The diagrammatic linked‐cluster many‐body perturbation theory is applied to study the hyperfine constant a (in a I⇒·S⇒) for free 55 Mn +2 ion. The calculation leads to a hyperfine constant of −363 ± 3 MHz , composed of −358 MHz due to the perturbation of the s cores by the 3d electrons, −14 MHz from consistency effects associated with this perturbation and +9 MHz from correlation effects. The first of these contributions is in very good agreement with the results of moment‐ perturbation (MP) calculations. Results of MP calculations for the divalent iron‐group ions and a few trivalent and one quadrivalent ion are presented and discussed.