Calculations of the Hartree-Fock ground-state wave function and total energy of crystalline ${\mathrm{MgCO}}_3$ have been performed using the ab initio crystal program. Contracted Gaussian-type functions have been used to represent 18, 18, and 14 (including d) atomic orbitals for Mg, O, and C, respectively. The rhombohedral calcite-type structure has been fully relaxed, determining the equilibrium lattice constants and coordinate of the O atom as a function of volume. The bulk elastic modulus and the ${\mathit{C}}_{33}$ and ${\mathit{C}}_{11}$+${\mathit{C}}_{12}$ elastic constants have been calculated. Deviations from experimental data are within 1% for the structural parameters and amount to +6.8% for the bulk modulus. The computed binding energy (including a correction for the electron correlation based on local-density-functional theory) is smaller by 6% than the measured value. Mulliken electron charges are +1.750, -0.986, and +1.207 ‖e‖ for Mg, O, and C. Energy bands, density of states, and electron-density maps permit the characterization of chemical bonding within the ${\mathrm{CO}}_3$ molecular unit and between ${\mathrm{CO}}_3$ groups and Mg atoms.