The half-projected Hartree-Fock (HPHF) theory set forth by Smeyers (An
. Fis., 67 (1971) 17) is extended in order to obtain all the necessary
expressions for the calculations of the first and second derivatives
of the energy functional. This permits the implementation of well know
n direct optimization techniques in the framework of the HPHF method.
We also propose a treatment of linear response properties based on a H
PHF reference function and derive the equation defining the Tamm-Danko
ff (monoexcited CI) approximation.