PUBLIC
GW : AUTOMATION, PRECISION AND ACCURACYMICHIEL VAN SETTEN
IMEC
▪ World-leading R&D and innovation hub in nanoelectronics and digital technologies.
▪ 4,000 researchers globally, 97 nationalities
▪ HQ in Leuven Belgium, 11 affiliated research groups at Flemish universities5 other sites in Europe, 3 in the USA and 5 in Asia.
▪ Modeling from ab initio to device level.
▪ Ab initio core group (4 permanent, 6 PhDs, 2 industrial residents)
▪ Around a dozen researchers in other groups involved in ab initio: quantum transport, qbits, materials science
2
IMEC RESEARCH
▪ CMOS and beyond CMOS
▪ Image sensors and vision systems
▪ Silicon photonics
▪ Wearables
▪ Photovoltaics
▪ GaN
▪ Sensor solutions for IoT
▪ Wireless IoT communication
▪ Radar sensing systems
▪ Solid state batteries
▪ Data science and data security
▪ Large-Area Electronics
▪ Life sciences
▪ Artificial intelligence
3
▪ Most advanced 300 mm (300 mm diameter wafers)cleanroom in the world
▪ Raman Spectroscopy and the related technique of Photo Luminescence (PL)
▪ Rutherford Backscattering (RBS) and related techniques of Elastic Recoil Detection (ERD) and Proton Induced X-ray Emission (PIXE)
▪ Scanning Probe Microscopy (SPM) inclusive of Atomic Force Microscopy (AFM), various electrical and physical variants thereof, as well as Scanning Tunneling Microscopy (STM)
▪ Secondary Ion Mass Spectrometry (SIMS)
▪ Transmission Electron Microscopy (TEM)
▪ X-ray Photoelectron Spectroscopy (XPS)
▪ AttoLab rt-Spectroscopies 20 as – 200 ps pump probe, up to 124 eV beam
PUBLIC
COMPUTATIONAL APPROACHES
▪ Density functional theory▪ Maps the many particle problem into a single particle problem
▪ Scalar effective potential Vxc(r)
▪ Applicable to large systems: > 2000 atoms
▪ Broadly used across many fields of sciences
▪ Description of electronic levels (charge transfer), long range interactions, no proper fundamental band gaps
▪ GW-method▪ Replace the potential by a self-energy matrix: Vxc(r) → Σ(r,r’,E)
▪ Available for bulk solids
▪ Becoming increasingly available for molecules and nano structures
▪ Significantly improved description of electronic levels (charge transfer), long range interactions, and band gaps
4
PUBLIC
HISTORICAL PERSPECTIVE
1965 New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas ProblemL. Hedin, Phys. Rev. 139, A796
1979 Many-Particle Effects in the Optical Excitations of a Semiconductor.
W. Hanke and L.J. Sham, Phys. Rev. Lett. 43, 387−390.
1985 First-Principles Theory of Quasiparticles: Calculation of Band Gaps in Semiconductors and Insulators (silicon and diamond)M. S. Hybertsen and S. G. Louie, Phys. Rev. Lett. 55, 1418
2005 A brief introduction to the ABINIT software packageX. Gonze et all. Zeit. Kristallogr. 220, 558-562
2006 Implementation and performance of the frequency-dependent GW method within the PAW framework (VASP)M. Shishkin and G. Kresse Phys. Rev. B 74, 035101
2006 Optical excitations in organic molecules, clusters, and defects studied by first-principles Green’s function methodsMurilo L. Tiago and James R. Chelikowsky Phys. Rev. B 73, 205334
2014 Predictive GW calculations using plane waves and pseudopotentialsJiří Klimeš, Merzuk Kaltak, and Georg Kresse Phys. Rev. B 90, 075125
2015 GW100: Benchmarking G0W0 for Molecular SystemsM. J. van Setten et all. J. Chem. Theory Comput., 2015, 11 (12), pp 5665–5687
2020 Reproducibility in G0W0 Calculations for Solids, 3 codes a few materialsRangel et all. in press
5
PUBLIC
GW FOR SOLIDS: BANDGAPS
VAN SCHILFGAARDE PRL 96, 226402 (2006) HEDIN J PHYS, COND MAT. 11 R489 (SHIRLEY) (1995)
6
PUBLIC
SCGW FOR SOLIDS: BANDGAPS
KRESSE PRB 75, 235102 (2007) VAN SCHILFGAARDE PRL 96, 226402 (2006)
7
HOW PRECISE ARE THE RESULTS?
HOW ACCURATE IS GW IN PRACTICE?
IS THERE ANY HOPE TO TURN IT IN AN AUTOMATIC PROCEDURE?
Should we do G0W0?
Which starting point?
What level of self consistency?
Which GW integration method?
What do we compare to?
What basis type can we trust?
Which core valence partitioning?
Pseudopotenials?
PUBLIC
DO WE CARE TOO LITTLE?
Only recently DFT was truly
Benchmarked
For just elemental systems
For just a few ground state
properties
Maybe it is just too hard a problem….
FORMALISM
PUBLICPUBLIC
KS V.S. QUASI-PARTICLE EQUATION
▪ Electron density parameterized by KS single particle states
▪ Greens function in spectral representation, expressed in terms of quasi-particle states leads to the quasi particle equation:
▪ The quasi-particle energies are the electron removal and addition energies
▪ 0th order correction to the KS energies:
)()()()()(2
1
)()()(
KSKSKS
XCextH
2
occ
*KSKS
rrrrr
rrr
nnn
n
nn
VVV
=
+++−
=
)()();,()()()(2
1 qp
,
qpqp
,
qpqp
,extH
2rrrrrrrr nrnnrnnr dVV =+
++−
G(r, ¢r ;z) =Yr,n
qp (r, z)Y l,n
qp†( ¢r , z)
z-enqp(z)+ ihsign(en
qp(z)-m)p
å
enG0W0 =en
KS + yn
KS S(enG0W0 )-VXC yn
KS
Vxc: exchange correlation potential
Σ: self-energy
HEDIN Phys Rev 139, A796, HYBERTSEN and LOUIE PRB 34, 539011
PUBLICPUBLIC
HEDIN EQUATIONS
▪ Space time notation (the numbers indicate a contracted space, time and spin index)
+
+
−=
+=
+−−=
+=
=
)1,4()2,4,3()3,1()34()2,1(
)2,4()4,3()3,1()34()2,1()2,1(
)3,7,6()5,7()6,4()5,4(
)2,1()4567()32()21()3,2,1(
)2,4()4,3()3,1()34()2,1()2,1(
)4,3,2()4,1()3,1()34()2,1(
00
GGdiP
WPvdvW
GGG
d
GGdGG
WGdi
12
PUBLICPUBLIC
HEDIN EQUATIONS
▪ Space time notation (the numbers indicate a contracted space, time and spin index)
▪ Neglecting the second term in the vertex function leads to the GW approximation for
the self-energy; Fourier transformed to frequency domain:
)1,2()2,1()2,1(
)2,4()4,3()3,1()34()2,1()2,1(
)2,4()4,3()3,1()34()2,1()2,1(
)2,1()2,1()2,1(
00
GGiP
WPvdvW
GGdGG
WGi
−=
+=
+=
=
+
dWEGei
E i )()(2
)( 0 −= +−
13
PUBLICPUBLIC
SELF-ENERGY METHODS
▪ Exact Analytic▪ Solve Casida equations > spectral representation of the response function
▪ Analytic evaluation of the GW integral
▪ Self-energy expression as an explicit sum over poles
▪ Analytic continuation of the self energy▪ Calculate the GW integral on the imaginary axis
▪ Fit an n-pole expansion for Sigma in the entire complex plane (e.g. Pade)
▪ Plasmon pole▪ approximate the response in a single pole
▪ analytic evaluation of the GW convolution
▪ Multipole response expansion▪ approximate the response in multiple poles
▪ analytic evaluation of the GW convolution
▪ Real energy direct numerical integration▪ brute force numerical integration on the real axis
▪ Contour deformation▪ replace the integral on the real axis with an integral on the imaginary axis and a sum over a finite number of include poles
14
dWEGei
E i )()(2
)( 0 −= +−
PUBLIC
FULL ANALYTIC
▪ Calculate response in spectral representation
▪ Close connection to TDDFT (actually TDH)
▪ Analytic expression of Sigma as a sum over
poles of G and W
▪ Calculate Sigma analytically
▪ Numerically exact except for finite basis
▪ Full analytic structure of Sigma
▪ Expensive
Re n Sc(en ) n( ) =
in rm( )2 en -ei +Wm
en -ei +Wm( )2+h2
i
occ
å
+ an rm( )2
a
unocc
åen -ea -Wm
en -ea -Wm( )2+h2
æ
è
ççççç
ö
ø
÷÷÷÷÷
m
å
15
PUBLIC
ANALYTIC CONTINUATION
▪ Calculate the GW integral on the imaginary axis
▪ Fit an n-pole expansion for Sigma in the entire complex plane
▪ Allows for a more detailed sigma
▪ Can be made exact
▪ May take many poles to converge
16
PUBLICPUBLIC
PLASMON POLE
▪ Approximate the response by one single pole
▪ Calculate response at a few imaginary frequencies
▪ Analytic continuation to the real axis
▪ Calculate Sigma analytically
▪ Cheap
▪ Many different approaches
▪ Justification for complex systems
17
PUBLICPUBLIC
CONTOUR DEFORMATION
▪ Calculate the GW integral on the imaginary axis
▪ Add pole contributions of G in the contour
▪ Allows for a more detailed sigma
▪ Can be made exact
▪ Integration grid parameters
18
BENCHMARKING GW
19
PUBLICPUBLIC20
BENCHMARK SET FOR MOLECULES: GW100
▪ Original Collaboration: KIT Karlsruhe, FHI Berlin, and Berkeley Lab US DoE
▪ TURBOMOLE: Gaussian basis sets, spectral representation via Casida
▪ FHI-Aims: numerical local orbitals, analytic continuation
▪ BerkeleyGW: plane waves, plasmon pole and real frequency integration
▪ 5 different ways to evaluate the self-energy
▪ well converged all electron reference values for IP and EA
HOMO level data sets comparison
PUBLICPUBLIC21
BENCHMARK SET FOR MOLECULES: GW100
▪ Original Collaboration: KIT Karlsruhe, FHI Berlin, and Berkeley Lab US DoE
▪ TURBOMOLE: Gaussian basis sets, spectral representation via Casida
▪ FHI-Aims: numerical local orbitals, analytic continuation
▪ BerkeleyGW: plane waves, plasmon pole and real frequency integration
▪ 5 different ways to evaluate the self-energy
▪ well converged all electron reference values for IP and EA
▪ Follow ups
▪ CCSD(T) total energy reference, approximate GW (Klopper)
▪ Plane wave results by VASP (Kresse) and WEST (Galli)
▪ CP2k results (testing the O(3) GW implementation)
▪ (partial) Stochastic GW results (testing O(1) implementation)
▪ MolGW, Fiesta, Abinit, Yambo
▪ Evaluation of 6 types of (partial) self-consistency
▪ Several non-GW projects picking up GW100 as a test set
LDA ½ and Koopmans compliant functionals
▪ 2 more sets of CCSD on the way
HOMO level 48 data sets comparison
PUBLICPUBLIC
GW100 TODAY
22
GW100.WORDPRESS.COM
▪ online database with all contributed data sets with python tools on git
▪ unified data format
▪ web interface with interactive analysis tools
▪ two sets in full detail
▪ any combination of sets comparedto one reference
▪ all against all
PUBLICPUBLIC
MOLECULES IN GW100
23
He
Ne
Ar
Kr
Xe
C7H8
C8H10
C6F6
C6H5OH
C6H5NH2
C5H5N
C5H5N5O
C5H5N5O
C4H5N3O
C5H6N2O2
C4H4N2O2
CH4N2O
H2
Li2Na2
Na4
Na6
K2
Rb2
N2
P2
As2
F2
Cl2Br2
I2CH4
C2H6
C3H8
C4H10
C2H4
C2H2
C4
C3H6
C6H6
C8H8
C5H6
C2H3F
C2H3Cl
C2H3Br
C2H3I
CF4
CCl4CBr4
CI4
SiH4
GeH4
Si2H6
Si5H12
LiH
KH
BH3
B2H6
NH3
HN3
PH3
AsH3
SH2
FH
ClH
Ag2
Cu2
NCCu
LiF
F2Mg
TiF4
AlF3
BF
SF4
BrK
GaCl
NaCl
MgCl2AlI3
BN
NCH
PN
H2NNH2
H2CO
CH4O
C2H6O
C2H4O
C4H10O
CH2O2
HOOH
BeO
MgO
H2O
CO2
CS2
OCS
OCSe
CO
O3
SO2
PUBLICPUBLIC
ELEMENTS IN GW100
24
PUBLICPUBLIC
VIOLIN AND BOX PLOTS
25
some quantity
regular box plot
median value
25% edge
25% edge
violin plot (kernel density)
whisker
beyond which lie statistical outlyers
REPRODUCIBILITY
26
If I do the ‘exact’ same thing with two codes, do I get the same answer?
PUBLICPUBLIC
FIRST SANITY CHECK
▪ MOLGW compared to TURBOMOLE
▪ same basis (def2-QZVP)
▪ same fully analytic GW approach
27
TWO COMPLETELY DIFFERENT CODES BUT THE SAME APPROACH
BeO
PUBLICPUBLIC
ALL QZVP RESULTS FROM LOCAL ORBITAL CODES
▪ G0W0@PBE
▪ Same local orbital basis set
▪ Most converged self energy
parameters
▪ (compared to full analytic)
▪ the box plot in the center collapses
for all comparisons:
▪ for more than 50% the deviations is
meV small
▪ we do have outliers
28
PUBLICPUBLIC
THE PADE APPROXIMATION
▪ Analytic continuation of the self-energy
▪ QZVP
▪ G0W0@PBE
▪ Pade for the Homo does converge
▪ ‘automatic’ solving of the QPE can pick up wrong intersections.
▪ new AC method in FIESTA outperforms
29
PUBLICPUBLIC
SOLVING THE QUASIPARTICLE EQUATION
▪ multiple intersections
▪ a solver may overshoot in the first
step
▪ most problematic in strongly polar
molecules
▪ check for slope
30
enG0W0 =en
KS + yn
KS S(enG0W0 )-VXC yn
KS
PRECISION
31
How big is the error in my final result due to numerical / mathematical approximations?
PUBLICPUBLIC
BASIS SET EXTRAPOLATION
▪ Dunning basis sets and def2 basis sets converge similar.
▪ def2 are contracted gaussians, i.e., less actual functions
▪ Number of basis functions extrapolation and cardinal number extrapolation are similar
▪ Checked for all molecules individually
32
SVP
TZVP
QZVP
T
Q
5
PUBLICPUBLIC
CONVERGENCE WITH BASIS SET SIZE
33
▪ Turbomole
▪ Cbas (auxiliary basis set)
▪ G0W0@PBE
▪ triple zeta is usually sufficient
for ground state
▪ quadruple still 0.1 eV of on average
PUBLICPUBLIC
TYPE OF BASIS
34
PLANE WAVE V.S. LOCAL ORBITALS
extrapolated PW FF v.s. extrapolated local basis set
PW numerical FF
▪ If done correctly and carefully
converged PW and Local
basis do lead to the same
results
PW CD
PW PP
WEST
BGW
BGW
PUBLICPUBLIC
CD AND PLASMON POLE
35
▪ If done correctly and carefully converged PW and Local basis do lead to the same results
▪ CD leads to the same as fully analytic, results could be under converged
▪ Numerical FF also ok, but again signs of under converged results
▪ (HL )Plasmon Pole is not able to describe the complexity of the molecule response function
PUBLICPUBLIC
MOST CONVERGED G0W0@PBE PER CODE
36
extrapolated
planewave nc (partial set)
gaussian + plane wave
plane wave nc
plane wave paw
Fiesta datasets are close to completion
Abinit and StochasticGW: only partial sets but decent agreement.
BGW numerical full frequency: reasonable agreement (under converged due to too heavy numerics)
local basis set
local basis set
realspace nc (partial set) not
extrapolated
PUBLICPUBLIC
CONCLUDING NUMBERS FOR THE HOMO
▪ Self-energy
▪ 12 pole Pade approximation within 0.05 eV
▪ 128 plot Pade approximation within 0.01 eV
▪ CD and other FF methods converge to within 0.1 eV
▪ Plasmon pole model mean 0.5 (up to eV) error
▪ Basis
▪ TZVP mean 0.3 (up to 0.6 eV) error
▪ QZVP mean 0.1 (up to 0.3 eV) error
▪ auxiliary basis mean 0.04 (up to 0.2 eV) error
▪ in the converged limit extrapolated local basis and extrapolated pw align, 68% within 0.1 eV
37
ACCURACY
38
How good do my results represent experimental results or results from a higher level of theory?
PUBLICPUBLIC
G0W0 STARTING POINTS
39
100%
50%
25%
0%
CCSD(T) reference
monotonic
trend following
the amount
of exact exchange
in the starting point
CCSD(T) reference
def2-TZVPP
PUBLICPUBLIC
STARTING POINT AND LEVELS OF SELF-CONSISTENCY
40
qsGW
scGW
G0W0@BH-LYP
CCSD(T) reference
def2-TZVPP
partial self consistency
reduces starting point
dependence
PUBLICPUBLIC
LEVELS OF SELF-CONSISTENCY
41
the most self-consistent
is not the best match
CCSD(T) reference
def2-TZVPP
cheapest way to a close
match: 50% EX starting point
the most self-consistent
is not the best match
PUBLICPUBLIC
NON-GW DEVELOPMENT IS ALSO STARTING TO USE GW100
42
PUBLICPUBLIC
TAKE HOME MESSAGES ACCURACY
▪ Technical implementation details are under control
▪ Calculations with different types of basis sets converge to the same results
▪ G0W0 shifts ~ 1 eV starting from HF to PBE
▪ ~ 50% Exact exchange optimizes agreement with CCSD(T)
▪ qsGW underestimates
▪ scGW overestimates
▪ Partial self-consistency in G reduces starting point dependence by half
43
PUBLICPUBLIC
Michiel J. van Setten, Fabio Caruso, Patrick Rinke,
Ferdinand Evers, Florian Weigend, Jeffrey B. Neaton,
Sahar Sharifzadeh, Xinguo Ren, Matthias Scheffler,
Fang Liu, Johannes Lischner, Lin Lin, Jack R. Deslippe,
Steven G. Louie, Chao Yang, Katharina Krause,
Michael E. Harding, Wim Klopper, Matthias Dauth,
Emanuele Maggio, Peitao Liu, Georg Kresse, Marco
Govoni, Giulia Galli, Jan Wilhelm, Jürg Hutter,
Christof Holzer, Rodrigues Pela, Andris Gulans,
Claudia Draxl, Nicola Colonna, Ngoc Linh Nguyen,
Andrea Ferretti, Nicola Marzari, Xavier Blase, Fabien
Bruneval
CONTRIBUTORS GW100
gw100.wordpress.com
github.com/setten/GW100
44
AUTOMATION FOR SOLIDS
PUBLICPUBLIC
HIGH-THROUGHPUT GW
from a structure
without any human intervention
to converged GW results
▪ Automatic calculations
▪ Screening for new compounds
▪ Database building
▪ Uniform results
▪ No human bias
PUBLICPUBLIC
HIGH-THROUGHPUT GW
▪ additional difficulties as compared to DFT
▪ Pseudo potentials
▪ 4 step calculation
▪ N4 (at best N3) scaling
▪ More convergence parameters
▪ No ‘safe’ parameter set (converged results for all)
▪ No ‘safe’ computational settings (# cpu’s, memory, time, ...)
PUBLIC
BN
THE CONVERGENCE PROBLEM
▪ Coupled parameters:
▪ converging one at a low value of the
other and vice versa will lead to
under converged results
▪ Many systems converge similar, but
not all
▪ no safe works for all short cuts
▪ No way to perform a overcovered
calculations to obtain a reference
▪ System by system convergence testing
is needed
PUBLIC
THE MEMORY PROBLEM
GW tasks that finish at a given memory limit
▪ Many calculations will finish with
reasonable amount of computational
resources.
▪ During a convergence test, some,
however, will not.
▪ In automatic mode, needed for high
throughput, this needs to be fixed
automatically, i.e., no human
intervention.
PUBLIC
THE PSEUDO PROBLEMAuCl
Normal 19 electron Au potential
4f unfrozen Au potential
▪ DFT only cares about occupied states
▪ GW also cares about unoccupied
states
▪ also ‘no occupied states’ GW
methods care about the quality of the
Hilbert space
▪ occupied states needed down to
about 40 eV below EF
▪ And again: system dependend
PUBLICPUBLIC
HIGH-THROUGHPUT GW
▪ additional difficulties as compared to DFT
▪ Pseudo potentials
▪ 4 step calculation
▪ N4 (at best N3) scaling
▪ More convergence parameters
▪ No ‘safe’ parameter set (converged results for all)
▪ No ‘safe’ computational settings (# cpu’s, memory, time, ...)
PUBLICPUBLIC
HIGH-THROUGHPUT GW
▪ additional difficulties as compared to DFT
▪ Pseudo potentials
▪ 4 step calculation
▪ N4 (at best N3) scaling
▪ More convergence parameters
▪ No ‘safe’ parameter set (converged results for all)
▪ No ‘safe’ computational settings (# cpu’s, memory, time, ...)
DFT babysitting
problem
PUBLICPUBLIC
HIGH-THROUGHPUT GW
▪ additional difficulties as compared to DFT
▪ Pseudo potentials
▪ 4 step calculation
▪ N4 (at best N3) scaling
▪ More convergence parameters
▪ No ‘safe’ parameter set (converged results for all)
▪ No ‘safe’ computational settings (# cpu’s, memory, time, ...)
GW babysitting
problem
PUBLICPUBLIC
HIGH-THROUGHPUT GW
▪ additional difficulties
▪ Pseudo potentials
▪ 4 step calculation
▪ N4 (at best N3) scaling
▪ More convergence parameters
▪ No ‘safe’ parameter set (converged results for all)
▪ No ‘safe’ computational settings (# cpu’s, memory, time, ...)
PUBLICPUBLIC
3 XC-functionals / 3 formats (codes) / 70.000 test per table
Don Hamann PRB 88, 085117 (2013)
Computer Physics Communications 226, 39-54 (2018)
PSEUDO DOJO
▪ Optimized Norm Conserving Vanderbild Pseudo Potentials
▪ multiple projectors
▪ multiple gradient constraints
▪ Package to facilitate PSP
generation
▪ Graphical interface
▪ Automatized testing (6) www.pseudo-dojo.org
Log derivatives made to agree up to 8 Ha
PUBLICPUBLIC
Flow generation:
GUI or scripted
based Python package
• Workflow management
• ABINIT I/O
• Post processing
AUTOMATING GW
PUBLICPUBLIC
Scheduling the flow on the cluster
Error handling (‘custodian like’)
Convergence testing
SLURM
PBSPro
Torque
SGE
…
AUTOMATING GW
PUBLICPUBLIC
Storing results:
query-able entries
+ netcdf data files
(via gridfs)
Interactive analysis
and presentation
of
results
AUTOMATING GW
PUBLIC
AUTOMATIC GW FLOW
▪ On a low k-point density (2x2x2):
▪ Set of single parameter ground state convergence studies
▪ Grid of nbands X encuteps
▪ For each nbands extrapolate in encuteps
▪ For the extrapolated encuteps find the converged nbands
▪ if not found > extend grid and retest
▪ On the final high k-point density:
▪ Test derivatives.
(in most cases the high density derivatives turn out smaller)
▪ Post process
(create scissor, apply scissor, plots, statistical analysis…)
(pw cutoff, …)
PUBLIC
CONVERGENCE STUDY
▪ On a low k-point density (2x2x2):
▪ Set of single parameter ground state convergence studies
▪ Grid of nbands X encuteps
▪ For each nbands extrapolate in encuteps
▪ For the extrapolated encuteps find the converged nbands
▪ if not found > extend grid and retest
▪ On the final high k-point density:
▪ Test derivatives.
(in most cases the high density derivatives turn out smaller)
▪ Post process
(create scissor, apply scissor, plots, statistical analysis…)
(pw cutoff, …)
PUBLIC61
PUBLIC
CONVERGENCE STUDY
▪ On a low k-point density (2x2x2):
▪ Set of single parameter ground state convergence studies
▪ Grid of nbands X encuteps
▪ For each nbands extrapolate in encuteps
▪ For the extrapolated encuteps find the converged nbands
▪ if not found > extend grid and retest
▪ On the final high k-point density:
▪ Test derivatives.
(in most cases the high density derivatives turn out smaller)
▪ Post process
(create scissor, apply scissor, plots, statistical analysis…)
(pw cutoff, …)
PUBLIC
Gold
2x2x2 kpoint mesh
14x14x14 kpoint mesh
0.35 eV
0.35 eV
shift in energy with k-grid
shape is maintained
PUBLIC
AUTOMATIC GW FLOW
▪ On a low k-point density (2x2x2):
▪ Set of single parameter ground state convergence studies
▪ Grid of nbands X encuteps
▪ For each nbands extrapolate in encuteps
▪ For the extrapolated encuteps find the converged nbands
▪ if not found > extend grid and retest
▪ On the final high k-point density:
▪ Test derivatives.
(in most cases the high density derivatives turn out smaller)
▪ Post process
(create scissor, apply scissor, plots, statistical analysis…)
(pw cutoff, …)
WHAT CAN WE CONCLUDE FOR SOLIDS
PUBLIC
KS V.S. GW GAPS
▪ Close correlation between PBE and
G0W0@PBE gaps.
▪ no clear distinction between
compounds with transition metals
(TM) and those without (noTM)
PUBLIC
G0W0GN@PBE
▪ GW gaps should not reproduce
experiment:
▪ no ZPE renormalization
▪ no SO effects
▪ no finite temperature correction
▪ The 0K electronically exact theory
should overestimate the experimental
gaps, the blue lines indicate an
estimate.
PUBLIC
ERROR ANALYSIS
▪ remapping to error v.s. experimental
full values
▪ distinction between TM and noTM
▪ very light elements cause under
estimation (zpe renormalization)
▪ heavy elements, not so clear
PUBLIC
COMPARING TO EMPIRICAL MODELING
▪ Can we remove the linear component
of the error in PBE?
▪ to a large level we can
▪ but G0W0@PBE still slightly
outperforms corrected PBE
PUBLIC
CONCLUDING
▪ Can we automate GW sufficiently to go high-throughput?
▪ It is much harder than for DFT
▪ no safe computational settings: #CPUs, memory, etc. :
▪ no safe parameter sets: either noting will finish or noting will be converged
▪ But if we have
▪ automated input generation
▪ automated output processing
▪ automated job generation, submission, monitoring
▪ failure detection
▪ algorithms and rules to recover from problems
70
PUBLIC71