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:T456,Dielectric capacitors with high energy storage density (W_rec) and efficiency (η) are in great demand for high/pulsed power electronic systems, but the state-of-the-art lead-free dielectric materials are facing the challenge of increasing one parameter at the cost of the other. Herein, we report that high W_rec of 6.3 J cm^-3 with η of 90% can be simultaneously achieved by constructing a room temperature M2-M3 phase boundary in (1-x)AgNbO₃-xAgTaO₃ solid solution system. The designed material exhibits high energy storage stability over a wide temperature range of 20-150 °C and excellent cycling reliability up to 10⁶ cycles. All these merits achieved in the studied solid solution are attributed to the unique relaxor antiferroelectric features relevant to the local structure heterogeneity and antiferroelectric ordering, being confirmed by scanning transmission electron microscopy and synchrotron X-ray diffraction. This work provides a good paradigm for developing new lead-free dielectrics for high-power energy storage applications.

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