  We proposed a distributed approximating functional method for efficiently
describing the electronic dynamics in atoms and molecules in the presence of
the Coulomb singularities, using the kernel of a grid representation derived by
using the solutions of the Coulomb differential equation based upon the
Schwartz's interpolation formula, and a grid representation using the
Lobatto/Radau shape functions. The elements of the resulted Hamiltonian matrix
are confined in a narrow diagonal band, which is similar to that using the
(higher order) finite difference methods. However, the spectral convergence
properties of the original grid representations are retained in the proposed
distributed approximating functional method for solving the Schr\"odinger
equation involving the Coulomb singularity. Thus the method is effective for
solving the electronic Schr\"odinger equation using iterative methods where the
action of the Hamiltonian matrix on the wave function need to evaluate many
times. The method is investigated by examining its convergence behaviours for
calculating the electronic states of the H atom, H$_2^+$ molecule, the H atom
in a parallel magnetic and electric fields, as the radial basis functions.
