Deriving gradient formulae for SCF methods by using Brillouin-type theorems. Gradient in the HPHF method

It is discussed that the derivation of different SCF-type equations through the relevant (generalized) Brillouin theorems can be utilized to obtain the energy gradients of the method studied. This is illustrated for the case of the UHF method and used to obtain the gradient formula applicable in the framework of the half-projected Hartree—Fock method. The approach should also be applicable to MC-SCF theories.