Madelung constants for ionic crystals using the Ewald sum
Ionic crystal configuration energies have always been one of the bugbears of computational thermodynamics due to the inherent long-range interactions. Unlike the van der Waals forcer associated with non-ionic compounds, it is not possible to utilize a long-range cutoff,' ionic interactions r...
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| Format: | Article |
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2001
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| Online Access: | http://journalarticle.ukm.my/1380/ http://journalarticle.ukm.my/1380/ |
| Summary: | Ionic crystal configuration energies have always been one of the bugbears of
computational thermodynamics due to the inherent long-range interactions. Unlike the
van der Waals forcer associated with non-ionic compounds, it is not possible to utilize
a long-range cutoff,' ionic interactions require summation over an infinitely large
crystal lattice. The situation is further complicated by the fact that the resulting
infinite series for an ordered crystal lattice is non-convergent. This means that a direct
summation over the charged particles is not feasible. This paper develops and
analyzas a powerful yet under utilized method for calculating these lattice energies,
the Ewald sum. Not only is this a powerful and accurate of calculating the
configuration energies of ionic crystals, it is also not dependent on existence of crystal
structure. Hence this method is useful in any application involving Coulonbic
interactions, including substances in the liquid phase. The general Ewald method is
presented with some simplifying assumptions to produce a working equation
amenable to computer evaluations and sample computations are made for NaCI and
CsCI. Extensive discussion is presented on determining the optimum splitting
parameter: A simple yet general FORTRAN program for calculating the Madelung
constant for an ionic system of any phase is presented and a sensitivity analysis is
performed |
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