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The structural, electronic, and magnetic properties of two-dimensional (2D) manganese dibromide (MnBr2) and manganese diiodide (MnI2) are investigated using first principles calculations. The dynamical and thermal stabilities of 2D MnBr2 and MnI2 have been illustrated from the phonon dispersion and molecular dynamic calculations. From the phonon dispersion, three Raman-active and three infrared-active vibration modes are found. The calculated formation energies and cleavage energies indicate that 2D MnBr2 and MnI2 are energetically stable and could be potentially obtained by exfoliation. The hybrid functional theory is employed to discover that 2D MnBr2 and MnI2 are wide gap semiconductors. The magnetic frustration is revealed by the calculation of magnetic exchange interaction and magnetocrystalline anisotropy interaction. By analyzing different magnetic orders, the relatively weak magnetic exchange is attributed to the competition of the direct exchange and the superexchange interaction. [ABSTRACT FROM AUTHOR]