IMIX

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

Description: IMIX specifies the type of density 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

For 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 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:

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 velocity Verlet algorithm is used to integrate this equation. The discretized equation 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/":): {\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}} ,

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 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, while 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. To determine the 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, 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		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 and Pulay-mixing method (default)

For WC=0, VASP uses Broyden's 2^nd 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]

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.

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.

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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