IMIX

From VASP Wiki
Revision as of 10:05, 8 February 2011 by Mmars (talk | contribs)

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

Description: IMIX specifies the type of 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.
  • IMIX=2: A variant of the popular Tchebycheff mixing scheme.[2]
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}}}}}
  • IMIX=4: Broyden's 2nd method,[3][4] or Pulay's mixing method[5] (depending on the choice of WC).

Related Tags and Sections

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

References

  1. ↑ G. P. Kerker, Phys. Rev. B 23, 3082 (1981).
  2. ↑ H. Akai and P.H. Dederichs, J. Phys. C 18 (1985).
  3. ↑ S. Blügel, PhD Thesis, RWTH Aachen (1988).
  4. ↑ D. D. Johnson, Phys. Rev. B38, 12807 (1988).
  5. ↑ P. Pulay, Chem. Phys. Lett. 73, 393 (1980).

Contents

Retrieved from "https://www.vasp.at/wiki/index.php?title=IMIX&oldid=255"