The transition from
weak (noncovalent) interactions to fully developed
covalent bonds is examined using the quantum theory of atoms in molecules
in a series of halogen-bonded (XB) complexes of bromosubstituted electrophiles,
RBr, with 1,4-diazabicyclo[2.2.2]octane (DABCO) and Cl
–
and Br
–
anions. The gradual decrease in the XB
lengths in these associations,
d
Br···Y
(where Y = Cl
–
, Br
–
, or N),
was accompanied by the exponential increase in the binding energies
and charge transfer, as well as electron densities and magnitudes
of the kinetic and potential energy densities at the bond critical
points (BCPs) on the Br···Y bond path. These indices,
as well as characteristics of the adjacent bonds in the XB donor,
followed remarkably close trend lines when plotted against the normalized
XB length
R
BrY
=
d
Br···Y
/(
r
Br
+
r
Y
) (where
r
Br
and
r
Y
are the van der Waals radii) regardless of
the methods [MP2/6-311+G(d,p) or M062X/6-311+G(d,p)], media (gas phase
or dichloromethane), and nucleophiles (Cl
–
, Br
–
, or DABCO). In the systems with an
R
BrY
higher than about 0.78, the energy densities
H
(
r
) at BCPs at the Br···Y bond
path were small and positive, and XBs did not substantially affect
the characteristics of the adjacent R–Br covalent bond in the
XB donor. Accordingly, the XB can be identified as noncovalent in
this range. In the complexes with
R
BrY
values between about 0.67 and 0.78, energy densities
H
(
r
) at Br···Y BCPs were negative, and
their magnitudes increased with the decrease in the Br···Y
separation. In this range, formation of XBs was accompanied by the
increase in the R–Br bond length in the XB donor and the decrease
in the magnitude of the (negative)
H
(
r
) values at the BCPs of the R–Br bonds. XBs can be classified
as partially covalent in this
R
BrY
range.
At an
R
BrY
less than about 0.67, electron
densities were larger, and energy densities were more negative at
BCPs of the Br···Y bond than those at BCPs of the R–Br
bond in the XB donor. This indicates that Br···Y bonds
were stronger than R–Br bonds, and these (Br···Y)
XBs can be regarded as essentially covalent. The synchronous change
of a variety of (R–Br and Br···Y) bonding characteristics
with
R
BrY
suggests that the normalized
XB bond length can be used as a basic parameter in the identification
of the type of intermolecular i...