The document discusses the concept of multicenter bonding from the perspective of topological theories of bonding. It introduces the electron localization function (ELF) which can be used to analyze localization domains and classify bonds. ELF analysis provides definitions of multicenter bonds like 3c-2e bonds seen in B2H6 and 3c-4e bonds in hypervalent molecules like XeF2. The synaptic order of a localization basin, defined as the number of cores it shares a boundary with, is proposed as a descriptor of multicenter bonds that is complementary to the valence concept. While ELF provides a way to rigorously analyze bonding, the choice of localization function remains an open issue.

1. The synaptic order: a key concept to understand multicenter bonding Bernard Silvi Laboratoire de Chimie Théorique Université Pierre et Marie Curie 4, place Jussieu 75252 -Paris

12. Il me faut cependant avouer que la chimie proprement dite ne m’a jamais beaucoup intéressé. Pourquoi ? Peut être parce que des notions telles que celles de valence, de liaison chimique etc., m’ont toujours semblé peu claires du point de vue conceptuel. René Thom Paraboles et catastrophes However I have to confess that I have never been very interested in Chemistry Why? Maybe because notions such as those of valence, chemical bond, etc., seem to me unclear from a conceptual point of view

18. A meteorological example: V( r {  i })=-P Basin 2 Basin 1

25. Detailed diagram: Parent domain C(O ) valence C(S) V(S) Valence O V(S,O ) V 1 (O)+V 2 (O) V 1 (O) V 2 (0)

28. The two processes filled-filled: 2 chemical single chemical objects (or more) complex, ionic pair, physisorption hollowed-filled: 1 chemical single chemical object molecule, ion, chemisorption

30. Synaptic order: CH 3 F mon osynaptic disynaptic Protonated disynaptic

38. Planar tetracoordinated carbons R. Choukroun, B. Donnadieu, J-S. Zhao, P. Cassoux, C. Lepetit et B. Silvi , Organometallics , 19, 1901-1911 (2000)

39. Planar pentacoordinated carbon P. v. R. Schleyer, private communication

40. Planar hexacoordinated carbon P. v. R. Schleyer, private communication

47. Nevertheless… Many forms of localization functions have been tried, and will be tried in this world of sin and woe. No one pretends that ELF is perfect or all-wise. Indeed, it has been the worst form of localization function except all those others that have been tried from time to time. Many forms of government have been tried, and will be tried in this world of sin and woe. No one pretends that democracy is perfect or all-wise. Indeed, it has been the worst form of government except all those others that have been tried from time to time. W. Churchill

49. That's all folks

51. Nevertheless… Many forms of localization functions have been tried, and will be tried in this world of sin and woe. No one pretends that ELF is perfect or all-wise. Indeed, it has been the worst form of localization function except all those others that have been tried from time to time. Many forms of government have been tried, and will be tried in this world of sin and woe. No one pretends that democracy is perfect or all-wise. Indeed, it has been the worst form of government except all those others that have been tried from time to time. W. Churchill