- Access by Xinjiang University
Density functional theory: Its origins, rise to prominence, and future
Rev. Mod. Phys. 87, 897 – Published 25 August, 2015
DOI: https://doi.org/10.1103/RevModPhys.87.897
Abstract
In little more than 20 years, the number of applications of the density functional (DF) formalism in chemistry and materials science has grown in an astonishing fashion. The number of publications alone shows that DF calculations make up a huge success story, and many younger colleagues are surprised to learn that the widespread application of density functional methods, particularly in chemistry, began only after 1990. This is indeed unexpected, because the origins are usually traced to the papers of Hohenberg, Kohn, and Sham more than a quarter of a century earlier. The DF formalism, its applications, and prospects were reviewed for this journal in 1989. About the same time, the combination of DF calculations with molecular dynamics promised to provide an efficient way to study structures and reactions in molecules and extended systems. This paper reviews the development of density-related methods back to the early years of quantum mechanics and follows the breakthrough in their application after 1990. The two examples from biochemistry and materials science are among the many current applications that were simply far beyond expectations in 1990. The reasons why—50 years after its modern formulation and after two decades of rapid expansion—some of the most cited practitioners in the field are concerned about its future are discussed.
Article Text
References (280)
- Akola, J., and R. O. Jones, 2007, “Structural phase transitions on the nanoscale: The crucial pattern in the phase-change materials and GeTe,” Phys. Rev. B 76, 235201.
- Akola, J., and R. O. Jones, 2008, “Density functional study of amorphous, liquid and crystalline : homopolar bonds and/or AB alternation?,” J. Phys. Condens. Matter 20, 465103.
- Allen, M. J., and D. J. Tozer, 2002, “Helium dimer dispersion forces and correlation potentials in density functional theory,” J. Chem. Phys. 117, 11113–11120.
- Almbladh, C.-O., and U. von Barth, 1985, “Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues,” Phys. Rev. B 31, 3231–3244.
- Anderson, P. W., 1980, “The Great Solid State Physics Dream Machine,” La Recherche 11, 98–102.
- Anderson, P. W., 1999, “Why do they leave physics?,” Phys. Today 52, No. 9, 11.
- Anderson, P. W., 2011, More and Different: notes from a thoughtful curmudgeon (World Scientific, Singapore).
- Anisimov, V. I., F. Aryasetiawan, and A. I. Lichtenstein, 1997, “First-principles calculations of the electronic structure and spectra of strongly correlated systems: The method,” J. Phys. Condens. Matter 9, 767–808.
- Anisimov, V. I., J. Zaanen, and O. K. Andersen, 1991, “Band theory and Mott insulators—Hubbard-U instead of Stoner-I,” Phys. Rev. B 44, 943–954.
- Aras, M., and Ç. Kiliç, 2014, “Combined hybrid functional and calculations for metal chalcogenides,” J. Chem. Phys. 141, 044106.
- Ashcroft, N. W., 1995, “Inhomogeneous fluids and the freezing transition,” in Density Functional Theory, edited by E. K. U. Gross and R. Dreizler (Plenum, New York), pp. 581–623.
- Austin, B. J., and V. Heine, 1966, “Pseudopotentials, the sizes of atoms and their s-p splittings,” J. Chem. Phys. 45, 928–933.
- Bacskay, G. B., and S. Nordholm, 2013, “Covalent bonding: the fundamental role of the kinetic energy,” J. Phys. Chem. A 117, 7946–7958.
- Bader, R. F. W., 1990, Atoms in Molecules—A Quantum Theory (Oxford University Press, Oxford).
- Barnett, R. N., and U. Landman, 1993, “Born-Oppenheimer molecular-dynamics simulations of finite systems: Structure and dynamics of ,” Phys. Rev. B 48, 2081–2097.
- Baus, M., 1990, “The present status of the density-functional theory of the liquid-solid transition,” J. Phys. Condens. Matter 2, 2111–2126.
- Becke, A. D., 1982, “Numerical Hartree-Fock-Slater calculations on diatomic molecules,” J. Chem. Phys. 76, 6037–6045.
- Becke, A. D., 1985, “Local exchange-correlation approximations and first-row molecular dissociation energies,” Int. J. Quantum Chem. 27, 585–594.
- Becke, A. D., 1988, “Density functional exchange energy approximation with correct asymptotic behavior,” Phys. Rev. A 38, 3098–3100.
- Becke, A. D., 1993, “Density functional thermochemistry. 3. The role of exact exchange,” J. Chem. Phys. 98, 5648–5652.
- Becke, A. D., 2013, “Communication: Two-determinant mixing with a strong-correlation density functional,” J. Chem. Phys. 139, 021104.
- Becke, A. D., 2014, “Perspective: Fifty years of density-functional theory in chemical physics,” J. Chem. Phys. 140, 18A301.
- Behler, J., and M. Parrinello, 2007, “Generalized neural-network representation of high-dimensional potential-energy surfaces,” Phys. Rev. Lett. 98, 146401.
- Bender, M., P. Heenen, and P. G. Reinhard, 2003, “Self-consistent mean-field models for nuclear structure,” Rev. Mod. Phys. 75, 121–180.
- Berland, K., C. A. Arter, V. R. Cooper, K. Lee, B. I. Lundqvist, E. Schröder, T. Thonhauser, and P. Hyldgaard, 2014, “Van der Waals density functionals built upon the electron-gas tradition: Facing the challenge of competing interactions,” J. Chem. Phys. 140, 18A539.
- Berlin, T., 1951, “Binding regions in diatomic molecules,” J. Chem. Phys. 19, 208–213.
- Bloch, F., 1929, “Bemerkung zur Elektronentheorie des Ferromagnetismus und der elektrischen Leitfähigkeit,” Z. Phys. 57, 545–555.
- Blöchl, P. E., C. F. J. Walther, and T. Pruschke, 2011, “Method to include explicit correlations into density-functional calculations based on density-matrix functional theory,” Phys. Rev. B 84, 205101.
- Boese, A. D., and N. C. Handy, 2001, “A new parametrization of exchange-correlation generalized gradient approximation functionals,” J. Chem. Phys. 114, 5497–5503.
- Booth, G. H., A. Grueneis, G. Kresse, and A. Alavi, 2013, “Towards an exact description of electronic wavefunctions in real solids,” Nature (London) 493, 365–370.
- Born, M., 1926a, “Zur Quantenmechanik der Stoßvorgänge,” Z. Phys. 37, 863–867.
- Born, M., 1926b, “Das Adiabatenprinzip in der Quantenmechanik,” Z. Phys. 40, 167–192.
- Born, M., and V. Fock, 1928, “Beweis des Adiabatensatzes,” Z. Phys. 51, 165–180.
- Botti, S., A. Schindlmayr, R. Del Sole, and L. Reining, 2007, “Time-dependent density-functional theory for extended systems,” Rep. Prog. Phys. 70, 357–407.
- Brillouin, L., 1934, “Le champ self-consistent de Fock pour les électrons des métaux,” J. Phys. Radium 5, 413–418.
- Brunk, E., and U. Rothlisberger, 2015, “Mixed quantum mechanical/molecular mechanical molecular dynamics simulations of biological systems in ground and electronically excited states,” Chem. Rev. 115, 6217–6263.
- Buijse, M. A., and E. J. Baerends, 2002, “An approximate exchange-correlation hole density as a functional of the natural orbitals,” Mol. Phys. 100, 401–421.
- Burke, K., 2012, “Perspective on density functional theory,” J. Chem. Phys. 136, 150901.
- Burke, K., J. Werschnik, and E. K. U. Gross, 2005, “Time-dependent density functional theory: Past, present, and future,” J. Chem. Phys. 123, 062206.
- Car, R., and M. Parrinello, 1985, “Unified approach for molecular dynamics and density functional theory,” Phys. Rev. Lett. 55, 2471–2474.
- Carloni, P., U. Röthlisberger, and M. Parrinello, 2002, “The role and perspective of ab initio molecular dynamics in the study of biological systems,” Acc. Chem. Res. 35, 455–464.
- Carlsson, B. G., J. Toivanen, and U. von Barth, 2013, “Fluctuating parts of nuclear ground-state correlation energies,” Phys. Rev. C 87, 054303.
- Ceperley, D. M., and B. J. Alder, 1980, “Ground state of the electron gas by a stochastic method,” Phys. Rev. Lett. 45, 566–569.
- Chan, G. K-L., and N. C. Handy, 1999, “Optimized Lieb-Oxford bound for the exchange-correlation energy,” Phys. Rev. A 59, 3075–3077.
- Civalleri, B., D. Presti, R. Dovesi, and A. Savin, 2012, “On choosing the best density functional approximation,” Chemical Modelling: Applications and Theory, edited by M. Springborg (Royal Society of Chemistry, London), Vol. 9, pp. 168–185 [doi:10.1039/9781849734790-00168].
- Cococcioni, M., and S. de Gironcoli, 2005, “Linear response approach to the calculation of the effective interaction parameters in the method,” Phys. Rev. B 71, 035105.
- Cohen, A. J., P. Mori-Sánchez, and W. Yang, 2008a, “Fractional charge perspective on the band gap in density-functional theory,” Phys. Rev. B 77, 115123.
- Cohen, A. J., P. Mori-Sánchez, and W. Yang, 2008b, “Insights into current limitations of density functional theory,” Science 321, 792–794.
- Colonna, F., and A. Savin, 1999, “Correlation energies for some two- and four-electron systems along the adiabatic connection in density functional theory,” J. Chem. Phys. 110, 2828–2835.
- Crick, F., 1990, What Mad Pursuit (Penguin, London).
- Curioni, A., 2013 (personal communication).
- Curtin, W. A., and N. W. Ashcroft, 1985, “Weighted density functional theory of inhomogeneous liquids and the freezing transition,” Phys. Rev. A 32, 2909–2919.
- Darwin, C., 1887, “Letter to J. D. Hooker, 1 February 1871,” in The Life and Letters of Charles Darwin, Vol. 3, edited by F. Darwin (John Murray, London), p. 18.
- Dederichs, P. H., S. Blügel, R. Zeller, and H. Akai, 1984, “Ground-states of constrained systems—application to cerium impurities,” Phys. Rev. Lett. 53, 2512–2515.
- Delle Site, L., L. M. Ghiringhelli, and D. M. Ceperley, 2013, “Electronic energy functionals: Levy-Lieb principle within the ground state path integral quantum Monte Carlo,” Int. J. Quantum Chem. 113, 155–160.
- Dion, M., H. Rydberg, E Schröder, D. C. Langreth, and B. I. Lundqvist, 2004, “Van der Waals density functional for general geometries,” Phys. Rev. Lett. 92, 246401.
- Dirac, P. A. M., 1929a, “Quantum mechanics of many-electron systems,” Proc. R. Soc. A 123, 714–733.
- Dirac, P. A. M., 1929b, “The basis of statistical quantum mechanics,” Math. Proc. Cambridge Philos. Soc. 25, 62–66.
- Dirac, P. A. M., 1930a, “Note on exchange phenomena in the Thomas atom,” Math. Proc. Cambridge Philos. Soc. 26, 376–385.
- Dirac, P. A. M., 1930b, “On the annihilation of electrons and protons,” Math. Proc. Cambridge Philos. Soc. 26, 361–375.
- DiStasio, Jr., R. A., V. V. Gobre, and A. Tkatchenko, 2014, “Many-body van der Waals interactions in molecules and condensed matter,” J. Phys. Condens. Matter 26, 213202.
- Dobson, J. F., and B. P. Dinte, 1996, “Constraint Satisfaction in Local and Gradient Susceptibility Approximations: Application to a van der Waals Density Functional,” Phys. Rev. Lett. 76, 1780–1783.
- Dobson, J. F., and T. Gould, 2012, “Calculation of dispersion energies,” J. Phys. Condens. Matter 24, 073201.
- Dobson, J. F., and J. Wang, 1999, “Successful test of a seamless van der Waals density functional,” Phys. Rev. Lett. 82, 2123–2126.
- Dreizler, R. M., and E. K. U. Gross, 1990, Density Functional Theory (Springer, Berlin/Heidelberg).
- Drut, J. E., R. J. Furnstahl, and L. Platter, 2010, “Toward ab initio density functional theory for nuclei,” Prog. Part. Nucl. Phys. 64, 120–168.
- Drut, J. E., and L. Platter, 2011, “Exact-exchange density functional theory for neutron drops,” Phys. Rev. C 84, 014318.
- Dunlap, B. I., J. W. D. Connolly, and J. R. Sabin, 1979a, “First-row diatomic molecules and local density models,” J. Chem. Phys. 71, 4993–4999.
- Dunlap, B. I., J. W. D. Connolly, and J. R. Sabin, 1979b, “Some approximations in applications of theory,” J. Chem. Phys. 71, 3396–3402.
- Ehrenfest, P., 1916, “Adiabatische Invarianten und Quantentheorie,” Ann. Phys. (Leipzig) 356, 327–352.
- Ehrenfest, P., 1927, “Bemerkung über die angenäherte Gültigkeit der klassischen Mechanik innerhalb der Quantenmechanik,” Z. Phys. 45, 455–457.
- Erler, J., N. Birge, M. Kortelainen, W. Nazarewicz, E. Olsen, A. M. Perhac, and M. Stoitsov, 2012, “The limits of the nuclear landscape,” Nature (London) 486, 509–512.
- Ernzerhof, M., 1996, “Construction of the adiabatic connection,” Chem. Phys. Lett. 263, 499–506.
- Eshuis, H., J. E. Bates, and F. Furche, 2012, “Electron correlation methods based on the random phase approximation,” Theor. Chem. Acc. 131, 1084.
- Evans, R., 1979, “The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids,” Adv. Phys. 28, 143–200.
- Evans, R., 1992, “Density functionals in the theory of nonuniform fluids,” in Fundamentals of Inhomogeneous Liquids, edited by D. Henderson (Marcel Dekker, New York), pp. 85–175.
- Farmelo, G., 2009, The Strangest Man. The Hidden Life of Paul Dirac, Quantum Genius (Faber and Faber, London).
- Fermi, E., 1927, “Un metodo statistico per la determinazione di alcune prioprietà dell’atomo,” Rend. Accad. Naz. Lincei 6, 602–607.
- Fermi, E., 1928, “Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente,” Z. Phys. 48, 73–79.
- Feynman, R. P., 1939, “Forces in molecules,” Phys. Rev. 56, 340–343.
- Fock, V., 1930, “Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems,” Z. Phys. 61, 126–148.
- Frost, A. A., 1967, “Floating spherical Gaussian orbital model of molecular structure,” J. Chem. Phys. 47, 3707–3713.
- Furche, F., and J. P. Perdew, 2006, “The performance of semilocal and hybrid density functionals in 3d transition-metal chemistry,” J. Chem. Phys. 124, 044103.
- Gáspár, R., 1954, “Über eine Approximation des Hartree-Fock’schen Potentials durch eine universelle Potentialfunktion,” Acta Phys. Hung. 3, 263–286.
- Georges, A., G. Kotliar, W. Krauth, and M. J. Rozenberg, 1996, “Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions,” Rev. Mod. Phys. 68, 13–125.
- Giesbertz, K. J. H., R. van Leeuwen, and U. von Barth, 2013, “Towards nonlocal density functionals by explicit modeling of the exchange-correlation hole in inhomogeneous systems,” Phys. Rev. A 87, 022514.
- Gilbert, T. L., 1975, “Hohenberg-Kohn theorem for nonlocal external potentials,” Phys. Rev. B 12, 2111–2120.
- Gill, P. M. W., 2001, “Obituary: density functional theory (1927-1993),” Aust. J. Chem. 54, 661–662.
- Gill, P. M. W., B. G. Johnson, J. A. Pople, and M. J. Frisch, 1992, “An investigation of the performance of a hybrid of Hartree-Fock and density functional theory,” Int. J. Quantum Chem., Quantum Chem. Symp., Vol. 44, Issue S26, pp. 319–331.
- Gori-Giorgi, P., M. Seidl, and G. Vignale, 2009, “Density-functional theory for strongly interacting electrons,” Phys. Rev. Lett. 103, 166402.
- Görling, A., and M. Levy, 1997, “Hybrid schemes combining the Hartree-Fock method and density-functional theory: Underlying formalism and properties of correlation functionals,” J. Chem. Phys. 106, 2675–2680.
- Grimme, S., 2006, “Semiempirical GGA-type density functional constructed with a long-range dispersion correction,” J. Comput. Chem. 27, 1787–1799.
- Grimme, S., J. Antony, S. Ehrlich, and H. Krieg, 2010, “A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu,” J. Chem. Phys. 132, 154104.
- Gritsenko, O., K. Pernal, and E. J. Baerends, 2005, “An improved density matrix functional by physically motivated repulsive corrections,” J. Chem. Phys. 122, 204102.
- Gritsenko, O. V., P. R. T. Schipper, and E. J. Baerends, 1997, “Exchange and correlation energy in density functional theory: Comparison of accurate density functional theory quantities with traditional Hartree-Fock based ones and generalized gradient approximations for the molecules , , ,” J. Chem. Phys. 107, 5007–5015.
- Guerra, F., and N. Robotti, 2008, “Ettore Majorana’s forgotten publication on the Thomas-Fermi model,” Phys. Perspect. 10, 56–76.
- Gunnarsson, O., J. Harris, and R. O. Jones, 1977, “Muffin-tin orbitals and the total energy of atomic clusters,” Phys. Rev. B 15, 3027–3038.
- Gunnarsson, O., and P. Johansson, 1976, “Spin-density functional formalism for quantum-mechanical calculations—Test on diatomic molecules with an efficient numerical method,” Int. J. Quantum Chem. 10, 307–323.
- Gunnarsson, O., and R. O. Jones, 1980, “Density functional calculations for atoms, molecules, and clusters,” Phys. Scr. 21, 394–401.
- Gunnarsson, O., and R. O. Jones, 1981, “Self-interaction corrections in the density functional formalism,” Solid State Commun. 37, 249–252.
- Gunnarsson, O., and R. O. Jones, 1985, “Total energy differences—sources of error in local-density approximations,” Phys. Rev. B 31, 7588–7602.
- Gunnarsson, O., M. Jonson, and B. I. Lundqvist, 1979, “Descriptions of exchange and correlation effects in inhomogeneous electron systems,” Phys. Rev. B 20, 3136–3164.
- Gunnarsson, O., and B. I. Lundqvist, 1976, “Exchange and correlation in atoms, molecules, and solids by spin-density functional formalism,” Phys. Rev. B 13, 4274–4298.
- Güttinger, P., 1931, “Das Verhalten von Atomen im magnetischen Drehfeld,” Z. Phys. 73, 169–184.
- Handy, N. C., 2002, “Understanding electron correlation,” Abstract, 223rd National Meeting of the American Chemical Society, Orlando, FL.
- Handy, N. C., 2009, “The importance of Colle-Salvetti for computational density functional theory,” Theor. Chem. Acc. 123, 165–169.
- Harriman, J. E., 1981, “Orthonormal orbitals for the representation of an arbitrary density,” Phys. Rev. A 24, 680–682.
- Harris, J., 1984, “Adiabatic-connection approach to Kohn-Sham theory,” Phys. Rev. A 29, 1648–1659.
- Harris, J., 1985, “Simplified method for calculating the energy of weakly interacting fragments,” Phys. Rev. B 31, 1770–1779.
- Harris, J., and R. O. Jones, 1974, “Surface energy of a bounded electron gas,” J. Phys. F 4, 1170–1186.
- Harris, J., and R. O. Jones, 1979a, “Bonding trends in the group-IV A dimers ,” Phys. Rev. A 19, 1813–1818.
- Harris, J., and R. O. Jones, 1979b, “Density functional theory and molecular binding. 3. Iron-series dimers,” J. Chem. Phys. 70, 830–841.
- Hartree, D. R., 1928a, “The wave mechanics of an atom with a non-Coulomb central field. Part I. Theory and methods,” Math. Proc. Cambridge Philos. Soc. 24, 89–110.
- Hartree, D. R., 1928b, “The wave mechanics of an atom with a non-Coulomb central field. Part II. Some results and discussion,” Math. Proc. Cambridge Philos. Soc. 24, 111–132.
- Hasnip, P. J., K. Refson, M. I. J. Probert, J. R. Yates, S. J. Clark, and C. J. Pickard, 2014, “Density functional theory in the solid state,” Phil. Trans. R. Soc. A 372, 20130270.
- Hayes, E. F., and R. G. Parr, 1965, “Time-dependent Hellmann-Feynman theorems,” J. Chem. Phys. 43, 1831–1832.
- Haymet, A. D. J., and D. W. Oxtoby, 1981, “A molecular theory for the solid-liquid interface,” J. Chem. Phys. 74, 2559–2565.
- Heijser, W., A. T. van Kessel, and E. J. Baerends, 1976, “Self-consistent molecular Hartree-Fock-Slater calculations IV. Electron densities, spectroscopic constants, and proton affinities of some small molecules,” Chem. Phys. 16, 371–379.
- Heine, V., 2002, “European collaboration in ab-initio computer simulations,” Newsletter, Ab initio (from Electronic Structure), Calculations of Complex Processes in Materials 50, 7–19 [http://www.psi-k.net/download/newsletters/newsletter_50.pdf].
- Hellmann, H., 1933, “Zur Rolle der kinetischen Energie für die zwischenatomaren Kräfte,” Z. Phys. 85, 180–190.
- Hellmann, H., 1937, Einführung in die Quantenchemie (Deuticke, Leipzig, Wien), Chap. 8.
- Herman, F., J. P. Van Dyke, and I. B. Ortenburger, 1969, “Improved statistical exchange approximation for inhomogeneous many-electron systems,” Phys. Rev. Lett. 22, 807–811.
- Heyd, J., G. E. Scuseria, and M. Ernzerhof, 2003, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118, 8207–8215.
- Hoffmann, R., 1977 (personal communication).
- Hohenberg, P., and W. Kohn, 1964, “Inhomogeneous Electron Gas,” Phys. Rev. B 136, B864–B871.
- Hurley, A. C., 1954a, “The electrostatic calculation of molecular energies. I. Methods of calculating molecular energies,” Proc. R. Soc. A 226, 170–178.
- Hurley, A. C., 1954b, “The electrostatic calculation of molecular energies. II. Approximate wave functions and the electrostatic method,” Proc. R. Soc. A 226, 179–192.
- Hurley, A. C., 1954c, “The electrostatic calculation of molecular energies. III. The binding energies of saturated molecules,” Proc. R. Soc. A 226, 193–205.
- Imada, M., A. Fujimori, and Y. Tokura, 1998, “Metal-insulator transitions,” Rev. Mod. Phys. 70, 1039–1263.
- Isegawa, M., R. Peverati, and D. G. Truhlar, 2012, “Performance of recent and high-performance approximate density functionals for time-dependent density functional theory calculations of valence and Rydberg electronic transition energies,” J. Chem. Phys. 137, 244104.
- Johnson, B. G., P. M. W. Gill, and J. A. Pople, 1992, “Preliminary results on the performance of a family of density functional methods,” J. Chem. Phys. 97, 7846–7848.
- Johnson, B. G., P. M. W. Gill, and J. A. Pople, 1993, “The performance of a family of density functional methods,” J. Chem. Phys. 98, 5612–5626.
- Johnson, M., and S. Nordholm, 1981, “Generalized van der Waals theory. 6. Application to adsorption,” J. Chem. Phys. 75, 1953–1957.
- Jones, R. O., 1979, “Molecular bonding in group IIA dimers ,” J. Chem. Phys. 71, 1300–1308.
- Jones, R. O., 1983, “Density functional calculations for low-lying states of ,” J. Chem. Phys. 79, 1885–1890.
- Jones, R. O., 1984a, “Das Dichtefunktional—die Methode zur Berechnung von Bindungseigenschaften?,” Phys. Bl. 40, 149–152.
- Jones, R. O., 1984b, “Density functional calculations for ozone—striking results for an important molecule,” Phys. Rev. Lett. 52, 2002–2005.
- Jones, R. O., 1985, “Energy surfaces of low-lying states of and ,” J. Chem. Phys. 82, 325–332.
- Jones, R. O., 1991, “Molecular structures from density functional calculations with simulated annealing,” Angew. Chem., Int. Ed. Engl. 30, 630–640.
- Jones, R. O., 2012, “Density Functional Theory: A Personal View,” in Strongly Correlated Systems. Theoretical Methods, edited by A. Avella and F. Mancini (Springer, Berlin/Heidelberg), Chap. 1, pp. 1–28 [DOI:10.1007/978-3-642-21831-6_1].
- Jones, R. O., and O. Gunnarsson, 1989, “The density functional formalism, its applications and prospects,” Rev. Mod. Phys. 61, 689–746.
- Jones, R. O., and D. Hohl, 1990, “Structure of phosphorus clusters using simulated annealing— to ,” J. Chem. Phys. 92, 6710–6721.
- Kaduk, B., T. Kowalczyk, and T. Van Voorhis, 2012, “Constrained Density Functional Theory,” Chem. Rev. 112, 321–370.
- Kalikka, J., J. Akola, and R. O. Jones, 2014, “Simulation of crystallization in : A memory effect in the canonical phase-change material,” Phys. Rev. B 90, 184109.
- Kalikka, J., J. Akola, J. Larrucea, and R. O. Jones, 2012, “Nucleus-driven crystallization of amorphous : A density functional study,” Phys. Rev. B 86, 144113.
- Karasiev, V. V., T. Sjostrom, J. Dufty, and S. B. Trickey, 2014, “Accurate homogeneous electron gas exchange-correlation free energy for local spin-density calculations,” Phys. Rev. Lett. 112, 076403.
- Karasiev, V. V., T. Sjostrom, and S. B. Trickey, 2014, “Finite-temperature orbital-free DFT molecular dynamics: Coupling PROFESS and QUANTUM ESPRESSO,” Comput. Phys. Commun. 185, 3240–3249.
- Kato, T., 1957, “On the eigenfunctions of many-particle systems in quantum mechanics,” Commun. Pure Appl. Math. 10, 151–177.
- Klimeš, J., and A. Michaelides, 2012, “Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory,” J. Chem. Phys. 137, 120901.
- Klüpfel, P., P.-G. Reinhard, T. J. Bürvenich, and J. A. Maruhn, 2009, “Variations on a theme by Skyrme: A systematic study of adjustments of model parameters,” Phys. Rev. C 79, 034310.
- Kohn, W., 1971, in Electronic Density of States. Nat. Bur. Stand. (U.S.), Spec. Publ. 323, edited by L. H. Bennett (U.S. Government Printing Office, Washington, D.C.), p. 249.
- Kohn, W., 1999, “Nobel Lecture: Electronic structure of matter—wave functions and density functionals,” Rev. Mod. Phys. 71, 1253–1266.
- Kohn, W., and N. Rostoker, 1954, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111–1120.
- Kohn, W., and L. J. Sham, 1965, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133–A1138.
- Kohn, W., and C. D. Sherrill, 2014, “Editorial: Reflections on fifty years of density functional theory,” J. Chem. Phys. 140, 18A201.
- Korringa, J., 1947, “On the calculation of the energy of a Bloch wave in a metal,” Physica (Utrecht) 13, 392–400.
- Kortelainen, M., T. Lesinski, J. More, W. Nazarewicz, J. Sarich, N. Schunck, M. V. Stoitsov, and S. Wild, 2010, “Nuclear energy density optimization,” Phys. Rev. C 82, 024313.
- Kotliar, G., and D. Vollhardt, 2004, “Strongly correlated materials: Insights from dynamical mean-field theory,” Phys. Today 57, No. 3, 53–59.
- Krieger, J. B., Y. Li, and G. J. Iafrate, 1992, “Systematic approximations to the optimized effective potential—application to orbital density functional theory,” Phys. Rev. A 46, 5453–5458.
- Kümmel, S., and L. Kronik, 2008, “Orbital-dependent density functionals: Theory and applications,” Rev. Mod. Phys. 80, 3–60.
- Kutzelnigg, W., 1973, “The Physical Mechanism of the Chemical Bond,” Angew. Chem., Int. Ed. Engl. 12, 546–562.
- Kutzelnigg, W., 2006, “Density functional theory in terms of a Legendre transformation for beginners,” J. Mol. Struct. Theochem 768, 163–173.
- Kutzelnigg, W., and W. H. E. Schwarz, 1982, “Formation of the chemical bond and orbital contraction,” Phys. Rev. A 26, 2361–2367.
- Lang, N. D., and W. Kohn, 1970, “Theory of metal surfaces: Charge density and surface energy,” Phys. Rev. B 1, 4555–4568.
- Langreth, D. C., and J. P. Perdew, 1975, “Exchange-correlation energy of a metallic surface,” Solid State Commun. 17, 1425–1429.
- Langreth, D. C., and J. P. Perdew, 1977, “Exchange-correlation energy of a metallic surface: Wave-vector analysis,” Phys. Rev. B 15, 2884–2901.
- Langreth, D. C., and J. P. Perdew, 1980, “Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works,” Phys. Rev. B 21, 5469–5493.
- Lee, C., W. Yang, and R. G. Parr, 1988, “Development of the Colle-Salvetti correlation energy formula into a functional of the electron density,” Phys. Rev. B 37, 785–789.
- Levy, M., 1979, “Universal variational functionals of electron densities, 1st-order density matrices, and natural spin-orbitals and solution of the V-representability problem,” Proc. Natl. Acad. Sci. U.S.A. 76, 6062–6065.
- Levy, M., 1982, “Electron densities in search of Hamiltonians,” Phys. Rev. A 26, 1200–1208.
- Levy, M., 1991, “Density-functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole,” Phys. Rev. A 43, 4637–4646.
- Levy, M., and J. P. Perdew, 1985, “Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms,” Phys. Rev. A 32, 2010–2021.
- Levy, M., J. P. Perdew, and V. Sahni, 1984, “Exact differential equation for the density and ionization energy of a many-particle system,” Phys. Rev. A 30, 2745–2748.
- Li, Z., J. R. Kermode, and A. De Vita, 2015, “Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces,” Phys. Rev. Lett. 114, 096405.
- Lieb, E. H., 1981, “Thomas-Fermi and related theories of atoms and molecules,” Rev. Mod. Phys. 53, 603–641.
- Lieb, E. H., 1983, “Density functionals for Coulomb systems,” Int. J. Quantum Chem. 24, 243–277.
- Lieb, E. H., and S. Oxford, 1981, “Improved lower bound on the indirect Coulomb energy,” Int. J. Quantum Chem. 19, 427–439.
- Lieb, E. H., and B. Simon, 1973, “Thomas-Fermi theory revisited,” Phys. Rev. Lett. 31, 681–683.
- Lin, H., and D. G. Truhlar, 2007, “QM/MM: what have we learned, where are we, and where do we go from here?” Theor. Chem. Acc. 117, 185–199.
- Ma, S.-K., and K. A. Brueckner, 1968, “Correlation energy of an electron gas with a slowly varying high density,” Phys. Rev. 165, 18–31.
- Mahan, G. D., 1980, “Modified Sternheimer equation for polarizability,” Phys. Rev. A 22, 1780–1785.
- Marques, M. A. L., C. A. Ullrich, F. Noguiera, A. Rubio, K. Burke, and E. K. U. Gross, 2006, Eds., Time-Dependent Density Functional Theory, Lecture Notes in Physics Vol. 706 (Springer, Berlin/Heidelberg).
- Mavropoulos, P., 2015 (personal communication).
- Mermin, N. D., 1965, “Thermal properties of inhomogeneous electron gas,” Phys. Rev. 137, A1441–A1443.
- Montanari, B., P. Ballone, and R. O. Jones, 1998, “Density functional study of molecular crystals: Polyethylene and a crystalline analog of bisphenol-A polycarbonate,” J. Chem. Phys. 108, 6947–6951.
- Montanari, B., and R. O. Jones, 1997, “Density functional study of crystalline polyethylene,” Chem. Phys. Lett. 272, 347–352.
- Mori-Sánchez, P., A. J. Cohen, and W. Yang, 2006, “Many-electron self-interaction error in approximate density functionals,” J. Chem. Phys. 125, 201102.
- Mott, N. F., 1968, “Metal-insulator transition,” Rev. Mod. Phys. 40, 677–682.
- Müller, A. M. K., 1984, “Explicit approximate relation between reduced 2-particle and one-particle density matrices,” Phys. Lett. 105A, 446–452.
- Müller, J. E., R. O. Jones, and J. Harris, 1983, “Density functional calculations for , , and using localized muffin-tin orbitals,” J. Chem. Phys. 79, 1874–1884.
- Musher, J. I., 1966, “Comment on some theorems of quantum chemistry,” Am. J. Phys. 34, 267–268.
- Nair, N. N., E. Schreiner, and D. Marx, 2008, “Peptide synthesis in aqueous environments: the role of extreme conditions on amino acid activation,” J. Am. Chem. Soc. 130, 14148–14160.
- Nordholm, S., 1987, “Analysis of covalent bonding by nonergodic Thomas-Fermi theory,” J. Chem. Phys. 86, 363–369.
- Nordholm, S., and A. D. J. Haymet, 1980, “Generalized van der Waals theory. 1. Basic formulation and application to uniform fluids,” Aus. J. Chem. 33, 2013–2027.
- Odashima, M. M., and K. Capelle, 2007, “How tight is the Lieb-Oxford bound?” J. Chem. Phys. 127, 054106.
- Painter, G. S., and F. W. Averill, 1982, “Bonding in the first-row diatomic molecules within the local spin-density approximation,” Phys. Rev. B 26, 1781–1790.
- Parr, R. G., 1983, “Density functional theory,” Annu. Rev. Phys. Chem. 34, 631–656.
- Parr, R. G., and W. Yang, 1989, Density-functional theory of atoms and molecules (Oxford, New York).
- Pauli, W., 1933, “Die allgemeinen Prinzipien der Wellenmechanik,” in Handbuch der Physik, 2. Auflage, Band 24.1, edited by A. Smekal (Springer, Berlin), Chap. 2, pp. 83–272.
- Percus, J. K., 1978, “Role of model systems in few-body reduction of n-Fermion problem,” Int. J. Quantum Chem. 13, 89–124.
- Perdew, J. P., 1985, “Accurate density functional for the energy: Real-space cutoff of the gradient expansion for the exchange hole,” Phys. Rev. Lett. 55, 1665–1668.
- Perdew, J. P., 1986, “Density functional approximation for the correlation energy of the inhomogeneous electron gas,” Phys. Rev. B 33, 8822–8824.
- Perdew, J. P., K. Burke, and M. Ernzerhof, 1996, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868.
- Perdew, J. P., and M. Levy, 1983, “Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities,” Phys. Rev. Lett. 51, 1884–1887.
- Perdew, J. P., R. G. Parr, M. Levy, and J. L. Balduz, Jr., 1982, “Density-functional theory for fractional particle number: Derivative discontinuities of the energy,” Phys. Rev. Lett. 49, 1691–1694.
- Perdew, J. P., and Y. Wang, 1986, “Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation,” Phys. Rev. B 33, 8800–8802.
- Perdew, J. P., and A. Zunger, 1981, “Self-interaction correction to density-functional approximations for many-electron systems,” Phys. Rev. B 23, 5048–5079.
- Peverati, R., and D. G. Truhlar, 2012, “Screened-exchange density functionals with broad accuracy for chemistry and solid-state physics,” Phys. Chem. Chem. Phys. 14, 16187–16191.
- Post, D., and E. J. Baerends, 1982, “On the Hartree-Fock and descriptions of small copper cluster electronic structures,” Chem. Phys. Lett. 86, 176–180.
- Pupyshev, V. I., 2000, “The nontriviality of the Hellmann-Feynman theorem,” Russ. J. Phys. Chem. 74, Suppl. 2, S267–S278.
- Rajagopal, A. K., and J. Callaway, 1973, “Inhomogeneous Electron Gas,” Phys. Rev. B 7, 1912–1919.
- Rapcewicz, K., and N. W. Ashcroft, 1991, “Fluctuation attraction in condensed matter: A nonlocal functional approach,” Phys. Rev. B 44, 4032–4035.
- Rellich, F., 1937a, “Störungstheorie der Spektralzerlegung. I. Mitteilung. Analytische Störung der isolierten Punkteigenwerte eines beschränkten Operators,” Math. Ann. 113, 600–619.
- Rellich, F., 1937b, “Störungstheorie der Spektralzerlegung. II. Mitteilung. Stetige Abhängigkeit der Spektralschar von einem Parameter,” Math. Ann. 113, 677–685.
- Rellich, F., 1941, “Störungstheorie der Spektralzerlegung. V.,” Math. Ann. 118, 462–484.
- Ren, X., P. Rinke, C. Joas, and M. Scheffler, 2012, “Random-phase approximation and its applications in computational chemistry and materials science,” J. Mater. Sci. 47, 7447–7471.
- Rohr, D. R., J. Toulouse, and K. Pernal, 2010, “Combining density-functional theory and density-matrix-functional theory,” Phys. Rev. A 82, 052502.
- Ruedenberg, K., 1962, “The physical nature of the chemical bond,” Rev. Mod. Phys. 34, 326–376.
- Runge, E., and E. K. U. Gross, 1984, “Density functional theory for time-dependent systems,” Phys. Rev. Lett. 52, 997–1000.
- Savin, A., 2014, “Towards a systematic way to correct density functional approximations,” J. Chem. Phys. 140, 18A509.
- Savin, A., F. Colonna, and J.-M. Teuler, 1998, “Adiabatic coupling in the helium and the beryllium series,” in Electronic Density Functional Theory: Recent Progress and New Directions, edited by J. F. Dobson, G. Vignale, and M. P. Das (Plenum, New York), pp. 69–80.
- Schipper, P. R. T., O. V. Gritsenko, S. J. A. van Gisbergen, and E. J. Baerends, 2000, “Molecular calculations of excitation energies and (hyper)polarizabilities with a statistical average of orbital model exchange-correlation potentials,” J. Chem. Phys. 112, 1344–1352.
- Schreiner, E., N. N. Nair, and D. Marx, 2008, “Influence of extreme thermodynamic conditions and pyrite surfaces on peptide synthesis in aqueous media,” J. Am. Chem. Soc. 130, 2768–2770.
- Schreiner, E., N. N. Nair, C. Wittekindt, and D. Marx, 2011, “Peptide synthesis in aqueous environments: the role of extreme conditions and pyrite mineral surfaces on formation and hydrolysis of peptides,” J. Am. Chem. Soc. 133, 8216–8226.
- Schrödinger, E., 1926a, “Quantisierung als Eigenwertproblem (Dritte Mitteilung),” Ann. Phys. (Leipzig) 385, 437–490.
- Schrödinger, E., 1926b, “Quantisierung als Eigenwertproblem (Vierte Mitteilung),” Ann. Phys. (Leipzig) 386, 109–139.
- Schwinger, J., 1980, “Thomas-Fermi model—the leading correction,” Phys. Rev. A 22, 1827–1832.
- Segrè, G., 2007, Faust in Copenhagen: A struggle for the soul of physics (Jonathan Cape, London).
- Sham, L. J., and M. Schlüter, 1983, “Density-functional theory of the energy gap,” Phys. Rev. Lett. 51, 1888–1891.
- Sharma, S., J. K. Dewhurst, N. N. Lathiotakis, and E. K. U. Gross, 2008, “Reduced density matrix functional for many-electron systems,” Phys. Rev. B 78, 201103.
- Sharp, R. T., and G. K. Horton, 1953, “A variational approach to the unipotential many-electron problem,” Phys. Rev. 90, 317.
- Shepherd, J. J., G. H. Booth, and A. Alavi, 2012, “Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models,” J. Chem. Phys. 136, 244101.
- Skyrme, T. H. R., 1956, “The nuclear surface,” Philos. Mag. 1, 1043–1054.
- Skyrme, T. H. R., 1959, “The effective nuclear potential,” Nucl. Phys. 9, 615–634.
- Slater, J. C., 1929, “The theory of complex spectra,” Phys. Rev. 34, 1293–1322.
- Slater, J. C., 1930, “Note on Hartree’s method,” Phys. Rev. 35, 210–211.
- Slater, J. C., 1934, “The electronic structure of metals,” Rev. Mod. Phys. 6, 209–280.
- Slater, J. C., 1937, “Wave functions in a periodic potential,” Phys. Rev. 51, 846–851.
- Slater, J. C., 1951, “A simplification of the Hartree-Fock method,” Phys. Rev. 81, 385–390.
- Slater, J. C., 1968, “Exchange in spin-polarized energy bands,” Phys. Rev. 165, 658–669.
- Slater, J. C., 1972a, “The Self-consistent Field for Molecules and Solids,” Quantum Theory of Molecules and Solids, Vol. 4 (McGraw-Hill, New York).
- Slater, J. C., 1972b, “Statistical exchange-correlation in the self-consistent field,” Adv. Quantum Chem. 6, 1–92.
- Slater, J. C., 1974, “The History of the Method,” in The World of Quantum Chemistry, edited by R. Daudel and B. Pullman (Reidel, Dordrecht), pp. 3–15.
- Smith, R. F., et al., 2014, “Ramp compression of diamond to five terapascals,” Nature (London) 511, 330–333.
- Snyder, J. C., M. Rupp, K. Hansen, K.-R. Müller, and K. Burke, 2012, “Finding density functionals with machine learning,” Phys. Rev. Lett. 108, 253002.
- Spruch, L., 1991, “Pedagogic notes on Thomas-Fermi theory (and on some improvements)—atoms, stars, and the stability of bulk matter,” Rev. Mod. Phys. 63, 151–209.
- Stott, M. J., and E. Zaremba, 1980, “Linear-response theory within the density-functional formalism: Application to atomic polarizabilities,” Phys. Rev. A 21, 12–23.
- Strømsheim, M. D., N. Kumar, S. Coriani, A. M. Sagvolden, and T. Helgaker, 2011, “Dispersion interactions in density-functional theory: An adiabatic-connection analysis,” J. Chem. Phys. 135, 194109.
- Talman, J. D., and W. F. Shadwick, 1976, “Optimized effective atomic central potentials,” Phys. Rev. A 14, 36–40.
- Tao, J. M., J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, 2003, “Climbing the density functional ladder: Nonempirical meta-generalized gradient approximation designed for molecules and solids,” Phys. Rev. Lett. 91, 146401.
- Tarazona, P., 1984, “A density functional theory of melting,” Mol. Phys. 52, 81–96.
- Teale, A. M., S. Coriani, and T. Helgaker, 2010, “Accurate calculation and modeling of the adiabatic connection in density functional theory,” J. Chem. Phys. 132, 164115.
- Teare, P. W., 1959, “The crystal structure of orthorhombic hexatriacontane ,” Acta Crystallogr. 12, 294–300.
- Teller, E., 1962, “On stability of molecules in Thomas-Fermi theory,” Rev. Mod. Phys. 34, 627–631.
- ter Haar, D., 1960, “On the density matrices used in Hartree-Fock calculations,” Physica (Utrecht) 26, 1041–1044.
- Thomas, L. H., 1927, “The calculation of atomic fields,” Proc. Cambridge Philos. Soc. 23, 542–548.
- Tkatchenko, A., A. Ambrosetti, and R. A. DiStasio, Jr., 2013, “Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem,” J. Chem. Phys. 138, 074106.
- Tkatchenko, A., and M. Scheffler, 2009, “Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data,” Phys. Rev. Lett. 102, 073005.
- Tong, B. Y., and L. J. Sham, 1966, “Application of a self-consistent scheme including exchange and correlation effects to atoms,” Phys. Rev. 144, 1–4.
- Toulouse, J., I. C. Gerber, G. Jansen, A. Savin, and J. G. Ángyán, 2009, “Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation,” Phys. Rev. Lett. 102, 096404.
- Trickey, S. B., F. R. Green, and F. W. Averill, 1973, “One-Electron Theory of the Bulk Properties of Crystalline Ar, Kr, and Xe,” Phys. Rev. B 8, 4822–4832.
- van Leeuwen, R., and E. J. Baerends, 1994, “Exchange-correlation potential with correct asymptotic behavior,” Phys. Rev. A 49, 2421–2431.
- van Meer, R., O. V. Gritsenko, and E. J. Baerends, 2014, “Physical meaning of virtual Kohn-Sham orbitals and orbital energies: an ideal basis for the description of molecular excitations,” J. Chem. Theory Comput. 10, 4432–4441.
- Vignale, G., and M. Rasolt, 1988, “Current density functional and spin density functional theory for inhomogeneous electronic systems in strong magnetic fields,” Phys. Rev. B 37, 10685–10696.
- von Barth, U., and L. Hedin, 1972, “Local exchange-correlation potential for spin-polarized case: I,” J. Phys. C 5, 1629–1642.
- Vydrov, O. A., and T. Van Voorhis, 2009, “Nonlocal van der Waals density functional made simple,” Phys. Rev. Lett. 103, 063004.
- Wächtershäuser, G., 1988, “Before enzymes and templates—Theory of surface metabolism,” Microbiol. Rev. 52, 452–484.
- Wigner, E., 1934, “On the interaction of electrons in metals,” Phys. Rev. 46, 1002–1011.
- Wigner, E., and F. Seitz, 1933, “On the constitution of metallic sodium,” Phys. Rev. 43, 804–810.
- Wigner, E., and F. Seitz, 1934, “On the constitution of metallic sodium. II,” Phys. Rev. 46, 509–524.
- Wilson, E. B., 1962, “Four-Dimensional Electron Density Function,” J. Chem. Phys. 36, 2232–2233.
- Wood, B., N. D. M. Hine, W. M. C. Foulkes, and P. García-González, 2007, “Quantum Monte Carlo calculations of the surface energy of an electron gas,” Phys. Rev. B 76, 035403.
- Wu, J., and Z. Li, 2007, “Density functional theory for complex fluids,” Annu. Rev. Phys. Chem. 58, 85–112.
- Xiao, B., J. Sun, A. Ruzsinszky, J. Feng, R. Haunschild, G. E. Scuseria, and J. P. Perdew, 2013, “Testing density functionals for structural phase transitions of solids under pressure: Si, , and Zr,” Phys. Rev. B 88, 184103.
- Yang, W., 2014, “Preface: Special Topic on Advances in Density Functional Theory,” J. Chem. Phys. 140, 18A101.
- Zangwill, A., 2013, “Hartree and Thomas: the forefathers of density functional theory,” Arch. Hist. Exact Sci. 67, 331–348.
- Zangwill, A., 2014, “The education of Walter Kohn and the creation of density functional theory,” Arch. Hist. Exact Sci. 68, 775–848.
- Zangwill, A., and P. Soven, 1980, “Density-functional approach to local-field effects in finite systems: Photoabsorption in the rare gases,” Phys. Rev. A 21, 1561–1572.
- Zeller, R., 2008, “Linear-scaling total energy calculations with the tight-binding Korringa-Kohn-Rostoker Green function method,” Philos. Mag. 88, 2807–2815.
- Zhao, Y., and D. G. Truhlar, 2008, “Density functionals with broad applicability in chemistry,” Acc. Chem. Res. 41, 157–167.