Occupation probabilities as variables in electronic structure theory: cooper pairing, OP-NSOFT-Cs,t, and the homogeneous electron liquid

The energy functional of a novel electronic structure theory, OP-NSOFT, has as variables the natural spin orbitals (NSO) of the trial function and their joint occupation probabilities in the search for the ground state energy. When occupancy is restricted to the spin-paired NSOs of DOCI, the resulting theory, OP-NSOFT-0, scales as M³, with M the size of the one-electron basis set. Accurate results were obtained for small molecules, particularly near dissociation where single reference theories like DFT are inaccurate. The homogeneous electron liquid (HEL) could serve as a test bed of OP-NSOFT for condensed systems, but OP-NSOFT-0 reduces to the Hartree–Fock approximation for the HEL. Cooper pairing is introduced instead, both singlet pairing, OP-NOFT-Cs, and fully polarized triplet pairing, OP-NSOFT-Ct. The former yields 1/3 of the diffusion-Monte-Carlo correlation energy, the latter 1/2 to 1/3 with decreasing electron density for r_s values between 1 and 10. Both yield the discontinuity in the single-particle occupation number required by the Luttinger theorem. Two-state joint occupation probabilities illustrate the importance of electron–electron small-angle scattering in establishing electron correlation in the unpolarized HEL.