Ligand field theory (LFT)

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The ligand field theory, abbreviated as LFT, provides a complete, complex picture of chemical bonding present in transition metal complexes. It is also known as the molecular orbital theory (MOT) of organometallic complexes. It justifies orbital overlap and proposes the formation of new molecular orbitals by combining atomic orbitals of the metal ion and the ligands.

 In this article, we have tried to summarize the main concepts related to LFT. So that you may have a better idea about what is the ligand field theory, its postulates, applications and importance.

So, without any further delay, dive into the article and let’s start reading!

What is ligand field theory (LFT) – Definition

Ligand field theory (LFT) proposes that when a new transition metal complex is formed, the s, p and d orbitals of the metal ion combine with the ligand atomic orbitals to form a new set of orbitals called molecular orbitals. N number of atomic orbitals combine to form N molecular orbitals (MOs), including bonding and anti-bonding MOs. Only those atomic orbitals of metal will combine with the atomic orbitals of the ligands that are in right symmetry with the latter.

History and origin of LFT

The ligand field theory (LFT) was first documented in 1957 in an article authored by Orgel and Griffith. However, its foundation was laid back in 1929 by J.H Van Vleck. Thus, LFT is an evolved version of the crystal field theory (CFT). However, it is very different from CFT.

Why is LFT superior to CFT or VBT of coordination complexes?

  • CFT is a relatively simple model that considers metal-ligand (M-L) interactions to be purely ionic or electrostatic in nature. On the other hand, valence bond theory (VBT) predominantly discusses metal complex formation via covalent bonding.
  •  In contrast, LFT combines ideas from both the previous theories with the molecular orbital theory (MOT) of chemical bonding. In this way, it provides a bigger and better pictorial model for the formation of transition metal complexes.
  • CFT only takes into consideration the role of d-orbitals in metal complex formation, while LFT highlights the importance of s and p orbitals as well.
  • LFT also provides a reasonable explanation for the color, stability, reactivity and magnetic properties of metal complexes, along with explaining orbital overlap.
  • Therefore, some scientists call LFT an ever-modern theory of chemical bonding that is most relevant from its time of conception till today.

Postulates and fundamentals of LFT

  • LFT considers both the covalent as well as the ionic nature of bonding in metal complexes.
  • A ligand being a nucleophilic (electron-rich) specie, contains high lying lone pair of electrons. Contrarily, a metal atom or ion being electrophilic (electron deficient) in nature have empty d orbitals available, lying at lower energy.
  • The nucleophilic ligand can thus attack the electrophilic metal.
  • Metal-ligand (M-L) interaction develops, and a new metal complex is formed. 

Applications of LFT

Now let’s see how to draw a molecular orbital diagram for different metal complexes by applying the concepts of ligand field theory (LFT).

Molecular orbital diagram for an octahedral complex

Example: [Co(NH3)6]3+

The electronic configuration of Co3+ is 1s2 2s2 2p6 3s2 3p6 3d6 4s0 4p0.

As there are a total of six electrons in the d-subshell of Co3+, so it is a d6 system.

 Five d-orbitals from the penultimate (n-1) shell while two s and three p orbitals from the nth outermost shell of Co3+ make a total of nine atomic orbitals available for bonding. However, orbital overlap will occur only between those six atomic orbitals of Co3+ and the atomic orbitals of six incoming NH3 molecules that are symmetrically aligned.  The remaining three orbitals of Co3+ will stay non-bonded.

In an octahedral complex such [Co(NH3)6]3+, dz2 and dx2-y2 get involved in bonding while dxy, dyz and dxz (i.e., t2g set) stay non-bonded.

A total of 12 atomic orbitals will combine to form 6 bonding MOs and 6 anti-bonding MOs, as shown in the diagram below.

There are a total of 18 electrons available to be placed in [Co(NH3)6]3+, including six d-electrons of Co3+ and a lone pair provided by each of the six NH3 molecule.

The available electrons occupy positions in the molecular orbitals of the complex following the Aufbau rule, Hund’s rule and Pauli Exclusion principle.

The first three electrons are singly filled in the lowest energy bonding MO (σp). These are then paired up. The next two are placed in the same manner in σs followed by two electrons in σd. The remaining six electrons fill the t2g set in a similar manner.

There are no electrons in the anti-bonding MOs in this case. Also, all the electrons present in this complex are paired. Thus, it is a diamagnetic spin-paired complex, also known as low-spin.

The energy difference between the ground state non-bonded atomic orbitals and the highest energy anti-bonding molecular orbital σ*p is known as the ligand field splitting energy (LFSE).

The higher the LFSE value, the greater the stability of the complex.

Metal complex stability explained through LFT.

Cr(CO)6 is an octahedral complex with a d6 system just like [Co(NH3)6]3+ we discussed above. However, the former is more stable than the latter. Why is it?

Well, its stability can be explained as per ligand field theory.

Molecular orbital diagram for Cr(CO)6

The electronic configuration of Cr is 1s2 2s2 2p6 3s2 3p6 3d5 4s1 4p0.

Carbon monoxide (CO) is a strong field ligand. So, when 6 CO molecules approach a Cr atom, it causes the 4s electron of chromium to shift into its 3d orbital and get paired up.

This results in a d6 system.

Two d orbitals, one s and three p atomic orbitals of Cr, then combine with six atomic orbitals of the ligand atoms to form 12 MOs. These include 6 bonding MO and 6 anti-bonding MOs. The remaining three orbitals of Cr (t2g set) stay non-bonded.

Electrons are filled in these orbitals in an ascending order of energy, as discussed in the previous example.

However, an interesting fact is that, in this case, CO is a pi-acceptor ligand. The molecular orbital diagram for carbon monoxide shows that it has empty anti-bonding MOs available to accept electrons back from the metal atom. This concept is called donation, followed by back donation of electrons. Also known as bonding followed by back bonding. It results in an extra M-L pi bond in addition to M-L sigma bonding.

The non-bonded t2g set available in Cr can back donate electrons to two LUMO (lowest unoccupied molecular orbitals) available in each CO molecule. Only those anti-bonding MOs of CO will receive back electrons that are in right symmetry with the t2g set of the metal atom. There are 6 CO molecules forming M-L interactions in Cr(CO)6; thus, 6(2) = 12 LUMOs available. But as per symmetry nomenclature, only 3 are in the right symmetry with the three t2g orbitals of the metal atom. Furthermore, at a time, only 1 LUMO out of the 3 will be receiving back electrons from t2g.

3 t2g orbitals of the metal combined with 3 LUMO of CO molecules form 6 new molecular orbitals represented as πt2g (bonding MOs) and π*t2g (anti-bonding MOs), as shown in the figure above.

All images in this article are by Ammara W.

The six t2g electrons then occupy the lower energy πt2g, so the energy difference (ligand field splitting energy) is increased. This explains the incredible stability of Cr(CO)6.

Cr(CO)6 is also a low-spin diamagnetic complex as there are no unpaired electrons present in it.

However, Cr(CO)6 is colorless due to its high ligand field splitting energy, because of which the complex does not absorb electromagnetic radiations in the visible range to undergo electronic transitions.

You may also like 9 classical theories of chemical bonding.


1. Bhatt, Vasishta. 2016. ‘Chapter 1 – Basic Coordination Chemistry.’ in Vasishta Bhatt (ed.), Essentials of Coordination Chemistry (Academic Press).

2. H. Crabtree, Robert. 2014. The organometallic chemistry of the transition metals (Wiley). Pg. 19-27.

3. Neese, Frank. 2013. ‘Chapter 2 – Introduction to Ligand Field Theory.’ in Robert R. Crichton and Ricardo O. Louro (eds.), Practical Approaches to Biological Inorganic Chemistry (Elsevier: Oxford).

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