Mixing coefficients for d orbitals in copper(II) complexes with lower symmetry. Part 2.—Ionic radii of copper(II) ions in complexes

Abstract

The ionic radii of low-symmetry copper(II) compounds have been investigated in the xy plane and are shown to be reasonably represented by linear equations. The theoretical expression is r_i=K(r)_i〈ψ²₁〉/E_|(z²)〉+r_0i(i=x, y). When evaluated for six compounds whose structure is known this becomes r_y/Å= 1.00556(a₁–b₁/[graphic omitted])²/E_|(z²)〉+ 0.6706 and r_x/Å= 0.5832(–a₁–b₁/[graphic omitted])²/_|(z²)〉+ 0.6787, where a₁ and b₁ are the mixing coefficients of the d_x²–y² and d_z² orbitals in the ground-state wavefunction, and E_|(z²)〉 is the energy of the ²A_g|(Z²)〉â†�²A_g|(X²–Y²)〉 transition in kK. The values for the mixing coefficients a₁ and b₁ can be calculated for compounds of copper(II) if the radii and E_|(z²)〉 are known. The least-squares equations for all compounds are r_y/Å= 1.0464/E_|(z²)〉+ 0.6706 and r_x/Å= 0.4446/E_|(z²)〉+ 0.6787. The average error is ca. 3–4%. An equation was also developed for the average radius in the xy plane.