omnidirectional electrostatic attraction). Some atoms have one connector, some
two, etc. With this simple idea chemists devised what has been said [1] to be
“perhaps the most powerful theory in the whole of science”, the structural theory of
organic chemistry. This simple theory enabled chemists to rationalize the structures
of and, even more impressively, to synthesize many thousands of chemical com-
pounds. At a “higher” (if not more utilitarian!) level a bond can be defined
mathematically in terms of the bond order between two atoms, which in molecular
orbital theory can be calculated from the basis functions on the atoms; in detail
there are several ways to do this. The theory of atoms in molecules (quantum theory
of atoms in molecules, AIM, QTAIM) offers possibly the most sophisticated
definition of a bond, in terms of the variation of electron density in a molecule
[2]. AIM theory has been often used to answer (?) the question whether there is a
bond between two atoms [3].
So how does the program know where the bonds are? There are (at least) three
ways to answer this:
- At the simplest level, a program maydraw on the graphical user interface
(GUI) a bond between atoms that are within a certain distance, the cutoff
distance being determined by stored data of standard bond lengths. For exam-
ple, with one popular program Cartesians for the water molecule with an O/H
internuclear distance of 1.0 A ̊ or less will result in a depiction with a bond
between the O and each H, but with an internuclear distance of more than 1.0 A ̊
the GUI will show an oxygen atom and two separate hydrogens. It should be
clear that this is only a formality, arising somewhat arbitrarily from strict
adherence to standard bond lengths. Another popular program uses a different
convention to display bond lengths. Accepting as input for a calculation a
structure assembled with a GUI by clicking together atoms with attached
bonds, the program will display all these original bonds even if after a
geometry optimization some of the atoms have moved so far apart that they
are by no sensible criterion still bonded (the result can be confusing to look at,
but may make sense if viewed as a space-filling model, or if absurdly long
bonds are deleted using the GUI). Again, this result is only a formality,
resulting from maintenance of the bonds(really just formal connectors) that
were shown before the geometry optimization. - If one wants information on bonding that is based on more than the proximity of
nuclei, this can be extracted from the wavefunction by requesting that after a
calculation of, say, energy or optimized geometry , a bond order calculation be
performed, or the wavefunction can be used for an AIM calculation (possibly by
a specialized program). - A few hardy souls may say it doesn’t matter. A molecule is a collection of nuclei
and electrons, with a certain charge and spin multiplicity. One might stop there
and say that this defines the molecule. This austere view was expressed by
Charles Coulson, a pioneer of, of all things, valence: “...a bond does not really
exist at all: it is a most convenient fiction...” [4]. However, the bond concept
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