The slow-cooling mode

In this mode you define a starting temperature T₀ and a finishing temperature T_f, with T₀ > T_f. At any time step t during the minimisation, the temperature T will be given by T = T₀ - t(T₀ - T_f)/t_total, where t_total is the total number of time steps for the minimisation. In the slow cooling mode the maximum move sizes (as defined above) are linearly dependent on both time and the current R-factor, with max($\Delta_{{\rm t}}^{}$) = 0.5Rt/t_total and max($\Delta_{{\kappa}}^{}$) = $\pi$Rt/t_total, where R is the current R-factor, t is the current time step and t_total is the total number of time steps for the minimisation. The dependence on R is justified on the grounds that as we approach a minimum of the target function, we should be sampling the configurational space on a finer grid¹⁹. The time dependence follows from a similar argument.

Footnotes

... grid¹⁹

The word ``grid'' is used here metaphorically. For all practical purposes the values returned by the random number generator in the 0.0-1.0 range are continuous (if the generator returns values in the range 0 to 2³¹ - 1, then the `grid size' on $\Delta_{{\kappa}}^{}$ for example, is only 0.00000008 degrees)