IMIX: Difference between revisions
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::<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>. | ||
:For {{TAG|BMIX}}≈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 | |||
eigenvalues of (default mixing * dielectric matrix) | |||
:in the {{FILE|OUTCAR}} file. 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|IMIX}}=4 | *{{TAG|IMIX}}=4 |
Revision as of 17:31, 7 February 2011
IMIX = 0 | 1 | 2 | 4
Default: IMIX = 4
Description: IMIX specifies the type of mixing.
- IMIX=0: no mixing.
- [math]\displaystyle{ \rho_{\rm mix}=\rho_{\rm out} }[/math]
- 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.
- 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:
- IMIX=4
Related Tags and Sections
INIMIX, MAXMIX, AMIX, BMIX, AMIX_MAG, BMIX_MAG, AMIN, MIXPRE, WC