From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method
Georg Kresse, D Joubert
Physical Review B Condensed Matter 59(3), 1758 (1999)
The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blöchl’s projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modiﬁed PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modiﬁed PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efﬁciency of the PAW and the US pseudo- potential method with relaxed core all electron methods. These tests include small molecules ( H₂, H₂O, Li₂, N₂, F₂, BF₃, SiF₄) and several bulk systems (diamond, Si, V, Li, Ca, CaF₂, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.