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Density Functional Theory Computation of Electronic Structure

In: Deterministic, Stochastic, and Deep Learning Methods for Computational Electromagnetics

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  • Wei Cai

    (Southern Methodist University, Department of Mathematics)

Abstract

Understanding the electronic structure of an N-electron system requires solving an eigenvalue problem of a 3N-dimensional Schrödinger equation, which suffers from the curse of dimensionality in computational costs. For small systems, quantum Monte Carlo methods [1] have been used quite effectively. For large systems and bulk material studies, the density functional theory (DFT) has become the main computational method for various chemistry, biology, and material science applications. The DFT transforms a high-dimensional linear eigenvalue value problem to a nonlinear 3-D eigenvalue problem for an electron density-dependent Hermitian operator.

Suggested Citation

  • Wei Cai, 2025. "Density Functional Theory Computation of Electronic Structure," Springer Books, in: Deterministic, Stochastic, and Deep Learning Methods for Computational Electromagnetics, edition 0, chapter 0, pages 509-532, Springer.
    • Handle: RePEc:spr:sprchp:978-981-96-0100-4_17
    DOI: 10.1007/978-981-96-0100-4_17
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