├── .gitattributes ├── Applications_of_DFT.mlx ├── HFrho.mat ├── KS_DFT_Solution_Exercise1.mlx ├── LICENSE ├── Lecture10_Kohn_Sham_DFT.mlx ├── Lecture1_Particle_in_Box.mlx ├── Lecture2_SphericallySymmetricPotential.mlx ├── Lecture3_GaussianWavePacket.mlx ├── Lecture4_HydrogenAtom.ipynb ├── Lecture4_HydrogenAtom.mlx ├── Lecture5_Hartree_Method.mlx ├── Lecture6_Hartree_Fock_Method.mlx ├── Lecture7_Thomas_Fermi_Approximation.mlx ├── Lecture8_From_Many_Body_WaveFunction_to_DFT.mlx ├── Lecture9_Orbital_Free_DFT.mlx ├── QuantumHarmonicOScillator_1d.mlx ├── README.md ├── SECURITY.md ├── Solution_Exercise7_Orbital_Free_DFT.mlx └── TFchi.mat /.gitattributes: -------------------------------------------------------------------------------- 1 | *.fig binary 2 | *.mat binary 3 | *.mdl binary diff merge=mlAutoMerge 4 | *.mdlp binary 5 | *.mexa64 binary 6 | *.mexw64 binary 7 | *.mexmaci64 binary 8 | *.mlapp binary linguist-language=MATLAB 9 | *.mldatx binary 10 | *.mlproj binary 11 | *.mlx binary merge=mlAutoMerge linguist-language=MATLAB 12 | *.p binary 13 | *.sfx binary 14 | *.sldd binary 15 | *.slreqx binary merge=mlAutoMerge 16 | *.slmx binary merge=mlAutoMerge 17 | *.sltx binary 18 | *.slxc binary 19 | *.slx binary merge=mlAutoMerge 20 | *.slxp binary 21 | 22 | ## Other common binary file types 23 | *.docx binary 24 | *.exe binary 25 | *.jpg binary 26 | *.pdf binary 27 | *.png binary 28 | *.xlsx binary 29 | 30 | # Ignore HTML 31 | 32 | *.html linguist-detectable=false 33 | -------------------------------------------------------------------------------- /Applications_of_DFT.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Applications_of_DFT.mlx -------------------------------------------------------------------------------- /HFrho.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/HFrho.mat -------------------------------------------------------------------------------- /KS_DFT_Solution_Exercise1.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/KS_DFT_Solution_Exercise1.mlx -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Copyright (c) 2023, The MathWorks, Inc. 2 | All rights reserved. 3 | Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 4 | 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 5 | 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. 6 | 3. In all cases, the software is, and all modifications and derivatives of the software shall be, licensed to you solely for use in conjunction with MathWorks products and service offerings. 7 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -------------------------------------------------------------------------------- /Lecture10_Kohn_Sham_DFT.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture10_Kohn_Sham_DFT.mlx -------------------------------------------------------------------------------- /Lecture1_Particle_in_Box.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture1_Particle_in_Box.mlx -------------------------------------------------------------------------------- /Lecture2_SphericallySymmetricPotential.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture2_SphericallySymmetricPotential.mlx -------------------------------------------------------------------------------- /Lecture3_GaussianWavePacket.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture3_GaussianWavePacket.mlx -------------------------------------------------------------------------------- /Lecture4_HydrogenAtom.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture4_HydrogenAtom.mlx -------------------------------------------------------------------------------- /Lecture5_Hartree_Method.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture5_Hartree_Method.mlx -------------------------------------------------------------------------------- /Lecture6_Hartree_Fock_Method.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture6_Hartree_Fock_Method.mlx -------------------------------------------------------------------------------- /Lecture7_Thomas_Fermi_Approximation.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture7_Thomas_Fermi_Approximation.mlx -------------------------------------------------------------------------------- /Lecture8_From_Many_Body_WaveFunction_to_DFT.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture8_From_Many_Body_WaveFunction_to_DFT.mlx -------------------------------------------------------------------------------- /Lecture9_Orbital_Free_DFT.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Lecture9_Orbital_Free_DFT.mlx -------------------------------------------------------------------------------- /QuantumHarmonicOScillator_1d.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/QuantumHarmonicOScillator_1d.mlx -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Density Functional Theory 2 | Fundamentals and Applications of Density Functional Theory with interactive live scripts and intuitive codes. 3 | Curriculum Module created in collaboration with Xin Jing, Graduate Research Assistant at Georgia Institute of Technology. 4 | 5 | # Fundamentals and Applications of Density Functional Theory 6 | 7 | 8 | [![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/155050-density-functional-theory) or [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Density-Functional-Theory) 9 | 10 | **Curriculum Module** 11 | 12 | _Created with R2023a. Compatible with R2020b and later releases._ 13 | 14 | # Information 15 | 16 | This curriculum module contains interactive [MATLAB® live scripts](https://www.mathworks.com/products/matlab/live-editor.html) that teach the fundamental concepts in density functional theory, show how to develop numerical solvers for orbital-free and Kohn-Sham implementations of DFT and highlight the usage of two MATLAB-based DFT toolboxes. 17 | 18 | 19 | ## Background 20 | 21 | You can use these live scripts to teach an introduction to density functional theory, or learn basics of DFT, an inherently computational topic. The first few live scripts review the fundamentals of single-particle quantum mechanics and highlight usage of symbolic computations. Then Hartree and Hartree-Fock variational methods are introduced and simple numerical codes are provided for calculating the ground state energy of helium atom. Next, we present the Thomas-Fermi model of an atom, introducing the key notion of the energy functional of electron density. Density functional theory and its orbital-free and Kohn-Sham implementations are covered in the later live scrips. Numerical implementations of OFDFT and KS-DFT are provided for systems with spherically symmetric ground state electron densities. 22 | 23 | 24 | The instructions inside the live scripts will guide you through the exercises. Get started with each live script by running it one section at a time. To stop running the script or a section midway, use the Stop button in the **RUN** section of the **Live Editor** tab in the MATLAB Toolstrip. 25 | 26 | ## Contact Us 27 | 28 | Hints to solutions for challenging exercises are provided after such exercises. The solutions to two exercises: one for the numerical implementation of Kohn-Sham method including orbitals with nonzero angular momentum and another for solving OFDFT as an eigen problem for effective hamiltonian, are provided as separate live scripts. Contact the [MathWorks teaching resources team](mailto:onlineteaching@mathworks.com) if you would like to provide feedback, or if you have a question. 29 | 30 | 31 | ## Prerequisites 32 | 33 | This module assumes knowledge of quantum mechanics fundamentals and basic to moderate MATLAB knowledge. 34 | 35 | 36 | ## Getting Started 37 | ### Accessing the Module 38 | ### **On MATLAB Online:** 39 | 40 | Use the [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Density-Functional-Theory) link to download the module. 41 | 42 | ### **On Desktop:** 43 | 44 | 45 | Download all live scripts and 2 .mat files to the same directory. Ensure you have all the required products listed below installed. 46 | 47 | 48 | ## Products 49 | 50 | MATLAB® and Symbolic Math Toolbox™ are used throughout this module. 51 | 52 | 53 | # Scripts 54 | * live script 1: Particle in Box 55 | * live script 2: Spherically Symmetric Potential 56 | * live script 3: Gaussian Wave Packet 57 | * live script 4: Hydrogen Atom 58 | * live script 5: Hartree Method 59 | * live script 6: Hartree-Fock Method 60 | * live script 7: Thomas-Fermi Approximation 61 | * live script 8: From Many-Body Wave Function Description to Density Functional Theory 62 | * live script 9: Orbital-Free DFT 63 | * live script 10: Kohn-Sham DFT 64 | * live script 11: Applications of DFT 65 | * live script 12: Solution to Exercise 1 in KS-DFT 66 | * live script 13: Solution to Exercise 7 in Orbital-Free DFT 67 | * live script 14: Solution to Exercise 3 in Hydrogen Atom - Quantum Harmonic Oscillator in 1, 2, and 3-Dimensions 68 | 69 | 70 | # License 71 | 72 | The license for this module is available in the [LICENSE](https://github.com/MathWorks-Teaching-Resources/Density-Functional-Theory/blob/main/LICENSE). 73 | 74 | 75 | 76 | # Educator Resources 77 | - [Educator Page](https://www.mathworks.com/academia/educators.html) 78 | 79 | # Contribute 80 | 81 | Looking for more? Find an issue? Have a suggestion? Please contact the [MathWorks teaching resources team](mailto:%20onlineteaching@mathworks.com). 82 | 83 | 84 | © Copyright 2023 The MathWorks, Inc 85 | 86 | 87 | -------------------------------------------------------------------------------- /SECURITY.md: -------------------------------------------------------------------------------- 1 | # Reporting Security Vulnerabilities 2 | 3 | If you believe you have discovered a security vulnerability, please report it to 4 | [security@mathworks.com](mailto:security@mathworks.com). Please see 5 | [MathWorks Vulnerability Disclosure Policy for Security Researchers](https://www.mathworks.com/company/aboutus/policies_statements/vulnerability-disclosure-policy.html) 6 | for additional information. -------------------------------------------------------------------------------- /Solution_Exercise7_Orbital_Free_DFT.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/Solution_Exercise7_Orbital_Free_DFT.mlx -------------------------------------------------------------------------------- /TFchi.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MathWorks-Teaching-Resources/Density-Functional-Theory/4f7e624c703c254c186eca426d57e83917c90071/TFchi.mat --------------------------------------------------------------------------------