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Floating Orbitals Reconsidered: The Difference an Imaginary Part Can Make.

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Floating orbitals with an imaginary component can influence electron spin states in quantum chemistry. This effect is generally small for valence electrons but significant in specific core-valence interactions.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Floating orbitals, often real spherical Gaussians, are used in quantum chemistry as basis functions and for developing subatomistic force fields.
  • Complex Gaussians offer computational advantages, prompting an investigation into the utility of an imaginary component within these orbitals.

Purpose of the Study:

  • To explore the potential utility and impact of an imaginary component in floating orbitals for valence electrons.
  • To analyze the effects on electron spin states and energy contributions, particularly exchange and kinetic energy.

Main Methods:

  • Development and application of analytical equations for two mobile electrons.
  • Investigation of the interplay between imaginary orbital components, exchange energy, and kinetic energy.
  • Analysis of core-valence exchange interactions.

Main Results:

  • An imaginary component in floating orbitals shifts the balance of exchange energy contributions, influencing parallel versus antiparallel electron spin preferences.
  • A significant kinetic energy penalty is associated with the imaginary part, generally making it negligible for valence electrons.
  • Exceptions exist where strong core-valence exchange interactions make the imaginary part relevant.

Conclusions:

  • The imaginary part of floating orbitals is typically negligible for valence electrons due to kinetic energy costs.
  • This finding enables a self-consistent model differentiating nd2 triplet ground states in transition metal ions from ns2 singlet ground states in main group ions.
  • Highlights the nuanced role of orbital properties in determining electronic ground states.