Chemistry Reference
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given by a polarizability tensor whose nonvanishing components depend
on molecular symmetry (Buckingham, 1967). The isotropic polarizability
of molecules can be directly compared with the polarizability of atoms.
The key role of atomic polarizabilities in assessing intermolecular poten-
tials in a variety of systems has been widely documented (Cambi et al.,
1991; Aquilanti et al., 1996).
We now turn to consideration of VdW interactions.
4.5 THE van der WAALS INTERACTIONS
As we have seen, the second-order VdW interactions are: (i) the distortion
(induction or polarization) interaction, where an atom or molecule is
distorted by the permanent electric field provided by a second molecule;
and (ii) the dispersion interaction, whose leading term arises from the
simultaneous coupling of the mutually induced dipoles on the two
molecules (Buckingham, 1967; Stone, 1996; Magnasco, 2007, 2009a).
The dispersion energy, whose name is derived from the fact that the
physical quantities involved are the same as those determining the
dispersion of the refractive index inmedia, is recognized as an interatomic
or intermolecular electron correlation (Magnasco and McWeeny, 1991),
and is called London attraction from the name of the scientist who first
explained why two ground state H atoms attract each other in long range
(London, 1930a, 1930b).
At the large distances at which they usually occur, VdW forces result
mostly from weak attractive interactions described by second-order
processes whose energy lowering is:
b
2
D«
<
D
E
¼
0
ð
4
:
40
Þ
as we have shown before. Here,
D« ¼ «
i
or
«
j
for induction (single exci-
tation on A or B),
D« ¼ «
i
þ«
j
for dispersion (double simultaneous excita-
tions on A and B), and, for the leading terms,
b
2
2
, where
m
i
is
¼ m
i
2
ð
F
B
Þ
the dipole on A induced by the field of B.
Let us consider in greater detail the long-range interaction of an atom A
(at the origin of the coordinate system) with an atom (or linear molecule) B,
whose centre of mass has coordinates R,
u
,
w
. The problem has been fully
treated by Buckingham (1967) using Rayleigh-Schr
€
odinger perturbation
theory in terms of cartesian tensors, and byMagnasco et al. (1988, 1990b)
in terms of spherical tensors. For the sake of simplicity, we shall give here an
elementary derivation in terms of classical electrostatics by considering the
