A modified cusp condition for the single density equations of DFT and orbital-free DFT for atoms

Although the electron density has the largest value at the nuclear site, the associated Coulomb singularity does not allow its determination in the numerical solution of the Euler-Lagrange equation in density functional theory (DFT) through the corresponding single density equation, or equivalently, in the orbital-free DFT. The problem may be bypassed by using the cusp condition, which, in its conventional form, may turn out to be inadequate for the related mixed boundary value problem. For this purpose, a new generalized cusp condition has been derived.