In octahedral complexes, CFSE is given by the formula

Introduction:
In octahedral complexes, the d-electron configurations can be classified into low spin and high spin configurations. The crystal field splitting energy (CFSE) is the energy difference between the lower t2g and higher eg orbitals caused by the crystal field splitting. The CFSE is influenced by the d-electron configuration, and the configuration with the maximum CFSE is the most stable.

Explanation:
The CFSE for each d-electron configuration can be calculated by considering the number of electrons in the t2g and eg orbitals and multiplying them by the corresponding crystal field splitting energy. Let's analyze each option to determine the d-electron configuration that gives the maximum CFSE:

a) Low spin d4:
In the low spin configuration, the electrons occupy the lower energy t2g orbitals first, followed by the higher energy eg orbitals. Since there are 4 electrons, all of them occupy the t2g orbitals. The CFSE for this configuration is given by: CFSE = (4 * Δt2g) + (0 * Δeg) = 4 * Δt2g.

b) High spin d4:
In the high spin configuration, the electrons fill both the t2g and eg orbitals before pairing up. In this case, 2 electrons occupy the t2g orbitals and the remaining 2 electrons occupy the eg orbitals. The CFSE for this configuration is: CFSE = (2 * Δt2g) + (2 * Δeg).

c) Low spin d5:
In the low spin configuration, the 5 electrons occupy the t2g orbitals before pairing up. The CFSE for this configuration is given by: CFSE = (5 * Δt2g) + (0 * Δeg) = 5 * Δt2g.

d) High spin d5:
In the high spin configuration, all 5 electrons occupy both the t2g and eg orbitals before pairing up. The CFSE for this configuration is: CFSE = (3 * Δt2g) + (2 * Δeg).

Conclusion:
Comparing the CFSE values for each d-electron configuration, we can see that the low spin d5 configuration (CFSE = 5 * Δt2g) gives the maximum CFSE among the given options. Therefore, option C is the correct answer.