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:T449,Oxygen electrochemistry plays a key role in renewable energy technologies such as fuel cells and electrolyzers, but the slow kinetics of the oxygen evolution reaction (OER) limit the performance and commercialization of such devices. Here we report an iridium oxide/strontium iridium oxide (IrO_x/SrIrO₃) catalyst formed during electrochemical testing by strontium leaching from surface layers of thin films of SrIrO₃ This catalyst has demonstrated specific activity at 10 milliamps per square centimeter of oxide catalyst (OER current normalized to catalyst surface area), with only 270 to 290 millivolts of overpotential for 30 hours of continuous testing in acidic electrolyte. Density functional theory calculations suggest the formation of highly active surface layers during strontium leaching with IrO₃ or anatase IrO₂ motifs. The IrO_x/SrIrO₃ catalyst outperforms known IrO_x and ruthenium oxide (RuO_x) systems, the only other OER catalysts that have reasonable activity in acidic electrolyte.

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