• Corpus ID: 118884253

On the Nature of Self-Consistency in Density Functional Theory

@article{Woods2018OnTN,
  title={On the Nature of Self-Consistency in Density Functional Theory},
  author={N D Woods},
  journal={arXiv: Other Condensed Matter},
  year={2018}
}
  • N. Woods
  • Published 5 March 2018
  • Computer Science
  • arXiv: Other Condensed Matter
A thesis providing a pedagogical introduction to the problem of achieving self-consistency in density functional theory. Contained is an introduction to the framework of Kohn-Sham density functional theory, leading then to the considerations required to solve the equations of Kohn-Sham density functional theory. Specifically, a focus is placed on where current self-consistent field methodology is inefficient and/or fails to converge to a solution. As such, this review spans sub-disciplines such… 
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References

SHOWING 1-10 OF 80 REFERENCES
Auxiliary density functionals: a new class of methods for efficient, stable density functional theory calculations
A new class of methods is introduced for solving the Kohn-Sham equations of density functional theory, based on constructing a mapping dynamically between the Kohn-Sham system and an auxiliary
Self-consistency iterations in electronic-structure calculations
The convergence of self-consistency iterations in electronic-structure calculations based on density-functional theory is examined by the linearization of the self-consistency equations around the
Applicability of Kerker preconditioning scheme to the self-consistent density functional theory calculations of inhomogeneous systems.
TLDR
A modified Kerker preconditioning scheme is developed which captures the long-range screening behavior of inhomogeneous systems and thus improves the SCF convergence.
A Second-Variational Prediction Operator for Fast Convergence in Self-Consistent Electronic-Structure Calculations
We propose a new way to reduce the number of iterations required to reach self-consistency in electronic-structure calculations in the framework of the plane-wave pseudopotential method. A prediction
Long-wavelength behavior of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems
The polarization dependence of the exchange-correlation (re) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a O(1/q(2)) divergence in the re kernel
A bird's-eye view of density-functional theory
This paper is the outgrowth of lectures the author gave at the Physics Institute and the Chemistry Institute of the University of Sao Paulo at Sao Carlos, Brazil, and at the VIII'th Summer School on
Jacob’s ladder of density functional approximations for the exchange-correlation energy
The ground-state energy and density of a many-electron system are often calculated by Kohn-Sham density functional theory. We describe a ladder of approximations for the exchange-correlation energy
Real-space Kerker method for self-consistent calculation using non-orthogonal basis functions
TLDR
The proposed real-space Kerker method is identical to the method in reciprocal space, with the following two advantages: the method is suitable for massively parallel computation since it does not use the fast Fourier transform and the preconditioning is performed in an acceptable computational time.
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