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Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2019 Impact Factor: 2.502

Frontiers of Physics  2020, Vol. 15 Issue (2): 23603   https://doi.org/10.1007/s11467-019-0948-6
  本期目录
Exact orbital-free kinetic energy functional for general many-electron systems
Thomas Pope1(), Werner Hofer1,2()
1. School of Natural and Environmental Sciences, Newcastle University, Newcastle NE1 7RU, United Kingdom
2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
 全文: PDF(627 KB)  
Abstract

The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory (DFT). This has been the main stumbling block for the development of a generalpurpose framework on this basis. Here, we show that on the basis of a two-density model, which represents many-electron systems by mass density and spin density components, we can derive the exact form of such a functional. The exact functional is shown to contain previously suggested functionals to some extent, with the notable exception of the Thomas–Fermi kinetic energy functional.

Key wordscondensed matter    density functional theory (DFT)    extended electrons
收稿日期: 2019-09-12      出版日期: 2020-01-20
Corresponding Author(s): Thomas Pope,Werner Hofer   
 引用本文:   
. [J]. Frontiers of Physics, 2020, 15(2): 23603.
Thomas Pope, Werner Hofer. Exact orbital-free kinetic energy functional for general many-electron systems. Front. Phys. , 2020, 15(2): 23603.
 链接本文:  
https://academic.hep.com.cn/fop/CN/10.1007/s11467-019-0948-6
https://academic.hep.com.cn/fop/CN/Y2020/V15/I2/23603
1 M. Levy, Universal variational functionals of electron densities, first-order density matrices, and natural spinorbitals and solution of the v-representability problem, Proc. Natl. Acad. Sci. USA 76(12), 6062 (1979)
https://doi.org/10.1073/pnas.76.12.6062
2 M. Levy, J. P. Perdew, and V. Sahni, Exact differential equation for the density and ionization energy of a manyparticle system, Phys. Rev. A 30(5), 2745 (1984)
https://doi.org/10.1103/PhysRevA.30.2745
3 M. Pearson, E. Smargiassi, and P. Madden, Ab initio molecular dynamics with an orbital-free density functional, J. Phys.: Condens. Matter 5(19), 3221 (1993)
https://doi.org/10.1088/0953-8984/5/19/019
4 T. A. Wesolowski and Y. A. Wang, Recent Progress in Orbital Free Density Functional Theory, Vol. 6, World Scientific, 2013
https://doi.org/10.1142/8633
5 J. Lehtomäki, I. Makkonen, M. A. Caro, A. Harju, and O. Lopez Acevedo, Orbital-free density functional theory implementation with the projector augmented-wave method, J. Chem. Phys. 141(23), 234102 (2014)
https://doi.org/10.1063/1.4903450
6 V. V. Karasiev and S. B. Trickey, Frank discussion of the status of ground-state orbital-free DFT, in: Advances in Quantum Chemistry, Vol. 71, Elsevier, 2015, pp 221–245
https://doi.org/10.1016/bs.aiq.2015.02.004
7 D. García-Aldea and J. Alvarellos, Approach to kinetic energy density functionals: Nonlocal terms with the structure of the von Weizsäcker functional, Phys. Rev. A 77(2), 022502 (2008)
https://doi.org/10.1103/PhysRevA.77.022502
8 C. Huang and E. A. Carter, Nonlocal orbital-free kinetic energy density functional for semiconductors, Phys. Rev. B 81(4), 045206 (2010)
https://doi.org/10.1103/PhysRevB.81.045206
9 I. Shin and E. A. Carter, Enhanced von Weizsäcker Wang–Govind–Carter kinetic energy density functional for semiconductors, J. Chem. Phys. 140, 18A531 (2014)
https://doi.org/10.1063/1.4869867
10 W. Mi, A. Genova, and M. Pavanello, Nonlocal kinetic energy functionals by functional integration, J. Chem. Phys. 148(18), 184107 (2018)
https://doi.org/10.1063/1.5023926
11 L. A. Constantin, E. Fabiano, and F. Della Sala, Semilocal Pauli–Gaussian kinetic functionals for orbital-free density functional theory calculations of solids, J. Phys. Chem. Lett. 9(15), 4385 (2018)
https://doi.org/10.1021/acs.jpclett.8b01926
12 L. A. Constantin, E. Fabiano, and F. Della Sala, Nonlocal kinetic energy functional from the jellium-with-gap model: Applications to orbital-free density functional theory, Phys. Rev. B 97(20), 205137 (2018)
https://doi.org/10.1103/PhysRevB.97.205137
13 M. Seidl, J. P. Perdew, and S. Kurth, Simulation of allorder density-functional perturbation theory, using the second order and the strong-correlation limit, Phys. Rev. Lett. 84(22), 5070 (2000)
https://doi.org/10.1103/PhysRevLett.84.5070
14 T. Pope and W. Hofer, Spin in the extended electron model, Front. Phys. 12(3), 128503 (2017)
https://doi.org/10.1007/s11467-017-0669-7
15 T. Pope and W. Hofer, A two-density approach to the general many-body problem and a proof of principle for small atoms and molecules, Front. Phys. 14(2), 23604 (2019)
https://doi.org/10.1007/s11467-018-0872-1
16 P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136(3B), B864 (1964)
https://doi.org/10.1103/PhysRev.136.B864
17 C. Doran and A. Lasenby, Geometric Algebra for Physicists, Cambridge University Press, 2003
https://doi.org/10.1017/CBO9780511807497
18 S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. Probert, K. Refson, and M. C. Payne, First principles methods using CASTEP, Z. Kristallogr. Cryst. Mater. 220(5/6), 567 (2005)
https://doi.org/10.1524/zkri.220.5.567.65075
19 P. Hasnip and M. Probert, Auxiliary density functionals: a new class of methods for efficient, stable density functional theory calculations, arXiv: 1503.01420 (2015)
20 W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140(4A), A1133 (1965)
https://doi.org/10.1103/PhysRev.140.A1133
21 J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23(10), 5048 (1981)
https://doi.org/10.1103/PhysRevB.23.5048
22 C. Von Weizsacker, On the theory of nuclear masses, Z. Phys. 96, 431 (1935)
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