LSINGLES

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

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

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

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:

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

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.

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

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

where $\gamma_{HF}$ is the Hartree-Fock density matrix, determined for the Hartree-Fock Hamiltonian $\hat h_{HF}$ and $\gamma_{DFT}$ 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

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

where $\gamma_{RPA}$ is the RPA density matrix. 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

• NATURALO natural orbital selection for RPA and GW calculations
• ALGO for response functions and RPA calculations
• for an overview on total energies using the ACFDT/RPA formalism
• for a practical guide to GW calculations
• Basis set convergence of ACFDT/RPA calculations

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