IMIX | = | type of mixing |

AMIX | = | linear mixing parameter |

BMIX | = | cutoff wave vector for Kerker mixing scheme |

AMIX_MAG | = | linear mixing parameter for magnetization |

BMIX_MAG | = | cutoff wave vector for Kerker mixing scheme for mag. |

WC | = | weight factor for each step in Broyden mixing scheme |

INIMIX | = | type of initial mixing in Broyden mixing scheme |

MIXPRE | = | type of preconditioning in Broyden mixing scheme |

MAXMIX | = | maximum number steps stored in Broyden mixer |

Default (please rely on these defaults)

US-PP | PAW | ||

IMIX | = | 4 | 4 |

AMIX | = | 0.8 | 0.2 |

BMIX | = | 1.0 | 0.00001 |

WC | = | 1000. | 1000. |

INIMIX | = | 1 | 1 |

MIXPRE | = | 1 | 1 |

MAXMIX | = | -45 | -45 |

`MAXMIX` is only available in vasp.4.4 and newer versions,
and it is strongly
recommended to use this option for molecular dynamics and relaxations.

With the default setting, a Pulay mixer[24] with an initial approximation for the charge dielectric function according to Kerker, Ref. [38]

is used (linear mixing for PAW).
This is a very save setting resulting in good convergence for most
systems. In vasp.4.X for magnetic systems, the initial setup for the
mixing parameters for the magnetization density
can be supplied seperately in the INCAR file. The defaults for `AMIX`,
`BMIX`,
`AMIX_MAG` and `BMIX_MAG` are different from paramagnetic calculations:

US-PP | PAW | ||

AMIX | = | 0.5 | 0.2 |

BMIX | = | 1.0 | 0.00001 |

AMIX_MAG | = | 2.0 | 0.8 |

BMIX_MAG | = | 1.0 | 0.00001 |

The above setting is equivalent to an (initial) spin enhancement
factor of 4, which is usually a reasonable approximation.
There are only a few other parameter combinitions
which can be tried if convergence turns out to be very slow. In particular,
for slabs, magnetic systems and insulating systems
(e.g. molecules and clusters),
an initial ``linear mixing'' can result in faster convergence than
the Kerker model function (the initial linear
mixing is the default setting for PAW but not for the US-PP method).
One can therefore try to use the following setting

AMIX | = | 0.2 |

BMIX | = | 0.0001 ! almost zero, but 0 will crash some versions |

AMIX_MAG | = | 0.8 |

BMIX_MAG | = | 0.0001 ! almost zero, but 0 will crash some versions |

In vasp.4.x the eigenvalue spectrum of the charge dielectric matrix is calculated and written to the OUTCAR file at each electronic step. This allows a rather easy optimization of the mixing parameters, if required. Search in the OUTCAR file for

eigenvalues of (default mixing * dielectric matrix)The parameters for the mixing are optimal if the mean eigenvalue is 1, and if the width of the eigenvalue spectrum is minimal. For an initial linear mixing (

One important option which might help to reduce the number of iterations
for MD's and ionic relaxations is the option `MAXMIX`,
which is only available in vasp.4.4. `MAXMIX` specifies the maximum number
of vectors stored in the Broyden/Pulay mixer, in other
words it corresponds to the maximal rank of the approximation
of the charge dielectric function build up by the mixer.
`MAXMIX` can be either negative or positive. If a negative value
is specified for `MAXMIX` the mixer is reset
after each ionic step or if the number of electronic steps
exceeds abs( `MAXMIX`) (this is the default and similar to the behavior of
vasp.4.3 and vasp.3.2).
If `MAXMIX` is positive, the charge density mixer is only reset if
the storage capabilities are exceeded. The reset is
done ``smoothly'' by removing
the five oldest vectors from the iteration history.
Therefore, if `MAXMIX`
is positive the approximation for the charge dielectric
function which was obtained in previous ionic steps is
``reused'' in the current ionic step, and this in turn can reduce the number
of electronic steps during relaxations and MD's. Especially
for relaxations which start in the vicinity of the
ionic groundstate and for systems with a
strong charge sloshing behavior the speedup can be significant.
We found that for a 12 A long box containing 16 Fe atoms
the number of electronic iterations
decreased from 8 to 2-3 when `MAXMIX` was set to 40. For
a carbon surface the number of iterations decreased also from
7 to 3. At the same
time the energy stability increase significantly.
But be careful - this option increases the memory requirements
for the mixer considerably, and thus the option is not recommended for
systems were charge sloshing is anyway negligible (like bulk simple metals).
The optimal setting for `MAXMIX` is usually around twice
the number of electronic steps required in the first iteration.
Too large values for `MAXMIX` might cause the code to crash (because
linear dependencies between input vectors might develop).

Please go to the next section if you are not interested in a more detailed dicussion of the flags which influence the mixer.

`IMIX` determines the type of mixing

**0)**- no mixing ()
**1)**- Kerker mixing, the mixed output density is given by
If

`BMIX`is very small i.e.`BMIX`=0.0001, a simple straight mixing is obtained. Please mind, that`BMIX`=0 causes floating point exceptions. **2)**- A variant of the popular Tchebycheff mixing scheme is used[25].
In our implementation a second order equation of motion is
used, that reads:
is supplied by the parameter

`AMIN`in the INCAR file. A simple velocity Verlet algorithm is used to integrate this equation, and the discretized equation reads (the index N now refers to the electronic iteration,*F*is the force acting on the charge):For BMIX 0, no model for the dielectric matrix is used. It is easy to see, that for a simple straight mixing is obtained. Therefore , corresponds to maximal damping, and obviously means no damping. Optimal parameters for the and

`AMIX`can be determined by converging first with the Pulay mixer (`IMIX`=4) to the groundstate. Then the eigenvalues of the charge dielectric matrix as given in the OUTCAR file must be inspected. Search for the last orrurance ofeigenvalues of (default mixing * dielectric matrix)

in the OUTCAR file. The optimal parameters are then given by:`AMIX``AMIX`(as used in Pulay run)* smallest eigenvalue`AMIN`=2*SQRT(smallest eigenvalue/ largest eigenvalue) **4)**- Broyden's 2. method[22, 23], or Pulay's mixing method [24] (depending on the
choice of WC)

The parameters `WC`, `INIMIX` and `MIXPRE` are meaningful only for the Broyden
scheme:

WC determines the weight factors for each iteration

**>0**- set all weights identical to
`WC`(resulting in Pulay's mixing method), up to now Pulay's scheme was always superior to Broyden's 2nd method. **=0**- switch to Broyden's 2nd method, i.e. set the weight for the last step equal to 1000 and all other weights equal to 0.
**<0**- try some automatic setting of the weights according to
in order to set small weights for the first steps and increasing
weights for the last steps (not recommended - this was only
implemented during the test period).

`INIMIX` determines the functional form of the initial mixing
matrix (i.e. for the Broyden scheme).
The initial mixing matrix might influence the convergence speed for complex
situations (especially surfaces and magnetic systems), nevertheless
`INIMIX` must not be changed from the default setting: anything
which can be done with `INIMIX` can also be done with `AMIX` and
`BMIX`, and
changing `AMIX` and `BMIX` is definitely preferable.

Anyway, possible choices for `INIMIX` are:

**0**- linear mixing according to the setting of
`AMIX` **1**- Kerker mixing according to the settings of
`AMIX`and`BMIX` **2**- no mixing (equal to
`INIMIX=2`and`AMIX=1`, not recommended)

`MIXPRE` determines the metric for the Broyden scheme

**0**- no preconditioning, metric=1
**1**- "inverse Kerker" metric with automatically
determined
`BMIX`(determined in such a way that the variation of the preconditioning weights covers a range of a factor 20) **2**- "inverse Kerker" metric with automatically
determined
`BMIX`(determined in such a way that the variation of the preconditioning weights covers a range of a factor 200) **3**- "inverse Kerker" metric with
`BMIX`from`INCAR`, for*G*>0 the weights for the metric are given by(implemented during test period, do not use this setting)

Mon Mar 29 10:38:29 MEST 1999