On the importance of the "density per particle" (shape function) in the density functional theory

Journal of Chemical Physics

Volumn 120, Issue 21, 2004, Pages 9969-9973

  De Proft, F ^a   Ayers, P W ^b   Sen, K D ^c   Geerlings, P ^a  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b MCMASTER UNIVERSITY   (Canada)

^c UNIVERSITY OF HYDERABAD   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CARRIER CONCENTRATION; ENTROPY; GROUND STATE; HARDNESS; INTEGRAL EQUATIONS; INTEGRATION; IONIZATION; LAGRANGE MULTIPLIERS; MATHEMATICAL TRANSFORMATIONS; MOLECULAR STRUCTURE; PROBABILITY DENSITY FUNCTION; VARIATIONAL TECHNIQUES;

CHEMICAL POTENTIAL; DENSITY FUNCTIONAL THEORY (DFT); REACTIVITY INDICES; SHAPE FUNCTION;

MOLECULAR DYNAMICS;

EID: 2942683313     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1729856     Document Type: Article

References (49)

1. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989); R. M. Dreizler and E. K. U. Gross, Density Functional Theory: An Approach to the Quantum Many Body Problem (Springer, Berlin, 1990); R. G. Parr and W. Yang, Annu. Rev. Phys. Chem. 46, 710 (1995); W. Kohn, A. D. Becke, and R. G. Parr, J. Phys. Chem. 100, 12974 (1996).
2. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989); R. M. Dreizler and E. K. U. Gross, Density Functional Theory: An Approach to the Quantum Many Body Problem (Springer, Berlin, 1990); R. G. Parr and W. Yang, Annu. Rev. Phys. Chem. 46, 710 (1995); W. Kohn, A. D. Becke, and R. G. Parr, J. Phys. Chem. 100, 12974 (1996).
3. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989); R. M. Dreizler and E. K. U. Gross, Density Functional Theory: An Approach to the Quantum Many Body Problem (Springer, Berlin, 1990); R. G. Parr and W. Yang, Annu. Rev. Phys. Chem. 46, 710 (1995); W. Kohn, A. D. Becke, and R. G. Parr, J. Phys. Chem. 100, 12974 (1996).
4. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989); R. M. Dreizler and E. K. U. Gross, Density Functional Theory: An Approach to the Quantum Many Body Problem (Springer, Berlin, 1990); R. G. Parr and W. Yang, Annu. Rev. Phys. Chem. 46, 710 (1995); W. Kohn, A. D. Becke, and R. G. Parr, J. Phys. Chem. 100, 12974 (1996).
5. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
6. R. G. Parr and L. J. Bartolotti, J. Phys. Chem. 87, 2810 (1983).
7. P. W. Ayers, Proc. Natl. Acad. Sci. U.S.A. 97, 1959 (2000).
8. H. Chermette, J. Comput. Chem. 20, 129 (1999); P. Geerlings, F. De Proft, and W. Langenaeker, Adv. Quantum Chem. 33, 303 (1999); P. Geerlings, F. De Proft, and W. Langenaeker, Chem. Rev. 103, 1793 (2003).
9. H. Chermette, J. Comput. Chem. 20, 129 (1999); P. Geerlings, F. De Proft, and W. Langenaeker, Adv. Quantum Chem. 33, 303 (1999); P. Geerlings, F. De Proft, and W. Langenaeker, Chem. Rev. 103, 1793 (2003).
10. H. Chermette, J. Comput. Chem. 20, 129 (1999); P. Geerlings, F. De Proft, and W. Langenaeker, Adv. Quantum Chem. 33, 303 (1999); P. Geerlings, F. De Proft, and W. Langenaeker, Chem. Rev. 103, 1793 (2003).
11. R. G. Parr and R. G. Pearson, J. Am. Chem. Soc. 105, 7512 (1983).
12. W. Yang and R. G. Parr, Proc. Natl. Acad. Sci. U.S.A. 82, 6723 (1985).
13. R. G. Parr and W. Yang, J. Am. Chem. Soc. 106, 4049 (1984).
14. C. Lee, W. Yang, and R. G. Parr, J. Mol. Struct.: THEOCHEM 163, 305 (1988).
15. (a) M. M. Morell, R. G. Parr, and M. Levy, J. Chem. Phys. 62, 549 (1975)
16. (b) M. Levy and R. G. Parr, ibid. 64, 2707 (1976);
17. (c) J. Katriel and E. R. Davidson, Proc. Natl. Acad. Sci. U.S.A. 77, 4403 (1980)
18. (d) M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, Phys. Rev. A 16, 1782 (1977);
19. (e) R. Ahlrichs, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and J. D. Morgan III, ibid. 23, 2106 (1981);
20. (f) M. Levy, J. P. Perdew, and V. Sahni, ibid. 30, 2745 (1984)
21. (g) C. O. Ambladh and U. von Barth, Phys. Rev. B 31, 3231 (1985);
22. (h) S. H. Patil, J. Phys. B 22, 2051 (1989).
23. P. W. Ayers and M. Levy, J. Chem. Phys. 115, 4438 (2001).
24. O. V. Gritsenko, M. Grüning, and E. J. Baerends, Rev. Modern Quantum Chemistry (Parr Festshrift) 1, 731 (2002).
25. M. Ho, D. F. Weaver, V. H. Smith, Jr., R. P. Sagar, and E. O. Esquivel, Phys. Rev. A 57, 4512 (1998).
26. S. P. Fazal, K. D. Sen, G. Gutierrez, and P. Fuentealba, Indian J. Chem. A39, 48 (2000).
27. K. Fukui, Y. Yonezawa, and H. Shinghu, J. Chem. Phys. 20, 722 (1952); K. Fukui, Theory of Orientation and Stereoselection (Springer, Berlin, 1973); K. Fukui, Science 218, 747 (1987).
28. K. Fukui, Y. Yonezawa, and H. Shinghu, J. Chem. Phys. 20, 722 (1952); K. Fukui, Theory of Orientation and Stereoselection (Springer, Berlin, 1973); K. Fukui, Science 218, 747 (1987).
29. K. Fukui, Y. Yonezawa, and H. Shinghu, J. Chem. Phys. 20, 722 (1952); K. Fukui, Theory of Orientation and Stereoselection (Springer, Berlin, 1973); K. Fukui, Science 218, 747 (1987).
30. P. W. Ayers and M. Levy, Theor. Chem. Acc. 103, 353 (2000).
31. R. G. Parr, R. A. Donnelly, M. Levy, and W. E. Palke, J. Chem. Phys. 68, 3801 (1978).
32. P. K. Chattaraj, A. Cedillo, and R. G. Parr, J. Chem. Phys. 103, 7645 (1995).
33. M. Berkowitz and R. G. Parr, J. Chem. Phys. 88, 2554 (1988).
34. P. K. Chattaraj, A. Cedillo, and R. G. Parr, J. Chem. Phys. 103, 10621 (1995).
35. G. K. L. Chan and N. C. Handy, J. Chem. Phys. 109, 6287 (1998).
36. B. G. Baekelandt, A. Cedillo, and R. G. Parr, J. Chem. Phys. 103, 8548 (1995).
37. F. De Proft and P. Geerlings, J. Phys. Chem. A 101, 5344 (1997); F. De Proft, S. Liu, and R. G. Parr, J. Chem. Phys. 107, 3000 (1997); P. Fuentealba, J. Phys. Chem. A 102, 4747 (1998); F. De Proft, S. Liu, and P. Geerlings, J. Chem. Phys. 108, 7549 (1998).
38. F. De Proft and P. Geerlings, J. Phys. Chem. A 101, 5344 (1997); F. De Proft, S. Liu, and R. G. Parr, J. Chem. Phys. 107, 3000 (1997); P. Fuentealba, J. Phys. Chem. A 102, 4747 (1998); F. De Proft, S. Liu, and P. Geerlings, J. Chem. Phys. 108, 7549 (1998).
39. F. De Proft and P. Geerlings, J. Phys. Chem. A 101, 5344 (1997); F. De Proft, S. Liu, and R. G. Parr, J. Chem. Phys. 107, 3000 (1997); P. Fuentealba, J. Phys. Chem. A 102, 4747 (1998); F. De Proft, S. Liu, and P. Geerlings, J. Chem. Phys. 108, 7549 (1998).
40. F. De Proft and P. Geerlings, J. Phys. Chem. A 101, 5344 (1997); F. De Proft, S. Liu, and R. G. Parr, J. Chem. Phys. 107, 3000 (1997); P. Fuentealba, J. Phys. Chem. A 102, 4747 (1998); F. De Proft, S. Liu, and P. Geerlings, J. Chem. Phys. 108, 7549 (1998).
41. S. Liu and R. G. Parr, J. Chem. Phys. 106, 5578 (1997).
42. P. Geerlings, G. Boon, C. Van Alsenoy, and F. De Proft, Int. J. Quantum Chem. (in press).
43. R. Carbó, M. Arnau, and L. Leynda, Int. J. Quantum Chem. 17, 1185 (1980); R. Carbó, B. Colabuig, L. Vera, and E. Besalu, Adv. Quantum Chem. 25, 253 (1994); E. Besalu, R. Carbó, J. Mestres, and M. Solà, Top. Curr. Chem. 173, 31 (1995); M. Solà, J. Mestres, and J. M. Oliva, Int. J. Quantum Chem. 58, 36 (1996); R. Carbó, E. Besalu, and X. Gironés, Adv. Quantum Chem. 38, 1 (2000).
44. R. Carbó, M. Arnau, and L. Leynda, Int. J. Quantum Chem. 17, 1185 (1980); R. Carbó, B. Colabuig, L. Vera, and E. Besalu, Adv. Quantum Chem. 25, 253 (1994); E. Besalu, R. Carbó, J. Mestres, and M. Solà, Top. Curr. Chem. 173, 31 (1995); M. Solà, J. Mestres, and J. M. Oliva, Int. J. Quantum Chem. 58, 36 (1996); R. Carbó, E. Besalu, and X. Gironés, Adv. Quantum Chem. 38, 1 (2000).
45. R. Carbó, M. Arnau, and L. Leynda, Int. J. Quantum Chem. 17, 1185 (1980); R. Carbó, B. Colabuig, L. Vera, and E. Besalu, Adv. Quantum Chem. 25, 253 (1994); E. Besalu, R. Carbó, J. Mestres, and M. Solà, Top. Curr. Chem. 173, 31 (1995); M. Solà, J. Mestres, and J. M. Oliva, Int. J. Quantum Chem. 58, 36 (1996); R. Carbó, E. Besalu, and X. Gironés, Adv. Quantum Chem. 38, 1 (2000).
46. R. Carbó, M. Arnau, and L. Leynda, Int. J. Quantum Chem. 17, 1185 (1980); R. Carbó, B. Colabuig, L. Vera, and E. Besalu, Adv. Quantum Chem. 25, 253 (1994); E. Besalu, R. Carbó, J. Mestres, and M. Solà, Top. Curr. Chem. 173, 31 (1995); M. Solà, J. Mestres, and J. M. Oliva, Int. J. Quantum Chem. 58, 36 (1996); R. Carbó, E. Besalu, and X. Gironés, Adv. Quantum Chem. 38, 1 (2000).
47. R. Carbó, M. Arnau, and L. Leynda, Int. J. Quantum Chem. 17, 1185 (1980); R. Carbó, B. Colabuig, L. Vera, and E. Besalu, Adv. Quantum Chem. 25, 253 (1994); E. Besalu, R. Carbó, J. Mestres, and M. Solà, Top. Curr. Chem. 173, 31 (1995); M. Solà, J. Mestres, and J. M. Oliva, Int. J. Quantum Chem. 58, 36 (1996); R. Carbó, E. Besalu, and X. Gironés, Adv. Quantum Chem. 38, 1 (2000).
48. P. G. Mezey, Mol. Phys. 96, 169 (1999); P. G. Mezey, J. Chem. Inf. Comput. Sci. 39, 224 (1999).
49. P. G. Mezey, Mol. Phys. 96, 169 (1999); P. G. Mezey, J. Chem. Inf. Comput. Sci. 39, 224 (1999).