Revealing the regularities of electron correlation energies associated with valence electrons in atoms in the first three rows of the periodic table

Although correlation energy in an atom can be decomposed into different components such as inter- and intra-orbital pair-correlation energies (PCE), it is generally believed that the PCEs in different atoms cannot be the same. In this work, we find that when the correlation energy is defined as the difference between the exact ground-state energy and the unrestricted Hartree–Fock energy, the PCEs associated with the valence electrons of the atoms in the same row of the periodic table have the same values. For two specific orbitals, the inter-orbital correlation energy is the same between two electrons of parallel or anti-parallel spins.