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Ab-initio �Density Functional Theory (DFT) and beyond-DFT methods: A short review

Abdul Muhaymin

Graduate student, MSN, Bilkent University

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Outline

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What

    • Ab-initio or first-principles
    • Density Functional Theory (DFT)

Why

    • Laboratories ❌, Computers ✅
    • High-throughput investigations

How

    • Quantum ESPRESSO, PySCF, FLEUR…
    • ChatGPT!?

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Ab-initio or first-principle methods

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  • No empirical/experimental input
  • Based on fundamental theory

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    • Density Functional Theory (DFT)
    • Molecular Dynamics (MD)
    • Quantum Monte Carlo (QMC)
    • …

Multiscale modeling?

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  • Hohenberg-Kohn Theorem:
    • One-to-one mapping between ground state electron density and ground state Hamiltonian
    • There exists a ground state energy functional whose global minimum value is the true ground state energy (and corresponding density is the true density)

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  • Kohn-Sham equation:
    • Non-interacting version of the Schrödinger equation

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Density Functional Theory

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Many-Body Hamiltonian

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(Hung et al, 2021)

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Kohn-Sham Equation

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(Hung et al, 2021)

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Approximations

  • Born-Oppenheimer
  • Pseudopotential (PP)
    • LDA
    • GGA
    • meta-GGA
    • hyper-GGA
    • RPA
  • Basis sets – periodic (plane-wave) or local
  • Relativistic effect – scalar or full

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DFT as a black box

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  • Only a ground state theory
  • Fails miserably in case of *almost everything*

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Why should one use DFT?

  • To understand, predict, and design materials and devices
  • To support, guide, streamline, and inspire experimental efforts
  • To suggest novel microscopic physical theories

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(Marzari et al, 2021)

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Structural

  • Crystal structure
  • Bond length, angle, dihedral

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Electronic

  • Band structure
  • Density of states
  • Charge density

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Magnetic

    • Spin-polarized DFT
  • Magnetic moment
  • Magnetic order
  • Half-metallicity

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  • Curie temperature
  • Superconductivity

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(Durgun et al, 2006)

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Mechanical

  • Pressure/stress tensor
  • Young modulus
  • bulk modulus
  • Strain induced properties

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(Barai et al, 2020)

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Vibrational and Thermal

  • Phonon dispersion
  • Phonon DOS
  • Thermal conductivity
  • Heat capacity
  • Thermoelectric Figure of Merit

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(Çakıroğlu et al, 2020)

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(Shakouri, 2011)

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And many more…

  • Optical properties
  • Spectroscopic properties
  • Material simulated under E-field, H-field, strain
  • Anisotropy

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Most cited papers in journals published by APS�(12 in top 100 in Nature)

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Why should one use DFT?

❌ Impossible to fabricate millions of materials in a day

✅ With a supercomputer, high-throughput calculations are possible

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✅ Not just fabrication, but characterization too!

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However, ❌ excited states

❌ magnetic system

❌ band gap problem

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Beyond regular DFT

  • DFT+U: Hubbard corrected, localization
  • DFT+U+V: on-site U, inter-site V
  • DFT+U+J: Hund correction J
  • Hybrid functionals (exact exchange)
  • GW : Many-Body Perturbation Theory
  • TDDFT: excited states
  • BSE: electron-hole interaction

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How to use DFT?

  • Quantum ESPRESSO
    • PP, plane wave basis set, open-source, free, community

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  • FLEUR
    • All electron, FLAPW+lo basis set, open-source, free

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  • PySCF
    • PP, localized basis set (Gaussian), open-source, free

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See wikipedia.org/wiki/List_of_quantum_chemistry_and_solid-state_physics_software

for a comprehensive list with summary of the main functionalities.

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DFT with ChatGPT!?

  • Not quite right! But…

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  • Synthesized over 700 materials within 2023.
  • The future is GNoME, Ferminet, chemGPT…

(Merchant et al, 2023)

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Thanks for your attention. Question?

  • Barai, P., Ngo, A. T., Narayanan, B., Higa, K., Curtiss, L. A., & Srinivasan, V. (2020). The role of local inhomogeneities on dendrite growth in LLZO-based solid electrolytes. Journal of the Electrochemical Society, 167(10), 100537.
  • Çakıroğlu, O., Mehmood, N., Çiçek, M. M., Aikebaier, A., Rasouli, H. R., Durgun, E., & Kasırga, T. S. (2020). Thermal conductivity measurements in nanosheets via bolometric effect. 2D Materials, 7(3), 035003.
  • Durgun, E., Senger, R. T., Mehrez, H., Dag, S., & Ciraci, S. (2006). Nanospintronic properties of carbon-cobalt atomic chains. Europhysics Letters, 73(4), 642.
  • Hung, N. T., Nugraha, A. R., & Saito, R. (2022). Quantum ESPRESSO Course for Solid-State Physics. CRC Press.
  • Marzari, N., Ferretti, A., & Wolverton, C. (2021). Electronic-structure methods for materials design. Nature materials, 20(6), 736-749.
  • Merchant, A., Batzner, S., Schoenholz, S. S., Aykol, M., Cheon, G., & Cubuk, E. D. (2023). Scaling deep learning for materials discovery. Nature, 1-6.
  • Shakouri, A. (2011). Recent developments in semiconductor thermoelectric physics and materials. Annual review of materials research, 41, 399-431.

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References