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Next: 7.20 POTIM-tag Up: 7 The INCAR File Previous: 7.18 NBLOCK and KBLOCK-tag

7.19 IBRION-tag, NFREE-tag



if NSW=0 or 1 -1
else 0

IBRION determines how the ions are updated and moved. For IBRION=0, a molecular dynamics is performed, whereas all other algorithms are destined for relaxations into a local energy minimum. For difficult relaxation problems it is recommended to used the conjugate gradient algorith (IBRION=2), which - at present - posses the most reliable backup routines. Damped molecular dynamics are often usefull, when starting from very bad initial guesses. Close to the local minimum the RMM-DIIS is usually the best choice.

No update; ions are not moved, but NSW outer loops are performed. In each outer loop the electronic degrees of freedom are re-optimized (for NSW>0 this makes obviously not much sense, except for test purposes). If no ionic updated is required use NSW=0 instead.
Standard ab-initio molecular dynamics. A Verlet algorithm (or fourth order predictor corrector if vasp was linked with stepprecor.o) is used to integrate Newton's equations of motion. POTIM supplies the timestep in femto seconds. The parameter SMASS allows additional control (see Sec. 7.27).

Mind: At the moment only constant volume MD's are possible.

A quasi-Newton (or variable metric) algorithm is used to relax the ions into their instantaneous groundstate. The forces and the stress tensor are used as search directions to find the equilibrium position. Total energy is not taken into account. This algorithm was updated in vasp.4.2 (in comparison to vasp.3.2) and seems to be almost as stable IBRION=2 and is close to the minimum much faster than IBRION=2.

A RMM-DIIS quasi-Newton[24] algorithm is used in which an approximation for the inverse Hessian matrix is build up by taking into account information from previous iterations. The initial Hessian matrix is diagonal and equal to POTIM. Old informations (which can lead to linear dependencies) are automatically removed from the iteration history. Usualy not more information must be kept in the iteration history than degrees of freedom. Naively the number of degrees of freedom is 3*(NIONS-1) or 3*(NIONS-2) for isoltated molecules. However symmetry, or constrained minimization can reduce the 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. 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 values (i.e. 10-20), however systems of low dimensionality require a carfull setting of NFREE (possibly even 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 numbers the RMM-DIIS algorithm might even blow up. It can also blow up if the algorithm is started far from the equilibrium position.

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).

A conjugate-gradient algorithm (a simple discussion of this algorithm can be found for instance in [26]) 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 7.20). Then the energy and the forces are recalculated. ii) The approximate minimum of the total energy is calculated form 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[26].

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 was sufficiently accurate, the cycle starts again, resulting in the following sequence:

1 initial position
2 trial step
3 corrector step, i.e. positions corresponding to anticipated minimum
4 trial step
5 corrector step
If a damping factor is supplied in the INCAR file by means of the SMASS tag, a damped second order equation of motion is used for the update of the ionic degrees of freedom:


where SMASS supplies the damping factor tex2html_wrap_inline4918 , and POTIM controls tex2html_wrap_inline4739 . In fact a simple velocity Verlet algorithm is used to integrate the equation, the discretized equation reads:



It is easy to see that for tex2html_wrap_inline4922 a simple steepest descent algorithm is obtained. Therefore tex2html_wrap_inline4922 corresponds to maximal damping, tex2html_wrap_inline4926 corresponds to no damping. The optimal damping factor depends on the Hessian matrix (second derivate matrix) of the ionic system. A reasonable first guess for tex2html_wrap_inline4918 is usually 0.4.

If SMASS is not set in the INCAR file (respectively SMASS<0), a velocity quench algorithm is used. In that case ions are updated according to a second order equation of motion using the Verlet algorithm (i.e. energy would be conserved), and whenever the force on one ion is anti-parallel to the current velocity, the velocities on that ion are zeroed.

Mind: For IBRION=3, a reasonable time step must be supplied by the POTIM parameter. Too large time steps will result in divergence, too small one will slow down the convergence. The stable time step is usually the twice the smallest line minimization step in the conjugate gradient algorithm.

For IBRION=1,2 and 3, the flag ISIF (see section 7.21) determines whether the ions and/or the cell shape is changed. No update of the cell shape is supported for molecular dynamics (IBRION=0).

Within all relaxation algorithms (IBRION=1,2 and 3) the parameter POTIM should be supplied in the INCAR file. It should be stressed that for IBRION>0, the forces are scaled internally before calling the minimization routine. Therefore for relaxations, POTIM has no physical meaning and serves only as a scaling factor. For many systems, the optimal POTIM is around 0.5.

Because the Quasi-Newton algorithm and the damped algorithms are sensible to the choice of this parameter, use IBRION=2 if you are not sure how large the optimal POTIM is. In that case the OUTCAR file and stdout will contain both a line indicating a reliable POTIM. For IBRION=2, the following lines will be written to stdout after each corrector step (usually each odd step):

 trial: gam=  .00000 g(F)=   .152E+01 g(S)=  .000E+00 ort = .000E+00
 (trialstep = .82)
The quantity gam is the conjugation parameter to the previous step, g(F) and g(S) are the norm of the force respectively the norm of the stress tensor. The quantity ort is an indicator whether this search direction is orthogonal to the last search direction (for an optimal step this quantity should be much smaller than (g(F) + g(S)). The quantity trialstep is the size of the current trialstep. This value is the average step size leading to a line minimization in previous ionic step. An optimal POTIM can be determined, by multiplying the current POTIM with the quantity trialstep.

After at the end of a trial step, the following lines are written to stdout:

 trial-energy change:   -1.153185  1.order   -1.133   -1.527  -.739
 step:   1.7275(harm=  2.0557)  dis=  .12277  
                            next Energy= -1341.57 (dE= -.142E+01)
The quantity trial-energy change is the change of the energy in the trial step. The first value after 1.order is the expected energy change calculated from the forces ( tex2html_wrap_inline4934 change of positions). The second and third value corresponds to tex2html_wrap_inline4577 change of positions and tex2html_wrap_inline4579 change of positions. The first value in the second line is the size of the step leading to a line minimization along the current search direction. It is calculated from a third order interpolation formula using data form the start and trial step (forces and energy change). harm is the optimal step using a second order (or harmonic) interpolation. Only information on the forces is used for the harmonic interpolation. Close to the minimum both values should be similar. dis is the maximum distance moved by the ions in fractional (direct) coordinates. next Energy gives an indication how large the next energy should be (i.e. the energy at the minimum of the line minimization), dE is the estimated energy change.

The OUTCAR file will contain the following lines, at the end of each trial step:

 trial-energy change:   -1.148928  1.order   -1.126  -1.518  -.735
  (g-gl).g =  .152E+01      g.g   =  .152E+01    =  .000E+00
 g(Force)  =  .152E+01   g(Stress)=  .000E+00 ortho     =  .000E+00
 gamma     =    .00000
 opt step  =   1.72745  (harmonic =   2.05575) max dist = .12277085
 next E    = -1341.577507   (d E  =   1.42496)
The line trial-energy change was already discussed. g(Force) corresponds to g(F), g(Stress) to g(S), ortho to ort, gamma to gam. The values after gamma correspond to the second line (step: ...) previously described.

For IBRION=1 less information is printed. IBRION=1 should be used only close to the minimum with an already known setting for POTIM (determined with a run with IBRION=2).

next up previous contents
Next: 7.20 POTIM-tag Up: 7 The INCAR File Previous: 7.18 NBLOCK and KBLOCK-tag

Mon Mar 29 10:38:29 MEST 1999