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222. MADE: Coulombic Lattice Energy of an Ionic Crystal
by A. B. Blake, Department of Chemistry, University of
Hull, Hull, England
A knowledge of the lattice energies of crystals
containing complex ions is useful in the estimation of
bond energies and charge distributions from
thermochemical data. This program calculates the
electrostatic ("Madelung") part of the cohesive energy
of an ionic crystal of any structure and complexity by
the method of Bertaut.
The net electrostatic cohesive energy of a crystal is
changed if the point-charge ions are replaced by
equivalent spherical-distributions of charge density
s(r). The (negative) energy per mole is then
where n is the number of formula units per unit cell.
WT is the total electrostatic energy of the periodic
charge distribution, per unit cell, and is given by
where V is the unit-cell volume; F'(hkl) (the 'electric
structure factor') is defined as
where qj is the charge on the ion whose fractional
coordinates in the unit cell are xj,uj,zj; F(S) is the
Fourier transform of the normalised charge-density
function s(r); and S (hkl) is the distance of the point
h, k, l from the origin of the reciprocal lattice,
given by
.
Here O(a,~)*, O(b,~)*, and O(c,~)* are the edges of
the reciprocal cell. The sum over h, k, l is to
include all positive and negative integral values of
these indices except h=k=1=0; however, it converges
fairly rapidly and may be terminated by setting a
maximum to the value of S. Wp is a correction for the
overlap of the individual ionic charge-distributions
s(r), and is zero if these are chosen so that s(r) = 0
for r > ro, where 2ro,
The program provides four alternative choices for the
form of s(r). These are uniform, linear, parabolic,
and Gaussian.
FORTRAN
Lines of Code: 715
Recommended Citation: A. B. Blake, QCPE 11, 222
(1972).
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