IMIX

IMIX = 0 | 1 | 2 | 4
Default: IMIX = 4 

Description: IMIX specifies the type of mixing.

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• IMIX=0: no mixing.

$\rho _{\rm {mix}}=\rho _{\rm {out}}\,$

• IMIX=1: Kerker mixing.

The mixed density is given by

$\rho _{\rm {mix}}\left(G\right)=\rho _{\rm {in}}\left(G\right)+A{\frac {G^{2}}{G^{2}+B^{2}}}{\Bigl (}\rho _{\rm {out}}\left(G\right)-\rho _{\rm {in}}\left(G\right){\Bigr )}$

with $A$=AMIX and $B$=BMIX

If BMIX is chosen to be very small, e.g. BMIX=0.0001, a simple straight mixing is obtained. Please mind, that BMIX=0 might cause floating point exceptions on some platforms.

• IMIX=2: A variant of the popular Tchebycheff mixing scheme.

In our implementation a second order equation of motion is used, that reads:

${\ddot {\rho }}_{\rm {in}}\left(G\right)=2*A{\frac {G^{2}}{G^{2}+B^{2}}}{\Bigl (}\rho _{\rm {out}}\left(G\right)-\rho _{\rm {in}}\left(G\right){\Bigr )}-\mu {\dot {\rho }}_{\rm {in}}\left(G\right)$

with $A$=AMIX, $B$=BMIX, and $\mu$=AMIN.

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):

${\dot {\rho }}_{N+1/2}={\Bigl (}\left(1-\mu /2\right){\dot {\rho }}_{N-1/2}+2*F_{N}{\Bigr )}/\left(1+\mu /2\right)$

where

$F\left(G\right)=A{\frac {G^{2}}{G^{2}+B^{2}}}{\Bigl (}\rho _{\rm {out}}\left(G\right)-\rho _{\rm {in}}\left(G\right){\Bigr )}$

and

$\rho _{N+1}=\rho _{N+1}+{\dot {\rho }}_{N+1/2}$.

For BMIX≈0, no model for the dielectric matrix is used. It is easy to see, that for $\mu =2$ a simple straight mixing is obtained. Therefore, $\mu =2$ corresponds to maximal damping, and obviously $\mu =0$ implies no damping. Optimal parameters for $\mu$ 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 of

eigenvalues of (default mixing * dielectric matrix)

in the OUTCAR file. The optimal parameters are then given by:

AMIX		$={\rm {AMIX}}({\rm {as\;used\;in\;Pulay\;run}})*{\rm {smallest\;eigenvalue}}$
AMIN		$=\mu =2{\sqrt {{\rm {smallest\;eigenvalue}}/{\rm {largest\;eigenvalue}}}}$

• IMIX=4: Broyden's 2^nd method, or Pulay's mixing method (depending on the choice of WC).

With the default settings, a Pulay mixer with an initial approximation for the charge dielectric function according to Kerker is used

$A\times \min \left({\frac {G^{2}}{G^{2}+B^{2}}},A_{\rm {min}}\right)$

where $A$=AMIX, $B$=BMIX, and $A_{\rm {min}}$=AMIN.

A reasonable choice for AMIN is usually AMIN=0.4. AMIX depends very much on the system, for metals this parameter usually has to be rather small, e.g. AMIX= 0.02.

In the Broyden scheme, the functional form of the initial mixing matrix is determined by AMIX and BMIX (or alternatively specified by means of the INIMIX-tag). The metric used in the Broyden scheme is specified through MIXPRE.

Related Tags and Sections

INIMIX, MAXMIX, AMIX, BMIX, AMIX_MAG, BMIX_MAG, AMIN, MIXPRE, WC

Examples that use this tag

References

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