8. Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford UP, New
York
9. Ayers PW, Anderson JSM, Bartolotti LJ (2005) Perturbative perspectives on the chemical
reaction prediction problem. Int J Quantum Chem 101:520–534
10. Chattaraj PK, Sarkar U, Roy DR (2006) Electrophilicity index. Chem Rev 106:2065–2091
11. Gazquez J (2008) Perspectives on density functional theory of chemical reactivity. J Mex
Chem Soc 52(1):3–10
12. Liu S-B (2009) Conceptual density functional theory and some recent developments. Acta
Phys-Chim Sinica 25(03):590–600
13. Fuentealba P, Cardenas C (2015) Density functional theory of chemical reactivity. In:
Chemical modelling: volume 11, vol 11. The Royal Society of Chemistry, pp 151–174
14. Geerlings P, De Proft F, Langenaeker W (2003) Conceptual density functional theory. Chem
Rev 103:1793–1873
15. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871
16. Parr RG, Donnelly RA, Levy M, Palke WE (1978) Electronegativity: the density functional
viewpoint. J Chem Phys 68:3801–3807
17. Perdew JP, Parr RG, Levy M, Balduz JL Jr (1982) Density-functional theory for fractional
particle number: derivative discontinuities of the energy. Phys Rev Lett 49:1691–1694
18. Chan GKL (1999) A fresh look at ensembles: derivative discontinuities in density functional
theory. J Chem Phys 110:4710–4723
19. Yang WT, Zhang YK, Ayers PW (2000) Degenerate ground states and fractional number of
electrons in density and reduced density matrix functional theory. Phys Rev Lett 84:5172–
5175
20. Cohen MH, Wasserman A (2003) Revisiting N-continuous density-functional theory:
chemical reactivity and “atoms” in “molecules”. Isr J Chem 43:219–227
21. Cohen MH, Wasserman A (2007) On the foundations of chemical reactivity theory. J Phys
Chem A 111:2229–2242
22. Ayers PW (2008) The continuity of the energy and other molecular properties with respect to
the number of electrons. J Math Chem 43(1):285–303
23. Cohen AJ, Mori-Sanchez P, Yang WT (2008) Insights into current limitations of density
functional theory. Science 321(5890):792–794
24. Fuentealba P, Cardenas C (2013) On the exponential model for energy with respect to number
of electrons. J Mol Model 19:2849–2853
25. Bultinck P, Cardenas C, Fuentealba P, Johnson PA, Ayers PW (2013) How to compute the
Fukui matrix and function for systems with (quasi-)degenerate states. J Chem Theory Comput
10(1):202–210
26. Bultinck P, Cardenas C, Fuentealba P, Johnson PA, Ayers PW (2013) Atomic charges and the
electrostatic potential are Ill-defined in degenerate ground states. J Chem Theory Comput 9
(11):4779–4788
27. Cardenas C, Ayers PW, As Cedillo (2011) Reactivity indicators for degenerate states in the
density-functional theoretic chemical reactivity theory. J Chem Phys 134(17):174103
28. Ayers PW, Levy M (2000) Perspective on “density functional approach to the frontier-electron
theory of chemical reactivity” by Parr RG, Yang W (1984). Theor Chem Acc 103:353–360
29. Echegaray E, Rabi S, Cárdenas C, Zadeh FH, Rabi N, Lee S, Anderson JS, Toro-Labbe A,
Ayers PW (2014) In pursuit of negative Fukui functions: molecules with very small band gaps.
J Mol Model 20(3):1–7
30. Bultinck P, Carbo-Dorca R, Langenaeker W (2003) Negative Fukui functions: new insights
based on electronegativity equalization. J Chem Phys 118:4349–4356
31. Melin J, Ayers PW, Ortiz JV (2007) Removing electrons can increase the electron density: a
computational study of negative Fukui functions. J Phys Chem A 111:10017–10019
32. Bultinck P, Clarisse D, Ayers PW, Carbo-Dorca R (2011) The Fukui matrix: a simple
approach to the analysis of the Fukui function and its positive character. Phys Chem Chem
Phys 13(13):6110–6115
8 Topological Analysis of the Fukui Function
239
York
9. Ayers PW, Anderson JSM, Bartolotti LJ (2005) Perturbative perspectives on the chemical
reaction prediction problem. Int J Quantum Chem 101:520–534
10. Chattaraj PK, Sarkar U, Roy DR (2006) Electrophilicity index. Chem Rev 106:2065–2091
11. Gazquez J (2008) Perspectives on density functional theory of chemical reactivity. J Mex
Chem Soc 52(1):3–10
12. Liu S-B (2009) Conceptual density functional theory and some recent developments. Acta
Phys-Chim Sinica 25(03):590–600
13. Fuentealba P, Cardenas C (2015) Density functional theory of chemical reactivity. In:
Chemical modelling: volume 11, vol 11. The Royal Society of Chemistry, pp 151–174
14. Geerlings P, De Proft F, Langenaeker W (2003) Conceptual density functional theory. Chem
Rev 103:1793–1873
15. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871
16. Parr RG, Donnelly RA, Levy M, Palke WE (1978) Electronegativity: the density functional
viewpoint. J Chem Phys 68:3801–3807
17. Perdew JP, Parr RG, Levy M, Balduz JL Jr (1982) Density-functional theory for fractional
particle number: derivative discontinuities of the energy. Phys Rev Lett 49:1691–1694
18. Chan GKL (1999) A fresh look at ensembles: derivative discontinuities in density functional
theory. J Chem Phys 110:4710–4723
19. Yang WT, Zhang YK, Ayers PW (2000) Degenerate ground states and fractional number of
electrons in density and reduced density matrix functional theory. Phys Rev Lett 84:5172–
5175
20. Cohen MH, Wasserman A (2003) Revisiting N-continuous density-functional theory:
chemical reactivity and “atoms” in “molecules”. Isr J Chem 43:219–227
21. Cohen MH, Wasserman A (2007) On the foundations of chemical reactivity theory. J Phys
Chem A 111:2229–2242
22. Ayers PW (2008) The continuity of the energy and other molecular properties with respect to
the number of electrons. J Math Chem 43(1):285–303
23. Cohen AJ, Mori-Sanchez P, Yang WT (2008) Insights into current limitations of density
functional theory. Science 321(5890):792–794
24. Fuentealba P, Cardenas C (2013) On the exponential model for energy with respect to number
of electrons. J Mol Model 19:2849–2853
25. Bultinck P, Cardenas C, Fuentealba P, Johnson PA, Ayers PW (2013) How to compute the
Fukui matrix and function for systems with (quasi-)degenerate states. J Chem Theory Comput
10(1):202–210
26. Bultinck P, Cardenas C, Fuentealba P, Johnson PA, Ayers PW (2013) Atomic charges and the
electrostatic potential are Ill-defined in degenerate ground states. J Chem Theory Comput 9
(11):4779–4788
27. Cardenas C, Ayers PW, As Cedillo (2011) Reactivity indicators for degenerate states in the
density-functional theoretic chemical reactivity theory. J Chem Phys 134(17):174103
28. Ayers PW, Levy M (2000) Perspective on “density functional approach to the frontier-electron
theory of chemical reactivity” by Parr RG, Yang W (1984). Theor Chem Acc 103:353–360
29. Echegaray E, Rabi S, Cárdenas C, Zadeh FH, Rabi N, Lee S, Anderson JS, Toro-Labbe A,
Ayers PW (2014) In pursuit of negative Fukui functions: molecules with very small band gaps.
J Mol Model 20(3):1–7
30. Bultinck P, Carbo-Dorca R, Langenaeker W (2003) Negative Fukui functions: new insights
based on electronegativity equalization. J Chem Phys 118:4349–4356
31. Melin J, Ayers PW, Ortiz JV (2007) Removing electrons can increase the electron density: a
computational study of negative Fukui functions. J Phys Chem A 111:10017–10019
32. Bultinck P, Clarisse D, Ayers PW, Carbo-Dorca R (2011) The Fukui matrix: a simple
approach to the analysis of the Fukui function and its positive character. Phys Chem Chem
Phys 13(13):6110–6115
8 Topological Analysis of the Fukui Function
239