To explain bonding in complexes valence bond theory was proposed by Linus Pauling. The main postulates of VB theory are as follows:

(i) The central atom loses a requisite number of electrons to form the cation. The number of electrons lost is equal to the valence of the resulting cation.

(ii) The central cation makes available a number of vacant orbitals equal to its coordination number for the formation of dative bonds with the ligands.

(iii) The cation orbitals hybridize to form new set of equivalent hybrid orbitals with definite directional characteristics.

(iv) The non-bonding metal electrons occupy the inner d-orbitals and do not participate in the hybridization.

(v) In the presence of strong ligands such as CN^-, NO, CO, the d-electrons are rearranged vacating some d-orbitals (when the number of d-electrons are more than 3 only) which can participate in hybridization.

(vi) In the presence of weak ligands such as F^-, Cl^-, H₂O, etc., the d-electrons are not rearranged.

(vii) The d-orbitals involved in the hybridization may be either (n - 1)d orbitals or outer d-orbitals.

The complexes formed by the involvement of (n - 1)d orbitals in hybridization are called inner orbital complexes or low spin complexes. The complexes formed by the involvement of d-orbitals of outer orbit are called outer orbital complexes or high spin complexes.

(viii) Each ligand contains a lone pair of electrons. A dative bond is formed by the overlap of a vacant hybrid orbital of metal ion and a filled orbital of ligand.

(ix) The complex will be paramagnetic, if any unpaired electrons present, otherwise diamagnetic.

(x) The number of unpaired electrons in a complex gives out the geometry of the complexes or vice versa.

In hexacyano manganate (II) ion, the Mn atom assumes d²sp³ hybrid state. The number of unpaired electrons in the complex is

1

The given compound is hexacyano manganate (II) ion and its formula is \([Mn(CN)_6]^{4-}\). The hybridization of the compound is \(d^2sp^3\).

The oxidation number of the central metal ion Mn is +2

The electronic configuration of \(Mn^{2+}\)is

Cyanide ligand is a strong field ligand and forms a σ-donor π-acceptor bond with the central metal ion, splitting the d orbitals. For a d²sp³ hybrid state, the d orbitals split into two sets: one set with lower energy (t_2g) containing one orbital and the other set with higher energy (e_g*) containing one orbital. In the t_2g set, there is one unpaired electron, while in the eg* set, there are no unpaired electrons.

Therefore, the number of unpaired electrons in the complex is: (1) 1