Figure 2.5 shows the performance of the L-BFGS minimiser as a function of . We used the following additional L-BFGS specific settings. The number of corrections in the BFGS update was set to (Nocedal's recommendation for the number of corrections is , see Reference lbfgs), the maximum step size was , and we limited the step size for each image separately, i.e.

(4.38) |

where is the step for image . The diagonal elements of the inverse Hessian were initially set to .

From Figure 2.5 it can be seen that the performance of L-BFGS minimisation is relatively independent of the choice of force constant. All the optimisations with converged to the steepest-descent path, and, for most of this range, in less than 100 iterations. This method therefore gives roughly an order of magnitude improvement in speed over SQVV minimisation [see Figure 2.4 (a)].

We found it helpful to limit the step size while optimising the NEB with the L-BFGS minimiser. The magnitude and direction of the gradient on adjacent images can vary significantly. Taking bigger steps can cause the appearance of temporary discontinuities and kinks in the NEB. The NEB still converges to the correct path, but it takes a while for these features to disappear and the algorithm does not converge any faster.