Practical guide to GW calculations
The GW approximation is an approximation to the self-energy. GW calculations are available as of VASP.5.X. For details on the implementation and use of the GW routines, we recommend the papers by Shishkin et al. ^{[1]}^{[2]}^{[3]} and Fuchs et al.^{[4]}
Single step procedure: GW in one go
As of VASP.6.3 all GW approximations can be run in one single run by selecting the corresponding ALGO tag and omitting NBANDS), for instance like so
System = SiC ALGO = EVGW0, QPGW0, EVGW, QPGW, GW0R or GWR # use an algorithgm described below NELMGW = 1,2,.. # number of self-consistency cycles ISMEAR = 0 ; SIGMA = 0.05 ! small sigma is required to avoid partial occupancies LOPTICS = .TRUE. # for insulators, omit for metals
Note, NBANDS must not be present in the INCAR to select this procedure.
Important: In older versions a two step procedure is required, where the first step is always a DFT calculation and the second step the actual GW calculation. |
The two-step procedure is described below.
Caveats
The single-step GW procedure performs a DFT step internally with an exact diagonalization of the Kohn-Sham Hamiltonian using the maximum available NBANDS supported for the chosen ENCUT value. Consequently, a large number of unoccupied bands is initialized with random plane-wave coefficients. In rare cases, this yields two linearly dependent column vectors in the Hamiltonian and results in LAPACK errors like "ZPOTRF fails". These errors can be prevented using the two-step GW procedure as described below. Furthermore, one can "ramp up" NBANDS to the maximum value by repeatedly restarting the DFT calculation from a pre-converged WAVECAR with fewer bands.
First step: DFT calculation
GW calculations always require a one-electron basis set. Usually this set is obtained from a standard DFT calculation and written into the WAVECAR file and can be calculated for instance the following INCAR file:
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 ! small sigma is required to avoid partial occupancies LOPTICS = .TRUE.
Note, that a significant number of empty bands is required for GW calculations, so that it might be better to perform the calculations in two steps: first a standard ground-state calculation with few unoccupied orbitals only,
System = SiC ground-state occupied orbitals ISMEAR = 0 ; SIGMA = 0.05 ! small sigma is required to avoid partial occupancies EDIFF = 1E-8 ! required tight tolerance for ground-state orbitals
and, second, a calculation of a large number of unoccupied orbitals
System = SiC unoccupied orbitals ALGO = Exact ! use exact diagonalization of the Hamiltonian NELM = 1 ! since we are already converged stop after one step NBANDS = 512 ! maybe even larger ISMEAR = 0 ; SIGMA = 0.05 ! small sigma is required to avoid partial occupancies LOPTICS = .TRUE.
Furthermore, note that the flag LOPTICS=.TRUE. is required to write the file WAVEDER, which contains the derivative of the orbitals with respect to k. This derivative is used to construct the head and wings of the dielectric matrix employing k·p perturbation theory and is important to accelerate k-point convergence for insulators and semiconductors.
Warning: For metals, in general, we recommend omitting the LOPTICS tag and removing the WAVEDER file from the directory. |
Optional: Use Hybrid functionals
Optionally, one can start a GW calculation from a hybrid functional, such as HSE. For hybrid functionals, the two step procedure will accordingly involve the following INCAR files. In the first step, converged HSE03 orbitals are determined (see here for a selection of available hybrid functionals):
System = SiC ground-state occupied orbitals ISMEAR = 0 ; SIGMA = 0.05 ALGO = Damped ; TIME = 0.5 ! or ALGO = Conjugate LHFCALC = .TRUE. ; AEXX = 0.25 ; HFSCREEN = 0.3 EDIFF = 1E-6 ! required tight tolerance for ground-state orbitals
Secondly, determine the HSE03 orbitals for unoccupied states:
System = SiC unoccupied orbitals NBANDS = 512 ! maybe even larger ALGO = Exact NELM = 1 ! since we are already converged stop after one step ISMEAR = 0 ; SIGMA = 0.05 LHFCALC = .TRUE. ; AEXX = 0.25 ; HFSCREEN = 0.3 LOPTICS = .TRUE. # for insulators
Second step: GW calculation
The actual GW calculation is done in a second step. Here different GW flavors are possible and are selected with the ALGO tag.
Note that as of VASP.6 the GW ALGO tags have been renamed, see here for VASP.5.X tags.
Single shot quasiparticle energies: G_{0}W_{0}
This is the simplest GW calculation and computationally the most efficient one. A single-shot calculation is often referred to as G_{0}W_{0} and calculates the quasiparticle energies from a single GW iteration by neglecting all off-diagonal matrix elements of the self-energy and employing a Taylor expansion of the self-energy around the DFT energies . The corresponding equation becomes
with the renormalization factor
In VASP, G_{0}W_{0} calculations are selected using an INCAR file such as
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 NELMGW = 1 ! use NELM for VASP.6.2 and older ALGO = EVGW0 ! use "GW0" for VASP.5.X NOMEGA = 50
Mind: Convergence with respect to the number of empty bands NBANDS and with respect to the number of frequencies NOMEGA must be checked carefully. |
To avoid complicated inter-nested tests, we recommend calculating all orbitals that the plane-wave basis set allows to calculate (except for simple tests). For further reading, please consult the section on ENCUTGW.
After a successful G_{0}W_{0} run, VASP will write the quasiparticle energies into the OUTCAR file for a set of NBANDSGW bands for every k-point in the Brillouin zone. Look for lines similar to
QP shifts <psi_nk| G(iteration)W_0 |psi_nk>: iteration 1 for sc-GW calculations column KS-energies equals QP-energies in previous step and V_xc(KS)= KS-energies - (<T + V_ion + V_H > + <T+V_H+V_ion>^1 + <V_x>^1) k-point 1 : 0.0000 0.0000 0.0000 band No. KS-energies QP-energies sigma(KS) V_xc(KS) V^pw_x(r,r') Z occupation Imag(sigma) 1 -7.1627 -8.3040 -14.5626 -12.7276 -21.6682 0.6219 2.0000 1.2037 2 -2.0901 -3.4347 -15.7660 -14.2799 -21.7439 0.9048 2.0000 0.6914 3 -2.0901 -3.4347 -15.7660 -14.2799 -21.7439 0.9048 2.0000 0.6914 4 -2.0901 -3.4347 -15.7660 -14.2799 -21.7439 0.9048 2.0000 0.6914 5 0.4603 -0.4663 -13.7603 -12.5200 -18.1532 0.7471 2.0000 0.2167 6 0.4603 -0.4663 -13.7603 -12.5200 -18.1532 0.7471 2.0000 0.2167
The first column is the band index and the third column denotes the quasiparticle energies . Column two, four, five and seven refer to the DFT energies , diagonal matrix elements of the self-energy , the exchange-correlation potential and the renormalization factor defined above, respectively.
Partially self-consistent calculations: EVGW_{0}
In most cases, the best results (i.e., closest to experiment) are obtained by iterating only via the spectral representation
but keeping and the orbitals fixed to the initial DFT level. This method goes back to Hybertsen and Louie ^{[5]} and can be achieved in two ways.
If the spectral method is not selected (LSPECTRAL=.FALSE., requiring much more compute time), the quasiparticle (QP) shifts are iterated automatically four times, and one finds four sets of QP shifts in the OUTCAR file. The first one corresponds to the G_{0}W_{0} case. The INCAR file is simply:
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 ALGO = EVGW0 ! use "GW0" in VASP.5.X LSPECTRAL =.FALSE.
Tip: In self-consistent GW calculations, convergence with the number of updated bands NBANDSGW must be checked carefully. |
For technical reasons, it is not possible to iterate in this manner if LSPECTRAL=.TRUE. is set in the INCAR file (this is the default). In this case, an iteration number must be supplied in the INCAR file using the NELMGW tag. Usually, three to four iterations are sufficient to obtain accurate QP shifts.
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 ALGO = EVGW0 ! use "GW0" in VASP.5.X NELMGW = 4 ! use NELM in VASP.6.2 and older
The results are found again in the OUTCAR file
QP shifts <psi_nk| G(iteration)W_0 |psi_nk>: iteration 4 k-point 1 : 0.0000 0.0000 0.0000 band No. old QP-enery QP-energies sigma(KS) T+V_ion+V_H V^pw_x(r,r') Z occupation Imag(sigma) 1 -8.6924 -8.7107 -14.2871 5.5647 -21.6681 0.6076 2.0000 1.1648 2 -3.4692 -3.4806 -15.6742 12.1894 -21.7437 0.7304 2.0000 0.6351 3 -3.4692 -3.4806 -15.6742 12.1894 -21.7437 0.7304 2.0000 0.6351 4 -3.4692 -3.4806 -15.6742 12.1894 -21.7437 0.7304 2.0000 0.6351 5 -0.6957 -0.7006 -13.6827 12.9802 -18.1531 0.7264 2.0000 0.2769 6 -0.6957 -0.7006 -13.6827 12.9802 -18.1531 0.7264 2.0000 0.2769 7 -0.6957 -0.7006 -13.6827 12.9802 -18.1531 0.7264 2.0000 0.2769
In contrast to single shot GW calculations, the second column represent now the QP-energies from the previous iteration.
Partially self-consistent quasiparticle calculations: QPGW_{0}
If non diagonal components of the self-energy (in the orbital basis) should be included use ALGO=QPGW0. The following setting can be used:
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 ALGO = QPGW0 ! or "scGW0" for VASP.5.2.11 and older LOPTICS = .TRUE. ; LPEAD = .TRUE. ! ommit this lines for metals NELMGW = 4 ! use NELM for VASP.6.2 and older
In this case, the orbitals are updated as well by constructing a hermitian (energy independent) approximation to the self-energy ^{[3]}. The "static" COHSEX approximation can be selected by setting NOMEGA = 1 ^{[6]}. To improve convergence to the ground-state, the charge density (and the charge density only) is mixed using a Kerker type mixing in VASP.5.3.2 and more recent versions (see IMIX). The mixing parameters AMIX, BMIX, AMIX_MAG, BMIX_MAG, AMIN can be adjusted, if convergence problems are encountered.
We strongly urge the user to monitor convergence by inspecting the lines
charge density residual
in the OUTCAR files.
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=Damped. This method is generally more reliable for metals and materials with strong charge sloshing.
After every iteration, VASP writes the following lines into the OUTCAR file
QP shifts <psi_nk| G(iteration)W_0 |psi_nk>: iteration 1 GWSYM: cpu time 15.8978: real time 15.9528 k-point 1 : 0.0000 0.0000 0.0000 band No. DFT-energies QP-energies QP-e(diag) sigma(DFT) Z occupation 1 -7.1626 -8.4217 -8.3038 -8.9978 0.6219 2.0000 2 -2.0899 -3.4394 -3.4347 -3.5765 0.9047 2.0000 3 -2.0899 -3.4394 -3.4347 -3.5765 0.9047 2.0000 4 -2.0899 -3.4394 -3.4347 -3.5765 0.9047 2.0000 5 0.4604 -0.4787 -0.4663 -0.7800 0.7471 2.0000 6 0.4604 -0.4787 -0.4663 -0.7800 0.7471 2.0000 7 0.4604 -0.4787 -0.4663 -0.7800 0.7471 2.0000 8 5.1013 4.1883 4.2149 3.9518 0.7711 2.0000
For the first iteration, here, the fourth column should be identical to the third column of the G_{0}W_{0} results discussed above. The third column reports the quasiparticle energies obtained from including the off-diagonal matrix elements in the eigenvalue equation.
Caveats
The QPGW0 (or scGW0 in VASP.5.2.11 and older) must be used with great caution, particularly in combination with symmetry. Symmetry is handled in a rather sophisticated manner. Specifically, only the minimal number of required combinations of q and k points is considered. In this case, symmetry must be applied to restore the full star of q. This is done by determining degenerate eigenvalue/eigenvector pairs and restoring their symmetry according to their irreducible representation. Although the procedure is generally relatively reliable, it fails to work properly if the degenerate states do not possess eigenvalues that are sufficiently close due to insufficient convergence in the preceding DFT calculations. That is because states are treated as degenerate if, and only if, their eigenenergies are within 0.01 eV.
For large supercells with low symmetry, we strongly recommend switching off symmetry.
Self-consistent EVGW and QPGW calculations
Self-consistent QPGW calculations are only supported in a QP picture. As for QPGW_{0}, it is possible to update the eigenvalues only (ALGO=EVGW or GW for VASP.5.X), or the eigenvalues and one-electron orbitals (ALGO=QPGW or scGW in VASP.5.2.11 and older). In all cases, a QP picture is maintained, i.e., satellite peaks (shake ups and shake downs) can not be accounted for in the self-consistency cycle. Self-consistent QPGW calculations can be performed by simply repeatedly calling VASP using:
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 ALGO = EVGW ! "GW" in VASP.5.X, eigenvalues only or alternatively ALGO = QPGW ! "scGW" in VASP.5.2.11 and older, eigenvalues and one electron orbitals
For QPGW0 or QPGW, nondiagonal terms in the Hamiltonian are accounted for, e.g. the linearized QP equation is diagonalized, and the one-electron orbitals are updated ^{[3]}. Alternatively (and preferably), the user can specify an electronic iteration counter using NELMGW (NELM in VASP.6.2 and older):
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 NELMGW = 3 ! use NELM in VASP.6.2 and older ALGO = EVGW ! "GW" in VASP.5.X # or ALGO = QPGW ! "scGW" in VASP.5.2.11 and older
In this case, the one-electron energies (=QP energies) are updated 3 times (starting from the DFT eigenvalues) in both G and W. For ALGO=QPGW (or ALGO=scGW in VASP.5.2.11 and older), the one electron energies and one electron orbitals are updated 3 times ^{[3]}. As for ALGO = QPGW0 (or scGW0 in vasp.5.2.11 and older), the "static" COHSEX approximation can be selected by setting NOMEGA=1 ^{[6]}.
To improve convergence to the ground-state, the charge density is mixed using a Kerker type mixing starting with VASP.5.3.2 (see IMIX). 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=Damped. This method is generally more reliable for metals and materials with strong charge sloshing.
Additional information about this method is found here.
Caveats
Fully self-consistent QPGW calculations with an update of the orbitals in and ^{[3]} require significant care and are prone to diverge (QPGW0 calculations are usually less critical). As discussed, above, one can select this mode using:
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 ALGO = QPGW ! or "scGW" in VASP.5.2.11 and older, eigenvalues and one-electron orbitals NELMGW = number of steps ! use NELM for VASP.6.2 and older
However, one caveat applies to this case: when the orbitals are updated, the derivatives of the orbitals with respect to (stored in the WAVEDER file) will become incompatible with the orbitals. This can cause severe problems and convergence to the incorrect solution.
Warning: For metals, in general, we recommend omitting the LOPTICS tag and removing the WAVEDER file from the directory. |
For insulators, VASP (version 5.3.2 or higher) can update the WAVEDER file in each electronic iteration if the finite difference method is used to calculate the first derivative of the orbitals with respect to :
System = SiC NBANDS = 512 ISMEAR = 0 ; SIGMA = 0.05 ALGO = QPGW ! "scGW" in VASP.5.2.11 and older, eigenvalues and one-electron orbitals NELMGW = 10 ! use NELM in VASP.6.2 and older LOPTICS = .TRUE. ; LPEAD = .TRUE.
The combination LOPTICS=.TRUE.; LPEAD=.TRUE. is required since is not available for GW like methods. LPEAD=.TRUE. circumvents this problem by calculating the derivatives of the orbitals using numerical differentiation on the finite k-point grid (this option is presently limited to insulators).
Vertex corrections are presently not documented. This is a feature still under construction, and we recommend collaborating with the Vienna group if you desperately need that feature.
Low scaling GW algorithms
The GW implementations in VASP described in the papers of Shishkin et al.^{[1]} ^{[2]} avoids storage of the Green's function as well as Fourier transformations between time and frequency domain entirely. That is, all calculations are performed solely on the real frequency axis using Kramers-Kronig transformations for convolutions in the equation of and in reciprocal space.
As of VASP.6 a new cubic scaling GW algorithm ^{[7]} (called space-time implementation in the following) can be selected. This approach follows the idea of Rojas et al. ^{[8]} and performs the GW self-consistency cycle on imaginary time and imaginary frequency axes .
Tip: Using the low-scaling GW algorithm also calculates the total energy in the Random Phase approximation (RPA), which is described in a separate article. |
Low scaling, single shot GW calculations: G_{0}W_{0}R
The low-scaling analogue of G_{0}W_{0} is selected with ALGO=G0W0R. In contrast to the single-shot GW calculations on the real-axes, here the self-energy is determined on the imaginary frequency axis. To this end, the overall scaling is reduced by one order of magnitude and is cubic with respect to the system size, because a small value for NOMEGA can be used (usually <20).
This algorithm evaluates:
- Single-shot GW quasiparticle energies (from an analytical continuation of the self-energy to the real axis)^{[7]}
- Natural orbitals from the first order change of the density matrix (i.e. ), see the NATURALO tag for more information ^{[9]}.
Mind: This selection ignores NELMGW. |
Following INCAR file selects the low-scaling GW algorithm:
System = SiC ISMEAR = 0 ; SIGMA = 0.05 LOPTICS = .TRUE. ALGO = G0W0R NOMEGA = 12 ! small number of frequencies necessary
Search the OUTCAR file for the following lines
QP shifts evaluated in KS or natural orbital/ Bruckner basis k-point 1 : 0.0000 0.0000 0.0000 band No. KS-energies sigma(KS) QP-e(linear) Z QP-e(zeros) Z occupation Imag(E_QP) QP_DIFF TAG 1 -7.1627 -8.6732 -8.2451 0.7166 -8.2346 0.7026 2.0000 -1.3101 0.0000 2 2 -2.0901 -3.4155 -3.0350 0.7129 -3.0272 0.7011 2.0000 -0.5582 -0.0000 2 3 -2.0901 -3.4155 -3.0350 0.7129 -3.0272 0.7011 2.0000 -0.5582 0.0000 2 4 -2.0901 -3.4155 -3.0350 0.7129 -3.0272 0.7011 2.0000 -0.5582 -0.0000 2 5 0.4603 -0.8219 -0.4904 0.7414 -0.4814 0.7273 2.0000 -0.1902 0.0000 2 6 0.4603 -0.8219 -0.4904 0.7414 -0.4814 0.7273 2.0000 -0.1902 -0.0000 2
Here column four is obtained by a linearization of the self-energy around the Kohn-Sham energies (second column) and can be compared to the third column of single-shot GW calculations on the real axis. Column six represents another set of QP-energies that is obtained from the roots of the following equation
These roots represent the poles of the Green's function in the spectral representation.
Output description
The meaning of each column is explained briefly in the following.
band No.
the band index of KS orbital at given k-pointKS-energies
eigenenergies corresponding to band indexsigma(KS)
diagonal matrix elements of self-energy evaluated at KS energiesQP-e(linear)
quasiparticle energies obtained from linearizing frequency dependence of diagonal self-energy around KS energiesZ
renormalization factor obtained from five-point stencil for derivative of self-energy w.r.t. frequencyQP-e(zeros)
quasiparticle energies obtained from full frequency dependence of self-energy, i.e. real part of complex pole of Green's functionZ
renormalization factor obtained from central difference for derivative of self-energy w.r.t. frequencyoccupation
occupation number for band at given k-pointImag(E_QP)
imaginary part of complex pole , i.e. measure for inverse lifetime of quasi-particleQP_DIFF
difference of QP energies (of linearized self-energy) obtained from Eq. 77 of Liu et. al.^{[7]} and M. Grumets thesis^{[10]}.
Optional: RPA Forces
Optionally, RPA forces can be calculated by adding following line to the INCAR:
LRPAFORCE = .TRUE.
After the QP-energies, VASP performs a linear-response calculation that is required for the RPA forces.^{[11]} Following data block in the OUTCAR file can be found after a successful run:
POSITION TOTAL RPA FORCE (eV/Angst) ----------------------------------------------------------------------------------- 0.17542 -0.22348 0.17542 -0.292069 7.581315 -0.292069 1.12850 1.31044 1.12850 0.304683 -7.605527 0.304683 ----------------------------------------------------------------------------------- total drift: 0.012614 -0.024212 0.012614 SUGGESTED UPDATED POSCAR (direct coordinates) step ----------------------------------------------------------------------------------- -0.00958461 -0.00958461 0.13485779 0.04179056 0.04179056 0.00283088 0.25787833 0.25787833 0.22191754 -0.04337198 -0.04337198 0.00431513
Warning: Currently RPA forces for metallic systems are not supported. |
Low scaling, partially self-consistent GW calculations: EVGW_{0}R
Mind: available as of vasp 6.4.0 |
The low-scaling analogue of EVGW_{0} is selected with ALGO=EVGW0R. Following INCAR file selects this algorithm:
System = SiC ISMEAR = 0 ; SIGMA = 0.05 LOPTICS = .TRUE. ALGO = EVGW0R NELMGW = 4 ! number of iterations in G NOMEGA = 12 ! small number of frequencies necessary
After each iteration, a similar block of data as for ALGO=G0W0R calculations is written to OUTCAR showing the NBANDSGW updated quasi-particle energies (poles) of the Green's function.
Partially self-consistent GW calculations: GW_{0}R
The space-time implementation allows for true self-consistent GW calculations. That is, the solution of the Dyson equation for the Green's function can be obtained with a modest computational effort. The main procedure of a self-consistent GW calculation consists of four main steps
- Obtain Green's function
- Compute irreducible polarizability
- Determine screened potential
- Calculate GW self-energy
This procedure can be selected with the following INCAR settings
System = SiC ISMEAR = 0 ; SIGMA = 0.05 LOPTICS = .TRUE. ; LPEAD = .TRUE. NELMGW = number of iterations wanted ! NELM in 6.2 and older ALGO = GW0R ! ALGO = scGW0R has the same effect here, that is self-consistency in G, no update in W
The number of self-consistency steps can be set with the NELMGW tag.
Due to efficiency, VASP performs each step in the Hartree-Fock basis. This is the reason why there are two sets of QP-energies found after the first iteration (one for the QP-energies in the KS-basis and one for the QP energies in the HF basis) After the second iteration, only the QP energies obtained in the HF basis are printed, and a similar output as follows is found in the OUTCAR file
QP shifts evaluated in HF basis k-point 1 : 0.0000 0.0000 0.0000 band No. KS-energies sigma(KS) QP-e(linear) Z QP-e(zeros) Z occupation Imag(E_QP) QP_DIFF TAG 1 -7.1626 -8.6510 -8.2275 0.7154 -8.2173 0.7017 2.0000 -1.3177 0.0000 2 2 -2.0899 -3.4157 -3.0348 0.7127 -3.0269 0.7008 2.0000 -0.5614 0.0000 2 3 -2.0899 -3.4157 -3.0348 0.7127 -3.0269 0.7008 2.0000 -0.5614 -0.0000 2 4 -2.0899 -3.4157 -3.0348 0.7127 -3.0269 0.7008 2.0000 -0.5614 0.0000 2 5 0.4604 -0.8170 -0.4857 0.7407 -0.4768 0.7266 2.0000 -0.1945 0.0000 2 6 0.4604 -0.8170 -0.4857 0.7407 -0.4768 0.7266 2.0000 -0.1945 -0.0000 2 7 0.4604 -0.8170 -0.4857 0.7407 -0.4768 0.7266 2.0000 -0.1945 0.0000 2 8 5.1013 4.0069 4.2594 0.7693 4.2645 0.7598 2.0000 -0.0602 0.0000 2
Here the meaning of each column is the same as for the other low-scaling GW algorithms.
Fully self-consistent GW caluclations: GWR
If the screened potential should be updated during the self-consistency circle ^{[12]} the following INCAR file can be used
System = SiC ISMEAR = 0 ; SIGMA = 0.05 LOPTICS = .TRUE. ; LPEAD = .TRUE. NELMGW = number of iterations wanted ! use NELM in VASP.6.2 and older ALGO = GWR ! ALGO = scGWR has the same effect here, that is self-consistency in G and W
The output is similar to partially self-consistent GW calculations, with the difference that KS-energies are replaced by the QP energies from previous iteration.
Caveats
Using this option, similar caveats can be expected as for ALGO=EVGW and QPGW calculations and we recommend to leave out the LOPTICS and LPEAD line for metals.
The cubic scaling space-time GW algorithm requires considerably more memory than the corresponding quartic-scaling implementations, two Green's functions have to be stored in real-space. To reduce the memory overhead, VASP exploits Fast Fourier Transformations (FFT) to avoid storage of the matrices on the (larger) real space grid, on the one hand. The precision of the FFT can be selected with PRECFOCK, where usually the values Fast sufficient.
On the other hand, the code avoids storage of redundant information, i.e., both the Green's function and polarizability matrices are distributed as well as the individual imaginary grid points. The distribution of the imaginary grid points can be set by hand with the NTAUPAR and NOMEGAPAR tags, which splits the imaginary grid points NOMEGA into NTAUPAR time and NOMEGAPAR groups. For this purpose both tags have to be divisors of NOMEGA.
The default values are usually reasonable choices provided the tag MAXMEM is set correctly and we strongly recommend to set MAXMEM instead of NTAUPAR.
Important: As of version 6.2, MAXMEM is estimated automatically (if not set) from the "MemAvailable" entry of the Linux kernel in "/proc/meminfo". |
The required storage for a low-scaling RPA or GW calculation depends mostly on NTAUPAR, the number of MPI groups that share same imaginary time points. A rough estimate for the required bytes is given by
(NGX*NGY*NGZ)*(NGX_S*NGY_S*NGZ_S) / ( NCPU / NTAUPAR ) * 16
where "NCPU" is the number of MPI ranks used for the job,"NGX,NGY,NGZ" denotes the number of FFT grid points for the exact exchange and "NGX_S,NGY_S,NGZ_S" the number of FFT grid points for the supercell. Note, both grids are written to the OUTCAR file after the lines
FFT grid for exact exchange (Hartree Fock) FFT grid for supercell:
The smaller NTAUPAR is set, the less memory per node the job requires to finish successfully.
The approximate memory requirement is calculated in advance and printed to screen and OUTCAR as follows:
min. memory requirement per mpi rank 1234 MB, per node 9872 MB
Related tags and articles
- ALGO for response functions and GW calculations
- LOPTICS, derivative of wavefunction w.r.t.
- LPEAD, derivative of wavefunction with finite differences
- LMAXFOCKAE overlap densities and multipoles
- MAXMEM, memory available to one mpi rank on each node
- NOMEGA, NOMEGAR number of frequency points
- LSPECTRAL, use the spectral method for the polarizability
- LSPECTRALGW, use the spectral method for the self-energy
- OMEGAMAX, OMEGATL and CSHIFT
- ENCUTGW, energy cutoff for response function
- ENCUTGWSOFT, soft cutoff for Coulomb kernel
- ODDONLYGW and EVENONLYGW, reducing the k-grid for the response functions
- LSELFENERGY, the frequency dependent self energy
- LWAVE, self-consistent GW
- NOMEGAPAR, frequency grid parallelization
- NTAUPAR, time grid parallelization
- NATURALO, natural orbitals
- LALL_IN_ONE, all-in-one GW mode
- IALL_IN_ONE, all-in-one GW mode
- NBANDSEXACT, number of KS bands in all-in-one mode
- NBANDS_WAVE, number of bands written to WAVECAR in all-in-one mode
- LSINGLES, singles contribution to correlation energy
References
- ↑ ^{a} ^{b} M. Shishkin and G. Kresse, Phys. Rev. B 74, 035101 (2006).
- ↑ ^{a} ^{b} M. Shishkin and G. Kresse, Phys. Rev. B 75, 235102 (2007).
- ↑ ^{a} ^{b} ^{c} ^{d} ^{e} M. Shishkin, M. Marsman, and G. Kresse, Phys. Rev. Lett. 99, 246403 (2007).
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