Pseudopotentials: design, testing, typical errors

Transcription

1 Pseudopotentials: design, testing, typical errors Kevin F. Garrity Part 3 National Institute of Standards and Technology (NIST) Uncertainty Quantification in Materials Modeling 2015

2 Testing Basis Sets What level of precision is possible?

3 Is this still typical? Not anymore. Historical published Si lattice constants with PBE. Graphic Kurt Lejaeghere et al

4 Older PSP s vs a difficult test Older HGH and TM sets perform very poorly (>2% error) BR set improved (0-2% latt. const. error) Still not very good. Bennet Phys. Proc (2012)

5 Upcoming work on DFT numerical accuracy Major effort to systematically calculate and compare 15 codes, 40 basis sets many only recently available Focused on elemental crystals With best basis sets / convergence, agreement 1-2 mev/ atom, lattice constant 0.1%, bulk modulus 4% (This is inter-code comparison, not with expt.)

6 Delta test Summarize difference in equation of state: Calculate 7-9 energy vs volume points, fit equation of state Good agreement 1-2 mev/atom Not only possible test, but a reasonable one. K. Lejaeghere et al, Crit. Rev. in Sol. State and Mat. Sci 39, 1-24 (2014)

7 Delta comparison matrix, all-electron Highest convergence settings Good agreement with each other Detailed settings will be published

8 Delta comparison matrix all-codes Recent PSP sets are accurate Only slightly worse than AE This is only elements Need to test compounds Accuracy is not only factor: Speed Compatibility Availability See also

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10 Typical psps: Motivation my psp set Created ad hoc, often unpublished Only designed / tested for one material Testing not public Quality of public potentials unknown Difficult to reproduce previous work Duplication of effort Doesn t work for high throughput computing

11 1-3 PRL , PRL , PRL 110, See references in Nature Materials 12, (2013), Comp. Mater. Sci 50, 2295 (2011) First principles high-throughput computing Explore many materials to optimize a property At Rutgers Piezoelectrics, ferroelectric, antiferroelectrics 1-3 aflowlib.org, materials project, etc Attempting to calculate ICSD, search for thermoelectrics, etc (~17,000 compounds so far) Searches for stable binary and ternary compounds, photovoltaics, catalysts, battery materials, hydrogen storage, etc 4-5 Most use VASP proprietary

12 Challenges of high-throughput Run 1000's of calculations Need library of atoms Need soft potentials single cutoff Need high transferability Unusual chemical environments Cannot test environments individually

13 My PSP set GBRV pseudopotential library Compatible with Quantum Espresso Abinit jdft, Castep, etc Designed for high-throughput calculations Tested in many structures Fast and accurate K.F. Garrity, J.W. Bennett, K.M. Rabe and D. Vanderbilt, Comput. Mater. Sci. 81, 446 (2014)

14 Specifications of GBRV psp set Optimized for high-throughput Includes H to Bi (except noble gases, f-block) 40 Ryd plane wave-cutoff Accurate stresses Highly transferable Public testing data Reduce duplication of effort Open-source Can be used/improved by community Methodology Ultrasoft pseudopotentials / PAW

15 Ultrasoft potentials / PAWs Relax norm-conserving constraint Add 'missing' charge back later Allows for softer potentials Norm-conserving Oxygen Ultrasoft Oxygen Vanderbilt PRB 41, 7892 (1990)

16 Solid state tests crucial Testing Procedure Test trade-offs of speed / accuracy Compare to all-electron (AE), same approximations Many chemical environments Covalent, ionic, metallic Cubic for convenience

17 Libraries to test GBRV - QE Ultrasoft library for quantum espresso Abinit PAW library for abinit Low 40 Ryd PW cutoff JTH - Abinit PAW library Low 40 Ryd PW cutoff PSLIB - qe-forge.org/gf/project/pslibrary/ Quantum Espresso PAW library High PW cutoff Ryd Low PW cutoff 40 Ryd VASP - PAW library for VASP code PW cutoff Ryd Proprietary

18 Test1: fcc/bcc lattice constants Isolates each atom Metallic bonding

19 Test2: rock salt lattice constants Ionic bonding Note higher errors for other sets

20 Test3: perovskite lattice constants Ionic bonding Test +3, +4, +5 oxidation states

21 Test4: Half-heusler lattice constant Complicated covalent/ionic bonding Shorter bond lengths

22 Test5: zinc blende delta test Covalent bonding Shorter bond lengths

23 Testing Summary My potentials are good combination: 1) Speed 2) Accuracy 3) Transferability

24 Testing Summary My potentials are good combination: 1) Speed 2) Accuracy 3) Transferability

25 Testing Summary My potentials are good combination: 1) Speed 2) Accuracy 3) Transferability

26 Typical errors summary Expected accuracy For well-designed and efficient potentials In unknown chemical environment half-heusler error distribution 0.15% rms error lattice constant 1-2 mev/atom delta test 5% bulk modulus 90% within +/- 0.2% lattice constant Poorly tested potentials can be very bad. Especially but not exclusively older potentials

27 Designing pseudopotentials

28 Constructing Potentials Things to adjust: -r c -semicore/valence -nlcc, etc Ultrasoft Oxygen Testing is key: -Average psp goes though iterations

29 Start I want a psp Initial psp (similar atom) Guided by: Periodic trends Trial and error Adjust r c s Look at log deriv. Increase r c Remove semicore Solid State Tests Reduce r c Add Semicore Adjust local potential Extra projectors Too Hard Good? Yes! Bad Testing The End

30 Examples from code you will use Optimized norm-conserving Vanderbilt pseudopotentials D. R. Hamann, PRB (2013) Nice new code, much easier than back in my day. Supports multiple projects, optimization.

31 Si input file Atom name, Z 3 Core 2 valence 1s2s2p 3s3p

32 Atomic states: 1s 2 2s 2 2p 6 3s 2 3p 2 Si input file

33 Si input file Maximum angular momentum L=2 means d

34 r c for s,p,d Si input file

35 Si input file q target for s,p,d q 2 / 2 = E cut

36 Si input file

37 Number of projectors Energy of extra projector For s,p,d Si input file

38 Si graphical output v_pseudo