During the BH trajectory, new structures were obtained by perturbing the unminimized structure from the previous step, rather than applying perturbations to the minimized structures. One reason for this decision is that, since unit cell angles are not fixed during local minimization, unit cells can become quite flat after minimization (i.e. having very acute or obtuse unit cell angles). These flat unit cells can correspond to physically realistic structures, but lead to difficulties in applying further perturbation and minimization.