FROM RESEARCH TO INDUSTRY www.cea.fr « PROJECTOR AUGMENTED-WAVE » METHOD: GENERATION OF ATOMIC DATASETS François Jollet, Marc Torrent CEA, DAM, DIF. Arpajon, France International school Lattice Dynamics of Solids with ABINIT May 12-17, 2014 - Lyon, France
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FROM RESEARCH T O INDUST RY
www.cea.fr
« PROJECTOR AUGMENTED-WAVE »
METHOD: GENERATION OF ATOMIC
DATASETS
François Jollet, Marc Torrent
CEA, DAM, DIF. Arpajon, France
International school
Lattice Dynamics of Solids with ABINIT
May 12-17, 2014 - Lyon, France
PAW atomic datasets | May 12, 2014 | PAGE 2
OUTLINE
The PAW data set
Generation of PAW atomic data
Validation of PAW atomic data
THE PAW DATASET
PAW atomic datasets | May 12, 2014 | PAGE 4
L
L
ijeffjcxcZcHi
jcxcZcHi
L
L
ijeffij
dQvnnnvnnnv
nnvnnv
dQvD
rrr
rrr
)(ˆ)(~~~ˆ~~ˆ~
2
~
2
)()(~
111
11
ATOMIC DATA: WHAT DO WE NEED?
Wavefunction: n
i
niiinn p ψ~ψ~~~ψ~ψ
Hamiltonian:
L
L
ijeff
xc
ij
kl
ijklklijij dQvDEDD rrr )(ˆ)(~0
nnn SH ~~~
= + -
Inside circles: atomic data needed
R
j
R
j
R
i
R
j
R
i
ijR
R
i ppS ~~~~1,
PAW atomic datasets | May 12, 2014 | PAGE 5
Constraints:
• Precision of the calculation
• Speed of convergence (number of plane waves)
Have to generate an adapted basis
In order to perform a PAW calculation, following atomic data are needed:
0,~,,~,~,~
, ijccZcH
R
i
R
i
R
i DnnnVp
For each atomic specie
All electron partial waves
Pseudized soft partial waves Hartree potential due to nuclueus
and core electrons (local pot.)
Core density Pseudized
core density Projectors (dual of ) R
i~
R
i~ Frozen part
of Dij term
Definitions of radial grids are also needed
THE PAW ATOMIC DATASETS
PAW atomic datasets | May 12, 2014 | PAGE 6
THE « PAW DATASETS »
Generation process
1- Solve "exactly" the atomic problem (for the given LDA/GGA functional)
2- Transform some quantities into smooth ones ("pseudization")
3- Build the partial wave basis and projectors
Independent of ABINIT (initiated by N. Holzwarth from Wake Forest University)
Automatically download and installed by ABINIT build system
http://pwpaw.wfu.edu
GENERATION OF PAW ATOMIC DATA
PAW atomic datasets | May 12, 2014 | PAGE 8
Choose an electronic valence configuration O : 1s22s22p4
Solve atomic Schrödinger equation Get
Choose an energy set an radii
and invert the Schrödinger equation Get
BUILDING PAW ATOMIC DATA
i)(),( rVrn aec
)(ri
Step 1 All electrons atomic calculation (with ATOMPAW for instance)
iiiAE rVT )(
ir
Step 2 Pseudo functions
Apply a soft pseudization scheme
locaeloc
corecc
iii
rVV
rnn
r
at joinand
at joinand
at joinand~
~
PAW atomic datasets | May 12, 2014 | PAGE 9
BUILDING PAW ATOMIC DATA
ZcH nv ~
)(~ rpi
Step 3 Projectors
Step 5 Additional data
Apply a scheme (Vanderbilt or Bloechl) to calculate (optimized)
Step 4 Local potential
Compute from Vloc
rdQnvnvnvDlm R
lm
ijZcHjZcHijZcHiij
ˆ~~~
2
~
2
0
PAW atomic datasets | May 12, 2014 | PAGE 10
The logarithmic derivatives of wavefunctions must be equal to the ones of
a reference calculation (good diffusion properties)
The energies of excited configurations must be equal to the all electron
ones
Transferability
VALIDATION AT THE ATOMIC LEVEL
R
l
R
lllll drrrdr
d
d
drrrrV
0
22 ),(),(ln),(),(),()(
The PAW calculation must give the same physical
results as a reference all electrons calculation
AE log derivatives and "base 2" log derivatives are superimposed
PAW atomic datasets | May 12, 2014 | PAGE 11
Radius of augmentation regions (spheres).
Spheres are in principle not allowed to overlap
In practice a little overlap is allowed
Number of partial waves per atom
Pseudization scheme
Size of radial grids
Softness of Vloc
Good atomic data are always a compromise between accuracy and
efficiency
ATOMIC DATA EFFICIENCY
The plane wave basis must be as small as possible
PAW atomic datasets | May 12, 2014 | PAGE 12
THE PAW ATOMIC DATASETS
Approximations can be controlled
Frozen-core approximation: adding more semicore states
Size of PW basis: choosing the radius of spheres, the pseudization scheme
Size of partial waves basis: adding more basis elements
Efficiency can be controlled
Plane wave basis:
Adjusting the radius of spheres, choosing a « soft » pseudization scheme
Partial waves basis:
Reducing the number of basis elements by choosing them judiciously