The crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic, arising purely from electrostatic interactions between the metal ion and the ligand. Ligands are treated as point charges in case of anions or point dipoles in case of neutral molecules. The five d orbitals in an isolated gaseous metal atom/ion have the same energy, that is, they are degenerate. In an octahedral coordination entity, the d orbitals split into a lower set of three t2g orbitals and a higher set of two eg orbitals. The energy separation is denoted by Δo: the energy of the two eg orbitals increases by (3/5)Δo and that of the three t2g orbitals decreases by (2/5)Δo.
What is the net change in the energy of the d electrons, caused by crystal field splitting, in a high spin d4 octahedral complex?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −0.6Δo
In an octahedral field each electron in a t2g orbital is lowered by (2/5)Δo and each electron in an eg orbital is raised by (3/5)Δo, both measured from the average energy of the d orbitals.
d electrons: 4.
High spin: Δo < P, so the fourth electron enters an eg orbital instead of pairing: t2g3eg1.
Pairing: no electrons are paired, so P does not enter the result.
\( \displaystyle \Delta E = n_{t_{2g}}\left(-\frac{2}{5}\Delta_o\right) + n_{e_g}\left(+\frac{3}{5}\Delta_o\right) \)
\( \displaystyle \Delta E = 3\left(-\frac{2}{5}\Delta_o\right) + 1\left(+\frac{3}{5}\Delta_o\right) = -\frac{6}{5}\Delta_o + \frac{3}{5}\Delta_o \)
\( \displaystyle \Delta E = -\frac{3}{5}\Delta_o = -0.6\,\Delta_o \)
The minus sign means the four d electrons are lower in energy by 0.6Δo than in a spherical field.
NCERT (2026-27 edition):
5.5.4 Crystal Field Theory – “… the dxy, dyz and dxz orbitals which are directed between the axes will be lowered in energy relative to the average energy in the spherical crystal field.”
“(i) If Δo < P, the fourth electron enters one of the eg orbitals giving the configuration t2g3eg1. Ligands for which Δo < P are known as weak field ligands and form high spin complexes.”