Figure shows how the total number of gradient evaluations required to perform the entire scan (in green) and the number of gradient evaluations per scan step (in red) scale as a function of the number of scan steps used. For this scan, between 12 and 360 steps were used, which corresponds to a dihedral angle step size of between 30°and 1°. Though the total number of gradient evaluations tends to increase with the number of steps used in the scan, the relationship is not perfectly linear. One possible explanation for this is that larger steps in the scan will tend to perturb the unconstrained degrees of freedom more, therefore requiring more gradient evaluations to converge. The upper limit of this plot indicates that when 360 1°steps are used, only 1.61 gradient evaluations are required per grid point. This is very close to the theoretical lower limit of 1 gradient evaluation per step (the dashed red line), in which each step of the scan converges in a single gradient evaluation. Such performance is only possible due to our use of null-space SQP constrained optimization, which projects the gradient to