LSINGLES: Difference between revisions

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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>
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</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}}
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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>
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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)
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   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>
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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]][[Category:VASP6]]

Revision as of 08:45, 20 October 2023

LSINGLES = .TRUE. | .FALSE.
Default: LSINGLES = .FALSE. 

Description: Switch on singles contribution to correlation energy for GW algorithms.[1]


LSINGLES enables the calculation of the singles contributions to the correlation energy that can be represented by the following Feynman (time-ordered) diagrams:[2][1]

LSINGLES is used in combination with the low-scaling ACFDT/RPA and GW algorithms.

If the ACFDT/RPA algorithm is selected with ALGO=RPAR|ACFDTR and 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:[3]

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.[1]

In contrast, the HF single shot energy change line contains the somewhat simpler contribution[1]

where is the Hartree-Fock density matrix, determined for the Hartree-Fock Hamiltonian and 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 GW algorithm is selected with ALGO=G0W0R, the OUTCAR contains also the singles contribution beyond the Hartree-Fock level

where is the RPA density matrix.[1] 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
Mind: The singles contribution is calculated correctly only for the default NATURALO=2.

The ACFDT total energy in the limit of infinite energy cutoff is then obtained by adding the singles contribution to the value of

HF+E_corr(extrapolated)    =      -153.98810072 eV

Related tags and articles

References