Question

For a complex ( d6 - configuration) having Δ0=25000 cm−1 and P=15000 cm−1, the crystal field stabilisation energy is:

Answer 1

-30000

Answer 2

For a d6 configuration in an octahedral complex, the crystal field splitting energy is Δ₀ and the pairing energy is P. Given Δ₀ = 25000 cm⁻¹ and P = 15000 cm⁻¹.

Since Δ₀ (25000 cm⁻¹) > P (15000 cm⁻¹), the complex is low spin.

In the low spin configuration for d6, the electrons will preferentially occupy the lower energy t₂g orbitals before pairing up or occupying the higher energy eg orbitals. The electron configuration is t₂g⁶ eg⁰.

The Crystal Field Stabilisation Energy (CFSE) relative to the barycenter is calculated as: CFSE (relative to barycenter) = n(t₂g) * (-0.4 Δ₀) + n(eg) * (0.6 Δ₀) where n(t₂g) is the number of electrons in the t₂g orbitals and n(eg) is the number of electrons in the eg orbitals.

For the low spin d6 configuration (t₂g⁶ eg⁰): n(t₂g) = 6 n(eg) = 0

CFSE (relative to barycenter) = 6 * (-0.4 Δ₀) + 0 * (0.6 Δ₀) CFSE (relative to barycenter) = -2.4 Δ₀

Substituting the value of Δ₀: CFSE (relative to barycenter) = -2.4 * (25000 cm⁻¹) CFSE (relative to barycenter) = -60000 cm⁻¹

However, the pairing energy P is also given, which implies it should be considered in the calculation of "the crystal field stabilisation energy". The total energy of the configuration includes the CFSE relative to the barycenter and the energy penalty for pairing electrons. The pairing energy term is often included when comparing the stability of different spin states or when the question explicitly provides P.

The total energy of the low spin state relative to the hypothetical spherical field state (barycenter) is given by: Total Energy (LS) = CFSE (relative to barycenter, LS) + n(pairs in LS) * P

For the low spin d6 configuration (t₂g⁶ eg⁰), there are 3 pairs of electrons in the t₂g orbitals. n(pairs in LS) = 3

Total Energy (LS) = (-2.4 Δ₀) + 3 * P

Substituting the given values of Δ₀ and P: Total Energy (LS) = -2.4 * (25000 cm⁻¹) + 3 * (15000 cm⁻¹) Total Energy (LS) = -60000 cm⁻¹ + 45000 cm⁻¹ Total Energy (LS) = -15000 cm⁻¹

This value represents the total energy of the low spin configuration relative to the barycenter, including the pairing energy penalty. Sometimes, this total energy is referred to as the crystal field stabilisation energy in contexts where the pairing energy is relevant for determining the stable spin state.

The formula CFSE = [-0.4 * n(t₂g) + 0.6 * n(eg)] * Δ₀ + n(P) * P calculates the total energy relative to the spherical field (barycenter) minus the pairing energy of the high spin state.

Using this method: CFSE = -2.4 Δ₀ + 2P = -30000 cm⁻¹.