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].

For BMIX≈0, no model for the dielectric matrix is used. It is easy to see, that for [math]\displaystyle{ \mu=2 }[/math] a simple straight mixing is obtained. Therefore, [math]\displaystyle{ \mu=2 }[/math] corresponds to maximal damping, and obviously [math]\displaystyle{ \mu=0 }[/math] implies no damping. Optimal parameters for [math]\displaystyle{ \mu }[/math] 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		[math]\displaystyle{ ={\rm AMIX}({\rm as\; used\; in\; Pulay\; run})*{\rm smallest\; eigenvalue} }[/math]
AMIN		[math]\displaystyle{ =\mu=2\sqrt{{\rm smallest\; eigenvalue}/{\rm largest\; eigenvalue}} }[/math]

• 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

[math]\displaystyle{ A\times\min\left(\frac{G^2}{G^2+B^2},A_{\rm min}\right) }[/math]

where [math]\displaystyle{ A }[/math]=AMIX, [math]\displaystyle{ B }[/math]=BMIX, and [math]\displaystyle{ A_{\rm min} }[/math]=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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