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Efficient construction of exchange and correlation potentials by inverting the Kohn–Sham equations
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1.
1. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
http://dx.doi.org/10.1103/PhysRev.140.A1133
2.
2. P. C. Hohenberg, W. Kohn, and L. J. Sham, Adv. Quantum Chem. 21, 7 (1990).
http://dx.doi.org/10.1016/S0065-3276(08)60589-4
3.
3. E. Engel and R. M. Dreizler, Density Functional Theory: An Advanced Course (Springer, Berlin, 2011).
4.
4. R. van Leeuwen, O. V. Gritsenko, and E. J. Baerends, Top. Curr. Chem. 180, 107 (1996).
http://dx.doi.org/10.1007/3-540-61091-X_4
5.
5. O. V. Gritsenko, P. R. T. Schipper, and E. J. Baerends, Chem. Phys. Lett. 302, 199 (1999).
http://dx.doi.org/10.1016/S0009-2614(99)00128-1
6.
6. V. N. Staroverov, J. Chem. Phys. 129, 134103 (2008).
http://dx.doi.org/10.1063/1.2982791
7.
7. R. J. Bartlett, Mol. Phys. 108, 3299 (2010).
http://dx.doi.org/10.1080/00268976.2010.532818
8.
8. P. Verma and R. J. Bartlett, J. Chem. Phys. 137, 134102 (2012).
http://dx.doi.org/10.1063/1.4755818
9.
9. C. Filippi, C. J. Umrigar, and M. Taut, J. Chem. Phys. 100, 1290 (1994).
http://dx.doi.org/10.1063/1.466658
10.
10. C. J. Umrigar and X. Gonze, Phys. Rev. A 50, 3827 (1994).
http://dx.doi.org/10.1103/PhysRevA.50.3827
11.
11. O. V. Gritsenko and E. J. Baerends, Theor. Chem. Acc. 96, 44 (1997).
http://dx.doi.org/10.1007/s002140050202
12.
12. P. R. T. Schipper, O. V. Gritsenko, and E. J. Baerends, Theor. Chem. Acc. 98, 16 (1997).
http://dx.doi.org/10.1007/s002140050273
13.
13. M. E. Mura, P. J. Knowles, and C. A. Reynolds, J. Chem. Phys. 106, 9659 (1997).
http://dx.doi.org/10.1063/1.473838
14.
14. P. de Silva and T. A. Wesolowski, Phys. Rev. A 85, 032518 (2012).
http://dx.doi.org/10.1103/PhysRevA.85.032518
15.
15. M. J. G. Peach, D. G. J. Griffiths, and D. J. Tozer, J. Chem. Phys. 136, 144101 (2012).
http://dx.doi.org/10.1063/1.3700436
16.
16.The right-hand sides of Eqs. (5) and (7) are real despite the presence of complex-valued terms. This is because the eigenfunctions ϕi of a static Kohn–Sham Hamiltonian are either real or occur in degenerate pairs which are complex conjugates of one another, so the terms are also either real or occur in pairs of complex conjugates.
17.
17. R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994).
http://dx.doi.org/10.1103/PhysRevA.49.2421
18.
18. O. V. Gritsenko, R. van Leeuwen, and E. J. Baerends, Phys. Rev. A 52, 1870 (1995).
http://dx.doi.org/10.1103/PhysRevA.52.1870
19.
19. R. A. King and N. C. Handy, Phys. Chem. Chem. Phys. 2, 5049 (2000).
http://dx.doi.org/10.1039/b005896n
20.
20. J. D. Goodpaster, N. Ananth, F. R. Manby, and T. F. Miller III, J. Chem. Phys. 133, 084103 (2010).
http://dx.doi.org/10.1063/1.3474575
21.
21.J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996);
http://dx.doi.org/10.1103/PhysRevLett.77.3865
21.J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 78, 1396(E) (1997).
http://dx.doi.org/10.1103/PhysRevLett.78.1396
22.
22. C. R. Jacob, J. Chem. Phys. 135, 244102 (2011).
http://dx.doi.org/10.1063/1.3670414
23.
23. E. V. R. de Castro and F. E. Jorge, J. Chem. Phys. 108, 5225 (1998).
http://dx.doi.org/10.1063/1.475959
24.
24. A. P. Gaiduk, I. G. Ryabinkin, and V. N. Staroverov, “Removal of basis-set artifacts in Kohn–Sham potentials recovered from electron densities,” J. Chem. Theory Comput. (published online).
http://dx.doi.org/10.1021/ct4004146
25.
25. T. Grabo, T. Kreibich, S. Kurth, and E. K. U. Gross, in Strong Coulomb Correlations in Electronic Structure Calculations: Beyond the Local Density Approximation, edited by V. I. Anisimov (Gordon and Breach, Amsterdam, 2000).
26.
26. E. Engel, in A Primer in Density Functional Theory, edited by C. Fiolhais, F. Nogueira, and M. Marques (Springer, Berlin, 2003).
27.
27. A. Görling, J. Chem. Phys. 123, 062203 (2005).
http://dx.doi.org/10.1063/1.1904583
28.
28. S. Kümmel and L. Kronik, Rev. Mod. Phys. 80, 3 (2008).
http://dx.doi.org/10.1103/RevModPhys.80.3
29.
29. M. Ernzerhof and G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999).
http://dx.doi.org/10.1063/1.478401
30.
30. C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999).
http://dx.doi.org/10.1063/1.478522
31.
31. J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003).
http://dx.doi.org/10.1103/PhysRevLett.91.146401
32.
32. A. Seidl, A. Görling, P. Vogl, J. A. Majewski, and M. Levy, Phys. Rev. B 53, 3764 (1996).
http://dx.doi.org/10.1103/PhysRevB.53.3764
33.
33. A. V. Arbuznikov, M. Kaupp, V. G. Malkin, R. Reviakine, and O. L. Malkina, Phys. Chem. Chem. Phys. 4, 5467 (2002).
http://dx.doi.org/10.1039/b207171a
34.
34. A. V. Arbuznikov and M. Kaupp, Chem. Phys. Lett. 381, 495 (2003).
http://dx.doi.org/10.1016/j.cplett.2003.10.009
35.
35. A. V. Arbuznikov and M. Kaupp, Int. J. Quantum Chem. 104, 261 (2005).
http://dx.doi.org/10.1002/qua.20513
36.
36. A. V. Arbuznikov, M. Kaupp, and H. Bahmann, J. Chem. Phys. 124, 204102 (2006).
http://dx.doi.org/10.1063/1.2196883
37.
37. A. D. Becke, J. Chem. Phys. 131, 244118 (2009).
http://dx.doi.org/10.1063/1.3280730
38.
38. J. C. Slater, Phys. Rev. 81, 385 (1951).
http://dx.doi.org/10.1103/PhysRev.81.385
39.
39. F. A. Bulat, M. Levy, and P. Politzer, J. Phys. Chem. A 113, 1384 (2009).
http://dx.doi.org/10.1021/jp809406p
40.
40. E. Engel and S. H. Vosko, Phys. Rev. A 47, 2800 (1993).
http://dx.doi.org/10.1103/PhysRevA.47.2800
41.
41. E. Engel and R. M. Dreizler, J. Comput. Chem. 20, 31 (1999).
http://dx.doi.org/10.1002/(SICI)1096-987X(19990115)20:1<31::AID-JCC6>3.0.CO;2-P
42.
42. E. Engel, private communication.
43.
43. R. Baltin, Phys. Lett. A 117, 317 (1986).
http://dx.doi.org/10.1016/0375-9601(86)90671-7
44.
44. A. Holas and N. H. March, Phys. Rev. A 51, 2040 (1995).
http://dx.doi.org/10.1103/PhysRevA.51.2040
45.
45. A. Holas and N. H. March, Int. J. Quantum Chem. 56, 371 (1995).
http://dx.doi.org/10.1002/qua.560560423
46.
46. N. H. March, Top. Curr. Chem. 203, 201 (1999).
http://dx.doi.org/10.1007/3-540-48972-X_11
47.
47. V. Sahni, Quantal Density Functional Theory (Springer, Berlin, 2004).
48.
48. I. G. Ryabinkin and V. N. Staroverov, J. Chem. Phys. 137, 164113 (2012).
http://dx.doi.org/10.1063/1.4763481
49.
49. I. G. Ryabinkin and V. N. Staroverov, Int. J. Quantum Chem. 113, 1626 (2013).
http://dx.doi.org/10.1002/qua.24374
50.
50. A. Görling and M. Ernzerhof, Phys. Rev. A 51, 4501 (1995).
http://dx.doi.org/10.1103/PhysRevA.51.4501
51.
51. A. Holas and N. H. March, Top. Curr. Chem. 180, 57 (1996).
http://dx.doi.org/10.1007/3-540-61091-X_3
52.
52. F. Della Sala and A. Görling, J. Chem. Phys. 115, 5718 (2001).
http://dx.doi.org/10.1063/1.1398093
53.
53. Á. Nagy, Phys. Rev. A 55, 3465 (1997).
http://dx.doi.org/10.1103/PhysRevA.55.3465
54.
54. I. G. Ryabinkin, A. A. Kananenka, and V. N. Staroverov, Phys. Rev. Lett. 111, 013001 (2013).
http://dx.doi.org/10.1103/PhysRevLett.111.013001
55.
55. J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Rev. A 45, 101 (1992).
http://dx.doi.org/10.1103/PhysRevA.45.101
56.
56. O. V. Gritsenko and E. J. Baerends, Phys. Rev. A 64, 042506 (2001).
http://dx.doi.org/10.1103/PhysRevA.64.042506
57.
57. V. N. Staroverov, G. E. Scuseria, and E. R. Davidson, J. Chem. Phys. 125, 081104 (2006).
http://dx.doi.org/10.1063/1.2345650
58.
58. A. F. Izmaylov, V. N. Staroverov, G. E. Scuseria, E. R. Davidson, G. Stoltz, and E. Cancès, J. Chem. Phys. 126, 084107 (2007).
http://dx.doi.org/10.1063/1.2434784
59.
59. A. F. Izmaylov, V. N. Staroverov, G. E. Scuseria, and E. R. Davidson, J. Chem. Phys. 127, 084113 (2007).
http://dx.doi.org/10.1063/1.2768351
60.
60. A. Holas and M. Cinal, Phys. Rev. A 72, 032504 (2005).
http://dx.doi.org/10.1103/PhysRevA.72.032504
61.
61. H. Ou-Yang and M. Levy, Phys. Rev. Lett. 65, 1036 (1990).
http://dx.doi.org/10.1103/PhysRevLett.65.1036
62.
62. M. Levy and J. P. Perdew, Phys. Rev. A 32, 2010 (1985).
http://dx.doi.org/10.1103/PhysRevA.32.2010
63.
63. M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 09, Revision B.1, Gaussian, Inc., Wallingford, CT, 2010.
64.
64. A. P. Gaiduk and V. N. Staroverov, J. Chem. Phys. 128, 204101 (2008).
http://dx.doi.org/10.1063/1.2920197
65.
65. M. S. Miao, Chem. Phys. Lett. 324, 447 (2000).
http://dx.doi.org/10.1016/S0009-2614(00)00647-3
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/content/aip/journal/jcp/139/7/10.1063/1.4817942
2013-08-19
2014-10-23

Abstract

Given a set of canonical Kohn–Sham orbitals, orbital energies, and an external potential for a many-electron system, one can invert the Kohn–Sham equations in a single step to obtain the corresponding exchange-correlation potential, . For orbitals and orbital energies that are solutions of the Kohn–Sham equations with a multiplicative this procedure recovers (in the basis set limit), but for eigenfunctions of a non-multiplicative one-electron operator it produces an orbital-averaged potential. In particular, substitution of Hartree–Fock orbitals and eigenvalues into the Kohn–Sham inversion formula is a fast way to compute the Slater potential. In the same way, we efficiently construct orbital-averaged exchange and correlation potentials for hybrid and kinetic-energy-density-dependent functionals. We also show how the Kohn–Sham inversion approach can be used to compute functional derivatives of explicit density functionals and to approximate functional derivatives of orbital-dependent functionals.

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Scitation: Efficient construction of exchange and correlation potentials by inverting the Kohn–Sham equations
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