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A conjugate-gradient algorithm (a simple discussion of this algorithm can be found for instance in [28]) is used to relax the ions into their instantaneous groundstate. In the first step ions (and cell shape) are changed along the direction of the steepest descent (i.e. the direction of the calculated forces and stress tensor). The conjugate gradient method requires a line minimization, which is performed in several steps: i) first a trial step into the search direction (scaled gradients) is done, with the length of the trial step controlled by the POTIM parameter (section 6.23). Then the energy and the forces are recalculated. ii) The approximate minimum of the total energy is calculated from a cubic (or quadratic) interpolation taking into account the change of the total energy and the change of the forces (3 pieces of information), then a corrector step to the approximate minimum is performed. iii) After the corrector step the forces and energy are recalculated and it is checked whether the forces contain a significant component parallel to the previous search direction. If this is the case, the line minimization is improved by further corrector steps using a variant of Brent's algorithm[28].

To summarize: In the first ionic step the forces are calculated for the initial configuration read from POSCAR , the second step is a trial (or predictor step), the third step is a corrector step. If the line minimization is sufficiently accurate in this step, the next trial step is performed.

1 initial positions
2 trial step
3 corrector step, i.e. positions corresponding to anticipated minimum
4 trial step
5 corrector step

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