Improving the dielectric function - Revision history

Liebetreu: Reverted edit by Liebetreu (talk) to last revision by Karsai

2026-04-15T12:38:49Z

Reverted edit by Liebetreu (talk) to last revision by Karsai

← Older revision		Revision as of 12:38, 15 April 2026
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	*In our example we use <math>n=4</math> and <math>m=4</math>: Effectively we use <math>16\times 16\times 16</math> k-points.		*In our example we use <math>n=4</math> and <math>m=4</math>: Effectively we use <math>16\times 16\times 16</math> k-points.
	[[File:Fig BSE example2 1.png\|500px]]		[[File:Fig BSE example2 1.png\|500px]]
	*In the script ''doall-average.sh'' the scheme is written for <math>n=4</math> and <math>n=\~~mathrm~~{\$NKPT}</math>. At the end the dielectric functions are extracted and averaged accordingly. You can choose up to which level of theory (DFT, RPA, BSE) the dielectric function is computed by commenting out the corresponding lines in the script (default is all the way up to BSE).		*In the script ''doall-average.sh'' the scheme is written for <math>n=4</math> and <math>n=\textrm{\$NKPT}</math>. At the end the dielectric functions are extracted and averaged accordingly. You can choose up to which level of theory (DFT, RPA, BSE) the dielectric function is computed by commenting out the corresponding lines in the script (default is all the way up to BSE).
	*Because of the shifted grids we have to use density functional perturbation theory to calculate the derivatives of the wave functions with respect to <math>\mathbf{k}</math> and not the finite difference scheme. We also have to switch off all k-points symmetry in all {{TAG\|INCAR}} files. These two important parameters look like the following in the {{TAG\|INCAR}} file:		*Because of the shifted grids we have to use density functional perturbation theory to calculate the derivatives of the wave functions with respect to <math>\mathbf{k}</math> and not the finite difference scheme. We also have to switch off all k-points symmetry in all {{TAG\|INCAR}} files. These two important parameters look like the following in the {{TAG\|INCAR}} file:
	{{TAGBL\|PREC}} = Normal ; {{TAGBL\|ENCUT}} = 250.0		{{TAGBL\|PREC}} = Normal ; {{TAGBL\|ENCUT}} = 250.0

Liebetreu: /* Averaging over multiple grids */

2026-04-14T11:36:04Z

Averaging over multiple grids

← Older revision		Revision as of 11:36, 14 April 2026
Line 49:		Line 49:
	*In our example we use <math>n=4</math> and <math>m=4</math>: Effectively we use <math>16\times 16\times 16</math> k-points.		*In our example we use <math>n=4</math> and <math>m=4</math>: Effectively we use <math>16\times 16\times 16</math> k-points.
	[[File:Fig BSE example2 1.png\|500px]]		[[File:Fig BSE example2 1.png\|500px]]
	*In the script ''doall-average.sh'' the scheme is written for <math>n=4</math> and <math>n=\~~textrm~~{\$NKPT}</math>. At the end the dielectric functions are extracted and averaged accordingly. You can choose up to which level of theory (DFT, RPA, BSE) the dielectric function is computed by commenting out the corresponding lines in the script (default is all the way up to BSE).		*In the script ''doall-average.sh'' the scheme is written for <math>n=4</math> and <math>n=\mathrm{\$NKPT}</math>. At the end the dielectric functions are extracted and averaged accordingly. You can choose up to which level of theory (DFT, RPA, BSE) the dielectric function is computed by commenting out the corresponding lines in the script (default is all the way up to BSE).
	*Because of the shifted grids we have to use density functional perturbation theory to calculate the derivatives of the wave functions with respect to <math>\mathbf{k}</math> and not the finite difference scheme. We also have to switch off all k-points symmetry in all {{TAG\|INCAR}} files. These two important parameters look like the following in the {{TAG\|INCAR}} file:		*Because of the shifted grids we have to use density functional perturbation theory to calculate the derivatives of the wave functions with respect to <math>\mathbf{k}</math> and not the finite difference scheme. We also have to switch off all k-points symmetry in all {{TAG\|INCAR}} files. These two important parameters look like the following in the {{TAG\|INCAR}} file:
	{{TAGBL\|PREC}} = Normal ; {{TAGBL\|ENCUT}} = 250.0		{{TAGBL\|PREC}} = Normal ; {{TAGBL\|ENCUT}} = 250.0

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
Line 40:		Line 40:

	* 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 ===