Calculations carried out via quantum mechanical framework are used in practically every field of chemistry, but not many know what is behind these computations. This framework allows one to probe molecular structure, chemical reactivity, spectroscopic behaviour, magnetic and electric properties of matter. On the market, there are a lot of programs offering these computations with simple user interfaces, but they are inherently black boxes. In this work the black box has been opened. First with the basic theoretical background and then with a practical implementation that is simple yet effective. The made program was used to calculate the energies of simple systems with the Hartree-Fock method and density functionals method. Energy levels, electron potentials, electric dipole and quadrupole moment, and partial charges were computed. For the hydrogen molecule, the potential energy surface with both methods was computed as well.
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