The Armiento and Mattsson 2005 (AM05) functional

Publications

• Functional designed to include surface effects in
  self-consistent density functional theory
  • Rickard Armiento and Ann E. Mattsson
  • Physical Review B 72, 085108 (2005).
  • Link to PRB (subscription needed)

• Implementing and testing the AM05 spin density functional
  • Ann E. Mattsson and Rickard Armiento
  • Physical Review B 79, 155101 (2009)
  • Link to PRB (subscription needed)

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 article above describing the implementation of the AM05 spin density functional not only gives the necessary formulas for implementing AM05 but also other functionals of GGA type (using the density and the magnitude of the gradient of the density).
• This easily adaptable gzipped AM05 Fortran 77 subroutine can be used as a starting point.
• This gzipped AM05 energy Fortran 77 subroutine only gives out the energy, which is enough for some types of codes.
• If you do not need spin-polarized routines you might want to use this gzipped non-spin polarized AM05 Fortran 77 subroutine as a starting point instead.
• Important formulas and background information for implementing non-spin AM05 into DFT codes can be found in this implementation guide in pdf format.
• The required subroutine for the Lambert W function is available not only in the subroutines provided on this web page but also as supplemental material to the spin AM05 article.

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).

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.

Summary

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 (Ångström)	Bulk Modulus (GPa)
	ME	MAE	ME	MAE
AM05	0.001	0.025	-4.5	8.1
PBE0	0.007	0.022	-0.1	7.9
HSE06	0.010	0.023	-1.6	8.6
PBE (JCP)	0.039	0.045	-12.3	12.4
PBE	0.039	0.046	-14.1	14.2
LDA	-0.070	0.070	7.5	10.7
BLYP	0.093	0.100	-26.0	26.1

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