1 / 20

Large-Scale Density Functional Calculations

This overview explores the utilization of Density Functional Theory (DFT) in large-scale simulations for materials science, chemistry, and physics. It addresses challenges and solutions in simulating electron transport in metals and semiconductors, as well as coupled mechanical-electronic interactions. Key methods such as plane-wave basis functions and localized atomic-like functions are discussed. The documentation highlights innovative techniques like Conformal Computing to enhance computational efficiency and opportunities for using grid computing to facilitate parallel calculations, pushing the boundaries of computational materials science.

blanca
Télécharger la présentation

Large-Scale Density Functional Calculations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Large-Scale Density Functional Calculations James E. Raynolds, College of Nanoscale Science and Engineering Lenore R. Mullin, College of Computing and Information

  2. Overview • Using computers to carry out “numerical experiments” in Materials Science, Chemistry and Physics • Quantum Mechanical equations solved for a system of atoms in a representative unit cell • Measurable properties obtained from “first-principles” • mechanical, thermodynamic, electronic • optical, magnetic, transport

  3. + V Phenolate/Benzenediazonium Benzene Example: Transport in molecular wire

  4. Peierls Distortion dimerized pair Pi stacked pair mechanical relaxation insulator metal

  5. Frontier Problems • Non-equilibrium spin-transport in metals and semiconductors (Spintronics) • Transport and coupled mechanical / electronic interactions in molecules (metal - insulator transition due to mechanical relaxation) • Industrial applications: Modeling Chemical Vapor Deposition (CVD) processes atom by atom • Challenges: correlated motion of electrons • Coupled electron-phonon interactions (electron - vibration coupling)

  6. Density Functional Theory • Density Functional Theory (DFT) is a “mean-field” solution to the many-electron problem. • Each electron interacts with an effective average field produced by all of the other electrons • Non-linear set of coupled differential equations

  7. Density Functional Equations Looks linear but... depends on the charge density through: Example: Local density approximation

  8. DFT solution approach • Expand the wave-functions in a basis set: • Matrix eigenvalue-eigenvector problem: • Orthogonality: • Iterative solution to “self-consistency” (i.e. output V(r) coincides with input)

  9. Popular implementations • Plane wave basis functions (Fourier Series): • Drawback: • Benefit: easy to code, sophisticated non-linear response calculations possible • Localized “atomic-like” basis functions scaling • - exponential distance decay for • insulators • power law distance decay for • metals

  10. Contrasting Implementations • Abinit: www.abinit.org • Very sophisticated array of calculated properties • Calculations become prohibitive for more than a few dozen atoms • VASP (Vienna Ab-Initio Simulation Package) • Less sophisticated by much faster • few hundred atoms possible • Siesta: (Spanish Initiative for Electronic Simulations with Thousands of Atoms) • O(N) scaling: fast but less sophisticated • few thousand atoms possible

  11. Public Access • Many codes are freely available: go to http://psi-k.dl.ac.uk/data/codes.html for a list of more than 20 • Most codes still not user-friendly and take months to years to master

  12. The Brick Wall!! • All of these methods run out of steam very quickly in terms of run time and memory • Calculations with scaling take days or weeks to run!! • Even calculations with scaling run into memory bottlenecks • Materials Science simulations require thousands of atoms for thousands of time steps

  13. Key Algorithms • For plane wave based codes: the Fast Fourier Transform • We have gained factor’s of 4 improvement in speed and storage using Conformal Computing • A number of new developments are being implemented for further increases • Matrix diagonalization routines for very large matrices

  14. Conformal Computing • Density Functional Calculations are an ideal setting for Conformal Computing! • In fact: any array (matrix) based computational setting is ripe for Conformal Computing • Why? Conformal Computing eliminates temporary arrays and un-necessary loops!

  15. Opportunities • Current electronic band structures fairly fast (on the order of one hour):

  16. Contrasting: electron-phonon • Electron-phonon calculations: on the order of 1 day for small systems • Superconductivity in • “conventional” materials • determined by the electron - • phonon interaction • Aluminum (1 atom) takes roughly 1 day of computing • Imagine several dozen atoms with scaling

  17. Electron-Phonon improvements • Many quantities currently written to files then later combined • The size and number of these files is becoming prohibitively expensive • Opportunities for parallelization of integrals • Opportunities to eliminate temporaries through the use of direct indexing

  18. Grid Computing • Even with highly optimized code (which is still a way off) there is always a need for more and more resources • For example: electron-phonon calculations involve dozens of separate calculations that could be run on independent machines • Grid computing allows many independent calculations to be run in parallel

  19. Grid Computing: First Steps • QMolDyn GAT: a template for submitting Density Functional Calculations over the grid • Vision: QMolDyn will eventually have a variety of codes (modules) • Presently: Siesta ( ) running on the grid, 8, 16, 32, 64, 128, 256, 512- atom systems

  20. Summary / Conclusions • There is a great demand for large-scale array (matrix) based calculations in materials science • Quantum calculations are increasingly important for Materials Science, Chemistry and Physics • Grid computing combined with Conformal Computing techniques is very promising

More Related