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From ultrasoft pseudopotentials to the projector augmented-wave method

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TLDR
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.

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Citations
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A major advance in crystal structure prediction.

TL;DR: A hybrid method is used, developed by one of the authors, for the calculation of lattice energies that combines density functional theory (DFT) simulations using the Vienna Ab initio Simulation Package (VASP) program with an empirical van der Waals (vdW) correction expressed in terms of a sum over isotropic atom–atom pair potentials.
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Toward Computational Materials Design: The Impact of Density Functional Theory on Materials Research

TL;DR: Density functional theory (DFT) has had a rapidly growing impact not only on fundamental but also industrial research as discussed by the authors, and the fundamental principles of DFT and the highly efficient computational tools that have been developed for its application to complex problems in materials science.
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Catalytic activity of Co–Nx/C electrocatalysts for oxygen reduction reaction: a density functional theory study

TL;DR: First-principles DFT computations are performed to explain the origin and the mechanism of oxygen reduction reaction (ORR) on Co-N(x) (x = 2, 4) based self-assembled carbon supported electrocatalysts in alkaline and acidic media and show that the formation of graphitic Co-n(4) defect is energetically more favorable than the formationof graphitic co-N (2) defect.
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Binding Site Diversity Promotes CO2 Electroreduction to Ethanol.

TL;DR: A bimetallic Ag/Cu catalyst is developed that implements the proposed design toward an improved ethanol catalyst and presents a framework to design multimetallic catalysts to control reaction paths in CO2 reductions toward desired products.
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Precisely Tuning the Number of Fe Atoms in Clusters on N-Doped Carbon toward Acidic Oxygen Reduction Reaction

TL;DR: In this article, the number of Fe atoms in clusters anchored on N-doped carbon is tuned at the atomic level from the angle of both active sites and catalyst supports, which offers the capabilities of altering O2 adsorption from superoxo-like to peroxolike configuration.
References
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Book

Planewaves, Pseudopotentials, and the LAPW Method

TL;DR: The linearized augmented planewave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged.
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