Excitations in Carbon Fullerenes calculated by GW Bethe ...pk7/talks/KENT_Fullerenes... · Kent /...
Transcript of Excitations in Carbon Fullerenes calculated by GW Bethe ...pk7/talks/KENT_Fullerenes... · Kent /...
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