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c CCLRC

Section 2.4

2.4.3

Coulomb Sum with Distance Dependent Dielectric

This potential attempts to address the difficulties of applying the direct Coulomb sum, without the
brutal truncation of the previous case. It hinges on the assumption that the electrostatic forces are
effectively `screened' in real systems - an effect which is approximated by introducing a dielectric
term that increases with distance.

The interatomic potential for two charged ions is

U (r

) =

)

(2.134)

with q the charge on an atom labelled , and r

the magnitude of the separation vector r

= r

-r

(r) is the distance dependent dielectric function. In DL POLY 3 it is assumed that this function

has the form

(r) =

r ,

(2.135)

where

is a constant. Inclusion of this term effectively accelerates the rate of convergence of the

Coulomb sum.

The force on an atom j derived from this potential is

(2.136)

with the force on atom i the negative of this.

The contribution to the atomic virial is

W = -r

· f

(2.137)

which is -2 times the potential term.

The contribution to be added to the atomic stress tensor is given by

= r

(2.138)

where , are x, y, z components. The atomic stress tensor is symmetric.

In DL POLY 3 these forces are handled by the routine coul dddp forces.

2.4.4

Reaction Field

In the reaction field method it is assumed that any given molecule is surrounded by a spherical
cavity of finite radius within which the electrostatic interactions are calculated explicitly. Outside
the cavity the system is treated as a dielectric continuum. The occurrence of any net dipole within
the cavity induces a polarisation in the dielectric, which in turn interacts with the given molecule.
The model allows the replacement of the infinite Coulomb sum by a finite sum plus the reaction
field.

The reaction field model coded into DL POLY 3 is the implementation of Neumann based on
charge-charge interactions [

]. In this model, the total coulombic potential is given by

0 j<n

(2.139)