Electron correlation in Hooke's law atom in the high-density limit

摘要

Closed-form expressions for the first three terms in the perturbation expansion of the exact energy and Hartree-Fock energy of the lowest singlet and triplet states of the Hooke's law atom are found.These yield elementary formulas for the exact correlation energies(-49.7028 and-5.807 65 mE_h)of the two states in the high-density limit and lead to a pair of necessary conditions on the exact correlation kernel G(w)in Hartree-Fock-Wigner theory.