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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.

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Density Functional Theory Computation of Electronic Structure

  • 章节

  • 发表日期：

    2025年

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  • Wei Cai

摘要

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.