Electronic Configurations with Orbital Angular Momentum Contribution in Octahedral Environment

In an octahedral environment, the d-orbitals split into two sets of different energies due to the crystal field effect. The lower energy set, called the t²g set, consists of three orbitals (dxy, dyz, and dxz), while the higher energy set, called the eg set, consists of two orbitals (dx²-y² and dz²).

The electronic configurations that have orbital angular momentum contribution in an octahedral environment are d¹ and d². Let's understand why:

A. d¹ and high spin d⁴:
- In an octahedral environment, a d¹ configuration means that only one electron occupies the t²g set.
- The electron occupies one of the three t²g orbitals (dxy, dyz, or dxz).
- Since there is only one electron, there is no orbital angular momentum contribution.

B. d¹ and d²:
- In an octahedral environment, a d² configuration means that two electrons occupy the t²g set.
- The two electrons can occupy any two of the three t²g orbitals (dxy, dyz, or dxz).
- The presence of two electrons in the t²g set introduces orbital angular momentum contribution.
- The two electrons have opposite spins, resulting in a net orbital angular momentum.

C. d² and high spin d⁵:
- In an octahedral environment, a d² configuration means that two electrons occupy the t²g set.
- The two electrons can occupy any two of the three t²g orbitals (dxy, dyz, or dxz).
- The presence of two electrons in the t²g set introduces orbital angular momentum contribution.
- The two electrons have opposite spins, resulting in a net orbital angular momentum.
- A d⁵ configuration means that five electrons occupy the t²g and eg sets.
- The five electrons can occupy any combination of the t²g and eg orbitals.
- However, the presence of five electrons in the d orbitals does not introduce additional orbital angular momentum contribution.

D. high spin d⁴ and high spin d⁶:
- A high spin d⁴ configuration means that four electrons occupy the t²g and eg sets.
- The four electrons can occupy any combination of the t²g and eg orbitals.
- However, the presence of four electrons in the d orbitals does not introduce additional orbital angular momentum contribution.
- Similarly, a high spin d⁶ configuration means that six electrons occupy the t²g and eg sets, but it also does not introduce additional orbital angular momentum contribution.

Therefore, the only electronic configurations that have orbital angular momentum contribution in an octahedral environment are d¹ and d², making option B the correct answer.