Theor Chem Acc (2015) 134:117
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topological feature is a maximum, minimum, or saddle.
If s = +r a minimum results; s = −r denotes a maximum; if −r < s < r , a saddle results. The trivial case
occurs when rank and signature are identically zero.
This represents a critical point at infi nity and occurs in
all systems at an infi nite distance away from the molecule. Table 1 summarizes the ABIM classifi cation of
radial density critical architectures.
3.2.2 Atomic topology
The radial density topology of atoms is fairly simple,
though not featureless. At the nucleus, the radial distance
is zero, and thus, a minimum critical point (PM) occurs.
Radially outward from the nucleus, a series of maximum
critical spheres (SX) and minimum critical spheres (SM)
are observed. For atoms in the fi rst three periods, the
Fig. 3 Radial density in the
xy -plane of H 2 and the second
period hydrides. The central
atom is located at (0, 0). The
hydrogen nuclei are clearly
identifi ed by the distinct depressions (dimples) in the graphs
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Reprinted from the journal