total electron energy density at BCP, H BCP , is negative what means that the
interaction is at least partly covalent in nature. The similar situation is observed for
all five Br–F connections—the positive ∇
2
ρ BCP values and the negative H BCP ones.
It seems that the strong interaction of the BrF 5 species with the Cl
− anion extorts the
greater electron density changes in the complex, particularly in the BF 5 moiety. One
lone electron pair of bromine is observed in the complex within the NBO approach,
similarly as in the isolated BrF 5 species; however the lone pairs in the complex
possesses s-character in 99.2 %. This is confirmed by the QTAIM approach since
Fig. 15.10 shows the spherical electron charge density concentration around bromine center. The change of the location of the bromine electron lone pair results in
the existence of the straight bond path linking the Br and Cl centers in contrary to
the interactions of the BrF 5 molecule with weak Lewis bases (see Fig. 15.9).
The positive values of the laplacian of electron density at all BCPs corresponding to the Br–F and Br–Cl links in the BrF 5 –Cl
− complex may indicate the
ionic character of interactions since it was pointed out that such values are typical
for the closed-shell interactions [5–7]. This means that in the latter complex all
bonds (links) are strongly polarized; the NBO approach shows that the polarization
for the Br–F bonds is equal to 23.2 % and it amounts 33.6 % for the Br–Cl bond (%
of the electron density at the Br center). The Br atomic charge calculated within
NBO and QTAIM approaches is equal to +2.25 au and +2.32 au, respectively.
Figure 15.10 clearly shows the concentration of the electron density at attractors
and not at interatomic regions; the similar situation is observed for all BrF 3 and
BrF 5 complexes.
There is another interesting finding for the BrF 5 -Cl
− complex; the NBO
approach shows that there are tri-center four-electron (3c-4e) linear bonds here.
They concern the following linear triads in the BF 5 Cl
− moiety; two F–Br–F triads
and one F–Br–Cl triad. Such 3c-4e bonds were analyzed earlier in literature; for
example Weinhold and Landis analyzed numerous hypervalent centers [21] and
they extended the 3c-4e concept of Pimentel and Rundle [39, 40].
15.3 Lewis Acid–Lewis Base Interactions
The σ-hole concept mentioned in the previous section which explains the mechanisms of formation of the halogen bond is also useful to analyze other Lewis acid–
Lewis base interactions [26, 27, 41]. One can mention tetrel [42–45], pnicogen [46–
50] and chalcogen bonds [51–53] where the elements of Groups IV, V and VI,
respectively, play the role of the Lewis acid centers. The mechanism of the formation of those bonds is practically the same as that one of the halogen bond; a
region of positive electrostatic potential (designated as σ-hole) on the extension of
the bond to the atom being the acidic center is an effect of the electron charge shift
from the outermost part of this center. These centers possessing σ-holes are usually
characterized by the unshared electron pairs thus they may act simultaneously as the
Lewis acids and the Lewis bases. The situation is slightly different for the tetrel
412
S.J. Grabowski
interaction is at least partly covalent in nature. The similar situation is observed for
all five Br–F connections—the positive ∇
2
ρ BCP values and the negative H BCP ones.
It seems that the strong interaction of the BrF 5 species with the Cl
− anion extorts the
greater electron density changes in the complex, particularly in the BF 5 moiety. One
lone electron pair of bromine is observed in the complex within the NBO approach,
similarly as in the isolated BrF 5 species; however the lone pairs in the complex
possesses s-character in 99.2 %. This is confirmed by the QTAIM approach since
Fig. 15.10 shows the spherical electron charge density concentration around bromine center. The change of the location of the bromine electron lone pair results in
the existence of the straight bond path linking the Br and Cl centers in contrary to
the interactions of the BrF 5 molecule with weak Lewis bases (see Fig. 15.9).
The positive values of the laplacian of electron density at all BCPs corresponding to the Br–F and Br–Cl links in the BrF 5 –Cl
− complex may indicate the
ionic character of interactions since it was pointed out that such values are typical
for the closed-shell interactions [5–7]. This means that in the latter complex all
bonds (links) are strongly polarized; the NBO approach shows that the polarization
for the Br–F bonds is equal to 23.2 % and it amounts 33.6 % for the Br–Cl bond (%
of the electron density at the Br center). The Br atomic charge calculated within
NBO and QTAIM approaches is equal to +2.25 au and +2.32 au, respectively.
Figure 15.10 clearly shows the concentration of the electron density at attractors
and not at interatomic regions; the similar situation is observed for all BrF 3 and
BrF 5 complexes.
There is another interesting finding for the BrF 5 -Cl
− complex; the NBO
approach shows that there are tri-center four-electron (3c-4e) linear bonds here.
They concern the following linear triads in the BF 5 Cl
− moiety; two F–Br–F triads
and one F–Br–Cl triad. Such 3c-4e bonds were analyzed earlier in literature; for
example Weinhold and Landis analyzed numerous hypervalent centers [21] and
they extended the 3c-4e concept of Pimentel and Rundle [39, 40].
15.3 Lewis Acid–Lewis Base Interactions
The σ-hole concept mentioned in the previous section which explains the mechanisms of formation of the halogen bond is also useful to analyze other Lewis acid–
Lewis base interactions [26, 27, 41]. One can mention tetrel [42–45], pnicogen [46–
50] and chalcogen bonds [51–53] where the elements of Groups IV, V and VI,
respectively, play the role of the Lewis acid centers. The mechanism of the formation of those bonds is practically the same as that one of the halogen bond; a
region of positive electrostatic potential (designated as σ-hole) on the extension of
the bond to the atom being the acidic center is an effect of the electron charge shift
from the outermost part of this center. These centers possessing σ-holes are usually
characterized by the unshared electron pairs thus they may act simultaneously as the
Lewis acids and the Lewis bases. The situation is slightly different for the tetrel
412
S.J. Grabowski