We proposed a general and effective approach for accurate calculating
method of the electron-electron, nuclear-electron and nuclear-nuclear
Coulomb electrostatic interaction energies. It is well known that
electron-electron, nuclear-electron and nuclear-nuclear Coulomb
electrostatic interaction energies reduced to basic two-center Coulomb
integrals. The analytical calculation of electrostatic interaction
energies with respect to basic two-center Coulomb integrals over Slater
type orbitals (STOs) in molecular coordinate systems allows us the
routine evaluation of molecular structures and related properties. In
this study we have introduced a new full analytical algorithm for
calculation of the basic two-center Coulomb integrals over STOs by using
Guseinov’s auxiliary functions especially interactions between
electrons. The auxiliary functions has been calculated by using the
exact recurrence relations which developed by Guseinov. The new approach
is successfully tested on earlier published studies data and can be
recommended for evaluation of related problems in atomic and molecular
physics.