Estimates and error distribution of EPR g-factors and hyperfine coupling constants

Abstract

The least-squares method yields well-known estimates which will be called G 2 and K 2 for the G 2 and K 2 tensors related to the hyperfine tensor T 2 by T 2 = G −1 K 2 G −1. However, very little is known about how to estimate the eigenvalues of G 2 and T 2, which are the important EPR parameters. The common procedure used in estimating these EPR parameters consists in computing the eigenvalues of G 2 and T 2. The statistical characteristics of these eigenvalue estimators are studied by simulation. An empirical description of the joint distribution of the eigenvalue estimators is generated. The authors show that a good experimental design is necessary to prevent biased and highly correlated eigenvalue estimators.