Abstract: Correlation energies for all like ions of two electrons systems (P+13, S+14, Cl+15, Ar+16, K+17and Ca+18) and three electrons systems (P+12, S+13, Cl+14, Ar+15, K+16and Ca+17) are obtained by taking difference between theoretical total energies of Hartree- Fock calculations and experimental total energies. The atomic properties are calculated very important to describe the dynamics in atomic systems. In this research used the division technique for the analysis the three electron system, also all the examining atomic properties were normalized and we used the atomic units in our calculations and the results is get by using Mathcad 14 program. Keywords: correlation energy, Hartree- Fock, atomic units, atomic properties, Hamiltonian operator. Title: Evaluation of the ground state correlation energy for two and three electron systems have (Z=15 – 20) Author: Ameer F. Shamkhi, Maryam Hakim AL-Quraishi, Qassim Shamkhi AL-Khafaji, Shaymaa awad kadhim, Hawraah hashem abbasde International Journal of Novel Research in Physics Chemistry & Mathematics ISSN 2394-9651 Vol. 10, Issue 3, September 2023 - December 2023 Page No: 107-114 Novelty Journals Website: www.noveltyjournals.com Published Date: 10-November-2023 DOI: https://doi.org/10.5281/zenodo.10100749 Paper Download Link (Source) https://www.noveltyjournals.com/upload/paper/Evaluation%20of%20the%20ground%20state-10112023-1.pdf