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Tests of a ladder of density functionals for bulk solids and surfaces
Abstract
The local spin-density approximation (LSDA) and the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) are fully non-empirical realizations of the first two rungs of ``Jacob's ladder'' of exchange-correlation density functionals. The recently proposed non-empirical meta-GGA of Tao, Perdew, Staroverov, and Scuseria (TPSS), featuring the kinetic energy density as an additional local ingredient, completes the third rung. A hierarchy of these functionals, complemented by the meta-GGA of Perdew, Kurth, Zupan, and Blaha (PKZB), is tested in self-consistent Gaussian-type orbital calculations of equilibrium lattice constants, bulk moduli, and cohesive energies for 18 solids, and in studies of the jellium surface energy. The ascent of the ladder generally results in better performance, although most of the improvement for bulk solids occurs in the transition from LSDA to PBE. For the jellium surface energy, PBE is less accurate than LSDA, but PKZB and TPSS are more accurate. We support the idea that most of the error of these functionals for bulk solids arises in the description of core--valence interaction, by demonstrating that it can be removed through adjustment of the corresponding term in the equation of state. Overall, TPSS gives the best description of solids and surfaces, as it was found to do for molecules in earlier work.
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Citations
Cites
Generalized Gradient Approximation Made Simple
Perdew, J. P., Burke, K., & Ernzerhof, M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.3865 · Cited by 215,824
Self-citationLee, C., Yang, W., & Parr, R. G. (1988) · Physical Review B · doi:10.1103/physrevb.37.785 · Cited by 100,874
Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Density-functional exchange-energy approximation with correct asymptotic behavior
Becke, A. D. (1988) · Physical Review A · doi:10.1103/physreva.38.3098 · Cited by 53,711
Accurate and simple analytic representation of the electron-gas correlation energy
Perdew, J. P., & Wang, Y. (1992) · Physical Review B · doi:10.1103/physrevb.45.13244 · Cited by 25,089
Self-citationStephens, P. J., Devlin, F. J., Chabalowski, C. F., & Frisch, M. J. (1994) · The Journal of Physical Chemistry · doi:10.1021/j100096a001 · Cited by 23,248
Self-interaction correction to density-functional approximations for many-electron systems
Perdew, J. P., & Zunger, A. (1981) · Physical Review B · doi:10.1103/physrevb.23.5048 · Cited by 20,887
Self-citationVosko, S. H., Wilk, L., & Nusair, M. (1980) · Canadian Journal of Physics · doi:10.1139/p80-159 · Cited by 20,768
Hay, P. J., & Wadt, W. R. (1985) · The Journal of Chemical Physics · doi:10.1063/1.448975 · Cited by 15,577
Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]
Perdew, J. P., Burke, K., & Ernzerhof, M. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.1396 · Cited by 14,614
Self-citationGround State of the Electron Gas by a Stochastic Method
Ceperley, D. M., & Alder, B. J. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.566 · Cited by 14,384
The Compressibility of Media under Extreme Pressures
Murnaghan, F. D. (1944) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.30.9.244 · Cited by 8,729
Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr
Miehlich, B., Savin, A., Stoll, H., & Preuss, H. (1989) · Chemical Physics Letters · doi:10.1016/0009-2614(89)87234-3 · Cited by 7,295
Tao, J., Perdew, J. P., Staroverov, V. N., & Scuseria, G. E. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.146401 · Cited by 7,093
Self-citationGeneralized gradient approximation for the exchange-correlation hole of a many-electron system
Perdew, J. P., Burke, K., & Wang, Y. (1996) · Physical Review B · doi:10.1103/physrevb.54.16533 · Cited by 6,861
Self-citationAssessment of the Perdew–Burke–Ernzerhof exchange-correlation functional
Ernzerhof, M., & Scuseria, G. E. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478401 · Cited by 5,497
Self-citationStaroverov, V. N., Scuseria, G. E., Tao, J., & Perdew, J. P. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1626543 · Cited by 2,824
Self-citationVitos, L., Ruban, A. V., Skriver, H. L., & Kollár, J. (1998) · Surface Science · doi:10.1016/s0039-6028(98)00363-x · Cited by 2,768
Curtiss, L. A., Raghavachari, K., Redfern, P. C., & Pople, J. A. (1997) · The Journal of Chemical Physics · doi:10.1063/1.473182 · Cited by 2,130
Theory of Metal Surfaces: Charge Density and Surface Energy
Lang, N. D., & Kohn, W. (1970) · Physical Review B · doi:10.1103/physrevb.1.4555 · Cited by 1,930
Exchange-correlation energy of a metallic surface: Wave-vector analysis
Langreth, D. C., & Perdew, J. P. (1977) · Physical Review B · doi:10.1103/physrevb.15.2884 · Cited by 1,040
Self-citationLevy, M., & Perdew, J. P. (1985) · Physical Review A · doi:10.1103/physreva.32.2010 · Cited by 985
Self-citationPerdew, J. P., Kurth, S., Zupan, A., & Blaha, P. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.2544 · Cited by 895
Self-citationStability of the wurtzite-type structure under high pressure: GaN and InN
Ueno, M., Yoshida, M., Onodera, A., Shimomura, O., & Takemura, K. (1994) · Physical Review B · doi:10.1103/physrevb.49.14 · Cited by 876
Exchange holes in inhomogeneous systems: A coordinate-space model
Becke, A. D., & Roussel, M. R. (1989) · Physical Review A · doi:10.1103/physreva.39.3761 · Cited by 848
A novel form for the exchange-correlation energy functional
Van Voorhis, T., & Scuseria, G. E. (1998) · The Journal of Chemical Physics · doi:10.1063/1.476577 · Cited by 780
Self-citationVan der Waals Density Functional for Layered Structures
Rydberg, H., Dion, M., Jacobson, N., Schröder, E., Hyldgaard, P., Simak, S. I., Langreth, D. C., & Lundqvist, B. I. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.126402 · Cited by 703
Molecular and solid-state tests of density functional approximations: LSD, GGAs, and meta-GGAs
Kurth, S., Perdew, J. P., & Blaha, P. (1999) · International Journal of Quantum Chemistry · doi:10.1002/(sici)1097-461x(1999)75:4/5<889::aid-qua54>3.0.co;2-8 · Cited by 680
Self-citationTemperature Variation of the Elastic Constants of Cubic Elements. I. Copper
Overton, W. C., & Gaffney, J. (1955) · Physical Review · doi:10.1103/physrev.98.969 · Cited by 556
Improved lower bound on the indirect Coulomb energy
Lieb, E. H., & Oxford, S. (1981) · International Journal of Quantum Chemistry · doi:10.1002/qua.560190306 · Cited by 518
Achieving Linear Scaling for the Electronic Quantum Coulomb Problem
Strain, M. C., Scuseria, G. E., & Frisch, M. J. (1996) · Science · doi:10.1126/science.271.5245.51 · Cited by 444
Self-citationLow-Temperature Elastic Moduli of Aluminum
Kamm, G. N., & Alers, G. A. (1964) · Journal of Applied Physics · doi:10.1063/1.1713309 · Cited by 366
Spin scaling of the electron-gas correlation energy in the high-density limit
Wang, Y., & Perdew, J. P. (1991) · Physical Review B · doi:10.1103/physrevb.43.8911 · Cited by 350
Self-citationA new inhomogeneity parameter in density-functional theory
Becke, A. D. (1998) · The Journal of Chemical Physics · doi:10.1063/1.476722 · Cited by 349
Phase transitions in fiber materials
Sandler, U., & Wyler, A. (2000) · Physical Review B · doi:10.1103/physrevb.61.16 · Cited by 334
Calculated elastic constants and deformation potentials of cubic SiC
Lambrecht, W. R. L., Segall, B., Methfessel, M., & van Schilfgaarde, M. (1991) · Physical Review B · doi:10.1103/physrevb.44.3685 · Cited by 330
Zhang, Y., Pan, W., & Yang, W. (1997) · The Journal of Chemical Physics · doi:10.1063/1.475105 · Cited by 312
Levy, M. (1991) · Physical Review A · doi:10.1103/physreva.43.4637 · Cited by 295
Exchange functionals and potentials
Neumann, R., Nobes, R. H., & Handy, N. C. (1996) · Molecular Physics · doi:10.1080/00268979600100011 · Cited by 268
Spin-density gradient expansion for the kinetic energy
Oliver, G. L., & Perdew, J. P. (1979) · Physical Review A · doi:10.1103/physreva.20.397 · Cited by 247
Self-citationFuchs, M., Bockstedte, M., Pehlke, E., & Scheffler, M. (1998) · Physical Review B · doi:10.1103/physrevb.57.2134 · Cited by 213
Surfaces of real metals by the variational self-consistent method
Monnier, R., & Perdew, J. P. (1978) · Physical Review B · doi:10.1103/physrevb.17.2595 · Cited by 210
Self-citationFilippi, C., Singh, D. J., & Umrigar, C. J. (1994) · Physical Review B · doi:10.1103/physrevb.50.14947 · Cited by 196
Gradient expansion of the exchange energy from second-order density response theory
Svendsen, P. S., & von Barth, U. (1996) · Physical Review B · doi:10.1103/physrevb.54.17402 · Cited by 180
Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model
Alchagirov, A. B., Perdew, J. P., Boettger, J. C., Albers, R. C., & Fiolhais, C. (2001) · Physical review. B, Condensed matter · doi:10.1103/physrevb.63.224115 · Cited by 152
Self-citationAdamo, C., Ernzerhof, M., & Scuseria, G. E. (2000) · The Journal of Chemical Physics · doi:10.1063/1.480838 · Cited by 151
Self-citationKudin, K. N., & Scuseria, G. E. (1998) · Chemical Physics Letters · doi:10.1016/s0009-2614(98)00468-0 · Cited by 145
Self-citationPerdew, J. P., Wang, Y., & Engel, E. (1991) · Physical Review Letters · doi:10.1103/physrevlett.66.508 · Cited by 133
Self-citationApplication of the generalized-gradient approximation to rare-gas dimers
Patton, D. C., & Pederson, M. R. (1997) · Physical Review A · doi:10.1103/physreva.56.r2495 · Cited by 128
A fast multipole method for periodic systems with arbitrary unit cell geometries
Kudin, K. N., & Scuseria, G. E. (1998) · Chemical Physics Letters · doi:10.1016/s0009-2614(97)01329-8 · Cited by 118
Self-citationDensity functionals for the strong-interaction limit
Seidl, M., Perdew, J. P., & Kurth, S. (2000) · Physical Review A · doi:10.1103/physreva.62.012502 · Cited by 115
Self-citationNew τ-dependent correlation functional combined with a modified Becke exchange
Proynov, E. I., Chermette, H., & Salahub, D. R. (2000) · The Journal of Chemical Physics · doi:10.1063/1.1321309 · Cited by 82
Exchange-correlation density functional beyond the gradient approximation
Filatov, M. J., & Thiel, W. (1998) · Physical Review A · doi:10.1103/physreva.57.189 · Cited by 74
Elastic Constants of Magnesium Oxide
Marklund, K., & Mahmoud, S. A. (1971) · Physica Scripta · doi:10.1088/0031-8949/3/2/005 · Cited by 62
Pitarke, J. M., & Perdew, J. P. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.67.045101 · Cited by 43
Self-citationTheoretical investigation of Na adsorption on the Al(111) surface
Boettger, J. C., Birkenheuer, U., Krüger, S., Rösch, N., & Trickey, S. B. (1995) · Physical review. B, Condensed matter · doi:10.1103/physrevb.52.2025 · Cited by 19
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Self-citationVan der Waals density functionals applied to solids
Klimeš, J., Bowler, D. R., & Michaelides, A. (2011) · Physical Review B · doi:10.1103/physrevb.83.195131 · Cited by 4,624
Heyd, J., & Scuseria, G. E. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1760074 · Cited by 2,573
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Wu, Z., & Cohen, R. E. (2006) · Physical Review B · doi:10.1103/physrevb.73.235116 · Cited by 2,383
Heyd, J., Peralta, J. E., Scuseria, G. E., & Martin, R. L. (2005) · The Journal of Chemical Physics · doi:10.1063/1.2085170 · Cited by 2,046
Self-citation
Metadata
- Authors
- Staroverov, V. N., Scuseria, G. E., Tao, J., & Perdew, J. P.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2004-02-13
- Volume
- 69
- Issue
- 7
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2002484561
- Cited by
- 414
- References
- 56
- FWCI
- 19.25
- Type
- journal article
- Language
- en
- Open access
- closed
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