Evaluation of anisotropic non-coincident g2, A2, D, P and gn2 from EPR and endor data by the method of least-squares fitting

Details of a rigorous least-squares (LSF) procedure for the evaluation of the components of non-coincident tensors $\text{g}{}^2$, $\text{A}{}^2$, $\text{D}$, $\text{P}$ and $\text{g}{}_{\mathrm{n}}{}^2$ using eigenvalues calculated tt second-order in perturbation for electron-nuclear spin-coupled systems are given. The complexities associated with the presence of non-coincident tensors in the spin Hamiltonian are discussed. Details are provided of how the components of the various tensors can be evaluated by choosing either special, or arbitrary, coordinate axes for their descriptions. The procedure is illustrated by application to the X-band EPR data obtained at room temperature for VO²⁺-doped K₂C₂O₄·H₂O single crystal. It is found that, for this case, the LSF procedure, based on the use of second-order eigenvalues, as described here, yields the χ² value, representing the goodness of fit, one-fortieth that found employing the LSF procedure, based on the use of first-order eigenvalues.