EWALD SUMMATION VERSUS DIRECT SUMMATION OF SHIFTED-FORCE POTENTIALS FOR THE CALCULATION OF ELECTROSTATIC INTERACTIONS IN SOLIDS - A QUANTITATIVE STUDY

The calculated Madelung energies and Madelung forces of the electrosta tic interaction for nine crystal structures are reported. The method o f direct summation with two different shifted-force potentials is comp ared to the Ewald summation. There is a considerable difference in the convergence of the energy and the force for the two shifted-force pot entials regarding the cutoff radius. The convergence depends not only on the potential itself, but also on the crystal structure. One of the shifted-force potentials used is implemented in the CHARMM force fiel d. The energy calculated with this potential shows a good convergence for small cutoff radii. With the other shifted-force potential, the fo rce shows a better convergence for small cutoff radii. The number of p air interactions for obtaining the Madelung limit using the Ewald summ ation and the direct summation of a shifted-force potential is also re ported. For complex structures like zeolites, the number of relevant p air interactions is smaller using the direct summation of a shifted-fo rce potential. For simple structures such as cesium chloride, the numb er of significant pair interactions is smaller using the Ewald summati on. (C) 1997 by John Wiley & Sons, Inc.