Estimation of atomic correlation energies from the electron density at the nucleus and atomic additivity of the correlation energy in molecules

A new method based on electron density at the nucleus is presented to determine electron correlation energy in atomic species. Using the nuclear-electron coalescence cusp condition, we have shown that the atomic correlation energy can be well represented by different power of atomic number for different isoelectronic series. The computed correlation energies have been achieved chemical accuracy with average absolute deviation in the order of 1 kcal/mol for 17 isoelectronic series. Also it is shown that the correlation energy for a molecule can be expressed in terms of the correlation energies of its constituent atoms and its number of electrons. The proposed formula confirms that in a molecule the electron correlation is larger than the sum over electron correlations of its corresponding constituent atoms.