Page 84 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

H 63
H
C C SECTION 1.4
C C
Representation of
H Electron Density
H Distribution
C D
The NBO resonance structures for benzyl cation reveals the importance of charge
delocalization to the ortho and para positions. The resonance structures shown for
formate ion and formamide represent the important cases of carboxylate anions and
amides and coincide with the qualitative ideas about the relative importance of
resonance structures discussed on pp. 19–20.

1.4.3. Atoms in Molecules
Chemists have long thought of a molecule as the sum of its constituent atoms and
groups. The homologous hydrocarbons, for example, have closely related properties,
many of which can be quantitatively expressed as the sum of contributions from the
CH ,CH , CH, and C groups in the molecule. The association of properties with
3 2
constituent atoms is also inherent in the concept of functional groups and its implication
that a particular combination of atoms, such as a hydroxy group, has properties that are
largely independent of the remainder of the molecule. There is now a vast amount of
both experimental and computational data on nuclear positions and electron distribution
in molecules. The question is whether these data can be interpreted as being the sum
of atomic properties and, if so, how one would go about “dividing” a molecule into
its constituent atoms.
R. F. W. Bader and associates at Canada’s McMaster University have derived
a means of describing the electron distribution associated with specific atoms in a
molecule, called the atoms in molecules (AIM) method. 83 The foundation of this
approach is derived from quantum mechanics and principles of physics. It uses the
methods of topology to identify atoms within molecules. The electron density of a
molecule is depicted by a series of contours. Bond paths are the paths of maximum
electron density between any two atoms. The critical point is a point on the bond path
where the electron density is a maximum or a minimum with respect to dislocation in
any direction. The bond critical point is defined by the equation

! r N r = 0 (1.24)
The critical point is the point at which the gradient vector field for the charge density is
zero, that is, either a maximum or minimum along N. The condition ! r ·N r = 0
applied to other paths between two atoms defines a unique surface that can represent
the boundary of the atoms within the molecule. The electron density within these
boundaries then gives the atomic charge. The combination of electron density contours,
bond paths, and critical points defines the molecular graph. This analysis can be
applied to electron density calculated by either MO or DFT methods. For a very
simple molecule such as H , the bond path is a straight line between the nuclei. The
2
83
R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, Oxford, 1990. For
an introductory discussion of the AIM method for describing electron density, see C. F. Matta and
R. J. Gillespie, J. Chem. Ed., 79, 1141 (2002).