chaotic and disordered world” [4]. Everyone knows how it looks despite nobody
ever having seen one [4–6]. This line of reasoning is similar to Coulson’s comment:
“Sometimes it seems to me that a bond between two atoms has become so real, so
tangible, so friendly, that I can almost see it. Then I awake with a little shock, for a
chemical bond is not a real thing. It does not exist. No one has ever seen one. No
one ever can. It is a figment of our own imagination” [7]. Even chemical bonds
have been described as “noumena” rather than “phenomena” [8–10].
Chemical bonds together with other concepts such as atomic orbitals, electron
shells, lone pairs, aromaticity, atomic charges, (hyper-) conjugation, strain, etc. do
not correspond to physical observables. Such concepts therefore cannot be unambiguously defined in pure quantum theory, but constitute a rich set of “fuzzy”, yet
invaluably useful concepts [11–14]. They lead to constructive ideas and developments when appropriately used and defined.
In chemistry as well as in physics, advanced theories are held by two milestones:
(i) a mathematical structure/formalism disclosing the basic entities of the theory and
their mathematical relationships, and (ii) an “interpretative” recipe of basic entities
of the theory. The latter discloses the qualitative meaning of the basic entities and
their relation to other known entities within and beyond the theory. It is important to
highlight that the connection between the mathematical formalism and its interpretation is always subtle. This problem can be traced back to the lack of a clear and
unambiguous definition of a bond in quantum mechanics and the plethora of
interpretations that have been introduced with various “meanings” of the “mathematical symbols/entities” of the theory [15].
In front of this quandary, two opposite attitudes can be envisaged. On the one
hand, the old and negative statement of the French mathemathician R. Thom: “Il me
faut cependant avouer que la chimie proprement dite ne m’a jamais beaucoup
intéressée. 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.” (I should admit that chemistry never really interested me. Why? Perhaps
because notions such as those of valence, chemical bond, etc., always appeared
unclear to me from the conceptual point of view). On the other hand, the more
recent and pragmatic comment of Alvarez et al.: “Chemistry has done more than
well in a universe of structure and function on the molecular level with just this
imperfectly defined concept of a chemical bond. Or maybe it has done so well
precisely because the concept is flexible and fuzzy” [16].
However, it is important to note that scientific arguments, debates, and controversies are at the heart of chemistry. This situation has been clearly stated in the
very recent paper entitled “The Nature of the Fourth Bond in the Ground State of
C 2 : The Quadruple Bond Conundrum” by Danovich et al. [17] in which these
authors recongnize that they are in front of a “Rashomon effect”, in which the
bonding picture is becoming too fuzzy to be constructive anymore.
In trying to overcome this dichotomy, topological analysis has become one of
the most useful tools to characterize chemical interactions. Visualization of bonding
interactions between atoms and molecules is a long-standing quest in theoretical
and computational chemistry. The main interest lies in creating a tool that enables
18 A Complete NCI Perspective: From New Bonds to Reactivity
493
ever having seen one [4–6]. This line of reasoning is similar to Coulson’s comment:
“Sometimes it seems to me that a bond between two atoms has become so real, so
tangible, so friendly, that I can almost see it. Then I awake with a little shock, for a
chemical bond is not a real thing. It does not exist. No one has ever seen one. No
one ever can. It is a figment of our own imagination” [7]. Even chemical bonds
have been described as “noumena” rather than “phenomena” [8–10].
Chemical bonds together with other concepts such as atomic orbitals, electron
shells, lone pairs, aromaticity, atomic charges, (hyper-) conjugation, strain, etc. do
not correspond to physical observables. Such concepts therefore cannot be unambiguously defined in pure quantum theory, but constitute a rich set of “fuzzy”, yet
invaluably useful concepts [11–14]. They lead to constructive ideas and developments when appropriately used and defined.
In chemistry as well as in physics, advanced theories are held by two milestones:
(i) a mathematical structure/formalism disclosing the basic entities of the theory and
their mathematical relationships, and (ii) an “interpretative” recipe of basic entities
of the theory. The latter discloses the qualitative meaning of the basic entities and
their relation to other known entities within and beyond the theory. It is important to
highlight that the connection between the mathematical formalism and its interpretation is always subtle. This problem can be traced back to the lack of a clear and
unambiguous definition of a bond in quantum mechanics and the plethora of
interpretations that have been introduced with various “meanings” of the “mathematical symbols/entities” of the theory [15].
In front of this quandary, two opposite attitudes can be envisaged. On the one
hand, the old and negative statement of the French mathemathician R. Thom: “Il me
faut cependant avouer que la chimie proprement dite ne m’a jamais beaucoup
intéressée. 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.” (I should admit that chemistry never really interested me. Why? Perhaps
because notions such as those of valence, chemical bond, etc., always appeared
unclear to me from the conceptual point of view). On the other hand, the more
recent and pragmatic comment of Alvarez et al.: “Chemistry has done more than
well in a universe of structure and function on the molecular level with just this
imperfectly defined concept of a chemical bond. Or maybe it has done so well
precisely because the concept is flexible and fuzzy” [16].
However, it is important to note that scientific arguments, debates, and controversies are at the heart of chemistry. This situation has been clearly stated in the
very recent paper entitled “The Nature of the Fourth Bond in the Ground State of
C 2 : The Quadruple Bond Conundrum” by Danovich et al. [17] in which these
authors recongnize that they are in front of a “Rashomon effect”, in which the
bonding picture is becoming too fuzzy to be constructive anymore.
In trying to overcome this dichotomy, topological analysis has become one of
the most useful tools to characterize chemical interactions. Visualization of bonding
interactions between atoms and molecules is a long-standing quest in theoretical
and computational chemistry. The main interest lies in creating a tool that enables
18 A Complete NCI Perspective: From New Bonds to Reactivity
493