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To assist the laboratory $identificationh$ of the first Mg-bearing interstellar molecule MgNC, we carried our {ab initio} molecular orbital calculations of the spectroscopic constants of $X \mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}\Sigma +$ and MgNC by the SDCI (frozen core)/TZ2P method as is described in our previous $papers.i$ This time, we calculated potential energy surfaces (PES) of $X \mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}\Sigma +$ states of MgNC and MgCN by the CASSCF-ACPF/TZ2P+f method with core- valence electron correlation, and derived spectroscopic constants therefrom. Calculated rotational constant $B0$, centrifugal distortion constant $Du$, und vibration frequencies $\omega 1,\omega 2$, and $\omega 3$, with corresponding experimental values for $MgNCa$ and for $MgCNi$ in parentheses, are 5969.3 (5966.8969) MHz, 0.0029 (0.0042)MHz, and 2097.9, 90.4 (86), and $538.5cm-1$ for MgNC, and 5989.3 (5094.80351)MHz, 0.0025 (0.00277) MHz, and 2177.2, 159.9, and $468.6cm-1$ for MgCN, respectively. Great improvement, resulted from the inclusion of corevalence electron correlation Similar calculations have been carried out for CaNC and CaCN, where the inclusion of both core-core electron and core-valence electron correlations is found to be very important While the PES for the ground state CaCN is quite normal and shallow, the PES for the ground state CaNC is shallow but of very complicated character. The predicted $B0$ of CaNC is 3982.8 MHz against the experimental $Valuek$ of 4048.742 MHz. Preliminary calculations for $Bc$ of FeCO have also been carried out.