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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
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In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
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Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
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Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F−
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Orbital Energies for Seniority-Zero Wave Functions.

Peter A Limacher1

  • 1Institute of Physical Chemistry, Karlsruhe Institute of Technology , D-76131 Karlsruhe, Germany.

Journal of Chemical Theory and Computation
|November 18, 2015
PubMed
Summary

A novel operator provides orbital energies for model Hamiltonians, enabling accurate prediction of ionization potentials and efficient calculation of molecular dissociation and lattice properties.

Area of Science:

  • Quantum chemistry
  • Computational physics
  • Many-body theory

Background:

  • Conventional Hartree-Fock theory relies on single-particle operators, which are absent in many model Hamiltonians.
  • Orbital energies are crucial for understanding electronic structure and predicting properties.

Purpose of the Study:

  • Introduce a new single-pair operator for seniority-zero wave functions.
  • Develop orbital energies for model Hamiltonians.
  • Apply these concepts to predict ionization potentials and study molecular/lattice systems.

Main Methods:

  • Definition of a new single-pair operator analogous to the Fock operator.
  • Application of Koopmans' theorem-like predictions for double ionization potentials.
  • Development of a second-order perturbation scheme for seniority-zero wave functions.

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  • Extension to full seniority for intruder-free perturbation theory.

    • Main Results:

    • Successful prediction of atomic double ionization potentials.
    • Efficient, quadratically scaling computation of nitrogen dissociation.
    • Application to strongly correlated 2D Heisenberg lattices.
    • Improved asymptotic convergence in perturbation theory.

    Conclusions:

    • The new operator provides valuable orbital energies for model Hamiltonians.
    • The method offers accurate predictions and efficient computations for complex systems.
    • The extension to full seniority enhances the robustness of perturbation theory.