monosynaptic. ELF and CD clearly show how charge donation towards beryllium is
less effective with BeF 2 with respect to BeH 2 and offer a much unambiguous
interpretation than QTAIM.
There are other interesting features in Fig. 17.7. For instance, when the BeF 2 :
NH 3 complex is formed, not only the V(N) monosynaptic basin on ammonia
changes into a V(Be,N) disynaptic basin, but also undergoes a significant volume
contraction, in spite of the fact that its total population decreases only slightly. This
is a direct consequence of the strength of the interaction leading to a very short
Be···N distance and therefore the volume of the basin becomes almost 1/3 the one
in the isolated base. Similar changes are observed for the other complexes. It can
also be noted in agreement with our previous CD and QTAIM analysis that the
population of the V(Be,F) disynaptic basin decreases quite significantly in the
binary complexes with respect to the isolated BeF 2 molecule, leading to a weaker
and longer Be–F bond. In addition, the net population at the F lone pairs increases.
The description of the NBO is in line with that obtained by means of these
approaches, showing that the formation of a beryllium bond involves the interaction
of the lone-pair of the base with both the empty 2p orbitals of Be and the σBeX*
antibonding orbitals. The latter interaction is directly responsible of the lengthening
of the Be–X linkages already discussed, whereas the former accounts for the
bending of the BeX 2 moiety, because the population of the initially empty p orbital
of Be, changes its hybridization from sp to sp
n , n being greater than one [19].
It is now interesting to look at the information that CD scheme can provide in the
quantification of the different charge flows associated with the bond formation. As a
suitable example, we will study the beryllium bond formation in the complexes of
H 2 O and H 2 S, taking advantage of the symmetry of these complexes. Indeed, the
electron density difference can be partitioned according to the irreducible representation of the point group to which both the molecule and the fragments belong
[87]. This permits the separation of the electron density difference into symmetry
components, according to the following equations:
Dq ¼ R p Dq p
ð17:2Þ
Dq ¼ R i2p j/ i AB
ð Þj
2 À R i2p j/ i A
ð Þj
2 À R i2p j/ i B
ð Þj
2
ð17:3Þ
where p labels the different irreducible representations. A, B and AB represent the
two monomers and the complex, respectively, while ϕi are Kohn-Sham orbitals.
This decomposition permits the separation of the overall CD function into additive
symmetry component.
The H 2 Be–OH 2 complex belongs to the C 2 v symmetry point group with all
nuclei laying in the σv(yz) plane. The other symmetry plane σv(xz), containing the
Be and O nuclei, cut in half both the H–Be–H, and the H–O–H angles.
Accordingly, the A1 component is expected to correlate with the donation from
occupied lone pairs of water to unoccupied spz orbital (of beryllium atom) and σ*
(of the Be–H bond) of BeH 2 . The B1 symmetry correlates with the donation to the
out-of-plane unoccupied px orbital of Be and B2 corresponds to the backdonation
472
K. Mykolayivna Lemishko et al.
less effective with BeF 2 with respect to BeH 2 and offer a much unambiguous
interpretation than QTAIM.
There are other interesting features in Fig. 17.7. For instance, when the BeF 2 :
NH 3 complex is formed, not only the V(N) monosynaptic basin on ammonia
changes into a V(Be,N) disynaptic basin, but also undergoes a significant volume
contraction, in spite of the fact that its total population decreases only slightly. This
is a direct consequence of the strength of the interaction leading to a very short
Be···N distance and therefore the volume of the basin becomes almost 1/3 the one
in the isolated base. Similar changes are observed for the other complexes. It can
also be noted in agreement with our previous CD and QTAIM analysis that the
population of the V(Be,F) disynaptic basin decreases quite significantly in the
binary complexes with respect to the isolated BeF 2 molecule, leading to a weaker
and longer Be–F bond. In addition, the net population at the F lone pairs increases.
The description of the NBO is in line with that obtained by means of these
approaches, showing that the formation of a beryllium bond involves the interaction
of the lone-pair of the base with both the empty 2p orbitals of Be and the σBeX*
antibonding orbitals. The latter interaction is directly responsible of the lengthening
of the Be–X linkages already discussed, whereas the former accounts for the
bending of the BeX 2 moiety, because the population of the initially empty p orbital
of Be, changes its hybridization from sp to sp
n , n being greater than one [19].
It is now interesting to look at the information that CD scheme can provide in the
quantification of the different charge flows associated with the bond formation. As a
suitable example, we will study the beryllium bond formation in the complexes of
H 2 O and H 2 S, taking advantage of the symmetry of these complexes. Indeed, the
electron density difference can be partitioned according to the irreducible representation of the point group to which both the molecule and the fragments belong
[87]. This permits the separation of the electron density difference into symmetry
components, according to the following equations:
Dq ¼ R p Dq p
ð17:2Þ
Dq ¼ R i2p j/ i AB
ð Þj
2 À R i2p j/ i A
ð Þj
2 À R i2p j/ i B
ð Þj
2
ð17:3Þ
where p labels the different irreducible representations. A, B and AB represent the
two monomers and the complex, respectively, while ϕi are Kohn-Sham orbitals.
This decomposition permits the separation of the overall CD function into additive
symmetry component.
The H 2 Be–OH 2 complex belongs to the C 2 v symmetry point group with all
nuclei laying in the σv(yz) plane. The other symmetry plane σv(xz), containing the
Be and O nuclei, cut in half both the H–Be–H, and the H–O–H angles.
Accordingly, the A1 component is expected to correlate with the donation from
occupied lone pairs of water to unoccupied spz orbital (of beryllium atom) and σ*
(of the Be–H bond) of BeH 2 . The B1 symmetry correlates with the donation to the
out-of-plane unoccupied px orbital of Be and B2 corresponds to the backdonation
472
K. Mykolayivna Lemishko et al.