1e:T44e,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.1f:T44d,A variety of nickel oxide compounds have long been studied for their manifestation of various correlated electron phenomena. Recently, superconductivity was observed in nanoscale infinite layer nickelate thin films of Nd_0.8Sr_0.2NiO₂, epitaxially stabilized on SrTiO₃ substrates via topotactic reduction from the perovskite precursor phase. Here, we present the synthesis and properties of PrNiO₂ thin films on SrTiO₃. Upon doping in Pr_0.8Sr_0.2NiO₂, we observe superconductivity with a transition temperature of 7-12 K and robust critical current density at 2 K of 334 kA/cm². These findings indicate that superconductivity in the infinite layer nickelates is relatively insensitive to the details of the rare earth 4f configuration. Furthermore, they motivate the exploration of a broader family of compounds based on two-dimensional NiO₂ planes, which will enable systematic investigation of the superconducting and normal state properties and their underlying mechanisms.

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