Large-scale multiconfiguration Dirac-Hartree-Fock calculations for astrophysics: n=4 levels in P-like ions from Mn~XI to Ni~XIV

Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the lowest 546 (623, 701, 745) states of the $3p^{4}3d$, $3s3p^{2}3d^2$, $3s3p^{3}4p$, $3s3p^4$, $3s^{2}3d^3$, $3s^2 3p^2 3d$,$3s^2 3p^2 4d$,$3s^2 3p^2 4s$,$3p^3 3d^2$,$3p^5$,$3s 3p 3d^3$,$3s 3p^3 3d$,$3s 3p^3 4s$,$3s^2 3p 3d^2$,$3s^2 3p^2 4f$,$3s^2 3p^2 4p$,$3s^2 3p^3$ configurations in Mn~XI (Fe~XII, Co~XIII, Ni~XIV) is provided. The comparison between calculated excitation energies for the $n=4$ states and available experimental values for Fe XII indicate that the calculations are highly accurate, with uncertainties of only a few hundred cm${}^{-1}$. Lines from these states are prominent in the soft X-rays. With the present calculations, several recent new identifications are confirmed. Other identifications involving $3p^{2}4d$ levels in Fe~XII that were found questionable are discussed and a few new assignments are recommended. As some $n=4$ states of the other ions also show large discrepancies between experimental and calculated energies, we reassess their identification. The present study provides highly accurate atomic data for the $n=4$ states of P-like ions of astrophysical interest, for which experimental data are scarce.