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.
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.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
Magnetization process of the kagome magnetsRyutaro Okuma
First, well known properties of kagome isotropic antiferromagnet are briefly described. Then a unique kagome mineral, synthesized in my lab, whose magnetic interaction is along one direction antiferromagnetic and along other ones ferromagnetic is introduced.The results of exact diagonalization of Heisenberg Hamiltonian of finite sites present a phase diagram of magnetization in magnetic field and coupling ratio plot.Whether or not plateaus and jump will appear in the magnetization process of the material is discussed.
A DFT & TDDFT Study of Hybrid Halide Perovskite Quantum DotsAthanasiosKoliogiorg
Perovskite quantum dots (QDs) constitute a novel and rapidly developing field of nanotechnology with promising potential for optoelectronic applications. However, few perovskite materials for QDs and other nanostructures have been theoretically explored. In this study, we present a wide spectrum of different hybrid halide perovskite cuboid-like QDs with the general formula of FABX3 (A = (NH2)CH(NH2), B = Pb, Sn, Ge, and X = Cl, Br, I) with varying sizes below and near the Bohr exciton radius. Density functional theory (DFT) and time-dependent DFT calculations were employed to determine their structural, electronic, and optical properties. Our calculations include both stoichiometric model, proved to be close to experimental results where available, and our results reveal several materials with high optical absorption and application-suitable electronic and optical gaps. Our study highlights the potential as well as the challenges and issues regarding nanostructured halide perovskite materials, laying the background for future theoretical and experimental work.
Research proposal on organic-inorganic halide perovskite light harvesting mat...Rajan K. Singh
Organic-Inorganic perovskite materials has many applications in the field of opto-electronics such as photo-voltaic cells, LEDs, sensors, memory devices etc. due to its excellent optical and electrical properties. Presence of Pb in such type of perovskite is the biggest challenge for researchers.
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.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
Magnetization process of the kagome magnetsRyutaro Okuma
First, well known properties of kagome isotropic antiferromagnet are briefly described. Then a unique kagome mineral, synthesized in my lab, whose magnetic interaction is along one direction antiferromagnetic and along other ones ferromagnetic is introduced.The results of exact diagonalization of Heisenberg Hamiltonian of finite sites present a phase diagram of magnetization in magnetic field and coupling ratio plot.Whether or not plateaus and jump will appear in the magnetization process of the material is discussed.
A DFT & TDDFT Study of Hybrid Halide Perovskite Quantum DotsAthanasiosKoliogiorg
Perovskite quantum dots (QDs) constitute a novel and rapidly developing field of nanotechnology with promising potential for optoelectronic applications. However, few perovskite materials for QDs and other nanostructures have been theoretically explored. In this study, we present a wide spectrum of different hybrid halide perovskite cuboid-like QDs with the general formula of FABX3 (A = (NH2)CH(NH2), B = Pb, Sn, Ge, and X = Cl, Br, I) with varying sizes below and near the Bohr exciton radius. Density functional theory (DFT) and time-dependent DFT calculations were employed to determine their structural, electronic, and optical properties. Our calculations include both stoichiometric model, proved to be close to experimental results where available, and our results reveal several materials with high optical absorption and application-suitable electronic and optical gaps. Our study highlights the potential as well as the challenges and issues regarding nanostructured halide perovskite materials, laying the background for future theoretical and experimental work.
Research proposal on organic-inorganic halide perovskite light harvesting mat...Rajan K. Singh
Organic-Inorganic perovskite materials has many applications in the field of opto-electronics such as photo-voltaic cells, LEDs, sensors, memory devices etc. due to its excellent optical and electrical properties. Presence of Pb in such type of perovskite is the biggest challenge for researchers.
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.
Computational Discovery of Two-Dimensional Materials, Evaluation of Force-Fie...KAMAL CHOUDHARY
JARVIS (Joint Automated Repository for Various Integrated Simulations) is a repository designed to automate materials discovery using classical force-field, density functional theory, machine learning calculations and experiments.
The Force-field section of JARVIS (JARVIS-FF) consists of thousands of automated LAMMPS based force-field calculations on DFT geometries. Some of the properties included in JARVIS-FF are energetics, elastic constants, surface energies, defect formations energies and phonon frequencies of materials.
The Density functional theory section of JARVIS (JARVIS-DFT) consists of thousands of VASP based calculations for 3D-bulk, single layer (2D), nanowire (1D) and molecular (0D) systems. Most of the calculations are carried out with optB88vDW functional. JARVIS-DFT includes materials data such as: energetics, diffraction pattern, radial distribution function, band-structure, density of states, carrier effective mass, temperature and carrier concentration dependent thermoelectric properties, elastic constants and gamma-point phonons.
The Machine-learning section of JARVIS (JARVIS-ML) consists of machine learning prediction tools, trained on JARVIS-DFT data. Some of the ML-predictions focus on energetics, heat of formation, GGA/METAGGA bandgaps, bulk and shear modulus. The ML webpage is visible to NIST employees only right now, but will be available publicly soon.
Presentation on machine learning and materials science at Computing in Engineering Forum 2018, Machine Ground Interaction Consortium (MaGIC) 2018, Wisconsin, Madison, December 4, 2018
Prof Ong gave a webinar talk on the AI Revolution in Materials Science for the Singapore Agency of Science Technology and Research (A*STAR). In this talk, he discussed the big challenges in materials science where AI can potentially make a huge impact towards addressing as well as outstanding challenges and opportunities to bringing forth the AI revolution to the materials domain.
(PhD Dissertation Defense) Theoretical and Numerical Investigations on Crysta...James D.B. Wang, PhD
(I'm no longer in this academic field, and thus sharing my PhD dissertation slide here to anyone who would be interested in it)
=================================================
In order to prevent the spurious wave reflections and to improve the computational efficiency in nanomechanical simulation, this dissertation performs a series of theoretical/numerical studies on the crystalline nano material, including nanomechanics of monatomic lattice, isothermally non-reflecting boundary condition, fast updating of neighbor list, and the application/simulation in laser-assisted nano-imprinting.
Real-Time Analysis of Streaming Synchotron Data: SCinet SC19 Technology Chall...Globus
This project, which involved streaming light source data from the SC19 show floor to Argonne’s Leadership Computing Facility (ALCF) outside Chicago, won the top prize at the inaugural SCinet Technology Challenge at SC19 in Denver, CO.
ChemNLP: A Natural Language Processing based Library for Materials Chemistry ...KAMAL CHOUDHARY
In this work, we present the ChemNLP library that can be used for 1) curating open access datasets for materials and chemistry literature, developing and comparing traditional machine learning, transformers and graph neural network models for 2) classifying and clustering texts, 3) named entity recognition for large-scale text-mining, 4) abstractive summarization for generating titles of articles from abstracts, 5) text generation for suggesting abstracts from titles, 6) integration with density functional theory dataset for identifying potential candidate materials such as superconductors, and 7) web-interface development for text and reference query. We primarily use the publicly available arXiv and Pubchem datasets but the tools can be used for other datasets as well. Moreover, as new models are developed, they can be easily integrated in the library.
Database of Topological Materials and Spin-orbit SpillageKAMAL CHOUDHARY
We present the results of a high-throughput, first principles search for topological materials based on identifying materials with band inversion induced by spin-orbit coupling. Out of the currently available 30000 materials in our database, we investigate more than 4507 non-magnetic materials having heavy atoms and low bandgaps. We compute the spillage between the spin-orbit and non-spin-orbit wave functions, resulting in more than 1699 high-spillage candidate materials. We demonstrate that in addition to Z2 topological insulators, this screening method successfully identifies many semimetals and topological crystalline insulators. Our approach is applicable to the investigation of disordered or distorted materials, because it is not based on symmetry considerations, and it can be extended to magnetic materials. After our first screening step, we use Wannier-interpolation to calculate the topological invariants and to search for band crossings in our candidate materials. We discuss some individual example materials, as well as trends throughout our dataset, that is available at JARVIS-DFT website: http://jarvis.nist.gov
Computational Database for 3D and 2D materials to accelerate discoveryKAMAL CHOUDHARY
The Density functional theory section of JARVIS (JARVIS-DFT) consists of thousands of VASP based calculations for 3D-bulk, single layer (2D), nanowire (1D) and molecular (0D) systems. Most of the calculations are carried out with optB88vDW functional. JARVIS-DFT includes materials data such as: energetics, diffraction pattern, radial distribution function, band-structure, density of states, carrier effective mass, temperature and carrier concentration dependent thermoelectric properties, elastic constants and gamma-point phonons.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
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Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
block diagram and signal flow graph representation
NIST-JARVIS infrastructure for Improved Materials Design
1. NIST-JARVIS infrastructure for Improved
Materials Design
Kamal Choudhary
https://jarvis.nist.gov/
NIST, Gaithersburg, MD, USA
CECAM workshop, 10/11/2022
1
Joint Automated Repository for Various Integrated Simulations
2. Acknowledgement and Collaboration
2
A. Biacchi
(NIST)
D. Wines
(NIST)
R. Gurunathan
(NIST)
B. DeCost
(NIST)
Bobby sumpter
(ORNL)
A. Agarwal
(Northwestern
University)
S. Kalidindi
(GAtech)
A. Reid
(NIST)
Ruth Pachter
(AFRL)
Karen Sauer
(George
Mason University)
K. Garrity
(NIST)
David Vanderbilt
(Rutgers
University)
Sergei
Kalinin
(ORNL)
F. Tavazza
(NIST)
8. JARVIS-DFT: Electronic structure calculations
• Schrödinger equation for electrons: wave–particle duality,
• Schrödinger equation of a fictitious system (the "Kohn–Sham system") of non-interacting
particles (typically electrons) that generate the same density as any given system of interacting
particles
• Uses density vs wavefunction quantity
• Although a complete theory, several approximations such as:
1) K-points, 2) vdW interactions, 3) kinetic energy deriv., 4) spin-orbit coupling, 5) e-ph coupling
(Convergence, OptB88vdW, TBmBJ, SOC topology, Superconducting prop. )
r
r
E
r
r
V
m
i
i
i
Eff
2
2
2
XC
ee
Ne
Eff V
V
V
T
V
E
H
Walter Kohn (2013)
Exchange-correlation
8
Many DFT databases with GGA-PBE, fixed k-point, no-SOC, …
9. JARVIS-DFT
9
Motivation: Functional and structural materials design using quantum mechanical methods
~70000 materials, millions of calculated properties, compared with experiments if possible
https://jarvis.nist.gov/jarvisdft/
10. JARVIS-DFT MatProj. OQMD
#Materials (Struct., Ef, Eg ) 70870 144595 (41697 common) 1022663
DFT functional/methods vdW-DFT-OptB88, TBmBJ, DFT+SOC GGA-PBE, PBE+U, GLLBSC GGA-PBE, PBE+U
K-point/cut-off Converged for each material Fixed (1000-3000) kp/atom, 520 eV Fixed kp/atom, cutoff
SCF convergence criteria Energy & Forces Energy Energy
Elastic tensors & point phonons 17402 14072 -
Piezoelectric, IR spectra 4801 3402 -
Dielectric tensors (w/o ion) 4801 (15860) 3402 -
Electric field gradients 11865 - -
XANES spectra - 22000 -
2D monolayers 1011 - -
Raman spectra 400 50 -
Seebeck, Power F 23210 48000 -
Solar SLME 8614 - -
Spin-orbit Coupling Spillage 11383 - -
WannierTB 1771 - -
STM images 1432 - -
11. K-point convergence
11
• Energy per cell convergence of 0.001 eV/cell for each material
• Most DFT high-throughput workflows use per reciprocal atom (pra) =>1000
12. vdW interactions: 3D, 2D, 1D & 0D materials
• vdW materials: high lattice error, is converse true?
• Van der Waals (vdW) bonding in x, y, z-directions; exfoliation energy
• If the error => 5%, we predict them to be low-D materials,
• 1100 mats. with OptB88vdW functionals, tight DFT convergence
• Improved lattice parameters with OptB88vdW
ICSD
ICSD
PBE
l
l
l
12
3D: Si 2D: MoS2
0D: BiI3
1D-MoBr3
Nature: Scientific Reports, 7, 5179 (2017)
Nature:Scientific Data 5, 180082 (2018)
Phys. Rev. B, 98, 014107 (2018)
13. MetaGGA & optoelectronic properties
13
• Bandgap, frequency dependent dielectric function from OptB88vdW (OPT) and Modified Becke-Johnson formalisms (MBJ)
• MBJ gives excellent bandgap with low computational cost, also better dielectric function with linear optics
Nature:Scientific Data 5, 180082 (2018)
~20000 TBmBJ bandgaps and dielectric function
MAE bandgap (eV):
• MatProj: 1.45
• AFLOW: 1.23
• OQMD: 1.14
• OptB88vdW: 1.33
• TBmBJ: 0.51
• HSE06: 0.41
(wrt 54 exp. data)
14. Solar cells & linear optics
14
Scientific Data 5, 180082 (2018)
Chemistry of Materials, 31, 15, 5900 (2019).
Spectroscopic Limited Maximum Efficiency (SLME)
15. Spin-orbit coupling & Topological Materials
New class of materials
(electronic bandgap perspective)
15
Email: kamal.choudhary@nist.gov
https://phys.org/news/2014-01-quantum-natural-3d-counterpart-graphene.html
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSzMKD5ICIkR9neJRre3prqIjp_iqLMu6TQp7mXKJqmmh-HqjFB
(2016 Nobel prize)
Metal
Semiconductor
Insulator
16. Spin-orbit Spillage
• Majority of the topological materials driven by spin-orbit coupling (SOC)
• Simple idea: Compare wavefunctions of a material with and without SOC?
• Spillage initially proposed for insulators only, now extended to metals also
• Advantages over symmetry-based approaches:
disordered and magnetic mats.
• For trivial materials, spillage 0.0, non-trivial materials ≥ 0.25
16
https://www.ctcms.nist.gov/~knc6/jsmol/JVASP-1067
𝜂 𝐤 = 𝑛𝑜𝑐𝑐(𝐤) − Tr 𝑃 ෨
𝑃 ; 𝑃 𝐤 =
𝑛=1
)
𝑛𝑜𝑐𝑐(𝐤
ۧ
|𝜓𝑛𝐤 ൻ𝜓𝑛𝐤|
Sci. Rep., 9, 8534 (2019)
NPJ Comp. Mat., 6, 49 (2020)
Phys Rev B, 103, 054602 (2021)
18. 18
BCS Superconductors & E-Ph coupling
Debye
Temp
DOS at
EFermi
https://arxiv.org/abs/2205.00060
Superconductors: Materials to conduct electricity without energy loss when they are cooled below a critical temperature, Tc
MgB2 (Tc = 39 K): Highest Tc ambient condition conventional superconductor
19. Other electronic structure databases
19
JARVIS-TB3Py
Tight-binding models
JARVIS-QMC
Quantum Monte Carlo
22. 22
From ANNs to Graph Convolution Networks
𝑧[𝑙]
= 𝑊
[𝑙]
𝑎
[𝑙−1]
+ 𝑏
[𝑙]
𝑎[1]
= σ( 𝑧[𝑙]
); 𝑎[0]
= 𝑋
1) Forward propagation
2) 𝐶𝑜𝑠𝑡, 𝐽(𝑊, 𝑏) = 𝑓(𝑦 −
𝑦)
X1
X2
Hidden
Layer
Input
Layer
Output
layer
𝑦
3) Gradient descent (∇J):
minimize cost with W,b
4) Backpropagation:
chain rule to get,
𝜕𝐽
𝜕𝑊
1) Convolution:
element-wise multiplication & sum
2) Pool: Max, Average, Sum
3) Fully Connected: Standard NN
Shared weights (Learnable filters),
regularized version of NNs
መ
𝐴 = ෩
𝐷−
1
2 𝐴෩
𝐷−
1
2 𝐻𝑙+1 = σ 𝑊 መ
𝐴𝐻𝑙
Adjacency matrix, A
1 0 1
0 1 0
1 0 1
1) Adjacency matrix, N x N (N: #nodes),
2) D: degree of node
3) Update node representation using
message passing, GPU efficient
4) Update equation is local, neighborhood
of a node only, independent of graph size
Standard NN ConvolutionNN GraphConvNN
Types: un/weighted, un/directed, line,
Hetero/Homogenous, Multigraph
23. 23
Line Graph
Explicitly represent pairwise and triplet (bond angle) interactions using line graph
Possible to extend for n-body, e.g. line graph of line graph
nisaba.nist.gov Tesla V100
25. 25
Performance on the Materials Project Dataset
Trained on 69239 materials (DFT data)
#Epochs: 300
Batch_size: 64
• ~44 % improvement by ALIGNN with similar/better training speed
• Similar performance enhancement on QM9 molecule dataset
• Also available on MatBench: https://matbench.materialsproject.org
26. 26
Performance on the JARVIS-DFT Dataset
Trained on ~55k materials
Total energy, Formation energy , Ehull
Bandgap (OPT), Bandgap (MBJ)
Kv, Gv
Mag. mom
єx (OPT/MBJ), єy (OPT), єz (OPT), є
(DFPT:elec+ionic)
Max. piezo. stress coeff (eij)
Solar-SLME (%)
Topological-Spillage
2D-Exfo. energy
Kpoint-length
Plane-wave cutoff
Max. Electric field gradient
avg. me, avg. mh
n-Seebeck, n-PF, p-Seebeck, p-PF
27. 27
Evac with ALIGNN Energy model
No ML training defect structures/data ! Directly predicting with energy/atom model
Total 508 datapoints, MAE wrt Exp. for subset: 0.3 eV
(Elemental solids+Alloys+Oxides+2D monolayers)
~34 % improvement with scissor shift
https://arxiv.org/abs/2205.08366
pretrained.py --model_name jv_optb88vdw_total_energy_alignn--file_format poscar --file_path POSCAR
28. 28
BCS Superconductors
• Prediction on 10 % test data
• 8293 out of 431778 materials in COD as superconductors
• First predicting Eliashberg function, then Tc 6 % improvement
• ALIGNN for both scalar and spectral learning
Best
32. 32
CO2 Isotherms: AI for Climate Change
DL model for predicting CO2 adsorption in MOFs (using hMOF GCMC data)
Choudhary et al., Computational Materials Science 210, 111388 (2022)
35. 35
Scanning Transmission Electron Microscope Image
PPdSe: JVASP-6316
C: JVASP-667 FeTe: JVASP-6667
Convolution approximation: accurate for thin films mainly (here 2D mats.)
Based on Rutherford scattering model
36. 36
Image classification and semantic segmentation
2D Bravais lattice classification (DenseNet):
1) hexagonal, 2) square, 3) rectangle, 4) rhombus, 5) parallelogram
Baseline accuracy 1/5 = 20 %
Semantic segmentation using U-Net:
Atom vs background, pixelwise classification
38. Background: Feynman’s seminal papers
38
http://physics.whu.edu.cn/dfiles/wenjian/1_00_QIC_Feynman
“Nature is quantum, goddamn it! So if we
want to simulate it, we need a quantum
computer.”
39. Variational Quantum Eigensolver (VQE) &
Variation Quantum Deflation(VQD)
39
http://openqemist.1qbit.com/docs/vqe_microsoft_qsharp.html
Notes:
• Quantum computers are good in preparing states, not good at sum, optimizers, multiplying etc.
• QC to prepare a wavefunction ansatz of the system and estimate the expectation value
VQD: Deflate other eigensatets once ground state is found using VQE
VQE: a hybrid classical-quantum algorithm using Ritz variational principle
40. Typical Flowchart
40
https://github.com/usnistgov/jarvis
https://github.com/usnistgov/atomqc
K. Choudhary, J. Phys.: Condens. Matter 33 (2021) 385501
Wannier functions:
• Complete orthonormalized basis set,
• Acts as a bridge between a delocalized plane wave representation and a localized atomic orbital basis
• All major density functional theory (DFT) codes support generation WFs for a material
𝐻 = ℎ𝑃𝑃
𝑃∈ 𝐼,𝑋,𝑌,𝑍 ⨂𝑛
𝐻𝑗 = 𝐻 + 𝛽𝑖|𝜓(𝜽0
∗)ۧ 𝜓(𝜽0
∗)|
𝑗−1
𝑖=0
𝐺(𝑘, ꞷ𝑛) = [ꞷ𝑛 + 𝜇 − 𝐻(𝑘) − 𝛴(ꞷ𝑛)]−1
http://www.wannier.org/
42. FCC Aluminum Example
42
a) Monitoring VQE optimization progress with several local optimizers such COBYLA, L_BFGS_B, SLSQP, CG, and SPSA
for Al electronic WTBH and at X-point.
b) Electronic bandstructure calculated from classical diagonalization (Numpy-based exact solution) and VQD algorithm for
Al.
c) Phonon bandstructure for Al
43. Dynamical Mean Field Theory
43
Imaginary part of Al’s DMFT hybridization function for a few components considering zero self-energy. a)Δ00, b)Δ01,
c)Δ10, d)Δ11
• Dynamical mean-field theory (DMFT): commonly used
techniques for solving predicting electronic structure of
correlated systems using impurity solver models.
• DMFT maps a many-body lattice problem to a many-
body local problem with impurity models.
• In DMFT one of the central quantities of interest is the
Green’s function such as
𝐺(𝑘, ꞷ𝑛) = [ꞷ𝑛 + 𝜇 − 𝐻(𝑘) − 𝛴(ꞷ𝑛)]−1
• Spectral function (𝐴) & DMFT hybridization function (𝛥)
𝐴(ꞷ) = −
1
𝜋
𝐼𝑚(𝐺(ꞷ + 𝑖𝛿))
𝑘
𝛥(ꞷ + 𝑖𝛿) = ꞷ − (𝐺)−1
• Next, integrate with quantum impurity solvers
𝛴 = 0