From ultrasoft pseudopotentials to the projector augmented-wave method
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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- Authors
- Kresse, G., & Joubert, D.
- Affiliations
- University of Vienna (AT)
- TU Wien (AT)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1999-01-15
- Volume
- 59
- Issue
- 3
- Pages
- 1758-1775
- ISSN
- 0163-1829 (ISSN-L)
- 1095-3795
- OpenAlex
- W1979544533
- Semantic Scholar
- 7b7ed4669c5f451fe8b33d14f953c2934232e369
- Cited by
- 85,307
- References
- 44
- Citations by year
- 2026: 7066 · 2025: 8611 · 2024: 7947 · 2023: 6865 · 2022: 6610 · 2021: 6234 · 2020: 5654 · 2019: 5098 · 2018: 4598 · 2017: 4073 · 2016: 3670 · 2015: 3230 · 2014: 2791 · 2013: 2394 · 2012: 2165
- FWCI
- 33.43
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. B, Condensed matter (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Engineering › Mechanical Engineering › Thermodynamic and Structural Properties of Metals and Alloys
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Keywords
- ultrasoft pseudopotentials, projector augmented wave method, total energy functional, Hamiltonian, magnetic energy, transition metals, bulk properties
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