Hautman Klein Ewald Optimisation

Setting the HKE parameters can also be achieved rather simply, by the use of a hke precision directive in the CONTROL file e.g.

hke precision 1d-6 1 1

which specifies the required accuracy of the HKE convergence functions, plus two additional integers; the first specifying the order of the HKE expansion (nhko) and the second the maximum lattice parameter (nlatt). DL_POLY_2 will permit values of nhko from 1-3, meaning the HKE Taylor series expansion may range from zeroth to third order. Also nlatt may range from 1-2, meaning that (1) the nearest neighbour, and (2) and next nearest neighbour, cells are explicitly treated in the real space part of the Ewald sum. Increasing either of these parameters will increase the accuracy, but also substantially increase the cpu time of a simulation. The recommended value for both these parameters is 1 and if both these integers are left out, the default values will be adopted.

As with the standard Ewald and SPME methods, the user may set alternative control parameters with the CONTROL file hke sum directive e.g.

hke sum 0.05 6 6 1 1

which would set $\alpha=0.05~$Å$^{-1}$, kmax1 = 6, kmax2 = 6. Once again one may check the accuracy by comparing the Coulombic energy with the virial, as described above. The last two integers specify, once again, the values of nhko and nlatt respectively. (Note it is possible to set either of these to zero in this case.)

Estimating the parameters required for a given simulation follows a similar procedure as for the standard Ewald method (above), but is complicated by the occurrence of higher orders of the convergence functions. Firstly a suitable value for $\alpha$ may be obtained when nlatt=0 from the rule: $\alpha=\beta/r_{cut}$, where $r_{cut}$ is the largest real space cutoff compatible with a single MD cell and $\beta$=(3.46,4.37,5.01,5.55) when nhko=(0,1,2,3) respectively. Thus in the usual case where nhko=1, $\beta$=4.37. When nlatt$\ne$0, this $\beta$ value is multiplied by a factor $1/(2*nlatt+1)$.

The estimation of kmax1,2 is the same as that for the standard Ewald method above. Note that if any of these parameters prove to be insufficiently accurate, DL_POLY_2 will issue an error in the OUTPUT file, and indicate whether it is the real or reciprocal space sums that is questionable.