中央研究院 原子與分子科學研究所

In the present work, we present an investigation of Collins Conjecture, a hypothesismade 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 3Sstate energies of the helium iso-electronic sequence, with Z = 2–15. By using exten-sive orthonormal configuration interaction (CI) type wave functions with B-Splinebasis up to about 6000 terms, linear entropy and von Neumann entropy for theabovementioned atomic systems are determined. Together with the Hartree-Fockenergies obtained following a self-consistent field theory, we have found that thereexist linearly proportionalities between the renormalized correlation energies andentanglement entropies of both linear and von Neumann, showing a support forCollins Conjecture applicable to the ground and singly-excited triplet-spin states inthe helium sequence, for a range of finite Z-values.