Large-scale multiconfiguration Dirac-Fock calculations of hyperfine interaction constants for ${\mathit{nd}}^2$ levels of ${\mathrm{Sc}}^{+}$ and ${\mathrm{Y}}^{+}$

The multiconfiguration Dirac-Fock model is employed to study the effects of relativity and electron correlation on the hyperfine interaction constants of the 3${\mathit{d}}^2$ ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_1$, ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_2$, ${}_{}{}^1{}_{}{}^{}$ ${\mathit{D}}_2$, and ${}_{}{}^3{}_{}{}^{}$ ${\mathit{F}}_2$ levels of ${\mathrm{Sc}}^{+}$ and the 4${\mathit{d}}^2$ ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_1$ level of ${\mathrm{Y}}^{+}$. The wave function expansions are obtained with the active space method, where configuration state functions of a specific parity and J value are generated by excitations from the most important reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the hyperfine interaction constants to be studied. It is demonstrated that expansions generated by single excitations from the reference configurations, together with the most important double excitations, account for the dominant contributions to the hyperfine interaction constants and lead to very good agremeent between theoretical and experimental values. To obtain converged values of these constants within the single excitation approach, typically a few thousand configuration state functions are needed.