Accelerating convergence in orbital magnetization calculations through a single point formula and applications to defect EPR g-tensor fingerprints

Accurate EPR $g$-tensors of point defects in solids often require supercells containing hundreds to thousands of atoms to suppress defect--image interactions. In this regime, perturbative linear-response implementations can become impractical because the induced-current response is highly sensitive to Brillouin-zone sampling, typically demanding dense $k$-point meshes. Here we implement a \textit{single-point} formulation of the converse orbital-magnetization approach for EPR $g$-tensor calculations in periodic systems. Relative to converse schemes based on covariant finite-difference $k$-derivatives, the present formulation removes the auxiliary diagonalizations at $\mathbf{k}\!\pm\!\mathbf{q}$ and avoids explicit $k$-space summations, improving both computational efficiency and numerical stability under $\Gamma$-only sampling. We validate the implementation through a benchmark set of charged and neutral defects in Si, diamond, and $\alpha$-quartz, comparing against (i) the covariant converse method and (ii) linear-response calculations in \textsc{QE-GIPAW} and \textsc{CASTEP}. Using the absolute relative deviation of the principal $g$-tensor components from experiment as a metric, we find that the single-point scheme consistently delivers smooth, accelerated supercell-size convergence and remains stable in challenging cases with partially delocalized spin densities, where the covariant finite-difference approach can exhibit non-monotonic trends (notably for $\mathrm{V}^{+}$ in Si). Overall, the single-point converse formulation provides a practical accuracy-per-cost advantage for large-scale defect EPR modeling.