Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix. The Mathematica software was used to program the matrix diagonalization process from the overlap and Hamiltonian core matrices and to make the recursion loop of the density matrix. Finally we obtained a value for the ground state energy of helium.