Cu²⁺ (d⁹) octahedral complexes almost always show tetragonal elongation — four short equatorial bonds and two long axial bonds. Why?
ACu²⁺ is too small to accommodate six equivalent ligands
BThe d⁹ configuration places three electrons in the eg set (one orbital filled, one half-filled), creating an unequal occupation that is stabilized by elongating along the z-axis, which lowers d_z² below d_x²−y² and places the paired electrons in the lower orbital
CCrystal packing forces always favor elongation over compression for copper compounds
For d⁹ in Oh, the electron configuration is t₂g⁶ eg³ — three electrons in two eg orbitals (one orbital must have 2, the other must have 1). This unequal occupation creates an orbital degeneracy: either d_z² has 2 and d_x²−y² has 1, or vice versa. The Jahn-Teller theorem says this degeneracy is unstable. Tetragonal elongation along z weakens the axial bonds, lowering the d_z² orbital energy. The configuration becomes (d_z²)² (d_x²−y²)¹ — placing the pair in the lower orbital. This is why virtually all Cu²⁺ octahedral complexes show two long axial bonds and four shorter equatorial bonds.
Question 2 True / False
The Jahn-Teller effect applies only to complexes with eg orbital degeneracy; t₂g orbital degeneracy does not cause significant structural distortion.
TTrue
FFalse
Answer: False
The Jahn-Teller theorem applies to ANY orbital degeneracy. However, the magnitude of the distortion depends on which orbitals are involved. Unequal occupation of the eg orbitals (which point directly at the ligands) causes large distortions because these orbitals are strongly antibonding and their occupancy directly affects metal-ligand bond lengths. Unequal occupation of the t₂g orbitals (which point between the ligands) causes much smaller distortions because these orbitals are weakly bonding or nonbonding. The distinction is between 'strong' (eg) and 'weak' (t₂g) Jahn-Teller effects. d¹ and d² configurations have t₂g degeneracy but show only minor structural effects.
Question 3 True / False
A d⁴ high-spin octahedral complex (t₂g³ eg¹) is expected to show a Jahn-Teller distortion, while a d³ octahedral complex (t₂g³ eg⁰) is not.
TTrue
FFalse
Answer: True
d³ has the configuration t₂g³ — one electron in each of the three t₂g orbitals. The t₂g set is evenly occupied (no degeneracy), and eg is empty, so there is no Jahn-Teller distortion. d⁴ high-spin has t₂g³ eg¹ — the single eg electron can be in either d_z² or d_x²−y², creating an orbital degeneracy. The Jahn-Teller effect removes this degeneracy through tetragonal distortion. This is seen in Cr²⁺ (d⁴) and Mn³⁺ (d⁴) octahedral complexes, which show characteristic elongated octahedral geometries with measurably different axial and equatorial bond lengths.
Question 4 Short Answer
Explain why the double-humped shape of the lattice energy curve across the first-row transition metal divalent ions (the 'double-humped' plot of hydration enthalpy vs. atomic number) provides evidence for both crystal field stabilization energy and the Jahn-Teller effect.
Think about your answer, then reveal below.
Model answer: If crystal field effects were absent, hydration enthalpies would decrease smoothly across the transition series (due to the steady increase in effective nuclear charge and decrease in ionic radius). The actual plot shows two humps: values for d³ (Cr²⁺ is anomalous due to JT) and d⁸ are higher than the smooth baseline, while d⁰, d⁵ (high-spin), and d¹⁰ fall on the baseline. The humps reflect CFSE — configurations with large CFSE (d³, d⁶ low-spin, d⁸) gain extra stabilization in the octahedral aqua complex. The anomalously high value for Cu²⁺ (d⁹) — higher than expected from CFSE alone — is attributed to the additional stabilization from the Jahn-Teller distortion, which lowers the total energy by splitting the eg degeneracy and placing the electron pair in the lower orbital.
This plot is one of the most cited pieces of evidence for crystal field effects in real chemistry. The Jahn-Teller contribution at d⁹ (and to a lesser extent at d⁴) adds a specific, identifiable increment above the CFSE-only prediction.