Interpretation of the correlation energy of atoms, and its dependence with atomic number Z up to Z = 18

Abstract

Accurate correlation energies Ecorr of neutral atoms with atomic number Z =1–18, calculated from a combination of experimental and theoretical information, are available in the literature. Those empirical correlation energies show a grossly linear behaviour with Z. However, in more detail Ecorr deviates from global linearity and reveals a piece-wise linear behaviour with different slopes as the different electronic shells are progressively filled. This behaviour can be explained by writing Ecorr as a sum of pairing-correlation contributions. The pairing- correlation energies have been obtained from the empirical total correlation energies of atoms. Those pairing- correlations are very weak for electrons in different main shells (K, L, M shells) and larger for electrons in the same main shell. In addition, the pairing-correlation energies depend on the angular momenta of the two electronic orbitals. Those features are due to the role of the quantum overlap between the wave functions of the electrons involved in the pairing. Pairs of electrons showing a very small orbital overlap lead to negligible pairing-correlation energies. Keeping a reasonable number of terms, the shell- and angular momentum- dependent pairing-correlation energies explain well the intricate piece-wise linear behaviour of Ecorr(Z) up to Z =18. Also, certain approximations applied to the pairing-correlation energies permit to justify the grossly linear trend of Ecorr with Z, and the more precise faster-than-linear behaviour of Ecorr(Z).