Analysis of the half‐projected Hartree–Fock function: Density matrix, natural orbitals, and configuration interaction equivalence

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Abstract
The half‐projected Hartree–Fock function for singlet states (HPHF) is analysed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced.It is found that the HPHF function does not contain any contribution from odd‐times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed‐shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more that two atoms is criticized.