Multiplicity, instability, and SCF convergence problems in Hartree-Fock solutions

The authors present a study of the instability and convergence of Hartree-Fock (HF) ab initio solutions for the diatomic systems H2, LiH, CH, C2, and N2. In the study, they consider real molecular orbitals (MOs) and analyze the classes of single-determinant functions associated to Hartree-Fock-Roothaan (HFR) and Hartree-Fock-Pople-Nesbet (HFPN) equations. To determine the multiple HF solutions, they used either an SCF iterative procedure with aufbau and non-aufbau ordering rules or the algebraic method (AM). Stability conditions were determined using TICS and ASDW stability matrices, derived from the maximum and minimum method of functions (MMF). They examined the relationship between pure SCF convergence criterion with the aufbau ordering rule, and the classification of the HF solution as an extremum point in its respective class of functions. The results show that (1) in a pure converged SCF calculation, with the aufbau ordering rule, the solutions are not necessarily classified as a minimum of the HF functional with respect to the TICS or ASDW classes of solutions, and (2) for all studied systems, they obtained local minimum points associated only with the aufbau rule and the solutions of lower energies