Mixing coefficients for d orbitals in copper(II) complexes of lower symmetry

Abstract

A study has been made of the effect of D_2h symmetry on the wavefunctions of copper(II) complexes. The wavefunction becomes an extended orbital with the form ψ_n=a_n|(x²–y²)⁺〉+b_n|(z²)⁺〉+c_n|(xy)⁺〉+d_n|(xz)^–〉+e_n|(yz)^–〉. Mixing coefficient (a–e) have been calculated in two different ways from spectral and e.s.r. data and are compared. The relative potential and equations have been derived and can reproduce spectral and e.s.r. g values within experimental error. The mixing coefficients a₁ and b₁ for the ground state [²A_g, |(X²–Y²)〉] are related to the radii in the xy plane, and the b₂ mixing coefficient [²A_g, |(Z²)〉] for the excited state is related to the radius in the z direction by a simple linear equation of the form r=K(r)〈ψ*|ψ〉+r₀. The ratio of the radii in the xy plane has been calculated. The radius in the z direction has been calculated by assuming that the radius is proportional to the energy of the |(Z²)〉 excited state, giving the equation r_z/Å= 0.01384(2b₂)²E_|(Z2)〉+ 0.68. A most likely electronic configuration can be determined if the symmetry is approximately correct, although the symmetry used in this paper is probably too high for many compounds.