1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
f
Koopmans’ springs to life
Rent:
Rent this article for
Access full text Article
/content/aip/journal/jcp/131/23/10.1063/1.3269030
1.
1.T. C. Koopmans, Physica (Amsterdam) 1, 104 (1934).
http://dx.doi.org/10.1016/S0031-8914(34)90011-2
2.
2.J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
http://dx.doi.org/10.1103/PhysRevB.23.5048
3.
3.J. P. Perdew and M. R. Norman, Phys. Rev. B 26, 5445 (1982).
http://dx.doi.org/10.1103/PhysRevB.26.5445
4.
4.J. P. Perdew and M. Levy, Phys. Rev. Lett. 51, 1884 (1983).
http://dx.doi.org/10.1103/PhysRevLett.51.1884
5.
5.A. R. Williams and U. von Barth, in Theory of the Inhomogeneous Electron Gas, edited by S. Lundqvist and N. H. March (Plenum, London, 1983).
6.
6.C. O. Almbladh and U. Von Barth, Phys. Rev. B 31, 3231 (1985).
http://dx.doi.org/10.1103/PhysRevB.31.3231
7.
7.P. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).
8.
8.R. Stowasser and R. Hoffmann, J. Am. Chem. Soc. 121, 3414 (1999).
http://dx.doi.org/10.1021/ja9826892
9.
9.D. P. Chong, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 116, 1760 (2002).
http://dx.doi.org/10.1063/1.1430255
10.
10.O. V. Gritsenko and E. J. Baerends, J. Chem. Phys. 117, 9154 (2002).
http://dx.doi.org/10.1063/1.1516800
11.
11.O. V. Gritsenko, B. Braïda, and E. J. Baerends, J. Chem. Phys. 119, 1937 (2003).
http://dx.doi.org/10.1063/1.1582839
12.
12.T. Körzdörfer, S. Kümmel, N. Marom, and L. Kronik, Phys. Rev. B 79, 201205 (2009).
http://dx.doi.org/10.1103/PhysRevB.79.201205
13.
13.S. Kümmel and L. Kronik, Rev. Mod. Phys. 80, 3 (2008).
http://dx.doi.org/10.1103/RevModPhys.80.3
14.
14.J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Phys. Rev. Lett. 49, 1691 (1982).
http://dx.doi.org/10.1103/PhysRevLett.49.1691
15.
15.A. Seidl, A. Gorling, P. Vogl, J. A. Majewski, and M. Levy, Phys. Rev. B 53, 3764 (1996).
http://dx.doi.org/10.1103/PhysRevB.53.3764
16.
16.R. Baer, E. Livshits, and U. Salzner, Annu. Rev. Phys. Chem. 61, 85 (2010).
17.
17.L. S. Cedérbaum, G. Hohlneicher, and W. Niessen, Chem. Phys. Lett. 18, 503 (1973).
http://dx.doi.org/10.1016/0009-2614(73)80451-8
18.
18.L. S. Cederbaum, G. Hohlneicher, and S. Peyerimhoff, Chem. Phys. Lett. 11, 421 (1971).
http://dx.doi.org/10.1016/0009-2614(71)80375-5
19.
19.J. D. Doll and Wp. Reinhard, J. Chem. Phys. 57, 1169 (1972).
http://dx.doi.org/10.1063/1.1678374
20.
20.L. J. Sham and W. Kohn, Phys. Rev. 145, 561 (1966).
http://dx.doi.org/10.1103/PhysRev.145.561
21.
21.E. Livshits and R. Baer, Phys. Chem. Chem. Phys. 9, 2932 (2007).
http://dx.doi.org/10.1039/b617919c
22.
22.A. M. Teale, F. De Proft, and D. J. Tozer, J. Chem. Phys. 129, 044110 (2008).
http://dx.doi.org/10.1063/1.2961035
23.
23.D. J. Tozer and N. C. Handy, J. Chem. Phys. 109, 10180 (1998).
http://dx.doi.org/10.1063/1.477711
24.
24.A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
http://dx.doi.org/10.1063/1.464913
25.
25.M. E. Casida, K. C. Casida, and D. R. Salahub, Int. J. Quantum Chem. 70, 933 (1998).
http://dx.doi.org/10.1002/(SICI)1097-461X(1998)70:4/5<933::AID-QUA39>3.0.CO;2-Z
26.
26.M. E. Casida and D. R. Salahub, J. Chem. Phys. 113, 8918 (2000).
http://dx.doi.org/10.1063/1.1319649
27.
27.S. Ivanov and R. J. Bartlett, J. Chem. Phys. 114, 1952 (2001).
http://dx.doi.org/10.1063/1.1342809
28.
28.L. Veseth, J. Chem. Phys. 114, 8789 (2001).
http://dx.doi.org/10.1063/1.1364676
29.
29.D. J. Tozer, J. Chem. Phys. 119, 12697 (2003).
http://dx.doi.org/10.1063/1.1633756
30.
30.F. Della Sala and A. Gorling, J. Chem. Phys. 118, 10439 (2003).
http://dx.doi.org/10.1063/1.1560132
31.
31.A. J. Cohen, P. Mori-Sanchez, and W. T. Yang, J. Chem. Phys. 126, 191109 (2007).
http://dx.doi.org/10.1063/1.2741248
32.
32.A. Savin, in Recent Advances in Density Functional Methods Part I, edited by D. P. Chong (World Scientific, Singapore, 1995), p. 129.
33.
33.H. Iikura, T. Tsuneda, T. Yanai, and K. Hirao, J. Chem. Phys. 115, 3540 (2001).
http://dx.doi.org/10.1063/1.1383587
34.
34.T. Yanai, D. P. Tew, and N. C. Handy, Chem. Phys. Lett. 393, 51 (2004).
http://dx.doi.org/10.1016/j.cplett.2004.06.011
35.
35.J. Toulouse, A. Savin, and H. J. Flad, Int. J. Quantum Chem. 100, 1047 (2004).
http://dx.doi.org/10.1002/qua.20259
36.
36.R. Baer and D. Neuhauser, Phys. Rev. Lett. 94, 043002 (2005).
http://dx.doi.org/10.1103/PhysRevLett.94.043002
37.
37.I. C. Gerber and J. G. Angyan, Chem. Phys. Lett. 415, 100 (2005).
http://dx.doi.org/10.1016/j.cplett.2005.08.060
38.
38.M. J. G. Peach, T. Helgaker, P. Salek, T. W. Keal, O. B. Lutnaes, D. J. Tozer, and N. C. Handy, Phys. Chem. Chem. Phys. 8, 558 (2006).
http://dx.doi.org/10.1039/b511865d
39.
39.O. A. Vydrov and G. E. Scuseria, J. Chem. Phys. 125, 234109 (2006).
http://dx.doi.org/10.1063/1.2409292
40.
40.Y. Zhao and D. G. Truhlar, J. Phys. Chem. A 110, 13126 (2006).
http://dx.doi.org/10.1021/jp066479k
41.
41.J. D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008).
http://dx.doi.org/10.1063/1.2834918
42.
42.R. Baer, E. Livshits, and D. Neuhauser, Chem. Phys. 329, 266 (2006).
http://dx.doi.org/10.1016/j.chemphys.2006.06.041
43.
43.E. Livshits and R. Baer, J. Phys. Chem. A 112, 12789 (2008).
http://dx.doi.org/10.1021/jp803606n
44.
44.E. Livshits, R. Baer, and R. Kosloff, J. Phys. Chem. A 113, 7521 (2009).
http://dx.doi.org/10.1021/jp900892r
45.
45.T. Stein, L. Kronik, and R. Baer, J. Am. Chem. Soc. 131, 2818 (2009).
http://dx.doi.org/10.1021/ja8087482
46.
46.H. R. Eisenberg and R. Baer, Phys. Chem. Chem. Phys. 11, 4674 (2009).
http://dx.doi.org/10.1039/b902589h
47.
47.J. T. H. Dunning, J. Chem. Phys. 90, 1007 (1989).
http://dx.doi.org/10.1063/1.456153
48.
48.Y. Shao, L. F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. T. Brown, A. T. B. Gilbert, L. V. Slipchenko, S. V. Levchenko, D. P. O’Neill, R. A. DiStasio, Jr., R. C. Lochan, T. Wang, G. J. O. Beran, N. A. Besley, J. M. Herbert, C. Y. Lin, T. Van Voorhis, S. H. Chien, A. Sodt, R. P. Steele, V. A. Rassolov, P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J. Baker, E. F. C. Byrd, H. Dachsel, R. J. Doerksen, A. Dreuw, B. D. Dunietz, A. D. Dutoi, T. R. Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C. -P. Hsu, G. Kedziora, R. Z. Khalliulin, P. Klunzinger, A. M. Lee, M. S. Lee, W. Liang, I. Lotan, N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y. M. Rhee, J. Ritchie, E. Rosta, C. D. Sherrill, A. C. Simmonett, J. E. Subotnik, H. Lee Woodcock III, W. Zhang, A. T. Bell, and A. K. Chakraborty, Phys. Chem. Chem. Phys. 8, 3172 (2006).
http://dx.doi.org/10.1039/b517914a
49.
49.M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 03, Gaussian, Inc., Wallingford CT, 2003.
50.
50.A. W. Potts and W. C. Price, Proc. R. Soc. London, Ser. A 326, 181 (1972).
http://dx.doi.org/10.1098/rspa.1972.0004
51.
51.K. L. Nixon, W. D. Lawrance, and M. J. Brunger, Chem. Phys. Lett. 474, 23 (2009).
http://dx.doi.org/10.1016/j.cplett.2009.04.017
52.
52.H. Van Lonkhuyzen and C. A. De Lange, Chem. Phys. 89, 313 (1984).
http://dx.doi.org/10.1016/0301-0104(84)85319-7
53.
53.J. A. Nichols, D. L. Yeager, and P. Jorgensen, J. Chem. Phys. 80, 293 (1984).
http://dx.doi.org/10.1063/1.446445
54.
54.A. J. Cohen, P. Mori-Sanchez, and W. T. Yang, Phys. Rev. B 77, 115123 (2008).
http://dx.doi.org/10.1103/PhysRevB.77.115123
55.
55.J. Janak, Phys. Rev. B 18, 7165 (1978).
http://dx.doi.org/10.1103/PhysRevB.18.7165
56.
56.M. Levy and A. Nagy, Phys. Rev. Lett. 83, 4361 (1999).
http://dx.doi.org/10.1103/PhysRevLett.83.4361
57.
57.S. T. Epstein, Am. J. Phys. 22, 613 (1954).
http://dx.doi.org/10.1119/1.1933856
58.
58.A. Ruzsinszky, J. P. Perdew, G. I. Csonka, O. A. Vydrov, and G. E. Scuseria, J. Chem. Phys. 126, 104102 (2007).
http://dx.doi.org/10.1063/1.2566637
59.
59.J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, V. N. Staroverov, and J. Tao, Phys. Rev. A 76, 040501 (2007).
http://dx.doi.org/10.1103/PhysRevA.76.040501
60.
60.A. J. Cohen, P. Mori-Sanchez, and W. T. Yang, Science 321, 792 (2008).
http://dx.doi.org/10.1126/science.1158722
61.
61.See EPAPS supplementary material at http://dx.doi.org/10.1063/1.3269030 for experimental and computed vertical ionization energies (eV) for various molecules.[Supplementary Material]
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/23/10.1063/1.3269030
Loading
/content/aip/journal/jcp/131/23/10.1063/1.3269030
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/jcp/131/23/10.1063/1.3269030
2009-12-16
2014-10-25

Abstract

The meaning of orbital energies (OOEs) in Kohn–Sham (KS) density functional theory(DFT) is subject to a longstanding controversy. In local, semilocal, and hybrid density functionals (DFs) a Koopmans’ approach, where OOEs approximate negative ionization potentials (IPs), is unreliable. We discuss a methodology based on the Baer–Neuhauser–Livshits range-separated hybrid DFs for which Koopmans’ approach “springs to life.” The OOEs are remarkably close to the negative IPs with typical deviances of ±0.3 eV down to IPs of 30 eV, as demonstrated on several molecules. An essential component is the ab initio motivated range-parameter tuning procedure, forcing the highest OOE to be exactly equal to the negative first IP. We develop a theory for the curvature of the energy as a function of fractional occupation numbers to explain some of the results.

Loading

Full text loading...

/deliver/fulltext/aip/journal/jcp/131/23/1.3269030.html;jsessionid=35qxpn6eknp9v.x-aip-live-03?itemId=/content/aip/journal/jcp/131/23/10.1063/1.3269030&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/jcp
true
true
This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Koopmans’ springs to life
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/23/10.1063/1.3269030
10.1063/1.3269030
SEARCH_EXPAND_ITEM