Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, i.e. He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quan-tum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational re-sults for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 a.u., respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient cal-culations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in their ground state, HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature. Hartree-Fock-Roothaan (HFR) calculations for ground states of some atoms, ie He, Be, Ne, Ar, and Kr have been performed using minimal basis sets of Slater type orbitals (STOs) with integer and noninteger principal quan tum numbers (integer n-STOs and noninteger n-STOs). The obtained total energies for these atoms using minimal basis sets of integer n-STOs are in good agreement with those in the previous literature. On the other hand, for the case of minimal basis sets of noninteger n-STOs, although the calculated total energies of these atoms agree well with the results in literature, some striking results have been obtained for atoms Ar and Kr. Our computational re-sults for the energies of atoms Ar and Kr are slightly better than those in literature, by amount of 0.00222 and 0.000054 au, respectively. The improvement in the energies of atoms Ar and Kr may result from the efficient cal-culations of one-center two-electron integrals over noninteger n-STOs. For some atomic ions in t heir ground state, HFR calculations have been carried out using minimal basis sets of noninteger n-STOs. The obtained total energies for these atomic ions are substantially lower than those available in literature.