Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.5 Three- and many-body interactions 453
M 1
E M μ F r
[8.66]
ind
( ) =− ∑ ( m)
ind m
2m= 1
the index m runs over all the sites of the molecule M. The dipole moment of site m is decomposed
into a static and an induction dipole:
0
μ = μ + μ
m m
ind
m
[8.67]
with the induction term α m depending on the polarizability and on the total electric field F tot .
The latter comes from the other permanent charges and dipoles, as well as from the induced
dipoles present in the system:
( )
ind
tot
μ = α F = α F r
m
m
S
∑ 1
m s m
s=
[8.68]
Generally, the calculation of F is not limited to three-body contributions but includes
higher order terms; for example, in simulation methods the contributions coming from all
the molecules included in the simulation box, which may be of the order of hundreds. These
contributions are not computed separately, but just used to have a collective value of F.
The sum of three- and higher body contributions to IND thus may be written and computed
in the following way:
tot
( ) ind ( )
IND many −body ≈∑ E m; F
[8.69]
m
When the system contains molecules of large size it is advisable to use a many-site description
of the molecular polarizability α. This of course means to increase the computational
effort, which is not negligible, especially in computer simulations.
The many-body contribution to IND may be negative as well as positive. In general, it
reinforces with a negative contribution minima on the PES.
The non-additive DIS contributions are described in terms of the first dipole dynamic
polarizability or by the corresponding approximate expression we have introduced for the
dimeric case.
DIS contributions are already present and are quite important for the liquid aggregation
of spherical systems. Even spherical monomers exhibit dynamical dipoles and the related
two- and many-body contributions to DIS.
The most important term is known as the Axilrod-Teller term and describes the interaction
of three instantaneous dipoles. The sign of the Axilrod-Teller term strongly depends
on the geometry. It is negative for almost linear geometries and positive in triangular arrangements.
Four body contributions of the same nature are generally of opposite sign and
thus they reduce the effect of these terms on the PES shape.
The potentials for polar liquids generally neglect many-body dispersion contributions.
Screening many-body effects
When the material condensed system contains mobile charges, the electrostatic interactions,
which are strong and with the slowest decay with the distance, are severely damped.
Every charged component of the system tends to attract mobile components bearing the op-