Ab initio Calculation Tutorial: For Materials Analysis, Informatics and Design

Preface
Tutorial Environment
Cost Estimation for Simulation Environment
Acknowledgements
Contents
Acronyms
Part ITracing the Whole Picture First
1 Introduction
1.1 What Is ab initio Electronic Structure Calculation in Practice?
1.1.1 What Solution It Provides?
1.1.2 What Is Calculated?
1.2 What May Be Confusing to Beginners
1.2.1 Not What One Would Normally Expect from a Simulation Study
1.2.2 Hierarchical Structure of Scientific Pictures
1.2.3 Kernel Calculation and Outer Loop
1.3 What Is the Goal to Aim at as a Practitioner?
1.3.1 Why Learn the Kernel Calculation Part?
1.3.2 Tips for Surveying Preceding Studies
1.3.3 Finding a Tracing Calculation Task
1.3.4 Learning Approach to Be Avoided
1.3.5 Goal to Aim at for Beginners
1.4 Why It Is an Opportune Time to Jump in
1.4.1 Affinity with Data Science
1.4.2 Outer Loop Linked to Artificial Intelligence
1.4.3 Confluence with Computational Thermodynamics
1.4.4 Materials Genome
1.4.5 Chance for Latecomers
1.5 Contents of the Following Chapters
1.5.1 Policy on Content
1.5.2 Teaching with Command Line
1.5.3 Machine Dependence of the Tutorial Environment
2 Preparing Tutorial Environments
2.1 Minimum Guide for Linux Beginners
2.2 Preparing Terminal Environment
2.2.1 Assembling RaspberryPi
2.2.2 Getting Used to Shortcuts
2.2.3 Preparing Terminal Environment
2.2.4 Hierarchical Structure of Directories
2.3 Installation of Required Tools
2.3.1 Network Installation Using Sudo Command
2.3.2 Installing Operation
2.3.3 Remote Connection from Your Familiar PC
2.4 Setting Up Working Directory
2.4.1 Preparing Working Directory
2.4.2 Obtaining Tutorial File Sets
2.4.3 Setup Alias File
2.5 Tips for Successful Learning
2.5.1 Cease Habit of Handwritten Notebook
2.5.2 Tips to Prevent Discouraging Your Learning
3 Sequence of Computational Procedure
3.1 What Is the Self-Consistent Calculation
3.2 Preparing Input Files
3.2.1 How to Prepare Structure/Geometry Files
3.2.2 Obtaining Structure Files
3.2.3 Conversion of Structure Format
3.2.4 Preparing Pseudopotentials
3.3 SCF Calculation
3.3.1 Preparing for Calculations
3.3.2 Executing SCF Calculations
3.3.3 Checking the Results
3.4 Quick Check Using Plotter
3.4.1 Useful Commands for Text Editing
3.4.2 Script to Utilize of Past Knowledge
3.4.3 Using a Plotter
3.5 Calculating Electronic Structure
3.5.1 NSCF Calculations for DOS
3.5.2 Depicting DOS
3.5.3 Depicting Partial DOS
3.5.4 Depicting DOS Using xFroggie
3.6 Depicting Band Dispersion
3.6.1 NSCF Calculation for Band Dispersion
3.6.2 Preparing Band Dispersion Data Using ``bands.x''
3.6.3 Depicting Band Dispersion Using ``plotband.x''
3.6.4 Depicting Band Dispersion Using ``xFroggie''
3.7 Calculating Properties as a Quick Check
Part IIToward Understanding Theoretical Background
4 Determining Computational Conditions
4.1 Why the Determination of Calculation Conditions is Important?
4.1.1 To Get Reliable Predictions
4.1.2 Applying Identical Condition to Predict Series Trend
4.2 Parameters for Accuracy via Resolution
4.2.1 k-Mesh
4.2.2 Cutoff Energy
4.2.3 Physical Image of Truncation
4.3 Procedure to Determine the Resolution Specifications
4.3.1 Determining Cutoff Energy
4.3.2 Determining Optimal k-Mesh
4.4 Choice of Pseudopotentials
4.4.1 Specification of Pseudopotentials
4.4.2 Dependence on the Pseudopotential Choice
4.5 Choice of Exchange-Correlation Potentials
4.5.1 Starting from Rough Description
4.5.2 Dependence on Exchange-Correlation Potentials
4.6 How the Computational Conditions Affect
4.6.1 How to Read the Results
4.6.2 Importance to Understand the Dependence on the Computational Conditions
5 Points to Understand in Background Theories
5.1 Significance to Learn Kernel Calculation
5.1.1 Kernel Calculation as a Seed
5.1.2 Geometrical Optimization
5.1.3 Why Kernel Calculations with Command Line
5.2 Tips to Understand Kernel Calculation
5.2.1 Categorizing Input Parameters
5.2.2 Input Parameters to Be Understood First
5.3 Overview of Density Functional Theory: For Understanding …
5.3.1 Formulation of Our Problem
5.3.2 Introducing Density Functional Theory
5.3.3 Exchange–Correlation Potentials
5.3.4 Kohn–Sham Equation
5.3.5 Self-consistent Field Form
5.3.6 Variation of Exchange–Correlation Functionals
5.3.7 Further Notes on Exchange–Correlation Potentials
5.4 Basis Set Functions
5.4.1 Basis Set Expansion
5.4.2 Basis Set Choice Based on Physical Perspective
5.4.3 Basis Sets in Modern Context
5.4.4 Cost Reduction via Basis Set
5.5 Pseudopotentials
5.5.1 Core/Valence Partitioning
5.5.2 Practical Categorizing Pseudopotentials
5.5.3 Two More Practical Specs of Pseudopotentials
5.6 How to Choose Appropriate Package for Your Project
5.6.1 Starting with Basis Sets
5.6.2 Tips for the Choice
5.6.3 Kernel, Package, and Wrapper
Part IIIAdvanced Topics
6 Toward Practical Applications
6.1 Toward Advanced Geometries
6.1.1 Construction of Geometries
6.1.2 Finite Size Error
6.2 Toward Evaluations of Advanced Properties
6.2.1 Sorting Out the Form of Computational Evaluations
6.2.2 Prediction Based on Data Correlation
6.3 What the Speed of Simulation Brings
6.3.1 High-Throughput Handling
6.3.2 Workflow Automation
6.3.3 Quantum Monte Carlo Electronic Structure Calculations
6.3.4 What the Simulation Speed Brings
7 Materials Informatics Based on Structural Search
7.1 Formulation of Materials Search
7.1.1 Descriptors to Introduce Search-Space
7.1.2 For Efficiency to Sample Search-Space
7.1.3 Regression to Describe Properties
7.2 Search Methods
7.2.1 Particle Swarm Optimization
7.2.2 Genetic Algorithm
7.2.3 Beysian Search
7.3 Regression Using Descriptors
7.3.1 Binary Tree Regression
7.3.2 Regression Using Neuralnetwork
7.3.3 Evaluating and Improving Regressions
7.4 Structural Search
7.4.1 Structural Search Using Regression
7.4.2 How ab Initio Calculation Used
8 Tips in Project Management
8.1 How to Drive the Collaboration Effectively
8.1.1 The Age of Experimental Practitioners Running Their Own Calculations
8.1.2 What Makes it Different from a Simple Analytical Collaboration
8.1.3 How to do a Literature Search
8.1.4 How to Perform Tracing Studies
8.2 Tips for Successful Collaboration
8.2.1 Standardizing any Format
8.2.2 Pitfalls in Simulation Collaboration
8.2.3 Pitfalls in Reporting and Consulting
8.3 Tips to Train Practitioners
8.3.1 Computational Operations Are Not the Hard Issue to Non-experts
8.3.2 Aspects of Work Sharing
9 Appendix A: A Short Course of Linux Command Operation
9.1 Getting Familiar with Directory Structure
9.1.1 Directory Structure Instead of Folders
9.1.2 Moving Between Directories
9.1.3 File Operations
9.1.4 Editting Files
9.2 Use It More Conveniently
9.2.1 Using Alias
9.2.2 Pipe and Redirect
9.2.3 Activating Alias Automatically
10 Appendix B: Supplementals to the Tutorial
10.1 Generating k-Point Path
10.2 Improving SCF Convergence
10.2.1 Sloshing and Smearing
10.2.2 Convergence Controlled by Smearing Parameter
10.2.3 Convergence Acceleration by Mixing and Resume Calculation
11 Appendix C: Band Theory
11.1 Overview
11.1.1 Fundamental Information to Understand Materials Response
11.1.2 Mode Separation Used for the Analysis
11.1.3 Symmetric Transformation of Wavefunctions
11.1.4 Indexing Energy Levels of Periodic Systems
11.1.5 Concept of Elementary Excitations
11.1.6 Band Dispersion Gives What Information?
11.2 Mode Separation and Diagonalization
11.2.1 Introduction of Mode Separation
11.2.2 Prescription of Mode Separation
11.2.3 Mode Separation for Symmetric Operations
11.2.4 Fourier Expansion as a Mode-Separation
11.3 Index for Symmetric Operations and Energy
11.3.1 Representation of Symmetry Using Commutation Relation
11.3.2 Energy Index Sorted by Symmetry
11.4 Wavevector, Reciprocal Lattice, Brillouin Zone
11.4.1 Imagine the Wave Number as a Picture
11.4.2 Introducing Reciprocal Lattice
11.4.3 Bloch Function
11.5 Twisted Boundary Condition
11.5.1 Mesh Shift
11.5.2 Twisting Average
11.5.3 A Rough Description of Polarization Theory
12 Appendix D: A Brief Explanation of DFT+U
12.1 The Problem of Damage to Self-interaction Cancellation
12.1.1 Cancellation of Self-interaction
12.1.2 Damage to Self-interaction Cancellation
12.2 DFT+U Method
12.2.1 Problem of Bandgap Underestimation
12.2.2 Mechanism of Gap Underestimation
12.2.3 Cancellation of Self-interaction Depending on the Locality
12.2.4 Strategies to Cope with Gap Underestimation
12.2.5 Strategy in DFT+U
12.2.6 Summary/Possible Misleadings on DFT+U
12.3 Universal Consequences Derived From Bare Interaction
13 Appendix E: Appendix for Data Scientic Topics
13.1 Bayesian Update of the Parameters of Distribution
13.2 Sparse Modeling by Norm Regularization