act in principles. Rigorously speaking, the KS single鄄particle energies and wave functions in general do not have any physical meanings, but in practice they are often used to interpret excited state properties as probed by direct and inverse photo鄄emission spectroscopy and optical absorption. This practice, however, can only be exercised with caution. Even for weakly correlated systems such as sp semiconductors, the KS鄄DFT within LDA/GGA gives band gaps that are systematically underestimated when compared to experiment, and can predict metallic ground state for small鄄gap semiconductors, e.g., Ge, InN and so on. The problem can become even more severe for systems with open d- or f鄄 shell, often called strongly correlated systems, for which even wide gap insulators can be predicted to be metallic. Other ground state properties like magnetic ordering can also be qualitatively wrong in LDA/GGA descriptions. This is best illustrated in the notorious failure of the LDA/GGA for late 3d transition metal oxides[4]. The difficulty of the LDA/GGA for d/f鄄electron systems is actually common for all mean鄄field band鄄theory based approaches, which was already realized soon after the birth of the band theory. As a result, the "standard" theoretical approaches for strongly correlated d/f鄄electron systems are often based on some highly simplified model Hamiltonian, such as the Anderson impurity model [5] and the Hubbard model [6], which usually aims to represent only a particular aspect of the system under study, and neglect all other, usually materials specific, details. These model approaches are very useful to analyse experimental data in simple pictures. Some of these models, in spite of its formal simpleness, can have very rich physics, and in the meanwhile theoretically highly demanding. Nevertheless the model Hamiltonian approaches are usually not first鄄principles and often rely on empirical parameters. In the recent years, a lot of efforts have been invested to develop first鄄principles approaches beyond LDA/ GGA in the DFT framework that can treat d/f鄄electron systems correctly. The most widely used correlated band theory approaches, as they are often called, are the LDA+U [7-8], the self鄄 interaction corrected LDA [9-11], and hybrid functionals approaches [12-13]. These approaches can dramatically improve the descriptions of many d/f鄄electron systems within reasonable computation efforts, but at the price of a certain conceptual rigorousness. For example, the LDA+U approach relies on the system鄄specific parameter U, the on鄄site Coulomb interaction term, which is difficult, if not impossible, to be uniquely determined, and in practice is often treated as an empirically adjustable parameter. Even more serious is that these correlated band theory approaches mainly aim to improve the descriptions of ground state properties. The quality of the single鄄particle spectrum from these approaches is not guaranteed by their improvement of the ground state properties. Compared to the ground state properties, excited states properties are more strongly dependent on proper treatment of correlation effects, even for weakly correlated sp systems. Excited states properties can in principles be described ex-

上一页下一页