Regular representation of irregular charge distributions

The electrostatic potential of a non-symmetric arrangement of charges and dielectrics may be calculated numerically by a finite difference iterative procedure, provided that the charges are associated only with points of a three dimensional cartesian grid. This condition is not met for real systems of interest. An algorithm is derived for the distribution of each real charge to the eight surrounding grid points, which minimises the error in the calculated electrostatic potential of the distributed charge system. The errors remaining are due to quadrupolar and higher 2 n -pole moments of distributed charge system which give rise to a potential which falls off with distance, R, from the charges as 1/R 3 or faster. The derived algorithm has been applied to the electrostatic potential around a complex protein and allows more accurate calculations than have to date been possible, particularly in regions close to the potential-generating charged groups. For all points further from the charge than twice the grid...

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