IMIX: Difference between revisions
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eigenvalues of (default mixing * dielectric matrix) | eigenvalues of (default mixing * dielectric matrix) | ||
:in the {{FILE|OUTCAR}} file. The optimal parameters are then given by: | :in the {{FILE|OUTCAR}} file. The optimal parameters are then given by: | ||
::{| | <!--::{| | ||
|{{TAG|AMIX}}||=||{{TAG|AMIX}}(as used in Pulay run)* smallest eigenvalue | |{{TAG|AMIX}}||=||{{TAG|AMIX}}(as used in Pulay run)* smallest eigenvalue | ||
|- | |- | ||
|{{TAG|AMIN}}||=||2*SQRT(smallest eigenvalue/largest 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|AMIN}}||=||<math>2\sqrt{{\rm smallest\; eigenvalue}/{\rm largest\; eigenvalue}}</math> | |||
|} | |} | ||
Revision as of 10:05, 8 February 2011
IMIX = 0 | 1 | 2 | 4
Default: IMIX = 4
Description: IMIX specifies the type of mixing.
- IMIX=0: no mixing.
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \rho _{{{\rm {mix}}}}=\rho _{{{\rm {out}}}}\,
- The mixed density is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): A =AMIX and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 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.
- In our implementation a second order equation of motion is used, that reads:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): A =AMIX, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): B =BMIX, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \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):
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\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
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 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
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \mu =2 a simple straight mixing is obtained. Therefore, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \mu =2 corresponds to maximal damping, and obviously Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \mu =0 implies no damping. Optimal parameters for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \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 = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {{\rm {AMIX}}}({{\rm {as\;used\;in\;Pulay\;run}}})*{{\rm {smallest\;eigenvalue}}} AMIN = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 2{\sqrt {{{\rm {smallest\;eigenvalue}}}/{{\rm {largest\;eigenvalue}}}}}
Related Tags and Sections
INIMIX, MAXMIX, AMIX, BMIX, AMIX_MAG, BMIX_MAG, AMIN, MIXPRE, WC
References
- ↑ G. P. Kerker, Phys. Rev. B 23, 3082 (1981).
- ↑ H. Akai and P.H. Dederichs, J. Phys. C 18 (1985).
- ↑ S. Blügel, PhD Thesis, RWTH Aachen (1988).
- ↑ D. D. Johnson, Phys. Rev. B38, 12807 (1988).
- ↑ P. Pulay, Chem. Phys. Lett. 73, 393 (1980).