Exact orbital-free kinetic energy functional for general many-electron systems

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.

Keywords

condensed matter / density functional theory (DFT) / extended electrons

References

[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)

[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)

[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)

[4] T. A. Wesolowski and Y. A. Wang, Recent Progress in Orbital Free Density Functional Theory, Vol. 6, World Scientific, 2013

[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)

[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

[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)

[8] C. Huang and E. A. Carter, Nonlocal orbital-free kinetic energy density functional for semiconductors, Phys. Rev. B 81(4), 045206 (2010)

[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)

[10] W. Mi, A. Genova, and M. Pavanello, Nonlocal kinetic energy functionals by functional integration, J. Chem. Phys. 148(18), 184107 (2018)

[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)

[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)

[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)

[14] T. Pope and W. Hofer, Spin in the extended electron model, Front. Phys. 12(3), 128503 (2017)

[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)

[16] P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136(3B), B864 (1964)

[17] C. Doran and A. Lasenby, Geometric Algebra for Physicists, Cambridge University Press, 2003

[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)

[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)

[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)

[22] C. Von Weizsacker, On the theory of nuclear masses, Z. Phys. 96, 431 (1935)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature