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Numerical analysis of finite dimensional approximations of Kohn–Sham models

Abstract

In this paper, we study finite dimensional approximations of Kohn–Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite dimensional approximations and derive the a priori error estimates for ground state energies and solutions. We also provide numerical simulations for several molecular systems that support our theory.

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Correspondence to Aihui Zhou.

Additional information

This work was partially supported by the National Science Foundation of China under grants 10871198 and 10971059, the Funds for Creative Research Groups of China under grant 11021101, and the National Basic Research Program of China under grant 2011CB309703.

Communicated by Zhongying Chen.

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Chen, H., Gong, X., He, L. et al. Numerical analysis of finite dimensional approximations of Kohn–Sham models. Adv Comput Math 38, 225–256 (2013). https://doi.org/10.1007/s10444-011-9235-y

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Keywords

  • Convergence
  • Density functional theory
  • Error estimate
  • Kohn–Sham equation
  • Nonlinear eigenvalue problem

Mathematics Subject Classifications (2010)

  • 35Q55
  • 65N15
  • 65N25
  • 65N30
  • 81Q05