This document summarizes methods available in the WIEN2k software for treating exchange and correlation effects beyond semilocal density functional theory. It discusses the semilocal generalized gradient approximation and meta-GGA functionals, the modified Becke-Johnson potential for improving band gaps, dispersion correction methods, and on-site corrections like DFT+U and hybrid functionals for strongly correlated materials. Input parameters and keywords for selecting these methods in the WIEN2k code are also outlined.
This is a series of slides prepared by Heather Kulik (http://www.stanford.edu/~hkulik or email hkulik at stanford dot edu) for a talk given at the University of Pennsylvania in February 2012. It covers a basic introduction to DFT+U and related approaches for improving descriptions of transition metals and other systems with localized electrons.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
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
This is a series of slides prepared by Heather Kulik (http://www.stanford.edu/~hkulik or email hkulik at stanford dot edu) for a talk given at the University of Pennsylvania in February 2012. It covers a basic introduction to DFT+U and related approaches for improving descriptions of transition metals and other systems with localized electrons.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
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
(If visualization is slow, please try downloading the file.)
Part 2 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
(If visualization is slow, please try downloading the file.)
Part 1 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
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.
Lecture 8: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
In this talk I will discuss different approximations in DFT: pseduo-potentials, exchange correlation functions.
The presentation can be downloaded here:
http://www.attaccalite.com/wp-content/uploads/2022/03/dft_approximations.odp
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
In computational physics and Quantum chemistry, the Hartree–Fock (HF) method also known as self consistent method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system or many electron system in a stationary state
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.
Some "accumulated wisdom" from several years of using the Vienna ab initio Simulation Package (VASP) code for computational modelling. Includes tips on convergence and parallelisation.
An updated tutorial on using Wannier90 with the VASP code for electronic-structure calculations. Includes tips on how to build VASP with Wannier90 support, how to use the VASP-to-Wannier90 interface, and a worked example of calculating the electronic band structure and density of states of SnS2 using the PBE and HSE06 functionals and the GW routines.
Quantum chemical molecular dynamics simulations of graphene hydrogenationStephan Irle
Chemical adsorption of hydrogen atoms on graphite
surfaces has attracted considerable interest due to its
relevance for a broad range of areas including
plasma/fusion physics, gap tuning in graphene, and hydrogen storage. We adjusted the C-H repulsive potential of the spin-polarized self-consistent-charge density-functional tight-binding (sSCC-DFTB) method to reproduce
CCSD(T)-based relaxed potential energy curves for the
attack of atomic hydrogen on a center carbon atom of
pyrene and coronene at a tiny fraction of the computational
cost. Using this cheap quantum chemical potential, we performed direct on-the-fly Born-Oppenheimer
MD simulations while “shooting” H atoms with varying collision energies on a periodic graphene target
equilibrated at 300 Kelvin. We compared reaction cross sections for a) elastic collisions, b)
chemisorption reactions, c) penetration reactions in dependence of H/D/T kinetic energies, and found
remarkable differences to previously reported classical MD simulations of the same process. Using the
same potential, in simulations involving the shooting of up to 400 hydrogen atoms on the graphene sheet,
we observed the self-assembly of C4H, a novel polymer with localized aromatic hexagons, in agreement
with recent experimental findings.
Dielectrics in a time-dependent electric field: density-polarization functi...Claudio Attaccalite
In presence of a time-dependent macroscopic electric field the electron dynamics of dielectrics cannot be described by the time-dependent density only. We present a real-time formalism that has the density and the macroscopic polarization P as key quantities. We show that a simple local function of P already captures long-range correlation in linear and non-linear optical response functions.
(If visualization is slow, please try downloading the file.)
Part 2 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
(If visualization is slow, please try downloading the file.)
Part 1 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
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.
Lecture 8: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
In this talk I will discuss different approximations in DFT: pseduo-potentials, exchange correlation functions.
The presentation can be downloaded here:
http://www.attaccalite.com/wp-content/uploads/2022/03/dft_approximations.odp
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
In computational physics and Quantum chemistry, the Hartree–Fock (HF) method also known as self consistent method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system or many electron system in a stationary state
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.
Some "accumulated wisdom" from several years of using the Vienna ab initio Simulation Package (VASP) code for computational modelling. Includes tips on convergence and parallelisation.
An updated tutorial on using Wannier90 with the VASP code for electronic-structure calculations. Includes tips on how to build VASP with Wannier90 support, how to use the VASP-to-Wannier90 interface, and a worked example of calculating the electronic band structure and density of states of SnS2 using the PBE and HSE06 functionals and the GW routines.
Quantum chemical molecular dynamics simulations of graphene hydrogenationStephan Irle
Chemical adsorption of hydrogen atoms on graphite
surfaces has attracted considerable interest due to its
relevance for a broad range of areas including
plasma/fusion physics, gap tuning in graphene, and hydrogen storage. We adjusted the C-H repulsive potential of the spin-polarized self-consistent-charge density-functional tight-binding (sSCC-DFTB) method to reproduce
CCSD(T)-based relaxed potential energy curves for the
attack of atomic hydrogen on a center carbon atom of
pyrene and coronene at a tiny fraction of the computational
cost. Using this cheap quantum chemical potential, we performed direct on-the-fly Born-Oppenheimer
MD simulations while “shooting” H atoms with varying collision energies on a periodic graphene target
equilibrated at 300 Kelvin. We compared reaction cross sections for a) elastic collisions, b)
chemisorption reactions, c) penetration reactions in dependence of H/D/T kinetic energies, and found
remarkable differences to previously reported classical MD simulations of the same process. Using the
same potential, in simulations involving the shooting of up to 400 hydrogen atoms on the graphene sheet,
we observed the self-assembly of C4H, a novel polymer with localized aromatic hexagons, in agreement
with recent experimental findings.
Dielectrics in a time-dependent electric field: density-polarization functi...Claudio Attaccalite
In presence of a time-dependent macroscopic electric field the electron dynamics of dielectrics cannot be described by the time-dependent density only. We present a real-time formalism that has the density and the macroscopic polarization P as key quantities. We show that a simple local function of P already captures long-range correlation in linear and non-linear optical response functions.
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.
We approach the screening problem - i.e. detecting which inputs of a computer model significantly impact the output - from a formal Bayesian model selection point of view. That is, we place a Gaussian process prior on the computer model and consider the $2^p$ models that result from assuming that each of the subsets of the $p$ inputs affect the response. The goal is to obtain the posterior probabilities of each of these models. In this talk, we focus on the specification of objective priors on the model-specific parameters and on convenient ways to compute the associated marginal likelihoods. These two problems that normally are seen as unrelated, have challenging connections since the priors proposed in the literature are specifically designed to have posterior modes in the boundary of the parameter space, hence precluding the application of approximate integration techniques based on e.g. Laplace approximations. We explore several ways of circumventing this difficulty, comparing different methodologies with synthetic examples taken from the literature.
Authors: Gonzalo Garcia-Donato (Universidad de Castilla-La Mancha) and Rui Paulo (Universidade de Lisboa)
The driving engine for the exponential growth of digital information processing systems is scaling down the transistor dimensions. For decades, this has enhanced the device performance and density. However, the International Technology Roadmap for Semiconductors (ITRS) states the end of Moore’s law in the next decade due to the scaling challenges of silicon-based CMOS electronics, e.g. extremely high power density. The forward-looking solutions are the utilization of emerging materials and devices for integrated circuits, e.g. carbon-based materials. The presentation of my Ph.D. work focuses on graphene, one atomic layer of carbon sheet, experimentally discovered in 2004. Since fabrication technology of emerging materials is still in early stages, transistor modeling has been playing an important role for evaluating futuristic graphene-based devices and circuits. The device has been simulated by solving a quantum transport model based on non-equilibrium Green’s function (NEGF) approach, which fully treats short channel-length electrostatic effects and the quantum tunneling effects, leading to the technology exploration of graphene nanoribbon field effect transistors (GNR FETs) for the future. This research presents a comprehensive study of the width-dependence performance of the GNR FETs and the scaling of its channel length down to 2.5 nanometer, investigating its potential use beyond-CMOS emerging technology.
From Atomistic to Coarse Grain Systems - Procedures & MethodsFrank Roemer
The physical and mathematical basis as well as the historical background of the most popular coarse graining methods (Reverse/Inverse Monte-Carlo, Iterative Boltzmann Inversion and Force Matching method) in the field of fluids and soft matter are presented here. In terms of lengths and time scale, I refer here to the classical coarse grain systems, which are in between the atomistic and mesoscale systems. The focus is on the path to derive the coarse grain force fields from reference data obtained from atomistic simulations.
NANO281 is the University of California San Diego NanoEngineering Department's first course on the application of data science in materials science. It is taught by Professor Shyue Ping Ong of the Materials Virtual Lab (http://www.materialsvirtuallab.org).
Lecture: Interatomic Potentials Enabled by Machine LearningDanielSchwalbeKoda
Lecture for the 4th IKZ-FairMAT Winter School. Describes recent advances in neural network interatomic potentials, deep learning models accelerating quantum chemistry, and more.
Similar to Methods available in WIEN2k for the treatment of exchange and correlation effects (20)
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Methods available in WIEN2k for the treatment of exchange and correlation effects
1. Methods available in WIEN2k for the treatment
of exchange and correlation effects
F. Tran
Institute of Materials Chemistry
Vienna University of Technology, A-1060 Vienna, Austria
23rd WIEN2k workshop, 4-7 June2016, McMaster University,
Hamilton, Canada
I
W
E
N
2k
2. Outline of the talk
◮ Introduction
◮ Semilocal functionals:
◮ GGA and MGGA
◮ mBJ potential (for band gap)
◮ Input file case.in0
◮ The DFT-D3 method for dispersion
◮ On-site methods for strongly correlated electrons:
◮ DFT+U
◮ Hybrid functionals
◮ Hybrid functionals
◮ GW
3. Total energy in Kohn-Sham DFT 1
Et ot =
1
2
.
i
¸
i
s x¸
T
¸
s
2 3
|∇ψ (r)| d r +
2
1
¸ ¸
ρ(r)ρ(r′
) 3 3 ′
s
|r − r′|
d rd r +
¸
en
3
v (r)ρ(r)d r
x s x
E
¸
e
¸
e E
¸
e
¸
n
A,B
Aƒ=
B
2 |RA − RB|
s x
E
¸
n
¸
n
+
1 . ZAZB
+Exc
◮ Ts : kinetic energy of the non-interacting electrons
◮ Eee : electron-electron electrostatic Coulomb energy
◮ Een : electron-nucleus electrostatic Coulomb energy
◮ Enn : nucleus-nucleus electrostatic Coulomb energy
◮ Exc = Ex + Ec : exchange-correlation energy
Approximations for Exc have to be used in practice
=⇒ The reliability of the results depends mainly on Exc!
1
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965)
4. Approximations for Exc (Jacob’s ladder 1)
Exc =
¸
ǫxc (r)d 3r
The accuracy, but also the computational cost, increase when climbing up the ladder
1
J. P. Perdew et al., J. Chem. Phys. 123, 062201 (2005)
5. The Kohn-Sham Schr¨odinger equations
Minimization of Etot leads to
.
1
.
− ∇2 + vee(r) + ven(r) + vˆxc(r) ψi(r) = ǫiψi(r)
2
Two types of vˆxc:
◮ Multiplicative: vˆxc = δExc/δρ = vxc (KS method)
◮ LDA
◮ GGA
i ,◮ Non-multiplicative: vˆxc = (1/ψi )δExc/δψ∗ = vxc i (generalized KS)
◮ Hartree-Fock
◮ LDA+U
◮ Hybrid (mixing of GGA and Hartree-Fock)
◮ MGGA
◮ Self-interaction corrected (Perdew-Zunger)
6. Semilocal functionals: trends with GGA
ǫGGA
xc
LDA(ρ, ∇ρ)= ǫx (ρ)Fxc(rs,s)
where Fxc is the enhancement factorand
rs =
1
. 4
3πρ
.1/3
(Wigner-Seitz radius)
s=
|∇ρ|
2(3π2)1/3
ρ4/3
(inhomogeneity parameter)
There are two types of GGA:
◮ Semi-empirical: contain parametersfitted to accurate (i.e.,
experimental) data.
◮ Ab initio: All parametersweredetermined byusing
mathematical conditions obeyed by the exact functional.
7. Semilocal functionals: GGA
Fx(s) = ǫGGA/ǫLDA
x x
0 0.5 3
0.9
1
1.4
1.3
1.2
1.1
1.5
1.6
1.7
1.8
1 1.5 2 2.5
inhomogeneity parameter s
Fx
LDA
PBEsol
PBE
B88
good for atomization energy of molecules
good for atomization energy of solids
good for lattice constant of solids
good for nothing
8. Construction of an universal GGA: A failure
Test of functionals on 44 solids1
0 2
0
4
6
8
PBEsol
WC
RGE2 PBE
PBEint
PBEalpha
SG4
0.5 1 1.5
Mean absolute percentage error for latticeconstant
Meanabsolutepercentageerrorforcohesiveenergy
2
The accurate GGA for solids (cohesive energy/lattice constant).
They are ALL very inaccurate for the atomization of molecules
1
F. Tran et al., J. Chem. Phys. 144, 204120 (2016)
9. Semilocal functionals: meta-GGA
ǫMGGA
xc
LDA(ρ, ∇ρ, t) = ǫxc (ρ)Fxc(rs,s,α)
where Fxc is the enhancement factorand
◮ α= t−tW
t T F
◮ α= 1 where the electron density is uniform
◮ α= 0 in one- and two-electron regions
◮ α≫1between closed shell atoms
=⇒ MGGA functionals are more flexible
Example: SCAN1 is
◮ as good as the best GGA for atomization energies of molecules
◮ as good as the best GGA for lattice constant of solids
1
J. Sun et al., Phys. Rev. Lett. 115, 036402 (2015)
10. Semilocal functionals: meta-GGA
0 0.5 2.5 3
1.2
1.1
1
0.9
1.3
1.4
1.5
1 1.5 2
inhomogeneity parameter s
Fx
Fx(s,α) = ǫMGGA/ǫLDA
x x
1.6
LDA
PBE
PBEsol
SCAN (=0)
SCAN (=1)
SCAN (=5)
11. Semilocal functionals: MGGA MS2 andSCAN
Test of functionals on 44 solids1
0
0
2
4
6
8
PBEsol
WC
PBEint
PBEalpha
RGE2 PBE
SG4
MGGA_MS2
SCAN
Meanabsolutepercentageerrorforcohesiveenergy
The accurate GGA for solids (cohesive energy/lattice constant).
They are ALL very inaccurate for the atomization of molecules
MGGA_MS2 and SCAN are very accurate for the atomization of molecules
0.5 1 1.5 2
Mean absolute percentage error for latticeconstant
1
F. Tran et al., J. Chem. Phys. 144, 204120 (2016)
12. Semilocal potential for band gap: modified Becke-Johnson
◮ Standard LDA and GGA functionals underestimate the band gap
◮ Hybrid and GWaremuchmoreaccurate, but also muchmore
expensive
◮ A cheapalternative is to usethe modified Becke-Johnson(mBJ)
potential: 1
vmBJ
x
BR(r) = cvx (r) + (3c − 2)
1
. .
5 t(r)
π 6 ρ(r)
xwherev BR is the Becke-Roussel potential, t is the kinetic-energy
density and c is given by
c = α+ β
V
cell
¸
cell
1 |∇ρ(r)|
ρ(r)
3
d r
p
mBJ is a MGGA potential
1
F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)
14. How to run a calculation with the mBJ potential?
1. init lapw (choose LDA or PBE)
2. init mbj lapw (create/modify files)
1. automatically done: case.in0modified and case.inm vresp
created
2. run(sp) lapw -i 1 -NI (creates case.r2v and case.vrespsum)
3. save lapw
3. init mbj lapw and chooseoneof the
parametrizations: 0: Original mBJ values1
1: New parametrization2
2: New parametrization for semiconductors2
3: Original BJ potential3
4. run(sp) lapw ...
1
F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)
2
D. Koller et al., Phys. Rev. B 85, 155109 (2012)
3
A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 (2006)
15. Input file case.in0: keywords for the xc-functional
The functional is specifiedat the 1st line of case.in0.Three different
ways:
1. Specifya global keyword for Ex, Ec, vx, vc:
◮ TOT XC NAME
2. Specify a keyword for Ex, Ec, vx, vc individually:
◮ TOT EX NAME1 EC NAME2 VX NAME3 VCNAME4
3. Specify keywords to use functionals from LIBXC1:
◮ TOT XC TYPE X NAME1 XC TYPE C NAME2
◮ TOT XC TYPE XC NAME
where TYPE is the family name: LDA, GGA or MGGA
1
M. A. L. Marques et al., Comput. Phys. Commun. 183, 2272 (2012)
http://www.tddft.org/programs/octopus/wiki/index.php/Libxc
16. Input file case.in0: examples with keywords
◮ PBE:
TOT XC PBE
or
TOT EX PBE EC PBE VX PBE VCPBE
or
TOT XC GGA X PBE XC GGA C PBE
◮ mBJ (with LDA for the xc-energy):
TOT XC MBJ
◮ MGGA MS2:
TOT XC MGGA MS 0.504 0.14601 4.0
s x
κ
¸
,c
¸
,b
All available functionals are listed in tables of the UG. and in
$WIENROOT/SRC lapw0/xc funcs.h for LIBXC (if installed)
17. Dispersion methods for DFT
Problem with semilocal functionals:
◮ They do not include London dispersion interactions
◮ Resultsarequalitatively wrong for systemswhere dispersion
plays a majorrole
Two common dispersion methodsfor DFT:
◮ Pairwise term1:
EPW
c,disp = −
. .
A<B n=6,8,10,...
dampfn (RAB )
CAB
n
Rn
AB
◮ Nonlocal term2:
ENL
c,disp
2
1
¸ ¸
= ρ(r)φ(r, r′)ρ(r′)d3rd3r′
1
S. Grimme, J. Comput. Chem. 25, 1463 (2004)
2
M. Dion et al., Phys. Rev. Lett. 92, 246401 (2004)
18. The DFT-D3 method1 in WIEN2k
◮ Features of DFT-D3:
◮ Very cheap (pairwise)
◮ CAB
n depend on positions of the nuclei (via coordination
number)
◮ Functional-dependent parameters
◮ Energy and forces (minimization of internal parameters)
◮ 3-body term
◮ Installation:
◮ Not included in WIEN2k
◮ Download and compile the DFTD3 packagefrom
http://www.thch.uni-bonn.de/tc/index.php
copy the dftd3 executable in $WIENROOT
◮ input file case.indftd3 (if not present a default one is copied
automatically)
◮ run(sp) lapw -dftd3 . . .
◮ case.scfdftd3 is included in case.scf
1
S. Grimme et al., J. Chem. Phys. 132, 154104 (2010)
19. The DFT-D3 method: the input file case.indftd3
Default (and recommended) input file:
damping function f damp
n
the one in case.in0∗
forces
method
func
grad
pbc
abc
cutoff
cnthr
num
bj
def ault
yes
yes
yes
95
40
no
periodic boundary conditions
3-body term
interaction cutoff
coordination number cutoff
numerical gradient
∗default will work for PBE, PBEsol, BLYP and TPSS. For other
functionals, the functional namehasto bespecified(seedftd3.f of
DFTD3 package)
21. Strongly correlated electrons
Problem with semilocal functionals:
◮ They give qualitatively wrong results for solids which contain
localized 3d or 4f electrons
◮ The band gap is too small or even absent like in FeO
◮ The magnetic moments are too small
◮ Wrong ground state
Why?
◮ The strong on-site correlations arenot correctly accountedfor by
semilocal functionals.
(Partial) solution to the problem:
◮ Combine semilocal functionals with Hartree-Fock theory:
◮ DFT+U
◮ Hybrid
Even better:
◮ LDA+DMFT (DMFT codesusing WIEN2k orbitals asinput
exist)
22. On-site DFT+U and hybrid methods in WIEN2k
◮ Forsolids,the hybrid functionals arecomputationally very
expensive.
◮ In WIEN2k the on-site DFT+U 1 and on-site hybrid2,3
methods areavailable. Thesemethodsareapproximations of the
Hartree-Fock/hybrid methods
◮ Applied only inside atomic spheresof selectedatomsand
electrons of a given angular momentum ℓ.
On-site methods → As cheap as LDA/GGA.
1
V. I. Anisimov et al., Phys. Rev. B 44, 943 (1991)
2
P. Nov´ak et al., Phys. Stat. Sol. (b) 243, 563 (2006)
3
F. Tran et al., Phys. Rev. B 74, 155108 (2006)
23. DFT+U and hybrid exchange-correlation functionals
The exchange-correlation functional is
xc
EDFT+ U/hybrid DFT onsite= Exc [ρ] + E [nmm′ ]
where nmm′ is the density matrix of the correlated electrons
◮ For DFT+U both exchange and Coulomb are corrected:
Eonsite = EHF DFT DFT
x + ECoul −Ex −ECoul
s
corr
¸
ec
¸
tion
x s
double
¸
c
¸
ounting
x
There are several versions of the double-counting term
◮ For the hybrid methods only exchange is corrected:
Eonsite = αEHF − αELDA
x
d
s
.c
¸
o
¸
unt
x
.
x
s
c
¸
or
¸
r.
x
where αis a parameter ∈ [0,1]
24. How to run DFT+U and on-site hybrid calculations?
1. Create the input files:
◮ case.inorb and case.indm for DFT+U
◮ case.ineecefor on-site hybrid functionals (case.indm created
automatically):
2. Run the job (can only be run with runsp lapw):
◮ LDA+U : runsp lapw -orb . . .
◮ Hybrid: runsp lapw -eece . ..
Foracalculation without spin-polarization (ρ↑ = ρ↓):
runsp c lapw -orb/eece . ..
25. Input file case.inorb
LDA+U applied to the 4f electrons of atomsNo. 2 and 4:
1 2 0
PRATT, 1. 0
2 1 3
4 1 3
1
0.61 0.07
0.61 0.07
nmod, natorb, i p r
mixmod, amix
iatom, nlorb, lorb
iatom, nlorb, lorb
nsic (LDA+U(SIC) used)
U J (Ry)
U J (Ry)
nsic=0 for the AMF method (lessstrongly correlated electrons)
nsic=1 for the SIC method
nsic=2 for the HMF method
26. Input file case.ineece
On-site hybrid functional PBE0applied to the 4f electrons of
atomsNo. 2 and 4:
-12.0 2
2 1 3
4 1 3
HYBR
0.25
emin, natorb
iatom, nlorb, lorb
iatom, nlorb, lorb
HYBR/EECE
fraction of exact exchange
27. SCF cycle of DFT+U in WIEN2k
lapw0 xc,σ ee en→ v D F T
+ v + v (case.vspup(dn), case.vnsup(dn))
orb -up mm′→ v↑
(case.vorbup)
orb -dn mm′→ v↓
(case.vorbdn)
lapw1 -up -orb nk nk
→ ψ↑
, ǫ↑
(case.vectorup, case.energyup)
lapw1 -dn -orb nk nk
→ ψ↓
, ǫ↓
(case.vectordn, case.energydn)
lapw2 -up va l
→ ρ↑
(case.clmvalup)
lapw2 -dn va l
→ ρ↓
(case.clmvaldn)
lapwdm -up mm′
lapwdm -dn mm′
→ n↑
(case.dmatup)
→ n↓
(case.dmatdn)
lcore -up core
lcore -dn core
→ ρ↑
(case.clmcorup)
→ ρ↓
(case.clmcordn)
mixer σ→ mixed ρ and nσ
mm′
28. Hybrid functionals
◮ On-site hybrid functionals can be applied only to localized electrons
◮ Full hybrid functionals are necessary (but expensive) for solids with
delocalized electrons (e.g., in sp-semiconductors)
Two types of full hybrid functionals available in WIEN2k1:
◮ unscreened:
Exc = EDFT
xc
HF DFT+ α
.
Ex −Ex
.
− λ |r− r′|
|r−r′| |r−r′|
◮ screened (short-range), 1 → e :
Exc = EDFT
xc
SR−HF SR−DFT+ α
.
Ex −Ex
.
screening leads to faster convergence with k-points sampling
1
F. Tran and P. Blaha, Phys. Rev. B 83, 235118 (2011)
29. Hybrid functionals: technical details
◮ 10-1000 times more expensive than LDA/GGA
◮ k-point and MPI parallelization
◮ Approximations to speed up the calculations:
◮ Reduced k-meshfor the HF potential. Example:
For a calculation with a 12× 12× 12 k-mesh, thereduced
k-meshfor the HF potential can be:
6× 6× 6, 4 × 4× 4, 3 × 3× 3, 2× 2 × 2 or 1× 1× 1
◮ Non-self-consistent calculation of the band structure
◮ Underlying functionals for unscreened and screend hybrid:
◮ LDA
◮ PBE
◮ WC
◮ PBEsol
◮ B3PW91
◮ B3LYP
◮ Use run bandplothf lapw for band structure
30. Hybrid functionals: input file case.inhf
Example for YS-PBE0 (similar to HSE06 from Heyd, Scuseria and Ernzerhof1
)
0.25
T
0. 165
20
6
3
3
1d-3
fraction α of HF exchange
screened (T, YS-PBE0) or unscreened ( F , PBE0)
screening parameter λ
number of bands for the 2nd Hamiltonian
GMAX
lmax for the expansion of o r b i t a l s
lmax for the product of two o r b i t a l s
r a d i a l i n t e g r a l s below t h i s value neglected
Important: The computational time will dependstrongly on the
number of bands, GMAX, lmax and the number of k-points
1
A. V. Krukau et al., J. Chem. Phys. 125, 224106 (2006)
31. How to run hybrid functionals?
1. init lapw
2. Recommended: run(sp) lapw for the semilocal functional
3. save lapw
4. init hf lapw (this will create/modify input files)
1. adjust case.inhf according to your needs
2. reduced k-meshfor the HF potential? Yes or no
3. specify the k-mesh
5. run(sp) lapw -hf (-redklist) (-diaghf) ...
32. SCF cycle of hybrid functionals in WIEN2k
lapw0 -grr → v DFT (case.r2v), αEDFT (:AEXSL)
x x
lapw0 xc
→ vDFT + vee + ven (case.vsp, case.vns)
lapw1 nk nk
→ ψDFT, ǫDFT (case.vector,case.energy)
lapw2 nk
→
.
n k ǫDFT (:SLSUM)
hf
lapw2 -hf
→ ψnk, ǫnk (case.vectorhf, case.energyhf)
→ ρval (case.clmval)
lcore
mixer
→ ρcore (case.clmcor)
→ mixed ρ
33. Calculation of quasiparticle spectra from many-body theory
◮ In principle the Kohn-Shameigenvalues should beviewed as
mathematical objects and not compareddirectly to experiment
(ionization potential and electron affinity).
◮ The true addition and removal energiesǫiarecalculated from the
equation of motion for the Green function:
2
¸ , ¸
1
− ∇2
+ ven(r) + vH(r) + Σ(r, r′
, ǫi)ψi(r′
)d3
r′
= ǫiψi (r)
◮ The self-energy Σ is calculated from Hedin’s self-consistent
equations1:
Σ(1, 2) = i
¸
G(1, 4)W (1+
, 3)Γ(4, 2, 3)d(3, 4)
W (1, 2) = v(1, 2) +
¸
v(4, 2)P(3, 4)W (1, 3)d(3, 4)
P(1, 2) = −i
¸
G(2, 3)G(4, 2)Γ(3, 4, 1)d(3, 4)
δG(4,5)
Γ(1, 2, 3) = δ(1, 2)δ(1, 3) +
¸ δΣ(1, 2)
G(4, 6)G(7, 5)Γ(6, 7, 3)d(4, 5, 6, 7)
1
L. Hedin, Phys. Rev. 139, A769 (1965)
34. The GW and G0W0 approximations
◮ GW: vertex function Γ in Σ set to 1:
Σ(1, 2) = i
¸
G(1, 4)W (1+, 3)Γ(4, 2,3)d(3, 4) ≈ iG(1, 2+)W (1, 2)
2π
∞
− ∞
Σ(r, r′, ω)=
i
¸
G(r, r′, ω+ ω′)W(r, r′, ω′)e−iδω′
dω′
′
G(r, r ,ω) =
∞
. i i
∗ ′ψ(r)ψ (r )
i=1
ω− ǫi − iηi
W (r, r′, ω) =
¸
v(r, r′′)ǫ−1(r′′, r′, ω)d3r′′
◮ G0W0 (one-shot GW ):
Gand W arecalculated using the Kohn-Shamorbitals and
eigenvalues. 1st order perturbation theory gives
i
ǫGW K S K S K S K S= ǫi + Z (ǫi )(ψi |ℜ(Σ(ǫi
K S)) − vxc|ψi )
35. A few remarks on GW
◮ GW calculations require very large computational ressources
◮ Gand W dependon all (occupied and unoccupied) orbitals (up
to parameter emax in practice)
◮ GWis the state-of-the-art for the calculation of (inverse)
photoemissionspectra, but not for optics sinceexcitonic effects
are still missing in GW (BSE code from R. Laskowski)
◮ GW is more accurate for systems with weak correlations
36. FHI-gap: a LAPW GW code1
◮ Based on the FP-LAPW basis set
◮ Mixed basis set to expand the GW-related quantities
◮ Interfaced with WIEN2k
◮ G0W0, GW0 @LDA/GGA(+U )
◮ Parallelized
◮ http://www.chem.pku.edu.cn/jianghgroup/codes/fhi-gap.html
1
H. Jiang et al., Comput. Phys. Comput. 184, 348 (2013)
38. How to run the FHI-gap code?
1. Run a WIEN2k SCF calculation (in w2kdir)
2. In w2kdir, executethe script gapinit to preparethe input files for
GW:
gap init -d <gwdir> -nkp <nkp> -s 0/1/2 -orb -emax <emax>
3. Eventually modify gwdir.ingw
4. Execute gap.x or gap-mpi.x in gwdir
5. Analyse the results from:
1. gwdir.outgw
2. the plot of the DOS/band structure generated by gap analy
39. Parameters to be converged for a GW calculation
◮ Usual WIEN2k parameters:
◮ Size of the LAPW basis set (RKmax)
◮ Number of k-points for the Brillouin zone integrations
◮ GW-specific parameters:
◮ Size of the mixed basis set
◮ Number of unoccupiedstates (emax)
◮ Number of frequencies ωfor the calculation of Σ =
¸
GWd ω
41. Some recommendations
Before using a method or a functional:
◮ Read a few papers concerning the method in order to know
◮ why it has been used
◮ for which properties or types of solids it is supposedto be
reliable
◮ if it is adapted to your problem
◮ Do you have enough computational ressources?
◮ hybrid functionals and GW require (substantially) more
computational ressources (and patience)