Which of the following orbitals does not belong to t_2g orbitals?

d_z²

The correct answer is option 4. \(d_{z^2}\).

In an octahedral coordination complex, the five \(d\) orbitals of the central metal ion split into two sets based on their energy levels in the presence of ligand field. These two sets are called \(t_{2g}\) and \(e_g\) orbitals.

The \(t_{2g}\) set consists of three degenerate orbitals:

1. \(d_{xy}\)

2. \(d_{yz}\)

3. \(d_{xz}\)

The \(e_g\) set consists of two degenerate orbitals:

1. \(d_{z^2}\)

2. \(d_{x^2-y^2}\)

Therefore, the \(dz^2\) orbital does not belong to the \(t_{2g}\) set.