# 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} }

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

- Computer Science
- 2008

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

- Physics
- 2015

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

- Mathematics
- 1983

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.

- Computer SciencePhysical review. E
- 2018

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

- Materials Science
- 2004

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.

- PhysicsPhysical review. B, Condensed matter
- 1995

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

- Physics
- 1997

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

- Computer ScienceSIAM J. Sci. Comput.
- 2013

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

- Physics
- 1965

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…