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The ground state molecular frame dipole moments of alkaline earth metal monofluorides and Group ІІB‐monohydrides have been computed using two analytic methods, namely the Z‐vector technique and the linear expectation value method within the four‐component relativistic coupled cluster singles and doubles framework. We have compared our results with the experimentally measured permanent dipole moments wherever available. It is found that the Z‐vector method, which is an energy‐derivative approach predicts the molecular permanent dipole moment more accurately than the linear expectation value approach in DZ and TZ quality basis set. Further, our study shows that the high‐energy virtual spinors seem to have almost no influence on the permanent dipole moment whereas the core electron correlation slightly affects this molecular property. [ABSTRACT FROM AUTHOR]