A simple generalized gradient approximation for the noninteracting kinetic energy density functional

Luo, Kai; Karasiev, Valentin V.; Trickey, S. B.

doi:10.1103/PhysRevB.98.041111

Title: A simple generalized gradient approximation for the noninteracting kinetic energy density functional

Journal Article · 26 July 2018 · Physical Review B

DOI: https://doi.org/10.1103/PhysRevB.98.041111 · OSTI ID:1465779

Luo, Kai ^[1]; Karasiev, Valentin V. ^[2]; Trickey, S. B. ^[3]

Univ. of Florida, Gainesville, FL (United States). Quantum Theory Project, Dept. of Physics; Laboratory for Laser Energetics, University of Rochester
Univ. of Rochester, NY (United States). Lab. for Laser Energetics
Univ. of Florida, Gainesville, FL (United States). Quantum Theory Project, Dept. of Physics and Dept. of Chemistry

A simple, novel, non-empirical, constraint-based orbital-free generalized gradient approximation (GGA) non-interacting kinetic energy density functional is presented along with illustrative applications. The innovation is adaptation of constraint-based construction to the essential properties of pseudo-densities from the pseudo-potentials that are essential in plane-wave-basis ab initio molecular dynamics. This contrasts with constraining to the qualitatively different Kato-cusp-condition densities. The single parameter in the new functional is calibrated by satisfying Pauli potential positivity constraints for pseudo-atom densities. Finally, in static lattice tests on simple metals and semiconductors, the new LKT functional outperforms the previous best constraint-based GGA functional, VT84F (Phys. Rev. B 88, 161108(R) (2013)), is generally superior to a recently proposed meta-GGA, is reasonably competitive with parametrized two-point functionals, and is substantially faster.

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Research Organization:: Univ. of Rochester, NY (United States). Lab. for Laser Energetics

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0001944; SC0002139

OSTI ID:: 1465779

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 4 Vol. 98; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (49)

On the eigenfunctions of many-particle systems in quantum mechanics Kato, Tosio Communications on Pure and Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1002/cpa.3160100201	journal	January 1957
Some open problems about Coulomb systems Lieb, E. H. Mathematical Problems in Theoretical Physics https://doi.org/10.1007/3-540-09964-6_308	book	January 1980
Density Functional Theory Dreizler, Reiner M.; Gross, Eberhard K. U. Springer Berlin, Heidelberg https://doi.org/10.1007/978-3-642-86105-5	book	January 1990
Zur Theorie der Kernmassen Weizs�cker, C. F. v. Zeitschrift f�r Physik, Vol. 96, Issue 7-8 https://doi.org/10.1007/BF01337700	journal	July 1935
Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente Fermi, E. Zeitschrift f�r Physik, Vol. 48, Issue 1-2 https://doi.org/10.1007/BF01351576	journal	January 1928
Generalized gradient approximation for the fermion kinetic energy as a functional of the density Perdew, John P. Physics Letters A, Vol. 165, Issue 1 https://doi.org/10.1016/0375-9601(92)91058-Y	journal	May 1992
The role of the kinetic energy density in approximations to the exchange energy Ernzerhof, M. Journal of Molecular Structure: THEOCHEM, Vol. 501-502 https://doi.org/10.1016/S0166-1280(99)00414-5	journal	April 2000
Generating relativistic pseudo-potentials with explicit incorporation of semi-core states using APE, the Atomic Pseudo-potentials Engine Oliveira, Micael J. T.; Nogueira, Fernando Computer Physics Communications, Vol. 178, Issue 7 https://doi.org/10.1016/j.cpc.2007.11.003	journal	April 2008
ABINIT: First-principles approach to material and nanosystem properties Gonze, X.; Amadon, B.; Anglade, P. -M. Computer Physics Communications, Vol. 180, Issue 12 https://doi.org/10.1016/j.cpc.2009.07.007	journal	December 2009
Introducing PROFESS 2.0: A parallelized, fully linear scaling program for orbital-free density functional theory calculations Hung, Linda; Huang, Chen; Shin, Ilgyou Computer Physics Communications, Vol. 181, Issue 12 https://doi.org/10.1016/j.cpc.2010.09.001	journal	December 2010
Finite-temperature orbital-free DFT molecular dynamics: Coupling Profess and Quantum Espresso Karasiev, Valentin V.; Sjostrom, Travis; Trickey, S. B. Computer Physics Communications, Vol. 185, Issue 12 https://doi.org/10.1016/j.cpc.2014.08.023	journal	December 2014
Ab Initio Molecular Dynamics Marx, Dominik; Hutter, Jurg https://doi.org/10.1017/CBO9780511609633	book	January 2009
The calculation of atomic fields Thomas, L. H. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 23, Issue 5 https://doi.org/10.1017/S0305004100011683	journal	January 1927
Petascale Orbital-Free Density Functional Theory Enabled by Small-Box Algorithms Chen, Mohan; Jiang, Xiang-Wei; Zhuang, Houlong Journal of Chemical Theory and Computation, Vol. 12, Issue 6 https://doi.org/10.1021/acs.jctc.6b00326	journal	May 2016
Transferable local pseudopotentials for magnesium, aluminum and silicon Huang, Chen; Carter, Emily A. Physical Chemistry Chemical Physics, Vol. 10, Issue 47 https://doi.org/10.1039/b810407g	journal	January 2008
On the atomic kinetic energy functionals with full Weizsacker correction Gázquez, J. L.; Robles, J. The Journal of Chemical Physics, Vol. 76, Issue 3 https://doi.org/10.1063/1.443107	journal	February 1982
Orbital-free density functional theory implementation with the projector augmented-wave method Lehtomäki, Jouko; Makkonen, Ilja; Caro, Miguel A. The Journal of Chemical Physics, Vol. 141, Issue 23 https://doi.org/10.1063/1.4903450	journal	December 2014
Nonlocal kinetic energy functionals by functional integration Mi, Wenhui; Genova, Alessandro; Pavanello, Michele The Journal of Chemical Physics, Vol. 148, Issue 18 https://doi.org/10.1063/1.5023926	journal	May 2018
Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem Levy, M. Proceedings of the National Academy of Sciences, Vol. 76, Issue 12 https://doi.org/10.1073/pnas.76.12.6062	journal	December 1979
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Finite Elastic Strain of Cubic Crystals Birch, Francis Physical Review, Vol. 71, Issue 11 https://doi.org/10.1103/PhysRev.71.809	journal	June 1947
Exact differential equation for the density and ionization energy of a many-particle system Levy, Mel; Perdew, John P.; Sahni, Viraht Physical Review A, Vol. 30, Issue 5 https://doi.org/10.1103/PhysRevA.30.2745	journal	November 1984
Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms Levy, Mel; Perdew, John P. Physical Review A, Vol. 32, Issue 4 https://doi.org/10.1103/PhysRevA.32.2010	journal	October 1985
Explicit estimation of ground-state kinetic energies from electron densities Herring, Conyers Physical Review A, Vol. 34, Issue 4 https://doi.org/10.1103/PhysRevA.34.2614	journal	October 1986
Exact properties of the Pauli potential for the square root of the electron density and the kinetic energy functional Levy, Mel Physical Review A, Vol. 38, Issue 2 https://doi.org/10.1103/PhysRevA.38.625	journal	July 1988
Self-interaction correction to density-functional approximations for many-electron systems Perdew, J. P.; Zunger, Alex Physical Review B, Vol. 23, Issue 10, p. 5048-5079 https://doi.org/10.1103/PhysRevB.23.5048	journal	May 1981
Nonlocal kinetic energy functional for nonhomogeneous electron systems Chacón, E.; Alvarellos, J. E.; Tarazona, P. Physical Review B, Vol. 32, Issue 12 https://doi.org/10.1103/PhysRevB.32.7868	journal	December 1985
Born-Oppenheimer molecular-dynamics simulations of finite systems: Structure and dynamics of ( H 2 O ) 2 Barnett, Robert N.; Landman, Uzi Physical Review B, Vol. 48, Issue 4 https://doi.org/10.1103/PhysRevB.48.2081	journal	July 1993
Orbital-free kinetic-energy functionals for first-principles molecular dynamics Smargiassi, Enrico; Madden, Paul A. Physical Review B, Vol. 49, Issue 8 https://doi.org/10.1103/PhysRevB.49.5220	journal	February 1994
Nonlocal kinetic-energy-density functionals García-González, P.; Alvarellos, J. E.; Chacón, E. Physical Review B, Vol. 53, Issue 15 https://doi.org/10.1103/PhysRevB.53.9509	journal	April 1996
Orbital-free kinetic-energy density functionals with a density-dependent kernel Wang, Yan Alexander; Govind, Niranjan; Carter, Emily A. Physical Review B, Vol. 60, Issue 24 https://doi.org/10.1103/PhysRevB.60.16350	journal	December 1999
Erratum: Orbital-free kinetic-energy density functionals with a density-dependent kernel [Phys. Rev. B 60 , 16 350 (1999)] Wang, Yan Alexander; Govind, Niranjan; Carter, Emily A. Physical Review B, Vol. 64, Issue 8 https://doi.org/10.1103/PhysRevB.64.089903	journal	August 2001
Transferable local pseudopotentials derived via inversion of the Kohn-Sham equations in a bulk environment Zhou, Baojing; Alexander Wang, Yan; Carter, Emily A. Physical Review B, Vol. 69, Issue 12 https://doi.org/10.1103/PhysRevB.69.125109	journal	March 2004
Properties of constraint-based single-point approximate kinetic energy functionals Karasiev, V. V.; Jones, R. S.; Trickey, S. B. Physical Review B, Vol. 80, Issue 24 https://doi.org/10.1103/PhysRevB.80.245120	journal	December 2009
Nonlocal orbital-free kinetic energy density functional for semiconductors Huang, Chen; Carter, Emily A. Physical Review B, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevB.81.045206	journal	January 2010
Generalized-gradient-approximation noninteracting free-energy functionals for orbital-free density functional calculations Karasiev, Valentin V.; Sjostrom, Travis; Trickey, S. B. Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115101	journal	September 2012
Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations Karasiev, Valentin V.; Chakraborty, Debajit; Shukruto, Olga A. Physical Review B, Vol. 88, Issue 16 https://doi.org/10.1103/PhysRevB.88.161108	journal	October 2013
Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory Constantin, Lucian A.; Fabiano, Eduardo; Della Sala, Fabio Physical Review B, Vol. 97, Issue 20 https://doi.org/10.1103/PhysRevB.97.205137	journal	May 2018
Importance of finite-temperature exchange correlation for warm dense matter calculations Karasiev, Valentin V.; Calderín, Lázaro; Trickey, S. B. Physical Review E, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevE.93.063207	journal	June 2016
Semiclassical Neutral Atom as a Reference System in Density Functional Theory Constantin, Lucian A.; Fabiano, E.; Laricchia, S. Physical Review Letters, Vol. 106, Issue 18 https://doi.org/10.1103/PhysRevLett.106.186406	journal	May 2011
Norm-Conserving Pseudopotentials Hamann, D. R.; Schlüter, M.; Chiang, C. Physical Review Letters, Vol. 43, Issue 20 https://doi.org/10.1103/PhysRevLett.43.1494	journal	November 1979
Inhomogeneous Electron Gas Rajagopal, A. K.; Callaway, J. Physical Review B, Vol. 7, Issue 5 https://doi.org/10.1103/physrevb.7.1912	journal	March 1973
A B I NITIO M OLECULAR D YNAMICS WITH D ENSITY F UNCTIONAL T HEORY Tse, John S. Annual Review of Physical Chemistry, Vol. 53, Issue 1 https://doi.org/10.1146/annurev.physchem.53.090401.105737	journal	October 2002
Orbital-free density functional theory for materials research Witt, William C.; del Rio, Beatriz G.; Dieterich, Johannes M. Journal of Materials Research, Vol. 33, Issue 7 https://doi.org/10.1557/jmr.2017.462	journal	January 2018
Non-empirical Generalized Gradient Approximation Free Energy Functional for Orbital-free Simulations Karasiev, Valentin V.; Chakraborty, Debajit; Shukruto, Olga A. arXiv https://doi.org/10.48550/arxiv.1308.2193	text	January 2013
Orbital-Free Density Functional Theory Implementation with the Projector Augmented-Wave Method Lehtomäki, J.; Makkonen, I.; Caro, M. A. arXiv https://doi.org/10.48550/arxiv.1408.4701	text	January 2014
The importance of finite-temperature exchange-correlation for warm dense matter calculations Karasiev, Valentin V.; Calderín, Lázaro; Trickey, S. B. arXiv https://doi.org/10.48550/arxiv.1601.04543	text	January 2016
Nonlocal Kinetic Energy Functionals By Functional Integration Mi, Wenhui; Genova, Alessandro; Pavanello, Michele arXiv https://doi.org/10.48550/arxiv.1704.08943	text	January 2017

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Quantum hydrodynamics for plasmas— Quo vadis ? Bonitz, M.; Moldabekov, Zh. A.; Ramazanov, T. S. Physics of Plasmas, Vol. 26, Issue 9 https://doi.org/10.1063/1.5097885	journal	September 2019
Upper bound to the gradient-based kinetic energy density of noninteracting electrons in an external potential Witt, William C.; Jiang, Kaili; Carter, Emily A. The Journal of Chemical Physics, Vol. 151, Issue 6 https://doi.org/10.1063/1.5108896	journal	August 2019
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