Projector-augmented wave

We now discuss the most important theoretical methods developed thus far the augmented plane wave (APW) and the Korringa-Kolm-Rostoker (KKR) methods, as well as the linear methods (linear APW (LAPW), the linear miiflfm-tin orbital [LMTO] and the projector-augmented wave [PAW]) methods. 

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT teclmiques [M]- PAW, however, provides all-electron one-particle wavefiinctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in tenns of a pseudo-wavefiinction (easily expanded in plane waves) tenn that describes mterstitial contributions well, and one-centre corrections expanded in tenns of atom-centred fiinctions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential fonnalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [, ]. PAW is also fonnulated to carry out DFT dynamics, where the forces on nuclei and wavefiinctions are calculated from the PAW wavefiinctions. (Another all-electron DFT molecular dynamics teclmique using a mixed-basis approach is applied in [84].)... 

Kresse, G. and Joubert, D. (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Physical Review B - Condensed Matter, 59, 1758-1775. 

Blochl, P. E., Margl, P, Schwarz, K., 1996, Ab Initio Molecular Dynamics With the Projector Augmented Wave Method in Chemical Applications of Density Functional Theory, Laird, B. B., Ross, R. B., Ziegler, T. (eds.), American Chemical Society, Washington DC. 

G. Kresse and D. Joubert, From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method, Phys. Rev. B 59 (1999), 1758. 

H. M. Petrilli, P. E. Blochl, P. Blaha and K. Schwarz, Electric-field-gradient calculations using the projector augmented wave method. Phys. Rev. B, 1998,57,14690-14697. 

Blochl PE, Forst CJ, Schimpl J, The Projector Augmented Wave Method Ab-initio Molecular Dynamics Simulations with Full Wave Functions, Bull Mater Sci 26, 33 (2003)... 

Blochl PE, Projector augmented-wave method, Phys Rev B, 50 17953 (1994)... 

PAW (projector augmented-wave) is a method designed to have the flexibility of FLAPW methods with the simplicity of pseudopotential methods. In the PAW method, all-electron one electron wave functions, are derived from pseudo-one electron wave functions, P , where n refers to the wth band by means of a linear transformation... 

Most plane wave calculations use ultrasoft pseudopotentials (USPP),15,28 which describe the core electrons of atoms in a mathematically efficient form that greatly reduces the computational cost associated with heavy atoms. An increasing number of calculations used the projector augmented wave (PAW) approach instead.28 In most circumstances where both approaches can be used, the differences between USPP and PAW calculations are minor. Some exceptions to this observation include transition metals with large magnetic moments (e.g., Fe) and alkali metals.28... 

The partitioning of the density introduced in (14) is borrowed from the projector augmented-wave approach [5]. Its special form separates the smooth contributions n, characteristic of the interatomic regions, from the quickly varying terms close to the atoms n.4. ua is a smooth local term which compensates for the overlap of the soft and the hard densities in the atomic region, so that the integrals can still be expanded over all space. In our current implementation the densities h r),nA r), and h-A(r) are expanded in plane-waves and products of primitive Gaussians centered on atom A, respectively... 

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