Detail:

Abstract:
　　The fundamental energy gap of a solid is not only an excitation energy but also a ground state energy difference (ionization energy minus electron affinity). The corresponding gap in the band structure of the exact Kohn-Sham theory is less than the fundamental gap, as found by Perdew and Levy, and by Sham and Schlueter, in 1982. The reason is that a multiplicative effective potential that yields both the exact ground-state electron density and the exact chemical potential has a discontinuity as the electron number crosses neutrality. Yet the band gaps of certain hybrid functionals, evaluated in a generalized Kohn-Sham scheme, can be close to the fundamental gap. The generalized Kohn-Sham potential is a multiplication operator (for the local density or generalized gradient approximations [GGAs]), a differential operator (for meta-GGAs), or an integral operator (for hybrids of GGA with exact exchange), without a discontinuity. We show analytically and numerically that generalized Kohn-Sham band gaps are ground-state total energy differences within a given approximation. Thus the improvement of generalized Kohn-Sham gaps from GGA to meta-GGA to hybrid reflects the corresponding improvement in the ground-state energy.

Biosketch：
　　Prof. John P. Perdew graduated from Gettysburg College with a Bachelor of Arts in physics and math in 1965, and received a Ph.D. in physics from Cornell University in 1971. He then went to the University of Toronto from 1971-1974 and Rutgers University from 1974-1977 as Postdoctoral Fellows. In 1977, he joined Tulane University and started his teaching career. In 2013, he moved to Temple University as a Laura H. Carnell Professor of Physics and Chemistry, as well as the founding director of the Center for the Computational Design of Functional Layered Materials. Prof. Perdew is a theoretical condensed matter physicist most widely known for his contributions to the fields of solid-state physics and quantum chemistry. His work on formal density functional theory (DFT) has earned him the reputation of being a “theorist for the theorists”. He is one of the world’s most cited physicists, with a total SCI citation of ~130,000, and the highest cited paper (on the PBE functional) collecting over 48,700 citations. He was elected to the National Academy of Sciences (USA) in 2011, and was awarded various prizes, including the Materials Theory Award of the Materials Research Society (2012), Humboldt Research Award (2014), and John Scott Award (2015).