The Armiento and Mattsson 2005 (AM05) functional


  • Functional designed to include surface effects in
    self-consistent density functional theory

Implementing AM05

AM05 can easily be implemented into any code where a generalized gradient approximation functional (GGA) is already implemented. We here post information to facilitate implementations. Please do not hesitate to contact us if you need more information.

The recently published PBEsol functional by Perdew et. al. gives very similar results as AM05 for solids. Since this fact contradicts the PBEsol article’s claim that the proper gradient expansion of exchange is an important constraint for good performance of a functional for solids, we have authored and published a Comment in PRL. Here is a more extensive list of solids that we and others have compared PBEsol and AM05 results for. A Reply by the authors is also published.

A study showing that AM05 performs as well as the hybrids PBE0 and HSE06, and far better than LDA and PBE, for solids, is published in

  • The AM05 density functional applied to solids
    • Ann E. Mattsson, Rickard Armiento, Joachim Paier, Georg Kresse, John M. Wills, and Thomas R. Mattsson
    • Journal of Chemical Physics128, 084714 (2008).
    • Link to JCP (Free Access)

A summary of these results follow:

*Broken Image*

We have assessed the performance of AM05 for the selection of 20 solids
used in Paier et al JCP 124,154709 (2006), (JCP).

Image of Walat
Lattice constants (Ångström)
Image of WB0
Bulk Modulus (GPa):

We have used the same PAW core potentials in our VASP calculations as in the JCP VASP calculations. How good the agreement is can be directly seen in how well our data compare to the JCP VASP PBE data (Table IV). The differences are minute and stem mainly from different choices in points for the fits to the Murnaghan Equation of State.

We should, however, note that different settings within a code, different pseudopotentials, different codes, different choices of equation of state for determining lattice constants and bulk modulus, and different choices of points to use, can result in a 0.02 Ångström difference in lattice constant and 10 % difference in bulk modulus, even when using the same functional. There are also uncertainties in the experimental values, in particular for bulk modulus. A functional performing like AM05 in the above tables could thus be consider, on average, to yield the experimental values for solids, within numerical errorbars. In the JCP article, and its erratum, the hybrids HSE06 and PBE0 are assessed, and they both have similar performance as AM05.


ME = mean error, MAE = mean absolute error. The PBE (JCP), PBE0, and HSE06 values in this table are from JCP and its erratum.

Lattice constants
Bulk Modulus
AM05 0.0010.025  -4.5  8.1
PBE0 0.0070.022  -0.1  7.9
HSE06 0.0100.023  -1.6  8.6
PBE (JCP) 0.0390.045-12.312.4
PBE 0.0390.046-14.114.2
LDA-0.0700.070   7.510.7
BLYP 0.0930.100-26.026.1

AM05 is performing similarly to the hybrids HSE06 and PBE0 for solids. AM05 calculations are, however, much faster than hybrid calculations.