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Ágnes Szabados1, János Daru2, András Gombás1,3

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Using redundant localized molecular orbitals (LMOs) with frame theory offers advantages in quantum chemistry. These frame LMOs, projected from atomic orbitals (PAOs), provide smoother transitions during chemical reactions, avoiding discontinuities in calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Quantum chemical bases are typically linearly independent.
  • Overcomplete sets of functions, like localized molecular orbitals (LMOs) projected from atomic orbitals (PAOs), offer advantages in specific applications.
  • The mathematical theory of frames facilitates the use of redundant LMOs.

Purpose of the Study:

  • To present the mathematical background for using redundant LMOs via frame theory.
  • To demonstrate the advantages of frame LMOs in quantum chemical calculations, particularly for reaction coordinate following.
  • To show that frame LMOs provide smoother transitions compared to orthogonal LMOs in high-symmetry scenarios.

Main Methods:

  • Application of the mathematical theory of frames to redundant localized molecular orbitals.
  • Derivation of a formula for the trace of one-electron operators using frame LMOs, analogous to the orthonormal case.
  • Analysis of LMO behavior along reaction coordinates, especially through high-symmetry points.

Main Results:

  • A formula for calculating the trace of one-electron operators (e.g., electronic dipole moment) using frame LMOs and their fractional populations.
  • Frame LMOs, particularly PAO-related ones, exhibit smooth transitions when a system passes through high-symmetry points.
  • Orthogonal LMOs often show abrupt changes at high-symmetry points due to discontinuities in LMO-based quantities.

Conclusions:

  • Frame theory provides a robust mathematical framework for utilizing overcomplete sets of LMOs in quantum chemistry.
  • Frame LMOs offer a significant advantage in studying chemical reactions by providing continuous and smooth representations of electronic structure.
  • The use of PAO-related frame LMOs eliminates the need for extra algorithmic effort to handle discontinuities during reaction pathway calculations.