IMIX - Revision history

Huebsch at 11:35, 18 October 2024

2024-10-18T11:35:43Z

← Older revision		Revision as of 11:35, 18 October 2024
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	----		----

	[[Category:INCAR tag~~]][[Category:Electronic minimization~~]][[Category:Density mixing]]		[[Category:INCAR tag]][[Category:Density mixing]]

Vaspmaster: /* {{TAG|IMIX}}=4: Broyden's 2nd method and Pulay-mixing method (default) */

2024-06-30T12:35:51Z

{{TAG|IMIX}}=4: Broyden's 2nd method and Pulay-mixing method (default)

← Older revision		Revision as of 12:35, 30 June 2024
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	:For {{TAG\|WC}}=0, VASP uses Broyden's 2<sup>nd</sup> method,<ref name="bluegel:thesis:88"/><ref name="johnson:prb:88"/> and, for {{TAG\|WC}}>0, VASP uses Pulay-mixing method<ref name="pulay:cpl:80"/>.		:For {{TAG\|WC}}=0, VASP uses Broyden's 2<sup>nd</sup> method,<ref name="bluegel:thesis:88"/><ref name="johnson:prb:88"/> and, for {{TAG\|WC}}>0, VASP uses Pulay-mixing method<ref name="pulay:cpl:80"/>.
	:The default is a Pulay mixer with an initial approximation for the charge-dielectric function according to Kerker<ref name="kerker:prb:81"/>		:The default is a Pulay mixer with an initial approximation for the charge-dielectric function according to Kerker<ref name="kerker:prb:81"/>
	::<math>A\times\~~min~~\left(\frac{G^2}{G^2+B^2},A_{\rm min}\right)</math>		::<math>A\times\max\left(\frac{G^2}{G^2+B^2},A_{\rm min}\right)</math>
	:where <math>A</math>={{TAG\|AMIX}}, <math>B</math>={{TAG\|BMIX}}, and <math>A_{\rm min}</math>={{TAG\|AMIN}}.		:where <math>A</math>={{TAG\|AMIX}}, <math>B</math>={{TAG\|BMIX}}, and <math>A_{\rm min}</math>={{TAG\|AMIN}}.

Miranda.henrique at 09:04, 26 July 2022

2022-07-26T09:04:05Z

← Older revision		Revision as of 09:04, 26 July 2022
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	{{TAGDEF\|IMIX\|0 {{!}} 1 {{!}} 2 {{!}} 4\|4}}		{{TAGDEF\|IMIX\|0 {{!}} 1 {{!}} 2 {{!}} 4\|4}}

	Description: {{TAG\|IMIX}} specifies the type of [[Density ~~Mixing~~\|density mixing]].		Description: {{TAG\|IMIX}} specifies the type of [[:Category:Density mixing\|density mixing]].
	----		----
	=={{TAG\|IMIX}}=0: No mixing ==		=={{TAG\|IMIX}}=0: No mixing ==

Karsai: /* References */

2022-04-08T14:22:33Z

References

← Older revision		Revision as of 14:22, 8 April 2022
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	</references>		</references>
	----		----
	~~[[The_VASP_Manual\|Contents]]~~

	[[Category:INCAR]][[Category:Electronic minimization]][[Category:Density mixing]]		[[Category:INCAR tag]][[Category:Electronic minimization]][[Category:Density mixing]]

Huebsch at 11:45, 6 April 2022

2022-04-06T11:45:00Z

← Older revision		Revision as of 11:45, 6 April 2022
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	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

	[[Category:INCAR]][[Category:Electronic ~~Minimization~~]][[Category:Density ~~Mixing~~]]		[[Category:INCAR]][[Category:Electronic minimization]][[Category:Density mixing]]

Huebsch at 16:53, 1 April 2022

2022-04-01T16:53:54Z

← Older revision		Revision as of 16:53, 1 April 2022
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	{{TAGDEF\|IMIX\|0 {{!}} 1 {{!}} 2 {{!}} 4\|4}}		{{TAGDEF\|IMIX\|0 {{!}} 1 {{!}} 2 {{!}} 4\|4}}

	Description: {{TAG\|IMIX}} specifies the type of mixing.		Description: {{TAG\|IMIX}} specifies the type of [[Density Mixing\|density mixing]].
	----		----
	*{{TAG\|IMIX}}=0: no mixing.		=={{TAG\|IMIX}}=0: No mixing ==
	::<math>\rho_{\rm mix}=\rho_{\rm out}\,</math>		::<math>\rho_{\rm mix}=\rho_{\rm out}\,</math>
	*{{TAG\|IMIX}}=1: Kerker mixing.<ref name="kerker:prb:81"/>		=={{TAG\|IMIX}}=1: Kerker mixing==
	~~:The~~ mixed density is given by		:For Kerker mixing<ref name="kerker:prb:81"/>, the mixed density is given by
	::<math>\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>		::<math>\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>A</math>={{TAG\|AMIX}} and <math>B</math>={{TAG\|BMIX}}		:with <math>A</math>={{TAG\|AMIX}} and <math>B</math>={{TAG\|BMIX}}. If {{TAG\|BMIX}} is very small, e.g., {{TAG\|BMIX}}=0.0001, a straight mixing is obtained.
			{{NB\|mind\|{{TAG\|BMIX}}{{=}}0 might cause floating-point exceptions on some platforms.\|:}}
	:If {{TAG\|BMIX}} is ~~chosen to be~~ very small, e.g. {{TAG\|BMIX}}=0.0001, a ~~simple~~ straight mixing is obtained. ~~Please~~ mind~~, that~~ {{TAG\|BMIX}}=0 might cause floating point exceptions on some platforms.		=={{TAG\|IMIX}}=2: Variant of Tchebycheff mixing==
			:VASP uses a variant of the popular Tchebycheff-mixing scheme<ref name="akai:jpc:85"/>. Here, the following second order equation of motion is used:
	*{{TAG\|IMIX}}=2: A variant of the popular Tchebycheff mixing scheme.<ref name="akai:jpc:85"/>
	~~:In our implementation a~~ second order equation of motion is used~~, that reads~~:
	::<math>\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>		::<math>\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>A</math>={{TAG\|AMIX}}, <math>B</math>={{TAG\|BMIX}}, and <math>\mu</math>={{TAG\|AMIN}}.		:with <math>A</math>={{TAG\|AMIX}}, <math>B</math>={{TAG\|BMIX}}, and <math>\mu</math>={{TAG\|AMIN}}. A velocity Verlet algorithm is used to integrate this equation. The discretized equation reads:
	: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>\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>		::<math>\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		:where
	::<math>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>		::<math>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		:and
	::<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>,
			:where the index ''N'' is the electronic iteration, and ''F'' is the force acting on the charge.

	: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		:For {{TAG\|BMIX}}≈0, no model for the dielectric matrix is used. For <math>\mu=2</math> a simple straight mixing is obtained. Therefore, <math>\mu=2</math> corresponds to maximal damping, while <math>\mu=0</math> implies no damping. To determine the optimal parameters for <math>\mu</math> and {{TAG\|AMIX}}, first converge to the ground state with the Pulay mixer ({{TAG\|IMIX}}=4). Then, search for the the eigenvalues of the charge-dielectric matrix in the {{FILE\|OUTCAR}} file at the last occurrence of
	eigenvalues of (default mixing * dielectric matrix)		eigenvalues of (default mixing * dielectric matrix)
	:~~in the {{FILE\|OUTCAR}} file.~~ The optimal parameters are then given by:		:The optimal parameters are then given by:
	~~<!--::{\|~~
	~~\|{{TAG\|AMIX}}\|\|=\|\|{{TAG\|AMIX}}(as used in Pulay run)* smallest eigenvalue~~
	\|-
	~~\|{{TAG\|AMIN}}\|\|=\|\|μ=2*SQRT(smallest eigenvalue/largest eigenvalue)~~
	~~\|}-->~~
	::{\|		::{\|
	\|{{TAG\|AMIX}}\|\| \|\|<math>={\rm AMIX}({\rm as\; used\; in\; Pulay\; run})*{\rm smallest\; eigenvalue}</math>		\|{{TAG\|AMIX}}\|\| \|\|<math>={\rm AMIX}({\rm as\; used\; in\; Pulay\; run})*{\rm smallest\; eigenvalue}</math>
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	\|}		\|}

	*{{TAG\|IMIX}}=4: Broyden's 2<sup>nd</sup> method,<ref name="bluegel:thesis:88"/><ref name="johnson:prb:88"/> or Pulay's mixing method<ref name="pulay:cpl:80"/> ~~(depending on the choice of {{TAG\|WC}})~~.		=={{TAG\|IMIX}}=4: Broyden's 2<sup>nd</sup> method and Pulay-mixing method (default) ==
	:~~With the~~ default ~~settings,~~ a Pulay mixer with an initial approximation for the charge dielectric function according to Kerker<ref name="kerker:prb:81"/> ~~is used~~		:For {{TAG\|WC}}=0, VASP uses Broyden's 2<sup>nd</sup> method,<ref name="bluegel:thesis:88"/><ref name="johnson:prb:88"/> and, for {{TAG\|WC}}>0, VASP uses Pulay-mixing method<ref name="pulay:cpl:80"/>.
			:The default is a Pulay mixer with an initial approximation for the charge-dielectric function according to Kerker<ref name="kerker:prb:81"/>
	::<math>A\times\min\left(\frac{G^2}{G^2+B^2},A_{\rm min}\right)</math>		::<math>A\times\min\left(\frac{G^2}{G^2+B^2},A_{\rm min}\right)</math>
	:where <math>A</math>={{TAG\|AMIX}}, <math>B</math>={{TAG\|BMIX}}, and <math>A_{\rm min}</math>={{TAG\|AMIN}}.		:where <math>A</math>={{TAG\|AMIX}}, <math>B</math>={{TAG\|BMIX}}, and <math>A_{\rm min}</math>={{TAG\|AMIN}}.

	:~~A reasonable choice for {{TAG\|AMIN}} is usually~~ {{TAG\|AMIN}}=0.4. {{TAG\|AMIX}} depends ~~very much~~ on the system, for ~~metals this parameter usually has to~~ be ~~rather~~ small, e.g. {{TAG\|AMIX}}= 0.02.		:{{TAG\|AMIN}}=0.4 usually yields good convergence. {{TAG\|AMIX}} strongly depends on the system, for instance, it should be small, e.g., {{TAG\|AMIX}}= 0.02, for metals.
	:In the Broyden scheme, the functional form of the initial mixing matrix is determined by {{TAG\|AMIX}} and {{TAG\|BMIX}} (or ~~alternatively specified by means of~~ the {{TAG\|INIMIX}}-tag). The metric used in the Broyden scheme is specified through {{TAG\|MIXPRE}}.		:In the Broyden scheme, the functional form of the initial mixing matrix is determined by {{TAG\|AMIX}} and {{TAG\|BMIX}} or the {{TAG\|INIMIX}} tag. The metric used in the Broyden scheme is specified through {{TAG\|MIXPRE}}.

	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and articles ==
	{{TAG\|INIMIX}},		{{TAG\|INIMIX}},
	{{TAG\|MAXMIX}},		{{TAG\|MAXMIX}},

Schlipf at 09:14, 10 May 2019

2019-05-10T09:14:20Z

← Older revision		Revision as of 09:14, 10 May 2019
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	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

	[[Category:INCAR]][[Category:Electronic Minimization]][[Category:Mixing]]		[[Category:INCAR]][[Category:Electronic Minimization]][[Category:Density Mixing]]

Karsai: /* References */

2019-03-07T11:12:52Z

References

← Older revision		Revision as of 11:12, 7 March 2019
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	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

	[[Category:INCAR]][[Category:Mixing]]		[[Category:INCAR]][[Category:Electronic Minimization]][[Category:Mixing]]

Karsai: /* Example Calculations using this Tag */

2017-03-20T09:55:52Z

Example Calculations using this Tag

← Older revision		Revision as of 09:55, 20 March 2017
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	{{sc\|IMIX\|Examples\|Examples that use this tag}}		{{sc\|IMIX\|Examples\|Examples that use this tag}}

	~~== Example Calculations using this Tag ==~~
	~~{{TAG\|Dielectric properties of Si using BSE}}, {{TAG\|Model BSE calculation on Si}}~~

	== References ==		== References ==

Karsai: /* Related Tags and Sections */

2017-03-20T09:55:45Z

Related Tags and Sections

← Older revision		Revision as of 09:55, 20 March 2017
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	{{TAG\|MIXPRE}},		{{TAG\|MIXPRE}},
	{{TAG\|WC}}		{{TAG\|WC}}

			{{sc\|IMIX\|Examples\|Examples that use this tag}}

	== Example Calculations using this Tag ==		== Example Calculations using this Tag ==