M&M Conference Columbus, OH 24-28 June, 2016 Theory and Parameter Free Calculations...
Transcript of M&M Conference Columbus, OH 24-28 June, 2016 Theory and Parameter Free Calculations...
Theory and Parameter Free Calculations of EELS and X-ray Spectra
J.J. Rehr1, J. J. Kas1, K. Jorissen2, and F. Vila1 1Department of Physics, University of Washington, 2Amazon Web Services
Seattle, WA
M&M Conference Columbus, OH 24-28 June, 2016
Theory and Parameter Free Calculations of EELS and X-ray Spectra
• GOAL: Ab initio theory & interpretation of core level EELS & XAS
IR VIS UV X-ray
• TALK: Advanced Codes & Workflow tools
Theory: FEFF/Green’s function + OCEAN/BSE
If I can’t calculate it,
I don’t understand it.
(Often attributed to R. P. Feynman)
Challenge: Full spectrum electron- and X-ray spectra
Cu loss function
Challenge: Improve on Hydrogenic model of EELS*
*L. Pauling, Proc. Roy Soc. A London 114, 181 (1927)
L. Konrad et al., MCM2015
~ 35 years later: Ab initio optical constants*
*http://feffproject.org/feff/desy
Cu loss function
Dielectric function
Energy Loss (EELS)
Absorption coefficient
Refractive index
Reflectivity
X-ray scattering factors
Hamaker constants
Optical constants
𝜖 = 𝜖1 + 𝑖𝜖2
−Im 𝜖−1
𝜇
𝑛 + 𝑖 𝑘
𝑅
𝑓 = 𝑓0 + 𝑓1 + 𝑖 𝑓2
𝜖 𝑖𝜔
fcc Al
UV Deep core
http://feffproject.org/feff/desy
Broad Spectrum Calculations: Theory vs. Expt.
Photon energy or Energy Loss (eV)
EELS Theory a lá Fermi’s golden rule
𝜕2𝜎
𝜕𝐸𝜕Ω𝐸,𝑸 = 𝜉
𝑘𝐹𝑘𝐼𝐼 𝑘𝐼 𝑉 𝑘𝐹𝐹
2 𝛿 𝐸𝐼 − 𝐸𝐹𝐼,𝐹
≈ 𝑆 𝑞, 𝜔
𝑉 = 1 𝑟 − 𝑟′ Coulomb interaction
Dynamic Structure Factor ~ Loss function
𝑆 𝑞, 𝜔 ~ 𝐼𝑚 𝜖−1 𝒒,𝜔
Computational bottleneck:
Too many states!
All state 𝑘𝐹, 𝑘𝐼 (probe) and 𝐹, 𝐼 (sample) contribute
Paradigm shift: Real-space Green’s
Function Approach
Golden rule via Green’s functions:
Golden rule via wavefunctions
Efficient:
No sums over final states!
𝜇 𝐸 ~ 𝑖 𝜖 ∙ 𝐫 𝑓 2𝑓
𝛿 𝐸 − 𝐸𝑓
𝜇 𝐸 ~ −1
𝜋 Im 𝑖 𝜖 ∙ 𝐫′𝐺 𝐫′, 𝐫, 𝐸 𝜖 ∙ 𝐫 𝑖
𝐺 = 1 𝐸 − ℎ − Σ
Ψ
J. J. Rehr & R.C. Albers, Rev. Mod. Phys. 72, 621 (2000)
XAS & EELS
Real-space Green’s function theory
http://feffproject.org/feff/desy
Core-hole SCF potentials Self-energy DW factors Efficient Core level spectra: EELS, XAS, XES
89 atom BN cluster
FEFF8
Parallel (MPI) FEFF
MPI: “Natural parallelization” Each proc. does a few energies Needed for state-of-the-art XANES simulations
𝜇 𝐸 ~ −1
𝜋 Im 𝑖 𝜖 ∙ 𝐫′𝐺 𝐫′, 𝐫, 𝐸 𝜖 ∙ 𝐫 𝑖
EELS in FEFF9: Impurity Green’s function
N K-edge ELNES of GaN*
Real space
*K. Jorissen & J. J. Rehr Phys. Rev. B 81, 245124 (2010)
EELS in periodic systems w/o supercell*
Recip. space
Expt
w/o supercell
+++
Relativistic corrections to EELS*
*P. Schattschneider et al., Phys. Rev. B 2005
and the abs. tensor is
Relativistic Coulomb interaction
𝜕2𝜎
𝜕𝐸𝜕Ω𝐸,𝑸 = 𝜉
𝑘′
𝑘
1
𝑄2 − 𝐸 ℏ𝑐 2 𝐼 𝒓 ∙ 𝑸′ 𝐹 2 𝛿 𝐸𝐼 − 𝐸𝐹 − 𝐸
𝐼,𝐹
𝑸′ = 𝑸 − 𝑄𝑧𝛽2𝒆𝑧
𝜕2𝜎
𝜕𝐸𝜕Ω𝐸,𝑸 = 𝑓 𝑄 𝑄𝑖
′𝑄𝑗′𝜎𝑖𝑗 𝐸
3
𝑖,𝑗=1
where
𝜎𝑖𝑗 𝐸 = 𝜉′𝐸 𝐹 𝑟𝑖 𝐼 𝐼 𝑟𝑗 𝐹 𝛿 𝐸𝐼 − 𝐸𝐹 − 𝐸
𝐼,𝐹
Relativistic EELS
Relativistic Magic Angle in FEFF9 agrees with expt.
Non-relat. Relat.
Incorrect Correct
2.4 mrad 0.6 mrad
FEFF9: Advanced methods
Cu K-edge
FEFF 8.4 FEFF 9
FEFF9: Advanced methods
+
Σ
x-ray
Inelastic Losses Self-energy Real-Space
Green’s Function
Screened core-hole
Ab initio: Mean free paths Self-energies Debye-Waller factors RPA core-hole screening Multi-electron excitations
J. J. Kas et al., PRB 76, 195116 (2007)
Cu Lo
ss F
un
ctio
n
Many-pole (full) much better than HL (dashed) vs better theory (dot-dashed)
Many-Pole Self-Energy (MPSE) Extension of Hedin-Lundqvist (HL) plasmon-pole (pp) GW SE model
Σ approximated as sum of PP models matched to loss function
MPSE corrections in BSE and DFT*
MgAl2O4 (ΔSCF-DFT+MPSE) LiF (BSE+MPSE)
*J. J. Kas et al., J. Phys. Conf. Series 190, 012009 (2009)
Energy (eV)
MPSE MPSE
V. Mauchamp, M. Jaouen, JJR, and J. J. Kas, U. Poiters, Preprint (2010)
Question: Can we improve
the theory?
AI2NBSE: Abinit+NIST BSE+UW MPSE Plane-wave, pseudo-potential GW/BSE code
UW + NIST collaboration
Answer: GW/BSE Ab initio optical & low-loss spectra
Si
Ab initio GW/BSE core-spectra: ELNES & XANES
OCEAN: Obtaining Core Excitations from Abinit and NBSE
LiF: F K edge SrTiO3: Ti L2,3 edge
UW + NIST Collaboration
Are we there yet? Optical constants: THz to X-ray
UV-VIS
X-ray
Challenge: Efficient phonon spectra Can we compute vibrational properties ab initio?
Ab initio Debye Waller Factors: 𝐞−𝟐𝝈𝑹𝟐𝒌𝟐
𝜎𝑅2 𝑇 =
ℏ
2𝜇𝑅 1
𝜔coth𝛽ℏ𝜔
2
∞
0
𝜌𝑅 𝜔 𝑑𝜔
𝜌𝑅 𝜔 = −2𝜔
𝜋Im 0
1
𝜔2 − D+ 𝑖휀0 ≅ 𝑤𝑣𝛿 𝜔 − 𝜔𝑣
𝑁
𝑣=1
Projected Vibrational DOS: Use efficient pole model
EXAFS MSRDs:
Helmholtz Free Energy:
𝐹 𝑇 = 𝐸 + 𝑘𝐵𝑇 ln 2 sinh𝛽ℏ𝜔
2
∞
0
𝜌𝑖 𝜔 𝑑𝜔
𝑁𝑐𝑜𝑜𝑟
𝑖
Ψ
Vila et al, Phys. Rev. B 76, 014301 (2007)
Vibrational Density of States
Cu
Typical Results
ZrW2O8: Complex unit cell
ZrW2O8: MSRDs
Phonon-contributions to final-state broadening in Cu
Satellites visible only at low T
User-friendly Java GUI: JFEFF
VESPA - Virtual EELS Software Package
Goal: Integrated EELS software for STEM using CORVUS Workflow Manager
Prototype: Virtual STEM in the Cloud State-of-the-art EELS modeling
FEFF9+JFEFF
AI2NBSE and OCEAN
TELNES
Precompiled & Optimized on the Amazon EC2
K. Jorissen et al. www.feffproject.org/feffproject-scc.html
CONCLUSIONS • Goals:
– Mostly achieved or in sight
• Complementary theoretical techniques: – Real-space
– Supercell/reciprocal space
• Next generation theory & codes including: – Many-body effects
– Relativistic effects
• Broad spectrum response: – IR VIS UV X-ray
From left to right: Ken Nagle Yoshi Takimoto Kevin Jorissen Towfiq Ahmed Hadley Lawler Aleksi Soininen Fernando Vila Adam Sorini Alex Ankudinov Micah Prange John Vinson (Shauna Story) John Rehr Josh Kas (Egor Clevac)
Acknowledgments: Thanks to DOE BES for $$ Rehr Group + L. Reining, M. Guzzo, E. Shirley,
K. Gilmore, et al.
Theory and Parameter Free Calculations of EELS and X-ray Spectra
J.J. Rehr1, J. J. Kas1, K. Jorissen2, and F. Vila1 1Department of Physics, University of Washington, 2Amazon Web Services
Seattle, WA
Thank you!
Thank you!