Jahn-Teller Effect Explained

The Jahn‐Teller effect is a geometrical distortion of a non‐linear molecule or ion in a degenerate electronic state. This distortion removes the degeneracy and lowers the overall energy of the species. In transition metal complexes, the effect is most commonly observed when the central metal ion has degenerate d‐orbitals that are unequally occupied. This typically occurs in octahedral complexes for d⁴ (high spin), d⁹, and low spin d⁷ configurations, and in tetrahedral complexes for d¹, d², d⁴, d⁶, d⁷, and d⁹ configurations.

Analyzing the Given Species

Let's examine each given molecule/ion to determine its electronic configuration and predict whether it is expected to exhibit the Jahn‐Teller effect.

A. [Mn(H₂O)₆]³⁺

• The central metal ion is Manganese (Mn). Its atomic number is 25.
• The electronic configuration of neutral Mn is [Ar] 3d⁵ 4s².
• The complex has a charge of +3, and water is a neutral ligand. Therefore, the oxidation state of Mn is +3.
• The electronic configuration of Mn³⁺ is [Ar] 3d⁴.
• This is an octahedral complex with H₂O, which is a weak field ligand. Thus, it is a high spin complex.
• The d⁴ high spin configuration in an octahedral field is t_2g³ e_g¹.
• The e_g orbitals (d_z² and d_x²−y²) are degenerate and unequally occupied (one electron in one of the orbitals, the other is empty).
• Unequal occupancy of degenerate orbitals leads to Jahn‐Teller distortion.
• Therefore, [Mn(H₂O)₆]³⁺ is expected to show the Jahn‐Teller effect.

B. [Ni(H₂O)₆]²⁺

• The central metal ion is Nickel (Ni). Its atomic number is 28.
• The electronic configuration of neutral Ni is [Ar] 3d⁸ 4s².
• The complex has a charge of +2. Therefore, the oxidation state of Ni is +2.
• The electronic configuration of Ni²⁺ is [Ar] 3d⁸.
• This is an octahedral complex with H₂O, a weak field ligand (though spin state doesn't significantly alter the eg occupancy pattern for d8).
• The d⁸ configuration in an octahedral field is t_2g⁶ e_g².
• The e_g orbitals (d_z² and d_x²−y²) are degenerate and equally occupied (each has one electron).
• The t_2g orbitals (d_xy, d_yz, d_xz) are degenerate and equally occupied (each has two electrons).
• Since all degenerate sets of orbitals (e_g and t_2g) are either completely filled or equally occupied, there is no strong Jahn‐Teller distortion expected.

C. VCl₄

• The central metal atom is Vanadium (V). Its atomic number is 23.
• The electronic configuration of neutral V is [Ar] 3d³ 4s².
• The molecule VCl₄ is neutral, and each chloride ligand has a charge of −1. Therefore, the oxidation state of V is +4 (x + 4(−1) = 0 ⇒ x = +4).
• The electronic configuration of V⁴⁺ is [Ar] 3d¹.
• VCl₄ is typically a tetrahedral molecule.
• In a tetrahedral field, the d−orbitals split into e (lower energy) and t₂ (higher energy).
• The d¹ configuration in a tetrahedral field is e¹ t₂⁰.
• The e orbitals (d_x²−y² and d_z²) are degenerate and unequally occupied (one electron in one of the orbitals, the other is empty).
• Unequal occupancy of degenerate orbitals leads to Jahn−Teller distortion.
• Therefore, VCl₄ is expected to show the Jahn−Teller effect.

Conclusion on Jahn-Teller Effect

Based on the analysis of their electronic configurations in their respective geometries:

• [Mn(H₂O)₆]³⁺ is expected to show the Jahn−Teller effect (d⁴ high spin octahedral).
• [Ni(H₂O)₆]²⁺ is not expected to show a strong Jahn−Teller effect (d⁸ octahedral).
• VCl₄ is expected to show the Jahn−Teller effect (d¹ tetrahedral).

Thus, the Jahn−Teller effect is expected for species A and C.