In the last example, although the reaction would be dominated by the electrostatic
attraction, the Fukui function is able to predict the matching of the fragments.
Finally, we would like to show two examples where this approximation was used
to predict the interaction of molecular oxygen with metallic copper clusters. It has
been shown that one can make useful predictions of the binding sites, based on the
knowledge of the donor local reactivity of the cluster, by using the condensed Fukui
function, f
À
k . In this way, it was reported that Cu 3 , Cu 5 , and Cu 5
− have the highest
reactivity toward molecular oxygen. In Fig. 8.5, the results for Cu 3 (panel a) and for
Cu 5
− (panel b) are shown. These results are similar to those reported in Ref. [57].
8.5 Conclusions
This chapter has provided an introduction to the topological analysis of the Fukui
function, a strategy that allows for a theoretical expression of the chemical concepts
of local reactivity, and enables one to employ these concepts in a quantitative
manner to predict and understand chemical problems. The applicability of the
method is presented through different examples, involving acids and basis of Lewis,
substituted benzenes, and as an orientation predictor for the most favorable interaction between clusters (used as building blocks) to form larger structures. We hope
that by using the remarkable on-going software developments, and processor
technology, the applicability of this method increase further in both scope and
reliability, for the different areas of chemistry.
Acknowledgments CC and PF acknowledges financial support from FONDECYT through
projects No 11090013 and 1130202, and also by Millennium Nucleus CILIS, Project
ICM-P10-003-F. WT and RP acknowledge financial support from FONDECYT through project
No 1140358.
References
1. Bader RFW (1990) Atoms in molecules: a quantum theory. Clarendon, Oxford
2. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and
molecular-systems. J Chem Phys 92(9):5397–5403
3. Silvi B, Savin A (1994) Classification of chemical-bonds based on topological analysis of
electron localization functions. Nature 371(6499):683–686
4. Savin A, Nesper R, Wengert S, Fassler TF (1997) ELF: the electron localization function.
Angew Chem 36(17):1809–1832
5. Parr RG, Yang WT (1984) Density functional approach to the frontier-electron theory of
chemical reactivity. J Am Chem Soc 106:4049–4050
6. Yang WT, Parr RG, Pucci R (1984) Electron density, Kohn-Sham frontier orbitals, and Fukui
functions. J Chem Phys 81:2862–2863
7. Yang WT, Parr RG (1985) Hardness, softness, and the fukui function in the electron theory of
metals and catalysis. PNAS 82:6723–6726
238
P. Fuentealba et al.
attraction, the Fukui function is able to predict the matching of the fragments.
Finally, we would like to show two examples where this approximation was used
to predict the interaction of molecular oxygen with metallic copper clusters. It has
been shown that one can make useful predictions of the binding sites, based on the
knowledge of the donor local reactivity of the cluster, by using the condensed Fukui
function, f
À
k . In this way, it was reported that Cu 3 , Cu 5 , and Cu 5
− have the highest
reactivity toward molecular oxygen. In Fig. 8.5, the results for Cu 3 (panel a) and for
Cu 5
− (panel b) are shown. These results are similar to those reported in Ref. [57].
8.5 Conclusions
This chapter has provided an introduction to the topological analysis of the Fukui
function, a strategy that allows for a theoretical expression of the chemical concepts
of local reactivity, and enables one to employ these concepts in a quantitative
manner to predict and understand chemical problems. The applicability of the
method is presented through different examples, involving acids and basis of Lewis,
substituted benzenes, and as an orientation predictor for the most favorable interaction between clusters (used as building blocks) to form larger structures. We hope
that by using the remarkable on-going software developments, and processor
technology, the applicability of this method increase further in both scope and
reliability, for the different areas of chemistry.
Acknowledgments CC and PF acknowledges financial support from FONDECYT through
projects No 11090013 and 1130202, and also by Millennium Nucleus CILIS, Project
ICM-P10-003-F. WT and RP acknowledge financial support from FONDECYT through project
No 1140358.
References
1. Bader RFW (1990) Atoms in molecules: a quantum theory. Clarendon, Oxford
2. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and
molecular-systems. J Chem Phys 92(9):5397–5403
3. Silvi B, Savin A (1994) Classification of chemical-bonds based on topological analysis of
electron localization functions. Nature 371(6499):683–686
4. Savin A, Nesper R, Wengert S, Fassler TF (1997) ELF: the electron localization function.
Angew Chem 36(17):1809–1832
5. Parr RG, Yang WT (1984) Density functional approach to the frontier-electron theory of
chemical reactivity. J Am Chem Soc 106:4049–4050
6. Yang WT, Parr RG, Pucci R (1984) Electron density, Kohn-Sham frontier orbitals, and Fukui
functions. J Chem Phys 81:2862–2863
7. Yang WT, Parr RG (1985) Hardness, softness, and the fukui function in the electron theory of
metals and catalysis. PNAS 82:6723–6726
238
P. Fuentealba et al.