Note on Interpolation Schemes

In DL_POLY_2 the short-range (Van der Waals) contributions to energy and force are evaluated by interpolation of tables constructed at the beginning of execution. DL_POLY_2 caters for three different interpolation schemes: 3-point and 4-point in $r$-space and linear interpolation in $r^2$-space. Tabulation in $r^2$ avoids the use of the square root function in evaluation of the non-bonded interactions, and thus typically decreases execution time by 10-15 %. Note that tabulation in $r^2$ usually requires more grid points (and hence more memory) than tabulation in $r$. This is to ensure sufficient accuracy is retained at small $r$.

A guide to the minimum number of grid points (mxgrid) required for interpolation in $r$ to give good energy conservation in a simulation is:

$${\tt mxgrid} \ge 100 ({\tt rcut/rmin})$$

where rmin is the smallest position minimum of the non-bonded potentials in the system. The parameter mxgrid is defined in the DL/SMALL>_PARAMS.INC file, and must be set before compilation.

A guide to the minimum number of grid points required for interpolation in $r^{2}$ is:

$${\tt mxgrid} \ge 100 ({\tt rcut/rmin})^2$$

where rmin is again the smallest position minimum of the non-bonded potentials in the system.

For users in doubt as whether to use $r$ or $r^2$-space interpolation we recommend the former. This is because tabulation in $r$ is less demanding on memory requirements and less prone to inaccuracy should too small a value of mxgrid, or too large a value of rcut, be used. Tabulation in $r$ is therefore the default option for DL_POLY, $r^2$ interpolation can be specified at compile time by `making' the executable with the directive TYPE=rsq.

The other issue of concern to users is the choice of 3 or 4 point schemes in $r$-space interpolation. The relative merits are as follows: 4 point interpolation may permit a smaller number of grid points to be used in the interpolation tables thus saving on memory requirements. 3 point interpolation is quicker than 4 point interpolation and normally sufficiently accurate. The choice involves decisions about speed, accuracy and memory requirements. 3-point interpolation is the default option.

A utility program TABCHK is provided in the DL_POLY utility sub-directory to help users choose a sufficiently accurate interpolation scheme (including array sizes) for their needs.