The document summarizes the LDA+U method for treating strongly correlated materials and applies it to two cases - CaFeO3 and La1/2Sr2/3FeO3. LDA+U adds an on-site Coulomb interaction term U to the LDA functional to better describe localized d-orbitals. It shows how LDA+U predicts charge disproportionation and an insulating state in both materials, driven by factors like lattice distortions, correlations, and disorder.
Branislav K. Nikoli
ć
Department of Physics and Astronomy, University of Delaware, U.S.A.
PHYS 624: Introduction to Solid State Physics
http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
Branislav K. Nikoli
ć
Department of Physics and Astronomy, University of Delaware, U.S.A.
PHYS 624: Introduction to Solid State Physics
http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
The all-electron GW method based on WIEN2k: Implementation and applications.ABDERRAHMANE REGGAD
The all-electron GW method based on WIEN2k:
Implementation and applications.
Ricardo I. G´omez-Abal
Fritz-Haber-Institut of the Max-Planck-Society
Faradayweg 4-6, D-14195, Berlin, Germany
15th. WIEN2k-Workshop
March, 29th. 2008
Localized Electrons with Wien2k
LDA+U, EECE, MLWF, DMFT
Elias Assmann
Vienna University of Technology, Institute for Solid State Physics
WIEN2013@PSU, Aug 14
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Toxic effects of heavy metals : Lead and Arsenicsanjana502982
Heavy metals are naturally occuring metallic chemical elements that have relatively high density, and are toxic at even low concentrations. All toxic metals are termed as heavy metals irrespective of their atomic mass and density, eg. arsenic, lead, mercury, cadmium, thallium, chromium, etc.
ANAMOLOUS SECONDARY GROWTH IN DICOT ROOTS.pptxRASHMI M G
Abnormal or anomalous secondary growth in plants. It defines secondary growth as an increase in plant girth due to vascular cambium or cork cambium. Anomalous secondary growth does not follow the normal pattern of a single vascular cambium producing xylem internally and phloem externally.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Strongly correlated electrons: LDA+U in practice
1. Strongly correlated electrons: LDA+U in
practice
Tanusri Saha-Dasgupta
Dept of Condensed Matter Physics & Materials Science
Thematic Unit of Excellence on Computational Materials Science
S.N. Bose National Centre for Basic Sciences
Salt Lake, Calcutta, INDIA
tanusri@bose.res.in
. – p.1/45
2. Outline
• Introduction: why strong correlations ?
- Failure of one-electron theories
- Examples of strongly correlated materials
- Different energy scales and MIT in TMO
• Methods to deal with correlations in realistic ways
- Concepts (LDA+U)
- Practical details
- Example of CaFeO3 and La1/2Sr2/3FeO3
. – p.2/45
3. Electronic Structure Calculations:
• Good description of many microscopic properties are obtained in
terms of -
Born-Oppenheimer Approximation
Nuclei and the electrons to a good approximation may be treated
separately.
One-electron Approximation
Each electron behaves as an independent particle moving in the
mean field of the other electrons plus the field of the nuclei.
. – p.3/45
4. LDA
Most satisfactory foundation of the one electron picture is provided
by the local approximation to the Hohenberg-Kohn-Sham density
functional formalism
≡ LDA
⇓
• LDA leads to an effective one electron potential which is a function
of local electron density.
• Leads to Self consistent solution to an one electron Schrödinger
Eqn.
. – p.4/45
5. Flow-chart for LDA self-consistency
First principles information: atomic no., crystal structure
⇓
Choose initial electron density ρ(r)
Calculate effective potential through LDA:
Veff (r) = Vion(r)+ d3
r′
Vee(r−r′
)ρ(r′
)+ δExc[ρ]
δr
Solve K-S eqns:
[−∆+Vion(r)++ d3
r′
Vee(r−r′
)ρ(r′
)+δExc[ρ]
δr ]φi(r) = ǫiφi(r)
Needs to expand K-S wavefunctions in terms of basis, Φilm
Calculate charge density: ρ(r) = |φi(r)|2
Iterate to selfconsistency
⇓
Total energy, inter-atomic forces, stress or pressure, band struc-
ture, . . . . – p.5/45
6. Strongly correlated electron materials
∗ The conventional band-structure calculations within the framework
of LDA is surprising successful for many materials.
∗ However, they fail for materials with strong e-e correlation !
• correlation effect necessarily arise, and
• the consideration of electron correlation effects provides the
natural way to understand the phenomena like the insulating nature
of CoO.
. – p.6/45
7. Strongly correlated electron materials
Energy
k
ρ (εF) = 0
Even No. of e’s
per unitcell
ρ (εF) = 0
ρ (εF) = 0
Odd No. of e’s
per unitcell
Ca, Sr
Energy
k
C
Energy
k
Ef
Na, K
Ef
Even No. of e’s
per unitcell
+ band overlap
Predictions from LDA (Bandstructure)
Accordingly to LDA, odd no. of e’s per unit cell always give rise to Metal ! . – p.7/45
8. Strongly correlated electron materials
Failure of Band Theory
Total No. of electrons = 9 +6 = 15
Band theory predicts CoO to be
metal, while it is the toughest
insulator known
−−) Importance of e−e interaction effects (Correlation)
Failure of LDA −) Failure of single particle picture
. – p.8/45
9. Strongly correlated electron materials
e
+ U3s
ε
3s
−
NaNa
+ −
0 ε
3s2
NaNa
0 0
ε
3s
energy
a (lattice constant)a0
2s
2p
3s
itinerant localizedenergy/atom
3s 3s/ tU
3s
ε
3s−At
3s
ε
H_3s = H_band + H_columb
. – p.9/45
10. Examples of strongly correlated materials
Transition metals:
- d-orbitals extend much further from the nucleus than the core
electrons.
- throughout the 3d series (and even more in 4d series), d-electrons
do have an itinerant character, giving rise to quasiparticle bands!
- electron correlations do have important physical effects, but not
extreme ones like localization.
. – p.10/45
11. Examples of strongly correlated materials
f-electrons: rare earths, actinides and their compounds:
- rare-earth 4f-electrons tend to be localized than itinerant,
contribute little to cohesive energy, other e- bands cross EF , hence
the metallic character.
- actinide (5f) display behavior intermediate between TM and rare
earths
- e- correln becomes more apparent in compounds involving
rare-earth or actinides.
- extremely large effective mass → heavy fermion behavior.
- At high temp local mag. mom and Curie law, low-temp screening
of the local moment and Pauli form → Kondo effect
. – p.11/45
12. Examples of strongly correlated materials - TMO
- direct overlap between d-orbitals small, can only move through
hybridization!
4
t2g
eg
10
2
2
4
2
2
2
d x2−y2
d 3z2−r2
2
2
2
d xy
d zx
d yz
Free Atom Cubic Tetragonal Orthorhombic
6
Crystal Field Splitting
. – p.12/45
13. Examples of strongly correlated materials- TMO
p σ
p π
2g
t
ge
d x2−y2 d x2−y2d x2−y2
d xy d xy
Ligands (orbitals p/O)
Hybridization via the
d xy d xz d yz
d 3z2−r2 d x2−y2
. – p.13/45
14. Examples of strongly correlated materials - TMO
Three crucial Energies
tpd Metal-ligand Hybridization
∆ = ǫd − ǫp Charge Transfer Energy
U On-site Coulomb Repulsion
Band-width is controlled by: teff = t2
pd/∆
. – p.14/45
15. Examples of strongly correlated materials - TMO
The infamous Hubbard U
Naively: φ∗
i↑φi↑
1
|r−r′|φ∗
i↓φi↓
But this is HUGE (10 -20 eV)!
SCREENING plays a key role, in particular by 4s electrons
- Light TMOs (left of V): p-level much below d-level; 4s close by : U
not so big U < ∆
- Heavy TMOs (right of V): p-level much closer; 4s much above
d-level : U is very big U > ∆ . – p.15/45
16. Examples of strongly correlated materials - TMO
The Mott phenomenon: turning a half-filled band into an insulator
Consider the simpler case first: U < ∆
Moving an electron requires creating a hole and a double
occupancy: ENERGY COST U
This object, once created, can move with a kinetic energy of order of
the bandwidth W!
U < W: A METALLIC STATE IS POSSIBLE
U > W: AN INSULATING STATE IS PREFERRED
. – p.16/45
17. Hubbard bands
d p∆ = | ε − ε |
Energy
p band
d band
U
Interaction U
The composite excitation hole+double occupancy forms a band (cf
excitonic band)
. – p.17/45
18. Charge transfer insulators
d p∆ = | ε − ε |
t
pd
t
eff
t
pdGain: ~ / ∆
2
Cost: ∆ = ε − ε
d p
Energy
d band
Heavy TMOs
p band
Fermi level
Interaction U
charge gap
Transition for ∆ >
Zaanen, Sawatzky, Allen; Fujimori and Minami
U
. – p.18/45
19. Methods
Strongly correlated Metal
LDA gives correct answer
U < W
Weakly correlated Metal
Intermediate regime − Hubbard bands +
QS peak (reminder of LDA metal)
?
U >> W
Mott insulator
Can be described
by "LDA+U" method
courtesy: K. Held
. – p.19/45
20. Methods
LDA gives correct answer
U < W
Weakly correlated Metal
U >> W
Mott insulator
Can be described
by "LDA+U" method
. – p.20/45
21. Basic Idea of LDA+U
PRB 44 (1991) 943, PRB 48 (1993) 169
• Delocalized s and p electrons: LDA
• Localized d or f-electrons: + U
using on-site d-d Coulomb interaction (Hubbard-like term)
U i=j ninj
instead of averaged Coulomb energy
U N(N-1)/2
. – p.21/45
22. n+1 n−1
n n
n+1 n−1
U
e
Hubbard U for localized d orbital:
U = E(d ) + E(d ) − 2 E(d )
n
. – p.22/45
23. LDA+U energy functional (Static Mean Field Theory):
ELDA+U
local = ELDA
−UN(N − 1)/2 +
1
2
U
i=j
ninj
LDA+U potential :
Vi(ˆr) =
δE
δni(ˆr)
= V LDA
(ˆr) + U(
1
2
− ni)
. – p.23/45
24. LDA+U eigenvalue :
ǫi =
δE
δni
= ǫLDA
i + U(
1
2
− ni)
For occupied state ni = 1 → ǫi = ǫLDA
− U/2
For unoccupied state ni = 0 → ǫi = ǫLDA
+ U/2
⇓
∆ǫi = U MOTT-HUBBARD GAP
U = δ
δnd
LDAε
ε
LDA
. – p.24/45
28. Rotationally Invariant LDA+U
LDA+U functional:
ELSDA+U
[ρσ
(r), {nσ
}] = ELSDA
[ρσ
(r)] + EU
[{nσ
}] − Edc[{nσ
}]
Screened Coulomb Correlations:
EU
[{nσ
}] =
1
2
{m},σ
{ m, m
′′
|Ve,e|m
′
, m
′′′
nσ
mm′ n−σ
m′′
m′′′′ +
( m, m
′′
|Ve,e|m
′
, m
′′′
− m, m
′′
|Ve,e|m
′′′
, m
′
nσ
mm′ nσ
m′′
m′′′′
LDA-double counting term:
Edc[{nσ
}] =
1
2
Un(n − 1) −
1
2
J[n↑
(n↑
− 1) + n↓
(n↓
− 1)]
. – p.28/45
29. Slater parametrization of U
Multipole expansion:
1
|r − r′
|
=
kq
4π
2k + 1
rk
<
rk+1
>
Y ∗
kq(ˆr)Ykq(ˆr
′
)
Coulomb Matrix Elements in Ylm basis:
mm
′
||m
′′
m
′′′
=
k
ak(m, m
′′
, m
′
, m
′′′
)Fk
Fk
→ Slater integrals
Average interaction: U and J
U = F0
; J (for d electrons) = 1
14 (F2
+ F4
)
. – p.29/45
32. How to calculate U and J
PRB 39 (1989) 9028
• Constrained DFT + Super-cell calculation
• Calculate the energy surface as a function of local charge
fluctuations.
• Mapped onto a self-consistent mean-filed solution of the
Hubbard model.
• Extract U and J from band structure results.
. – p.32/45
33. Notes on calculation of U
• Constrained DFT works in the fully localized limit. Therefore
often overestimates the magnitude of U.
• For the same element, U depends also on the ionicity in different
compounds → higher the ionicity, larger the U.
• One thus varies U in the reasonable range (Comparison with
photoemission..).
Better or more recent approach: Constrained RPA method
See e.g.
http://icts.res.in/media/uploads/Talk/Document/AryasetiawancRPA.pdf
for details.
. – p.33/45
34. Where to find U and J
PRB 44 (1991) 943 : 3d atoms
PRB 50 (1994) 16861 : 3d, 4d, 5d atoms
PRB 58 (1998) 1201 : 3d atoms
PRB 44 (1991) 13319 : Fe(3d)
PRB 54 (1996) 4387 : Fe(3d)
PRL 80 (1998) 4305 : Cr(3d)
PRB 58 (1998) 9752 : Yb(4f)
. – p.34/45
35. CO and Insulating state in CaFeO3,
La1/3Sr2/3FeO3
TSD, Z. S. Popovic, S. Satpathy
Phys. Rev. B 72, 045143
. – p.35/45
36. CaFeO3
2g
13
g
JT Instability
(cf: LaMnO )3
Charge Disproportionation
Mn−O covalency Fe−O covalency
Whangbo et al, Inorg Chem (2002)
Fe 4+ (t e ) HIGH SPIN STATE
CaFeO3 Ca
O 2−
2+ Fe 4+
Unusual high valence state of Fe
NOMINAL VALENCE CONSIDERATION:
. – p.36/45
42. La1/3Sr2/3FeO3
2+
3
La Sr FeO
1/3 2/3
Sr
O 2−
La 3+
Fe 3.67+
z
yx
NOMINAL VALENCE CONSIDERATION:
3 x Fe 3.67+
2 x Fe 3+ + 1 x Fe 5+
2 x Fe 4+ + 1 x Fe 3+
(AFM Insulating)(PM Metallic)
T
direction
[111] pseudo−cubicFeB
CDW of 3−fold periodicity
+ SDW of 6−fold periodicity
Neutron Diffraction (Battle et a.’90):
No sign of structural modulation
Electron Diffraction (Li et al, ’97):
Evidence of structural modulation
FeA
[Mossbauer data, Takano et. al.]
. – p.42/45
45. Summary
∗ Charge disproportionation in CaFeO3, driven by lattice distortion.
Insulating property needs the assistence from correlation.
∗ Charge disproportionation and insulating state in La1/2Sr2/3FeO3
driven by correlation, magnetism and disorder.
∗ Lattice of La1/2Sr2/3FeO3 reacts to the charge modulation.
. – p.45/45