Direct calculation of the Coulomb matrix: Slater-type orbitals

It is proved that the evaluation of the Coulomb potential and the calculation of its matrix elements can be carried out in separate steps whose costs formally increase as the square of the number of basis functions. The resulting method for computing the Coulomb matrix is reported, and its main features are tested with a trial program for Slater functions. A comparison of the Coulomb matrices obtained with this method and those computed from the repulsion integrals shows that the current procedure is potentially exact, highly accurate in practice, and much less expensive. The effects of basis product cutoff and long-range separation have been analyzed finding that the method tends to linear scaling with the size of the system. Moreover, the storage requirements are very low since two-electron integrals are completely absent, and it is well suited to be used in the density functional context.