IMIX

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

Description: IMIX specifies the type of mixing.

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• IMIX=0: no mixing.

[math]\displaystyle{ \rho_{\rm mix}=\rho_{\rm out} }[/math]

• IMIX=1: Kerker mixing.

The mixed density is given by

[math]\displaystyle{ \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) }[/math]

with [math]\displaystyle{ A }[/math]=AMIX and [math]\displaystyle{ B }[/math]=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:

[math]\displaystyle{ \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) }[/math]

with [math]\displaystyle{ A }[/math]=AMIX, [math]\displaystyle{ B }[/math]=BMIX, and [math]\displaystyle{ \mu }[/math]=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):

[math]\displaystyle{ \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) }[/math]

where

[math]\displaystyle{ 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) }[/math]

and

[math]\displaystyle{ \rho_{N+1}=\rho_{N+1}+\dot{\rho}_{N+1/2} }[/math].

• IMIX=4

Related Tags and Sections

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

References

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