Comments on Generating and Testing PAW Datasets * N. A. …Collaborators in France: Marc Torrent, François Jollet, Yann Pouillon Collaborators in USA: Xiao Xu (WFU Ph. D. 2012, current

4/16/2013 Abinit Workshop 2013 1

Comments on Generating and TestingPAW Datasets*

N. A. W. HolzwarthDepartment of Physics, Wake Forest University,

Winston-Salem, NC, 27109 USA

Collaborators in France: Marc Torrent, François Jollet, Yann Pouillon

Collaborators in USA: Xiao Xu (WFU Ph. D. 2012, current at Matlab), Nicholas Lepley and Qi Li (WFU graduate students), James Dreweryand Cameron Kates (WFU undergraduate students), Alan Wright (Sandia National Laboratory), Alan Tackett, Greg Walker, Rachael Hansel, Ryan Hatcher (Vanderbilt University)

*Supported by NSF Grant DMR-1105485.


Discussion pointsReview of basic content of PAW datasets for various codes

– abinit, quantum espresso, socorro, (pwpaw), GPAW??atompaw 3.0.1.9 4.0.0.0Modular programing structureMore robust atomic solver Some new options for pseudo functionsOption for systematic exploration of pseudo

parametersHartree-Fock and hybrid functionals Integration with features developed by Marc Torrent,

François Jollet, etc


Basic content of PAW datasetsBasic principles of “Projector Augmented Wave” method

(P. Blöchl, Phys. Rev. B 50,17953 (1994))Provides mapping between full (“all-electron”) wavefunctions and pseudo-wavefunctions ss

~

saiia

aai

aaiss p ~~~

,RrRr

full basis function

atom-centered functions:

pseudo basis function

projectorfunction


PAW evaluations – separated into extended “pseudo” and atom-centered contributions

compensation chargelocal pseudopotential

rVr

loca

a

~̂

core electron information


http://pwpaw.wfu.edu


http://pwpaw.wfu.edu

Past students contributing to this effort: John Tumbleston, Nick Dellaripa, David Harris, Xiao Xu, Nicholas Lepley, Sina Zolghadr


How hard could it be to generate efficient and accurate PAW datasets for the entire periodic table??

Unfortunately, I have not yet found the secret recipe…

With the help of two undergraduate students – James Drewer and Cameron Kates – we hope to update the PAW datasets on the http://pwpaw.wfu.edu web page including output for use in abinit, quantum espresso, and GPAW??


Example functions for Cl

r (bohr)

rf ai

ai

~

aip

3s


0 1 2

Example functions for Cl

3s

e s

3p

e p e’ d

e d


Quality measurements for datasets Logderivatives Binding energy curves for representative

solids Plane wave convergence properties


Logderivatives

cc rPAW

E

PAWEPAW

rAE

E

AEEAE

c

drdELdrdEL

rE

/)(/)(

:nctionsPAW wavefutedreconstrucand(AE)electron allcompareradiusaat ;energiesofrangefor equation r Schrodinge thesolve,each For

E

L0for

)(and)(

ELELPAWAE

Cl


Complete logderivatives for Cl

0

3

1

2


Another example of logderivatives – for Sn

1 2

E E

L


Binding energy curves

r (bohr)

E (R

y)

NaCl

PAW

LAPW


Another example of binding energy curves -- ZnO

ZnO

r (bohr)

E (R

y)

LAPW

PAW

Contol module


Some ideas

Modular program structure (from Xiao Xu)

Goal – make it easier to modify the code to implement new ideas and capabilities

Pseudo module Output resultsAll-electron generator

LDA.GGA

Hartree-Fock

LDA.GGA

Hartree-Fock abinit

quanutumespresso


Some ideas -- continued

More robust all-electron bound state solver

Traditional solver (from Hartree’s text book)

inward integrationoutward

integration

Slope discontinuity energy update

r

r f(r

)



More robust all-electron bound state solver – continuedHartree’s method works well for reasonable good guesses of the atomic bound state energies enl , but occasionally convergence is difficult.

r

.functionsfinalget tomethodHartreerun toneed,determinedareOnceation.diagonaliziterativeby determinedaresEigenvalueNumerov).as(such methoddifferencefiniteby thedeterminedareSandMboth where

generally moreor :problemeigenvaluematrix 11aas

0aluesboundary vand)(tion discretizagrid Use:ideaBasic

rf

SfMffMfNN

ffrff

nlnl

nl

nlnl

nl

nlnl

nl

nli

nlii

nlnli

e

ee

e

)( inlnl

i rff



Some new options for pseudo functions – “MODRRKJ”A new option to control the shape of the pseudo basisfunctions

can

c

S

s

ssa

n

rrrr

rrrCrrr

ii

i

ii

for

for ~:schemepolynomialVanderbilt 01

*

*D. Vanderbilt, PRB 41, 7892 (1990)**A. M. Rappe, K. M. Rabe, E. Kaxiras, J. D. Joannopoulos, PRB 41, 1227 (1990)

can

c

S

sssa

n

rrrr

rrrkjCrrr

ii

i

ii

for

for ~:schememodRRKJ 1**



“MODRRKJ” -- continued

**A. M. Rappe, K. M. Rabe, E. Kaxiras, J. D. Joannopoulos, PRB 41, 1227 (1990)

.near radii5at : tosolutions

singular -non theareand20/;//

that soand0rangein thenodesofnumber

correct thehas that sochosen isand5,...2,1for )3(:of values5choose wepractice,In .ofcoiceby thecontrolledarenodesThe

for

for ~:schememodRRKJ

1

0

0

000

1**

cqqanq

S

sqssq

sc

rn

n

r

c

s

ss

can

c

S

sssa

n

rrrrrkjCr

Ckrrr

drrrd rkrj

drrkrjd

rr

rkrjkskskkkk

rrrr

rrrkjCrrr

iii

cii

ii

ci

i

i

ii

i

ii



“MODRRKJ” – continuedExample for Na:

2s3s

r

r (bohr) r (bohr)

ai ai

ai

~a

i~



Options for systematic exploration of pseudo parameters

Problem: There are many pseudopotential parameters that can be varied in the preparation of PAW datasets .

Machine optimization solution: Developed by Alan Wright (Sandia National Laboratory), Alan Tackett, Greg Walker, and Rachael Hansel (Vanderbilt University). (Manuscript in preparation.)



Options for systematic exploration of pseudo parameters --continued

Partial solution implemented into atompaw 4.0.0.0 (with inspiration from Qi Li); for a given all-electron configuration, the new version of the program allows you to run up to 9999 sets of input parameters, keeping track of the best overall success value for each l channel.

Na 11LDA-PW loggrid 20013 2 0 0 0 03 0 10 0 0cvvv11.7 1.5 1.7 1.7ny4.6nMODRRKJ VANDERBILTORTHO Besselshape2 0 MTROULLIER1.51.71.51.72default3UPFDX 0.0125d0 UPFXMIN -7.d0 UPFZMESH 11.d004/16/2013 Abinit Workshop 2013 24


Options for systematic exploration of pseudo parameters --continued -- Example input file for Na

Atomic configuration

Pseudo parameters

Output datasets

11.7 1.5 1.7 1.7ny4.6nMODRRKJ VANDERBILTORTHO Besselshape2 0 MTROULLIER1.51.71.51.7


Some ideas -- continued Options for systematic exploration of pseudo parameters --

continued --Pseudo parameters for Na Variable

Na 11LDA-PW loggrid 20013 2 0 0 0 03 0 10 0 0cvvv11.7 1.5 1.7 1.7ny4.6nMODRRKJ VANDERBILTORTHO Besselshape2 0 MTROULLIER1.51.71.51.7

102000



Options for systematic exploration of pseudo parameters --continued -- Example input file for Na

Fixed atomic configuration

Initial pseudo parameters

New option index for “exploration”# of pseudo parameter variations

2000 pseudo parameter sets



Options for systematic exploration of pseudo parameters --continued --

E

PAWAEp

rPAW

E

PAWEPAW

rAE

E

AEEAE

ELELM

p

drdELdrdELcc

)(tan)(tan

:each for set parameter pseudofor merit ofFigure

/)(/)(

accuracyivelogderivaton basedcriterion Merit

th

(idea attributed to Alan Tackett)

For each l channel, choose set with smallest Mlp


Summaryatompaw 3.0.1.9 4.0.0.0Modular programing structure Intended to facilitate future modifications

More robust atomic solver Should be optimized; adapted to relativistic solver

Some new options for pseudo functionsMODRRKJ – further evaluation needed

Option for systematic exploration of pseudo parametersPromising??

Further work neededHartree-Fock and hybrid functionalsPreliminary version developed; not yet compatible with

abinit Integration with features developed by Marc Torrent,

François Jollet, etc


Summary -- continuedGoals for atompaw collaboration To develop a flexible atomic PAW dataset generator for

use in materials simulations Control the numerical representation and allow for

investigation of physical phenomena; in principle, PAW calculations should be competitive with all-electron frozen core calculations (such as LAPW or LMTO)

Provide outputs for use in several independent codes for solids (pwpaw, socorro, abinit, quantum espresso, perhaps GPAW??)

While a PAW dataset library is desirable, it will often be important to generate new datasets (for excited states, etc.)


Thanks to the abinit community for setting up and sustaining an

exemplary collaboration!

Documents

Comments on Generating and Testing PAW Datasets * N. A. …Collaborators in France: Marc Torrent, François Jollet, Yann Pouillon Collaborators in USA: Xiao Xu (WFU Ph. D. 2012, current