Improved quantum theory of many-electron systems. iii. the gf method

A general method of calculating accurate and useful many-electron wavefunctions for atoms and molecules has previously been described. This general method besides achieving lower energies than do the Hartree-Fock and unrestricted Hartree-Fock methods still yields an independent particle interpretation of the many-electron wavefunction, correctly describes dissociation of molecules and solids, and can be used on systems of any total spin. There are several possible approaches for the general method; here we concentrate on one of these, GF method, which is equivalent to optimizing the orbitals in the unrestricted Hartree-Fock method after spin projection rather than before. The detailed equations (the GF equations), for the GF method are derived here for all values of total spin and number of particles.