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The electronic band structures, density of states plots and magnetic momentsof Fe$_{2 }$MnSi, Fe$_{2 }$MnAl, and Co$_{2 }$MnGe are studied by using thefirst principles calculations. The FM solutions using LSDA without \textit{U}show the presence of half-metallic ferromagnetic (HFM) ground state in Fe$_{2}$MnSi, whereas the ground state of Fe$_{2 }$MnAl is found to be metallic. Inboth compounds the maximum contribution to the total magnetic moment is fromthe Mn atom, while the Fe atom contributes very less. The electronic structuresand magnetic moments of Fe-based compounds affected significantly by\textit{U}, whereas its effect is very less on Co$_{2}$MnGe. The magneticmoment of Fe atom in Fe$_{2 }$MnSi (Fe$_{2 }$MnAl), increased by $\sim$ 70 %($\sim$ 75 %) and in Mn atom it decreases by $\sim$ 50 % ($\sim$ 70 %) when thevalue of \textit{U} is increased from 1 to 5 eV. The Hund's like exchangeinteractions are increasing in Fe atom while decreasing in Mn atom withincrease in \textit{U}. The Fe and Mn moments are ferromagnetically coupled inFe$_{2 }$MnSi for all values of \textit{U}, whereas in Fe$_{2 }$MnAl theycoupled antiferromagnetically below \textit{U} = 2 eV and ferromagneticallyabove it. Above \textit{U} = 2 eV the metallic ground state of Fe$_{2 }$MnAlchanges to semiconducting ground state and the ferromagnetic coupling betweenFe and Mn atoms appears to be responsible for this.

{Effect of on-site Coulomb interaction (\textit{U}) on the electronic and magnetic properties of Fe$_{2}$MnSi, Fe$_{2}$MnAl and Co$_{2}$MnGe