### Abstract

State of the art first-principles calculations of electronic structures aim at finding the ground state electronic density distribution. The performance of such methodologies is determined by the effectiveness of the iterative solution of the nonlinear density functional Kohn-Sham equations. We first outline a solution strategy based on the Newton-Raphson method. A form of the algorithm is then applied to the simplest and earliest density functional model, i.e., the atomic Thomas-Fermi model. For the neutral atom, we demonstrate the effectiveness of a charge conserving Newton-Raphson iterative method for the computation, which is independent of the starting guess; it converges rapidly, even for a randomly selected normalized starting density.

Original language | English |
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Pages (from-to) | 349-352 |

Number of pages | 4 |

Journal | Journal of Computational Electronics |

Volume | 6 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Sep 2007 |

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### Keywords

- Density functional theory
- Kohn-Shamsystem
- Newton-Raphson algorithm
- Thomas-Fermi model

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Electrical and Electronic Engineering

### Cite this

*Journal of Computational Electronics*,

*6*(1-3), 349-352. https://doi.org/10.1007/s10825-006-0135-1

**Convergence of density functional iterative procedures with a Newton-Raphson algorithm.** / Jerome, J. W.; Sievert, P. R.; Ye, L. H.; Kim, I. G.; Freeman, Arthur J.

Research output: Contribution to journal › Article

*Journal of Computational Electronics*, vol. 6, no. 1-3, pp. 349-352. https://doi.org/10.1007/s10825-006-0135-1

}

TY - JOUR

T1 - Convergence of density functional iterative procedures with a Newton-Raphson algorithm

AU - Jerome, J. W.

AU - Sievert, P. R.

AU - Ye, L. H.

AU - Kim, I. G.

AU - Freeman, Arthur J

PY - 2007/9

Y1 - 2007/9

N2 - State of the art first-principles calculations of electronic structures aim at finding the ground state electronic density distribution. The performance of such methodologies is determined by the effectiveness of the iterative solution of the nonlinear density functional Kohn-Sham equations. We first outline a solution strategy based on the Newton-Raphson method. A form of the algorithm is then applied to the simplest and earliest density functional model, i.e., the atomic Thomas-Fermi model. For the neutral atom, we demonstrate the effectiveness of a charge conserving Newton-Raphson iterative method for the computation, which is independent of the starting guess; it converges rapidly, even for a randomly selected normalized starting density.

AB - State of the art first-principles calculations of electronic structures aim at finding the ground state electronic density distribution. The performance of such methodologies is determined by the effectiveness of the iterative solution of the nonlinear density functional Kohn-Sham equations. We first outline a solution strategy based on the Newton-Raphson method. A form of the algorithm is then applied to the simplest and earliest density functional model, i.e., the atomic Thomas-Fermi model. For the neutral atom, we demonstrate the effectiveness of a charge conserving Newton-Raphson iterative method for the computation, which is independent of the starting guess; it converges rapidly, even for a randomly selected normalized starting density.

KW - Density functional theory

KW - Kohn-Shamsystem

KW - Newton-Raphson algorithm

KW - Thomas-Fermi model

UR - http://www.scopus.com/inward/record.url?scp=34247342158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247342158&partnerID=8YFLogxK

U2 - 10.1007/s10825-006-0135-1

DO - 10.1007/s10825-006-0135-1

M3 - Article

VL - 6

SP - 349

EP - 352

JO - Journal of Computational Electronics

JF - Journal of Computational Electronics

SN - 1569-8025

IS - 1-3

ER -