Chemistry Reference
In-Depth Information
2
b
2
D
E
¼
Da
¼
D
e
ð
5
:
1
Þ
where, as usual, the
a
s replace the appropriate molecular orbital energies
«
,
Da ¼ a
LUMO
a
HOMO
«
LUMO
«
HOMO
, and the bond strength D
e
is
taken as the negative of the intermolecular energy at the minimum of the
potential energy curve. From Equation (5.1), an estimate of the intermo-
lecular interaction integral |
b
| is obtained if we use the data from the last
column of Table 4.4 of the previous chapter in conjunction with calcu-
lated values of
Da
:
1
=
2
D
e
Da
2
jbj¼
ð
5
:
2
Þ
Table 5.1 gives for four simple molecules the values of HOMO/LUMO
orbital energies calculated with accurate augccpVTZ-GTO
3
basis sets at
the University of Modena and the values of the intermolecular |
b
|s
resulting from Equation (5.2).
In the table, R is the distance between the centres of mass of the
interacting molecules, roughly corresponding to the sum of the van der
Waals radii of each monomer. It is seen that the estimated values of |
b
| for
the H-bonded dimers between the two dipolar molecules, (HF)
2
and
(H
2
O)
2
, are 5-10 times larger than the values resulting for the VdW
dimers of the centrosymmetric molecules H
2
and N
2
, whose first non-
vanishing electric moment is the quadrupole. This suggests the electro-
static interaction as a possible source of H-bonding, as we shall see in the
next section. These values of |
b
| have nearly the same order of magnitude
as those occurring for the corresponding monomers (see Table 2.8 of
Chapter 2), suggesting that the H-bond has a strength not far from that of
a weak chemical bond.
5.2 ELECTROSTATIC INTERACTIONS AND THE
HYDROGEN BOND
€
The Rayleigh-Schr
odinger perturbation theory of the previous chapter
(see Magnasco, 2007, 2009a) suggests that, in the VdW region, two
typical factors can originate a hydrogen bond in a dimer: (1) the first-
order electrostatic interaction in the case of homo- and heterodimers of
3
Augmented-correlation-consistent polarized-valence triple zeta GTOs (Magnasco, 2009a).
