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Non-linear eigensolver-based alternative to traditional SCF methods

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10.1063/1.4804419

### Abstract

The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem, i.e., H({ψ})ψ = Eψ. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm to account for the non-linearity of the Hamiltonian with the occupied eigenvectors. Using a series of numerical examples and the density functional theory-Kohn/Sham model, it will be shown that our approach can outperform the traditional SCF mixing-scheme techniques by providing a higher converge rate, convergence to the correct solution regardless of the choice of the initial guess, and a significant reduction of the eigenvalue solve time in simulations.

© 2013 AIP Publishing LLC

Received 18 November 2012
Accepted 26 April 2013
Published online 15 May 2013

Acknowledgments: The authors wish to acknowledge helpful discussions with Professor Joseph Jerome (The George Washington University), Professor Ahmed Sameh (Purdue University), and Dr. Ping Tak Peter Tang (Intel Corporation). This material is supported by NSF under Grant No. ECCS-0846457 and Intel Corporation.

Article outline:

I. INTRODUCTION

II. THE FEAST ALGORITHM

III. DIRECT SOLUTION OF THE NON-LINEAR EIGENVECTOR PROBLEM

IV. NUMERICAL EXPERIMENTS AND CAPABILITIES

A. Performance comparisons

B. Convergence rate and **Q**subspace size

C. Convergence rate and contour integration accuracy

D. Robustness and initial guess

V. CONCLUSION AND FUTURE WORK

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2013-05-15

2014-04-18

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