Ground- and excited-state cusp conditions for the electron density

Higher-order cusp relations are derived for the wave function and the elect ron density of the ground and the excited states of atoms, ions or molecule s. The total energy is expressed in terms of the electronic potential and d ensity terms defined at the nucleus. It is proved that the linear term of t he spherical part in the expansion of the Kohn-Sham potential, the classica l Coulomb arid the exchange correlation potentials around a nucleus are all equal to zero. A relationship involving the values of the density and its second and third derivatives at the nucleus is derived. (C) 2001 American I nstitute of Physics.