METAGGA

METAGGA = SCAN | RTPSS | MBJ | LIBXC | ... 

Default: The functional specified by LEXCH in the POTCAR if also GGA is not specified.

Description: Selects a meta-GGA functional.

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Mind: If you select a meta-GGA functional, make sure that you use POTCAR files that are suited for meta-GGA functionals. However, note that this requirement does not concern the deorbitalized meta-GGAs, i.e. those that do not depend on the kinetic-energy density, like SCANL. Depending on the meta-GGA that is chosen, it may be recommended to use a PAW potential that is more accurate than the standard/recommended one. This is particularly the case with functionals (e.g., MBJ or the Minnesota functionals) that are very different from the standard ones like PBE or SCAN. The reason is that for such special functionals, using a PAW potential that includes more states in the valence or that is harder may be required to obtain results that are closer to the results that would be obtained with an all-electron code. Thus, it may be a good idea to do test calculations with different PAW potentials. It is strongly recommended to set LASPH=.TRUE. to account for aspherical contributions to the PAW one-centre terms. Since VASP.6.4.0 it is possible to use hybrid functionals that mix meta-GGA and Hartree-Fock exchange (AEXX). Furthermore, two new tags, AMGGAX and AMGGAC, were created.

Available functionals

• METAGGA=LIBXC

The LIBXC tag allows to use a meta-GGA functional from the library of exchange-correlation functionals Libxc. Along with METAGGA=LIBXC, it is also necessary to specify the tags LIBXC1 and LIBXC2 that specify the particular functional. Note that it is necessary to have Libxc >= 5.2.0 installed and VASP.6.3.0 or higher compiled with precompiler options.

• METAGGA=TPSS, RTPSS, or M06L

The implementation of the TPSS and RTPSS (revTPSS) self-consistent meta-generalized gradient approximation within the projector-augmented-wave method in VASP is discussed by Sun et al.. For details on the M06-L functional, refer to the paper by Zhao and Truhlar.

• METAGGA=MS0, MS1, or MS2

The MS (where MS stands for "made simple") functionals are presented in detail in references and . These functionals are believed to improve the description of noncovalent interactions over PBE, TPSS and revTPSS but not over M06L. The MS functionals are available as of VASP version ≥ 5.4.1.

• METAGGA=SCAN

The SCAN (Strongly constrained and appropriately normed) functional is a semilocal density functional that fulfills all known constraints that the exact density functional must fulfill. There are indications that this functional is superior to most gradient corrected functionals . This functional is only available as of VASP version ≥ 5.4.3.

• METAGGA=RSCAN

The rSCAN (regularized SCAN) functional , introduces regularizations that improve the numerical sensitivity and convergence behavior. These regularizations break several of the exact constraints that the parent SCAN functional was designed to satisfy. However, testing has indicated that the accuracy of rSCAN can be inferior to SCAN in some cases . This functional is available as of VASP version ≥ 6.2.0.

• METAGGA=R2SCAN

The r$^2$SCAN (regularized-restored SCAN) functional modifies the regularizations introduced in rSCAN to enforce adherence to the exact constraints obeyed by SCAN. It fulfills all known constraints. However, it only recovers the slowly varying density-gradient expansion for exchange to second order, while SCAN recovers the expansion to 4th order. Testing indicates that r$^2$SCAN at least matches the accuracy of the parent SCAN functional but with significantly improved numerical efficiency and accuracy under low-cost computational settings. This functional is available as of VASP version ≥ 6.2.0, or in version 5.4.4 by patch 4.

• METAGGA=SREGTM1, SREGTM2, or SREGTM3

The functionals v1-sregTM, v2-sregTM, and v3-sregTM from Francisco et al.

• METAGGA=SCANL, RSCANL, or R2SCANL

The functionals SCAN-L, rSCAN-L, and r$^2$SCAN-L are deorbitalized versions of SCAN, rSCAN, and r$^2$SCAN, respectively. They do not depend on the kinetic-energy density $\tau$, but on the Laplacian of the density $\nabla^{2}n$, instead.

• METAGGA=OFR2

The OFR2 functional depends on the Laplacian of the density $\nabla^{2}n$, but not on the kinetic-energy density $\tau$.

• METAGGA=SREGTM2L

The functional v2-sregTM-L from Francisco et al., which depends on the Laplacian of the density $\nabla^{2}n$, but not on the kinetic-energy density $\tau$.

• METAGGA=MBJ

The modified Becke-Johnson (MBJ) potential yields band gaps with an accuracy similar to hybrid functionals or GW methods, but is computationally less expensive. The exchange part of the MBJ potential (that is combined with the LDA correlation potential, $v_{xc}^{\rm MBJ}=v_{x}^{\rm MBJ}+v_{c}^{\rm LDA}$) consists of two terms whose relative weights are determined by a system-dependent constant $c$:

$v_{x}^{\rm MBJ}(\mathbf{r}) = cv_{x}^{\rm BR}(\mathbf{r}) + (3c-2)\frac{1}{\pi}\sqrt{\frac{5}{6}}\sqrt{\frac{\tau(\mathbf{r})}{n(\mathbf{r})}}$

where $v_{x}^{\rm BR}$ is the Becke-Roussel (BR) potential that mimics the Coulomb potential created by the exchange hole and depends on $n$, $\nabla n$, $\nabla^{2}n$ and $\tau$.

The system-dependent $c$ is a function of the average of $|\nabla n|/n$ in the unit cell (of volume $V_{\mathrm{cell}}$):

$c=\alpha+\beta \left(\frac{1}{V_{\mathrm{cell}}}\int_{\mathrm{cell}}\frac{|\nabla n(\mathbf{r}')|}{n(\mathbf{r}')}d{\mathbf{r}'}\right)^{e}$

where $\alpha$, $\beta$, and $e$ are free parameters that can be set by means of the CMBJA, CMBJB, and CMBJE tags, respectively. The default values are $\alpha=-0.012$, $\beta=1.023$ bohr$^{1/2}$, and $e=1/2$. In Ref. , the alternative values $\alpha=0.488$, $\beta=0.5$ bohr, and $e=1$ were proposed.

Mind: The MBJ functional is a potential-only functional, i.e., there is no corresponding MBJ exchange-correlation energy, instead $E_{xc}$ is taken from LDA. This means that MBJ calculations can never be self-consistent with respect to the total energy, and thus we cannot compute Hellmann-Feynman forces (i.e., no ionic relaxation, etc.). Actually, MBJ calculations aim solely at a description of the electronic properties, primarily band gaps. MBJ calculations converge very slowly, so the number of maximum electronic steps (NELM) should be set higher than usual. In the presence of an extended vacuum region (e.g., surfaces) or an interface, the average of $|\nabla n|/n$ has no meaning. Therefore, MBJ calculations should be done with a fixed value of $c$, which can be done with the CMBJ tag.

• METAGGA=LMBJ

The local MBJ (LMBJ) potential is a variant of the MBJ potential that was modified such that it does not suffer from the problems related to the presence of vacuum or an interface mentioned above for MBJ. The LMBJ potential has the same analytical form as the MBJ potential:

$v_{x}^{\rm LMBJ}(\mathbf{r}) = c(\mathbf{r})v_{x}^{\rm BR}(\mathbf{r}) + (3c(\mathbf{r})-2)\frac{1}{\pi}\sqrt{\frac{5}{6}}\sqrt{\frac{\tau(\mathbf{r})}{n(\mathbf{r})}}$

with the difference that $c$ is now a position-dependent function:

$c(\mathbf{r})=\alpha+\beta(\tilde{g}(\mathbf{r}))^{e}$

where

$\tilde{g}(\mathbf{r})=\frac{1}{\left(2\pi\sigma^{2}\right)^{3/2}}\int g(\mathbf{r}')e^{-\frac{\left\vert\mathbf{r}-\mathbf{r}'\right\vert^2}{2\sigma^2}}d{\mathbf{r}'}$

with

$g(\mathbf{r})=\frac{1-\alpha}{\beta}\left(1-\mathrm{erf}\left(\frac{n(\mathbf{r})}{n_{\mathrm{th}}}\right)\right)+\frac{\left\vert\nabla n\right\vert}{n}\mathrm{erf}\left(\frac{n(\mathbf{r})}{n_{\mathrm{th}}}\right)$

The default values of the parameters in LMBJ are (see erratum of Ref. ) $\alpha=0.488$, $\beta=0.5$ bohr, $e=1$, $\sigma=2$ $\AA$ ($=3.78$ bohr), and $n_{\mathrm{th}}=6.96\times10^{-4}$ e/bohr$^{3}$. $\sigma$ is the smearing parameter that determines the size of the region over which the average of $g$ is calculated, and $n_{\mathrm{th}}$ is the threshold density, which corresponds to the Wigner–Seitz radius $r_{s}^{\mathrm{th}}=((4/3)\pi n_{\mathrm{th}})^{-1/3}=7$ bohr. $\alpha$, $\beta$, $e$, $\sigma$, and $r_{s}^{\mathrm{th}}$ can be set by means of the CMBJA, CMBJB, CMBJE, SMBJ, and RSMBJ tags, respectively.

The first two points mentioned above for the MBJ potential also apply for the LMBJ potential.

POTCAR files: required information

Calculations with a meta-GGA that depends on the kinetic-energy density require POTCAR files that include information on the kinetic-energy density of the core electrons. Almost all recent POTCAR files do fulfill this requirement, but there are some notable exceptions like O_GW. To check whether a particular POTCAR contains this information, type:

grep kinetic POTCAR

This should yield at least the following lines (for each element on the file):

kinetic energy-density
mkinetic energy-density pseudized

and for PAW datasets with partial core corrections:

kinetic energy density (partial)

Mind: For POTCAR files without core electrons (H, He, Li_sv, Be_sv, and _GW variants thereof) the grep command given above will not return the line about pseudized kinetic energy-density, since all electrons are considered as valence. These potentials can nevertheless be used for all meta-GGA functionals.

Aspherical contributions related to one-center terms

LASPH =.TRUE. should be selected if a meta-GGA functional is selected. If LASPH =.FALSE., the one-center contributions are only calculated for a spherically averaged density and kinetic-energy density. This means that the one-center contributions to the Kohn-Sham potential are also spherical. Since the PAW method describes the entire space using plane waves, errors are often small even if the non-spherical contributions to the Kohn-Sham potential are neglected inside the PAW spheres (additive augmentation, as opposed to the APW or FLAPW method where the plane wave contribution only describes the interstitial region between the atoms). Anyhow, if the density is strongly non-spherical around some atoms in your structure, LASPH =.TRUE. must be selected. Non-spherical terms are particularly encountered in d- and f-elements, dimers, molecules, and solids with strong directional bonds.

Convergence issues

If convergence problems are encountered, it is recommended to preconverge the calculations using the PBE functional and start the calculation from the WAVECAR file corresponding to the PBE ground state. Furthermore, ALGO = A (conjugate gradient algorithm for orbitals) is often more stable than charge density mixing, in particular if the system contains vacuum regions.

Related tags and articles

LIBXC1, LIBXC2, GGA, CMBJ, CMBJA, CMBJB, CMBJE, SMBJ, RSMBJ, LASPH, LMAXTAU, LMIXTAU, LASPH, AMGGAX, AMGGAC, Band-structure calculation using meta-GGA functionals

Examples that use this tag

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