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###

`IBRION`=1

For `IBRION`=1, a quasi-Newton (variable metric) algorithm is used to relax
the ions into their instantaneous
groundstate. The forces and the stress tensor are used to determine the search directions
for finding the equilibrium positions (the total energy is not taken into account).
This algorithm is very fast and efficient close to local minima, but
fails badly if the initial positions are a bad guess (use `IBRION`=2 in
that case).
Since the algorithm builds up an approximation of the Hessian matrix
it requires very accurate forces, otherwise it will fail
to converge. An efficient way to achieve this is to set
`NELMIN` to a value between 4 and 8 (for
simple bulk materials 4 is
usually adequate, whereas 8 might be required for complex surfaces
where the charge density converges very slowly).
This forces a minimum of 4 to 8
electronic steps between each ionic step, and guarantees that the
forces are well converged at each step.
The implemented algorithm is called RMM-DIIS[26]. It implicitly
calculates an approximation of the inverse Hessian
matrix by taking into account information from
previous iterations. On startup, the initial Hessian
matrix is diagonal and equal to `POTIM`.
Information from old steps (which can lead to linear dependencies)
is automatically removed from the iteration history, if required.
The number of vectors kept in the iterations history (which corresponds
to the rank of the Hessian matrix must not exceed the degrees of
freedom. Naively the number of degrees of freedom
is 3*(`NIONS`-1). But
symmetry arguments or constraints can reduce this number
significantly. There are two algorithms build in to remove
information from the iteration history.
i) If `NFREE` is set in the INCAR file,
only up to `NFREE` ionic steps are kept in the iteration history
(the rank of the approximate Hessian matrix is not larger than `NFREE`).
ii) If `NFREE` is not specified, the criterion whether information is removed from the
iteration history is based on the eigenvalue spectrum of the inverse Hessian matrix:
if one eigenvalue of the inverse Hessian matrix is larger than 8, information from
previous steps is discarded.
For complex problems `NFREE` can usually be set to a rather large
value (i.e. 10-20), however systems of low dimensionality
require a carful setting of `NFREE` (or preferably an exact counting of
the number of degrees of freedom). To increase `NFREE` beyond 20
rarely improves convergence. If `NFREE` is set to too large,
the RMM-DIIS algorithm might diverge.

The choice of a reasonable `POTIM` is also important and can speed up
calculations significantly, we recommend to find an optimal `POTIM`
using `IBRION`=2 or performing a few test calculations (see below).

** Next:** IBRION=2
** Up:** IBRION-tag, NFREE-tag
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N.B. Requests for support are to be addressed to: vasp.materialphysik@univie.ac.at