Probing Collins Conjecture with correlation energies and entanglement entropies for the ground and excited states in the helium iso-electronic sequence

In the present work, we present an investigation of Collins Conjecture, a hypothesis made by D. M. Collins in 1993 relating correlation energy and entanglement entropy, by calculating the ground state and singly-excited triplet-spin 1s2s ³S and 1s3s ³S state energies of the helium iso-electronic sequence, with Z = 2–15. By using extensive orthonormal configuration interaction (CI) type wave functions with B-Spline basis up to about 6000 terms, linear entropy and von Neumann entropy for the abovementioned atomic systems are determined. Together with the Hartree-Fock energies obtained following a self-consistent field theory, we have found that there exist linearly proportionalities between the renormalized correlation energies and entanglement entropies of both linear and von Neumann, showing a support for Collins Conjecture applicable to the ground and singly-excited triplet-spin states in the helium sequence, for a range of finite Z-values.