From ultrasoft pseudopotentials to the projector augmented-wave method

The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotent ials and Blochl's projector augmented wave (PAW) method is derived. It is s hown that the total energy functional for US pseudopotentials can be obtain ed by linearization of two terms in a slightly modified PAW total energy fu nctional. The Hamilton operator, the forces, and the stress tensor are deri ved for this modified PAW functional. A simple way to implement the PAW met hod 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 pseudopotential method with relaxed core a ll electron methods. These tests include small molecules (H-2, H2O, Li-2, N -2, F-2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magne tic energies of Fe, Co, and Ni. [S0163-1829(98)00848-0].