LSINGLES - Revision history

Huebsch at 06:32, 21 February 2024

2024-02-21T06:32:01Z

← Older revision		Revision as of 06:32, 21 February 2024
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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:VASP6~~]]		[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]][[Category:ACFDT]][[Category:Low-scaling GW and RPA]]

Kaltakm at 10:35, 20 October 2023

2023-10-20T10:35:07Z

← Older revision		Revision as of 10:35, 20 October 2023
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	{{TAGDEF\|LSINGLES\|.TRUE. {{!}} .FALSE.\|.FALSE.}}		{{TAGDEF\|LSINGLES\|.TRUE. {{!}} .FALSE.\|.FALSE.}}

	Description: Switch on singles contribution to correlation energy for [[[[Practical_guide_to_GW_calculations#Low_scaling_GW_algorithms\|GW algorithms]].{{cite\|klimes:jcp:143}}		Description: Switch on singles contribution to correlation energy for [[Practical_guide_to_GW_calculations#Low_scaling_GW_algorithms\|GW algorithms]].{{cite\|klimes:jcp:143}}
	----		----
	{{TAG\|LSINGLES}} enables the calculation of the singles contributions to the correlation energy that can be represented by the following Feynman (time-ordered) diagrams:{{cite\|kaltak:thesis2015}}{{cite\|klimes:jcp:143}}		{{TAG\|LSINGLES}} enables the calculation of the singles contributions to the correlation energy that can be represented by the following Feynman (time-ordered) diagrams:{{cite\|kaltak:thesis2015}}{{cite\|klimes:jcp:143}}

Kaltakm at 10:34, 20 October 2023

2023-10-20T10:34:26Z

← Older revision		Revision as of 10:34, 20 October 2023
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	{{TAGDEF\|LSINGLES\|.TRUE. {{!}} .FALSE.\|.FALSE.}}		{{TAGDEF\|LSINGLES\|.TRUE. {{!}} .FALSE.\|.FALSE.}}

	Description: Switch on singles contribution to correlation energy for [[GW algorithms]].{{cite\|klimes:jcp:143}}		Description: Switch on singles contribution to correlation energy for [[[[Practical_guide_to_GW_calculations#Low_scaling_GW_algorithms\|GW algorithms]].{{cite\|klimes:jcp:143}}
	----		----
	{{TAG\|LSINGLES}} enables the calculation of the singles contributions to the correlation energy that can be represented by the following Feynman (time-ordered) diagrams:{{cite\|kaltak:thesis2015}}{{cite\|klimes:jcp:143}}		{{TAG\|LSINGLES}} enables the calculation of the singles contributions to the correlation energy that can be represented by the following Feynman (time-ordered) diagrams:{{cite\|kaltak:thesis2015}}{{cite\|klimes:jcp:143}}

Huebsch: Huebsch moved page Construction:LSINGLES to LSINGLES without leaving a redirect

2023-10-20T10:30:25Z

Huebsch moved page Construction:LSINGLES to LSINGLES without leaving a redirect

← Older revision	Revision as of 10:30, 20 October 2023
(No difference)

Huebsch at 08:45, 20 October 2023

2023-10-20T08:45:21Z

Kaltakm: Created page with "{{TAGDEF|LSINGLES|.TRUE. {{!}} .FALSE.|.FALSE.}} Description: calculate singles contribution to correlation energy using GW algorithms.{{cite|klimes:jcp:143}} ---- This tag c..."

2023-09-29T09:44:31Z

Created page with "{{TAGDEF|LSINGLES|.TRUE. {{!}} .FALSE.|.FALSE.}} Description: calculate singles contribution to correlation energy using GW algorithms.{{cite|klimes:jcp:143}} ---- This tag c..."

New page

{{TAGDEF|LSINGLES|.TRUE. {{!}} .FALSE.|.FALSE.}}

Description: calculate singles contribution to correlation energy using GW algorithms.{{cite|klimes:jcp:143}}
----
This tag can be used to calculate the singles contributions to the correlation energy that can be represented by following Feynman (time-ordered) diagrams:{{cite|kaltak:thesis2015}}{{cite|klimes:jcp:143}}

[[File:SinglesDiagrams.png|320px]]

This tag is used in combination with the [[ACFDT/RPA_calculations#Low-scaling_ACFDT.2FRPA_algorithm|low-scaling ACFDT/RPA]] and [[Practical_guide_to_GW_calculations#Low_scaling_GW_algorithms|GW]] algorithms.

If the [[ACFDT/RPA_calculations#All-in-one_approach_to_calculate_ACFDT-RPA_total_energy|ACFDT/RPA algorithm]] is selected with {{TAG|ALGO}}=RPAR|ACFDTR and {{TAGBL|LSINGLES}} is set, the code calculates two singles contributions and writes following lines to OUTCAR

HF single shot energy change -1.23182672
renormalized HF singles -1.23310555

Here '''renomalized HF singles''' corresponds to the renormalized singles contribution suggested by Ren and coworkers:{{cite|ren:prb:88}}

<math>
E^{rSE}_c = -\sum_{a\in virt, i\in occ} \frac{|\langle i| V^{HF} - V_0^{KS}|a\rangle|^2 }{\epsilon_a-\epsilon_i}
</math>

This contribution accounts for the change of the mean field exchange energy and can be derived consistently within the AC-FDT framework as described in Sec. II D Eq. (28) of Klimeš et al.{{cite|klimes:jcp:143}}

In contrast, the '''HF single shot energy change''' line contains the somewhat simpler contribution{{cite|klimes:jcp:143}}

<math>
E_c^{rSE} = \mathrm{Tr}\left[ (\gamma_{HF} - \gamma_{DFT})\hat h_{HF} \right],
</math>

where <math>\gamma_{HF}</math> is the Hartree-Fock density matrix, determined for the Hartree-Fock Hamiltonian <math>\hat h_{HF}</math> and <math>\gamma_{DFT}</math> is the Kohn-Sham density matrix.
In all practical calculations we found that both values, the single-shot HF and renormalized singles contributions, are exceedingly close to each other.

If the [[Practical_guide_to_GW_calculations#Low_scaling.2C_single_shot_GW_calculations:_G0W0R|GW algorithm]] is selected with {{TAG|ALGO}}=G0W0R, the OUTCAR contains also the singles contribution beyond the Hartree-Fock level

<math>
E_c^{GWSE} = \mathrm{Tr}\left[ (\gamma_{RPA} - \gamma_{DFT})\hat h_{HF} \right],
</math>

where <math>\gamma_{RPA}</math> is the RPA density matrix.{{cite|klimes:jcp:143}}
For versions <= 6.4.2, this contribution is not directly printed to file. However, the first and second term is printed to OUTCAR:
Energies using frozen KS orbitals
Hartree-Fock free energy of the ion-electron system (eV)
...
eigenvalues EBANDS = -88.61789695 <--------Tr{ gam_DFT h_HF}---------
...
Energies after update of density matrix
Hartree-Fock free energy of the ion-electron system (eV)
...
eigenvalues EBANDS = -89.68870320 <--------Tr{ gam_RPA h_HF}---------
...
Version >6.4.2 writes the GWSE singles contribution to OUTCAR:
GWSE singles contribution: -1.07080625
{{NB|mind|The singles contribution is calculated correctly only for the default {{TAG|NATURALO}}{{=}}2.}}
The [[ACFDT/RPA calculations#Output of low-scaling ACFDT.2FRPA|total energy]] in the limit of [[ACFDT/RPA calculations#Basis set convergence|infinite energy cutoff]] is then obtained by adding the singles contribution to the value of

<code>HF+E_corr(extrapolated) = -153.98810072 eV</code>

== Related tags and articles ==

*{{TAG|NATURALO}} natural orbital selection for ''RPA'' and ''GW'' calculations
*{{TAG|ALGO}} for response functions and ''RPA'' calculations
* for an overview on total energies using the [[ACFDT/RPA calculations|ACFDT/RPA formalism]]
* for a practical guide to [[GW calculations]]
* [[ACFDT/RPA calculations#Basis set convergence|Basis set convergence]] of ACFDT/RPA calculations
== References ==
----
[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]] [[Category:ACFDT]][[Category:Low-scaling GW and RPA]][[Category:VASP6]]

← Older revision		Revision as of 08:45, 20 October 2023
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	{{TAGDEF\|LSINGLES\|.TRUE. {{!}} .FALSE.\|.FALSE.}}		{{TAGDEF\|LSINGLES\|.TRUE. {{!}} .FALSE.\|.FALSE.}}

	Description: ~~calculate~~ singles contribution to correlation energy ~~using~~ GW algorithms.{{cite\|klimes:jcp:143}}		Description: Switch on singles contribution to correlation energy for [[GW algorithms]].{{cite\|klimes:jcp:143}}
	----		----
	~~This tag can be used to calculate~~ the singles contributions to the correlation energy that can be represented by following Feynman (time-ordered) diagrams:{{cite\|kaltak:thesis2015}}{{cite\|klimes:jcp:143}}		{{TAG\|LSINGLES}} enables the calculation of the singles contributions to the correlation energy that can be represented by the following Feynman (time-ordered) diagrams:{{cite\|kaltak:thesis2015}}{{cite\|klimes:jcp:143}}

	[[File:SinglesDiagrams.png\|320px]]		[[File:SinglesDiagrams.png\|320px]]

	~~This tag~~ is used in combination with the [[ACFDT/RPA_calculations#Low-scaling_ACFDT.2FRPA_algorithm\|low-scaling ACFDT/RPA]] and [[Practical_guide_to_GW_calculations#Low_scaling_GW_algorithms\|GW]] algorithms.		{{TAG\|LSINGLES}} is used in combination with the [[ACFDT/RPA_calculations#Low-scaling_ACFDT.2FRPA_algorithm\|low-scaling ACFDT/RPA]] and [[Practical_guide_to_GW_calculations#Low_scaling_GW_algorithms\|GW]] algorithms.

	If the [[ACFDT/RPA_calculations#All-in-one_approach_to_calculate_ACFDT-RPA_total_energy\|ACFDT/RPA algorithm]] is selected with {{TAG\|ALGO}}=RPAR\|ACFDTR and {{TAGBL\|LSINGLES}} is set, the code calculates two singles contributions and writes following lines to OUTCAR		If the [[ACFDT/RPA_calculations#All-in-one_approach_to_calculate_ACFDT-RPA_total_energy\|ACFDT/RPA algorithm]] is selected with {{TAG\|ALGO}}=RPAR\|ACFDTR and {{TAGBL\|LSINGLES}} is set, the code calculates two singles contributions and writes following lines to {{FILE\|OUTCAR}}

	HF single shot energy change -1.23182672		HF single shot energy change -1.23182672
	renormalized HF singles -1.23310555		renormalized HF singles -1.23310555

	Here '''renomalized HF singles''' corresponds to the renormalized singles contribution suggested by Ren and coworkers:{{cite\|ren:prb:88}}		Here, '''renomalized HF singles''' corresponds to the renormalized singles contribution suggested by Ren and coworkers:{{cite\|ren:prb:88}}

	<math>		<math>
Line 20:		Line 20:
	</math>		</math>

	This contribution accounts for the change of the mean field exchange energy and can be derived consistently within the AC-FDT framework as described in Sec. II D Eq. (28) of Klimeš et al.{{cite\|klimes:jcp:143}}		This contribution accounts for the change of the mean-field exchange energy and can be derived consistently within the AC-FDT framework as described in Sec. II D Eq. (28) of Klimeš et al.{{cite\|klimes:jcp:143}}

	In contrast, the '''HF single shot energy change''' line contains the somewhat simpler contribution{{cite\|klimes:jcp:143}}		In contrast, the '''HF single shot energy change''' line contains the somewhat simpler contribution{{cite\|klimes:jcp:143}}
Line 29:		Line 29:

	where <math>\gamma_{HF}</math> is the Hartree-Fock density matrix, determined for the Hartree-Fock Hamiltonian <math>\hat h_{HF}</math> and <math>\gamma_{DFT}</math> is the Kohn-Sham density matrix.		where <math>\gamma_{HF}</math> is the Hartree-Fock density matrix, determined for the Hartree-Fock Hamiltonian <math>\hat h_{HF}</math> and <math>\gamma_{DFT}</math> is the Kohn-Sham density matrix.
	In all practical calculations we found that both values, the single-shot HF and renormalized singles contributions, are exceedingly close to each other.		In all practical calculations, we found that both values, the single-shot HF and renormalized singles contributions, are exceedingly close to each other.

	If the [[Practical_guide_to_GW_calculations#Low_scaling.2C_single_shot_GW_calculations:_G0W0R\|GW algorithm]] is selected with {{TAG\|ALGO}}=G0W0R, the OUTCAR contains also the singles contribution beyond the Hartree-Fock level		If the [[Practical_guide_to_GW_calculations#Low_scaling.2C_single_shot_GW_calculations:_G0W0R\|GW algorithm]] is selected with {{TAG\|ALGO}}=G0W0R, the {{FILE\|OUTCAR}} contains also the singles contribution beyond the Hartree-Fock level

	<math>		<math>
Line 38:		Line 38:

	where <math>\gamma_{RPA}</math> is the RPA density matrix.{{cite\|klimes:jcp:143}}		where <math>\gamma_{RPA}</math> is the RPA density matrix.{{cite\|klimes:jcp:143}}
	For versions <= 6.4.2, this contribution is not directly printed to file. However, the first and second term is printed to OUTCAR:		For versions <= 6.4.2, this contribution is not directly printed to file. However, the first and second term is printed to {{FILE\|OUTCAR}}:
	Energies using frozen KS orbitals		Energies using frozen KS orbitals
	Hartree-Fock free energy of the ion-electron system (eV)		Hartree-Fock free energy of the ion-electron system (eV)
Line 49:		Line 49:
	eigenvalues EBANDS = -89.68870320 <--------Tr{ gam_RPA h_HF}---------		eigenvalues EBANDS = -89.68870320 <--------Tr{ gam_RPA h_HF}---------
	...		...
	Version >6.4.2 writes the GWSE singles contribution to OUTCAR:		Version >6.4.2 writes the GWSE singles contribution to {{FILE\|OUTCAR}}:
	GWSE singles contribution: -1.07080625		GWSE singles contribution: -1.07080625
	{{NB\|mind\|The singles contribution is calculated correctly only for the default {{TAG\|NATURALO}}{{=}}2.}}		{{NB\|mind\|The singles contribution is calculated correctly only for the default {{TAG\|NATURALO}}{{=}}2.}}
	The [[ACFDT/RPA calculations#Output of low-scaling ACFDT.2FRPA\|total energy]] in the limit of [[ACFDT/RPA calculations#Basis set convergence\|infinite energy cutoff]] is then obtained by adding the singles contribution to the value of		The [[ACFDT/RPA calculations#Output of low-scaling ACFDT.2FRPA\|ACFDT total energy]] in the limit of [[ACFDT/RPA calculations#Basis set convergence\|infinite energy cutoff]] is then obtained by adding the singles contribution to the value of

	<code>HF+E_corr(extrapolated) = -153.98810072 eV</code>		<code>HF+E_corr(extrapolated) = -153.98810072 eV</code>
Line 65:		Line 65:
	== References ==		== References ==
	----		----
	[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]] [[Category:ACFDT]][[Category:Low-scaling GW and RPA]][[Category:VASP6]]		[[Category:INCAR tag]][[Category:Many-body perturbation theory]][[Category:GW]][[Category:ACFDT]][[Category:Low-scaling GW and RPA]][[Category:VASP6]]