Direct minimization and acceleration of electronic structure calculations

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School of Science | Doctoral thesis (article-based) | Defence date: 2012-08-17
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Date
2012
Major/Subject
Mcode
Degree programme
Language
en
Pages
108
Series
Aalto University publication series DOCTORAL DISSERTATIONS, 99/2012
Abstract
This dissertation investigates numerical methods for direct minimization and acceleration of electronic structure calculations. The focus is on methods for Kohn-Sham density functional theory and its extension to fractionally occupied electronic orbitals. The methods are derived in the setting of an abstract discretization of the electronic structure problem and then numerically verified. Verification is accomplished with genuine electronic structure codes or for a model problem capturing the nonlinearity originating from electron-electron interactions. The dissertation demonstrates that the quasi-Newton method is a fast and robust accelerator for the self consistent Kohn-Sham equations and that intrinsic inclusion of the geometric constraints improve the rate of convergence for direct minimization methods. It is also shown that ensemble density functional theory enables convergence of metallic systems without enforced broadening of the Fermi level. Furthermore, simultaneous updates of the electronic orbitals and occupation numbers are shown to reduced the number of iterations necessary for convergence of ensemble density functional theory.

Denna avhandling undersöker numeriska metoder för direkt optimering och acceleration av elektronstruktursberäkningar med tyngdpunkt på Kohn-Shams täthetsfunktionalteori samt utvidgad täthetsfunktionalteori. Metoderna härleds för en diskretiserad abstrakt elektronstruktursmodell och verifieras numeriskt. Verifikationen utförs med ett autentisk täthetsfunktionalprogram eller för ett modellproblem som återger svårigheter vilka förekommer i elektronstruktursberäkningar. Avhandlingen visar att sekantmetoder kan användas framgångsrikt för att söka en konsistent lösning till Kohn-Shams ekvationer samt att inbyggt beaktande av geometriska villkor minskar mängden iterationer som krävs vid direkt optimering av systemets totala energi. Vidare demonstreras att utvidgad täthetsfunktionalteori möjliggör beräkning av metalliska system utan att en fiktiv temperatur behöver införas och att samtidig uppdatering av elektronskal och skalens ockupationstal förbättrar konvergens i jämförelse med sekventiell uppdatering.
Description
Supervising professor
Eirola, Timo, Prof.
Thesis advisor
Eirola, Timo, Prof.
Keywords
electronic structure calculation, acceleration, direct minimization, density functional theory, ensemble density functional theory, Stiefel manifold, elektronstrukturberäkning, acceleration, direkt minimering, Stiefelmångfald, täthetsfunktionalteori
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Parts
  • [Publication 1]: K. Baarman, T. Eirola, and V. Havu. Robust acceleration of self-consistent field calculations for density functional theory. The Journal of Chemical Physics, 134, 134109; doi:10.1063/1.3574836, April 2011. © 2011 American Institute of Physics (AIP). By permission.
  • [Publication 2]: K. Baarman and J. VandeVondele. A comparison of accelerators for direct energy minimization in electronic structure calculations. The Journal of Chemical Physics, 134, 244104; doi:10.1063/1.3603445, June 2011. © 2011 American Institute of Physics (AIP). By permission.
  • [Publication 3]: K. Baarman, T. Eirola, and V. Havu. Direct minimization of electronic structure calculations with Householder reflections. arXiv:1204.1204, 16 pages, April 2012. © 2012 by authors.
  • [Publication 4]: K. Baarman, V. Havu, and T. Eirola. Direct minimization for ensemble electronic structure calculations. arXiv:1204.1205, 20 pages, April 2012. © 2012 by authors.
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