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An implementation of the Hartree-Fock (HF) method capable of robustconvergence for well-behaved arbitrary central potentials is presented. TheHartree-Fock equations are converted to a generalized eigenvalue problem byemploying a B-spline basis in a finite-size box. Convergence of theself-consistency iterations for the occupied electron orbitals is achieved byincreasing the magnitude of the electron-electron Coulomb interaction graduallyto its true value. For the Coulomb central potential, convergence patterns andenergies are presented for a selection of atoms and negative ions, and arebenchmarked against existing calculations. The present approach is also testedby calculating the ground states for an electron gas confined by a harmonicpotential and also by that of uniformly charged sphere (the jellium model ofalkali-metal clusters). For the harmonically confined electron-gas problem,comparisons are made with the Thomas-Fermi method and its accurate asymptoticanalytical solution, with close agreement found for the electron energy anddensity for large electron numbers. We test the accuracy and effectivecompleteness of the excited state manifolds by calculating the static dipolepolarizabilities at the HF level and using the Random-Phase Approximation.Using the latter is crucial for the electron-gas and cluster models, where theeffect of electron screening is very important. Comparisons are made for withexperimental data for sodium clusters of up to $\sim $100 atoms.

B-Spline basis Hartree-Fock method for arbitrary central potentials: atoms, clusters and electron gas