Skip to main content
SpringerLink
Log in

Orbital-free density functional theory for materials research

  • Review
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

Orbital-free density functional theory (OFDFT) is both grounded in quantum physics and suitable for direct simulation of thousands of atoms. This article describes the application of OFDFT for materials research over roughly the past two decades, highlighting computational studies that would have been impractical (or impossible) to perform with other techniques. In particular, we review the growing body of simulations of solids and liquids that have been conducted with planewave-pseudopotential (or related) techniques. We also provide an updated account of the fundamentals of OFDFT, emphasizing aspects—such as nonlocal density functionals for computing the kinetic energy of noninteracting electrons—that enabled much of the application work. The article concludes with a discussion of the OFDFT frontier, which contains brief descriptions of other topics at the forefront of OFDFT research.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

FIG. 1
FIG. 2
FIG. 3

Similar content being viewed by others

References

  1. Y.A. Wang and E.A. Carter: Orbital-free kinetic-energy density functional theory. In Theoretical Methods in Condensed Phase Chemistry, S.D. Schwartz, ed. (Springer, Dordrecht, 2002); pp. 117–184.

    Chapter  Google Scholar 

  2. H. Chen and A. Zhou: Orbital-free density functional theory for molecular structure calculations. Numer. Math. Theor. Meth. Appl. 1, 1 (2008).

    Google Scholar 

  3. T.A. Wesolowski and Y.A. Wang: Recent Progress in Orbital-Free Density Functional Theory (World Scientific, Singapore, 2013).

    Book  Google Scholar 

  4. V.V. Karasiev, D. Chakraborty, and S.B. Trickey: Progress on new approaches to old ideas: Orbital-free density functionals. In Many-Electron Approaches in Physics, Chemistry and Mathematics, V. Bach and L. Delle Site, eds. (Springer, Cham, Switzerland, 2014); pp. 113–134.

    Chapter  Google Scholar 

  5. R.G. Parr and W. Yang: Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1994).

    Google Scholar 

  6. R.M. Dreizler and E.K.U. Gross: Density Functional Theory: An Approach to the Quantum Many-Body Problem (Springer Science & Business Media, 1990).

    Book  Google Scholar 

  7. P. Hohenberg and W. Kohn: Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).

    Article  Google Scholar 

  8. W. Kohn and L.J. Sham: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).

    Article  Google Scholar 

  9. F. Graziani, M.P. Desjarlais, R. Redmer, and S.B. Trickey: Frontiers and Challenges in Warm Dense Matter (Springer Science & Business, Charm, Switzerland, 2014).

    Book  Google Scholar 

  10. C.R. Jacob and J. Neugebauer: Subsystem density-functional theory. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 4, 325 (2014).

    CAS  Google Scholar 

  11. A. Krishtal, D. Sinha, A. Genova, and M. Pavanello: Subsystem density-functional theory as an effective tool for modeling ground and excited states, their dynamics and many-body interactions. J. Phys.: Condens. Matter 27, 183202 (2015).

    Google Scholar 

  12. D.R. Bowler and T. Miyazaki: O(N) methods in electronic structure calculations. Rep. Prog. Phys. 75, 036503 (2012).

    Article  CAS  Google Scholar 

  13. S. Goedecker: Linear scaling electronic structure methods. Rev. Mod. Phys. 71, 1085 (1999).

    Article  CAS  Google Scholar 

  14. J. Aarons, M. Sarwar, D. Thompsett, and C.-K. Skylaris: Methods for large-scale density functional calculations on metallic systems. J. Chem. Phys. 145, 220901 (2016).

    Article  CAS  Google Scholar 

  15. E.V. Ludena and V.V. Karasiev: Kinetic energy functionals: History, challenges and prospects. Rev. Mod. Quantum Chem. 1, 612–665 (2002).

    Article  CAS  Google Scholar 

  16. D. García-Aldea and J.E. Alvarellos: The construction of kinetic energy functionals and the linear response function. In Theoretical and Computational Developments in Modern Density Functional Theory, A.K. Roy, ed. (Nova Science Publishers, Hauppauge, New York, 2012), pp. 255–280.

    Google Scholar 

  17. C.F. von Weizsäcker: Zur Theorie der Kernmassen. Z. Phys. 96, 431 (1935).

    Article  Google Scholar 

  18. L.H. Thomas: The calculation of atomic fields. Math. Proc. Cambridge Philos. Soc. 23, 542 (1927).

    Article  CAS  Google Scholar 

  19. E. Fermi: Un metodo statistico per la determinazione di alcune priorieta dell’atome. Rend. Accad. Naz. Lincei 6, 32 (1927).

    Google Scholar 

  20. J. Lindhard: On the properties of a gas of charged particles. Kgl. Dan. Vidensk. Selsk.: Mat.-Fys. Medd. 28, 8 (1954).

    Google Scholar 

  21. F. Perrot: Hydrogen-hydrogen interaction in an electron gas. J. Phys.: Condens. Matter 6, 431 (1994).

    CAS  Google Scholar 

  22. L.-W. Wang and M.P. Teter: Kinetic-energy functional of the electron density. Phys. Rev. B 45, 13196 (1992).

    Article  CAS  Google Scholar 

  23. E. Chacón, J.E. Alvarellos, and P. Tarazona: Nonlocal kinetic energy functional for nonhomogeneous electron systems. Phys. Rev. B 32, 7868 (1985).

    Article  Google Scholar 

  24. P. García-González, J.E. Alvarellos, and E. Chacón: Nonlocal kinetic-energy-density functionals. Phys. Rev. B 53, 9509 (1996).

    Article  Google Scholar 

  25. P. García-González, J.E. Alvarellos, and E. Chacón: Kinetic-energy density functional: Atoms and shell structure. Phys. Rev. A 54, 1897 (1996).

    Article  Google Scholar 

  26. P. García-González, J.E. Alvarellos, and E. Chacón: Nonlocal symmetrized kinetic-energy density functional: Application to simple surfaces. Phys. Rev. B 57, 4857 (1998).

    Article  Google Scholar 

  27. D. García-Aldea and J.E. Alvarellos: Kinetic-energy density functionals with nonlocal terms with the structure of the Thomas–Fermi functional. Phys. Rev. A 76, 052504 (2007).

    Article  CAS  Google Scholar 

  28. S. Gómez, L.E. González, D.J. González, M.J. Stott, S. Dalgiç, and M. Silbert: Orbital free ab initio molecular dynamics study of expanded liquid Cs. J. Non-Cryst. Solids 250, 163 (1999).

    Article  Google Scholar 

  29. D.J. González, L.E. González, J.M. López, and M.J. Stott: Dynamical properties of liquid Al near melting: An orbital-free molecular dynamics study. Phys. Rev. B 65, 184201 (2002).

    Article  CAS  Google Scholar 

  30. E. Smargiassi and P.A. Madden: Orbital-free kinetic-energy functionals for first-principles molecular dynamics. Phys. Rev. B 49, 5220 (1994).

    Article  CAS  Google Scholar 

  31. Y.A. Wang, N. Govind, and E.A. Carter: Orbital-free kinetic-energy functionals for the nearly free electron gas. Phys. Rev. B 58, 13465 (1998).

    Article  CAS  Google Scholar 

  32. E.H. Lieb: Some open problems about coulomb systems. In Mathematical Problem in Theoretical Physics, K. Osterwalder, ed. (Springer, Berlin, Germany, 1979); pp. 91–102.

    Google Scholar 

  33. X. Blanc and E. Cancès: Nonlinear instability of density-independent orbital-free kinetic-energy functionals. J. Chem. Phys. 122, 214106 (2005).

    Article  CAS  Google Scholar 

  34. M. Foley and P.A. Madden: Further orbital-free kinetic-energy functionals for ab initio molecular dynamics. Phys. Rev. B 53, 10589 (1996).

    Article  CAS  Google Scholar 

  35. Y.A. Wang, N. Govind, and E.A. Carter: Orbital-free kinetic-energy density functionals with a density-dependent kernel. Phys. Rev. B 60, 16350 (1999).

    Article  CAS  Google Scholar 

  36. G.S. Ho, V.L. Lignères, and E.A. Carter: Analytic form for a nonlocal kinetic energy functional with a density-dependent kernel for orbital-free density functional theory under periodic and Dirichlet boundary conditions. Phys. Rev. B 78, 045105 (2008).

    Article  CAS  Google Scholar 

  37. B. Zhou, V.L. Ligneres, and E.A. Carter: Improving the orbital-free density functional theory description of covalent materials. J. Chem. Phys. 122, 044103 (2005).

    Article  CAS  Google Scholar 

  38. J.-D. Chai and J.D. Weeks: Modified statistical treatment of kinetic energy in the Thomas–Fermi model. J. Phys. Chem. B 108, 6870 (2004).

    Article  CAS  Google Scholar 

  39. J.-D. Chai and J.D. Weeks: Orbital-free density functional theory: Kinetic potentials and ab initio local pseudopotentials. Phys. Rev. B 75, 205122 (2007).

    Article  CAS  Google Scholar 

  40. J.-D. Chai, V.L. Lignères, G. Ho, E.A. Carter, and J.D. Weeks: Orbital-free density functional theory: Linear scaling methods for kinetic potentials, and applications to solid Al and Si. Chem. Phys. Lett. 473, 263 (2009).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  42. J. Xia, C. Huang, I. Shin, and E.A. Carter: Can orbital-free density functional theory simulate molecules?J. Chem. Phys. 136, 084102 (2012).

    Article  CAS  Google Scholar 

  43. T.A. Wesolowski and A. Warshel: Frozen density functional approach for ab initio calculations of solvated molecules. J. Phys. Chem. 97, 8050 (1993).

    Article  CAS  Google Scholar 

  44. G. Senatore and K.R. Subbaswamy: Density dependence of the dielectric constant of rare-gas crystals. Phys. Rev. B 34, 5754 (1986).

    Article  CAS  Google Scholar 

  45. P. Cortona: Self-consistently determined properties of solids without band-structure calculations. Phys. Rev. B 44, 8454 (1991).

    Article  CAS  Google Scholar 

  46. N. Govind, Y.A. Wang, and E.A. Carter: Electronic-structure calculations by first-principles density-based embedding of explicitly correlated systems. J. Chem. Phys. 110, 7677 (1999).

    Article  CAS  Google Scholar 

  47. C. Huang and E.A. Carter: Toward an orbital-free density functional theory of transition metals based on an electron density decomposition. Phys. Rev. B 85, 045126 (2012).

    Article  CAS  Google Scholar 

  48. J. Xia and E.A. Carter: Density-decomposed orbital-free density functional theory for covalently bonded molecules and materials. Phys. Rev. B 86, 235109 (2012).

    Article  CAS  Google Scholar 

  49. J. Xia and E.A. Carter: Orbital-free density functional theory study of amorphous Li–Si alloys and introduction of a simple density decomposition formalism. Modell. Simul. Mater. Sci. Eng. 24, 035014 (2016).

    Article  CAS  Google Scholar 

  50. I. Shin and E.A. Carter: Enhanced von Weizsäcker Wang–Govind–Carter kinetic energy density functional for semiconductors. J. Chem. Phys. 140, 18A531 (2014).

    Article  CAS  Google Scholar 

  51. P.E. Blöchl: Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).

    Article  Google Scholar 

  52. M. Pearson, E. Smargiassi, and P.A. Madden: Ab initio molecular dynamics with an orbital-free density functional. J. Phys.: Condens. Matter 5, 3221 (1993).

    CAS  Google Scholar 

  53. I. Shin and E.A. Carter: First-principles simulations of plasticity in body-centered-cubic magnesium–lithium alloys. Acta Mater. 64, 198 (2014).

    Article  CAS  Google Scholar 

  54. F. Legrain and S. Manzhos: Highly accurate local pseudopotentials of Li, Na, and Mg for orbital free density functional theory. Chem. Phys. Lett. 622 (Suppl. C), 99 (2015).

    Article  CAS  Google Scholar 

  55. B. Wang and M.J. Stott: First-principles local pseudopotentials for group-IV elements. Phys. Rev. B 68, 195102 (2003).

    Article  CAS  Google Scholar 

  56. B. Zhou, Y.A. Alexander Wang, and E.A. Carter: Transferable local pseudopotentials derived via inversion of the Kohn–Sham equations in a bulk environment. Phys. Rev. B 69, 125109 (2004).

    Article  CAS  Google Scholar 

  57. S. Watson, B.J. Jesson, E.A. Carter, and P.A. Madden: Ab initio pseudopotentials for orbital-free density functionals. Europhys. Lett. 41, 37 (1998).

    Article  CAS  Google Scholar 

  58. B. Zhou and E.A. Carter: First principles local pseudopotential for silver: Towards orbital-free density-functional theory for transition metals. J. Chem. Phys. 122, 184108 (2005).

    Article  CAS  Google Scholar 

  59. C. Huang and E.A. Carter: Transferable local pseudopotentials for magnesium, aluminum and silicon. Phys. Chem. Chem. Phys. 10, 7109 (2008).

    Article  CAS  Google Scholar 

  60. M. Chen, L. Hung, C. Huang, J. Xia, and E.A. Carter: The melting point of lithium: An orbital-free first-principles molecular dynamics study. Mol. Phys. 111, 3448 (2013).

    Article  CAS  Google Scholar 

  61. M. Chen, J.R. Vella, A.Z. Panagiotopoulos, P.G. Debenedetti, F.H. Stillinger, and E.A. Carter: Liquid Li structure and dynamics: A comparison between OFDFT and second nearest-neighbor embedded-atom method. AIChE J. 61, 2841 (2015).

    Article  CAS  Google Scholar 

  62. J.M. Ziman: The method of neutral pseudo-atoms in the theory of metals. Adv. Phys. 13, 89 (1964).

    Article  CAS  Google Scholar 

  63. L. Dagens: A selfconsistent calculation of the rigid neutral atom density according to the auxiliary neutral atom model. J. Phys. C: Solid State Phys. 5, 2333 (1972).

    Article  CAS  Google Scholar 

  64. J.A. Anta and P.A. Madden: Structure and dynamics of liquid lithium: Comparison of ab initio molecular dynamics predictions with scattering experiments. J. Phys.: Condens. Matter 11, 6099 (1999).

    CAS  Google Scholar 

  65. L.E. González, D.J. González, and J.M. López: Pseudopotentials for the calculation of dynamic properties of liquids. J. Phys.: Condens. Matter 13, 7801 (2001).

    Google Scholar 

  66. B.G. del Rio and L.E. González: Orbital free ab initio simulations of liquid alkaline earth metals: From pseudopotential construction to structural and dynamic properties. J. Phys.: Condens. Matter 26, 465102 (2014).

    Google Scholar 

  67. B.G. del Rio, J.M. Dieterich, and E.A. Carter: Globally-optimized local pseudopotentials for (orbital-free) density functional theory simulations of liquids and solids. J. Chem. Theory Comput. 13, 3684 (2017).

    Article  CAS  Google Scholar 

  68. S.C. Watson and E.A. Carter: Linear-scaling parallel algorithms for the first principles treatment of metals. Comput. Phys. Commun. 128, 67 (2000).

    Article  CAS  Google Scholar 

  69. G.S. Ho, V.L. Lignères, and E.A. Carter: Introducing PROFESS: A new program for orbital-free density functional theory calculations. Comput. Phys. Commun. 179, 839 (2008).

    Article  CAS  Google Scholar 

  70. L. Hung, C. Huang, I. Shin, G.S. Ho, V.L. Lignères, and E.A. Carter: Introducing PROFESS 2.0: A parallelized, fully linear scaling program for orbital-free density functional theory calculations. Comput. Phys. Commun. 181, 2208 (2010).

    Article  CAS  Google Scholar 

  71. M. Chen, J. Xia, C. Huang, J.M. Dieterich, L. Hung, I. Shin, and E.A. Carter: Introducing PROFESS 3.0: An advanced program for orbital-free density functional theory molecular dynamics simulations. Comput. Phys. Commun. 190, 228 (2015).

    Article  CAS  Google Scholar 

  72. V.V. Karasiev, T. Sjostrom, and S.B. Trickey: Finite-temperature orbital-free DFT molecular dynamics: Coupling PROFESS and Quantum Espresso. Comput. Phys. Commun. 185, 3240 (2014).

    Article  CAS  Google Scholar 

  73. S. Das, M. Iyer, and V. Gavini: Real-space formulation of orbital-free density functional theory using finite-element discretization: The case for Al, Mg, and Al–Mg intermetallics. Phys. Rev. B 92, 014104 (2015).

    Article  CAS  Google Scholar 

  74. 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, 234102 (2014).

    Article  CAS  Google Scholar 

  75. W. Mi, X. Shao, C. Su, Y. Zhou, S. Zhang, Q. Li, H. Wang, L. Zhang, M. Miao, Y. Wang, and Y. Ma: ATLAS: A real-space finite-difference implementation of orbital-free density functional theory. Comput. Phys. Commun. 200, 87 (2016).

    Article  CAS  Google Scholar 

  76. V.L. Lignères and E.A. Carter: An introduction to orbital-free density functional theory. In Handbook of Materials Modeling, S. Yip, ed. (Springer, Dordrecht, 2005); pp. 137–148.

    Chapter  Google Scholar 

  77. L. Hung and E.A. Carter: Accurate simulations of metals at the mesoscale: Explicit treatment of 1 million atoms with quantum mechanics. Chem. Phys. Lett. 475, 163 (2009).

    Article  CAS  Google Scholar 

  78. U. Essmann, L. Perera, M.L. Berkowitz, T. Darden, H. Lee, and L.G. Pedersen: A smooth particle mesh Ewald method. J. Chem. Phys. 103, 8577 (1995).

    Article  CAS  Google Scholar 

  79. N. Choly and E. Kaxiras: Fast method for force computations in electronic structure calculations. Phys. Rev. B 67, 155101 (2003).

    Article  CAS  Google Scholar 

  80. A. Gupta and V. Kumar: The scalability of FFT on parallel computers. IEEE Trans. Parallel Distrib. Syst. 4, 922 (1993).

    Article  Google Scholar 

  81. M. Chen, X.-W. Jiang, H. Zhuang, L.-W. Wang, and E.A. Carter: Petascale orbital-free density functional theory enabled by small-box algorithms. J. Chem. Theory Comput. 12, 2950 (2016).

    Article  CAS  Google Scholar 

  82. J.M. Dieterich, W.C. Witt, and E.A. Carter: libKEDF: An accelerated library of kinetic energy density functionals. J. Comput. Chem. 38, 1552 (2017).

    Article  CAS  Google Scholar 

  83. V. Gavini, J. Knap, K. Bhattacharya, and M. Ortiz: Non-periodic finite-element formulation of orbital-free density functional theory. J. Mech. Phys. Solids 55, 669 (2007).

    Article  CAS  Google Scholar 

  84. B. Radhakrishnan and V. Gavini: Orbital-free density functional theory study of the energetics of vacancy clustering and prismatic dislocation loop nucleation in aluminium. Philos. Mag. 96, 2468 (2016).

    Article  CAS  Google Scholar 

  85. P. Motamarri, M. Iyer, J. Knap, and V. Gavini: Higher-order adaptive finite-element methods for orbital-free density functional theory. J. Comput. Phys. 231, 6596 (2012).

    Article  Google Scholar 

  86. N. Choly and E. Kaxiras: Kinetic energy density functionals for non-periodic systems. Solid State Commun. 121, 281 (2002).

    Article  CAS  Google Scholar 

  87. V. Gavini, K. Bhattacharya, and M. Ortiz: Quasi-continuum orbital-free density-functional theory: A route to multi-million atom non-periodic DFT calculation. J. Mech. Phys. Solids 55, 697 (2007).

    Article  CAS  Google Scholar 

  88. L. Hung, C. Huang, and E.A. Carter: Preconditioners and electron density optimization in orbital-free density functional theory. Commun. Comput. Phys. 12, 135 (2012).

    Article  Google Scholar 

  89. M. Fago, R.L. Hayes, E.A. Carter, and M. Ortiz: Density-functional-theory-based local quasicontinuum method: Prediction of dislocation nucleation. Phys. Rev. B 70, 100102 (2004).

    Article  CAS  Google Scholar 

  90. N. Choly, G. Lu, W. E, and E. Kaxiras: Multiscale simulations in simple metals: A density-functional-based methodology. Phys. Rev. B 71, 094101 (2005).

    Article  CAS  Google Scholar 

  91. B.G. Radhakrishnan and V. Gavini: Electronic structure calculations at macroscopic scales using orbital-free DFT. In Recent Progress in Orbital-Free Density Functional Theory, T.A. Wesolowski and Y.A. Wang, eds. (World Scientific, Singapore, 2013), pp. 147–163.

    Chapter  Google Scholar 

  92. R.O. Jones and O. Gunnarsson: The density functional formalism, its applications and prospects. Rev. Mod. Phys. 61, 689 (1989).

    Article  CAS  Google Scholar 

  93. D.B. Miracle and O.N. Senkov: A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448 (2017).

    Article  CAS  Google Scholar 

  94. K.M. Carling and E.A. Carter: Orbital-free density functional theory calculations of the properties of Al, Mg and Al–Mg crystalline phases. Modell. Simul. Mater. Sci. Eng. 11, 339 (2003).

    Article  CAS  Google Scholar 

  95. H. Zhuang, M. Chen, and E.A. Carter: Elastic and thermodynamic properties of complex Mg–Al intermetallic compounds via orbital-free density functional theory. Phys. Rev. Appl. 5, 064021 (2016).

    Article  CAS  Google Scholar 

  96. H.L. Zhuang, M. Chen, and E.A. Carter: Prediction and characterization of an Mg–Al intermetallic compound with potentially improved ductility via orbital-free and Kohn–Sham density functional theory. Modell. Simul. Mater. Sci. Eng. 25, 075002 (2017).

    Article  Google Scholar 

  97. J. Xia and E.A. Carter: Orbital-free density functional theory study of crystalline Li–Si alloys. J. Power Sources 254, 62 (2014).

    Article  CAS  Google Scholar 

  98. G. Ho, M.T. Ong, K.J. Caspersen, and E.A. Carter: Energetics and kinetics of vacancy diffusion and aggregation in shocked aluminium via orbital-free density functional theory. Phys. Chem. Chem. Phys. 9, 4951 (2007).

    Article  CAS  Google Scholar 

  99. B. Radhakrishnan and V. Gavini: Effect of cell size on the energetics of vacancies in aluminum studied via orbital-free density functional theory. Phys. Rev. B 82, 094117 (2010).

    Article  CAS  Google Scholar 

  100. R. Qiu, H. Lu, B. Ao, L. Huang, T. Tang, and P. Chen: Energetics of intrinsic point defects in aluminium via orbital-free density functional theory. Philos. Mag. 97, 2164 (2017).

    Article  CAS  Google Scholar 

  101. R. Hayes, M. Fago, M. Ortiz, and E. Carter: Prediction of dislocation nucleation during nanoindentation by the orbital-free density functional theory local quasi-continuum method. Multiscale Model. Simul. 4, 359 (2005).

    Article  Google Scholar 

  102. R.L. Hayes, G. Ho, M. Ortiz, and E.A. Carter: Prediction of dislocation nucleation during nanoindentation of Al3Mg by the orbital-free density functional theory local quasicontinuum method. Philos. Mag. 86, 2343 (2006).

    Article  CAS  Google Scholar 

  103. Q. Peng, X. Zhang, C. Huang, E.A. Carter, and G. Lu: Quantum mechanical study of solid solution effects on dislocation nucleation during nanoindentation. Modell. Simul. Mater. Sci. Eng. 18, 075003 (2010).

    Article  CAS  Google Scholar 

  104. E.B. Tadmor, M. Ortiz, and R. Phillips: Quasicontinuum analysis of defects in solids. Philos. Mag. A 73, 1529 (1996).

    Article  Google Scholar 

  105. E.B. Tadmor, R. Phillips, and M. Ortiz: Mixed atomistic and continuum models of deformation in solids. Langmuir 12, 4529 (1996).

    Article  CAS  Google Scholar 

  106. Q. Peng, X. Zhang, L. Hung, E.A. Carter, and G. Lu: Quantum simulation of materials at micron scales and beyond. Phys. Rev. B 78, 054118 (2008).

    Article  CAS  Google Scholar 

  107. G.S. Ho, C. Huang, and E.A. Carter: Describing metal surfaces and nanostructures with orbital-free density functional theory. Curr. Opin. Solid State Mater. Sci. 11, 57 (2007).

    Article  CAS  Google Scholar 

  108. X. Zhang and G. Lu: Calculation of fast pipe diffusion along a dislocation stacking fault ribbon. Phys. Rev. B 82, 012101 (2010).

    Article  CAS  Google Scholar 

  109. I. Shin, A. Ramasubramaniam, C. Huang, L. Hung, and E.A. Carter: Orbital-free density functional theory simulations of dislocations in aluminum. Philos. Mag. 89, 3195 (2009).

    Article  CAS  Google Scholar 

  110. M. Iyer, B. Radhakrishnan, and V. Gavini: Electronic-structure study of an edge dislocation in aluminum and the role of macroscopic deformations on its energetics. J. Mech. Phys. Solids 76, 260 (2015).

    Article  CAS  Google Scholar 

  111. S. Das and V. Gavini: Electronic structure study of screw dislocation core energetics in aluminum and core energetics informed forces in a dislocation aggregate. J. Mech. Phys. Solids 104, 115 (2017).

    Article  CAS  Google Scholar 

  112. I. Shin and E.A. Carter: Orbital-free density functional theory simulations of dislocations in magnesium. Modell. Simul. Mater. Sci. Eng. 20, 015006 (2012).

    Article  CAS  Google Scholar 

  113. I. Shin and E.A. Carter: Possible origin of the discrepancy in Peierls stresses of fcc metals: First-principles simulations of dislocation mobility in aluminum. Phys. Rev. B 88, 064106 (2013).

    Article  CAS  Google Scholar 

  114. I. Shin and E.A. Carter: Simulations of dislocation mobility in magnesium from first principles. Int. J. Plast. 60, 58 (2014).

    Article  CAS  Google Scholar 

  115. S.C. Watson and P.A. Madden: Grain boundary migration at finite temperature: An ab initio molecular dynamics study. PhysChemComm 1, 1 (1998).

    Article  Google Scholar 

  116. L. Hung and E.A. Carter: Ductile processes at aluminium crack tips: Comparison of orbital-free density functional theory with classical potential predictions. Modell. Simul. Mater. Sci. Eng. 19, 045002 (2011).

    Article  CAS  Google Scholar 

  117. A. Aguado, D.J. González, L.E. González, J.M. López, S. Núñez, and M.J. Stott: An orbital free ab initio method: Applications to liquid metals and clusters. In Recent Progress in Orbital-Free Density Functional Theory, T.A. Wesolowski and Y.A. Yang, eds. (World Scientific Publishing Company, Singapore, 2013), pp. 55–145.

    Chapter  Google Scholar 

  118. G.S. Ho and E.A. Carter: Mechanical response of aluminum nanowires via orbital-free density functional theory. J. Comput. Theor. Nanosci. 6, 1236 (2009).

    Article  CAS  Google Scholar 

  119. L. Hung and E.A. Carter: Orbital-free DFT simulations of elastic response and tensile yielding of ultrathin [111] Al nanowires. J. Phys. Chem. C 115, 6269 (2011).

    Article  CAS  Google Scholar 

  120. M. Foley, E. Smargiassi, and P.A. Madden: The dynamic structure of liquid sodium from ab initio simulation. J. Phys.: Condens. Matter 6, 5231 (1994).

    CAS  Google Scholar 

  121. J.A. Anta, B.J. Jesson, and P.A. Madden: Ion-electron correlations in liquid metals from orbital-free ab initio molecular dynamics. Phys. Rev. B 58, 6124 (1998).

    Article  CAS  Google Scholar 

  122. S. Şengül, D.J. González, and L.E. González: Structural and dynamical properties of liquid Mg. An orbital-free molecular dynamics study. J. Phys.: Condens. Matter 21, 115106 (2009).

    Google Scholar 

  123. D.J. González, L.E. González, J.M. López, and M.J. Stott: Orbital free ab initio molecular dynamics study of liquid Al near melting. J. Chem. Phys. 115, 2373 (2001).

    Article  CAS  Google Scholar 

  124. T.G. White, S. Richardson, B.J.B. Crowley, L.K. Pattison, J.W.O. Harris, and G. Gregori: Orbital-free density-functional theory simulations of the dynamic structure factor of warm dense aluminum. Phys. Rev. Lett. 111, 175002 (2013).

    Article  CAS  Google Scholar 

  125. T. Sjostrom and J. Daligault: Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory. Phys. Rev. E 92, 063304 (2015).

    Article  CAS  Google Scholar 

  126. L.E. González and D.J. González: Structure and dynamics of bulk liquid Ga and the liquid–vapor interface: An ab initio study. Phys. Rev. B 77, 064202 (2008).

    Article  CAS  Google Scholar 

  127. A. Delisle, D.J. González, and M.J. Stott: Structural and dynamical properties of liquid Si: An orbital-free molecular dynamics study. Phys. Rev. B 73, 064202 (2006).

    Article  CAS  Google Scholar 

  128. A. Delisle, D.J. González, and M.J. Stott: Pressure-induced structural and dynamical changes in liquid Si—An ab initio study. J. Phys.: Condens. Matter 18, 3591 (2006).

    CAS  Google Scholar 

  129. G. Jacucci, M. Ronchetti, and W. Schirmacher: Computer simulation of the liquid Li4Pb alloy. J. Phys., Colloq. 46, C8 (1985).

    Article  Google Scholar 

  130. A. Campa and E.G.D. Cohen: Fast sound in binary fluid mixtures. Phys. Rev. A 41, 5451 (1990).

    Article  CAS  Google Scholar 

  131. P. Westerhuijs, W. Montfrooij, L.A. de Graaf, and I.M. de Schepper: Fast and slow sound in a dense gas mixture of helium and neon. Phys. Rev. A 45, 3749 (1992).

    Article  CAS  Google Scholar 

  132. J. Blanco, D.J. González, L.E. González, J.M. López, and M.J. Stott: Collective ionic dynamics in the liquid Na–Cs alloy: An ab initio molecular dynamics study. Phys. Rev. E 67, 041204 (2003).

    Article  CAS  Google Scholar 

  133. D.J. González, L.E. González, J.M. López, and M.J. Stott: Microscopic dynamics in the liquid Li–Na alloy: An ab initio molecular dynamics study. Phys. Rev. E 69, 031205 (2004).

    Article  CAS  Google Scholar 

  134. J.S. Rowlinson and B. Widom: Molecular Theory of Capillarity (Clarendon Press, Oxford, U.K., 1982).

    Google Scholar 

  135. B.M. Ocko, X.Z. Wu, E.B. Sirota, S.K. Sinha, and M. Deutsch: X-ray reflectivity study of thermal capillary waves on liquid surfaces. Phys. Rev. Lett. 72, 242 (1994).

    Article  CAS  Google Scholar 

  136. M.J. Regan, E.H. Kawamoto, S. Lee, P.S. Pershan, N. Maskil, M. Deutsch, O.M. Magnussen, B.M. Ocko, and L.E. Berman: Surface layering in liquid gallium: An X-ray reflectivity study. Phys. Rev. Lett. 75, 2498 (1995).

    Article  CAS  Google Scholar 

  137. M.J. Regan, P.S. Pershan, O.M. Magnussen, B.M. Ocko, M. Deutsch, and L.E. Berman: X-ray reflectivity studies of liquid metal and alloy surfaces. Phys. Rev. B 55, 15874 (1997).

    Article  CAS  Google Scholar 

  138. G. Fabricius, E. Artacho, D. Sánchez-Portal, P. Ordejón, D.A. Drabold, and J.M. Soler: Atomic layering at the liquid silicon surface: A first-principles simulation. Phys. Rev. B 60, R16283 (1999).

    Article  CAS  Google Scholar 

  139. B.G. Walker, N. Marzari, and C. Molteni: Ab initio studies of layering behavior of liquid sodium surfaces and interfaces. J. Chem. Phys. 124, 174702 (2006).

    Article  CAS  Google Scholar 

  140. D.J. González, L.E. González, and M.J. Stott: Surface structure of liquid Li and Na: An ab initio molecular dynamics study. Phys. Rev. Lett. 92, 085501 (2004).

    Article  CAS  Google Scholar 

  141. D.J. González, L.E. González, and M.J. Stott: Surface structure in simple liquid metals: An orbital-free first-principles study. Phys. Rev. B 74, 014207 (2006).

    Article  CAS  Google Scholar 

  142. D.J. González and L.E. González: Structure of the liquid–vapor interfaces of Ga, in and the eutectic Ga–In alloy—an ab initio study. J. Phys.: Condens. Matter 20, 114118 (2008).

    Google Scholar 

  143. D.J. González, L.E. González, and M.J. Stott: Liquid-vapor interface in liquid binary alloys: An ab initio molecular dynamics study. Phys. Rev. Lett. 94, 077801 (2005).

    Article  CAS  Google Scholar 

  144. D.J. González and L.E. González: Structure and motion at the liquid-vapor interface of some interalkali binary alloys: An orbital-free ab initio study. J. Chem. Phys. 130, 114703 (2009).

    Article  CAS  Google Scholar 

  145. B.J. Jesson and P.A. Madden: Structure and dynamics at the aluminum solid–liquid interface: An ab initio simulation. J. Chem. Phys. 113, 5935 (2000).

    Article  CAS  Google Scholar 

  146. L.E. González and D.J. González: Orbital-free ab-initio study of the structure of liquid Al on a model fcc metallic wall: The influence of surface orientation. J. Phys.: Conf. Ser. 98, 062024 (2008).

    Google Scholar 

  147. D.K. Chokappa and P. Clancy: A computer simulation study of the melting and freezing properties of a system of Lennard-Jones particles. Mol. Phys. 61, 597 (1987).

    Article  CAS  Google Scholar 

  148. J.R. Morris, C.Z. Wang, K.M. Ho, and C.T. Chan: Melting line of aluminum from simulations of coexisting phases. Phys. Rev. B 49, 3109 (1994).

    Article  CAS  Google Scholar 

  149. A.B. Belonoshko, N.V. Skorodumova, A. Rosengren, and B. Johansson: Melting and critical superheating. Phys. Rev. B 73, 012201 (2006).

    Article  CAS  Google Scholar 

  150. E. Gregoryanz, L.F. Lundegaard, M.I. McMahon, C. Guillaume, R.J. Nelmes, and M. Mezouar: Structural diversity of sodium. Science 320, 1054 (2008).

    Article  CAS  Google Scholar 

  151. M. Marqués, M.I. McMahon, E. Gregoryanz, M. Hanfland, C.L. Guillaume, C.J. Pickard, G.J. Ackland, and R.J. Nelmes: Crystal structures of dense lithium: A metal-semiconductor-metal transition. Phys. Rev. Lett. 106, 095502 (2011).

    Article  CAS  Google Scholar 

  152. M. Marqués, D.J. González, and L.E. González: Structure and dynamics of high-pressure Na close to the melting line: An ab initio molecular dynamics study. Phys. Rev. B 94, 024204 (2016).

    Article  CAS  Google Scholar 

  153. J.P. Perdew and L.A. Constantin: Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy. Phys. Rev. B 75, 155109 (2007).

    Article  CAS  Google Scholar 

  154. S. Śmiga, E. Fabiano, L.A. Constantin, and F. Della Sala: Laplacian-dependent models of the kinetic energy density: Applications in subsystem density functional theory with meta-generalized gradient approximation functionals. J. Chem. Phys. 146, 064105 (2017).

    Article  CAS  Google Scholar 

  155. F. Tran and T.A. Wesolowski: Semilocal approximations for the kinetic energy. In Recent Progress in Orbital-Free Density Functional Theory, T.A. Wesolowski and Y.A. Wang, eds. (World Scientific, Singapore, 2012); pp. 429–442.

    Google Scholar 

  156. V.V. Karasiev, R.S. Jones, S.B. Trickey, and F.E. Harris: Properties of constraint-based single-point approximate kinetic energy functionals. Phys. Rev. B 80, 245120 (2009).

    Article  CAS  Google Scholar 

  157. V.V. Karasiev, D. Chakraborty, O.A. Shukruto, and S.B. Trickey: Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations. Phys. Rev. B 88, 161108 (2013).

    Article  CAS  Google Scholar 

  158. V.V. Karasiev and S.B. Trickey: Frank discussion of the status of ground-state orbital-free DFT. In Advances in Quantum Chemistry, J.R. Sabin and R. Cabrera-Trujillo,eds. (Academic Press, London, U.K., 2015); pp. 221–245.

    Google Scholar 

  159. A.C. Cancio, D. Stewart, and A. Kuna: Visualization and analysis of the Kohn–Sham kinetic energy density and its orbital-free description in molecules. J. Chem. Phys. 144, 084107 (2016).

    Article  CAS  Google Scholar 

  160. J. Xia and E.A. Carter: Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation. Phys. Rev. B 91, 045124 (2015).

    Article  CAS  Google Scholar 

  161. S.B. Trickey, V.V. Karasiev, and D. Chakraborty: Comment on “Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation”. Phys. Rev. B 92, 117101 (2015).

    Article  CAS  Google Scholar 

  162. J. Xia and E.A. Carter: Reply to “comment on ‘Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation’”. Phys. Rev. B 92, 117102 (2015).

    Article  CAS  Google Scholar 

  163. F. Della Sala, E. Fabiano, and L.A. Constantin: Kohn–Sham kinetic energy density in the nuclear and asymptotic regions: Deviations from the von Weizsäcker behavior and applications to density functionals. Phys. Rev. B 91, 035126 (2015).

    Article  CAS  Google Scholar 

  164. K. Finzel: Local conditions for the Pauli potential in order to yield self-consistent electron densities exhibiting proper atomic shell structure. J. Chem. Phys. 144, 034108 (2016).

    Article  CAS  Google Scholar 

  165. P. Elliott, D. Lee, A. Cangi, and K. Burke: Semiclassical origins of density functionals. Phys. Rev. Lett. 100, 256406 (2008).

    Article  CAS  Google Scholar 

  166. D. Lee, L.A. Constantin, J.P. Perdew, and K. Burke: Condition on the Kohn–Sham kinetic energy and modern parametrization of the Thomas–Fermi density. J. Chem. Phys. 130, 034107 (2009).

    Article  CAS  Google Scholar 

  167. L.A. Constantin, E. Fabiano, S. Laricchia, and F. Della Sala: Semiclassical neutral atom as a reference system in density functional theory. Phys. Rev. Lett. 106, 186406 (2011).

    Article  CAS  Google Scholar 

  168. E. Fabiano and L.A. Constantin: Relevance of coordinate and particle-number scaling in density-functional theory. Phys. Rev. A 87, 012511 (2013).

    Article  CAS  Google Scholar 

  169. A.C. Cancio and J.J. Redd: Visualisation and orbital-free parametrisation of the large-Z scaling of the kinetic energy density of atoms. Mol. Phys. 115, 618 (2017).

    Article  CAS  Google Scholar 

  170. K. Finzel: Shell-structure-based functionals for the kinetic energy. Theor. Chem. Acc. 134, 106 (2015).

    Article  CAS  Google Scholar 

  171. L.A. Constantin and A. Ruzsinszky: Kinetic energy density functionals from the Airy gas with an application to the atomization kinetic energies of molecules. Phys. Rev. B 79, 115117 (2009).

    Article  CAS  Google Scholar 

  172. A. Lindmaa, A.E. Mattsson, and R. Armiento: Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas. Phys. Rev. B 90, 075139 (2014).

    Article  CAS  Google Scholar 

  173. L.A. Constantin, E. Fabiano, S. Śmiga, and F. Della Sala: Jellium-with-gap model applied to semilocal kinetic functionals. Phys. Rev. B 95, 115153 (2017).

    Article  Google Scholar 

  174. L.A. Constantin, E. Fabiano, and F. Della Sala: Modified fourth-order kinetic energy gradient expansion with hartree potential-dependent coefficients. J. Chem. Theory Comput. 13, 4228 (2017).

    Article  CAS  Google Scholar 

  175. Y. Ke, F. Libisch, J. Xia, L-W. Wang, and E.A. Carter: Angular-momentum-dependent orbital-free density functional theory. Phys. Rev. Lett. 111, 066402 (2013).

    Article  CAS  Google Scholar 

  176. Y. Ke, F. Libisch, J. Xia, and E.A. Carter: Angular momentum dependent orbital-free density functional theory: Formulation and implementation. Phys. Rev. B 89, 155112 (2014).

    Article  CAS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors thank D.J. González for kindly providing Fig. 3, as well as Ms. Nari Baughman for her close review of the manuscript. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program [for WCW] under Grant No. 1656466. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. EAC further acknowledges support from the Office of Naval Research (Grant No. N00014-15-1-2218).

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey, 08544-5263, USA

    William C. Witt, Beatriz G. del Rio & Johannes M. Dieterich

  2. School of Engineering and Applied Science, Princeton University, Princeton, New Jersey, 08544-5263, USA

    Emily A. Carter

Authors
  1. William C. Witt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Beatriz G. del Rio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Johannes M. Dieterich
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Emily A. Carter
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emily A. Carter.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Witt, W.C., del Rio, B.G., Dieterich, J.M. et al. Orbital-free density functional theory for materials research. Journal of Materials Research 33, 777–795 (2018). https://doi.org/10.1557/jmr.2017.462

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2017.462

Search

Navigation