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Orbital-free density functional theory for materials research

Published online by Cambridge University Press:  02 January 2018

William C. Witt ,
Beatriz G. del Rio ,
Johannes M. Dieterich  and
Emily A. Carter
William C. Witt
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
Beatriz G. del Rio
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
Johannes M. Dieterich
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
Emily A. Carter*
Affiliation:
School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08544-5263, USA
*
a)Address all correspondence to this author. e-mail: [email protected]
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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.

Keywords

electronic structuresimulationnanostructure
Type
REVIEW
Information
Journal of Materials Research , Volume 33 , Issue 7: Focus Issue: Advanced Atomistic Algorithms in Materials Science , 13 April 2018 , pp. 777 - 795
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Copyright
Copyright © Materials Research Society 2017 

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Footnotes

Contributing Editor: Steven D. Kenny

This section of Journal of Materials Research is reserved for papers that are reviews of literature in a given area.

References

REFERENCES

Wang, Y.A. and Carter, E.A.: Orbital-free kinetic-energy density functional theory. In Theoretical Methods in Condensed Phase Chemistry, Schwartz, S.D., ed. (Springer, Dordrecht, 2002); pp. 117–184.CrossRefGoogle Scholar
Chen, H. and Zhou, A.: Orbital-free density functional theory for molecular structure calculations. Numer. Math. Theor. Meth. Appl. 1, 1 (2008).Google Scholar
Wesolowski, T.A. and Wang, Y.A.: Recent Progress in Orbital-Free Density Functional Theory (World Scientific, Singapore, 2013).CrossRefGoogle Scholar
Karasiev, V.V., Chakraborty, D., and Trickey, S.B.: Progress on new approaches to old ideas: Orbital-free density functionals. In Many-Electron Approaches in Physics, Chemistry and Mathematics, Bach, V. and Delle Site, L., eds. (Springer, Cham, Switzerland, 2014); pp. 113–134.CrossRefGoogle Scholar
Parr, R.G. and Yang, W.: Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1994).Google Scholar
Dreizler, R.M. and Gross, E.K.U.: Density Functional Theory: An Approach to the Quantum Many-Body Problem (Springer Science & Business Media, 1990).CrossRefGoogle Scholar
Hohenberg, P. and Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).CrossRefGoogle Scholar
Kohn, W. and Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965).CrossRefGoogle Scholar
Graziani, F., Desjarlais, M.P., Redmer, R., and Trickey, S.B.: Frontiers and Challenges in Warm Dense Matter (Springer Science & Business, Charm, Switzerland, 2014).CrossRefGoogle Scholar
Jacob, C.R. and Neugebauer, J.: Subsystem density-functional theory. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 4, 325 (2014).Google Scholar
Krishtal, A., Sinha, D., Genova, A., and Pavanello, M.: 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 ScholarPubMed
Bowler, D.R. and Miyazaki, T.: O(N) methods in electronic structure calculations. Rep. Prog. Phys. 75, 036503 (2012).CrossRefGoogle ScholarPubMed
Goedecker, S.: Linear scaling electronic structure methods. Rev. Mod. Phys. 71, 1085 (1999).CrossRefGoogle Scholar
Aarons, J., Sarwar, M., Thompsett, D., and Skylaris, C.-K.: Methods for large-scale density functional calculations on metallic systems. J. Chem. Phys. 145, 220901 (2016).CrossRefGoogle ScholarPubMed
Ludena, E.V. and Karasiev, V.V.: Kinetic energy functionals: History, challenges and prospects. Rev. Mod. Quantum Chem. 1, 612–665 (2002).CrossRefGoogle Scholar
García-Aldea, D. and Alvarellos, J.E.: The construction of kinetic energy functionals and the linear response function. In Theoretical and Computational Developments in Modern Density Functional Theory, Roy, A.K., ed. (Nova Science Publishers, Hauppauge, New York, 2012), pp. 255–280.Google Scholar
von Weizsäcker, C.F.: Zur Theorie der Kernmassen. Z. Phys. 96, 431 (1935).CrossRefGoogle Scholar
Thomas, L.H.: The calculation of atomic fields. Math. Proc. Cambridge Philos. Soc. 23, 542 (1927).CrossRefGoogle Scholar
Fermi, E.: Un metodo statistico per la determinazione di alcune priorieta dell’atome. Rend. Accad. Naz. Lincei 6, 32 (1927).Google Scholar
Lindhard, J.: On the properties of a gas of charged particles. Kgl. Dan. Vidensk. Selsk.: Mat.-Fys. Medd. 28, 8 (1954).Google Scholar
Perrot, F.: Hydrogen-hydrogen interaction in an electron gas. J. Phys.: Condens. Matter 6, 431 (1994).Google Scholar
Wang, L.-W. and Teter, M.P.: Kinetic-energy functional of the electron density. Phys. Rev. B 45, 13196 (1992).CrossRefGoogle ScholarPubMed
Chacón, E., Alvarellos, J.E., and Tarazona, P.: Nonlocal kinetic energy functional for nonhomogeneous electron systems. Phys. Rev. B 32, 7868 (1985).CrossRefGoogle ScholarPubMed
García-González, P., Alvarellos, J.E., and Chacón, E.: Nonlocal kinetic-energy-density functionals. Phys. Rev. B 53, 9509 (1996).CrossRefGoogle ScholarPubMed
García-González, P., Alvarellos, J.E., and Chacón, E.: Kinetic-energy density functional: Atoms and shell structure. Phys. Rev. A 54, 1897 (1996).CrossRefGoogle ScholarPubMed
García-González, P., Alvarellos, J.E., and Chacón, E.: Nonlocal symmetrized kinetic-energy density functional: Application to simple surfaces. Phys. Rev. B 57, 4857 (1998).CrossRefGoogle Scholar
García-Aldea, D. and Alvarellos, J.E.: Kinetic-energy density functionals with nonlocal terms with the structure of the Thomas–Fermi functional. Phys. Rev. A 76, 052504 (2007).CrossRefGoogle Scholar
Gómez, S., González, L.E., González, D.J., Stott, M.J., Dalgiç, S., and Silbert, M.: Orbital free ab initio molecular dynamics study of expanded liquid Cs. J. Non-Cryst. Solids 250, 163 (1999).CrossRefGoogle Scholar
González, D.J., González, L.E., López, J.M., and Stott, M.J.: Dynamical properties of liquid Al near melting: An orbital-free molecular dynamics study. Phys. Rev. B 65, 184201 (2002).CrossRefGoogle Scholar
Smargiassi, E. and Madden, P.A.: Orbital-free kinetic-energy functionals for first-principles molecular dynamics. Phys. Rev. B 49, 5220 (1994).CrossRefGoogle ScholarPubMed
Wang, Y.A., Govind, N., and Carter, E.A.: Orbital-free kinetic-energy functionals for the nearly free electron gas. Phys. Rev. B 58, 13465 (1998).CrossRefGoogle Scholar
Lieb, E.H.: Some open problems about coulomb systems. In Mathematical Problem in Theoretical Physics, Osterwalder, K., ed. (Springer, Berlin, Germany, 1979); pp. 91–102.Google Scholar
Blanc, X. and Cancès, E.: Nonlinear instability of density-independent orbital-free kinetic-energy functionals. J. Chem. Phys. 122, 214106 (2005).CrossRefGoogle ScholarPubMed
Foley, M. and Madden, P.A.: Further orbital-free kinetic-energy functionals for ab initio molecular dynamics. Phys. Rev. B 53, 10589 (1996).CrossRefGoogle ScholarPubMed
Wang, Y.A., Govind, N., and Carter, E.A.: Orbital-free kinetic-energy density functionals with a density-dependent kernel. Phys. Rev. B 60, 16350 (1999).CrossRefGoogle Scholar
Ho, G.S., Lignères, V.L., and Carter, E.A.: 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).CrossRefGoogle Scholar
Zhou, B., Ligneres, V.L., and Carter, E.A.: Improving the orbital-free density functional theory description of covalent materials. J. Chem. Phys. 122, 044103 (2005).CrossRefGoogle ScholarPubMed
Chai, J.-D. and Weeks, J.D.: Modified statistical treatment of kinetic energy in the Thomas–Fermi model. J. Phys. Chem. B 108, 6870 (2004).CrossRefGoogle Scholar
Chai, J.-D. and Weeks, J.D.: Orbital-free density functional theory: Kinetic potentials and ab initio local pseudopotentials. Phys. Rev. B 75, 205122 (2007).CrossRefGoogle Scholar
Chai, J.-D., Lignères, V.L., Ho, G., Carter, E.A., and Weeks, J.D.: Orbital-free density functional theory: Linear scaling methods for kinetic potentials, and applications to solid Al and Si. Chem. Phys. Lett. 473, 263 (2009).CrossRefGoogle Scholar
Huang, C. and Carter, E.A.: Nonlocal orbital-free kinetic energy density functional for semiconductors. Phys. Rev. B 81, 045206 (2010).CrossRefGoogle Scholar
Xia, J., Huang, C., Shin, I., and Carter, E.A.: Can orbital-free density functional theory simulate molecules? J. Chem. Phys. 136, 084102 (2012).CrossRefGoogle ScholarPubMed
Wesolowski, T.A. and Warshel, A.: Frozen density functional approach for ab initio calculations of solvated molecules. J. Phys. Chem. 97, 8050 (1993).CrossRefGoogle Scholar
Senatore, G. and Subbaswamy, K.R.: Density dependence of the dielectric constant of rare-gas crystals. Phys. Rev. B 34, 5754 (1986).CrossRefGoogle ScholarPubMed
Cortona, P.: Self-consistently determined properties of solids without band-structure calculations. Phys. Rev. B 44, 8454 (1991).CrossRefGoogle ScholarPubMed
Govind, N., Wang, Y.A., and Carter, E.A.: Electronic-structure calculations by first-principles density-based embedding of explicitly correlated systems. J. Chem. Phys. 110, 7677 (1999).CrossRefGoogle Scholar
Huang, C. and Carter, E.A.: Toward an orbital-free density functional theory of transition metals based on an electron density decomposition. Phys. Rev. B 85, 045126 (2012).CrossRefGoogle Scholar
Xia, J. and Carter, E.A.: Density-decomposed orbital-free density functional theory for covalently bonded molecules and materials. Phys. Rev. B 86, 235109 (2012).CrossRefGoogle Scholar
Xia, J. and Carter, E.A.: 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).CrossRefGoogle Scholar
Shin, I. and Carter, E.A.: Enhanced von Weizsäcker Wang–Govind–Carter kinetic energy density functional for semiconductors. J. Chem. Phys. 140, 18A531 (2014).CrossRefGoogle Scholar
Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).CrossRefGoogle ScholarPubMed
Pearson, M., Smargiassi, E., and Madden, P.A.: Ab initio molecular dynamics with an orbital-free density functional. J. Phys.: Condens. Matter 5, 3221 (1993).Google Scholar
Shin, I. and Carter, E.A.: First-principles simulations of plasticity in body-centered-cubic magnesium–lithium alloys. Acta Mater. 64, 198 (2014).CrossRefGoogle Scholar
Legrain, F. and Manzhos, S.: Highly accurate local pseudopotentials of Li, Na, and Mg for orbital free density functional theory. Chem. Phys. Lett. 622(Suppl. C), 99 (2015).CrossRefGoogle Scholar
Wang, B. and Stott, M.J.: First-principles local pseudopotentials for group-IV elements. Phys. Rev. B 68, 195102 (2003).CrossRefGoogle Scholar
Zhou, B., Alexander Wang, Y.A., and Carter, E.A.: Transferable local pseudopotentials derived via inversion of the Kohn–Sham equations in a bulk environment. Phys. Rev. B 69, 125109 (2004).CrossRefGoogle Scholar
Watson, S., Jesson, B.J., Carter, E.A., and Madden, P.A.: Ab initio pseudopotentials for orbital-free density functionals. Europhys. Lett. 41, 37 (1998).CrossRefGoogle Scholar
Zhou, B. and Carter, E.A.: First principles local pseudopotential for silver: Towards orbital-free density-functional theory for transition metals. J. Chem. Phys. 122, 184108 (2005).CrossRefGoogle ScholarPubMed
Huang, C. and Carter, E.A.: Transferable local pseudopotentials for magnesium, aluminum and silicon. Phys. Chem. Chem. Phys. 10, 7109 (2008).CrossRefGoogle ScholarPubMed
Chen, M., Hung, L., Huang, C., Xia, J., and Carter, E.A.: The melting point of lithium: An orbital-free first-principles molecular dynamics study. Mol. Phys. 111, 3448 (2013).CrossRefGoogle Scholar
Chen, M., Vella, J.R., Panagiotopoulos, A.Z., Debenedetti, P.G., Stillinger, F.H., and Carter, E.A.: Liquid Li structure and dynamics: A comparison between OFDFT and second nearest-neighbor embedded-atom method. AIChE J. 61, 2841 (2015).CrossRefGoogle Scholar
Ziman, J.M.: The method of neutral pseudo-atoms in the theory of metals. Adv. Phys. 13, 89 (1964).CrossRefGoogle Scholar
Dagens, L.: 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).CrossRefGoogle Scholar
Anta, J.A. and Madden, P.A.: Structure and dynamics of liquid lithium: Comparison of ab initio molecular dynamics predictions with scattering experiments. J. Phys.: Condens. Matter 11, 6099 (1999).Google Scholar
González, L.E., González, D.J., and López, J.M.: Pseudopotentials for the calculation of dynamic properties of liquids. J. Phys.: Condens. Matter 13, 7801 (2001).Google Scholar
del Rio, B.G. and González, L.E.: 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
del Rio, B.G., Dieterich, J.M., and Carter, E.A.: Globally-optimized local pseudopotentials for (orbital-free) density functional theory simulations of liquids and solids. J. Chem. Theory Comput. 13, 3684 (2017).CrossRefGoogle ScholarPubMed
Watson, S.C. and Carter, E.A.: Linear-scaling parallel algorithms for the first principles treatment of metals. Comput. Phys. Commun. 128, 67 (2000).CrossRefGoogle Scholar
Ho, G.S., Lignères, V.L., and Carter, E.A.: Introducing PROFESS: A new program for orbital-free density functional theory calculations. Comput. Phys. Commun. 179, 839 (2008).CrossRefGoogle Scholar
Hung, L., Huang, C., Shin, I., Ho, G.S., Lignères, V.L., and Carter, E.A.: Introducing PROFESS 2.0: A parallelized, fully linear scaling program for orbital-free density functional theory calculations. Comput. Phys. Commun. 181, 2208 (2010).CrossRefGoogle Scholar
Chen, M., Xia, J., Huang, C., Dieterich, J.M., Hung, L., Shin, I., and Carter, E.A.: Introducing PROFESS 3.0: An advanced program for orbital-free density functional theory molecular dynamics simulations. Comput. Phys. Commun. 190, 228 (2015).CrossRefGoogle Scholar
Karasiev, V.V., Sjostrom, T., and Trickey, S.B.: Finite-temperature orbital-free DFT molecular dynamics: Coupling PROFESS and Quantum Espresso. Comput. Phys. Commun. 185, 3240 (2014).CrossRefGoogle Scholar
Das, S., Iyer, M., and Gavini, V.: 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).CrossRefGoogle Scholar
Lehtomäki, J., Makkonen, I., Caro, M.A., Harju, A., and Lopez-Acevedo, O.: Orbital-free density functional theory implementation with the projector augmented-wave method. J. Chem. Phys. 141, 234102 (2014).CrossRefGoogle ScholarPubMed
Mi, W., Shao, X., Su, C., Zhou, Y., Zhang, S., Li, Q., Wang, H., Zhang, L., Miao, M., Wang, Y., and Ma, Y.: ATLAS: A real-space finite-difference implementation of orbital-free density functional theory. Comput. Phys. Commun. 200, 87 (2016).CrossRefGoogle Scholar
Lignères, V.L. and Carter, E.A.: An introduction to orbital-free density functional theory. In Handbook of Materials Modeling, Yip, S., ed. (Springer, Dordrecht, 2005); pp. 137–148.CrossRefGoogle Scholar
Hung, L. and Carter, E.A.: Accurate simulations of metals at the mesoscale: Explicit treatment of 1 million atoms with quantum mechanics. Chem. Phys. Lett. 475, 163 (2009).CrossRefGoogle Scholar
Essmann, U., Perera, L., Berkowitz, M.L., Darden, T., Lee, H., and Pedersen, L.G.: A smooth particle mesh Ewald method. J. Chem. Phys. 103, 8577 (1995).CrossRefGoogle Scholar
Choly, N. and Kaxiras, E.: Fast method for force computations in electronic structure calculations. Phys. Rev. B 67, 155101 (2003).CrossRefGoogle Scholar
Gupta, A. and Kumar, V.: The scalability of FFT on parallel computers. IEEE Trans. Parallel Distrib. Syst. 4, 922 (1993).CrossRefGoogle Scholar
Chen, M., Jiang, X.-W., Zhuang, H., Wang, L.-W., and Carter, E.A.: Petascale orbital-free density functional theory enabled by small-box algorithms. J. Chem. Theory Comput. 12, 2950 (2016).CrossRefGoogle ScholarPubMed
Dieterich, J.M., Witt, W.C., and Carter, E.A.: libKEDF: An accelerated library of kinetic energy density functionals. J. Comput. Chem. 38, 1552 (2017).CrossRefGoogle ScholarPubMed
Gavini, V., Knap, J., Bhattacharya, K., and Ortiz, M.: Non-periodic finite-element formulation of orbital-free density functional theory. J. Mech. Phys. Solids 55, 669 (2007).CrossRefGoogle Scholar
Radhakrishnan, B. and Gavini, V.: Orbital-free density functional theory study of the energetics of vacancy clustering and prismatic dislocation loop nucleation in aluminium. Philos. Mag. 96, 2468 (2016).CrossRefGoogle Scholar
Motamarri, P., Iyer, M., Knap, J., and Gavini, V.: Higher-order adaptive finite-element methods for orbital-free density functional theory. J. Comput. Phys. 231, 6596 (2012).CrossRefGoogle Scholar
Choly, N. and Kaxiras, E.: Kinetic energy density functionals for non-periodic systems. Solid State Commun. 121, 281 (2002).CrossRefGoogle Scholar
Gavini, V., Bhattacharya, K., and Ortiz, M.: Quasi-continuum orbital-free density-functional theory: A route to multi-million atom non-periodic DFT calculation. J. Mech. Phys. Solids 55, 697 (2007).CrossRefGoogle Scholar
Hung, L., Huang, C., and Carter, E.A.: Preconditioners and electron density optimization in orbital-free density functional theory. Commun. Comput. Phys. 12, 135 (2012).CrossRefGoogle Scholar
Fago, M., Hayes, R.L., Carter, E.A., and Ortiz, M.: Density-functional-theory-based local quasicontinuum method: Prediction of dislocation nucleation. Phys. Rev. B 70, 100102 (2004).CrossRefGoogle Scholar
Choly, N., Lu, G., E, W., and Kaxiras, E.: Multiscale simulations in simple metals: A density-functional-based methodology. Phys. Rev. B 71, 094101 (2005).CrossRefGoogle Scholar
Radhakrishnan, B.G. and Gavini, V.: Electronic structure calculations at macroscopic scales using orbital-free DFT. In Recent Progress in Orbital-Free Density Functional Theory, Wesolowski, T.A. and Wang, Y.A., eds. (World Scientific, Singapore, 2013), pp. 147–163.CrossRefGoogle Scholar
Jones, R.O. and Gunnarsson, O.: The density functional formalism, its applications and prospects. Rev. Mod. Phys. 61, 689 (1989).CrossRefGoogle Scholar
Miracle, D.B. and Senkov, O.N.: A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448 (2017).CrossRefGoogle Scholar
Carling, K.M. and Carter, E.A.: 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).CrossRefGoogle Scholar
Zhuang, H., Chen, M., and Carter, E.A.: Elastic and thermodynamic properties of complex Mg–Al intermetallic compounds via orbital-free density functional theory. Phys. Rev. Appl. 5, 064021 (2016).CrossRefGoogle Scholar
Zhuang, H.L., Chen, M., and Carter, E.A.: 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).CrossRefGoogle Scholar
Xia, J. and Carter, E.A.: Orbital-free density functional theory study of crystalline Li–Si alloys. J. Power Sources 254, 62 (2014).CrossRefGoogle Scholar
Ho, G., Ong, M.T., Caspersen, K.J., and Carter, E.A.: Energetics and kinetics of vacancy diffusion and aggregation in shocked aluminium via orbital-free density functional theory. Phys. Chem. Chem. Phys. 9, 4951 (2007).CrossRefGoogle ScholarPubMed
Radhakrishnan, B. and Gavini, V.: Effect of cell size on the energetics of vacancies in aluminum studied via orbital-free density functional theory. Phys. Rev. B 82, 094117 (2010).CrossRefGoogle Scholar
Qiu, R., Lu, H., Ao, B., Huang, L., Tang, T., and Chen, P.: Energetics of intrinsic point defects in aluminium via orbital-free density functional theory. Philos. Mag. 97, 2164 (2017).CrossRefGoogle Scholar
Hayes, R., Fago, M., Ortiz, M., and Carter, E.: Prediction of dislocation nucleation during nanoindentation by the orbital-free density functional theory local quasi-continuum method. Multiscale Model. Simul. 4, 359 (2005).CrossRefGoogle Scholar
Hayes, R.L., Ho, G., Ortiz, M., and Carter, E.A.: Prediction of dislocation nucleation during nanoindentation of Al3Mg by the orbital-free density functional theory local quasicontinuum method. Philos. Mag. 86, 2343 (2006).CrossRefGoogle Scholar
Peng, Q., Zhang, X., Huang, C., Carter, E.A., and Lu, G.: Quantum mechanical study of solid solution effects on dislocation nucleation during nanoindentation. Modell. Simul. Mater. Sci. Eng. 18, 075003 (2010).CrossRefGoogle Scholar
Tadmor, E.B., Ortiz, M., and Phillips, R.: Quasicontinuum analysis of defects in solids. Philos. Mag. A 73, 1529 (1996).CrossRefGoogle Scholar
Tadmor, E.B., Phillips, R., and Ortiz, M.: Mixed atomistic and continuum models of deformation in solids. Langmuir 12, 4529 (1996).CrossRefGoogle Scholar
Peng, Q., Zhang, X., Hung, L., Carter, E.A., and Lu, G.: Quantum simulation of materials at micron scales and beyond. Phys. Rev. B 78, 054118 (2008).CrossRefGoogle Scholar
Ho, G.S., Huang, C., and Carter, E.A.: Describing metal surfaces and nanostructures with orbital-free density functional theory. Curr. Opin. Solid State Mater. Sci. 11, 57 (2007).CrossRefGoogle Scholar
Zhang, X. and Lu, G.: Calculation of fast pipe diffusion along a dislocation stacking fault ribbon. Phys. Rev. B 82, 012101 (2010).CrossRefGoogle Scholar
Shin, I., Ramasubramaniam, A., Huang, C., Hung, L., and Carter, E.A.: Orbital-free density functional theory simulations of dislocations in aluminum. Philos. Mag. 89, 3195 (2009).CrossRefGoogle Scholar
Iyer, M., Radhakrishnan, B., and Gavini, V.: 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).CrossRefGoogle Scholar
Das, S. and Gavini, V.: 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).CrossRefGoogle Scholar
Shin, I. and Carter, E.A.: Orbital-free density functional theory simulations of dislocations in magnesium. Modell. Simul. Mater. Sci. Eng. 20, 015006 (2012).CrossRefGoogle Scholar
Shin, I. and Carter, E.A.: 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).CrossRefGoogle Scholar
Shin, I. and Carter, E.A.: Simulations of dislocation mobility in magnesium from first principles. Int. J. Plast. 60, 58 (2014).CrossRefGoogle Scholar
Watson, S.C. and Madden, P.A.: Grain boundary migration at finite temperature: An ab initio molecular dynamics study. PhysChemComm 1, 1 (1998).CrossRefGoogle Scholar
Hung, L. and Carter, E.A.: 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).CrossRefGoogle Scholar
Aguado, A., González, D.J., González, L.E., López, J.M., Núñez, S., and Stott, M.J.: An orbital free ab initio method: Applications to liquid metals and clusters. In Recent Progress in Orbital-Free Density Functional Theory, Wesolowski, T.A. and Yang, Y.A., eds. (World Scientific Publishing Company, Singapore, 2013), pp. 55–145.CrossRefGoogle Scholar
Ho, G.S. and Carter, E.A.: Mechanical response of aluminum nanowires via orbital-free density functional theory. J. Comput. Theor. Nanosci. 6, 1236 (2009).CrossRefGoogle Scholar
Hung, L. and Carter, E.A.: Orbital-free DFT simulations of elastic response and tensile yielding of ultrathin [111] Al nanowires. J. Phys. Chem. C 115, 6269 (2011).CrossRefGoogle Scholar
Foley, M., Smargiassi, E., and Madden, P.A.: The dynamic structure of liquid sodium from ab initio simulation. J. Phys.: Condens. Matter 6, 5231 (1994).Google Scholar
Anta, J.A., Jesson, B.J., and Madden, P.A.: Ion-electron correlations in liquid metals from orbital-free ab initio molecular dynamics. Phys. Rev. B 58, 6124 (1998).CrossRefGoogle Scholar
Şengül, S., González, D.J., and González, L.E.: Structural and dynamical properties of liquid Mg. An orbital-free molecular dynamics study. J. Phys.: Condens. Matter 21, 115106 (2009).Google ScholarPubMed
González, D.J., González, L.E., López, J.M., and Stott, M.J.: Orbital free ab initio molecular dynamics study of liquid Al near melting. J. Chem. Phys. 115, 2373 (2001).CrossRefGoogle Scholar
White, T.G., Richardson, S., Crowley, B.J.B., Pattison, L.K., Harris, J.W.O., and Gregori, G.: Orbital-free density-functional theory simulations of the dynamic structure factor of warm dense aluminum. Phys. Rev. Lett. 111, 175002 (2013).CrossRefGoogle ScholarPubMed
Sjostrom, T. and Daligault, J.: Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory. Phys. Rev. E 92, 063304 (2015).CrossRefGoogle ScholarPubMed
González, L.E. and González, D.J.: Structure and dynamics of bulk liquid Ga and the liquid–vapor interface: An ab initio study. Phys. Rev. B 77, 064202 (2008).CrossRefGoogle Scholar
Delisle, A., González, D.J., and Stott, M.J.: Structural and dynamical properties of liquid Si: An orbital-free molecular dynamics study. Phys. Rev. B 73, 064202 (2006).CrossRefGoogle Scholar
Delisle, A., González, D.J., and Stott, M.J.: Pressure-induced structural and dynamical changes in liquid Si—An ab initio study. J. Phys.: Condens. Matter 18, 3591 (2006).Google Scholar
Jacucci, G., Ronchetti, M., and Schirmacher, W.: Computer simulation of the liquid Li4Pb alloy. J. Phys., Colloq. 46, C8 (1985).CrossRefGoogle Scholar
Campa, A. and Cohen, E.G.D.: Fast sound in binary fluid mixtures. Phys. Rev. A 41, 5451 (1990).CrossRefGoogle ScholarPubMed
Westerhuijs, P., Montfrooij, W., de Graaf, L.A., and de Schepper, I.M.: Fast and slow sound in a dense gas mixture of helium and neon. Phys. Rev. A 45, 3749 (1992).CrossRefGoogle Scholar
Blanco, J., González, D.J., González, L.E., López, J.M., and Stott, M.J.: Collective ionic dynamics in the liquid Na–Cs alloy: An ab initio molecular dynamics study. Phys. Rev. E 67, 041204 (2003).CrossRefGoogle ScholarPubMed
González, D.J., González, L.E., López, J.M., and Stott, M.J.: Microscopic dynamics in the liquid Li–Na alloy: An ab initio molecular dynamics study. Phys. Rev. E 69, 031205 (2004).CrossRefGoogle ScholarPubMed
Rowlinson, J.S. and Widom, B.: Molecular Theory of Capillarity (Clarendon Press, Oxford, U.K., 1982).Google Scholar
Ocko, B.M., Wu, X.Z., Sirota, E.B., Sinha, S.K., and Deutsch, M.: X-ray reflectivity study of thermal capillary waves on liquid surfaces. Phys. Rev. Lett. 72, 242 (1994).CrossRefGoogle ScholarPubMed
Regan, M.J., Kawamoto, E.H., Lee, S., Pershan, P.S., Maskil, N., Deutsch, M., Magnussen, O.M., Ocko, B.M., and Berman, L.E.: Surface layering in liquid gallium: An X-ray reflectivity study. Phys. Rev. Lett. 75, 2498 (1995).CrossRefGoogle ScholarPubMed
Regan, M.J., Pershan, P.S., Magnussen, O.M., Ocko, B.M., Deutsch, M., and Berman, L.E.: X-ray reflectivity studies of liquid metal and alloy surfaces. Phys. Rev. B 55, 15874 (1997).CrossRefGoogle Scholar
Fabricius, G., Artacho, E., Sánchez-Portal, D., Ordejón, P., Drabold, D.A., and Soler, J.M.: Atomic layering at the liquid silicon surface: A first-principles simulation. Phys. Rev. B 60, R16283 (1999).CrossRefGoogle Scholar
Walker, B.G., Marzari, N., and Molteni, C.: Ab initio studies of layering behavior of liquid sodium surfaces and interfaces. J. Chem. Phys. 124, 174702 (2006).CrossRefGoogle ScholarPubMed
González, D.J., González, L.E., and Stott, M.J.: Surface structure of liquid Li and Na: An ab initio molecular dynamics study. Phys. Rev. Lett. 92, 085501 (2004).CrossRefGoogle Scholar
González, D.J., González, L.E., and Stott, M.J.: Surface structure in simple liquid metals: An orbital-free first-principles study. Phys. Rev. B 74, 014207 (2006).CrossRefGoogle Scholar
González, D.J. and González, L.E.: 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
González, D.J., González, L.E., and Stott, M.J.: Liquid-vapor interface in liquid binary alloys: An ab initio molecular dynamics study. Phys. Rev. Lett. 94, 077801 (2005).CrossRefGoogle ScholarPubMed
González, D.J. and González, L.E.: 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).CrossRefGoogle ScholarPubMed
Jesson, B.J. and Madden, P.A.: Structure and dynamics at the aluminum solid–liquid interface: An ab initio simulation. J. Chem. Phys. 113, 5935 (2000).CrossRefGoogle Scholar
González, L.E. and González, D.J.: 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
Chokappa, D.K. and Clancy, P.: A computer simulation study of the melting and freezing properties of a system of Lennard-Jones particles. Mol. Phys. 61, 597 (1987).CrossRefGoogle Scholar
Morris, J.R., Wang, C.Z., Ho, K.M., and Chan, C.T.: Melting line of aluminum from simulations of coexisting phases. Phys. Rev. B 49, 3109 (1994).CrossRefGoogle ScholarPubMed
Belonoshko, A.B., Skorodumova, N.V., Rosengren, A., and Johansson, B.: Melting and critical superheating. Phys. Rev. B 73, 012201 (2006).CrossRefGoogle Scholar
Gregoryanz, E., Lundegaard, L.F., McMahon, M.I., Guillaume, C., Nelmes, R.J., and Mezouar, M.: Structural diversity of sodium. Science 320, 1054 (2008).CrossRefGoogle ScholarPubMed
Marqués, M., McMahon, M.I., Gregoryanz, E., Hanfland, M., Guillaume, C.L., Pickard, C.J., Ackland, G.J., and Nelmes, R.J.: Crystal structures of dense lithium: A metal-semiconductor-metal transition. Phys. Rev. Lett. 106, 095502 (2011).CrossRefGoogle ScholarPubMed
Marqués, M., González, D.J., and González, L.E.: Structure and dynamics of high-pressure Na close to the melting line: An ab initio molecular dynamics study. Phys. Rev. B 94, 024204 (2016).CrossRefGoogle Scholar
Perdew, J.P. and Constantin, L.A.: Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy. Phys. Rev. B 75, 155109 (2007).CrossRefGoogle Scholar
Śmiga, S., Fabiano, E., Constantin, L.A., and Della Sala, F.: 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).CrossRefGoogle ScholarPubMed
Tran, F. and Wesolowski, T.A.: Semilocal approximations for the kinetic energy. In Recent Progress in Orbital-Free Density Functional Theory, Wesolowski, T.A. and Wang, Y.A., eds. (World Scientific, Singapore, 2012); pp. 429–442.Google Scholar
Karasiev, V.V., Jones, R.S., Trickey, S.B., and Harris, F.E.: Properties of constraint-based single-point approximate kinetic energy functionals. Phys. Rev. B 80, 245120 (2009).CrossRefGoogle Scholar
Karasiev, V.V., Chakraborty, D., Shukruto, O.A., and Trickey, S.B.: Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations. Phys. Rev. B 88, 161108 (2013).CrossRefGoogle Scholar
Karasiev, V.V. and Trickey, S.B.: Frank discussion of the status of ground-state orbital-free DFT. In Advances in Quantum Chemistry, Sabin, J.R. and Cabrera-Trujillo, R., eds. (Academic Press, London, U.K., 2015); pp. 221–245.Google Scholar
Cancio, A.C., Stewart, D., and Kuna, A.: Visualization and analysis of the Kohn–Sham kinetic energy density and its orbital-free description in molecules. J. Chem. Phys. 144, 084107 (2016).CrossRefGoogle ScholarPubMed
Xia, J. and Carter, E.A.: Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation. Phys. Rev. B 91, 045124 (2015).CrossRefGoogle Scholar
Trickey, S.B., Karasiev, V.V., and Chakraborty, D.: Comment on “Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation”. Phys. Rev. B 92, 117101 (2015).CrossRefGoogle Scholar
Xia, J. and Carter, E.A.: 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).CrossRefGoogle Scholar
Della Sala, F., Fabiano, E., and Constantin, L.A.: 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).CrossRefGoogle Scholar
Finzel, K.: 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).CrossRefGoogle ScholarPubMed
Elliott, P., Lee, D., Cangi, A., and Burke, K.: Semiclassical origins of density functionals. Phys. Rev. Lett. 100, 256406 (2008).CrossRefGoogle ScholarPubMed
Lee, D., Constantin, L.A., Perdew, J.P., and Burke, K.: Condition on the Kohn–Sham kinetic energy and modern parametrization of the Thomas–Fermi density. J. Chem. Phys. 130, 034107 (2009).CrossRefGoogle ScholarPubMed
Constantin, L.A., Fabiano, E., Laricchia, S., and Della Sala, F.: Semiclassical neutral atom as a reference system in density functional theory. Phys. Rev. Lett. 106, 186406 (2011).CrossRefGoogle ScholarPubMed
Fabiano, E. and Constantin, L.A.: Relevance of coordinate and particle-number scaling in density-functional theory. Phys. Rev. A 87, 012511 (2013).CrossRefGoogle Scholar
Cancio, A.C. and Redd, J.J.: Visualisation and orbital-free parametrisation of the large-Z scaling of the kinetic energy density of atoms. Mol. Phys. 115, 618 (2017).CrossRefGoogle Scholar
Finzel, K.: Shell-structure-based functionals for the kinetic energy. Theor. Chem. Acc. 134, 106 (2015).CrossRefGoogle Scholar
Constantin, L.A. and Ruzsinszky, A.: Kinetic energy density functionals from the Airy gas with an application to the atomization kinetic energies of molecules. Phys. Rev. B 79, 115117 (2009).CrossRefGoogle Scholar
Lindmaa, A., Mattsson, A.E., and Armiento, R.: Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas. Phys. Rev. B 90, 075139 (2014).CrossRefGoogle Scholar
Constantin, L.A., Fabiano, E., Śmiga, S., and Della Sala, F.: Jellium-with-gap model applied to semilocal kinetic functionals. Phys. Rev. B 95, 115153 (2017).CrossRefGoogle Scholar
Constantin, L.A., Fabiano, E., and Della Sala, F.: Modified fourth-order kinetic energy gradient expansion with hartree potential-dependent coefficients. J. Chem. Theory Comput. 13, 4228 (2017).CrossRefGoogle ScholarPubMed
Ke, Y., Libisch, F., Xia, J., Wang, L-W., and Carter, E.A.: Angular-momentum-dependent orbital-free density functional theory. Phys. Rev. Lett. 111, 066402 (2013).CrossRefGoogle ScholarPubMed
Ke, Y., Libisch, F., Xia, J., and Carter, E.A.: Angular momentum dependent orbital-free density functional theory: Formulation and implementation. Phys. Rev. B 89, 155112 (2014).CrossRefGoogle Scholar