IMIX

IMIX = 0 | 1 | 2 | 3 | 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

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

• IMIX=3
• IMIX=4

Related Tags and Sections

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

References

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