IMIX

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}}}}\,

IMIX=1: Kerker mixing.^[1]

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/":): =\mu =2{\sqrt {{{\rm {smallest\;eigenvalue}}}/{{\rm {largest\;eigenvalue}}}}}

IMIX=4: Broyden's 2^nd method,^[3]^[4] or Pulay's mixing method^[5] (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^[1] is used

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\times \min \left({\frac {G^{2}}{G^{2}+B^{2}}},A_{{{\rm {min}}}}\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/":): 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/":): 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.

Related Tags and Sections

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

Examples that use this tag

References

↑ ^a ^b 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).

Contents

[kerker:prb:81-1] G. P. Kerker, Phys. Rev. B 23, 3082 (1981).

[akai:jpc:85-2] H. Akai and P.H. Dederichs, J. Phys. C 18 (1985).

[bluegel:thesis:88-3] S. Blügel, PhD Thesis, RWTH Aachen (1988).

[johnson:prb:88-4] D. D. Johnson, Phys. Rev. B38, 12807 (1988).

[pulay:cpl:80-5] P. Pulay, Chem. Phys. Lett. 73, 393 (1980).

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