• 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 84 REFERENCES

Preconditioning of self-consistent-field cycles in density-functional theory: The extrapolar method

TLDR
An approximate preconditioner, with tremendously reduced prefactor, that makes the number of self-consistent cycle nearly independent of the size of the system, and bears little overhead up to the one hundred atom range is proposed.

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

Density-functional theory and the v-representability problem for model strongly correlated electron systems.

TLDR
The conclusion is made that the electron density corresponding to interacting systems of the type studied here is in fact not noninteracting v representable because the Kohn-Sham electrons are unable to reproduce the correlation-induced localization correctly.

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

Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn-Sham Density Functional Theory

TLDR
The elliptic preconditioner is shown to be more effective in accelerating the convergence of a fixed point iteration than the existing approaches for large inhomogeneous systems at low temperature.

Self-Consistent Equations Including Exchange and Correlation Effects

From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high
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