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# IMIX

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

Description: IMIX specifies the type of mixing.

• 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 2nd 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.