**6. What should be the convergence criteria?**

In contrast to the simple analytical functions that we have used to illustrate the operation of the various Minimization methods, in 'real' molecular modeling applications it is rarely possible to identify the 'exact' location of minima and saddle points. We can only ever hope to find an approximation to the true minimum or saddle point. Unless instructed otherwise, most Minimization methods would keep going forever, moving ever closer to the minimum. It is therefore necessary to have some means to decide when the Minimization calculation is sufficiently close to the minimum and so can be terminated. Any calculation is of course limited by the precision with which numbers can be stored on the computer, but in most instances it is usual to stop well before this limit is reached. A simple strategy is to monitor the energy from one iteration to the next and to stop when the difference in energy between successive steps falls below a specified threshold. An alternative is to monitor the change in coordinates and to stop when the difference between successive configurations is sufficiently small. A third method is to calculate the root-meansquare gradient. This is obtained by adding the squares of the gradients of the energy with respect to the coordinates, dividing by the number of coordinates and taking the square root. It is also useful to monitor the maximum value of the gradient to ensure that the Minimization has properly relaxed all the degrees of freedom and has not left a large amount of strain in one or two coordinates [23].
