory.
The molecular orbital theory can be very well applied to transition metal complexes to rationalize the covalent as well as the
ionic character in the metal-ligand bond. A transition metal ion has nine valence atomic orbitals which are consisted of five nd,
three (n+1)p, and one (n+1)s orbitals. These orbitals are of appropriate energy to form bonding interaction with ligands. The
molecular orbital theory is highly dependent on the geometry of the complex and can successfully be used for describing
octahedral complexes, tetrahedral and square-planar complexes. The main features of molecular orbital theory for metal
complexes are as follows:
1.The atomic orbital of the metal center and of surrounding ligands combine to form new orbitals, known as molecular orbitals.
2.The number of molecular orbitals formed is the same as that of the number of atomic orbitals combined.
3.The additive overlap results in the bonding molecular orbital while the subtractive overlap results in the antibonding overlap.
4.The energy of bonding molecular orbitals is lower than their nonbonding counterparts while the energy of antibonding
molecular orbitals is higher than that of nonbonding orbitals.
5.The energy of nonbonding orbitals remains the same.
6.The ionic character of the covalent bond arises from the difference in the energy of combining orbitals.
7.If the energy of a molecular orbital is comparable to an atomic orbital, it will not be very much different in nature from atomic
orbital.
Now let us discuss the molecular orbital diagram in sigma bonded and in complex involving both sigma and pie interaction for
octahedral, tetrahedral & square planar symmetry.
LIGAND FIELD THEORY
3. In octahedral complexes, the molecular orbitals created by the coordination of metal center can be seen as resulting from
the donation of two electrons by each of six σ-donor ligands to the d-orbitals on the metal.
• The metal orbitals taking part in this type of bonding are nd, (n+1)p and (n+1)s.
• It should be noted down that not all nd-orbitals but only dz2 and dx2-y2orbitals are capable of participating in the σ-
overlap.
• The dxy, dxz and dyz orbitals remain non-bonding orbitals. The ligands approach the metal center along the x, y and z-
axes in such a way that their σ-symmetry orbitals form bonding and anti-bonding combinations with metal’s s, px, py, pz,
dz2
and dx2
-y2
orbitals.
• For a first row transition metal series,the metal orbitals are :
• i. 3s & 3p; filled low energy ; hence ineffective for overlap with ligand orbitals.
• ii.five 3d orbitals;partially filled and may be involved in bonding.
• iii.One 4s and Three 4p ;empty and somewhat higher energy than the 3d,May be involve in bonding.
• Out of nine metal orbitals six (3dx2
-y2
,3dz2
,4s,4 px,4py,4pz) have their lobes projected along the corners of the
octahedron.
• A total of six bonding and six anti-bonding molecular orbitals formed. The symmetry designations of different metal
orbitals taking part in octahedral overlap are:
Symmetry of Oh Complexes
dz2
, dx2
-y2
- eg
s - a1g
px,py,pz - t1u
dxy, dxz,dyz - t2g
SIGMA BONDING IN OCTAHEDRAL COMPLEX
5. SIGMA BONDING IN TETRAHEDRAL COMPLEX
• For a tetrahedral ML4 complex (Td symmetry), the metal s and p orbitals have a1, and t2 symmetries
Respectively.
• The five d orbitals are split into two sets: e (dz2
d x 2-y2
) and t2 (dxz, dyz, and dxy).
• The four LGOs constructed from ligand lone-pair orbitals will consist of a t2 set one orbital of a1 symmetry.
• The t2 LGOs can interact with both sets of metal t2 orbitals (p and d) to give three sets of σ MOs-one bonding
one slightly antibonding, and one clearly antibonding.
ORBITAL DIAGRAM INVOLVING ONLY SIGMA BONDING FOR
TETRAHEDRAL COMPLEX
e orbitals lie in the axis and therefore these orbitals are
not capable of overlap with LGOs to form sigma bonds.
They are cosidered to be non-bonding orbitals.
6. SIGMA BONDING IN SQUARE PLANAR COMPLEX
• A number of four-coordinate complexes adopt a square planar geometry, which for four identical ligands leads to D 4h
symmetry. • In this environment the metal d level is split into a1g (dz2
), eg (dxy ,dyz) ,b1g (dx2
-y2
) and b2g (dxy) orbitals.
• The p level also loses its degeneracy, appearing as a2u (pz) and eu (px & py ).
• s-orbital forms non-degenerate a1g orbital.
• The four ligands, which will be oriented along the x and y axes, will give rise to ligand group orbitals of a a1g, b1g and eu
symmetry.
• They will interact with metal orbitals of the same symmetry leading to the σ MO diagram.
ORBITAL DIAGRAM INVOLVING ONLY SIGMA
BONDING FOR SQUARE PLANAR COMPLEX
7. PIE BONDING INTERACTIOIN & MOLECULR ORBITAL
THEORY
There are four different types of metal-ligand interactions which can be resulted from the sidewise overlap of the orbitals.
For O h symmetry
• The ligand group orbitals capable of π interactions in an octahedral complex fall into four symmetry categories:
t1g , t2g ; t1u and t2u
• Of these, a transition metal will possess orbitals of only two of the types: t2g (dxy, dxz, & dyz) and t1u (px , py & pz)
• The metal could use all of these orbitals for π bonds.
• However, the members of the t1u and set are directed towards the ligands and therefore participate in strong σ bonds.
• Formation of π bonds using these orbitals would tend to weaken the σ and hence will not be favoured.
• The t2g orbitals, on the other hand, are directed between the ligands which restricts them to a non bonding status in a σ-only
system.
• They can, however, readily π-bond to LGOs of matching symmetry.The t2u and t1g ligand group orbitals must remain
nonbonding.
• This is because there are no orbitals of matching symmetry on the metal, π bonding in an octahedral complex is thus limited
9. Overall,
• filled π* or p orbitals on ligands (frequently with relatively low energy) result in L→M π bonding and a smaller Δ o for the overall
complex.
• Empty higher energy π or d orbitals on the ligands result in M→ L π bonding and a larger Δ complex. o for the
• Ligand-to-metal π bonding usually gives decreased stability for the complex, favoring high-spin configurations;
• metal-to-ligand π bonding usually gives increased stability and favors low-spin configurations.
Oh with pie accepter ligands Oh with pie donor ligands
