The EPR of low spin heme complexes Relation of the τ 2g hole model to the directional properties of the g tensor, and a new method for calculating the ligand field parameters

Abstract

A simple method is presented for calculating the parameters of the hole model for distorted octahedral, low spin (τ 2g) 5 complexes. In the case of negligible covalent bonding explicit formulas for the coefficients of the Kramer's doublet, ± a| ξ ± > — ib | η ± > — c | ζ ∓ >, are a  ( g z + g y )/4 p, b  ( g z − g x )/4 p, c  ( g y − g x )/4 p, where g z + g y − g x  2 p 2 is inherently positive for all correct choices of sign for the principal g values. The two numerically largest g values define the plane and orientation of the orbital with the largest coefficient, which in turn indicates the directions of maximal unpaired spin density. The energy of η with respect to ξ (in units of λ, the spin-orbit coupling constant) is A  g x /( g z + g y ) + g y /( g z — g x ), and of ζ is B  g x /( g z + g y ) + g z /( g y − g x ). The tetragonal splitting, Δ λ , is thus B − ( A 2 ), and the rhombic, V λ , is A . For a proper axis system, where z is the tetragonal axis, | A B | < 1 2 . The product g z g y g x , independent of axes, and positive for free electrons, is shown to be positive for tetragonal and negative for nearly octahedral complexes. It is considered positive for hemes. In this method coefficients will only be normalized when there is no covalency. For the majority of published cases they are, to about 1%. Since this discrepancy is larger than can be caused by propagated errors, covalency must be the rule. For comparative purposes A and B, uncorrected for covalency, should still be useful. Examination of published complete g tensors for five hemes shows that the largest g value is nearly normal to the heme plane. If the g values are taken positive and labelled so that g z > g y > g x , then the proper tetragonal axis is roughly normal to plane of the ring in hemes, but not in chlorins.