Meta-GGA functionals and pseudopotentials in ONETEP

Author:

Joseph C. A. Prentice (with some functionality by James C. Womack

Date:

July 2026

Since v 4.5.3.63, ONETEP has had the option to use a meta-GGA (mGGA) exchange-correlation functional. mGGAs are the third rung of Jacob’s ladder of XC functionals, and are usually dependent on the density, the gradient of the density, and the kinetic energy density (the second derivative of the Kohn-Sham orbitals). The intention is that such functionals will give greater accuracy than GGAs, for a very modest increase in cost.

ONETEP’s implementation makes use of the functional derivative of orbitals (FDO) approach, which allows linear-scaling behaviour to be maintained. [Womack2016]

Available functionals and embedding

Before v 8.1.23, three mGGAs were available: the local-tau approximation (LTA) [Ernzerhof1999], B97M-V [Mardirossian2015], and PKZB [Perdew1999].

From v 8.1.23, the MS2 [Sun2013] and rSCAN [Bartok2019] mGGAs are also available. The SCAN family of functionals [Sun2015] (of which rSCAN is a member) have been shown to be particularly powerful for improving a variety of different properties.

From v 8.1.23, mGGAs have also become compatible with EMFT.

Pseudopotentials

To get the full benefit of mGGAs, it is necessary to use mGGA-specific pseudopotentials. These pseudopotentials contain not only the standard core density and local potential, but also the core kinetic energy density (\(\tau\)) and local \(\tau\)-dependent potential \(V_\tau\) (the functional derivative of the energy with respect to \(\tau\)). Using LDA or GGA pseudopotentials is perfectly possible, but they will miss these important corrections to the KE density and functional derivative of the energy with respect to the KE density, and will give worse results. [Bartok2019-2]

From v 8.1.23, ONETEP has the functionality to deal with these mGGA-specific pseudopotentials and the new quantities they introduce, for pseudopotentials in the .usp format. Unfortunately, there is not currently an agreed format for these new quantities to be provided in. In the absence of an agreed format, ONETEP reads in these quantities from a separate file: if the .usp file is called pspot_name.usp, this additional file should be called pspot_name_ke_dens.dat. The core KE density and \(V_\tau\) are provided in exactly the same format as the core density and \(V_{loc}\) in the .usp file.

KE density initialisation

At the beginning of a mGGA calculation, we need to initialise the KE density from the initial density. Assuming your calculation is well-converged, how you do this should make no difference to your final result, but might affect how long it takes to achieve convergence.

The options for initialisation are:

  1. Initialise to zero (GGA)

  2. The uniform electron gas expression \(\tau = \frac{3}{10} (3\pi^2)^{\frac{2}{3}} \rho^{\frac{5}{3}}\) (UNIFORM) [Sun2015]

  3. The von Weizsacker expression \(\tau = \frac{1}{8} \frac{|\nabla \rho|^2}{\rho}\) (WEIZSACKER) [Acharya1980]

The default is initialising to zero, although the uniform electron gas expression has also been found to work well.

Keywords

  • xc_functional [basic, string]: There are five mGGA options here:

    LTA, PKZB, B97M-V, MS2, and RSCAN.

  • active_xc_functional [basic, string]: See EMFT documentation for

    explanation of this keyword. It can take the same mGGA options as xc_functional.

  • use_core_ke_density [basic, logical, default = F]: Toggles

    whether ONETEP will try to read the core KE density and \(V_\tau\) from a file, as described above

  • ke_density_init [advanced, logical, default = GGA]: Decides

    how KE density is initialised. Options are GGA, UNIFORM, and WEIZSACKER.

[Ernzerhof1999] M. Ernzerhof and G. E. Scuseria, J. Chem. Phys. 111, 911 (1999).

[Mardirossian2015] N. Mardirossian and M. Head-Gordon, J. Chem. Phys. 142, 074111 (2015).

[Perdew1999] J. P. Perdew, S. Kurth, A. Zupan, and P. Blaha, Phys. Rev. Lett. 82, 2544 (1999).

[Sun2013] J. Sun, R. Haunschild, B. Xiao, I. W. Bulik, G. E. Scuseria, and J. P. Perdew, J. Chem. Phys. 138, 044113 (2013)

[Bartok2019] A. P. Bartok and J. R. Yates, J. Chem. Phys. 150, 161101 (2019).

[Sun2015] J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015).

[Bartok2019-2] A. P. Bartok and J. R. Yates, Phys. Rev. B 99, 235105 (2019).

[Acharya1980] P. K. Acharya, L. J. Bartolotti, S. B. Sears, and R. G. Parr, PNAS 77 6978 (1980).