# From ultrasoft pseudopotentials to the projector augmented-wave method

TL;DR: In this paper, the formal relationship between US Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived and the Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional.

Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl'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 pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.

...read more

##### Citations

^{1}, National Research Council

^{2}, International School for Advanced Studies

^{3}, Massachusetts Institute of Technology

^{4}, University of Paris

^{5}, Princeton University

^{6}, University of Minnesota

^{7}, ParisTech

^{8}, University of Milan

^{9}, International Centre for Theoretical Physics

^{10}, University of Paderborn

^{11}, ETH Zurich

^{12}, École Polytechnique Fédérale de Lausanne

^{13}

15,767 citations

8,251 citations

5,801 citations

5,741 citations

5,020 citations

##### References

1,111 citations

##### Related Papers (5)

[...]