Excitations in Carbon Fullerenes calculated by GW Bethe...
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Paul R. C. Kent Murilo L. Tiago Fernando A. Reboredo Oak Ridge National Laboratory Randolph Q. Hood Lawrence Livermore National Laboratory Excitations in Carbon Fullerenes calculated by GW Bethe-Salpeter and Quantum Monte Carlo
Transcript of Excitations in Carbon Fullerenes calculated by GW Bethe...
Paul R. C. KentMurilo L. Tiago
Fernando A. Reboredo Oak Ridge National Laboratory
Randolph Q. HoodLawrence Livermore National Laboratory
Excitations in Carbon Fullerenes calculated by GW Bethe-Salpeter and Quantum Monte Carlo
Kent / APS March Meeting New Orleans / March 2008
Acknowledgements
• Support− DOE
• Codes− PARSEC & RGWBS DFT, W-BSE, TDLDA− CASINO QMC
• Computational support− NCCS at ORNL− NERSC− LLNL− TACC
Kent / APS March Meeting New Orleans / March 2008
Questions that I will address
1. Do the GW-BSE and QMC correctly predict neutral and charged excitations of carbon fullerenes?− C60 is best characterized experimentally− We study 7 fullerenes C20-C80, including isomers
2. Where are improvements in computational methods required?
Kent / APS March Meeting New Orleans / March 2008
Methodology: QMC• Diffusion Monte Carlo is in principle exact, but fixed node
approximation introduces a variational error. First excitation energies of each symmetry are also exact, but non-variational in practice
• Trial wavefunction is single determinant of LDA orbitals− Costly &/or difficult to apply multi-determinants/orbital
optimization/backflow approaches in large systems
• More challenging calculation than for e.g. cohesive energy
LUMO
HOMO
Triplet energy = Etr ! Egs
Kent / APS March Meeting New Orleans / March 2008
• Full absorption spectrum, excitons. Bethe-Salpeter equation for e-h interactions
• We have applied two different levels of approximation
• GW0 and GWf often predict similar gaps, but differ in absolute energy levels compared to vacuum
GWf approximation
GW0 approximation
Methodology: GW-BSE
algorithm: Hybertsen & Louie (1985)
Tiago & Chelikowsky, PRB 73, 205334 (2006)
Del Sole et al., PRB 49, 8024 (1994)
Σ = i GWΓLDA
W = Vcoul + VcoulΠLDAVcoul
Σ = i GW
W = Vcoul + VcoulΠRPAVcoul
Kent / APS March Meeting New Orleans / March 2008
Fullerene geometries• DFT PBE geometries obtained from real-space and
plane-wave ground state calculations•
Kent / APS March Meeting New Orleans / March 2008
Focus on C50, C60, C70 for brevity
Kent / APS March Meeting New Orleans / March 2008
Results: Ionization Potentials• Good agreement for all methods
6
6.5
7
7.5
8
8.5
9
9.5
10
50 60 70
Ioni
zatio
n po
tent
ial (
eV)
Size (atoms)
ExperimentDelta SCF
GWfDMC
Kent / APS March Meeting New Orleans / March 2008
Results: Electron affinities• Systematic overestimation by GW, trends in DMC
unclear
2
2.5
3
3.5
4
4.5
5
50 60 70
Elec
tron
affin
ity (e
V)
Size (atoms)
ExperimentDelta SCF
GWfDMC
Kent / APS March Meeting New Orleans / March 2008
Results: First spin-triplet
• Stoke’s shifts estimated as max 0.2 eV from DFT not included in above data
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
50 60 70 80 90 100
Firs
t spi
n tri
plet
ene
rgy
(eV)
Size (atoms)
ExperimentTDLDA
GWBSEDMC
Kent / APS March Meeting New Orleans / March 2008
Results: First spin-triplet
• Stoke’s shifts estimated as max 0.2 eV from DFT not included in above data
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
50 60 70 80 90 100
Firs
t spi
n tri
plet
ene
rgy
(eV)
Size (atoms)
ExperimentTDLDA
GWBSEDMC
GW-BSE systematically low
Kent / APS March Meeting New Orleans / March 2008
Results: First spin-triplet
• Stoke’s shifts estimated as max 0.2 eV from DFT not included in above data
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
50 60 70 80 90 100
Firs
t spi
n tri
plet
ene
rgy
(eV)
Size (atoms)
ExperimentTDLDA
GWBSEDMC
DMC systematically high
Kent / APS March Meeting New Orleans / March 2008
Challenges to theory
• GW-BSE− Need to improve electron affinities without worsening other
quantities− Currently investigating self-consistent approaches
• QMC− Need improved trial wavefunctions with more optimal nodes− Non-systematic cancellation of nodal error is the primary error− Need compact multiconfigurational expansions &/or orbital
optimization for large systems− Pseudopotential evaluation related errors are small
Kent / APS March Meeting New Orleans / March 2008
Summary
• IP: well reproduced by all methods• EA: systematically overestimated by GW• Triplet: GW-BSE systematically low ~0.5eV (excl. Stokes)• Triplet: QMC systematically high ~0.8eV (excl. Stokes)•Delta SCF and TDLDA are surprisingly good, despite
being poor choices in nanotubes.
http://arxiv.org/abs/0803.0560
Kent / APS March Meeting New Orleans / March 2008
Kent / APS March Meeting New Orleans / March 2008
Results: Ionization Potentials
5
6
7
8
9
10
0 10 20 30 40 50 60 70 80 90 100 110 120
Ioni
zatio
n po
tent
ial (
eV)
Size (atoms)
Exp.dSCF
GWfDMC
Kent / APS March Meeting New Orleans / March 2008
Results: Electron affinities
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80 90 100 110 120
Elec
tron
affin
ity (e
V)
Size (atoms)
Exp.dSCF
GWfDMC
Kent / APS March Meeting New Orleans / March 2008
Results: First spin-triplet
• Stoke’s shifts estimated as max 0.2 eV from DFT not included in above data
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 10 20 30 40 50 60 70 80 90 100 110 120
Firs
t spi
n tri
plet
ene
rgy
(eV)
Size (atoms)
Exp.TDLDA
GWBSEDMC
