and −0.353 au. The H…C distance corresponding to the bond path is equal to 2.007
Å while the remaining distances amount 2.395–2.902 Å. This is worth to mention
that for the C 5 H 5
−
…HF complex a lone electron pair orbital within the NBO
approach is detected for the carbon atom of C 5 H 5
− and that this orbital is involved
in the most important n(C) → σ CH
* orbital-orbital overlap for which the energy of
interaction amounts 9.7 kcal/mol; this orbital is located at the C-atom connected by
the bond path with HF molecule.
One can see that for the A–H…π hydrogen bonds presented here there are
significant structural differences between them; those differences are reflected in the
geometry as well as in the electron charge distributions. One can observe hydrogen
bonds where the protic H-atom is linked with the Lewis base by atom-atom bond
path (in C 5 H 5
− …HF), by the atom-BCP bond path (in C 6 H 6 …HF or C 2 H 2 …HF)
and by the few equivalent atom-atom bond paths (in the C 6 H 6 …HCCH complex).
In such a situation the question arises if the meaning of the term A–H…π hydrogen
bonds should be revised. For example, maybe for the C 5 H 5
−
…HF complex the term
F–H…C hydrogen bond is more proper than the F–H…π one and maybe for the
C 6 H 6 …HCCH complex the bifurcated hydrogen bond (six F–H…C intermolecular
contacts) should be applied.
It is interesting that also σ-electrons may play a role of the proton acceptor in the
hydrogen bonds; they are designated as the A–H…σ interactions. Such systems
were analyzed theoretically for the FH…H 2 , H 3 O
+
…H 2 , NH 4
+
…H 2 and other
complexes where the molecular hydrogen acts as the Lewis base [69–72]. For all of
them the situation is similar to that one occurring for the C 2 H 2 …HF complex; i.e.
there is the bond path linking the hydrogen protic atom of the Lewis acid unit with
the bond critical point of H–H molecular hydrogen bond. Figure 15.21 presents the
molecular graph of the NH 4
+
…H 2 complex where one may observe this type of the
bond path. One can see that for this complex the N–H bond of ammonia cation is
located perpendicularly (or nearly so) to the H 2 molecule. Such T-shaped structures
are observed for other complexes mentioned here, where the σ-electrons of the
molecular hydrogen are the proton acceptor in hydrogen bonds [71]. For the
NH 4
+
…H 2 complex the binding energy is equal to −2.3 kcal/mol (MP2/6-311 +
+(3df,3pd) level, BSSE included), the ρ BCP and ∇
2
ρ BCP values for the BCP corresponding to the H…BCP bond path linking ammonia cation with H 2 molecule are
equal to 0.013 au and 0.041 au, respectively. This is interesting that the most
important orbital-orbital interaction corresponds here to the σ H-H → σ N–H
*
overlap
where σ H–H is the σ-bond orbital of molecular hydrogen while σ N–H
*
is the antibonding N–H orbital of ammonia cation, the corresponding energy of interaction is
equal to 3.6 kcal/mol (HF/6-311 ++G(d,p)//MP2/6-311 ++G(d,p) level).
The existence of the A–H…σ hydrogen bonds was confirmed by experiment.
For example, gas phase measurements of dipole moment and vibrational predissociation lifetimes as well as the determination of rotational constants performed for
the F–H…H 2 complex [73] confirmed its T-shaped structure. The high-resolution
infrared spectra were analyzed for the H 2 –HF, D 2 –HF and HD–HF complexes
solvated in helium nanodroplets and also for those species the T-shaped structure
was confirmed [74–76]. The infrared vibrational predissociation spectra
15 What Can Be Learnt from a Location of Bond Paths …
425
Å while the remaining distances amount 2.395–2.902 Å. This is worth to mention
that for the C 5 H 5
−
…HF complex a lone electron pair orbital within the NBO
approach is detected for the carbon atom of C 5 H 5
− and that this orbital is involved
in the most important n(C) → σ CH
* orbital-orbital overlap for which the energy of
interaction amounts 9.7 kcal/mol; this orbital is located at the C-atom connected by
the bond path with HF molecule.
One can see that for the A–H…π hydrogen bonds presented here there are
significant structural differences between them; those differences are reflected in the
geometry as well as in the electron charge distributions. One can observe hydrogen
bonds where the protic H-atom is linked with the Lewis base by atom-atom bond
path (in C 5 H 5
− …HF), by the atom-BCP bond path (in C 6 H 6 …HF or C 2 H 2 …HF)
and by the few equivalent atom-atom bond paths (in the C 6 H 6 …HCCH complex).
In such a situation the question arises if the meaning of the term A–H…π hydrogen
bonds should be revised. For example, maybe for the C 5 H 5
−
…HF complex the term
F–H…C hydrogen bond is more proper than the F–H…π one and maybe for the
C 6 H 6 …HCCH complex the bifurcated hydrogen bond (six F–H…C intermolecular
contacts) should be applied.
It is interesting that also σ-electrons may play a role of the proton acceptor in the
hydrogen bonds; they are designated as the A–H…σ interactions. Such systems
were analyzed theoretically for the FH…H 2 , H 3 O
+
…H 2 , NH 4
+
…H 2 and other
complexes where the molecular hydrogen acts as the Lewis base [69–72]. For all of
them the situation is similar to that one occurring for the C 2 H 2 …HF complex; i.e.
there is the bond path linking the hydrogen protic atom of the Lewis acid unit with
the bond critical point of H–H molecular hydrogen bond. Figure 15.21 presents the
molecular graph of the NH 4
+
…H 2 complex where one may observe this type of the
bond path. One can see that for this complex the N–H bond of ammonia cation is
located perpendicularly (or nearly so) to the H 2 molecule. Such T-shaped structures
are observed for other complexes mentioned here, where the σ-electrons of the
molecular hydrogen are the proton acceptor in hydrogen bonds [71]. For the
NH 4
+
…H 2 complex the binding energy is equal to −2.3 kcal/mol (MP2/6-311 +
+(3df,3pd) level, BSSE included), the ρ BCP and ∇
2
ρ BCP values for the BCP corresponding to the H…BCP bond path linking ammonia cation with H 2 molecule are
equal to 0.013 au and 0.041 au, respectively. This is interesting that the most
important orbital-orbital interaction corresponds here to the σ H-H → σ N–H
*
overlap
where σ H–H is the σ-bond orbital of molecular hydrogen while σ N–H
*
is the antibonding N–H orbital of ammonia cation, the corresponding energy of interaction is
equal to 3.6 kcal/mol (HF/6-311 ++G(d,p)//MP2/6-311 ++G(d,p) level).
The existence of the A–H…σ hydrogen bonds was confirmed by experiment.
For example, gas phase measurements of dipole moment and vibrational predissociation lifetimes as well as the determination of rotational constants performed for
the F–H…H 2 complex [73] confirmed its T-shaped structure. The high-resolution
infrared spectra were analyzed for the H 2 –HF, D 2 –HF and HD–HF complexes
solvated in helium nanodroplets and also for those species the T-shaped structure
was confirmed [74–76]. The infrared vibrational predissociation spectra
15 What Can Be Learnt from a Location of Bond Paths …
425