What is Stabilization Energy

Stabilization Energy

We have learnt that in octahedral field, the energies of five d-orbital split-up. Three orbitals are lowered in energy (t²g) and two orbitals are raised in energy (eg). We know that electrons always prefer to occupy an orbital of lower energy.

For example, in the case of d1 system (e.g. Ti³⁺ in [TiF₆]^3-), the d-electron will prefer to occupy a t²gorbital and is, therefore, stabilized by an amount equal to 0.4 Δ₀ or 4 Dq. The amount of stabilization provided by splitting of the d-orbitals into two levels is called crystal field stabilization energy. It is abbreviated as CFSE. Thus, in octahedral field for each electron entering into the t²g orbital, the crystal field stabilization is -4 Dq and for each electron entering into the eg orbital the crystal field destabilizing energy is +6 Dq. Thus, the CFSE is calculated as the algebraic sum of -4 Dq per electron in t²g level and +6 Dq for each electron in eg orbital.

CFSE for various octahedral complexes

(i) For a d₁ system (e.g. Ti³⁺ ion) electron will be present in any one of the three t²g orbitals. The electronic configuration may be written as t²g₁. The crystal field stabilization energy is -4Dq.

(ii) For a d₂ system (e.g. V₃⁺ ion) the electrons will occupy t²g orbitals with their spins parallel in accordance with Hund's rule. The electronic configuration is t²g² and crystal field stabilization energy is-8Dq.

(iii) Similarly, for a d₃ system (e.g. Cr³⁺), the electronic configuration is t²g³. The crystal field stabilization energy is -12 Dq.

(iv) For a d₄ system (e.g. Mn³⁺ ion), there are two possibilities:

(a) All the four electrons may occupy t²g orbitals with one electron getting paired. The electronic configuration may be written as t²g⁴.

(b) Three electrons occupy t²g orbitals and the fourth electron goes to one of the eg orbitals. The configuration may be written as t₂³e_g¹.

The actual configuration may be decided on the basis of Δ₀ and the pairing energy (P), i.e. the energy required to pair the electron with one another.

The configuration (a) is possible if Δ₀ > P. These complexes are called strong complexes because Δ₀ is large. In this case, the complex has less number of unpaired electrons and is called low spin complex.

The configuration (b) is possible if Δ₀ < P. It is called weak field and the complexes are called weak field complex. In that case, the maximum numbers of electrons remain unpaired and the complex is called high spin complex.

As shown above, for a low spin complex having t²g⁴ configuration, CFSE = 4 (-4 Dq) = -16 Dq. However, if we take into account pairing energy (P) also, the net CFSE becomes:

Net CFSE = - 16Dq + P

On the other hand, for a high spin complex, having the configuration t²g³e_g¹,

Net CFSE = 3(-4Dq) + 1 (6 Dq) = - 6 Dq

(v) Similarly, for a d₅, d₆ and d₇ systems there are two possibilities

The d₈, d₉ and d₁₀ systems have only one possible configuration.

The CFSE for metal ions having different number of d electrons (d₁ to d₁₀) can be calculated as discussed above.

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