Using Kohn-Sham density functional theory to describe charged excitations in finite systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 12, 2009, Pages

  Mera, Héctor ^a   Stokbro, Kurt ^b  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 63249118451     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.125109     Document Type: Article

References (52)

1. C. Delerue, M. Lannoo, and G. Allan, Phys. Rev. Lett. 84, 2457 (2000). 10.1103/PhysRevLett.84.2457
2. T. A. Niehaus, M. Rohlfing, F. Della Sala, A. Di Carlo, and T. Frauenheim, Phys. Rev. A 71, 022508 (2005). 10.1103/PhysRevA.71.022508
3. J. L. Gázquez, J. Garza, F. D. Hinojosa, and A. Vela, J. Chem. Phys. 126, 214105 (2007). 10.1063/1.2741529
4. G. Cappellini, F. Casula, J. Yang, and F. Bechstedt, Phys. Rev. B 56, 3628 (1997). 10.1103/PhysRevB.56.3628
5. K. A. Johnson and N. W. Ashcroft, Phys. Rev. B 58, 15548 (1998). 10.1103/PhysRevB.58.15548
6. G. Malloci, G. Cappellini, G. Mulas, and G. Satta, Phys. Rev. B 70, 205429 (2004). 10.1103/PhysRevB.70.205429
7. K. Capelle, M. Borgh, K. Kärkkäinen, and S. M. Reimann, Phys. Rev. Lett. 99, 010402 (2007). 10.1103/PhysRevLett.99.010402
8. F. P. Rosselli, A. B. F. da Silva, and K. Capelle (private communication).
9. S. Kümmel and L. Kronik, Rev. Mod. Phys. 80, 3 (2008). 10.1103/RevModPhys.80.3
10. A. Cehovin, H. Mera, J. H. Jensen, K. Stokbro, and T. B. Pedersen, Phys. Rev. B 77, 195432 (2008). 10.1103/PhysRevB.77.195432
11. P. Mori-Sanchez, A. J. Cohen, and W. Yang, Phys. Rev. Lett. 100, 146401 (2008). 10.1103/PhysRevLett.100.146401
12. A. J. Cohen, P. Mori-Sanchez, and W. Yang, Phys. Rev. B 77, 115123 (2008). 10.1103/PhysRevB.77.115123
13. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). 10.1103/PhysRev.136.B864
14. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). 10.1103/PhysRev.140.A1133
15. J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Phys. Rev. Lett. 49, 1691 (1982). 10.1103/PhysRevLett.49.1691
16. L. J. Sham and M. Schlüter, Phys. Rev. Lett. 51, 1888 (1983). 10.1103/PhysRevLett.51.1888
17. R. W. Godby, M. Schlüter, and L. J. Sham, Phys. Rev. Lett. 56, 2415 (1986). 10.1103/PhysRevLett.56.2415
18. R. W. Godby, M. Schluter, and L. J. Sham, Phys. Rev. B 37, 10159 (1988). 10.1103/PhysRevB.37.10159
19. R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).
20. R. O. Jones and O. Gunnarson, Rev. Mod. Phys. 61, 689 (1989). 10.1103/RevModPhys.61.689
21. R. W. Godby and P. García-González, in A Primer in Density Functional Theory, Lecture Notes in Physics vol. 620, edited by, C. Fiolhais, F. Nogueira, and, M. A. L. Marques, (Springer, Heidelberg, 2003).
22. C.-O. Almbladh and U. von Barth, Phys. Rev. B 31, 3231 (1985). 10.1103/PhysRevB.31.3231
23. A notable exception to this is Görling-Levy perturbation theory (Ref.).
24. A. B. Kunz and T. C. Collins, J. Phys. B 7, L69 (1974). 10.1088/0022-3700/7/3/020
25. T. C. Collins, A. B. Kunz, and P. W. Deutsch, Phys. Rev. A 10, 1034 (1974). 10.1103/PhysRevA.10.1034
26. W. J. Hunt and W. A. Goddard, Chem. Phys. Lett. 3, 414 (1969). 10.1016/0009-2614(69)80154-5
27. G. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2008).
28. In the calculations shown later in the paper, the geometrical relaxation that the systems considered might experience upon addition of an extra electron is neglected.
29. G. A. Baraff and M. Schlüter, Phys. Rev. B 30, 3460 (1984). 10.1103/PhysRevB.30.3460
30. M. Moshinsky, Am. J. Phys. 36, 52 (1968). 10.1119/1.1974410
31. Interestingly, in order for the model to have physical (convex) relation between total energy and particle number the interaction should be attractive. See Figs. 1 and 2 in Ref..
32. C.-O. Almbladh and A. C. Pedroza, Phys. Rev. A 29, 2322 (1984). 10.1103/PhysRevA.29.2322
33. P. Rinke, K. Delaney, P. García-González, and R. W. Godby, Phys. Rev. A 70, 063201 (2004). 10.1103/PhysRevA.70.063201
34. P. Rinke, Ph.D. thesis, University of York, 2003.
35. As obtained from the system's electron affinity.
36. J. P. Perdew and M. Levy, Phys. Rev. Lett. 51, 1884 (1983). 10.1103/PhysRevLett.51.1884
37. F. E. Zahariev and Y. A. Wang, Phys. Rev. A 70, 042503 (2004). 10.1103/PhysRevA.70.042503
38. We are aware that the term "electrostatics" means different things for different communities. What we call electrostatics here contains also the exchange contribution needed to remove the fictitious self-interaction term present in KS-DFT. Once this unphysical self-term is removed the actual physical electrostatics are recovered.
39. Other local and semilocal functionals were used, yielding quantitatively similar results and identical qualitative trends.
40. S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).
41. R. Muller, PyQuante Program Suite (http://pyquante.sourceforge.net).
42. NIST Computational Chemistry Comparison and Benchmark Database, (http://srdata.nist.gov/cccbdb/).
43. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, Jr., Comput. Chem. 14, 1347 (1993). 10.1002/jcc.540141112
44. V. Bonaić-Koutecký, P. Fantucci, and J. Koutecký, Phys. Rev. B 37, 4369 (1988). 10.1103/PhysRevB.37.4369
45. Ion Energetics Data in NIST Chemistry Webbook, NIST Standard Reference Database No. 69, edited by, P. J. Linstrom, and, W. G. Mallard, (National Institute of Standards and Technology, Gaithersburg, MD, 2001), http://webbook.nist.gov
46. C. Toher, A. Filippetti, S. Sanvito, and K. Burke, Phys. Rev. Lett. 95, 146402 (2005). 10.1103/PhysRevLett.95.146402
47. A. Filippetti and N. A. Spaldin, Phys. Rev. B 67, 125109 (2003). 10.1103/PhysRevB.67.125109
48. S.-H. Ke, H. U. Baranger, and W. Yang, J. Chem. Phys. 126, 201102 (2007). 10.1063/1.2743004
49. Recall that the HF Hamiltonian is orbital-dependent, cf. Sec. 1.
50. As far as we know the KS-DFT ionization potential theorems have only been proved for external potentials that vanish asymptotically. This result provides further evidence (see also Ref.) that they also apply to potentials that do not vanish asymptotically.
51. A. Görling and M. Levy, Phys. Rev. A 50, 196 (1994). 10.1103/PhysRevA.50.196
52. P. Phillips and E. R. Davidson, Int. J. Quantum Chem. 23, 185 (1983). 10.1002/qua.560230118