A well-scaling natural orbital theory
Significance Computations of locations of nuclei and movement of electrons within molecules and materials are widely used in science and technology. Direct computation of a system’s wave function for that purpose becomes impractical as system size grows. Current alternative methods can have difficulty with strongly correlated electron motion or spurious electron self-interaction. By using “natural spin-orbitals” to describe the motion of individual electrons, solving for them together with their joint and individual probabilities of occurrence within the system, we are able to account better for electron correlation when strong while avoiding self-interaction and maintaining the growth of computation cost with system size at the level of Hartree–Fock theory. Our numerical results for some small test molecules are very good. We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree–Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix.