Quantum ESPRESSO Tutorial: Exploring Electronic Structure of Materials PDF

Jude Asante-Amoah - 30/05/2024 Quantum ESPRESSO Tutorial: Exploring Electronic Structure of Materials Introduction to Density Functional Theory (DFT) 1 Lesson Outline What will we cover today? 1. Introduction to computational material science: - The ro...

Jude Asante-Amoah - 30/05/2024 Quantum ESPRESSO Tutorial: Exploring Electronic Structure of Materials Introduction to Density Functional Theory (DFT) 1 Lesson Outline What will we cover today? 1. Introduction to computational material science: - The role of computational material science (CMS) - The impact of CMS - CMS as a tool in Materials Science - Computational methods and procedures in materials Science 2. Overview of DFT: - Understand the fundamental background of DFT - History of DFT. 3. Key Components of DFT: - Electronic density - Exchange-correlation energy - Kohn-Sham equations - Pseudopotentials - Geometry Optimization 4. Applications and Limitations of DFT 2 Introduction to Computational Material Science (CMS) 3 Introduction to Computational Material Science The goal of CMS In CMS, the goal is to understand material properties and phenomena, leading to the design of better materials for society. This is achieved by modeling materials with computer programs based on theories and algorithms from physics, mathematics, chemistry, materials science, and computer science. For example, the sintering behaviour of metals or ceramics can be studied using molecular dynamics (MD) simulations on a computer, providing efficient and accurate data by varying input conditions. Focus on Electron Density: Unlike traditional quantum mechanical methods, DFT focuses on the electron density distribution around atomic nuclei rather than individual electron wavefunctions. 4 Introduction to Computational Material Science The Impact of CMS Computational approaches are crucial for studying materials under extreme and hostile conditions, such as high pressures, high temperatures, toxic substances, or nuclear radiation, which are impractical to achieve in a laboratory. CMS plays a significant role in the development of everyday technologies like IC chips in cell phones and computers, enabling the design of faster, smaller, and lighter components. This field has transformed materials research from traditional lab experiments to "keyboard science" on computers, making it an essential and routine part of the scientific process, often prioritized before physical experiments. Focus on Electron Density: Unlike traditional quantum mechanical methods, DFT focuses on the electron density distribution around atomic nuclei rather than individual electron wavefunctions. 5 Introduction to Computational Material Science CMS as a tool in Material Science Computational science serves as a convenient tool for materials scientists, similar to how a car operates. Just as one doesn't need to understand every detail of how a car's engine works to drive it effectively, materials scientists utilize computational methods without needing to grasp every theory or algorithm behind them. The focus is on using proven codes to run simulations, obtain data, and consult with experts if needed to interpret results. While it's not necessary to understand all the intricacies of the underlying theories or coding, a basic understanding is essential to avoid limitations in simulations and ensure meaningful interpretation of results. Focus on Electron Density: Unlike traditional quantum mechanical methods, DFT focuses on the electron density distribution around atomic nuclei rather than individual electron wavefunctions. 6  Introduction to Computational Material Science Computational methods in Material Science Computational materials science employs various methods to simulate and analyze material properties and phenomena. Four primary methods include: 1. Finite Element Method (FEM) - Numerical technique for solving partial differential equations governing physical phenomena. - Commonly applied to structural analysis, heat transfer, and fluid flow simulations in materials. - Enables the study of mechanical properties, stress distributions, and deformation behavior. 2. Monte Carlo (MC) Simulation - Utilizes random sampling to model statistical behaviour and explore phase spaces. - Particularly useful for systems with many degrees of freedom, such as complex fluids and polymers. - Provides insights into thermodynamic properties and equilibrium behaviour. 3. Molecular Dynamics (MD) - Simulates the motion of atoms and molecules over time. - Captures dynamic behavior, such as thermal fluctuations and phase transitions. - Valuable for studying processes like diffusion, melting, and chemical reactions. 4. Ab-initio Methods - Also known as first-principles methods, they provide accurate descriptions of material properties from basic principles. - Density Functional Theory (DFT) is a prominent example, revolutionizing computational materials science with its efficient treatment of electronic structure. - Ab-initio methods are essential for predicting diverse properties like band structures, reaction energies, and electronic properties. 7 8  Introduction to Computational Material Science Computational procedures in Material Science In materials science, the focus is primarily on the electromagnetic interaction, as encounters with the other three interactions are rare. Computational materials science revolves around understanding electromagnetic interactions between nuclei, electrons, and atoms. Key Procedures: 1. Define the calculation objectives. 2. Construct a model system that accurately represents the real system. 3. Choose appropriate rules and theories (classical mechanics, quantum mechanics, algorithms). 4. Select a suitable computational code or package. 5. Run simulations, analyze results, and refine under better-defined conditions. 6. Validate results by comparing with reported data from relevant studies and experiments. Simulation involves recreating a part of nature in a simplified and controlled manner within the simulation system. Critical examination of simulation results is essential, as they are derived from somewhat idealised situations and must be compared with experimental data. 9  Introduction to Computational Material Science Computational methods in Material Science Selection of the appropriate method depends on factors such as system complexity, timescale of interest, and computational resources available. Computation involves a trade-off between speed and accuracy, as there's no one-size- fits-all tool. Before starting computational work, it's crucial to address the following questions: 1. What method best suits my needs? 2. Which software is most appropriate? 3. Do I have access to suitable potentials for MD methods? 4. Is my computational power sufficient? 5. If resources are limited, what system size can I feasibly work with? 10 Overview of DFT 11 Overview of DFT What is DFT ? DFT stands for Density Functional Theory DFT is a computational method used in chemistry and materials science to study the electronic structure of molecules and materials. It allows researchers to predict various properties of materials, including molecular geometries, energies, and electronic properties, without the need for extensive experimental work. Unlike traditional quantum mechanical methods, DFT focuses on the electron density distribution around atomic nuclei rather than individual electron wavefunctions. In DFT, electron density is the central player. Focus on Electron Density: Unlike traditional quantum mechanical methods, DFT focuses on the electron density distribution around atomic nuclei rather than individual electron wavefunctions. 12 Overview of DFT What is DFT ? DFT utilizes mathematical equations to describe the interactions between electrons and nuclei within a given system. DFT has become one of the most widely used computational methods in chemistry and materials science due to its accuracy and efficiency. 13  Overview of DFT A Historical overview of DFT 1920s - Birth of Quantum 1964 - Hohenberg-Kohn Mechanics: 2000s-present - Re nements Theorems 1970s - First Applications Quantum mechanics and Extensions Foundational theorems link Initial applications are limited pioneers lay the Ongoing developments expand electron density to energy, by computational constraints. groundwork for DFT capabilities for studying establishing the basis for understanding electron complex systems. DFT. behavior. 1980s - Exchange-Correlation 1990s - Widespread Adoption Functionals Advances in computing lead to 1965 - Kohn-Sham Equations Improved functionals widespread use across Practical equations introduce non-interacting electrons to model enhance accuracy in solving scienti c elds. complex systems DFT equations. 1998 - Nobel Prize in Chemistry Recognition of Walter Kohn’s contributions to DFT. 14 fi fi fi Key Components of DFT 15 Key Components of DFT What comprises DFT? 1. Electron Density 2. Kohn-Sham Equations 3. Exchange-Correlation Energy 4. Pseudopotentials 5. Geometry Optimization 6. Periodic Boundary Conditions and Supercell 7. Brillouin Zone & K-point 16 Key Components of DFT Electron Density Electron density refers to the spatial distribution of electrons within a system. In DFT, electron density serves as a central player, providing crucial information about the electronic structure of molecules and materials. DFT calculations focus on determining the electron density, which is represented as a three-dimensional function in space. Properties such as energy, molecular structure, and chemical reactivity are closely correlated with the electron density distribution. 17 Key Components of DFT Kohn-Sham Equations Introduced by Walter Kohn and Lu Sham, the Kohn-Sham equations provide a theoretical framework for DFT calculations. These equations describe a system of non- interacting electrons moving in an effective potential, which simplifies the treatment of many- body interactions. DFT calculations involve solving the Kohn-Sham equations iteratively until self-consistency is achieved, ensuring that the electron density converges to a stable solution. Despite their simplifications, Kohn-Sham equations allow for efficient and accurate predictions of electronic structure and properties. 18 Key Components of DFT Pseudopotentials Pseudopotentials are used to approximate the effect of core electrons on valence electrons. By effectively freezing the motion of core electrons, pseudopotentials reduce the computational burden associated with explicitly treating all electrons in the system. DFT calculations can employ different types of pseudopotentials, including norm- conserving pseudopotentials and ultrasoft pseudopotentials, each suited for specific applications. The choice of pseudopotential depends on the balance between computational efficiency and the desired level of accuracy in the calculation. 19 Key Components of DFT Geometry Optimization Geometry optimization finds the lowest energy structure of a molecule or material by minimizing total energy with respect to atomic positions, ensuring accurate molecular geometries for further calculations. It involves the potential energy surface (PES), energy minimization, and convergence criteria for determining when the process is complete. Utilizes classical (force fields) or quantum mechanical (DFT, ab-initio) methods, starting from an initial guess, iteratively calculating energy and gradients, and updating positions until convergence. Involves handling complex PES with multiple local minima, balancing computational cost and accuracy, selecting appropriate software, and ensuring sufficient computational resources. 20  Key Components of DFT Supercell and Periodic Boundary Conditions (PBC) A supercell is a larger simulation cell used in computational materials science and solid-state physics to study larger systems and more complex structures. It consists of multiple unit cells, arranged in a periodic fashion, within a single simulation cell. In DFT, PBC are applied to simulate an infinite system within a finite cell. This approach allows researchers to study the properties of materials without having to model an infinitely large system. By imposing periodicity on the simulation cell, the properties of the material within the cell are representative of the entire bulk material. PBC are essential for accurately modeling the behaviour of crystals and other periodic structures in materials science. The Brillouin Zone is a concept used in solid-state physics to represent the first unit cell of reciprocal space. It plays a fundamental role in understanding the electronic structure and properties of crystalline materials 21 22 Applications & Limitations 23 Applications & Limitations Applications of DFT Materials Science: - Predicting electronic properties such as band structure and density of states. - Designing and optimizing materials for specific electronic, optical, and magnetic characteristics. - Investigating the behavior of defects, surfaces, and interfaces within materials. Nanotechnology: - Analysing and designing nano-structures, including nanotubes and nanoparticles. - Exploring the effects of quantum confinement on electronic properties. - Understanding and predicting the mechanical and electronic behavior of nanoscale materials. 24  Applications & Limitations Limitations of DFT Accuracy: - Approximations in exchange-correlation functionals can lead to inaccuracies in predicting certain properties, such as band gaps and weak interactions. - Struggles with strongly correlated electron systems. Dispersion Interactions: - Standard DFT often fails to accurately model van der Waals forces, requiring additional corrections or advanced functionals. Computational Cost: - High computational resources required for large systems or high-precision calculations. - Scalability issues for very large or complex systems. Complexity of Systems: - Difficulty in modeling dynamic processes and systems with significant anharmonicity. - Challenges in simulating systems with significant disorder or defects. 25