From ultrasoft pseudopotentials to the projector augmented-wave method

1999/01/15 by G. Kresse, Georg Kresse, D. Joubert +1 · 414 citations
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Boron and Carbon Nanomaterials Research #High-pressure geophysics and materials

paper · doi:10.1103/physrevb.59.1758

openalex publication_date 1999/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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 (H₂,H₂O,Li₂,N₂,F₂,BF₃,SiF₄) and several bulk systems (diamond, Si, V, Li, Ca, CaF₂, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.

Citations

• Projector augmented-wave method
• Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis
• Efficient iterative schemes for<i>ab initio</i>total-energy calculations using a plane-wave basis set
• Self-Consistent Equations Including Exchange and Correlation Effects

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• Adsorption of Metallic, Metalloidic, and Nonmetallic Adatoms on Two-Dimensional C3N
• Strain-Modulated Interlayer Charge and Energy Transfers in MoS2/WS2 Heterobilayer
• Hybrid Quantum-Classical Simulations of Graphene Analogues: Adsorption Energetics Beyond DFT
• Molecular Precursors-Induced Surface Reconstruction at Graphene/Pt(111) Interfaces
• Altermagnetic Shastry-Sutherland fullerene networks
• Thermoelectric transport properties of electron doped pyrite FeS2
• Electric-field induced half-metallicity in a two-dimensional ferromagnetic Janus VSSe bilayer
• Accurate Screening of Functional Materials with Machine-Learning Potential and Transfer-Learned Regressions: Heusler Alloy Benchmark
• Performance enhancement and degradation mechanism identification of a single-atom Co–N–C catalyst for proton exchange membrane fuel cells
• Kinetic pathways of coesite densification from metadynamics
• MnBr₂ on the graphene on Ir(110) substrate: growth, structure, and super-moirè
• Automated Modeling of Polarons: Defects and Reactivity on TiO₂(110) Surfaces
• Quasi-One-Dimensional Higher-Order Topological Insulators
• Wannier90 as a community code: new features and applications
• Investigating the Electrical Transport Properties and Electronic Structure of Zr2CuSb3
• Three-Dimensional Continuous Multi-Walled Carbon Nanotubes Network-Toughened Diamond Composite
• CuSbSe2 photovoltaic devices with 3% efficiency
• Re-Engineering Hematite: Synergistic Co-Doping Routes to Efficient Solar Water Splitting
• Revisiting thermal transport in CuCl: First-principles calculations and machine learning force fields
• Equivariant Electronic Hamiltonian Prediction with Many-Body Message Passing
• Investigating charge transfer dynamics at the nanoscale
• An accurate DFT-1/2 approach for shallow defect states: Efficient calculation of donor binding energies in silicon
• Mechanically tunable spontaneous vertical charge redistribution in few-layer WTe2
• Modeling oxygen-void interactions in uranium nitride
• An ab initio molecular dynamics exploration of associates in Ba-Bi liquid with strong ordering trends
• Machine-learning interatomic potentials achieving CCSD(T) accuracy for systems with extended covalent networks and van der Waals interactions
• NV-like Defects More Common Than Four-Leaf Clovers: A Perspective on High-Throughput Point Defect Data
• Atomistic mechanisms of phase transitions in all-temperature barocaloric material KPF₆
• Evidence for single variant in altermagnetic RuO2(101) thin films
• Effect of local crystal field environment on luminous properties of Er3+/Yb3+-doped titanate upconversion luminescent materials
• Dislocation-mediated short-range order evolution during thermomechanical processing
• Pressure-Driven Electronic Reconstruction and Anomalous Hall Transport Evolution in Monoclinic FeNbTe ₂
• Photo-induced chirality in a nonchiral crystal
• CoRuTiGe: A Possible Spin Gapless Semiconductor
• Phase transitions driven by solute concentration, temperature, and pressure in uranium-6wt % niobium alloy
• Photocatalytic CO2 Reduction Enhanced by Synergetic Interactions among Photon Phonon and Molecule
• Transport evidence of current-induced nematic Dirac valleys in a parity-time-symmetric antiferromagnet
• Evidence for ultra-water-rich ammonia hydrates stabilized in icy exoplanetary mantles
• Highly Reversible Lithium Host Materials for High‐Energy‐Density Anode‐Free Lithium Metal Batteries
• Theory of Spiral Magnetism in Weyl semimetal SmAlSi
• Tunable optical emissions of Eu3+ ions enabled by pressure-driven phase transition in ZnO
• Depth, relaxation and temperature dependence of defect complexes in\n scanning transmission electron microscopy
• One-dimensional electronics with edge states in two-dimensional altermagnets
• Realizing high Near-Room-Temperature Thermoelectric Performance in n-type Ag2Se through Rashba Effect and Entropy Engineering
• Phonon interference effects in GaAs-GaP superlattice nanowires
• A route to fully-compensated ferrimagnetic metal: electric-field annihilation of the bilayer bandgap
• Raman Spectroscopy and Aging of the Low-Loss Ferrimagnet Vanadium Tetracyanoethylene
• First-principles study of mechanical, electronic structure, optical, thermodynamic properties and hydrogen storage for new hydride perovskites XInH3 (X=Rb, Cs)*
• Investigating the Degradation of LATP Solid Electrolyte in High Alkaline Li-O₂ Batteries
• Short-Range Order and Li_xTM_4-x Probability Maps for Disordered Rocksalt Cathodes
• Ab-initio heat transport in defect-laden quasi-1D systems from a symmetry-adapted perspective
• Single-molecule infrared spectroscopy with scanning tunneling microscopy
• Role of idealized surface representations in computational area-selective atomic layer deposition: Assessing trimethoxypropylsilane blocking performance for Al2O3 deposition with crystalline SiO2
• Exsolution of Fe-based pyramidal nanostructures from a noble metal doped perovskite matrix
• Wafer-scale ultrathin and uniform van der Waals ferroelectric oxide
• Dopant precursor adsorption into single-dimer windows: Towards guided self-assembly of dopant arrays on Si(100)
• A Theoretical Study of Carbon Nanotube Formation: Carriers of the Diffuse Interstellar Bands?
• A literature-derived dataset of migration barriers for quantifying ionic transport in battery materials
• Multiorbital character of the density wave instability in La₄Ni₃O₁₀
• Isolated spin ladders in Ln₂Ti₉Sb₁₁ (Ln:La-Nd) metals
• Many-body perturbation theory vs. density functional theory: A systematic benchmark for band gaps of solids
• Double Helix of atomic displacements in Ferroelectric PbTiO₃
• electrochemically modeling a non-electrochemical system: hydrogen peroxide direct synthesis on palladium catalysts
• EAC-Net: Predicting real-space charge density via equivariant atomic contributions
• The structural, magnetic and optical properties of TMn@(ZnO)42 (TM = Fe, Co and Ni) hetero-nanostructure
• H2O and CO2 sorption in ion exchange sorbents: distinct interactions in amine versus quaternary ammonium materials
• The Open DAC 2025 Dataset for Sorbent Discovery in Direct Air Capture
• Open Molecular Crystals 2025 (OMC25) Dataset and Models
• Classical-to-Quantum Crossover in 2D TMD Field-Effect Transistors: A First-Principles Study via Sub-10 nm Channel Scaling Beyond the Boltzmann Tyranny
• Floquet odd-parity collinear magnets
• Electronic structure simulations in the cloud computing environment
• Local interface effects modulate global charge order and optical properties of 1T-TaS₂/1H-WSe₂ heterostructures
• Magnetism at the interface of MoSe₂/V₂O₅ heterostructures
• Structural and electronic properties of V₂O₅ and MoO₃ bulk and ultrathin layers
• Persistent spin textures, altermagnetism and charge-to-spin conversion in metallic chiral crystals TM₃X₆
• Extrinsic nature of the polarization in hafnia ferroelectrics
• High-fidelity electronic structure and properties of InSb: G₀W₀ and Bayesian-optimized hybrid functionals and DFT+U approaches
• Optimizing α''-Fe₁₆N₂ as permanent magnet via alloying
• Spin-State Engineering of Single Titanium Adsorbates on Ultrathin Magnesium Oxide
• Disorder driven crossover between anomalous Hall regimes in Fe₃GaTe₂
• Phase-engineered Non-degenerate Sliding Ferroelectricity Enables Tunable Photovoltaics in Monolayer Janus In2S2Se
• Thermodynamically driven tilt grain boundaries of monolayer crystals using catalytic liquid alloys
• Spin mapping of intralayer antiferromagnetism and spin-flop transition in monolayer CrTe₂
• Lattice tuning of charge and spin transport in β₁₂-borophene nanoribbons
• Electronic Structure of Bimetallic CoRu Catalysts Modulates SWCNT Nucleation
• Impressive optoelectronic and thermoelectric properties of\n two-dimensional XI₂ (X=Sn, Si): a first principle study
• Ultralow thermal conductivity via weak interactions in PbSe/PbTe monolayer heterostructure for thermoelectric design
• Active Learning for Predicting the Enthalpy of Mixing inBinary Liquids Based on Ab Initio Molecular Dynamics
• Bilayer Phosphorene: Effect of Stacking Order on Bandgap and its Potential Applications in Thin-Film Solar Cells
• First principles study of [111]-oriented epitaxially strained Rare-Earth Nickelate NdNiO₃
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• Evaluating First-Principles Electron-Phonon Couplings: Consistency Across Methods and Implementations
• Sliding Engineering Spin-Valley-Layer Coupling and Altermagnetism in Bilayer Antiferromagnetic Honeycomb Lattices
• Origin of superconductivity and giant phonon softening in TlInTe₂ under pressure
• Mo-Re-W Alloys for High Temperature Applications: Phase Stability, Elasticity, and Thermal Property Insights via Multi-Cell Monte Carlo and Machine Learning
• On the adsorption of oxygen to high entropy alloy surfaces up to 2ML coverage using Density Functional Theory and Monte Carlo calculations
• A first-principles study on the early-stage corrosion of a NiWNb alloy in a chloride salt environment
• Density functional calculation of the heats of formation of rare-earth\n orthophosphates
• Bond-Derived Orbitalwise Coordination Number as an Accurate Reactivity Descriptor for Oxygen Electrochemistry in Transition-Metal Oxides

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