## Main.DFTBackground History

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Changed line 39 from:

# Plane wave ~~calculations~~

to:

# Plane wave calculations and related techniques

Added lines 42-44:

** S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, “Phonons and related crystal properties from density-functional perturbation theory,” [[ http://dx.doi.org/10.1103/RevModPhys.73.515 | Rev. Mod. Phys., vol. 73, no. 2, p. 515, Jul. 2001.]]

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** P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials,” [[ http://dx.doi.org/10.1088/0953-8984/21/39/395502 | Journal of Physics: Condensed Matter, vol. 21, no. 39, p. 395502, 2009.]]

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** M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” [[ dx.doi.org/10.1103/RevModPhys.64.1045 | Rev. Mod. Phys., vol. 64, no. 4, p. 1045, Oct. 1992.]]

to:

** M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” [[ http://dx.doi.org/10.1103/RevModPhys.64.1045 | Rev. Mod. Phys., vol. 64, no. 4, p. 1045, Oct. 1992.]]

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** ~~[1] ~~P. Mori-Sanchez, A. J. Cohen, and W. Yang, “Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction,” [[ http://dx.doi.org/10.1103/PhysRevLett.100.146401 | Phys. Rev. Lett., vol. 100, no. 14, p. 146401–4, Apr. 2008.]]

to:

** P. Mori-Sanchez, A. J. Cohen, and W. Yang, “Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction,” [[ http://dx.doi.org/10.1103/PhysRevLett.100.146401 | Phys. Rev. Lett., vol. 100, no. 14, p. 146401–4, Apr. 2008.]]

Added lines 38-41:

# Plane wave calculations

** M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” [[ dx.doi.org/10.1103/RevModPhys.64.1045 | Rev. Mod. Phys., vol. 64, no. 4, p. 1045, Oct. 1992.]]

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# Energy discontinuities at integer electron ~~numbers~~

to:

# Energy discontinuities at integer electron numbers and the band gap problem

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** A. J. Cohen, P. Mori-Sanchez, and W. Yang, "Fractional charge perspective on the band gap in density-functional theory," [[ http://dx.doi.org/10.1103/PhysRevB.77.115123 | Phys. Rev. B, vol. 77, no. 11, p. 115123–6, Mar. 2008. ]]

** [1] P. Mori-Sanchez, A. J. Cohen, and W. Yang, “Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction,” [[ http://dx.doi.org/10.1103/PhysRevLett.100.146401 | Phys. Rev. Lett., vol. 100, no. 14, p. 146401–4, Apr. 2008.]]

** [1] P. Mori-Sanchez, A. J. Cohen, and W. Yang, “Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction,” [[ http://dx.doi.org/10.1103/PhysRevLett.100.146401 | Phys. Rev. Lett., vol. 100, no. 14, p. 146401–4, Apr. 2008.]]

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** J. P. Perdew, A. Ruzsinszky, L. A. Constantin, J. Sun, and G. I. Csonka, "Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed," [[ http://dx.doi.org/10.1021/ct800531s | Journal of Chemical Theory and Computation, vol. 5, no. 4, pp. 902–908, Apr. 2009.]

to:

** J. P. Perdew, A. Ruzsinszky, L. A. Constantin, J. Sun, and G. I. Csonka, "Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed," [[ http://dx.doi.org/10.1021/ct800531s | Journal of Chemical Theory and Computation, vol. 5, no. 4, pp. 902–908, Apr. 2009.]]

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** J. P. Perdew, A. Ruzsinszky, L. A. Constantin, J. Sun, and G. I. Csonka, "Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed," [[ http://dx.doi.org/10.1021/ct800531s | Journal of Chemical Theory and Computation, vol. 5, no. 4, pp. 902–908, Apr. 2009.]

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# Foundational ~~papers~~

to:

# Foundational papers and some general reviews of various sorts

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** R. G. Parr, "Density Functional Theory," [[ http://dx.doi.org/10.1146/annurev.pc.34.100183.003215 | Annu. Rev. Phys. Chem., vol. 34, no. 1, pp. 631–656, Oct. 1983.]]

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** E. Lieb, "Density functionals for Coulomb systems", [[http://~~www3~~.~~interscience~~.~~wiley.com~~/~~cgi-bin~~/~~abstract/109576163/ABSTRACT?CRETRY=1&SRETRY=0~~|Int. J. Quant. Chem. 24, 243 (1983).]]

to:

** E. Lieb, "Density functionals for Coulomb systems", [[http://dx.doi.org/10.1002/qua.560240302|Int. J. Quant. Chem. 24, 243 (1983).]]

Changed line 31 from:

# ~~Exact properties ~~of the exchange-correlation ~~hole~~

to:

# Properties of the exact exchange-correlation energy

Added lines 33-34:

** M. Levy and J. P. Perdew, "Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms ", [[http://prola.aps.org/abstract/PRA/v32/i4/p2010_1|Phys. Rev. A 32, 2010 (1985).]]

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**

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Added lines 31-36:

# Exact properties of the exchange-correlation hole

** J. Harris, "Adiabatic-connection approach to Kohn-Sham theory", [[http://prola.aps.org/abstract/PRA/v29/i4/p1648_1 | Phys. Rev. A 29, 1648 (1984).]]

**

**

**

** J. Harris, "Adiabatic-connection approach to Kohn-Sham theory", [[http://prola.aps.org/abstract/PRA/v29/i4/p1648_1 | Phys. Rev. A 29, 1648 (1984).]]

**

**

**

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** J. P. Perdew and M. Levy, "Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities ", [[http://prola.aps.org/abstract/PRL/v51/i20/p1884_1|Phys. Rev. Lett. 51, 1884 (1983).]]

** L. J. Sham and M. Schluter, "Density-Functional Theory of the Energy Gap ", [[http://prola.aps.org/abstract/PRL/v51/i20/p1888_1|Phys. Rev. Lett. 51, 1888 (1983).]]

** L. J. Sham and M. Schluter, "Density-Functional Theory of the Energy Gap ", [[http://prola.aps.org/abstract/PRL/v51/i20/p1888_1|Phys. Rev. Lett. 51, 1888 (1983).]]

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** T. L. Gilbert, "Hohenberg-Kohn theorem for nonlocal external potentials", [[http://prola.aps.org/abstract/PRB/v12/i6/p2111_1|Phys. Rev. B 12, 2111 (1975).]]

to:

** T. L. Gilbert, "Hohenberg-Kohn theorem for nonlocal external potentials", [[http://prola.aps.org/abstract/PRB/v12/i6/p2111_1|Phys. Rev. B 12, 2111 (1975).]] (N-representability v.s. V-representability)

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# Levy&Lieb constrained search over density or density matrices~~ ''and''~~

to:

# Levy&Lieb constrained search over density or density matrices

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to:

** T. L. Gilbert, "Hohenberg-Kohn theorem for nonlocal external potentials", [[http://prola.aps.org/abstract/PRB/v12/i6/p2111_1|Phys. Rev. B 12, 2111 (1975).]]

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# Levy&Lieb constrained search over density or density matrices ''and'' ~~energy discontinuities at integer electron numbers~~

to:

# Levy&Lieb constrained search over density or density matrices ''and''

Changed lines 17-19 from:

** E. Lieb, "Density functionals for Coulomb systems", [[~~|Int~~.~~ J~~.~~ Quant~~.~~ Chem~~. ~~24, 243 ~~(1983).]]

to:

** E. Lieb, "Density functionals for Coulomb systems", [[http://www3.interscience.wiley.com/cgi-bin/abstract/109576163/ABSTRACT?CRETRY=1&SRETRY=0|Int. J. Quant. Chem. 24, 243 (1983).]]

# Energy discontinuities at integer electron numbers

# Energy discontinuities at integer electron numbers

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# Levy constrained search over density or density matrices ''and'' energy discontinuities at integer electron numbers

to:

# Levy&Lieb constrained search over density or density matrices ''and'' energy discontinuities at integer electron numbers

Added lines 16-17:

** M. Levy, "Electron densities in search of Hamiltonians", [[http://prola.aps.org/abstract/PRA/v26/i3/p1200_1|Phys. Rev. A 26, 1200 (1982).]]

** E. Lieb, "Density functionals for Coulomb systems", [[|Int. J. Quant. Chem. 24, 243 (1983).]]

** E. Lieb, "Density functionals for Coulomb systems", [[|Int. J. Quant. Chem. 24, 243 (1983).]]

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to:

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** J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, [[http://prola.aps.org/abstract/PRL/v49/i23/p1691_1|Phys. Rev. Lett. 49, 1691 (1982).]]

to:

** J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, "Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy ", [[http://prola.aps.org/abstract/PRL/v49/i23/p1691_1|Phys. Rev. Lett. 49, 1691 (1982).]]

Changed line 12 from:

** N. D. Mermin, "Thermal properties of the inhomogeneous electron gas", [[~~|Phys~~. Rev. 137, A1441 (1965)]]

to:

** N. D. Mermin, "Thermal properties of the inhomogeneous electron gas", [[http://prola.aps.org/abstract/PR/v137/i5A/pA1441_1|Phys. Rev. 137, A1441 (1965)]]

Changed line 12 from:

**

to:

** N. D. Mermin, "Thermal properties of the inhomogeneous electron gas", [[|Phys. Rev. 137, A1441 (1965)]]

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# Mermin finite temperature and ensemble density functional theory

**

Changed lines 5-6 from:

to:

** Richard M. Martin, ''Electronic Structure: Basic Theory and Practical Methods'', Cambridge University Press (2004) ISBN: 0521782856

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Changed lines 5-6 from:

** R. G. Parr and W. Yang, ''Density-Functional Theory of Atoms and Molecules''~~ ~~ Oxford University Press (1994) ISBN: 0195092767

to:

** R. G. Parr and W. Yang, ''Density-Functional Theory of Atoms and Molecules'', Oxford University Press (1994) ISBN: 0195092767

Added lines 3-6:

# Books

** R. G. Parr and W. Yang, ''Density-Functional Theory of Atoms and Molecules'' Oxford University Press (1994) ISBN: 0195092767

** R. G. Parr and W. Yang, ''Density-Functional Theory of Atoms and Molecules'' Oxford University Press (1994) ISBN: 0195092767

Changed lines 15-16 from:

** J. F. Janak, "Proof that ∂E~~ ~~/~~ ~~∂ni=ε in density-functional theory", [[http://prola.aps.org/abstract/PRB/v18/i12/p7165_1 | Phys. Rev. B 18, 7165 (1978).]]

to:

** J. F. Janak, "Proof that ∂E/∂ni=ε in density-functional theory", [[http://prola.aps.org/abstract/PRB/v18/i12/p7165_1 | Phys. Rev. B 18, 7165 (1978).]]

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to:

# Foundational papers

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to:

# Levy constrained search over density or density matrices ''and'' energy discontinuities at integer electron numbers

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# Janak construction

** J. F. Janak, "Proof that ∂E / ∂ni=ε in density-functional theory", [[http://prola.aps.org/abstract/PRB/v18/i12/p7165_1 | Phys. Rev. B 18, 7165 (1978).]]

# Self-interaction correction

** J. F. Janak, "Proof that ∂E / ∂ni=ε in density-functional theory", [[http://prola.aps.org/abstract/PRB/v18/i12/p7165_1 | Phys. Rev. B 18, 7165 (1978).]]

# Self-interaction correction

Changed lines 15-16 from:

** J. P. Perdew and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems", [[http://prola.aps.org/abstract/PRB/v23/i10/p5048_1 | Phys. Rev. B 23, 5048~~ - 5079~~ (1981).]]

to:

** J. P. Perdew and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems", [[http://prola.aps.org/abstract/PRB/v23/i10/p5048_1 | Phys. Rev. B 23, 5048 (1981).]]

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* ~~M. ~~Levy~~, "Universal Variational Functionals of Electron Densities, First-Order Density Matrices, and Natural Spin-Orbitals and Solution of the v-Representability Problem~~"~~, [[http://www.pnas.org/cgi/reprint/76/12/6062 | Proc. Nat. Acad. Sci. 76, 6062 (1979).]]~~

* J. P . Perdew and M. Levy

* J. P.~~ Perdew, R~~.~~ G~~. ~~Parr, M~~. ~~Levy, and J~~. ~~L. Balduz~~, ~~[[http://prola~~.~~aps~~.~~org/abstract/PRL/v49/i23/p1691_1|Phys. Rev~~. ~~Lett. 49~~, ~~1691 (1982)~~.~~]]~~

SIC

J. P. Perdew and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems", [[http://prola.aps.org/abstract/PRB/v23/i10/p5048_1 | Phys. Rev. B 23, 5048 - 5079 (1981).]]

* J. P . Perdew and M. Levy

* J. P

SIC

J. P. Perdew and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems", [[http://prola.aps.org/abstract/PRB/v23/i10/p5048_1 | Phys. Rev. B 23, 5048 - 5079 (1981).]]

to:

* Levy constrained search over density or density matrices ''and'' energy discontinuities at integer electron numbers

** M. Levy, "Universal Variational Functionals of Electron Densities, First-Order Density Matrices, and Natural Spin-Orbitals and Solution of the v-Representability Problem", [[http://www.pnas.org/cgi/reprint/76/12/6062 | Proc. Nat. Acad. Sci. 76, 6062 (1979).]]

** J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, [[http://prola.aps.org/abstract/PRL/v49/i23/p1691_1|Phys. Rev. Lett. 49, 1691 (1982).]]

* Self-interaction correction

** J. P. Perdew and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems", [[http://prola.aps.org/abstract/PRB/v23/i10/p5048_1 | Phys. Rev. B 23, 5048 - 5079 (1981).]]

** M. Levy, "Universal Variational Functionals of Electron Densities, First-Order Density Matrices, and Natural Spin-Orbitals and Solution of the v-Representability Problem", [[http://www.pnas.org/cgi/reprint/76/12/6062 | Proc. Nat. Acad. Sci. 76, 6062 (1979).]]

** J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, [[http://prola.aps.org/abstract/PRL/v49/i23/p1691_1|Phys. Rev. Lett. 49, 1691 (1982).]]

* Self-interaction correction

** J. P. Perdew and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems", [[http://prola.aps.org/abstract/PRB/v23/i10/p5048_1 | Phys. Rev. B 23, 5048 - 5079 (1981).]]

Changed lines 3-4 from:

* ~~P. Hohenberg and W~~. ~~Kohn, "Inhomogeneous Electron Gas"~~, [[http://prola.aps.org/abstract/PR/v136/i3B/pB864_1|Physical Review 136, B864-B871 (1964).]]

* W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", [[http://prola.aps.org/abstract/PR/v140/i4A/pA1133_1|Physical Review 140, A1133 (1965).]]

* W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", [[http://prola.aps.org/abstract/PR/v140/i4A/pA1133_1|Physical Review 140, A1133 (1965).]]

to:

* Foundational papers

** P. Hohenberg and W. Kohn, "Inhomogeneous Electron Gas", [[http://prola.aps.org/abstract/PR/v136/i3B/pB864_1|Physical Review 136, B864-B871 (1964).]]

** W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", [[http://prola.aps.org/abstract/PR/v140/i4A/pA1133_1|Physical Review 140, A1133 (1965).]]

** P. Hohenberg and W. Kohn, "Inhomogeneous Electron Gas", [[http://prola.aps.org/abstract/PR/v136/i3B/pB864_1|Physical Review 136, B864-B871 (1964).]]

** W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", [[http://prola.aps.org/abstract/PR/v140/i4A/pA1133_1|Physical Review 140, A1133 (1965).]]

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Added lines 12-15:

SIC

J. P. Perdew and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems", [[http://prola.aps.org/abstract/PRB/v23/i10/p5048_1 | Phys. Rev. B 23, 5048 - 5079 (1981).]]

Added lines 6-7:

* M. Levy, "Universal Variational Functionals of Electron Densities, First-Order Density Matrices, and Natural Spin-Orbitals and Solution of the v-Representability Problem", [[http://www.pnas.org/cgi/reprint/76/12/6062 | Proc. Nat. Acad. Sci. 76, 6062 (1979).]]

Changed lines 3-4 from:

to:

* P. Hohenberg and W. Kohn, "Inhomogeneous Electron Gas", [[http://prola.aps.org/abstract/PR/v136/i3B/pB864_1|Physical Review 136, B864-B871 (1964).]]

* W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", [[http://prola.aps.org/abstract/PR/v140/i4A/pA1133_1|Physical Review 140, A1133 (1965).]]

* W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", [[http://prola.aps.org/abstract/PR/v140/i4A/pA1133_1|Physical Review 140, A1133 (1965).]]

Added line 6:

* J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, [[http://prola.aps.org/abstract/PRL/v49/i23/p1691_1|Phys. Rev. Lett. 49, 1691 (1982).]]

Changed lines 3-4 from:

to:

# P. Hohenberg and W. Kohn, "Inhomogeneous Electron Gas", [[http://prola.aps.org/abstract/PR/v136/i3B/pB864_1|Physical Review 136, B864-B871 (1964).]]

# W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", [[http://prola.aps.org/abstract/PR/v140/i4A/pA1133_1|Physical Review 140, A1133 (1965).]]

# W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", [[http://prola.aps.org/abstract/PR/v140/i4A/pA1133_1|Physical Review 140, A1133 (1965).]]

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W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange

and Correlation Effects", Phys. Rev. 140, A1133 (1965).

Changed lines 3-8 from:

to:

* P. Hohenberg and W. Kohn, "Inhomogeneous Electron Gas", [[http://prola.aps.org/abstract/PR/v136/i3B/pB864_1|Physical Review 136, B864-B871 (1964).]]

W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange

and Correlation Effects", Phys. Rev. 140, A1133 (1965).

W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange

and Correlation Effects", Phys. Rev. 140, A1133 (1965).