Evaluation of Statements on Crystal Field Theory

To determine the correctness of the given statements according to Crystal Field Theory (CFT):

1. Analysis of Statement I: In an octahedral crystal field, the electrostatic interaction between the five degenerate $d$-orbitals of the central transition metal ion and the surrounding ligands causes the $d$-orbitals to split into two sets of different energies around a barycenter (average energy level):

   • The higher energy $e_g$ set ($d_{x^2-y^2}, d_{z^2}$) is destabilized by an energy of $+0.6 \Delta_o$ (or $+\frac{3}{5}\Delta_o$) relative to the barycenter per electron.
   • The lower energy $t_{2g}$ set ($d_{xy}, d_{yz}, d_{zx}$) is stabilized by an energy of $-0.4 \Delta_o$ (or $-\frac{2}{5}\Delta_o$) relative to the barycenter per electron.

   The total Crystal Field Stabilization Energy (CFSE) is expressed as: $\text{CFSE} = \left( -0.4 n_{t_{2g}} + 0.6 n_{e_g} \right) \Delta_o$ where $n_{t_{2g}}$ and $n_{e_g}$ represent the number of electrons in the $t_{2g}$ and $e_g$ orbitals, respectively.

   Therefore, Statement I is correct.

2. Analysis of Statement II: In a free gaseous metal atom or ion, all five $d$-orbitals ($d_{xy}$, $d_{yz}$, $d_{zx}$, $d_{x^2-y^2}$, and $d_{z^2}$) possess identical energy, meaning they are completely degenerate. When ligands approach the metal ion to form a coordination complex, the asymmetric electrostatic field created by the ligands breaks this symmetry, thereby lifting/destroying the degeneracy of the $d$-orbitals.

   Therefore, Statement II is correct.

Conclusion: Since both Statement I and Statement II are correct, the correct option is A.