How do d-electrons influence the preferred geometry of coordination compounds?

Here’s a explanation:

How d-electrons affect geometry:

1. Different shapes split d-orbitals differently
   • Octahedral, tetrahedral, and square planar shapes make the five d-orbitals have different energies.
2. Electrons fill the d-orbitals
   • Metal ions put their d-electrons in the orbitals.
   • The way they fill determines which shape is more stable.
3. Crystal Field Stabilization Energy (CFSE)
   • Metals prefer the geometry where their d-electrons are most stable.
   • Example:
     • d⁸ metals (Ni²⁺, Pd²⁺, Pt²⁺) → square planar.
     • d³ metals → octahedral.
     • d¹⁰ metals → geometry depends more on ligand size, not electrons.
4. Special cases
   • Some metals (like Cu²⁺, d⁹) distort octahedral shape due to Jahn–Teller effect.
   • Metals with d⁰ or d¹⁰ have flexible geometries because there’s no energy preference.

In short:
The number of d-electrons controls which shape is most stable for a metal complex.