Optimized effective potential method

The optimized effective potential method (OEP)^[1]^[2] in Kohn-Sham (KS) density functional theory (DFT)^[3]^[4] is a method to determine the potentials as functional derivatives of the corresponding KS orbital-dependent energy density functionals. This can be in principle done for any arbitrary orbital-dependent functional,^[5] but is most common for exchange energy as the so-called exact exchange method (EXX),^[6]^[7] which will be considered here.

^ Kümmel, S.; Perdew, J. P. (2003). "Optimized effective potential made simple: Orbital functionals, orbital shifts, and the exact Kohn-Sham exchange potential". Physical Review B. 68 (3): 035103. arXiv:cond-mat/0303396. Bibcode:2003PhRvB..68c5103K. doi:10.1103/PhysRevB.68.035103.
^ Krieger, J. B.; Li, Y.; Iafrate, G. J. (1992). "Construction and application of an accurate local spin-polarized Kohn-Sham potential with integer discontinuity: Exchange-only theory". Physical Review A. 45 (1): 101–126. Bibcode:1992PhRvA..45..101K. doi:10.1103/PhysRevA.45.101. PMID 9906704.
^ Hohenberg, P.; Kohn, W. (1964). "Inhomogeneous Electron Gas". Physical Review. 136 (3B): B864. Bibcode:1964PhRv..136..864H. doi:10.1103/PhysRev.136.B864.
^ Kohn, W.; Sham, L. J. (1965). "Self-Consistent Equations Including Exchange and Correlation Effects". Physical Review. 140 (4A): A1133. Bibcode:1965PhRv..140.1133K. doi:10.1103/PhysRev.140.A1133.
^ Smiga, S.; Siecinska, S.; Fabiana, E. (2020). "Methods to generate reference total Pauli and kinetic potentials". Physical Review B. 101: 165144. arXiv:2005.03526. doi:10.1103/PhysRevB.101.165144.
^ Görling, A.; Levy, M. (1994). "Exact Kohn-Sham scheme based on perturbation theory". Physical Review A. 50 (1): 196–204. Bibcode:1994PhRvA..50..196G. doi:10.1103/PhysRevA.50.196. PMID 9910882.
^ Görling A. (1995). "Exact treatment of exchange in Kohn-Sham band-structure schemes". Physical Review B. 53 (11): 7024–7029. doi:10.1103/PhysRevB.53.7024. PMID 9982147.

[1] Kümmel, S.; Perdew, J. P. (2003). "Optimized effective potential made simple: Orbital functionals, orbital shifts, and the exact Kohn-Sham exchange potential". Physical Review B. 68 (3): 035103. arXiv:cond-mat/0303396. Bibcode:2003PhRvB..68c5103K. doi:10.1103/PhysRevB.68.035103.

[2] Krieger, J. B.; Li, Y.; Iafrate, G. J. (1992). "Construction and application of an accurate local spin-polarized Kohn-Sham potential with integer discontinuity: Exchange-only theory". Physical Review A. 45 (1): 101–126. Bibcode:1992PhRvA..45..101K. doi:10.1103/PhysRevA.45.101. PMID 9906704.

[HK-3] Hohenberg, P.; Kohn, W. (1964). "Inhomogeneous Electron Gas". Physical Review. 136 (3B): B864. Bibcode:1964PhRv..136..864H. doi:10.1103/PhysRev.136.B864.

[KS-4] Kohn, W.; Sham, L. J. (1965). "Self-Consistent Equations Including Exchange and Correlation Effects". Physical Review. 140 (4A): A1133. Bibcode:1965PhRv..140.1133K. doi:10.1103/PhysRev.140.A1133.

[5] Smiga, S.; Siecinska, S.; Fabiana, E. (2020). "Methods to generate reference total Pauli and kinetic potentials". Physical Review B. 101: 165144. arXiv:2005.03526. doi:10.1103/PhysRevB.101.165144.

[6] Görling, A.; Levy, M. (1994). "Exact Kohn-Sham scheme based on perturbation theory". Physical Review A. 50 (1): 196–204. Bibcode:1994PhRvA..50..196G. doi:10.1103/PhysRevA.50.196. PMID 9910882.

[7] Görling A. (1995). "Exact treatment of exchange in Kohn-Sham band-structure schemes". Physical Review B. 53 (11): 7024–7029. doi:10.1103/PhysRevB.53.7024. PMID 9982147.

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