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{{TAGDEF|IMIX|0 {{!}} 1 {{!}} 2 {{!}} 4|4}}
{{TAGDEF|IMIX|0 {{!}} 1 {{!}} 2 {{!}} 4|4}}


Description: {{TAG|IMIX}} specifies the type of mixing.
Description: {{TAG|IMIX}} specifies the type of [[:Category:Density mixing|density mixing]].
----
----
*{{TAG|IMIX}}=0: no mixing.
=={{TAG|IMIX}}=0: No mixing ==
::<math>\rho_{\rm mix}=\rho_{\rm out}\,</math>
::<math>\rho_{\rm mix}=\rho_{\rm out}\,</math>
*{{TAG|IMIX}}=1: Kerker mixing.<ref name="kerker:prb:81"/>
=={{TAG|IMIX}}=1: Kerker mixing==
:The mixed density is given by
:For Kerker mixing<ref name="kerker:prb:81"/>, the mixed density is given by
::<math>\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>
::<math>\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>A</math>={{TAG|AMIX}} and <math>B</math>={{TAG|BMIX}}
:with <math>A</math>={{TAG|AMIX}} and <math>B</math>={{TAG|BMIX}}. If {{TAG|BMIX}} is very small, e.g., {{TAG|BMIX}}=0.0001, a straight mixing is obtained.  
 
{{NB|mind|{{TAG|BMIX}}{{=}}0 might cause floating-point exceptions on some platforms.|:}}
:If {{TAG|BMIX}} is chosen to be very small, e.g. {{TAG|BMIX}}=0.0001, a simple straight mixing is obtained. Please mind, that {{TAG|BMIX}}=0 might cause floating point exceptions on some platforms.
=={{TAG|IMIX}}=2: Variant of Tchebycheff mixing==
 
:VASP uses a variant of the popular Tchebycheff-mixing scheme<ref name="akai:jpc:85"/>. Here, the following second order equation of motion is used:
*{{TAG|IMIX}}=2: A variant of the popular Tchebycheff mixing scheme.<ref name="akai:jpc:85"/>
:In our implementation a second order equation of motion is used, that reads:
::<math>\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>
::<math>\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>A</math>={{TAG|AMIX}}, <math>B</math>={{TAG|BMIX}}, and <math>\mu</math>={{TAG|AMIN}}.
:with <math>A</math>={{TAG|AMIX}}, <math>B</math>={{TAG|BMIX}}, and <math>\mu</math>={{TAG|AMIN}}. A velocity Verlet algorithm is used to integrate this equation. The discretized equation reads:  
: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>\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>
::<math>\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
:where
::<math>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>
::<math>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
:and
::<math>\rho_{N+1}=\rho_{N+1}+\dot{\rho}_{N+1/2}</math>.
::<math>\rho_{N+1}=\rho_{N+1}+\dot{\rho}_{N+1/2}</math>,
:where the index ''N'' is the electronic iteration, and ''F'' is the force acting on the charge.


:For {{TAG|BMIX}}&asymp;0, no model for the dielectric matrix is used. It is easy to see, that for <math>\mu=2</math> a simple straight mixing is obtained. Therefore, <math>\mu=2</math> corresponds to maximal damping, and obviously <math>\mu=0</math> implies no damping. Optimal parameters for <math>\mu</math> and {{TAG|AMIX}} can be determined by converging first with the Pulay mixer ({{TAG|IMIX}}=4) to the groundstate. Then the eigenvalues of the charge dielectric matrix as given in the {{FILE|OUTCAR}} file must be inspected. Search for the last orrurance of
:For {{TAG|BMIX}}&asymp;0, no model for the dielectric matrix is used. For <math>\mu=2</math> a simple straight mixing is obtained. Therefore, <math>\mu=2</math> corresponds to maximal damping, while <math>\mu=0</math> implies no damping. To determine the optimal parameters for <math>\mu</math> and {{TAG|AMIX}}, first converge to the ground state with the Pulay mixer ({{TAG|IMIX}}=4). Then, search for the the eigenvalues of the charge-dielectric matrix in the {{FILE|OUTCAR}} file at the last occurrence of
  eigenvalues of (default mixing * dielectric matrix)
  eigenvalues of (default mixing * dielectric matrix)
:in the {{FILE|OUTCAR}} file. The optimal parameters are then given by:
:The optimal parameters are then given by:
<!--::{|
|{{TAG|AMIX}}||=||{{TAG|AMIX}}(as used in Pulay run)* smallest eigenvalue
|-
|{{TAG|AMIN}}||=||2*SQRT(smallest eigenvalue/largest eigenvalue)
|}-->
::{|
::{|
|{{TAG|AMIX}}||=||<math>{\rm AMIX}({\rm as\; used\; in\; Pulay\; run})*{\rm smallest\; eigenvalue}</math>
|{{TAG|AMIX}}|| ||<math>={\rm AMIX}({\rm as\; used\; in\; Pulay\; run})*{\rm smallest\; eigenvalue}</math>
|-
|-
|{{TAG|AMIN}}||=||<math>2\sqrt{{\rm smallest\; eigenvalue}/{\rm largest\; eigenvalue}}</math>
|{{TAG|AMIN}}|| ||<math>=\mu=2\sqrt{{\rm smallest\; eigenvalue}/{\rm largest\; eigenvalue}}</math>
|}
|}


*{{TAG|IMIX}}=4: Broyden's 2<sup>nd</sup> method,<ref name="bluegel:thesis:88"/><ref name="johnson:prb:88"/> or Pulay's mixing method<ref name="pulay:cpl:80"/> (depending on the choice of {{TAG|WC}}).
=={{TAG|IMIX}}=4: Broyden's 2<sup>nd</sup> method and Pulay-mixing method (default) ==
:A reasonable choice for {{TAG|AMIN}} is usually {{TAG|AMIN}}=0.4. {{TAG|AMIX}} depends very much on the system, for metals this parameter usually has to be rather small, e.g. {{TAG|AMIX}}= 0.02.
:For {{TAG|WC}}=0, VASP uses Broyden's 2<sup>nd</sup> method,<ref name="bluegel:thesis:88"/><ref name="johnson:prb:88"/> and, for {{TAG|WC}}>0, VASP uses Pulay-mixing method<ref name="pulay:cpl:80"/>.
:In the Broyden scheme, the functional form of the initial mixing matrix is determined by {{TAG|AMIX}} and {{TAG|BMIX}} (or alternatively specified by means of the {{TAG|INIMIX}}-tag). The metric used in the Broyden scheme is specified through {{TAG|MIXPRE}}.
:The default is a Pulay mixer with an initial approximation for the charge-dielectric function according to Kerker<ref name="kerker:prb:81"/>
::<math>A\times\max\left(\frac{G^2}{G^2+B^2},A_{\rm min}\right)</math>
:where <math>A</math>={{TAG|AMIX}}, <math>B</math>={{TAG|BMIX}}, and <math>A_{\rm min}</math>={{TAG|AMIN}}.


== Related Tags and Sections ==
:{{TAG|AMIN}}=0.4 usually yields good convergence. {{TAG|AMIX}} strongly depends on the system, for instance, it should be small, e.g., {{TAG|AMIX}}= 0.02, for metals.
:In the Broyden scheme, the functional form of the initial mixing matrix is determined by {{TAG|AMIX}} and {{TAG|BMIX}} or the {{TAG|INIMIX}} tag. The metric used in the Broyden scheme is specified through {{TAG|MIXPRE}}.
 
== Related tags and articles ==
{{TAG|INIMIX}},
{{TAG|INIMIX}},
{{TAG|MAXMIX}},
{{TAG|MAXMIX}},
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{{TAG|MIXPRE}},
{{TAG|MIXPRE}},
{{TAG|WC}}
{{TAG|WC}}
{{sc|IMIX|Examples|Examples that use this tag}}


== References ==
== References ==
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</references>
</references>
----
----
[[The_VASP_Manual|Contents]]


[[Category:INCAR]][[Category:Mixing]]
[[Category:INCAR tag]][[Category:Density mixing]]

Latest revision as of 11:35, 18 October 2024

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

Description: IMIX specifies the type of density mixing.


IMIX=0: No mixing

IMIX=1: Kerker mixing

For Kerker mixing[1], the mixed density is given by
with =AMIX and =BMIX. If BMIX is very small, e.g., BMIX=0.0001, a straight mixing is obtained.
Mind: BMIX=0 might cause floating-point exceptions on some platforms.

IMIX=2: Variant of Tchebycheff mixing

VASP uses a variant of the popular Tchebycheff-mixing scheme[2]. Here, the following second order equation of motion is used:
with =AMIX, =BMIX, and =AMIN. A velocity Verlet algorithm is used to integrate this equation. The discretized equation reads:
where
and
,
where the index N is the electronic iteration, and F is the force acting on the charge.
For BMIX≈0, no model for the dielectric matrix is used. For a simple straight mixing is obtained. Therefore, corresponds to maximal damping, while implies no damping. To determine the optimal parameters for and AMIX, first converge to the ground state with the Pulay mixer (IMIX=4). Then, search for the the eigenvalues of the charge-dielectric matrix in the OUTCAR file at the last occurrence of
eigenvalues of (default mixing * dielectric matrix)
The optimal parameters are then given by:
AMIX
AMIN

IMIX=4: Broyden's 2nd method and Pulay-mixing method (default)

For WC=0, VASP uses Broyden's 2nd method,[3][4] and, for WC>0, VASP uses Pulay-mixing method[5].
The default is a Pulay mixer with an initial approximation for the charge-dielectric function according to Kerker[1]
where =AMIX, =BMIX, and =AMIN.
AMIN=0.4 usually yields good convergence. AMIX strongly depends on the system, for instance, it should be small, e.g., AMIX= 0.02, for metals.
In the Broyden scheme, the functional form of the initial mixing matrix is determined by AMIX and BMIX or the INIMIX tag. The metric used in the Broyden scheme is specified through MIXPRE.

Related tags and articles

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

Examples that use this tag

References