Advanced Quantum Chemical Methods for Open-Shell Systems

Closed-shell systems appearing in many stable molecules have only paired electrons that occupy the same spatial orbitals with α and β spins. On the other hand, open-shell systems have unpaired electrons, which were observed in most of atoms, radicals, and metal complexes. Furthermore, open-shell fragments are produced when a chemical bond is uniformly dissociated. This chapter describes the quantum chemical methods to treat the open-shell electron systems, focusing on the basic Hartree-Fock method. The theoretical backgrounds and features of two representative approaches, i.e., spin-unrestricted and spin-restricted open-shell methods, are explained. In addition, the electron correlation method based on the spin-unrestricted method is also described.