ESF SPLINES - Revision history

Kaltakm: Kaltakm moved page Construction:ESF SPLINES to ESF SPLINES

2024-12-18T14:09:17Z

Kaltakm moved page Construction:ESF SPLINES to ESF SPLINES

← Older revision	Revision as of 14:09, 18 December 2024
(No difference)

Huebsch: /* ESF-interpolation method vs k-p perturbation theory */

2024-06-12T08:24:22Z

ESF-interpolation method vs k-p perturbation theory

← Older revision		Revision as of 08:24, 12 June 2024
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	==ESF-interpolation method vs k-p perturbation theory==		==ESF-interpolation method vs k-p perturbation theory==
	{{NB\|warning\|Remove {{FILE\|WAVEDER}} and avoid setting {{TAG\|LOPTICS}}{{=}}T ~~before~~ running a job with {{TAG\|ESF_SPLINES}}{{=}}T.}}		{{NB\|warning\|Remove {{FILE\|WAVEDER}} and avoid setting {{TAG\|LOPTICS}}{{=}}T when running a job with {{TAG\|ESF_SPLINES}}{{=}}T.}}
	Note that the ESF-interpolation method is incompatible with k-p perturbation theory, where the largest q-point integration error		Note that the ESF-interpolation method is incompatible with k-p perturbation theory, where the largest q-point integration error
	:<math>		:<math>

Huebsch at 08:23, 12 June 2024

2024-06-12T08:23:39Z

← Older revision		Revision as of 08:23, 12 June 2024
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			{{DISPLAYTITLE:ESF_SPLINES}}
	{{TAGDEF\|ESF_SPLINES\|.FALSE. {{!}} .TRUE. \|.FALSE.}}		{{TAGDEF\|ESF_SPLINES\|.FALSE. {{!}} .TRUE. \|.FALSE.}}

	Description: Enable k-point interpolation of the electronic structure factor using tricubic splines in [[ACFDT/RPA calculations]].		Description: Enable k-point interpolation of the electronic structure factor using tricubic splines in [[ACFDT/RPA calculations]].
	----		----
	~~The~~ electronic structure factor (ESF) ~~in [[ACFDT/RPA calculations]] can be~~ interpolated using tricubic splines to accelerate k-point convergence of the [[RPA/ACFDT:_Correlation_energy_in_the_Random_Phase_Approximation\|RPA correlation energy]] ~~by setting~~ {{TAG\|~~ESF_SPLINES~~}} =T. This feature follows the same idea as in coupled cluster calculations.{{cite\|liao:jcp:2016}}		With {{TAG\|ESF_SPLINES}} =T, the electronic structure factor (ESF) is interpolated using tricubic splines to accelerate k-point convergence of the [[RPA/ACFDT:_Correlation_energy_in_the_Random_Phase_Approximation\|RPA-correlation energy]] in [[ACFDT/RPA calculations]]. The default settings of the maximum number of iteration steps ({{TAG\|ESF_NINTER}}) and convergence threshold ({{TAG\|ESF_CONV}}) typically yield similar k-point convergence compared to the k-p perturbation theory approach.
			{{NB\|tip\|By means of ESF interpolation, one can obtain the RPA-correlation energy for metals and insulators, in contrast to the k-p method that fails for metals.}}
	To ~~this end~~, the electronic structure factor in the RPA		==Algorithm==
			This feature follows the same idea as in coupled cluster calculations.{{cite\|liao:jcp:2016}}
			To compute the RPA-correlation energy, the electronic structure factor in the RPA

	<math>		<math>
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	is evaluated on the k-point grid defined in {{FILE\|KPOINTS}} and the correlation energy (as its trace) is stored.{{cite\|gelbenegger:thesis2018}}		is evaluated on the k-point grid defined in {{FILE\|KPOINTS}} and the correlation energy (as its trace) is stored.{{cite\|gelbenegger:thesis2018}}
	To obtain the correlation energy on a finer k-point grid, more q-points are added using tricubic spline interpolation ~~and the~~ resulting energy is compared to the previous correlation energy.		To obtain the correlation energy on a finer k-point grid, more q-points are added using tricubic spline interpolation. The resulting energy is compared to the previous correlation energy.
	This procedure is repeated {{TAG\|ESF_NINTER}} times until the difference in energy between the interpolation steps is less than {{TAG\|ESF_CONV}}.		This procedure is repeated {{TAG\|ESF_NINTER}} times or until the difference in energy between the interpolation steps is less than {{TAG\|ESF_CONV}}.
	~~The default settings of~~ {{TAG\|~~ESF_NINTER~~}} ~~and~~ {{TAG\|~~ESF_CONV~~}} ~~typically yield similar k~~-~~point convergence compared to the~~ k-p perturbation theory ~~approach~~, where the ~~limit~~
	<math>		==ESF-interpolation method vs k-p perturbation theory==
			{{NB\|warning\|Remove {{FILE\|WAVEDER}} and avoid setting {{TAG\|LOPTICS}}{{=}}T before running a job with {{TAG\|ESF_SPLINES}}{{=}}T.}}
			Note that the ESF-interpolation method is incompatible with k-p perturbation theory, where the largest q-point integration error
			:<math>
	\lim_{\bf q\to 0} \tilde\chi^0_{{\bf G G}'}({\bf q},{\rm i}\omega) \cdot {\bf V}_{\bf G G'}({\bf q})		\lim_{\bf q\to 0} \tilde\chi^0_{{\bf G G}'}({\bf q},{\rm i}\omega) \cdot {\bf V}_{\bf G G'}({\bf q})
	</math>		</math>
	is ~~stored~~ to ~~{{FILE\|WAVECAR}} in a preceding DFT calculation using {{TAG\|LOPTICS}}=T~~.		is added explicitly to the RPA integral. The long-wave limit is ill-defined for metallic systems; hence, the k-p method fails for metals. For the k-p method, the long-wave contribution is stored in the {{FILE\|WAVEDER}} file, and VASP assumes you want to add this term if the file is present in the working directory.
	~~{{NB\|tip\|This~~ method ~~works~~ for metals ~~and insulators~~.}}
	~~{{NB\|warning\|Remove~~ {{FILE\|WAVEDER}} ~~before running~~ the ~~job and avoid setting~~ {{~~TAG~~\|~~LOPTICS~~}}.}}		==Output==

			The result of the ESF interpolation is reported to the {{FILE\|OUTCAR}} file in the following format

			cutoff energy smooth cutoff RPA correlation Hartree contr. to MP2 RPA spline-interp.
			-----------------------------------------------------------------------------------------------------
			166.667 133.333 -12.9738715106 -19.7255874374 -13.4968000908
			158.730 126.984 -12.8840657072 -19.6294580403 -13.4017404001
			151.172 120.937 -12.7775593388 -19.5151822998 -13.3005326847
			143.973 115.178 -12.6604147404 -19.3892142669 -13.1868498210
			137.117 109.694 -12.5530911576 -19.2733151174 -13.0861120393
			130.588 104.470 -12.4659186304 -19.1786165194 -12.9778587892
			124.369 99.495 -12.3690601643 -19.0725742983 -12.8709666989
			118.447 94.758 -12.2461267475 -18.9372318755 -12.7590723870
			linear regression
			converged value -14.0340307585 -20.8751715586 -14.5828037654

			The last column contains the result from the spline interpolation for the selected energy cutoffs reported in the first column.
	{{NB\|mind\|Available as of VASP.6.5.0}}		{{NB\|mind\|Available as of VASP.6.5.0}}

	== Related tags and articles ==		== Related tags and articles ==
	{{TAG\|ESF_CONV}},		{{TAG\|ESF_CONV}},
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	==References==		==References==


	<!--[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]][[Category:ACFDT]][[Category:Low-scaling GW and RPA]]		<!--[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]][[Category:ACFDT]][[Category:Low-scaling GW and RPA]]

Huebsch at 07:34, 12 June 2024

2024-06-12T07:34:41Z

← Older revision		Revision as of 07:34, 12 June 2024
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	{{NB\|tip\|This method works for metals and insulators.}}		{{NB\|tip\|This method works for metals and insulators.}}
	{{NB\|warning\|Remove {{FILE\|WAVEDER}} before running the job and avoid setting {{TAG\|LOPTICS}}.}}		{{NB\|warning\|Remove {{FILE\|WAVEDER}} before running the job and avoid setting {{TAG\|LOPTICS}}.}}
	{{NB\|mind\|~~available~~ as of VASP.6.5.0}}		{{NB\|mind\|Available as of VASP.6.5.0}}

	== Related tags and articles ==		== Related tags and articles ==

Huebsch at 07:06, 12 June 2024

2024-06-12T07:06:31Z

← Older revision		Revision as of 07:06, 12 June 2024
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	{{TAGDEF\|ESF_SPLINES\|.FALSE. {{!}} .TRUE. \|.FALSE.}}		{{TAGDEF\|ESF_SPLINES\|.FALSE. {{!}} .TRUE. \|.FALSE.}}

	Description: ~~{{TAG\|ESF_SPLINES}} selects~~ k-point interpolation in ACFDT~~(R)~~ calculations ~~using tri-cubic splines~~.		Description: Enable k-point interpolation of the electronic structure factor using tricubic splines in [[ACFDT/RPA calculations]].
	----		----
	~~Interpolates the~~ electronic structure factor in [[ACFDT/RPA calculations]] using ~~tri-cubic~~ splines to accelerate k-point convergence of the [[RPA/ACFDT:_Correlation_energy_in_the_Random_Phase_Approximation\|RPA correlation energy]]. This feature follows the same idea as in coupled cluster calculations.{{cite\|liao:jcp:2016}}		The electronic structure factor (ESF) in [[ACFDT/RPA calculations]] can be interpolated using tricubic splines to accelerate k-point convergence of the [[RPA/ACFDT:_Correlation_energy_in_the_Random_Phase_Approximation\|RPA correlation energy]] by setting {{TAG\|ESF_SPLINES}} =T. This feature follows the same idea as in coupled cluster calculations.{{cite\|liao:jcp:2016}}

	To this end, the electronic structure factor in the RPA		To this end, the electronic structure factor in the RPA
Line 13:		Line 13:

	is evaluated on the k-point grid defined in {{FILE\|KPOINTS}} and the correlation energy (as its trace) is stored.{{cite\|gelbenegger:thesis2018}}		is evaluated on the k-point grid defined in {{FILE\|KPOINTS}} and the correlation energy (as its trace) is stored.{{cite\|gelbenegger:thesis2018}}
	To obtain the correlation energy on a finer k-point grid, more q-points are added using ~~tri-cubic~~ spline interpolation and the resulting energy is compared to the previous correlation energy.		To obtain the correlation energy on a finer k-point grid, more q-points are added using tricubic spline interpolation and the resulting energy is compared to the previous correlation energy.
	This procedure is repeated {{TAG\|ESF_NINTER}} times until the difference in energy between the interpolation steps is less than {{TAG\|ESF_CONV}}.		This procedure is repeated {{TAG\|ESF_NINTER}} times until the difference in energy between the interpolation steps is less than {{TAG\|ESF_CONV}}.
	The default settings of {{TAG\|ESF_NINTER}} and {{TAG\|ESF_CONV}} typically yield similar k-point convergence compared to the k-p perturbation theory approach, where the limit		The default settings of {{TAG\|ESF_NINTER}} and {{TAG\|ESF_CONV}} typically yield similar k-point convergence compared to the k-p perturbation theory approach, where the limit
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	{{sc\|ESF_SPLINES\|Examples\|Examples that use this tag}}		{{sc\|ESF_SPLINES\|Examples\|Examples that use this tag}}
	~~----~~

	[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]][[Category:ACFDT]][[Category:Low-scaling GW and RPA]]		==References==


			<!--[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]][[Category:ACFDT]][[Category:Low-scaling GW and RPA]]

Kaltakm at 06:54, 12 June 2024

2024-06-12T06:54:05Z

← Older revision		Revision as of 06:54, 12 June 2024
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	{{NB\|tip\|This method works for metals and insulators.}}		{{NB\|tip\|This method works for metals and insulators.}}
	{{NB\|warning\|Remove {{FILE\|WAVEDER}} before running the job and avoid setting {{TAG\|LOPTICS}}.}}		{{NB\|warning\|Remove {{FILE\|WAVEDER}} before running the job and avoid setting {{TAG\|LOPTICS}}.}}
	{{NB\|mind\|available as of VASP.6.4.0}}		{{NB\|mind\|available as of VASP.6.5.0}}

	== Related tags and articles ==		== Related tags and articles ==

Kaltakm at 06:53, 12 June 2024

2024-06-12T06:53:54Z

← Older revision		Revision as of 06:53, 12 June 2024
Line 22:		Line 22:
	{{NB\|tip\|This method works for metals and insulators.}}		{{NB\|tip\|This method works for metals and insulators.}}
	{{NB\|warning\|Remove {{FILE\|WAVEDER}} before running the job and avoid setting {{TAG\|LOPTICS}}.}}		{{NB\|warning\|Remove {{FILE\|WAVEDER}} before running the job and avoid setting {{TAG\|LOPTICS}}.}}
			{{NB\|mind\|available as of VASP.6.4.0}}

	== Related tags and articles ==		== Related tags and articles ==

Kaltakm at 07:51, 11 June 2024

2024-06-11T07:51:18Z

← Older revision		Revision as of 07:51, 11 June 2024
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	The default settings of {{TAG\|ESF_NINTER}} and {{TAG\|ESF_CONV}} typically yield similar k-point convergence compared to the k-p perturbation theory approach, where the limit		The default settings of {{TAG\|ESF_NINTER}} and {{TAG\|ESF_CONV}} typically yield similar k-point convergence compared to the k-p perturbation theory approach, where the limit
	<math>		<math>
	\lim_{\bf q\to 0} \tilde\chi^0_{{\bf G G}'}({\bf q},i\omega) \cdot {\bf V}_{\bf G G'}({\bf q})		\lim_{\bf q\to 0} \tilde\chi^0_{{\bf G G}'}({\bf q},{\rm i}\omega) \cdot {\bf V}_{\bf G G'}({\bf q})
	</math>		</math>
	is stored to {{FILE\|WAVECAR}} in a preceding DFT calculation using {{TAG\|LOPTICS}}=T.		is stored to {{FILE\|WAVECAR}} in a preceding DFT calculation using {{TAG\|LOPTICS}}=T.

Kaltakm at 07:50, 11 June 2024

2024-06-11T07:50:43Z

← Older revision		Revision as of 07:50, 11 June 2024
Line 17:		Line 17:
	The default settings of {{TAG\|ESF_NINTER}} and {{TAG\|ESF_CONV}} typically yield similar k-point convergence compared to the k-p perturbation theory approach, where the limit		The default settings of {{TAG\|ESF_NINTER}} and {{TAG\|ESF_CONV}} typically yield similar k-point convergence compared to the k-p perturbation theory approach, where the limit
	<math>		<math>
	\lim_{\bf q\to 0} \~~chi_~~{{\bf G G}'}({\bf q},i\omega) \cdot {\bf V}_{\bf G G'}({\bf q})		\lim_{\bf q\to 0} \tilde\chi^0_{{\bf G G}'}({\bf q},i\omega) \cdot {\bf V}_{\bf G G'}({\bf q})
	</math>		</math>
	is stored to {{FILE\|WAVECAR}} in a preceding DFT calculation using {{TAG\|LOPTICS}}=T.		is stored to {{FILE\|WAVECAR}} in a preceding DFT calculation using {{TAG\|LOPTICS}}=T.

Kaltakm at 07:50, 11 June 2024

2024-06-11T07:50:15Z

← Older revision		Revision as of 07:50, 11 June 2024
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	<math>		<math>
	S({\bf q}+{\bf G}) =~~\left[~~ \int {\rm d}\omega \ln( {\~~bf 1}+~~{~~\bf V~~}\~~cdot~~\chi(i\~~omega))-~~{~~\bf V~~}\~~cdot\chi(~~i\omega) \~~right~~]_{{\bf G},{\~~bf G~~}}({\bf q})		S({\bf q}+{\bf G}) =\int {\rm d}\omega
			\left\{(\mathrm{ln}[1-\tilde\chi^0({\mathbf{q}},\mathrm{i}\omega)V({\mathbf{q}})])_{{\mathbf{G,G}}} +V_{{\mathbf{G,G}}}({\mathbf{q}})\tilde\chi^0({\mathbf{q}},{\mathrm{i}}\omega) \right\}
	</math>		</math>