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This is the simplest case: each of the
subsystems (molecules) is considered as a distribution of charges with charge density
. The total charging energy is
We assume the molecules well separated with their center of mass at
. We first consider the contribution from two different molecules,
, and thus write
|
|
|
(2.2) |
and expand
for each pair
, using the Taylor expansion
with
and
.
We assume uncharged molecules, i.e.
|
|
|
(2.4) |
This yields
Here, the dipole moments are defined as
and the remaining terms are dipole-quadrupole, quadrupole-quadrupole etc interaction energies which decay faster with increasing
. Usually the dipole-dipole interaction terms are dominant over the higher multipoles for the interaction between molecules.
Summarizing, we have
Exercise: Derive the expression for
Subsections
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Tobias Brandes
2005-04-26