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

Example Calculations using this Tag

Dielectric properties of Si using BSE, Model BSE calculation on Si

References

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