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GW方法：G0W0、GW0、GW、scGW0、scGW、QPGW0、QPGW
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关注：
1） 几种GW方法的区别：原理及实现方法异同
一、ALGO
ALGO-tag
http://cms.mpi.univie.ac.at/vasp/vasp/ALGO_tag.html#4378
ALGO = Normal | VeryFast | Fast | Conjugate | All | Damped | Subrot | Eigenval | None | Nothing | Exact | Diag
Default
ALGO = Normal
ALGO for response functions and GW calculations
http://cms.mpi.univie.ac.at/vasp/vasp/ALGO_response_functions_GW_calculations.html#7667
ALGO= CHI | GW0 | GW | scGW | scGW0 | QPGW | QPGW0
Default: none.
G0W0
http://cms.mpi.univie.ac.at/vasp/vasp/Recipe_GW_calculations.html
System = Si
NBANDS = 96
ISMEAR = 0 ; SIGMA = 0.05
LOPTICS = .TRUE.
ALGO = GW0 ; NOMEGA = 50
GW0
http://cms.mpi.univie.ac.at/vasp/vasp/Recipe_partially_selfconsistent_GW_calculations.html
System = Si
NBANDS = 96
ISMEAR = 0 ; SIGMA = 0.05
ALGO = GW0 ; NOMEGA = 50
NELM = 4
scGW: Recipe for selfconsistent GW calculations
http://cms.mpi.univie.ac.at/vasp/vasp/Recipe_selfconsistent_GW_calculations.html
System = Si
NBANDS = 96
ISMEAR = 0 ; SIGMA = 0.05
ALGO = GW # or ALGO = scGW
NELM =3
scqp GW:Caveats for selfconsistent quasiparticle GW calculations
http://cms.mpi.univie.ac.at/vasp/vasp/Caveats_selfconsistent_quasiparticle_GW_calculations.html
System = Si
NBANDS = 96
ISMEAR = 0 ; SIGMA = 0.05
ALGO = scGW # eigenvalues and one electron orbitals
NELM = 10
LOPTICS = .TRUE. ; LPEAD = .TRUE.
NBANDSGW: Number of orbitals updated in GW
NBANDSGW = [integer] twice the number of occupied states
The flag NBANDSGW determines how many QP energies are calculated and updated in GW type calculations. T
his value usually needs to be increased somewhat for partially or fully selfconsistent calculations. Very accurate results are only obtained when NBANDSGW approaches NBANDS, although this dramatically increases the computational requirements.
二、Thanks to Huayun and Roald
I checked this system with some simple calculations. T
The single shot GW method, GW0, indeed cannot give a band gap.
But self-consistent GW, in which the orbitals in G and W are also updated, predicts a band gap about 1.2 eV (please see the attached figure).
This value is still 0.5 eV smaller than the experimental 1.7 eV, but can be considered as good at current theoretical level.
The discrepancy, in my opinion, might be due to the residual self-interaction introduced in mean-field theory, which cannot be removed completely with GW approxiamtion only (though much better results can be achieved).
To improve the result further, we can consider to employ better DFT orbitals, for example using DFT+U or hybrid functional orbitals instead of the pure LDA/GGA orbitals to feed in GW calculations.
Xiaoqiu, you can check the calculation using the attached scripts by performing a GW0 first and then followed by a self-consistent GW, scGW.
If everything is OK then you can proceed to the next step, using DFT+U or M06-HF hybrid functional to produce self-interaction corrected orbitals.
Using these orbitals to initialize the GW calculation, I think we can obtain the correct band gap.
Sincerely YOURS
Geng
资料：
Recipe for selfconsistent GW calculations
Selfconsistent GW calculations are only supported in a QP picture. As for GW0, it is possible to update the eigenvalues only (ALGO=GW), or the eigenvalues and one-electron orbitals (ALGO=scGW). In all cases, a quasiparticle picture is maintained, i.e. satellite peaks (shake ups and shake downs) can not be accounted for in the selfconsistency cycle. Selfconsistent GW calculations can be performed by simply repeatedly calling VASP using: System = Si NBANDS = 96 ISMEAR = 0 ; SIGMA = 0.05 ALGO = GW # eigenvalues only or alternatively ALGO = scGW # eigenvalues and one electron orbitalsFor scGW0 or scGW non diagonal terms in the Hamiltonian are accounted for, e.g. the linearized QP equation is diagonalized, and the one electron orbitals are updated.[114]
Alternatively (and preferably), the user can specify an electronic iteration counter using NELM: System = Si NBANDS = 96 ISMEAR = 0 ; SIGMA = 0.05 ALGO = GW # or ALGO = scGW NELM = 3In this case, the one electron energies (=QP energies) are updated 3 times (starting from the DFT eigenvalues) in both G and W. For ALGO = scGW (or ALGO = QPGW in VASP.5.2.13), the one electron energies and one electron orbitals are updated 3 times.[114] As for ALGO = scGW0, the ``static'' COHSEX approximation can be selected by setting NOMEGA = 1 [115]. To improve convergence to the groundstate, the charge density is mixed using a Kerker type mixing starting with VASP.5.2.13 (see Sec. 6.49). The mixing parameters AMIX, BMIX, AMIX_MAG, BMIX_MAG, AMIN can be adjusted, if convergence problems are encountered.
Alternatively the mixing may be switched off by setting IMIX=0 and controlling the step width for the orbitals using the parameter TIME (which defaults to 0.4). This selects a fairly sophisticated damped MD algorithm, that is also used for DFT methods when ALGO is set the ``Damped''. In general, this method is more reliable for metals and materials with strong charge sloshing.
http://onlinelibrary.wiley.com/doi/10.1002/qua.21136/abstract
Keywords:
B3LYP functional;
GW approximation;
nickel oxide;
perturbation theory
The electronic band structure of NiO in the ferromagnetic state is calculated using the B3LYP hybrid density functional, the Hartree–Fock (HF) method, and the GW approximation (GWA) with dielectric functions constructed using either B3LYP or HF wave functions and energy eigenvalues. The band structure from the GWA calculation based on B3LYP wave functions is quite similar to the parent B3LYP band structure; the main differences are in valence bandwidth and in the upward shift of the empty minority spin Ni 3d bands relative to the same bands in the B3LYP calculation.
The band structure from the GWA calculation based on HF wave functions differs in that there are large upward shifts in valence band positions in the GWA calculation relative to the HF calculation, which result from screening of the bare exchange term in the Fock operator. Matrix elements of the HF exchange operator are obtained using wave functions from self-consistent HF or B3LYP calculations. Magnitudes of these matrix elements for several states at the Γ point of the Brillouin zone are compared, and it is found that the only major difference occurs in the empty minority spin bands derived from Ni 3d states of e symmetry. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
https://blog.sciencenet.cn/blog-567091-805223.html
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