Improving the dielectric function - Revision history

Karsai: /* References */

2019-11-14T13:47:14Z

References

← Older revision		Revision as of 13:47, 14 November 2019
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	{{Template:BSE}}		{{Template:BSE}}



	~~Back to the [[The_VASP_Manual\|main page]]~~

	[[Category:Examples]]		[[Category:Examples]]

Karsai: /* Download */

2019-11-14T08:02:04Z

Download

← Older revision		Revision as of 08:02, 14 November 2019
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	== Download ==		== Download ==
	[~~http~~:~~//www.vasp.at/vasp-workshop/examples/Si_improve_eps~~.tgz Si_improve_eps.tgz]		[[Media:Si improve eps.tgz\| Si_improve_eps.tgz]]

	== References ==		== References ==

Cesare at 14:42, 17 September 2019

2019-09-17T14:42:20Z

← Older revision		Revision as of 14:42, 17 September 2019
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	=== Model-BSE ===		=== Model-BSE ===
	The dielectric function <math> \epsilon^{-1}_{\mathbf{G},\mathbf{G'}} (\mathbf{k})</math> is replaced by the local model function:		The dielectric function <math> \epsilon^{-1}_{\mathbf{G},\mathbf{G'}} (\mathbf{q})</math> is replaced by the local model function:

	:<math> {\varepsilon}_{\mathbf{G},\mathbf{G}}^{-1}(\mathbf{q})=~~{{\varepsilon}_{\infty}^{~~-~~1}}+~~(1-{{\varepsilon}_{\infty}^{-1}})~~[1-~~\text{exp}(-\frac{\|\mathbf{q+G}\|^2}{4{\lambda}^2})</math>.		:<math> {\varepsilon}_{\mathbf{G},\mathbf{G}}^{-1}(\mathbf{q})=1-(1-{{\varepsilon}_{\infty}^{-1}})\text{exp}(-\frac{\|\mathbf{q+G}\|^2}{4{\lambda}^2})</math>.

	This makes the screened Coulomb kernel diagonal <math>(\mathbf{G}=\mathbf{G'})</math> in the screened Coulomb potential:		This makes the screened Coulomb kernel diagonal <math>(\mathbf{G}=\mathbf{G'})</math> in the screened Coulomb potential:

	:<math> W^{cv\mathbf{k}}_{c'v'\mathbf{k}} = \frac{4\pi e^{2}}{\Omega} \sum\limits_{\mathbf{G}} B^{c\mathbf{k}}~~_{c'~~\mathbf{k}}(\mathbf{G}) \~~frac~~{~~\epsilon~~^{-1}(\mathbf{k}~~+\mathbf{G})~~}{\|\mathbf{k}+\mathbf{G}~~\|^{2}}~~ B^{v\mathbf{k}}_{v'\mathbf{k}}(\mathbf{G}) </math>,		:<math> W^{cv\mathbf{k}}_{c'v'\mathbf{k}} = \frac{4\pi e^{2}}{\Omega} \sum\limits_{\mathbf{G}} \frac{\epsilon^{-1}_{\mathbf{G},\mathbf{G}}(\mathbf{0})}{\|\mathbf{G}\|^{2}}B^{c\mathbf{k}}_{c'\mathbf{k}}(\mathbf{G}) [B^{v\mathbf{k}}_{v'\mathbf{k}}(\mathbf{G})]^* </math>,

	where <math> B^{n\mathbf{k}}_{n'\mathbf{k}}(\mathbf{G}) </math> denote Bloch integrals of the cell-periodic part of the Bloch waves.		where <math> B^{n\mathbf{k}}_{n'\mathbf{k}}(\mathbf{G}) </math> denote Bloch integrals of the cell-periodic part of the Bloch waves.

Cesare: /* Calculation */

2019-09-17T12:08:57Z

Calculation

← Older revision		Revision as of 12:08, 17 September 2019
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	* Model-BSE:		* Model-BSE:
	:Use a parametrized model<ref name="bokdam:scr:6"/>,<ref name="liu:bse"/> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.		:Use a parametrized model<ref name="bokdam:scr:6"/><ref name="liu:bse"/> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.

	=== Averaging over multiple grids ===		=== Averaging over multiple grids ===

Cesare: /* Calculation */

2019-09-17T12:08:29Z

Calculation

← Older revision		Revision as of 12:08, 17 September 2019
Line 40:		Line 40:

	* Model-BSE:		* Model-BSE:
	:Use a parametrized model<ref name="bokdam:scr:6", name="liu:bse"/> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.		:Use a parametrized model<ref name="bokdam:scr:6"/>,<ref name="liu:bse"/> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.

	=== Averaging over multiple grids ===		=== Averaging over multiple grids ===

Cesare: /* Calculation */

2019-09-17T12:06:26Z

Calculation

← Older revision		Revision as of 12:06, 17 September 2019
Line 40:		Line 40:

	* Model-BSE:		* Model-BSE:
	:Use a parametrized model<ref name="bokdam:scr:6"/> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.		:Use a parametrized model<ref name="bokdam:scr:6", name="liu:bse"/> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.

	=== Averaging over multiple grids ===		=== Averaging over multiple grids ===

Cesare: /* Calculation */

2019-09-17T12:05:58Z

Calculation

← Older revision		Revision as of 12:05, 17 September 2019
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	* Model-BSE:		* Model-BSE:
	:Use a parametrized model<ref name="bokdam:scr:6"/~~> <ref name="liu:bse"~~> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.		:Use a parametrized model<ref name="bokdam:scr:6"/> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.

	=== Averaging over multiple grids ===		=== Averaging over multiple grids ===

Cesare: /* Calculation */

2019-09-17T12:04:29Z

Calculation

← Older revision		Revision as of 12:04, 17 September 2019
Line 40:		Line 40:

	* Model-BSE:		* Model-BSE:
	:Use a parametrized model<ref name="bokdam:scr:6"/> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.		:Use a parametrized model<ref name="bokdam:scr:6"/> <ref name="liu:bse"> for the dielectric screening, and DFT eigenenergies moved with a ''scissor'' operator, instead of RPA screening and GW quasiparticle energies.

	=== Averaging over multiple grids ===		=== Averaging over multiple grids ===

Cesare: /* References */

2019-09-17T12:04:00Z

References

← Older revision		Revision as of 12:04, 17 September 2019
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	<references>		<references>
	<ref name="bokdam:scr:6">[https://www.nature.com/articles/srep28618 M.Bokdam et al., Scientific Reports 6, 28618 (2016).]</ref>		<ref name="bokdam:scr:6">[https://www.nature.com/articles/srep28618 M.Bokdam et al., Scientific Reports 6, 28618 (2016).]</ref>
			<ref name="liu:bse">[https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.2.075003 P.Liu et al., Phys. Rev. Materials 2, 075003 (2018).]</ref>
	</references>		</references>

Cesare: /* Model-BSE */

2019-09-17T12:00:56Z

Model-BSE

← Older revision		Revision as of 12:00, 17 September 2019
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	=== Model-BSE ===		=== Model-BSE ===
	The dielectric function <math> \epsilon^{-1}_{\mathbf{G},\mathbf{G'}} (\mathbf{k})</math> is replaced by the local model function:		The dielectric function <math> \epsilon^{-1}_{\mathbf{G},\mathbf{G'}} (\mathbf{k})</math> is replaced by the local model function:



	:<math> {\varepsilon}_{\mathbf{G},\mathbf{G}}^{-1}(\mathbf{q})={{\varepsilon}_{\infty}^{-1}}+(1-{{\varepsilon}_{\infty}^{-1}})[1-\text{exp}(-\frac{\|\mathbf{q+G}\|^2}{4{\lambda}^2})</math>.		:<math> {\varepsilon}_{\mathbf{G},\mathbf{G}}^{-1}(\mathbf{q})={{\varepsilon}_{\infty}^{-1}}+(1-{{\varepsilon}_{\infty}^{-1}})[1-\text{exp}(-\frac{\|\mathbf{q+G}\|^2}{4{\lambda}^2})</math>.