Van der Waals density functionals applied to solids
Open accessAbstract
The van der Waals density functional (vdW-DF) of M. Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] is a promising approach for including dispersion in approximate density functional theory exchange-correlation functionals. Indeed, an improved description of systems held by dispersion forces has been demonstrated in the literature. However, despite many applications, standard general tests on a broad range of materials including traditional ``hard'' matter such as metals, ionic compounds, and insulators are lacking. Such tests are important not least because many of the applications of the vdW-DF method focus on the adsorption of atoms and molecules on the surfaces of solids. Here we calculate the lattice constants, bulk moduli, and atomization energies for a range of solids using the original vdW-DF and several of its offspring. We find that the original vdW-DF overestimates lattice constants in a similar manner to how it overestimates binding distances for gas-phase dimers. However, some of the modified vdW functionals lead to average errors which are similar to those of PBE or better. Likewise, atomization energies that are slightly better than from PBE are obtained from the modified vdW-DFs. Although the tests reported here are for hard solids, not normally materials for which dispersion forces are thought to be important, we find a systematic improvement in cohesive properties for the alkali metals and alkali halides when nonlocal correlations are accounted for.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Projector augmented-wave method
Blöchl, P. E. (1994) · Physical Review B · doi:10.1103/physrevb.50.17953 · Cited by 92,732 · see citing works
From ultrasoft pseudopotentials to the projector augmented-wave method
Kresse, G., & Joubert, D. (1999) · Physical Review B · doi:10.1103/physrevb.59.1758 · Cited by 85,307 · see citing works
Kresse, G., & Furthmüller, J. (1996) · Computational Materials Science · doi:10.1016/0927-0256(96)00008-0 · Cited by 75,541 · see citing works
Ab initio molecular dynamics for liquid metals
Kresse, G., & Häfner, J. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.47.558 · Cited by 45,654 · see citing works
The SIESTA method for ab initio order- N materials simulation
Soler, J. M., Artacho, E., Gale, J. D., Garcı́a, A., Junquera, J., Ordejón, P., & Sánchez‐Portal, D. (2002) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/14/11/302 · Cited by 12,302 · see citing works
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
Perdew, J. P., Ruzsinszky, A., Csonka, G. I., Vydrov, O. A., Scuseria, G. E., Constantin, L. A., Zhou, X., & Burke, K. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.136406 · Cited by 11,970 · see citing works
Tkatchenko, A., & Scheffler, M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.073005 · Cited by 6,286 · see citing works
Van der Waals Density Functional for General Geometries
Dion, M., Rydberg, H., Schröder, E., Langreth, D. C., & Lundqvist, B. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.246401 · Cited by 5,631 · see citing works
Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
Gunnarsson, O., & Lundqvist, B. I. (1976) · Physical review. B, Solid state · doi:10.1103/physrevb.13.4274 · Cited by 3,682 · see citing works
Chemical accuracy for the van der Waals density functional
Klimeš, J., Bowler, D. R., & Michaelides, A. (2010) · Journal of Physics: Condensed Matter · doi:10.1088/0953-8984/22/2/022201 · Cited by 3,587 · see citing works
Self-citationComment on “Generalized Gradient Approximation Made Simple”
Zhang, Y., & Yang, W. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.890 · Cited by 2,937 · see citing works
Higher-accuracy van der Waals density functional
Lee, K., Murray, É., Kong, L., Lundqvist, B. I., & Langreth, D. C. (2010) · Physical Review B · doi:10.1103/physrevb.82.081101 · Cited by 2,765 · see citing works
Screened hybrid density functionals applied to solids
Paier, J. A., Marsman, M., Hummer, K., Kresse, G., Gerber, I. C., & Ángyán, J. G. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2187006 · Cited by 2,454 · see citing works
More accurate generalized gradient approximation for solids
Wu, Z., & Cohen, R. E. (2006) · Physical Review B · doi:10.1103/physrevb.73.235116 · Cited by 2,387 · see citing works
Jurečka, P., Šponer, J., Černý, J., & Hobza, P. (2006) · Physical Chemistry Chemical Physics · doi:10.1039/b600027d · Cited by 1,854 · see citing works
Román‐Pérez, G., & Soler, J. M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.096102 · Cited by 1,570 · see citing works
Nonlocal van der Waals density functional: The simpler the better
Vydrov, O. A., & Voorhis, T. V. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3521275 · Cited by 1,314 · see citing works
Paier, J. A., Hirschl, R., Marsman, M., & Kresse, G. (2005) · The Journal of Chemical Physics · doi:10.1063/1.1926272 · Cited by 1,050 · see citing works
Exchange-correlation energy of a metallic surface: Wave-vector analysis
Langreth, D. C., & Perdew, J. P. (1977) · Physical review. B, Solid state · doi:10.1103/physrevb.15.2884 · Cited by 1,047 · see citing works
Assessing the performance of recent density functionals for bulk solids
Csonka, G. I., Perdew, J. P., Ruzsinszky, A., Philipsen, P., Lebègue∥, S., Paier, J. A., Vydrov, O. A., & Ángyán, J. G. (2009) · Physical Review B · doi:10.1103/physrevb.79.155107 · Cited by 1,017 · see citing works
Calculation of the lattice constant of solids with semilocal functionals
Haas, P. M., Tran, F., & Blaha, P. (2009) · Physical Review B · doi:10.1103/physrevb.79.085104 · Cited by 957 · see citing works
The exchange-correlation energy of a metallic surface
Langreth, D. C., & Perdew, J. P. (1975) · Solid State Communications · doi:10.1016/0038-1098(75)90618-3 · Cited by 915 · see citing works
The SIESTA method; developments and applicability
Artacho, E., Anglada, E., Diéguez, O., et al. (2008) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/20/6/064208 · Cited by 834 · see citing works
Grimme, S., Antony, J., Schwabe, T., & Mück‐Lichtenfeld, C. (2007) · Organic & Biomolecular Chemistry · doi:10.1039/b615319b · Cited by 754 · see citing works
Workhorse Semilocal Density Functional for Condensed Matter Physics and Quantum Chemistry
Perdew, J. P., Ruzsinszky, A., Csonka, G. I., Constantin, L. A., & Sun, J. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.026403 · Cited by 646 · see citing works
Functional designed to include surface effects in self-consistent density functional theory
Armiento, R., & Mattsson, A. E. (2005) · Physical Review B · doi:10.1103/physrevb.72.085108 · Cited by 613 · see citing works
Exchange-hole dipole moment and the dispersion interaction revisited
Becke, A. D., & Johnson, E. R. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2795701 · Cited by 561 · see citing works
von Lilienfeld, O. A., Tavernelli, I., Röthlisberger, U., & Sebastiani, D. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.153004 · Cited by 524 · see citing works
Van der Waals density functional: An appropriate exchange functional
Cooper, V. R. (2010) · Physical Review B · doi:10.1103/physrevb.81.161104 · Cited by 522 · see citing works
van der Waals Interactions in Density-Functional Theory
Andersson, Y., Langreth, D. C., & Lundqvist, B. I. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.102 · Cited by 512 · see citing works
Antony, J., & Grimme, S. (2006) · Physical Chemistry Chemical Physics · doi:10.1039/b612585a · Cited by 510 · see citing works
Harl, J., Schimka, L., & Kresse, G. (2010) · Physical Review B · doi:10.1103/physrevb.81.115126 · Cited by 469 · see citing works
Chakarova-Käck, S. D., Schröder, E., Lundqvist, B. I., et al. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.146107 · Cited by 414 · see citing works
Improved hybrid functional for solids: The HSEsol functional
Schimka, L., Harl, J., & Kresse, G. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3524336 · Cited by 413 · see citing works
Tests of a ladder of density functionals for bulk solids and surfaces
Staroverov, V. N., Scuseria, G. E., Tao, J., & Perdew, J. P. (2004) · Physical Review B · doi:10.1103/physrevb.69.075102 · Cited by 411 · see citing works
Nonlocal van der Waals Density Functional Made Simple
Vydrov, O. A., & Voorhis, T. V. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.063004 · Cited by 390 · see citing works
On the large-gradient behavior of the density functional exchange energy
Becke, A. D. (1986) · The Journal of Chemical Physics · doi:10.1063/1.451353 · Cited by 378 · see citing works
Tran, F., Laskowski, R., Blaha, P., et al. (2007) · Physical Review B · doi:10.1103/physrevb.75.115131 · Cited by 375 · see citing works
Investigation of Exchange Energy Density Functional Accuracy for Interacting Molecules
Murray, É., Lee, K., & Langreth, D. C. (2009) · Journal of Chemical Theory and Computation · doi:10.1021/ct900365q · Cited by 323 · see citing works
A critical note on density functional theory studies on rare-gas dimers
van Mourik, T., & Gdanitz, R. J. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1476010 · Cited by 251 · see citing works
The AM05 density functional applied to solids
Mattsson, A. E., Armiento, R., Paier, J. A., Kresse, G., Wills, J. M., & Mattsson, T. R. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2835596 · Cited by 247 · see citing works
Santra, B., Michaelides, A., Fuchs, M., et al. (2008) · The Journal of Chemical Physics · doi:10.1063/1.3012573 · Cited by 242 · see citing works
Self-citationTwo- and three-body interatomic dispersion energy contributions to binding in molecules and solids
von Lilienfeld, O. A., & Tkatchenko, A. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3432765 · Cited by 239 · see citing works
Santra, B., Michaelides, A., & Scheffler, M. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2790009 · Cited by 230 · see citing works
Self-citationSato, T., & Nakai, H. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3269802 · Cited by 225 · see citing works
Dispersionless Density Functional Theory
Pernal, K., Podeszwa, R., Patkowski, K., et al. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.263201 · Cited by 195 · see citing works
Dobson, J. F., & Dinte, B. P. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.1780 · Cited by 195 · see citing works
To Wet or Not to Wet? Dispersion Forces Tip the Balance for Water Ice on Metals
Carrasco, J., Santra, B., Klimeš, J., et al. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.026101 · Cited by 189 · see citing works
Self-citationPotassium intercalation in graphite: A van der Waals density-functional study
Ziambaras, E., Kleis, J., Schröder, E., et al. (2007) · Physical Review B · doi:10.1103/physrevb.76.155425 · Cited by 174 · see citing works
Sony, P., Puschnig, P., Nabok, D., et al. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.176401 · Cited by 173 · see citing works
Linear-scaling self-consistent implementation of the van der Waals density functional
Guļāns, A., Puska, M. J., & Nieminen, R. M. (2009) · Physical Review B · doi:10.1103/physrevb.79.201105 · Cited by 168 · see citing works
Grüneis, A., Marsman, M., & Kresse, G. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3466765 · Cited by 165 · see citing works
Functional form of the generalized gradient approximation for exchange: The PBE α functional
Madsen, G. K. H. (2007) · Physical Review B · doi:10.1103/physrevb.75.195108 · Cited by 157 · see citing works
Binding energies in benzene dimers: Nonlocal density functional calculations
Puzder, A., Dion, M., & Langreth, D. C. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2189229 · Cited by 153 · see citing works
Insight into the performance of GGA functionals for solid-state calculations
Haas, P. M., Tran, F., Blaha, P., et al. (2009) · Physical Review B · doi:10.1103/physrevb.80.195109 · Cited by 143 · see citing works
Sato, T., Tsuneda, T., & Hirao, K. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2747243 · Cited by 135 · see citing works
Tosoni, S., & Sauer, J. (2010) · Physical Chemistry Chemical Physics · doi:10.1039/c0cp01261k · Cited by 132 · see citing works
Dispersion interactions from a local polarizability model
Vydrov, O. A., & Voorhis, T. V. (2010) · Physical Review A · doi:10.1103/physreva.81.062708 · Cited by 129 · see citing works
Moses, P. G., Mortensen, J. J., Lundqvist, B. I., & Nørskov, J. K. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3086040 · Cited by 127 · see citing works
Jenness, G. R., Karaltı, O., & Jordan, K. D. (2010) · Physical Chemistry Chemical Physics · doi:10.1039/c000988a · Cited by 124 · see citing works
Ab initiocalculation of ground-state properties of rare-gas crystals
Rościszewski, K., Paulus, B., Fulde, P., et al. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.60.7905 · Cited by 123 · see citing works
Improved interaction energy benchmarks for dimers of biological relevance
Podeszwa, R., Patkowski, K., & Szalewicz, K. (2010) · Physical Chemistry Chemical Physics · doi:10.1039/b926808a · Cited by 114 · see citing works
van der Waals forces in the noble metals
Rehr, J. J., Zaremba, E., & Kohn, W. (1975) · Physical review. B, Solid state · doi:10.1103/physrevb.12.2062 · Cited by 106 · see citing works
Vydrov, O. A., Wu, Q., & Voorhis, T. V. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2948400 · Cited by 86 · see citing works
Local response dispersion method. II. Generalized multicenter interactions.
Sato, T., & Nakai, H. (2010) · Journal of Chemical Physics · doi:10.1063/1.3503040 · Cited by 86 · see citing works
Kinetics of Proton Migration in Liquid Water
Chen, H., Voth, G. A., & Agmon, N. (2009) · The Journal of Physical Chemistry B · doi:10.1021/jp908126a · Cited by 84 · see citing works
Berland, K., Einstein, T. L., & Hyldgaard, P. (2009) · Physical Review B · doi:10.1103/physrevb.80.155431 · Cited by 77 · see citing works
Calculation of properties of crystalline lithium hydride using correlated wave function theory
Nolan, S. J., Gillan, M. J., Alfè, D., et al. (2009) · Physical Review B · doi:10.1103/physrevb.80.165109 · Cited by 77 · see citing works
Long-range van der Waals attraction and alkali-metal lattice constants
Tao, J., Perdew, J. P., & Ruzsinszky, A. (2010) · Physical Review B · doi:10.1103/physrevb.81.233102 · Cited by 72 · see citing works
Johnston, K., Kleis, J., Lundqvist, B. I., et al. (2008) · Physical Review B · doi:10.1103/physrevb.77.121404 · Cited by 72 · see citing works
Kelkkanen, A. K., Lundqvist, B. I., & Nørskov, J. K. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3193462 · Cited by 66 · see citing works
Lattice match in density functional calculations: ice Ih vs. β-AgI
Feibelman, P. J. (2008) · Physical Chemistry Chemical Physics · doi:10.1039/b808482n · Cited by 65 · see citing works
Dyer, M. S., Robin, A., Haq, S., et al. (2011) · ACS Nano · doi:10.1021/nn102610k · Cited by 63 · see citing works
First-principles theoretical study of Alq3∕Al interfaces: Origin of the interfacial dipole
Yanagisawa, S., Lee, K., & Morikawa, Y. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2940334 · Cited by 55 · see citing works
Friedel, J. (1952) · Proceedings of the Physical Society Section B · doi:10.1088/0370-1301/65/10/303 · Cited by 53 · see citing works
Role of van der Waals interactions in adsorption of Xe on Cu(111) and Pt(111)
Lazić, P., Crljen, Ž., Brako, R., et al. (2005) · Physical Review B · doi:10.1103/physrevb.72.245407 · Cited by 51 · see citing works
AM05 Density Functional Applied to the Water Molecule, Dimer, and Bulk Liquid
Mattsson, A. E., & Mattsson, T. R. (2009) · Journal of Chemical Theory and Computation · doi:10.1021/ct8004968 · Cited by 34 · see citing works
How strong is the bond between water and salt?
Li, B., Michaelides, A., & Scheffler, M. (2008) · Surface Science · doi:10.1016/j.susc.2008.09.039 · Cited by 26 · see citing works
Self-citationVan der Waals contribution to the binding energy of noble metals
Richardson, D. D., & Mahanty, J. (1977) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/10/20/006 · Cited by 19 · see citing works
Effect of Van der Waals forces on the crystal structure of heavy alkali metals
Upadhyaya, J. C., & Wang, S. (1979) · Physics Letters A · doi:10.1016/0375-9601(79)90719-9 · Cited by 6 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- 35 J. Friedel, Proc. Phys. Soc. B 65 , 769 (1952).
Cited by
Sorted by citations
Commentary: The Materials Project: A materials genome approach to accelerating materials innovation
Jain, A., Ong, S. P., Hautier, G., Chen, W., Richards, W. D., Dacek, S., Cholia, S., Gunter, D., Skinner, D., Ceder, G., et al. (2013) · APL Materials · doi:10.1063/1.4812323 · Cited by 13,094 · see citing works
Advanced capabilities for materials modelling with Q <scp>uantum</scp> ESPRESSO
Giannozzi, P., Andreussi, O., Brumme, T., Bunau, O., Buongiorno Nardelli, M., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Cococcioni, M., et al. (2017) · Journal of Physics: Condensed Matter · doi:10.1088/1361-648x/aa8f79 · Cited by 8,361 · see citing works
Zhu, S., Qin, X., Xiao, F., Yang, S., Xu, Y., Tan, Z., Li, J., Yan, J., Chen, Q., Chen, M., et al. (2021) · Nature Catalysis · doi:10.1038/s41929-021-00663-5 · Cited by 436 · see citing works
Zhu, L., Lin, H., Li, Y., Liao, F., Lifshitz, Y., Sheng, M., Lee, S.-T., & Shao, M. (2016) · Nature Communications · doi:10.1038/ncomms12272 · Cited by 351 · see citing works
Adsorption of CO <sub>2</sub> on Graphene: A Combined TPD, XPS, and vdW-DF Study
Takeuchi, K., Yamamoto, S., Hamamoto, Y., Shiozawa, Y., Tashima, K., Fukidome, H., Koitaya, T., Mukai, K., Yoshimoto, S., Suemitsu, M., et al. (2017) · The Journal of Physical Chemistry C · doi:10.1021/acs.jpcc.6b11373 · Cited by 116 · see citing works
Gas Separation in Nanoporous Graphene from First Principle Calculations
Ambrosetti, A., & Silvestrelli, P. L. (2014) · The Journal of Physical Chemistry C · doi:10.1021/jp504914u · Cited by 68 · see citing works
Lee, D., Kim, Y., Han, H., Kim, W. B., Chang, H., Chung, T.-M., Han, J. H., Kim, H. W., & Kim, H. J. (2020) · Journal of Materials Chemistry A · doi:10.1039/d0ta02509g · Cited by 30 · see citing works
CO <sub>2</sub> on Graphene: Benchmarking Computational Approaches to Noncovalent Interactions
Ehlert, C., Piras, A., & Gryn’ova, G. (2023) · ACS Omega · doi:10.1021/acsomega.3c03251 · Cited by 15 · see citing works
VASPilot: MCP-facilitated multi-agent intelligence for autonomous VASP simulations
Liu 刘, J. 家., Zhu 朱, T. 天., Ye 叶, C. 财., Fang 方, Z. 忠., Weng 翁, H. 红., & Wu 吴, Q. 泉. (2025) · Chinese Physics B · doi:10.1088/1674-1056/ae0681 · Cited by 7 · see citing works
- Authors
- Klimeš, J., Bowler, D. R., & Michaelides, A.
- Affiliations
- London Centre for Nanotechnology (GB)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2011-05-25
- Volume
- 83
- Issue
- 19
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2000536749
- Cited by
- 4,624
- References
- 80
- Citations by year
- 2026: 224 · 2025: 328 · 2024: 333 · 2023: 304 · 2022: 375 · 2021: 387 · 2020: 385 · 2019: 427 · 2018: 408 · 2017: 361 · 2016: 343 · 2015: 281 · 2014: 232 · 2013: 146 · 2012: 72
- FWCI
- 80.67
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- Engineering and Physical Sciences Research Council (EP/F067496/1)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- van der Waals density functional, dispersion interactions, exchange-correlation functionals, lattice parameters, bulk modulus, atomization energies, cohesive properties, alkali metals, alkali halides, nonlocal correlations, solids
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review