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<p>We present a molecular orbital (MO) localization scheme based on an information-theoretic measure of orbital delocalization. The method minimizes a Shannon-type functional constructed from the squared orbital amplitudes using a quadratic form derived from a Taylor expansion. This leads to a simple and computationally efficient localization criterion that depends only on quartic overlap integrals, thereby avoiding the costly electron repulsion terms required in some conventional approaches. The resulting orbitals exhibit a systematic reduction in entropy relative to canonical MOs while preserving chemically meaningful features such as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\pi \)</EquationSource> </InlineEquation> character. The method converges rapidly, particularly in ionic systems where the orbitals are already strongly localized, and shows a monotonic decrease of the rotation angles during the Jacobi sweeps, indicating stable numerical behavior.</p>

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Shannon entropy-driven localization of molecular orbitals

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Julio M. Hernández-Pérez,
  • Minhhuy Hô

摘要

We present a molecular orbital (MO) localization scheme based on an information-theoretic measure of orbital delocalization. The method minimizes a Shannon-type functional constructed from the squared orbital amplitudes using a quadratic form derived from a Taylor expansion. This leads to a simple and computationally efficient localization criterion that depends only on quartic overlap integrals, thereby avoiding the costly electron repulsion terms required in some conventional approaches. The resulting orbitals exhibit a systematic reduction in entropy relative to canonical MOs while preserving chemically meaningful features such as \(\sigma \) and \(\pi \) character. The method converges rapidly, particularly in ionic systems where the orbitals are already strongly localized, and shows a monotonic decrease of the rotation angles during the Jacobi sweeps, indicating stable numerical behavior.