LMAXFOCKAE

LMAXFOCKAE = [integer] 

Default: LMAXFOCKAE	= -1	DFT, Hartree-Fock
	= 4	post-DFT methods

Description: Sets the maximum angular momentum quantum number [math]\displaystyle{ L }[/math] up to which the all-electron charge density is restored on the plane-wave grid by shape restoration.

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Shape restoration adds radial functions with vanishing multipole moment to the PAW compensation charge, so that the shape of the all-electron density inside the augmentation spheres — and not only its moments — is reproduced on the plane-wave grid. The related tag LMAXFOCK controls the corresponding truncation for the ordinary compensation charge in Hartree-Fock-type routines.

Mind: Shape restoration applies to the Fock exchange and to many-body perturbation theory, i.e., GW, RPA and MP2. The default for DFT and Hartree-Fock, LMAXFOCKAE = -1, restores only the moments of the all-electron charge density.

Effective value

The requested value is not always the one used. For each species the effective maximum is the smallest of LMAXFOCK, [math]\displaystyle{ 2\,l_{\mathrm{max}} }[/math], and LMAXFOCKAE. Here, [math]\displaystyle{ l_{\mathrm{max}} }[/math] is the largest angular momentum quantum number among the projectors of that species' POTCAR dataset. Raising LMAXFOCKAE beyond this bound has no effect. Two consequences are worth keeping in mind:

• For a dataset with only s and p projectors, [math]\displaystyle{ 2\,l_{\mathrm{max}}=2 }[/math] and the effective maximum never exceeds 2, whatever is requested.
• For a dataset with f projectors, [math]\displaystyle{ 2\,l_{\mathrm{max}}=6 }[/math], so the default LMAXFOCK = 4 becomes the binding constraint. Requesting LMAXFOCKAE = 6 therefore requires raising LMAXFOCK as well; otherwise the effective maximum stays at 4.

The bound is applied per species, so in a cell with several species there is no single effective value for the whole calculation: each species is capped against its own dataset.

To check what VASP read from the INCAR file, look in the Exchange correlation treatment block near the top of the OUTCAR file:

grep -e LMAXFOCKAE -e NMAXFOCKAE OUTCAR

LMAXFOCKAE=   4    L truncation for all-electron charge restoration on plane wave grid
NMAXFOCKAE=   1    number of basis functions for all-electron charge restoration

The two lines do not mean the same thing. The echoed NMAXFOCKAE is the value in use, because out-of-range input is clamped while the INCAR file is read: a request of 5 appears here as 2. The echoed LMAXFOCKAE, by contrast, is the requested value, reported before the per-species cap is applied, so it can be larger than the value actually used. The capped value itself is never written to the OUTCAR file.

What is reported per species is the augmentation setup, further down the same file under Radii for the augmentation spheres in the non-local exchange. For a cell with two species:

grep -e 'augmentation radius' -e 'error exchange integrals' OUTCAR

for species   1 augmentation radius   1.277 (default was   1.277)
error exchange integrals (PW-AE in eV) (mean, max) 0.437 2.117 density error[0,qmax] 0.0233
for species   2 augmentation radius   1.062 (default was   1.062)
error exchange integrals (PW-AE in eV) (mean, max) 0.529 4.955 density error[0,qmax] 0.0275

The error exchange integrals line is written only while shape restoration is active, one line per species, and gives the mean and maximum difference between the plane-wave and the all-electron exchange integrals for that species together with the corresponding density error. Its presence for every species is therefore the practical confirmation that shape restoration was set up throughout, and the numbers show how well it succeeded for each dataset. When LMAXFOCKAE = -1 is set, the line is absent.

Recommendations

Choose LMAXFOCKAE according to the elements in the calculation:

• s and p elements: LMAXFOCKAE = 2
• d elements: LMAXFOCKAE = 4, since a d electron creates charge densities with [math]\displaystyle{ L }[/math] up to 4
• f elements: LMAXFOCKAE = 6 may be required; test for each case, and raise LMAXFOCK accordingly, as described in § Effective value

Setting LMAXFOCKAE = 4 or larger forces an accurate treatment of the charge augmentation on the plane-wave grid. This can be selected in Hartree-Fock-type calculations as well, but it introduces additional noise. To suppress that noise in the correlation energies, set LMAXFOCKAE = -1.

For DFT calculations the exact one-center terms are implemented, so shape restoration is not required and does not change the results. For post-DFT calculations the one-center terms are presently not implemented, and Refs. and report a substantial gain in accuracy from shape restoration there.

Mind: LMAXFOCKAE and NMAXFOCKAE are strongly coupled, and absolute correlation energies depend on both. Use consistent settings for both tags whenever energy differences are compared, and check both echoed values in the OUTCAR file.

Related tags and articles

NMAXFOCKAE, LMAXFOCK, QMAXFOCKAE, LFOCKAEDFT, LFOCKSTD, Projector-augmented-wave formalism

Workflows that use this tag